Home

User's manual for the groundwater flow model ZOOMQ3D

Contents

1. 0 inactive dry 1 active wet Positive into node Positive out of node Positive into node Positive out of node Positive into node Positive out of node Positive into node Positive values equivalent to outflow from node Positive into node Positive out of node Positive out of node Positive into node Positive out of node 94 References GOLDEN SOFTWARE INC 1994 Surfer for Windows User s Guide Golden Software Inc Colorado JACKSON C R AND SPINK A E F 2004 User s manual for ZETUP the set up program for the groundwater flow model ZOOMQ3D British Geological Survey Internal Report IR 04 139 MANSOUR M M AND HUGHES A G 2004 User s manual for the distributed recharge model ZOODRM British Geological Survey Internal Report IR 04 150 RILEY K F HOBSON M P AND BENCE S J 2002 Mathematical methods for physics and engineering Cambridge University Press 1232pp 95
2. Number of upstream nodes connections River node number o Comment line separator between blocks of river node data REPEATED FOR EACH RIVER NODE Comment line separator between blocks of river node data REPEATED FOR EACH RIVER NODE 56 see ZETUP manual number of branches inate Kz influent bed thickness f each upstream river node initialflow dat Format of data ed fl gt H i m U x ic id O i A fl A d rca A rca 4 Figure 31 44452 1 44452 1 44249 0 43751 0 43193 3 42610 3 36513 5 35861 3 35194 4 2250 34805 7 2500 0 34663 5 250 500 750 1000 1250 1500 1750 2000 O O O O O O O O O O O O O OQO oO aO oe etc for each node in the river Format of input file initialflow dat Number of rivers in the model Comment line separator between data relating to each river River number unique identifier number of river nodes in river River node number x and y co ordinates initial river flow m day Repeated for each river node 57 river_inputs dat Format of data Number of nodes at which specified time variant discharge to river Comment line 2 No of nodes at which an input is specified River number and node number for each Comment line ETI River number river node number 215 One line per number specified on line 2 Number of block time periods of discharge data Comment line 5 Numb
3. Figure 29 Specification of flow along or discharge into river at specific river nodes 9 5 5 Monitoring river baseflows over time The baseflow leaving a river node or reach can be monitored over time by creating a file with the following structure The name of this file for example gauging _stations dat is specified by the user in the input file zoomq3d dat see Section 14 2 The file has the format n start _block end_block ir irn one for each of n river nodes where n is the number of river nodes at which the baseflow is monitored start_block is the block number when monitoring starts end_block is the block number when monitoring ends ir is the river number and irn is the river node number 55 ed f gt H id m U x rca id O i A kl B A rca A ie a rivers dat Format of data riverl_map dat 1 1500 0 0 0 0 0 5 0 1500 0 250 0 0 0 5 0 301 77 0 1 0 05 1 0 1 1750 0 500 0 06 0 06 5 0 353 55 0 1 0 05 1 0 14 etc for each node in the river Figure 30 Format of file rivers dat Number of rivers in the model Comment line separator between data relating to each river Name of the river map file used to create the model river River number unique identifier number of river nodes Comment line separator between data relating to each river River node number Branch number x co ordinate y co ord Stage bed elevation width reach length Kz influent
4. Figure 33 Example code and map file for the entry of recharge data Recharge rates are specified in recharge dat for each stress period within the simulation Actually the name recharge dat is just an example as it is defined by the user in the input file zoomq3d dat Consider that for ten consecutive stress periods the recharge rates shown in Table 4 are defined Assuming that this data set relates to the code and map files shown in Figure 33 then during stress period 2 the recharge rate at the nodes represented by the letter a would be 0 99 mm day 0 9 x 1 1 mm day During stress period 10 the recharge rate at the nodes represented by the letter b would be 0 24 mm day 1 2 x 0 2 mm day Table 4 Hypothetical recharge rates mm day for ten stress periods In ZOOMQ3D the set of recharge data defined by a code file a map file and a set of rates for each stress period in the simulation is referred to as a recharge type This 59 terminology is adopted because more than one recharge type can be defined The rationale for implementing multiple recharge types is best illustrated using an example Suppose the groundwater system shown in Figure 34 is to be modelled This represents a slice through an aquifer from an interfluve in the west to a river valley in the east The slice is 3 km long and over the western 2 km the aquifer is covered by low permeability deposits which inhibit but do not lim
5. 16 Table 1 List of all ZOOMQ3D input files Input file name Relevant section 1 anisotropy map amp anisotropy cod OR _ anisotropy dat per layer 75 2 2 aquifer map 7 2 1 3 boundary dat 9 1 4 clock dat 8 5 contour_times dat 14 1 6 entry_method dat 7 3 1 7 fixedheads dat 9 2 8 gauging_stations dat 9 5 5 9 grids dat 7 1 10 hydcond map amp hydcond cod OR hydcond dat per layer 7 5 1 11 initialflow dat 9 5 3 12 initialh map amp initialh cod per layer 8 2 13 initialh dat 8 2 14 leakage dat 9 3 15 noflow map per layer 13 2 16 obsleak dat 9 3 1 17 obswells dat 10 2 2 18 pumping dat 10 2 1 19 recharge dat 10 1 3 20 recharge cod amp recharge map amp OR recharge_rates dat 10 1 21 rivers dat 9 5 2 22 river_inputs dat 9 5 4 23 sor dat 12 1 24 specstor map amp specstor cod specstor dat per layer 7 5 3 25 springs dat 9 4 26 syield map amp syield cod syield dat per layer 7 5 4 27 vcond t map amp vcond cod OR vcond dat per layer TA amp 7 5 5 28 vkd cod amp vkd map 11 2 1 29 vkd dat 11 2 2 30 vkdkx map amp vkdkx cod OR vkdkx dat per vkd scheme 11 2 2 31 vkdky map amp vkdky cod OR vkdky dat per vkd scheme 11 2 2 32 vkdzp map amp vkdzp cod OR vkdzp dat per vkd scheme 11 2 2 33 vkdgrad map amp vkdgrad cod OR vkdgrad dat per vkd scheme 11 2 2 34 wetflag map per layer 13 1 1 35 wethead map amp wethead cod wethead dat
6. Subgrid 1 array Subgrid 2 array Layer 2 Base grid array Subgrid array Subgrid 2 array Layer 3 Base grid array Subgrid 1 array Subgrid 2 array Time step 1 Layer 1 Base grid array Subgrid 1 array Subgrid 2 array Layer 2 Base grid array Subgrid 1 array Subgrid 2 array Layer 3 Base grid array Subgrid 1 array Subgrid 2 array Time step 3 Layer 1 Base grid array Subgrid array Subgrid 2 array Layer 2 Base grid array Subgrid 1 array Subgrid 2 array Layer 3 Base grid array Subgrid array Subgrid 2 array NB Example shows file structure for three time steps only for a model containing three layers and three grids Order of data output to heads txt Figure 58 16 15 2 All the components of flow into and out of a node are written to this file for each model node at the end of each time step of the simulation The flows are written in the following order Output file flowbal txt 1 For each time step of the simulation 93 2 For each layer in the model Starting with the top layer layer 1 3 For each model grid in the layer Listed in the same order as they are in grids dat The base grid is the first grid listed Grids are then listed in grid level order see Section 7 1 4 Data for each node within the model are written on separate
7. contour_times dat see Section 14 1 The format of this output file is simple and is suitable for contouring using Surfer Golden Software Inc 1994 The groundwater head at each horizontal location is written on a separate line The file has the following format Be Oy ho ge oo ue i where x is the x co ordinate of the grid point y is the y co ordinate of the grid point h is the groundwater head in the i layer 84 If a node is dry the groundwater head value is replaced by 999 ZETUP produces a Surfer Golden Software Inc 1994 blanking file which can be used to blank the data around the boundary of the model when contouring This file is called boundary bln 16 3 GROUNDWATER HEADS IN FORMAT TO RE START A SIMULATION Groundwater heads are written to an output file in a format that enables a model run to be re started from conditions modelled during the current simulation The name of this output file for example finalh out is specified in the input file zoomq3d dat It contains the groundwater head at each node of the model at the end of a single time step and is over written periodically during the simulation The frequency with which the file is produced is defined in clock dat It is created after either every time step stress period or block or only for the final time step in the simulation Each time it is written the previous data set is lost The file has exactly the same format as
8. These names are those of the example set of files which are used throughout this manual Even though some of the model features may not be included in a model and consequently some of their related input and output files not opened all eighteen file names must be listed in zoomq3d dat Table 6 sor dat fixedheads dat initialh dat obswells dat obswells out pumping dat recharge dat gauging stations dat gauging stations out riverflow out accretion out initialflow dat river _inputs dat obsleak dat obsleak out finalh out contour txt flowbal out Format of zoomq3d dat input file Description of named file not part of the file Numerical solver input file Input file specifying fixed heads inside the model boundary Input file containing initial groundwater head for the whole model Input file containing observation well data Output file storing groundwater head hydrographs at obs wells Input file containing abstraction well data Main recharge data input file Input file containing river baseflow monitoring point data Output file in which river baseflow hydrographs are stored Output file in which river baseflow at specific times are stored Output file in which river flow accretion profile data is stored Input specifying initial river baseflows Input file specifying time variant discharges to rivers Input file specifying which leakage nodes to monitor Output file storing flows to from leakage nodes over time
9. a text file with a bat extension e g runzoom bat and the name of this batch file can be typed on the command line omit the extension when doing this e g type runzoom lx Type the name of 4 program Folder document or Internet resource and Windows will open it For you Open cmd Cancel Browse Figure 2 Starting a command line window from the Windows start menu 13 MWINNT system32 cmd exe gt cd zoomgq3d_project zoomq3d_project gt help cd isplays the name of or changes the current directory HDIR D drive path HDIR D 7D drive I path D ha Specifies that you want to change to the parent directory ype CD drive to display the current directory in the specified drive ype CD without parameters to display the current drive and directory se the D switch to change current drive in addition to changing current irectory for a drive If Command Extensions are enabled CHDIR changes as follows he current directory string is converted to use the same case as he on disk names So CD C NTEMP would actually set the current irectory to C Temp if that is the case on disk HDIR command does not treat spaces as delimiters so it is possible to into a subdirectory name that contains a space without surrounding he name with quotes For example cd winntNprof iles username programs start menu is the same as cd winnt prof iles username programs start menu hi
10. amp initialh cod per layer 8 2 initialh dat 8 2 leakage dat 9 3 noflow map per layer 13 2 obsleak dat 9 3 1 obswells dat 10 2 2 pumping dat 10 2 1 recharge dat 10 1 3 x K recharge cod amp recharge map amp OR recharge_rates dat 10 1 x rivers dat 9 5 2 sor dat 12 1 specstor map amp specstor cod specstor dat per layer 7 5 3 x x springs dat 9 4 syield map amp syield cod syield dat per layer 7 5 4 vcond map amp vcond cod vcond dat per layer TA amp 7 5 5 vkd cod 11 2 1 wetflag map per layer 13 1 1 wethead map amp wethead cod wethead dat 13 1 3 wetthresh map amp wetthresh cod wetthresh dat 13 1 2 zbase map amp zbase cod zbase dat per layer 1 4 2 zoomgq3d dat 14 2 ztop map amp ztop cod ztop dat per layer 7 4 1 XR Ea O Ea B Eea O HH A E Note the names of these files are fixed The names of the remaining files can be specified by the user in the input file zoomq3d dat 19 7 Model structure 7 1 MODEL STRUCTURE The file describing the structure of the model is created by ZETUP and is called grids out For input to ZOOMQ3D it must be renamed grids dat The file contains nodal information for each point in each grid Blocks of grid data are listed in grid level order beginning with the base grid An example of grids dat is listed in Figure 7 This relates to the model mesh shown in Figure 6 which consists of a coarse base grid two
11. templates and require modification to complete the specification of the model Transfer files to ZOOMQ3D working directory Run ZOOMQ3D Process of constructing and running a ZOOMQ3D model 15 PART 2 Model input 6 Summary of input files required by ZOOMQ3D 6 1 THE PHILOSOPHY OF MODEL INPUT The philosophy behind the structure of ZOOMQ3D model input is to separate different types of data between files That is each file contains one specific type of information only Whilst this results in the model requiring many input files compared to other models they all have a very simple format and are easily modified using a text editor For example one file contains all information relating to pumping rates another to observation wells and another river gauging stations Generic templates of all of these files are generated by ZETUP These are in the correct format but the data contained within some requires modification in order to complete the model specification The following points should be recalled when modifying ZOOMQ3D input files 1 Values are read into the model in free format and consequently the user does not need to ensure that the number of decimal places and field width are correct for each input value contained in each file 2 The correct number of parameters must be entered on the correct line of an input file 3 Whilst it does not matter whether the user enters a decimal number as an integer it is
12. 7 7i 7 S yol 7 7 3 Figure 48 Example numeric data file vkdkx01 dat 75 12 The solution process 12 1 SUCCESSIVE OVER RELAXATION SOLUTION METHOD The point successive over relaxation SOR method is the only numerical solution technique currently implemented in ZOOMQ3D SOR is implemented first because it is easy to apply and thus modify and because it is generally robust In some models the matrix of coefficients of the finite difference equations is modified during the solution of a time step for example by updating transmissivity as groundwater head changes when simulating unconfined aquifers This process is not allowed within ZOOMQ3D and the matrix of coefficients remains fixed during the solution of a time step This eliminates some potential problems of convergence when using SOR The SOR solver in ZOOMQ3D scans each grid of the model mesh It begins by updating the solution on the base grid and then repeatedly steps down the grid hierarchy to the next finest grid level One SOR iteration is performed at each node on each grid within each grid level before moving to the next finest grid level After each of the grids has been scan the process returns to the base grid The solver converges after a number of scans across all the grids when the maximum nodal flow imbalance falls below a user defined value The simulation then progresses to the next time step The name of the file used to enter information relating to th
13. Comment line Layer x amp y co ordinates of well Block no followed by 1 abstraction rate for each stress period Rates multiplied by value on line 4 to give m day Abstraction rates are positive and injection negative One line per block Comment line Layer x amp y co ordinates of well Block no followed by 1 abstraction rate for each stress period Rates multiplied by value on line 4 to give m day Abstraction rates are positive and injection negative One line per block Comment line Conductance between multi layer wells and aquifer nodes mday Number of blocks of pumping data Comment line x amp y co ordinates of well Number of sections then layer number of each in ascending order Block no followed by 1 abstraction rate for each stress period Rates multiplied by value on line 4 to give m day Abstraction rates are positive and injection negative One line per block 67 REPEATED FOR REPEATED FOR REPEATED FOR EACH WELL EACH WELL EACH WELL 11 Variable hydraulic conductivity with depth VKD The accurate simulation of flow in Chalk aquifers requires the careful consideration of the conceptual model of Chalk groundwater systems It is then necessary to translate the conceptual model into a numerical model accurately if groundwater flow in the Chalk is to be simulated satisfactorily An important component of the conceptualisation of Chalk groundwater flow is the descript
14. NPxs NPs Top ae Eog Dapo ennn lo Ler where NS is the number of schemes in the model NP is the number of profiles in the i scheme i 1 to NS Ii op is the number of the top layer in the j profile in the scheme j 1 to NP Ifor is the number of the bottom layer in the j profile in the scheme j 1 to NP Therefore to define the eight schemes shown in Figure 43 vkd cod would contain the following lines of data Ne ePNUWEKPE HW BD Bowe BD ONHFPNNNAFO NWPPPPPE HS Once the configurations of the profiles within each scheme have been defined information relating to the distribution of the schemes in the horizontal must be entered This is performed using the text file vkd map which contains a map of the model mesh The format of the file is the same as that of the map files described in Section 7 3 For example consider the file shown in Figure 44 which represents the square mesh that is also shown in the figure At each node of the mesh a character is specified Each letter of the alphabet corresponds to a VKD scheme defined in vkd cod Fifty two letters and therefore schemes are allowed which are specified in the order a z and then A Z Letter a corresponds to the first scheme b to the second and z to the twenty sixth scheme Letter A corresponds to the twenty seventh scheme B to the twenty eighth and Z to the fifty second scheme Figure 44 shows an example
15. Output file in which final groundwater head profile is stored Output file to which head data is written for contouring Output file to which nodal flow balance information is written 82 PART 3 Model output 15 Summary of output files produced by ZOOMQ3D 15 1 THE PHILOSOPHY OF MODEL OUPUT The philosophy behind the structure of ZOOMQ3D model output is to separate different types of data between files That is each file contains one specific type of information only This simplifies the post processing of model output and means that standard software packages can be used to interpret and visualise results All the output files have a very simple format and are easily examined using a text editor or processed using spreadsheet software The list of output files produced by ZOOMQ3D is presented in Table 7 Though there are eighteen files listed not all of these are always produced For example if no rivers are included the model three fewer files are created Each of the ZOOMQ3D output files is described in the following section All output files containing columns of data are space separated Table 7 Model feature List of all ZOOMQ3D output files Relevant section Relevant file names Groundwater heads 1 Over time 2 For restarting model 3 For contouring obswells out 16 1 finalh out 16 3 contour txt contour_ _ _ HHHE txt 16 2 Boundary conditions 1 Head dependent leakage nodes 2 Springs obslea
16. Springs This model feature has been developed to simulated spring flows specifically The flow out of a spring depends on the transmissivity of the surrounding finite difference nodes Spring flows are represented by an abstraction which removes water from the aquifer at the location of the spring until the water table falls below the level of the ground surface 4 1 12 Time discretisation Simulation time is divided into time steps stress periods and blocks The length of a time step is equivalent to the length of time between which successive solutions are calculated for the model s state variables A stress period represents a period of time during which all model stresses remain constant e g recharge groundwater abstraction or discharge to rivers Stress periods are divided into one or more time steps A block is composed of one or more stress periods The rationale for the use of blocks is predominantly related to the simplification of the organisation of time variant data for example groundwater abstraction or recharge rates within input files The number of stress periods in each block is the same for all blocks within a simulation 4 2 CONSTRUCTING MODELS USING ZETUP ZETUP is the pre processor for the finite difference groundwater flow model ZOOMQ3D Jackson and Spink 2004 It is used to construct the model grid which may contain multiple areas of local grid refinement and to create rivers within these complex meshes ZET
17. The group of files accretion out contour txt finalh out flowbal out global out and riverflow out may be rewritten after every time step stress period or block or only at the end of the simulation The model runs more quickly if data is output less often and it is 39 recommended that this integer is generally set to 4 However the ability to output data after every time step for example means that if a simulation is aborted for any reason it can be re started from a later time thus reducing the subsequent run time The output files listed above are described in detail in Part 3 of this manual On line 28 a character flag specifies whether the simulation is a steady state or time variant run If a steady state simulation is selected the storage coefficient is set to zero at all nodes of the mesh In this case the model simulates a single time step only If rivers springs or unconfined conditions are incorporated in the model steady state conditions must be approached by simulating multiple time steps with constant stresses This means that a t must be entered on line 28 and that specific storage and specific yield must be specified using the relevant input files On line 30 of the example clock dat input file a character flag y or n is entered which specifies if initial the groundwater head profile is read from the file initialh dat described in Section 8 2 This file has
18. The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model The format of map files is described in Section 7 3 An example wetting flag map file is shown in Figure 51 z w r grid on level 1 Bottom left 0 0 Top right 10000 10000 D D h h h h h h h h h h h P O n n n n n n n n n n n n n E n n n n n n n n PISI paa a a I D T SS oo D D AE ee oe en ee ee oe ee eo PYyPvVD VDD VV VV vv Figure 51 Example wetflag map file 78 13 1 2 Wetting threshold A dry node will rewet if the groundwater head in either the node below or one of the horizontally neighbouring nodes rises above the dry nodes wetting threshold This threshold is specified at a user defined distance above the base of the node Figure 52 If any of the interrogated neighbouring node s heads are above the wetting threshold the end of the time step or transmissivity cycle see Section 7 2 2 the dry node is reactivated or re wetted The wetting threshold is entered into the model as a length or distance above the base of the node m and not as an elevation Top of node T Wetting threshold m Base of node Figure 52 Conceptualisation of wetting threshold at node Input file names and format The wetting threshold must be entered into the model using either 1 pairs of map and code files named wetthresh map
19. are being used e the names of the pair of map and code files associated with each recharge type e a recharge rate for each stress period for each recharge type in mm day e if a numeric data file is being used to specify recharge as an alternative to or in conjunction with the use of map and code files e the name of the numeric data file An example recharge dat file is shown in Figure 38 The first two lines of this file are a comment line and an integer flag The integer flag determines whether recharge types and their associated map and codes files are to be used 1 whether the numeric recharge data file is to be used 2 or whether both methods of recharge specification are implemented 3 The file is split into two sections after the first two lines The first section must begin with a comment line starting SECTION 1 Figure 38 line 4 and the second section must begin with a comment line starting SECTION 2 line 28 In the first section data is defined relating to the definition of recharge using recharge types In the second section information is defined relating to the specification of recharge using a numeric data file In section 1 the number of recharge types being applied is specified line 9 For each recharge type the name of the map and code file must be specified lines 11 14 After this the number of time blocks of recharge data is entered line 16 For each block the block number is enter
20. characterise the flow within a layer by means of a single head value and to use transmissivity as the parameter governing flow within the layer Storage within a layer is measured by the storage coefficient Vertical transfers between layers are determined by leakage rates at the upper and lower surfaces In mathematical terms the single groundwater head value is taken to be the average head across the layer If the groundwater head is d x y Z t at a general point the vertically integrated average value is h x y t which is calculated as e olx y z t dz Z Z h x y t Z Z where z and z2 are the base and top elevations of the layer respectively By a similar process of integrating over the vertical transmissivity and storage coefficient are evaluated as Z Zy T x y f k x y z dz and S x y f S x y z dz Z Z Z Z and the source term becomes a flow per unit surface area of the aquifer denoted by q x y t Unfortunately the process of integrating the three dimensional equation does not lead to the quasi three dimensional equation and the vertically integrated parameters except in some rather limiting circumstances In order to demonstrate the limitations it is necessary to look in detail at the integration of the three dimensional equation For the sake of clarity only the terms involving flow in the x z plane will be treated here as the behaviour in the y z plane is similar The problem then is the ev
21. dat is specified by the user in the input file zoomq3d dat see Section 14 2 On the first data line of the input file Figure 40 the number of single and multi layer wells is defined On the second data line a value is entered that must be used to transform the pumping rates listed below into units of m day Following this two sections of data are entered one relating to single layer wells and one to multi layer wells These two sections contain the number of time blocks of abstraction data followed by sets of data for each well in the model These data sets contain a comment line for example in which the name of the well is written the co ordinates of the well and then the pumping rates for each time block At the start of the set of data specifying multi layer wells an additional parameter is defined which is described in the next sub section This is the conductance between the multi layer boreholes and the aquifer nodes to which they are connected 10 2 1 1 MULTI LAYER WELLS The use of multi layer wells enables groundwater to be abstracted from specific layers at a single x y location That is groundwater can be abstracted from any one layer or any combination of more than one layers at any horizontal position The model calculates the flow rate of water that is drawn from each layer This is achieved by connecting the pumped layers to a multi layer well object which has associated with it a borehole water level The concep
22. files in which other spatially varying model parameters are specified see Section 7 3 Data for the base grid are always first for each stress period The first line of each recharge array corresponding to a grid is a comment line and the first line of each stress period data set is the stress period number and time block number File format File structure 0 001 Multiplier to convert rates to m day 1 1970 Stress period and block number x BASE GRID Comment line Replace rectangle with an array of Base grid recharge rates mm day with the same number of rows and columns as this grid SUBGRID 1 Comment line Replace rectangle with an array of Subgrid 1 Stress period 1 recharge rates mm day with the same number of rows and columns as this grid SUBGRID 2 Comment line Replace rectangle with an array of Subgrid 2 recharge rates mm day with the same number of rows and columns as this grid Stress period and block number x BASE GRID Comment line Replace rectangle with an array of recharge rates mm day with the same number of rows and columns as this grid Base Grid SUBGRID 1 Comment line Replace rectangle with an array of recharge rates mm day with the same Subgrid 1 number of rows and columns as this grid Stress period 2 SUBGRID 2 Comment line Replace rectangle with an array of recharge rates mm day with the same Subgr
23. h The SOR iteration scheme is very easy to incorporate into a computer program and it is generally reliable though not the most rapid technique currently available 3 2 1 Convergence criteria With any iterative scheme there must be some test which is applied to decide that the process has come sufficiently close to the true solution An apparently attractive option is to test the change in head which arises over an iteration When this is smaller than a selected value for every node convergence is assumed This should not normally be used in groundwater problems because it does not guarantee that the flow balance at a node is satisfied Flow rates are governed by Darcy s Law and therefore depend on the head gradient Significant errors can still occur in the gradient even though the head changes are small The basic equation represents a flow balance and therefore a test based on satisfying it is much more reliable This is the approach adopted in ZOOMQ3D The iterations stop when the basic equation is satisfied to within a specified flow rate Increased accuracy requires a larger number of iterations and very small errors often require an unacceptable increase in computer time Although there are limits imposed on it is necessary to select a value from within the allowed range This can be very important as the rate of convergence is often sensitive to the choice of and it may be worthwhile experimenting with different values particularl
24. is the base grid In the grids dat file shown in Figure 7 four blocks of grid data are defined which relate to the four grids shown in Figure 6 The first relates to the base grid The second and third blocks correspond to the grids on level two and the fourth block relates to the finest grid on grid level three Data describing the base grid is slightly different from that describing the subgrids Following the three lines at the start of each grid block information about each node is defined Nodes are listed in row and column sequential order from the bottom to the top of each grid Information associated with a node located on rows or columns of two or more grids is defined within the highest grid level block For example the second subgrid on level two consists of four mesh intervals in both the x and y directions Consequently it contains 5 or 25 nodes However the data file indicates that there are only 16 blocks of node data defined for this grid The reason for this is that nine of the nodes also exist in the base grid The first line in a block of node data is a comment line composed of a series of dashes This is used to separate data for each node On the second line of a block of node data a variable indicating node type is defined These variable are integers and take one of five values 7 11 13 14 or 15 The node types corresponding to each integer flag are shown in Figure 8 The first four values indicate nodes on the bo
25. of a map file which is used to distribute the VKD schemes defined in Figure 43 over the model domain VKD profiles are not created at the horizontal nodal locations where an appropriate letter is not specified i e in this example where the character is not in the range a to h At these points horizontal conductivity is uniform in 72 the vertical direction within each layer Again this example is not intended to be physically realistic but rather is used to illustrate the flexibility of the method Map of VKD schemes b abbccdd abccdddd abccddeee abcdddeef abcddeefff abcddeeffgg bcddeeffggh cddeeffghhh cddeeffghhh cdeefgghhhh Figure 44 Example a VKD scheme map file and b associated model grid 11 2 2 VKD profile data files After defining which VKD scheme applies at each horizontal nodal location values have to be read to parameterise each VKD profile in each scheme At horizontal nodal locations represented by the letter a in this example data for only one profile is required But at nodal locations represented by the letter b data for four profiles must be read in Four types of information are required for each VKD profile 1 The hydraulic conductivity in the x direction K below Zp 2 The hydraulic conductivity in the y direction Ky below Zp 3 The gradient of the profile VKDGrad above Z 4 The elevation
26. straight line distance between the adjacent two river nodes e River stage m e River bed elevation m e River bed thickness m e Vertical hydraulic permeability under effluent conditions m day e Vertical hydraulic permeability under influent conditions m day 9 5 1 Conceptualisation of river aquifer interaction In ZOOMQ3D river aquifer interaction is represented as a linear head dependent leakage mechanism The rate of leakage depends on the difference between groundwater head and river stage and is expressed by K W L h h c h h where Q is the leakage rate m day 51 K isthe vertical hydraulic conductivity of the river bed m day B is the thickness of the river bed m W isthe width of the river m L isthe length of the river reach m ha isthe head in the aquifer m and h is the river stage m This equation is modified when the head in the aquifer falls below the base of the river bed Zor B where Z 1S the elevation of the bed of the river Under these conditions the driving head is equal to the difference between the river stage and the base of the river bed Zz one B The leakage from the river under perched conditions is therefore defined as Q 2 W L Zaor B hy In addition to limiting the flow between the aquifer and the river when the groundwater head falls below the river bed different hydraulic conductivity values are applied bet
27. the input file described in Section 8 2 which is used to define initial conditions for a model Consequently in order to use this output file to re start a simulation it is only necessary to rename it appropriately 16 4 RIVER FLOW GAUGING The river nodes at which the baseflow is monitored over time are specified in the input file named in the file zoomq3d dat for example gauging stations dat The time discharge record at these nodes is output to the file also named in zoomgq3d dat for example gauging stations out This output file contains one line of data for each time step of the simulation with the following format day stress period block MJD time time_elapsed Q Q Q Q Q where day is the end of the day when the flow was recorded stress period is the stress period number block is the time block number of the flow measurement MJD_time is the time simulated from the start time in Modified Julian day format time_elapsed is the time simulated since the beginning of the model run days Q is the flow m day in the first river node defined in gauging_stations dat Q is the flow m day in the second river node defined in gauging_stations dat Q is the flow m day in the n river node defined in gauging_stations dat The river nodes are listed in the same order as they are defined in the input file The output file is space delimited and is easily opened using spreadsheet soft
28. the same format as one of ZOOMQ3D output files and contains the value of groundwater head at each node in the model If the flag is equal to y this file is opened and read This enables simulations to re run from a previously simulated condition On the last line of the input file the user specifies if information is to be output which enables particle tracking simulations to be run If the user does wish to track particles then two additional output files are produced heads txt and flows txt which are required by the particle tracking code ZOOPT for input 40 T 5 Example clock dat file Number of time steps stress periods and blocks 4 12 5 Number of the stress period and block after which to terminate simulation T225 Enter start time of simulation year month day hh mm ss 1970 1 1 00 00 00 Length of each of the stress periods in the blocks 3120 r200 310 300 37 20 302 0 30310 S003 i0 3000 Stress periods and blocks represent months and years y or n tO 00 on U a G N A y Method of calculating time step length 1 2 or 3 3 Data for method 1 of stress period length at end of time step 1 to number of time steps 1 10 0 25 0 50 0 Data for method 2 Geometric progression time step multiplier 1 5 Data for method 3 Specified time at end of time step 1 to number of time steps 1 4 0 10 0 18 0 Block number order one per line for each block 19
29. time time_elapsed Q Q H h total i where day is the end of the day when the flow was recorded stress period is the stress period number block is the time block number of the flow measurement MJD_time is the time simulated from the start time in Modified Julian day format time_elapsed is the time simulated since the beginning of the model run Qtotal is the pumping rate of the multi layer well calculated by summing the flow into the well from each aquifer node Q is the flow into the borehole from layer i Hw is the water level in the borehole hj is the head at the aquifer node in layer 1 There is one complete set of the columns Q a gt Qi H h for each multi layer well in the model Within each of set of these columns there are n columns of Q and n columns of h data where n is the number of layers to which the multi layer well is connected 91 16 13 CONVERGENCE OF SOLUTION Information describing the progress of the solution during each time step is written to the output file zoomq3d out At the end of each user defined number of iterations the last number entered in sor dat of the successive over relaxation solution process the following information is output e the sum of the absolute values of the flow imbalance residual at each model node m day e the location of the node with the greatest nodal flow imbalance residual and the value of this flow imbalance m day e the location of t
30. vertical at a horizontal nodal location VKD profiles can be specified in any layer and at both unconfined and convertible nodes The following points describe the use of VKD schemes 1 A VKD scheme defines the number of VKD profiles in the vertical at a horizontal nodal location 2 The number of VKD profiles in a scheme must be in the range zero to the number of numerical layers in the model 3 Within a scheme a single VKD profile can be defined to cross represent only one or more than one model layers The scheme defines which layers each VKD profile represents 4 VKD profiles can be defined to cross layers of confined nodes The confined nodes are not connected to the VKD profile and do not calculate their transmissivity by interrogating the profile 5 A different scheme can be defined at each horizontal nodal location of the model 6 The same scheme can be applied at multiple horizontal nodal locations Figure 43 shows a number of examples of different VKD schemes in a model with four layers Consequently the maximum number of profiles in the vertical is four These examples are not intended to be physically realistic but rather meant to illustrate the flexibility of the method This level of flexibility has been included with regard to the possible future development of the method It may be the case that more complex but realistic variations of hydraulic conductivity with depth are defined at a later stage of model development T
31. 00 1707 11 5 296000 571500 2207 11 etc for each node in each branch of river 1 River 2 Branch Node X downstream Bed Elevation Kz Effluent Kz Influent 14 292500 575500 67 13 293000 575500 z 15 03 12 293500 576000 5 E T S5 11 294000 576500 10 294000 576000 1 1 1 1 1 1 1 1 1 1 aE 1 9 294500 576000 etc for each node in branch 20 292000 578000 0 19 292500 578000 500 18 293000 578000 1000 etc for each node in branch 2 of Figure 55 Example output file containing river baseflow accretion data 87 16 7 DE WATERING AND RE WETTING At the end of each time step information is written to the file dewatering out informing the user of which nodes have de watered and which have re wetted The layer number and co ordinate of each of these nodes is written to the file 16 8 NODAL FLOW BALANCES Nodal flow balance information for every node in the model is written to the file flowbal out for example named in the input file zoomq3d dat This output file contains flow balance data for a single time step only and is over written periodically during the simulation The frequency with which the file is produced is defined in the input file clock dat It is created after either every time step stress period or block or only for the final time step in the simulation It is always re written at the end of the simulation The first line of the file is a text string that specifies the time at whic
32. 000 m3 d 3 nstream flow 1 26626e 006 m3 d pogenic input 1 217e 006 m3 d Ww He a D a eg Ee D 0 K O fe 4 tream flow 63027 3 m3 d nr pogenic inpu 24000 m3 d aquifer 56443 4 m3 d O 1 leakage out o outflow to fixed heads 0 m3 d l increase in aquifer storage 7 1706le 012 m3 d L INFLOW 1 46675e 006 m3 d TAL OUTFLOW 1 46673e 006 m3 d GLOBAL FLOW IMBALANCE 15 6715 m3 d 0 00106845 of total inflow Figure 56 Example global flow balance output file 16 9 1 Time variant global flow balances Global flow balance information for every time step of a simulation is written to the file global_tv out The file contains the columns of data listed in Table 9 One line of data is written to the file per time step The file is space delimited and is readily opened using spreadsheet software for manipulation 89 Table 9 Data contained in global_tv out Description of data Time within stress period days Stress period number Block number Time since start of simulation days Total recharge m day Total inflow at model boundary m day Total abstraction m day Total outflow from rivers m day 1 2 3 4 5 6 7 8 9 Total discharge inflow to rivers m day Total flow through leakage nodes m day Positive out of aquifer Total outflow to fixed head nodes m day Total storage increase
33. 13 1 3 36 wetthresh map amp wetthresh cod wetthresh dat 13 1 2 37 zbase map amp zbase cod OR zbase dat per layer 1 4 2 38 zoomq3d dat 14 2 39 ztop map amp ztop cod OR ztop dat per layer 7 4 1 Note the names of these files are fixed The names of the remaining files can be specified by the user in the input file zoomq3d dat 17 Table 2 Model feature ZOOMQ3D input files which are relevant to model features Relevant file names Relevant section Grid structure grids dat 7 1 Confined unconfined conditions aquifer map grids dat 7 2 1 7 1 Layer elevations 1 Layer top elevations 2 Layer base elevations ztop map amp ztop cod or ztop dat grids dat zbase map amp zbase cod or zbase dat 7 4 1 7 1 1 4 2 Entry of spatial data entry_method dat 7 3 1 Hydraulic parameters 1 Hydraulic conductivity 2 Anisotropy 3 Specific storage 4 Specific yield 5 Vertical conductance hydcond map amp hydcond cod or hydcond dat anisotropy map amp anisotropy cod or anisotropy dat specstor map amp specstor cod or specstor dat syield map amp syield cod or syield dat vcond map amp vcond cod or vcond dat 7 5 1 132 193 7 5 4 TA amp 7 5 5 Initial groundwater heads Boundary conditions Model edge boundary conditions Internal fixed heads No flow Head dependent leakage nodes Springs i
34. 70 EIFL 1972 1973 1974 Data output at end of every time step 1 stress period 2 block 3 or only at end of simulation 4 4 Steady state or time variant s or t t Rerunning y or n n Output particle tracking info y or n n 10 Le 12 13 14 15 16 Let 18 Figure 21 Example clock dat file 41 8 2 INITIAL GROUNDWATER HEADS Initial groundwater heads can be entered into the model using two different methods These methods employ either 1 a pair of map and code input files for each layer with the names initialh map and initialh cod or 2 a single numeric input data file containing initial groundwater heads for the whole model Note that this file does not have the same format as the numeric files for defining other spatially variable model parameter values When using the map and code files to input initial groundwater heads the symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model The format of these map and code files is described in Section 7 3 Initial groundwater heads can also be defined using a single input file the name of which is specified by the user in the input file zoomq3d dat This has the same format as one of the ZOOMQ3D output files whose name is also specified in
35. Code file 2 Code file 0 lt 0 0 0 Map file 1 aaaaaaaabbbbb aaaaaaaabbbbb aaaaaaaabbbbb Map file 2 aaaaaaaabbbbb aaaaaaaabbbbb aaaaaaaabbbbb Map file Figure 36 Example recharge time series recharge code file and recharge map file used to define two different recharge types 61 10 1 2 Applying recharge using a numeric data file The use of recharge types and associated map and code files is not obligatory Instead a single numeric data file can be used containing arrays of recharge rates in mm day for each stress period in the simulation This numeric recharge file can also be used in conjunction with recharge map and code files If both recharge data entry methods are used simultaneously the recharge rates defined by each are added together before being applied The name of the numeric recharge file is specified by the user in the main recharge file which is described in the next sub section The arrays contained in the numeric recharge file relate to each of the grids in the model The format of the file is shown in Figure 37 Recharge data is specified for each stress period of each simulation time block in the time block order specified in clock dat Within each stress period arrays of recharge data are defined for the base grid and for each refined grid within the model The recharge arrays for each grid are listed in the same order as the grids in the map and code files or dat
36. The format of these files is described in Section 7 3 13 1 4 Limitations of the de watering a re wetting mechanism A problem may arise if nodes on the boundary of a refined grid or one interval outside the refined grid de water In this case larger nodal flow imbalances may result at these nodes If this occurs the user may need to make the nodal convergence criterion smaller and or increase the number of cycles performed during the solution process see Section 12 1 13 2 DE ACTIVATING NODES Individual nodes can be permanently removed from the model grid using map files named noflow map The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model A map file is required for each of the model layers The format of these files is the same as that for the map files described in Section 7 3 The structure of a map file for a model containing a single base grid is shown in Figure 53 This contains a single character arrays representing the base grid preceded by a comment line The comment line contains information describing the grid to which the array relates ZETUP the set up program for ZOOMQ3D produces this file and writes the co ordinates of the bottom left and top right hand corners of the mesh within the comment lines The user need only adjust the letters in the arrays
37. UP produces the input files required by ZOOMQ3D that define the structure of the model mesh and the structure of rivers It also produces generic templates of all of the other files required by ZOOMQ3D in the correct format These can be modified subsequently using a text editor to complete the model specification Finally ZETUP produces a set of files that enable the 11 visualisation and checking of the model structure If modifications to the structure of the model are required it can be reloaded into ZETUP for alteration 43 TERMINOLOGY ZOOMQ3D is written using an object oriented programming language Whilst the users do not need to concern themselves with what this means the term object is used a number of times within this manual and consequently a brief explanation is required The user can think of an object in abstract terms as any distinct entity that stores data and perform tasks In ZETUP and ZOOMQ3D objects are defined to represent real world features For example a pumped well is represented by an object Pumped wells are described by data such as a depth and radius and have the capability to pump water out of an aquifer References are made in this manual to objects which represent finite difference grids and rivers 4 4 UNIT CONVENTION All lengths in ZOOMQ3D must be specified in metres The unit of time is specified as days All volumetric flow rates are input and output in m day 12 5 Running the model To i
38. aluation of is 2 x Daj ac D o s Bae Nae z OX Ox z OZ i OZ Zi Two terms in the equation the second on the left and right hand sides are relatively easy to deal with The second term on the left hand side evaluates to A _ 5 2 eA OZ Kol because it involves only variations in the z direction These terms correspond to the leakages in the quasi three dimensional equation Labove and Lbelow respectively The second term on the right can be replaced by a source term equal to the net effect of N over the layer thickness expressed as a flow per unit surface area q as shown in the quasi three dimensional equation When it comes to dealing with the remaining terms an important aid in the integration process is the Leibniz Integral Rule which is usually stated in a form used to calculate the differential of a definite integral Riley et al 2002 p182 col b x Of ob Oa ma f x z dz lee a dz f x b x ea f x a x a In the problem examined here it is in fact the integration of partial derivatives which is important and the rule is re arranged as follows vn OF p m A pe ae dz l f x z dz f x b x aut f x a x In evaluating the first term on the right hand side the function f is replaced by S This t oh i should reduce to Sr after integration for consistency with the quasi three dimensional t equation For this to occur two conditions must be met The first is that the inte
39. and wetthresh cod or 2 numeric data files named wetthresh dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 13 1 3 Post wetting head On re wetting the groundwater head of the previously inactive node has to be re set The elevation at which the groundwater head is set in the re wetted node is specified using the post wetting head variable As with the wetting threshold this is defined by a distance above the base of the node and not as an elevation Input file names and format The post wetting heads must be entered into the model using either 1 pairs of map and code files with the names wethead map and wethead cod or 2 numeric data files with the names wethead dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of 79 the model layers or a single numeric data file is required for each of the layers
40. area factor Comment line and two data lines for each node in the grid Blank lines do not exist User adjusted BASE GRID LEVEL 1 Comment line start of grid data block separator Grid level number of subgrids number of nodes in grid No intervals in x amp y directions co ords of SW amp NE corners no x amp y parent divisions Comment line node block separator i j x and y co ords of node node type Boundary node flag boundary node type nodal area factor Comment line and two data lines for each node in the grid Blank lines do not exist N 4 a gt fy E I A H A w m D n Comment line start of grid data block separator Grid level number of subgrids number of nodes in grid No intervals in x amp y directions co ords of SW amp NE corners no x amp y parent divisions Comment line node block separator i j x and y co ords of node node type Boundary node flag boundary node type nodal area factor Comment line and two data lines for each node in the grid Blank lines do not exist SUBGRID LEVEL 2 Comment line start of grid data block separator Grid level number of subgrids number of nodes in grid No intervals in x amp y directions co ords of SW amp NE corners no x amp y parent divisions Comment line node block separator i j x and y co ords of node node type Boundary node flag boundary node type nodal area factor Comment line and t
41. base grid and for each refined grid within the model The grid data blocks are listed in the same order as those in the map and code files or dat files in which other spatially varying model parameters are specified see Section 7 3 Data for the base grid are always entered at the start of a layer block The first line of each layer block is a comment line and the first line of each grid block is a comment line After the comment line at the start of each grid data block an array of groundwater head values is entered This array must have the same number of rows and columns as the finite difference grid to which it relates i e the base grid or one of the refined grids The first line of the array of head values relates to the top furthest in the positive y direction row of the grid Some points on a grid may be located outside the model boundary however a groundwater head value must be entered in all elements of the rectangular array or matrix of grid points The values corresponding to nodes located outside the model boundary are read but ignored 43 9 Boundary conditions 9 1 MODEL EDGE BOUNDARY CONDITIONS Boundary conditions around the edge of the model are specified using the file boundary dat This file is produced by ZETUP but may require modification before being used as a ZOOMQ3D input file The file is used to assign each finite difference node on the boundary of the model a fixed head value or a fixed inflow rate that wil
42. c uk Forde House Park Five Business Centre Harrier Way Sowton Exeter Devon EX2 7HU T 01392 445271 Fax 01392 445371 Geological Survey of Northern Ireland 20 College Gardens Belfast BT9 6BS 028 9066 6595 Fax 028 9066 2835 Maclean Building Crowmarsh Gifford Wallingford Oxfordshire OX10 8BB 01491 838800 Fax 01491 692345 Sophia House 28 Cathedral Road Cardiff CF11 9LJ T 029 2066 0147 Fax 029 2066 0159 Parent Body Natural Environment Research Council Polaris House North Star Avenue Swindon Wiltshire SN2 1EU 01793 411500 Fax 01793 411501 www nerc ac uk Foreword The development of the modelling software within the ZOOM family of which ZOOMQ3D is a part has been undertaken through a continuing tripartite collaboration between the University of Birmingham the Environment Agency and the British Geological Survey The development of ZETUP and ZOOMQ3D was initially undertaken at the University of Birmingham between 1998 and 2001 but continued after this time as a collaborative project between the three partner organisations Since the inception of the collaborative project the development of the software has been directed by the ZOOM steering committee the members of which are University of Birmingham Dr Andrew Spink Environment Agency Steve Fletcher Paul Hulme British Geological Survey Dr Denis Peach Dr Andrew Hughes Dr Chris Jackson Acknowledgements The authors would like to acknowledge
43. ch is what you would have to type if extensions were disabled zNzoomg3d_project gt _ Figure 3 Example of changing the working directory within a console window The size of the console box can be adjusted by clicking on the icon in the top left hand corner of its window and selecting Properties from the menu list Suitable values for the width and height of the window and its associated screen buffer are shown in Figure 3 CA WINNT system32 cmd exe Properties Dptions Font Layout Colors Window Preview m Screen Buffer Size Width fi 20 Height 300 Window Size Width ho Height 50 m Window Position Left 18 Top E IV Let system position window Figure 4 Changing the properties of the console window 14 5 1 THE PROCESS OF CONSTRUCTING A MODEL To construct a model and run ZOOMQ3D the process shown in Figure 5 is performed This involves running the pre processor ZETUP to construct i the ZOOMQ3D model input files defining the model structure and ii the remaining set of generic template input files for modification using a text editor to complete the specification of the model All the input files are then transferred to the directory where the zoomq3d exe executable file is located before ZOOMQ3D is run Figure 5 Run ZETUP to create 1 Set of ZOOMQ3D input files defining model structure 2 Set of remaining ZOOMQ3D input files These are generic
44. d abstraction The unknown head values can be found by forming an equation of the above type at each node and solving the resulting set of equations simultaneously At nodes along the interface between areas of mesh refinement the equations differ slightly from the structure given above The reason for this is that there are five nodes surrounding the central node in the plane of the layer There is therefore one extra unknown head and its associated coefficient The coefficients relating to flow between the nodes in the plane of the layer have a different composition to that illustrated above but the same process of forming a set of equations and solving them simultaneously applies The technique for solving the equations is outlined in the following section 3 2 SUCCESSIVE OVER RELAXATION Algorithms for dealing with simultaneous equations fall into two categories known as direct and iterative methods In a direct solution the results are obtained by applying a fixed set of operations to the equations the number and type of operations can be determined before they are carried out As the name suggests an iterative method involves the repetition of certain operations until a sufficiently close approximation to the real solution is obtained A measure of accuracy must be selected and this will determine how many iterations are needed There is no way of deciding how many iterations will be required a priori Iterative methods can also be classified a
45. del but this is not of relevance This system could not be modelled using a single recharge type because of the different time series of recharge in the different areas As stated previously over the area of the aquifer covered by superficial deposits recharge is constant but it varies seasonal in the valley area However using two recharge types it is straightforward to represent this recharge pattern and simple to produce the required data files The data contained in recharge dat and the code and map files for each recharge type are listed in Figure 36 It is apparent from examining recharge type 1 that this data set results in a constant recharge of 0 1 mm day being applied to the interfluve area and no recharge in the valley No recharge occurs in recharge type 2 over the area covered by superficial deposits but a time varying recharge is applied to the uncovered aquifer The recharge rates calculated in each recharge type are additive and so the scheme illustrated in Figure 34 produces the recharge pattern described by the conceptual model Recharge type 1 superficial cover Recharge type 2 uncovered aquifer Stress period Recharge mm day Stress period Recharge mm day Stress period Recharge mm day Stress period Recharge mm day 0 1 1 2 0 0 D n F w amp v w fan a v Of jh amp gt Es x Code file 1
46. divided into time steps stress periods and blocks The length of a time step is equivalent to the length of time between which successive solutions are calculated for the model s state variables A stress period represents a period of time during which all model stresses remain constant e g recharge or groundwater abstraction Stress periods are divided into one or more time steps A block is composed of one or more stress periods The rationale for the use of blocks is predominantly related to the simplification of the organisation of time variant data for example groundwater abstraction Section 10 2 or recharge Section 10 1 rates within input files The number of stress periods in each block is the same for all blocks within a simulation If twelve stress periods are defined in each block then the stress periods and blocks could be considered equivalent to months and years if the number of days in each stress period is equivalent to the number of days in each month Figure 20 shows the division of time into time steps stress periods and blocks Time step Stress period Block 1 1 1 Alo rmlelaA ofrm elalofrm efa olrm ela ofrm elaloulre iN N Figure 20 Division of time into time steps stress periods and blocks The length of each stress period is user defined as are the lengths of the time steps within stress periods The length of the time steps can be def
47. e which can be used to produce flow hydrographs 90 16 11 SPRING FLOWS The time discharge record at the springs included in the model is output to the file springs out This output file contains one line of data for each time step of the simulation with the following format day stress period block MJD time time_elapsed Q Q Q Q Q where day is the end of the day when the flow was recorded stress period is the stress period number block is the time block number of the flow measurement MJD_time is the time simulated from the start time in Modified Julian day format time_elapsed is the time simulated since the beginning of the model run days Q is the flow m day out of the first spring defined in springs dat Q is the flow m day out of the second spring defined in springs dat Q is the flow m day out of the n spring defined in springs dat The spring flows are listed in the same order as they are defined in the input file The output file is space delimited and is easily opened using spreadsheet software which can be used to produce spring flow hydrographs 16 12 MULTI LAYER WELLS Flow and head data associated with multi layer wells is output to the file multi_wells out This output file contains one line of data for each time step of the simulation It is a space separated column text file and contains columns of data in the following format day stress period block MJD
48. e solution method is specified by the user in the input file zoomq3d dat The format of the input file for example named sor dat is shown in Figure 49 where iSolve is an integer flag indicating which solution method is being used SOR is the only solution method currently implemented in ZOOMQ3D and thus only a 1 can be entered on this line is the successive over relaxation factor 1 0 lt lt 2 0 CErit is the convergence criterion as a maximum permissible nodal flow imbalance m day MaxIter is the maximum number of iterations per time step MaxTChange is the maximum permissible change in transmissivity m day over a cycle see Section 7 2 2 MaxCycles is the maximum number of cycles see Section 7 2 2 CheckIter isthe number of iterations after which to check for convergence WritelIter isthe number of iterations after which to output information on the progress of the solution process to zoomq3d out An example file sor dat is shown in Figure 50 i1Solve 0 CCrit MaxIter MaxTChange MaxCycles CheckIter WriteIter Figure 49 Format of SOR numerical solver input file 76 Figure 50 Example sor dat file 77 13 Activating de activating nodes 13 1 DE WATERING AND RE WETTING Model nodes de water when the groundwater head falls below their base When this occurs the node is made inactive and is removed from the matrix of finite difference equat
49. e used to specify specific storage values in layer 04 of the model i e three layers down from the top layer instead of the files specstor04 map and specstor04 cod The numeric data file has the same structure as the map file except that each character array is replaced by an array of numbers representing the parameter values that will be applied at the corresponding nodes of the finite difference mesh within the model layer that the file relates to An example numeric data file is shown in Figure 17 This specifies exactly the same model data as that specified in the example above in which a pair of map and code files are used for defining a hydraulic conductivity distribution pes Map for grid 0 1 0 1 0 lt Bottom right 700 700 Se MOY Be Fe a ATWNrFORBNO DOOONFEFRE DOOONFEFRE OOOOH RH DOOONFEFRE AWNrRFORBNO AWNrRFPORBNO Bottom 100 100 Top right 300 300 2 0 NNNNN NNNNN 5 EE a oOoo0oo0oo0oo0o0o00 N WNPOBRNOQ lt FPREPENNNNNO0 OOOONPrRPEPEO 0 0 0 0 0 0 z0 z0 PRPRPRENNNN ND PRPRPRENNNN ND PRPRPRPENNNN ND Ox CO OO O OrO e OO OOO OO oO det Bottom 400 400 Top right 600 600 io H D AOO l l iS AS SM al 0a Joe Lwwwwww lo DOGO GO 5 j CERO OOOO SSE O hb lt annnon oo oo Um ss D O GOOO GO GO Bottom lt 150 130 Top fights 250 250 0 5 AanannnanwsannnnndsodddsdsdD00D IYNWNHFOKBDND Aaaannanannnd
50. e x direction m Ay is the width of the node in the x direction m S is the specific yield and At is the time step length days Consequently the spring is set to abstract water from the aquifer during the next cycle of the transmissivity spring flow adjustment procedure At the end of the next cycle the spring flow is readjusted by examining the groundwater head again This cyclical procedure terminates and the simulation progresses to the next time step when both the transmissivity and spring flows stop varying between cycles If the groundwater head is simulated to be below the base of the spring its flows rate is set to zero 47 9 4 2 Input file format Springs are defined in the model using the file springs dat The name of this file is invariable Springs can only be placed in the top model layer at unconfined or convertible nodes The input file has the following structure n x Z AZ one line for each of n springs y pring T where n is the number of springs x 1s the x co ordinate of the spring m y is the y co ordinate of the spring m Z is the elevation of the top of the spring m and AZ is the depth of the spring m The base elevation of the spring is calculated by subtracting the spring depth from the top elevation An example springs dat input file is shown in Figure 25 Figure 25 Example springs dat input file 48 9 5 RIVERS ZOOMQ3D can simulate baseflow within de
51. each of n observation wells where n is the number of observation points at which the head is monitored over time start _block is the block number when monitoring starts end_block is the block number when monitoring ends Layer is the number of the layer in which the observation well is located x is the x co ordinate of the observation well and y is the y co ordinate of the observation well 66 pumping dat File format 1000 0 Well 1 2 5000 5000 1970 2 7 4 2 1971 2 7 4 2 1972 2 7 4 2 Well 2 2 7000 2000 1970 1 0 2 0 19 71 10 1 2 0 T972 AO A Multi well 1 3000 2000 2 1 2 1970 2 0 2 0 1971 2 0 2 0 1972 2 0 2 0 Figure 40 Number of single amp multi layer wells T ES Ae 5 9 4 7 E A E 065 O01 o E 2 SA 59 5 7 407 3 2 OPT 025 0 01 0 2 2 2 5 4 B29 S 7 4 7 3 2 1 7 0 5 O20 On2 1 2 etc for each block 20 in this example etc for each block 20 in this example Multi layer well data etc for each block a 1 gt 1 0 1 01 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 20 in this example Example pumping dat file and format of input Comment line Number of single amp multi layer wells Comment line Multiplier to convert pumping rates to m day Comment line Do not remove line if no single layer wells Number of blocks of pumping data
52. ecause it means that the system of finite difference equations is modified whilst their solution is sought Instead in ZOOMQ3D the transmissivity at convertible and unconfined nodes is recalculated at the end of a time step the solution of which can be repeated Unconfined behaviour is modelled within a cyclical process The finite difference equations can be solved once or repeatedly during each time step Each unconfined node calculates its transmissivity at the beginning of the time step based on the groundwater head A solution to the finite difference equations is then computed The transmissivity is subsequently recalculated using the newly calculated heads An average is then taken of the pre and post solution transmissivities at each convertible and unconfined node A new solution to the finite difference equations is computed again using these average transmissivity values This cyclical process continues until the change in transmissivity over a cycle falls below a maximum value or until a maximum number of cycles have been performed The test for convergence within the repetitive cycle is based on a maximum permissible change in transmissivity At the end of a cycle after the solution has been computed the change in transmissivity is examined at each node If the maximum change in transmissivity is below a user defined value the solution then progresses to the next time step This process is illustrated in Figure 12 The maximum permissib
53. ed This is followed by a line of recharge rates mm day for each recharge type Each line of recharge rate data must contain one value for each stress period In section 2 the name of the single numeric recharge file is specified line 31 It is possible to apply the recharge defined in the first stress period in this file throughout the simulation The user specifies whether this is to be implemented on line 33 63 Example recharge dat file File format Using map code files only 1 numeric files only 2 both 3 Comment line 1 Integer data entry method identifier None or any number of blank lines ECTION 1 Comment line must start SECTION 1 Comment line which must start SECTION 1 Data for recharge map and code files Comment line Multiplier to convert SECTION 1 rates to m day Comment line 0 001 Multiplier to convert SECTION 1 rates to m day Number of recharge types Comment line 2 Number of recharge types integer Map and code file names for each recharge typ Comment line rchl_pptn map Name of map file for recharge typ rchl_pptn cod Name of code file for recharg rch2_urban map Pair of file names for rch2_urban cod ach recharge typ Number of blocks of recharge data Comment line 3 umber of blocks of recharge data Data for each block for each recharge typ Comment line 1970 Block number for block 1 03 0 95 0 80 0 83 0 21 0 17 0 00 0 00 0 00 O Rate for each stress period f
54. ed aquifer A number of assumptions underlie this equation First the fluid is assumed to be of constant density this allows the flow balance to be a consequence of mass conservation within the element Next the Cartesian co ordinate system is aligned with the principal axes of the hydraulic conductivity tensor this avoids the need for cross derivatives A model based on the above equation incorporating appropriate boundary and initial conditions would be truly three dimensional ZOOMQ3D takes a simplifying approach to the solution of the three dimensional equation by recognising that in many aquifers it is possible to identify a layered structure If the layers are aligned parallel to the horizontal co ordinate axes then the three dimensional equation can be integrated vertically across the layer to produce an equation which describes the flow within a layer and its interactions with adjacent layers Such an equation is a n 4 i i 2 S Ti q E ee g Lpetow Ox ax dy dy t h x y t is the groundwater head value within a layer L where T x y sie x y are the transmissivity values in the x and y directions respectively LT S x y is the storage coefficient of the layer L q x y t is a source flow term as a flow per unit surface area LT Labove and Lyelow are leakage rates from layers above and below LT In layered models the general approach to obtaining an equation such as the one above is to
55. ed in the map file the hydraulic conductivity K of the profile will be assigned a value of 2 3 This method of data entry is identical for the three remaining sets of information required by each profile on each level K VKDGrad and Z The format of the numeric data files is described in Section 7 3 3 An example numeric data file defining K data on profile level 1 is shown in Figure 48 This specifies the same data as that defined by the map and code file shown in Figure 47 The example shown in this section has not included local grid refinement however the specifiation of VKD data in this case is the same as for any other spatially varying model parameter and is described in detail in Section 7 3 3 74 Code file Map file VKDKx code data Map for VKDKx parameter on profile level 1 2 1 7 aaaaaaa 2 3 aaaaaabb aaaaaabbb aaaaaabbb aaaaabbbbb aaaaabbbbbb aaaabbbbbbb aaabbbbbbbb aaabbbbbbbb aabbbbbbbbb Figure 47 Example code file vkdkx01 cod and map file vkdkx01 map Numeric data for VKDKx parameter ile level 1 JO9s G99 3999 99 9 2999 999 999 999 999 99 9 999 999 D ko WWWWWNNNNYNNO ERERKEN MN AE MEAR of 7 7 yi 7 7 3 3 3 3 3 3 NNNBPRPRPHPHPEB WwW wW WwWINNNNNN NNNNPPPEPEPEH WWWWJIJNNNNN NNNNNPP PEPEPEPE NNNNNNEBEBPBPEBPH WWWWWwWIdId ss NNNNNNNNEFEBHR WWWWW WWW III NNNNNNNNNHPB WW WWW WWW WwW I NNNNNNNNNHPB WWWWW WWW Ww J I
56. eeecseeeeeeeeeees 74 Figure 47 Example code file vkdkx01 cod and map file vkdkxO1l map ee 75 Figure 48 Example numeric data file VKdKXO dat oc eee eecesseceseeeeeeeeseesnaeeneeeseeeeaes 75 Figure 49 Format of SOR numerical solver input file 2 0 ee eee eeeeeeseeeeseeeeneecnaeeneeteees 76 Pisure 50 Example sordat Te istes ctsceinesatussaeeguranetararadeebeoeateadtedakenactaaeleeeateastedaaauatenaeet qe Figure 51 Example wetflag map file jcccsi cc cosatecneds henctantyecadaa seacasienianecndialaneeeeeeecks 78 Figure 52 Conceptualisation of wetting threshold at node oo eee eeeeeeeseeeneceteeeeeeeeaees 79 Figure 53 Example nowflowH map file 0 0 ceccececeeeceeeeeetseecessceceneeecentcecenseesontescenteeee 80 Figure 54 Example contour_times dat file oo eee eecesseceseceeeeeeseecsaeceseesseeesaeecsaeenseensees 81 Figure 55 Example output file containing river baseflow accretion data eee 87 Figure 56 Example global flow balance output file 0 0 eee eee ceeceeeeeeeeeeseecnaeeneessees 89 Figure 57 Example transcycle out output file oo eee eeeeeeneecseeceeeeseeesneecsaecneeesseeees 92 Figure 58 Order of data output to heads txt c scc ccesdstercei essevsanesaitetnteceende de teiseeneetasiancdae 93 vii TABLES Table 1 List of all ZOOMQ3D input files icc 2 el aaa neccndeede tite elege eet geeks 17 Table 2 ZOOMQ3D input files which are relevant to model features 20 0 eee ee
57. eeeeeee 18 Table 3 List of minimum set of input files required by ZOOMQ3D when rivers and VKD are not included in the model iz cseh testes ete iat pet sateen acti ati let ttc eMac e 19 Table 4 Hypothetical recharge rates mm day for ten stress periods ccscesseesseeseeeeeees 59 Table 5 Hypothetical recharge rates mm day for monthly stress periods 0000000 60 Table6 Format of zoomq3d da input file os ss cs csssceesassesagee saqateaacoceassteeqeds ciseededasdeanundespees 82 Table7 List of all ZOOMQ3D output files v ccccsiccvacsiesseacianscecasedeseatevavacateassdyeneaseseueedusseceens 83 Table 8 Data contained in nodal flow balance output file s ssnosssssessenssessseeesseeessseesseesseesse 88 Table9 Data contained in global_tv out sesseessssessesssesssesssserssseeesseesseessresseresseeesseesseesse 90 Table 10 Order of variables listed on line of flowbal txt eeeeseeeeeseseeesesresrieeresressseessee 94 viii PART 1 Discussion 1 Introduction Numerical groundwater flow models have become an essential tool in the solution of hydrogeological problems Their importance arises because they are the only real means by which testing of hypotheses can be conducted It is common to produce what is referred to as a conceptual model a description of the processes believed to be operating in the groundwater system However to assess the validity of the concepts it is essential to produce results from a more ph
58. en layers de water and re wet Another approach is to use a single layer but to allow hydraulic conductivity to vary within it That is to calculate transmissivity by integrating the hydraulic conductivity over the layer s saturated thickness as illustrated in Figure 41 This section describes the implementation of the same variation of hydraulic conductivity with depth YKD mechanism in the object oriented regional groundwater model ZOOMQ3D 68 11 1 IMPLEMENTATION OF VKD IN ZOOMQ3D The implementation of VKD in ZOOMQ3D is based on two principal concepts These are the definition of VKD profiles and VKD schemes These two terms are used to describe both the incorporation of the mechanism in the model code and the input of data to the model 11 1 1 VKD profiles A VKD profile describes the change in hydraulic conductivity with depth at a particular point in the aquifer An example VKD profile is shown in Figure 42 Currently VKD profiles represent the variation in hydraulic conductivity with elevation using a relatively simple method Profiles are defined by two sections In the lower section between Z op79 and Zp in Figure 42 hydraulic conductivity is constant In the upper section between Z and Zop hydraulic conductivity increases linearly with elevation Because different values of hydraulic conductivity can be specified in the two orthogonal horizontal directions x and y six values are required to parameterise an individual prof
59. ending on the conceptual model of the aquifer This feature is described in detail in Section 7 2 The parameter specified in the third of these three pairs of lines is used to specify whether the bottom elevations of model layers can be different from the top elevations of the layers beneath them If an n is entered in the input file the top elevations are read for the top model layer only The top elevations of each lower layer are made equal to the bottom elevation of the layer above it If a y is entered data files are read for both the bottom and top elevation of each model layer The facility to specify a gap between two numerical layers is implemented when for example a low permeability layer exists between two aquifers This feature is described in more detail in Section 7 2 1 7 1 2 Line 7 onwards of grids dat After the first six lines in grids dat data is specified defining the structure of the model mesh This data is generated by ZETUP and should not be adjusted by the user If the user wishes to modify the mesh structure the model should be uploaded into ZETUP and modified using this tool However it is worthwhile understanding the structure of this data The seventh and eight line of the input file are also a comment line and a data line The information specified here defines the number of grid levels in the model and the number of grids on each level There is only ever one grid on the first level as this
60. ent must be number 1 49 x ee Sy 1 ee E 5 e Pa e Le e Pa 2 4 oe 2 J e oe Ea 1 e Fa i J e 1 s j e 2 e ee bs 1 eee a Figure 26 10099 98 97 96 95 94 93 92 11 10 35 72 36 17 18 75 73 74 40 37 38 39 21 20 76 41 24 22 81 TI 42 23 80 79 78 43 33 32 31 30 29 28 26 27 87 85 86 83 84 49 48 57 47 45 46 44 89 88 56 55 71 54 70 53 69 52 68 51 67 50 66 65 58 64 59 60 61 62 63 b Numbering schemes in ZOOMQ3D for a river branches and b river nodes for an example model river Baseflow Interconnected gt River aquifer interaction river nodes P Me p ga Basefl a ad lt aseflow a gt P x _ BF Pa oP 2 S ff Baseflow n Upper most active finite difference node Figure 27 Schematic representation of connections between river and grid nodes sa As stated above rivers are represented by a series of linked river nodes which are also connected with upper most active aquifer node as illustrated in Figure 27 Each river node is located at the centre of the reach that it represents The limits of a reach are the midpoints between the central river node and its adjacent river nodes River nodes are characterised by the following set of parameters e Location specified by x and y co ordinates m e Width m e Reach length m Equivalent to the half the
61. ependent of groundwater head At unconfined nodes transmissivity is a function of saturated thickness and the storage term incorporates specific yield In the top model layer finite different nodes can be defined as being confined unconfined or convertible Convertible nodes switch between unconfined and confined behaviour when the groundwater head rises above its top elevation In each of the lower model layers all the nodes must be specified as being either confined or convertible Finite difference nodes dewater as the groundwater head drops below their base In this case the node is removed from the matrix of finite difference equations 4 1 4 Heterogeneity and anisotropy Models can be heterogeneous and anisotropic Different hydraulic parameter values can be specified at each finite difference node and hydraulic conductivity may be different in the x and y directions It is assumed that the Cartesian co ordinate system is aligned with the principal axes of the hydraulic conductivity tensor 4 1 5 Moving boundaries Model nodes can de water and re wet Nodes are made inactive when the groundwater level falls below their base and vice versa The re wetting of model nodes depends on the groundwater head in adjacent finite difference nodes 4 1 6 Variable hydraulic conductivity with depth VKD Vertical variations in hydraulic conductivity with depth can be specified within model layers or across model layers by defining VKD profiles The tran
62. er of block time periods of data For each block block no then 1 line of nSPs of flow rates m day for each node Comment line 1970 Block number 7602 6692 0 5879 3917 2739 3 1989 3 1637 6 2214 3221 4 5262 7 7107 1 Flow rate for each stress period for 1st node 30411 0 26768 0 23519 7 15668 1 10957 3 7957 3 6550 3 8857 12885 6 21050 9 28429 4 5 Flow rate for each stress period for 2nd node 1971 Repeated for each block 7602 8 6692 0 5879 3917 0 2739 3 1989 3 1637 6 2214 3221 5262 7 7107 2 Discharge rates in m day 30411 0 26768 0 23519 7 15668 1 10957 3 7957 3 6550 8857 12885 21050 28429 4 1972 Repeated for each block 7602 8 6692 0 5879 3917 0 2739 3 1989 3 1637 6 2214 3221 5262 7 7107 Discharge rates in m day 30411 0 26768 0 23519 7 15668 1 10957 3 7957 3 6550 8857 12885 21050 28429 4 1973 Repeated for each block 7602 8 6692 0 5879 3917 0 2739 3 1989 3 1637 6 2214 3221 5262 7 7107 Discharge rates in m day 30411 0 26768 0 23519 7 15668 1 10957 3 7957 3 6550 8857 12885 21050 28429 4 1974 Repeated for each block 7602 6692 0 5879 9 3917 0 2739 3 1989 3 1637 6 2214 3221 4 5262 7 7107 AE Discharge rates in m day 30411 26768 0 23519 7 15668 1 10957 3 7957 3 6550 3 8857 12885 21050 9 28429 4 etc for each time block Figure 32 Format of input file river_inputs dat 58 10 Model stresses 10 1 RECHARGE The specification of recharge is perhaps the most complex of task
63. es Such mechanisms require that the top and bottom elevations of the layers be defined explicitly The equations used to calculate the vertical conductance between two nodes are presented in Figure 18 which also shows the two different representations of hydrogeological layers possible within the model The first illustrates the case where two nodes either fall within a single hydrogeological unit or are located at the midpoints of two vertically adjacent hydrogeological units The second case illustrates the inclusion of a semi permeable hydrogeological layer in the model without its explicit representation by a layer of finite difference nodes The input files used to specify vertical conductance within the model are described in Section 7 5 5 Kz O AZ Vertical 7 1 Conductance AZ 2 N AZ 2 K K Kz O AZ ZI Z2 a Vertical 7 1 Conductance AZ 2 _ AZ _ AZ 2 Kz K Ky Kz fe AZ b Figure 18 Calculation of the vertical conductance between layers 33 7 4 1 Layer bottom elevations The elevation of the bottom of each node within each layer must be specified using either 1 pairs of map and code files with the names zbase map and zbase cod or 2 numeric data files with the names zbase dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the botto
64. esdecesseseeveadesses 44 9 1 Model edge boundary conditions 30 Goo hG ais ea eee aes Ae es 44 9 27 Internal fixed headS morenen gated wie a daa ty gtelam age E NAR 44 9 3 Head dependent leakage nodes cs ccasc cates ascsasteccacteat sacsatesaaceteassaacontaausasalesseasseoeeuniees 45 QA SPANS Stn Pe elaine a a a ec Deluna tas sa lsd ada eal oa inode ad aes Maan ose 47 OES URIV ELS sca E AET EE seis uate teben io AE E EEE NEEE A eteehnas 49 10 M del Stresses cisccccussescetends cicesthcsectancac cceenestacantetaccstedceetancel scceensecaetbde esesten eo esseni oes oseese 59 TOA ARGC AG Gop a a a a a n a deneetates 59 10 2 Abstraction and observation wells ssssesesssesssesessseesseeesseesseesseeesseeesseessesseesseeesseee 65 11 Variable hydraulic conductivity with depth VKD esssesssessssesssccssocesocesoosesocessecssooesoseeo 68 11 1 Implementation of VKD in ZOOMQ3D sseesessesssseesssseesresseserssresseserssressessrssressesseesees 69 11 2 WIRD Soul TUES ossur a a a E En 12 12 The solution process ssscoesssoocsesooecesooccessscoesssoosessoocessssecesosocssssocesssooeessosecsssssossssoossssosessse 76 12 1 Successive over relaxation solution method sssssssessesssesssesesseresseeesseessresseesseeesseee 76 13 Activating de activating nodes sesssocescoesccocssocsssecssocesocescosesocesoccssocesocescosesocsssesssocesocsso 78 13 1 De waterng and re wettin garsi ros aa E aAa o eae 78 13 2 De a tiv
65. fic storage L Z is the elevation of the top of the node Z is the elevation of the base of the node Convertible nodes The transmissivity and storage of a convertible node is equivalent to that of a confined node if the groundwater head is above the top of the node However the transmissivity and confined storage coefficient depend on the groundwater head when it falls below the top of the node Convertible nodes then calculate transmissivity and elastic storage based on the difference between the groundwater head and the elevation of their base These are linear relationships as the horizontal hydraulic conductivity and specific storage are assumed to be uniform in the vertical direction When the groundwater head falls below the top of a convertible node releases of storage from the free surface i e specific yield contribute to the total storage The expressions used to calculate transmissivity are T K z z for h 2 zy T K h z for h lt Zy T 0 for h lt Z The expressions used to calculate total storage are S S z zp for h 2 z S S h z S for h lt Z S 0 for h lt Z where S is the specific yield 24 Unconfined nodes At unconfined nodes transmissivity and elastic storage depend on groundwater head The storage term also contains the component of specific yield The top elevation of the node is ignored and consequently there is no upper limit on the transmissivity or confined storage The ex
66. ft 400 400 Top right 600 600 abcde abcde abcde abcde abcde Map for grid Bottom left 150 150 Top right 250 250 aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa Figure 15 Example map file for the entry of spatial data within a layer Each letter in the array represents a value of a parameter that is specified in the corresponding code file i e the file with the same name but with the cod extension Code files have the same structure as map files except each of the character arrays is replaced by a set of data defining the values of the letters contained within the array The code file which corresponds to this example model and map file is shown in Figure 16 Similarly to the map file the code file contains four sets of data separated by comment lines The comment lines contain the information required to identify to which grid each data set relates Again ZETUP the set up program for ZOOMQ3D produces this file and writes the co ordinates of the bottom left and top right hand corners of the mesh within the comment lines Consequently the user need only adjust the parameter values for each grid In Figure 15 eight letters are used in the base grid so eight parameter values must be defined in the code file for this grid On the second grid listed in the map file only two zones are defined by the letters a and b and conseque
67. full range of Survey publications is available from the BGS Sales Desks at Nottingham Edinburgh and London see contact details below or shop online at www geologyshop com The London Information Office also maintains a reference collection of BGS publications including maps for consultation The Survey publishes an annual catalogue of its maps and other publications this catalogue is available from any of the BGS Sales Desks The British Geological Survey carries out the geological survey of Great Britain and Northern Ireland the latter as an agency service for the government of Northern Ireland and of the surrounding continental shelf as well as its basic research projects It also undertakes programmes of British technical aid in geology in developing countries as arranged by the Department for International Development and other agencies The British Geological Survey is a component body of the Natural Environment Research Council British Geological Survey offices Keyworth Nottingham NG12 5GG T 0115 936 3241 Fax 0115 936 3488 e mail sales bgs ac uk www bgs ac uk Shop online at www geologyshop com Murchison House West Mains Road Edinburgh EH9 3LA 0131 667 1000 Fax 0131 668 2683 e mail scotsales bgs ac uk London Information Office at the Natural History Museum Earth Galleries Exhibition Road South Kensington London SW7 2DE 020 7589 4090 020 7942 5344 45 Fax 020 7584 8270 email bgslondon bgs a
68. gration limits are constant z and z2 are independent of x This implies that the layer boundaries are horizontal The second is that S does not change over the layer thickness The second limitation is generally unimportant but the first is of considerable significance since layered models are frequently applied to aquifers where the structure is not one of horizontal layering The final integral dealing with the first term on the left hand side is also complex The function f is replaced by pZ x obtained if the layer boundaries are horizontal Further the value of k must be constant with the result that the transmissivity is evaluated as k z z2 and not the more general integral form This is a particularly important limitation when a model based on the quasi three dimensional equation is used to treat aquifers where hydraulic conductivity varies with depth within a layer Again the quasi three dimensional result can only be The previous discussion applies to layers where there is no free surface The uppermost layer in an unconfined aquifer will contain a free surface and requires further consideration In a quasi three dimensional formulation of a layer open to the atmosphere the usual treatment is to define a transmissivity value calculated based on the current saturated thickness of the upper layer The groundwater head value which characterises the layer is based on the value at the free surface not the average within the sa
69. h h h h where day is the end of the day when the flow was recorded stress period is the stress period number block is the time block number of the flow measurement MJD_time is the time simulated from the start time in Modified Julian day format time elapsed is the time simulated since the beginning of the model run days h is the head m in the first observation well defined in obswells dat h is the head m in the second observation well defined in obswells dat h is the head m in the n observation well defined in obswell dat The output file is space delimited and is easily opened using spreadsheet software which can be used to produce groundwater head hydrographs 16 2 CONTOURING GROUNDWATER HEADS The computed groundwater heads are written to an output file in a format suitable for contouring The name of the output file is specified in the input file zoomq3d dat This output file for example contour txt contains groundwater head data for a single time step only and is over written periodically during the simulation The frequency with which the file is produced is defined in the input file clock dat It is created after either every time step stress period or block or only for the final time step in the simulation Each time it is written the previous data set is lost However groundwater head data in this format can be saved by specifying the times of interest in the input file
70. h and days for the unit of time This has required slight modifications to be made to the format of the three input files i the abstraction file Section 10 2 ii the main recharge input file Section 10 1 3 and iii the numeric recharge rate file Section 10 1 2 e The rate of leakage between a river node and an aquifer node has been adjusted to better represent river aquifer interaction under perched conditions The head that drives leakage into the aquifer is now equivalent to the difference between the river stage and the base of the river bed Refer to Section 9 5 2 e All output files containing columns of data have been made space delimited Preface to the third edition The production of this third edition of the ZOOMQ3D manual coincides with the release of version 1 03 of the groundwater modelling code This manual did not need to be updated when version 1 02 was released Version 1 03 of the model incorporates only some minor adjustments to the code The changes that have been made are described in the following bulleted list To enable version 1 03 to run models developed using version 1 02 one data file needs to be modified This the clock file Section 10 2 DIFFERENCES BETWEEN VERSION 1 01 AND 1 03 OF ZOOMQ3D e A bug has been fixed to correct the calculation of transmissivity in the upper layer of unconfined aquifers In version 1 01 the transmissivity was limited by the top of the upper layer which was incorrect The to
71. h information is output The second line contains the headings for the following columns of data Each subsequent line represents one node in the model A description of each column is given in Table 8 The file is space delimited and is readily opened using spreadsheet software for manipulation Table 8 Data contained in nodal flow balance output file Column Description of data of file Rates of flow are for the last time step only Layer of the node x co ordinate of the node y co ordinate of the node Area of the node m Inflow to the node in the x direction from the left m day Outflow from the node in the x direction to the right m day Inflow to the node in the y direction from below m day 1 2 3 4 5 Flow imbalance at the node m day 6 7 8 9 Outflow from the node in the y direction to above m day Inflow to the node in the z direction through the base m day Outflow from the node in the z direction through the top m day Specified inflow at the boundary if a boundary node m day Rate of change of storage at node m day Positive values are increases in storage Recharge applied at the node m day Rate of leakage between the aquifer and the river m day Positive values represent influent river nodes Rate of leakage to a leakage node m day Positive values represent an outflow from the aquifer Rate of abstraction at the node m day Abstrac
72. he grids contained in the model These characters define zones across the model mesh at which a particular value of a parameter is specified The values of the parameters are specified in the corresponding file with the cod extension A maximum of fifty two zones can be used to define the spatial distribution of model parameters when using this method The name of each of these pairs of files is suffixed with a two digit number that represents the model layer that the data applies to For example the pair of files hydcond0O1 map and hydcond01 cod would be used to specify the spatial distribution of hydraulic conductivity in layer 01 the upper model layer In method 2 a single ASCII text file is required for each model layer with the dat file extension Each of these files contains a single array or multiple arrays of numeric data with each array representing one of the grids contained in the model These numbers specify the value of a specific parameter at each finite difference node within the model directly The name of each of these files is suffixed with a two digit number that represents the model layer that the data applies to For example the file hydcond03 dat would be used to specify the spatial distribution of hydraulic conductivity in layer 03 i e two layers below the top layer of finite difference nodes 7 3 1 Selection of spatial data entry method Either of the methods described above can be used to assign values fo
73. he known starting values for the next time step To illustrate the structure of the finite difference equations a typical node will be considered Figure 1 This node will be referred to as the central node and the groundwater head there will be denoted by he at the beginning of a time step and he at the end of the step In the plane of the layer containing the node there are usually four surrounding nodes Two are located at a distance Ax ahead of and behind the central node in the x direction These will be referred to as nodes 1 and 3 with groundwater heads h and h3 respectively There are similar nodes spaced at Ay in the y direction denoted as 2 and 4 with groundwater heads hz and hg In the layers above and below that under consideration nodes are located immediately above the central node These are referred to as a and b and the corresponding head values are ha and h The vertical separation is Az Only the head values at the end of the time step are required for the non central nodes in an implicit calculation Figure 1 Node numbering in the finite difference stencil The aquifer flow properties between the nodes form part of the governing equation and the storage and external source terms at each node also arise The relevant parameters are the x and y direction transmissivities T and 7 and the vertical hydraulic conductivities operating between the central node and nodes a and b above and below ka and kp These values are der
74. he model can easily be modified to incorporate such VKD profiles 70 Scheme 1 Scheme 2 Scheme 3 Scheme 4 Layer Profile Layer Profile Layer Profile Layer Profile Number 1 profile Level Number 4 profiles Level Number 2 profiles Level Number 2 profiles Level 1 f 1 f 1 1 j 1 f J A 7 Uy 2 1 2 Uf 2 2 r 1 2 p Yj Yj Uf 3 Y 3 Yj 3 3 F 3 i jj 7 j jf 2 4 Yj 4 Y 4 4 Uj 2 4 Yj Scheme 5 Scheme 6 Scheme 7 Scheme 8 Layer Profile Layer Profile Layer Profile Layer Profile Number 2 profiles Level Number 1 profile Level Number 2 profiles Level Number 0 profiles Level gt 1 A 1 1 1 1 A 2 2 2 1 2 YY 3 3 yj 3 3 Yu yj 1 J YP pA 4 A 2 4 FA 4 A 2 4 Figure 43 Specification of VKD schemes in ZOOMQ3D 71 11 2 VKD INPUT FILES 11 2 1 VKD scheme data files Input data to the model can be separated into two categories First information must be read to define the number and types of schemes in the model Second data must be entered to define the VKD profiles at each horizontal nodal location of the model mesh Two text input files are required to enter VKD scheme information into the model vkd cod and vkd map The first of these ASCII text files vkd cod contains the following lines of data NS 1 1 2 2 NP NP NP Top lior Top Jpop senene Ti Iior 1 1 2 2 NP NP NP For hor Eog Lorie wets Ls Lace 1 1 2 2 NPys
75. he node where the greatest change in groundwater head occurred during the last iteration When the numerical solver converges to the solution for a time step the global flow imbalance is also written to the output file 16 14 VARIATION IN TRANSMISSIVITY As described in Section 7 2 2 unconfined conditions are simulated by repeating the solution for a time step in a cyclical process At the beginning of each cycle transmissivity is calculated by integrating the hydraulic conductivity over the saturated thickness of the finite difference nodes The cyclical process ceases when either the change in transmissivity between cycles is below a user defined value or after the maximum number of cycles has been performed The variation in transmissivity m day over a cycle is written to the output file transcycle out to that the user can examine the progress of the process An example transcycle out file is shown in Figure 57 Change in transmissivity for each cycle 4 Month 1 Year 1970 le 1 Max T Change 1 25901 le 2 Max T Change 0 502317 Change in transmissivity for each cycle 10 Month ear 1970 le T nge 2 11305 le T nge 1 04613 T nge 0 518062 etc for each time step Figure 57 Example transcycle out output file 16 15 OUTPUT FILES REQUIRED FOR PARTICLE TRACKING Two space delimited ASCII text output files are produced by the model if the user specifies that particle tracking si
76. id 2 number of rows and columns as this grid etc for each stress period and for each grid within each stress period Figure 37 Format of numeric recharge data file This file format results in recharge rates being defined more than once at particular finite difference nodes when the model mesh is locally refined This occurs at those nodes on a 62 refined grid that are coincident with the nodes on a coarser grid Where this occurs the data defined on the refined grid will always override that defined on the coarse mesh Some points on a grid may be located outside the model boundary however a recharge rate value must be entered in all elements of the rectangular array or matrix of grid points The values corresponding to nodes located outside the model boundary are read but then ignored The ZOOM family recharge model ZOODRM Mansour and Hughes 2004 creates a recharge file in this format 10 1 3 The main recharge data file The name of the main recharge input file is specified by the user in the input file zoomq3d dat This file for example recharge dat contains the time series of recharge rates relating to each recharge type and the names of the associated map and code files The user also specifies if a numeric data file is being used and if so its name In summary the file is used to specify e if recharge types are used to specify recharge i e if map and code files are used e how many recharge type
77. ile 1 The elevation of the base of the profile Zorro 2 The elevation of the top of the profile Zrop 3 The elevation of the point of inflection Z 4 The hydraulic conductivity in the x direction K below Z 5 The hydraulic conductivity in the y direction K below Z 6 The gradient of the profile above Z VKDGrad This is equal to the increase in hydraulic conductivity per metre rise in elevation The value of the VKDGrad parameter may be either negative zero or positive Consequently in addition to an increase in hydraulic conductivity with depth above Z hydraulic conductivity can be specified to decrease or remain constant VKDGrad is given by dK VKDGrad ne dee ora dZ dZ To calculate transmissivity the following equations are used T Kt h Zorrom 0 5 VKDGrad h Z T K h Zyorrom 0 5 VKDGrad h Z Y for h gt Z and T K h Zsorrom T Ky h Zrorrom for h lt Zp where h is the water table elevation 69 Z TOP groundwater head h jy UY Tx Kx h Zgortom Yi 0 5 VKDGrad h Zp 1 Uj BOTTOM a Kx Hydraulic conductivity Kx x Figure 42 Parameters used to define VKD profiles in ZOOMQ3D 11 1 2 VKD schemes A VKD scheme defines the number of VKD profiles in the vertical at a horizontal point and the number of model layers that each profile in the scheme crosses That is a scheme simply stores how VKD profiles are arranged in the
78. in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 7 5 5 Vertical conductance The representation of layers in the model and the implementation of a vertical conductance term is described in Section 7 4 Vertical conductance is used to enable the inclusion of low 36 permeability layers between aquifers in which flow is assumed to be predominantly vertical without having to incorporate additional numerical layers of finite difference nodes Input file names and format The vertical conductance between finite difference nodes in adjacent layers must be entered into the model using either 1 pairs of map and code files with the names vcond map and vcond cod or 2 numeric data files with the names vcond dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and layer numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 37 8 Time discretisation and initial conditions 8 1 TIME DISCRETISATION Simulation time is
79. in order to remove nodes from the grid To remove nodes from the grid a lower case o is entered into the character array In the example shown in Figure 53 nodes are removed in the upper left hand corner of the mesh These nodes become no flow nodes Map for grid on level 1 Bottom left 0 0 Top right 10000 10000 oo0000000aaa oooooooaaaa ooooooaaaaa oooooaaaaaa oooaaaaaaaa ooaaaaaaaaa aaaaaaaaaaa aaaaaaaaaaa aaaaaaaaaaa aaaaaaaaaaa aaaaaaaaaaa Figure 53 Example nowflow map file 80 14 Additional model input files 14 1 SAVING GROUNDWATER HEADS FOR CONTOURING Groundwater heads are only written to an output file for all time steps of a simulation at all model nodes if the user specifies that the files required for particle tracking are to be generated in clock dat Generally the particle tracking files should only be produced if the particle tracking model is to be run subsequently A more efficient method of saving simulated groundwater heads for contouring is through the use of the input file contour_times dat This file is used to specify when during the simulation groundwater heads contours need be produced Using this approach less information is written to disk during the simulation which reduces model run times An example contour_times dat input file is shown in Figure 54 The first and third lines are comment lines or text strings The integer on the second line specifie
80. ined using one of three methods which all require the user to specify the number of time steps in the stress periods 1 The user explicitly specifies the time at the end of each time step as a percentage of the stress period length 2 The user specifies the ratio of the length of each time step to that of the preceding time step The model calculates the length of the first time step within a stress period 3 The user explicitly specifies the time at the end of each time step within stress periods 38 If the second method is implemented then the length of the time steps are calculated using the following expressions At x 1 At eee 1 a At ax At where At is the length of the i time step At is the length of the stress period a is the time step length multiplier n is the number of time steps in each stress period 8 1 1 Input file format The discretisation of time is specified using an input file with the structure shown in Figure 21 The name of this file is fixed and must be clock dat The file defines the discretisation of time in the model the frequency of some model output whether the simulation is a steady state or time variant run whether the model is being re run using a condition simulated in a previous model run and whether flow and head information is output to enable subsequent particle tracking simulations to be performed The input file contains comment lines which describe the data on sub
81. ion of the aquifer s hydraulic properties and in particular the representation of the variation of hydraulic conductivity For example modelling of Chalk aquifers has shown that it can be difficult to simulate river aquifer interaction spring flow and the response of groundwater heads to recharge correctly if the vertical variation of hydraulic conductivity is not represented properly Typically Chalk aquifers are highly permeable low storage systems which respond quickly to recharge The majority of groundwater flow occurs in the upper part of Chalk aquifers and hydraulic conductivity generally increases towards river valleys and decreases with depth A particular feature of Chalk catchments is that the head of ephemeral streams can move several kilometres seasonally because of the relationship between discharge groundwater head and hydraulic conductivity Transmissvity m day 0 200 400 600 800 1000 1200 1400 1600 1800 0 i i i 1 1 1 1 i i 20 4 40 Depth m 60 4 80 Hydraulic conductivity Transmissivity 100 o fi EEN E ay 20 40 60 80 Hydraulic conductivity m day Figure 41 Hypothetical hydraulic conductivity transmissivity versus depth profile The variation in hydraulic conductivity with depth can be incorporated in a groundwater model with the use of multiple layers However this can cause numerical difficulties wh
82. ions A mechanism is implemented to re wet nodes when groundwater levels rise again The mechanism is based on the examination of the groundwater head at the neighbouring nodes of the inactive node Two options are defined Either the horizontally adjacent nodes can be examined or the node in the layer beneath can be interrogated to determine if the de watered node should be reactivated Three parameters are defined to allow the re wetting of nodes each of which is described in the following three sub sections These parameters are 1 a wetting flag 2 a wetting threshold and 3 a post wetting head value 13 1 1 Wetting flag The wetting flag is a character variable which is either an h or a v If it is an h horizontal then the inactive node s neighbours on the same layer are examined to determine if their head has risen above the wetting threshold If it is a v vertical then the inactive node s neighbour in the layer below is examined to determine if its head has risen above the wetting threshold In the bottom model layer only an h can be defined Each node in the model must be assigned a wetting flag This is performed using the following inputs files Input file names and format The wetting flag is defined using a map file with the name wetflag map for each model layer The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer
83. is no penalty for using updated values as soon as they are calculated the Gauss Seidel method is almost always preferable To further develop the iteration formula the equation representing Gauss Seidel iteration is written in a more compact form All the terms with the exception of h are moved to the right hand side and incorporated into a single term R Then the value for h from the last iteration is added and subtracted giving n R h where the superfixes denote iteration number This does not alter the Gauss Seidel relationship instead it allows a useful interpretation to be made of the iteration formula The term in brackets gives a measure of the change which has been introduced over a single iteration If this moves the new value closer to the true solution then it can be argued that a larger change would speed convergence Within certain limits this is the case and SOR aims to exploit this fact A larger change is imposed by increasing the change by a factor which is larger than one If too big a change is imposed then the scheme becomes unstable An upper limit on of 2 avoids this difficulty It is the fact that a larger change than that defined by Gauss Seidel is applied which gives the process its name of over relaxation When is introduced the relationship is no longer an equality instead it provides a rule by which new iterations are defined It is usually expressed in the following form h R 1 a
84. it recharge Assume that a conceptual model has been developed in which recharge over the western 2 km is considered to occur at a low but constant rate but in the east where there is no superficial cover recharge is higher and seasonally varying Also assume a one year period is to be simulated for which recharge rates have been defined on a monthly basis for both the covered and uncovered areas of the aquifer These are listed in Table 5 The one year simulation period is split into twelve stress periods Table 5 Hypothetical recharge rates mm day for monthly stress periods Stress period Covered interfluve area Valley Constant rate low recharge Seasonal high recharge Yy M M M M M v v v y y y y y Y Superficial deposits Aquifer West East 2 km gt lt 1 km gt Figure 34 Example aquifer modelled using two recharge types 250 m square mesh West q Uncovered aquifer nodes Figure 35 Example model mesh used to simulate aquifer shown in Figure 34 60 The model mesh used to simulate this system is shown in Figure 35 The model is 3 km long in the west east direction and 500 m wide in the south north direction In the horizontal the grid is composed of a regular 250 m square mesh resulting in 39 nodes The fifteen nodes closest to the eastern boundary represent the part of the aquifer not covered by superficial deposits There is only one layer in the mo
85. ived from nodal hydraulic conductivities in the principal directions the layer thicknesses and the saturated depth of any unconfined layer which may be present Details of the relationships are not given here The structure of the finite difference approximations in the x and y directions are similar in form and so only the x direction term is examined in detail here The vertical leakage approximations also have a similar structure and only the term relating to flow between the central node and the layer above is quoted For flow through the aquifer in the x direction the following approximation holds 7 2 gp in care Ox Ox Ax i The second suffix on the transmissivity values indicates the appropriate part of the aquifer For example T is the transmissivity between the central node and node 1 For vertical leakage between the central and upper node oh k k x h h above z Oz Az a lt a For the rate of change of storage at the node ea sh h Ot At When all the terms are approximated the resulting equation has the following structure Ah A h Ah A h Ah A Ah Ah F where 4 7 gt 4 amp Ay Eo Wie Ay k k S A A gt A 3 F q Az Az At and A A A A A A4 4 A At the beginning of a time step values for all the A coefficients can be evaluated from the aquifer properties the mesh geometry and a knowledge of recharge an
86. k out 16 10 springs out 16 11 Rivers gauging _stations out accretion out riverflow out 16 4 16 6 Water balances 1 Global water balances 2 Nodal flow balances global out global_tv out flowbal out 16 9 16 8 De watering and re wetting dewatering out 16 7 Multi aquifer wells multi_wells out 16 12 Progress of solution zoomgq3d out transcycle out 16 13 16 14 heads txt flowbal txt 16 15 Output for particle tracking 15 2 PROCESSING MODEL OUTPUT Model output is readily processed and visualised using spreadsheet software Surfer Golden Software Inc 1994 and a text editor Because each model file contains only one type of data the user is not required to extract information from many different locations within a single file All text files are space delimited 83 16 Description of output file formats The format of each of the files listed in Table 7 is described in detail in the following sub sections 16 1 OBSERVATION WELL DATA The nodes at which groundwater head is monitored over time are specified in the input file named in the file zoomq3d dat for example obswells dat The time versus groundwater head record at these nodes is output to the file also named in zoomq3d dat for example obswells out This output file contains one line of data for each time step of the simulation with the following format day stress period block MJD time time_elapsed h
87. kal Survey NATURAL ENVIRONMENT RESEARCH COUNCIL User s manual for the groundwater flow model ZOOMQ3D Groundwater Systems amp Water Quality Programme Internal Report IR 04 140 BRITISH GEOLOGICAL SURVEY GROUNDWATER SYSTEMS amp WATER QUALITY PROGRAMME INTERNAL REPORT IR 04 140 User s manual for the groundwater flow model ZOOMQ3D C R Jackson and A E F Spink The National Grid and other Ordnance Survey data are used with the permission of the Controller of Her Majesty s Stationery Office Ordnance Survey licence number Licence No 100017897 2004 Keywords Groundwater flow model ZOOMQ3D Bibliographical reference C R JACKSON AND A E F SPINK 2004 User s manual for the groundwater flow model ZOOMQ3D British Geological Survey Internal Report TR 04 140 94pp Copyright in materials derived from the British Geological Survey s work is owned by the Natural Environment Research Council NERC and or the authority that commissioned the work You may not copy or adapt this publication without first obtaining permission Contact the BGS Intellectual Property Rights Section British Geological Survey Keyworth e mail ipr bgs ac uk You may quote extracts of a reasonable length without prior permission provided a full acknowledgement is given of the source of the extract NERC 2004 All rights reserved Keyworth Nottingham British Geological Survey 2004 BRITISH GEOLOGICAL SURVEY The
88. l be applied during the simulation Each node located on the boundary of the model is listed in this file which consists of multiple lines of text with the following format x y BC BCV BC BCV BC BCV scious BC BCV where x is the x co ordinate of the boundary node y is the y co ordinate of the boundary node BC is a character flag It is set to s to indicate that the boundary node is a specified inflow node and to f to specify a fixed head node BCV is either the inflow rate m day or the fixed head value m i represents the model layer number i 1 to the number of model layers The nodes are listed in the file in an order defined by a clockwise movement around the boundary A termination line must be included at the end of the file which contains two numbers whose values are negative one that is 1 0 1 0 9 2 INTERNAL FIXED HEADS Fixed head nodes inside of the model boundary are defined in a file with the following structure The name of this file is specified by the user in the input file zoomq3d dat The file has the format n layer x y h one line for each of the n nodes where n is the number of fixed head nodes specified in the file layer is the number of the model layer x is the x co ordinate of the fixed head y is the y co ordinate of the fixed head h is the elevation of the fixed head m If nodes are specified in this file that duplicate those in boundary dat then they wi
89. le change in transmissivity and the maximum number of cycles are defined by the user on the second line of the input file relating to the solver for example sor dat see Section 12 If the user specifies only one cycle then the solution for each time step will be calculated only once with transmissivity being recalculated at its start 26 Previous time step Calculate T based on current heads Solve finite difference equations Current time step Calculate T based on new heads Set T as average of old and new values Calculate maximum difference between old and new T values across all nodes Maximum difference lt limit Next time step Figure 12 Flow chart of the cyclical transmissivity updating process when simulating unconfined aquifers 27 7 3 FILE FORMATS FOR INPUTTING SPATIAL DATA Spatial information can be entered into the model using two different methods or sets of input files These methods employ either 1 map and code input files or 2 numeric input data files In method 1 a pair of ASCII text files is required for each model layer with the file extensions map and cod A map file contains a single array or multiple arrays if grid refinement is incorporated of characters in the range a b y z A B Y Z to define zones of different parameter values That is the range is composed of the lower case alphabet followed by the upper case alphabet Each array represents one of t
90. lines The grids are scanned sequentially by row Data are output for the nodes in the top row furthest in the positive y direction first and bottom row furthest in the negative y direction last Within each row nodes are scanned from left to right in the positive x direction Data for a node within a subgrid is only output to the file if it does not also exist on a grid at a coarser grid level i e if it is not located on a parent grid line Because the data is not structured in grid arrays dummy flow values relating to nodes outside the model boundary are not written to the file Table 10 shows the flow components that are listed within each line of nodal data The first parameter output is an integer flag which specifies if the node was active during the time step i e if it was wet 1 or dry 0 If the node was dry a zero is written on the line for the node but its flow components are not Flow data is only output if the node was active wet during the time step Table 10 Order of variables listed on line of flowbal txt Flow component 1 2 3 4 5 6 7 8 9 e e e e AA U N e O Active inactive integer flag Inflow from left x direction Outflow to right x direction Inflow from below y direction Outflow above y direction Inflow from base z direction Outflow through top z direction Specified inflow to node if boundary Increase in storage Recharge River leakage Leakage Pumping Spring flow
91. ll be ignored The conditions specified in boundary dat take precedence over those specified in this input file 44 9 3 HEAD DEPENDENT LEAKAGE NODES In addition to the inclusion of rivers in the model which are described in Section 9 5 a second head dependent leakage mechanism is incorporated in the model This can be used to simulate leaky aquifer layers or surface water bodies such as lakes or estuaries The conceptualisation of leakage nodes is similar to that of individual river nodes where inflow to or outflow from the aquifer is defined as a function of the difference between the elevation of the leakage node and the groundwater head The rate of transfer of water between a grid node and a leakage node is expressed by Q z C A h z where _Q is the leakage rate m day C is vertical conductance day A is the area of the grid node m hais the head in the aquifer m and Zz is the elevation of the leakage m The vertical conductance of the leakage nodes C is conceptualised as being equivalent to the vertical hydraulic conductivity of the material separating the aquifer from the leakage node divided by its thickness Two values of the vertical conductance term must be defined one when the leakage node is effluent or when water flows out of the aquifer and one when it is influent This is useful for example when modelling a spring for which one method would be to set the vertical conductance to
92. m day Positive values are increases in storage Total spring flow m day Global flow imbalance m day 16 10 MONITORING LEAKAGES The leakage nodes at which the flow is monitored over time are specified in the input file named in the file zoomq3d da for example obsleak dat The time discharge record at these nodes is output to the file also named in zoomq3d dat for example obsleak out This output file contains one line of data for each time step of the simulation with the following format day stress period block MJD time time_elapsed Q Q Q Q Q where day is the end of the day when the flow was recorded stress period is the stress period number block is the time block number of the flow measurement MJD_time is the time simulated from the start time in Modified Julian day format time_elapsed is the time simulated since the beginning of the model run days Q is the flow m day through the first leakage node defined in obsleak dat Q is the flow m day through the second leakage node defined in obsleak dat Q is the flow m day through the n leakage node defined in obsleak dat The leakage nodes are listed in the same order as they are defined in the input file The flow rates Q are positive when flow is out of the aquifer and negative when flow is into the aquifer The output file is space delimited and is easily opened using spreadsheet softwar
93. m of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 7 4 2 Layer top elevations Layer top elevations must be explicitly defined for either the top layer only or for all model layers The user selects which of these options applies by adjusting the character flag on line 6 of the input file grids dat The section of this input file containing this flag is shown in Figure 19 Figure 19 Lines 5 and 6 of input file grids dat The character variable on line 6 of grids dat is used to specify whether the bottom elevations of model layers can be different from the top elevations of the layers beneath them If an n is defined the top elevations are read for the top model layer only layer 01 In this case only the pair of input files ztopOl1 map and ztopOl cod or only the single input file ztop01 dat needs to be created The top elevations of each lower layer are then made equal to the bottom elevation of the layer above it If a y is entered on line 6 of grids dat data files containing the layer top elevations are required for each of the model layers In this case the elevation of the top of each node within each layer mu
94. model For example in Figure 14 the model mesh is composed of four grids the coarsest base grid two child grids on grid level 2 and one grandchild grid on grid level 3 Consequently four character arrays are required in each of the map files for this example model These are listed in grid level order and are separated by a comment line Grid level 1 Base grid 8 columns by 8 rows Grid level 2 5 columns by 5 rows Grid level 2 9x9 Grid level 3 9x9 a b Figure 14 a Example mesh composed of four grids and b representation of the grid hierarchy 29 The structure of the map file for this example model is shown in Figure 15 As described above this contains four character arrays separated by comment lines The comment lines contain information required to identify to which grid each array relates ZETUP the set up program for ZOOMQ3D produces this file and writes the co ordinates of the bottom left and top right hand corners of the mesh within the comment lines Consequently the user need only adjust the letters in the arrays in order to modify the model s parameter values Map for grid Bottom left rights 7007700 o o aaaaaaaa bbbbbbbb eccccccce dddddddd eeececes ffffffff Map for grid Bottom left 100 100 Top right 300 300 bbbbb bbbbb bbbbb bbbbbbbb bbbbbbbbb aaaaaaaaa aaaaaaaaa aaaaaaaaa aaaaaaaaa Map for grid Bottom le
95. most node in branch m Baseflow m day Groundwater head m River stage m SOOO a ONE OU dee Go S River bed elevation m River bed vertical hydraulic conductivity under effluent conditions m day River bed vertical hydraulic conductivity under influent conditions m day 16 6 RIVER BASEFLOWS IN A FORMAT TO RE START A SIMULATION River baseflows are written to an output file in a format that enables a model run to be re started from conditions modelled during the current simulation The name of this output file for example riverflow out is specified in the input file zoomq3d dat It contains the river baseflow at each node each river in the model at the end of a single time step and is over written periodically during the simulation The frequency with which the file is produced is defined in clock dat It is created after either every time step stress period or block or only for the final time step in the simulation Each time it is written the previous data set is lost The file has exactly the same format as the input file described in Section 9 5 3 which is used to define initial river baseflow conditions Consequently in order to use this output file to re start a simulation it is only necessary to rename it appropriately 86 Branch downstream Bed Elevation Kz Effluent Kz Influent 1 294500 572500 0 295000 572500 500 295500 572500 1000 6 296000 5720
96. mulations are to be performed after running the flow model These are named heads txt and flowbal txt The first contains simulated groundwater head values for each model node for each time step of the simulation The second contains the flow rates m day into and out of each node for each time step during the simulation The user specifies if these files are to be produced on the last line of the clock dat input file see Section 8 1 92 16 15 1 Heads are written to this file for each model node at the end of each time step of the simulation The heads are written in the following order Output file heads txt 1 For each time step of the simulation 2 For each layer in the model Starting with the top layer layer 1 3 For each model grid in the layer Listed in the same order as they are in grids dat The base grid is the first grid listed Grids are then listed in grid level order see Section 7 Heads are output as an array representing each grid The format of this file is illustrated in Figure 58 Some points on a grid may be located outside the model boundary however a groundwater head value is written for all elements of the rectangular array or matrix of grid points For the nodes outside the model boundary a dummy head value of 999 0 is output This head value is also output at those nodes that have de watered during the time step Time step 1 Layer 1 Base grid array
97. nconfined to confined conditions for example where the aquifer dips below a confining unit Map files are described in detail in the next section and consequently only a simple example of the file format is presented here Map for grid on level 1 Bottom left 0 0 Top right 10000 10000 uuuuvvveccc uuuuvvveccc uuuuvvveccc uuuuvvveccc uuuuvvveccce UUUUVVVCCCC UUUUVVVCCCC UUUUVVVCCCC UUUUVVVCCCC UUUUVVVCCCC UUUUVVVCCCC Figure 10 Example aquifer map file for defining aquifer conditions in the top model layer 25 The type of aquifer conditions operating in the lower layers is defined on line 4 of the input file grids dat Each layer including the top layer is defined as either confined c or convertible v on this line The character relating to the top layer is read but ignored as this information is specified in more detail in the input file aquifer map All nodes in lower layers are defined as either of confined type or convertible type Nodes can only be of the unconfined type if they are located within the top model layer Layer types confined c or convertible v From top to bottom Figure 11 Lines 3 and 4 of input file grids dat for a two layer model 7 2 2 Simulating unconfined conditions updating transmissivity Some groundwater models update transmissivity at the end of each iteration of a numerical solver during the solution of a time step This method is not adopted in ZOOMQ3D b
98. ndritic river basins Both the baseflow along the river and the interaction between the river and the aquifer can be modelled The structure of rivers within ZOOMQ3D is described using three terms rivers branches and river nodes which have the following definition Rivers a river is composed of both an interconnected series of river branches and a interconnected series of river nodes A river cannot be composed of two sets of interconnected river nodes that are not themselves connected i e a river cannot represent multiple separate catchments Branch a branch represents the main channel in a catchment or a tributary within the river catchment Only dendritic river catchments can be modelled and consequently each branch has one node at its upstream end and one node at its downstream end River node a river node represents a point on the river that coincides with a horizontal point of the finite difference mesh The characteristics of the river are defined at each river node A river node can have up to five upstream connections to river nodes but only one downstream connection Branches and river nodes are organised in a specific order described by a numbering scheme For river branches a numbering scheme must be adopted in which the upstream branches have a higher integer value Figure 26a River node numbers also increase upstream and from low branch numbers to high branch numbers Figure 26b The river node at the bottom of the catchm
99. nitialh map amp initialh cod or initialh dat boundary dat fixedheads dat noflow map leakage dat obsleak dat springs dat rivers dat initialflow dat gauging stations dat river_inputs dat 8 2 Recharge recharge dat recharge map recharge cod recharge_rates dat Wells 1 Abstraction wells 2 Observation wells De watering and re wetting pumping dat obswells dat wetflag map wetthresh map amp wetthresh cod or wetthresh dat wethead map amp wethead cod or wethead dat Variable hydraulic conductivity with depth VKD vkd cod amp vkd map vkd dat vkdkx map amp vkdkx cod or vkdkx dat vkdky map amp vkdky cod or vkdky dat vkdzp map amp vkdzp cod or vkdzp dat vkdgrad map amp vkdgrad cod or vkdgrad dat Time discretisation clock dat Numerical solver sor dat Producing head contours contour_times dat Controlling data input zoomg3d dat 18 Table 3 List of minimum set of input files required by ZOOMQ3D when rivers and VKD are not included in the model Input file name Relevant section x anisotropy map amp anisotropy cod OR _ anisotropy dat per layer Loe x aquifer map 7 2 1 x boundary dat 9 1 clock dat 8 contour_times dat 14 1 xX xX K entry_method dat 7 3 1 fixedheads dat 9 2 grids dat 7 1 hydcond map amp hydcond cod OR hydcond dat per layer 7 5 1 initialh map
100. not permissible to enter an integer as a decimal number 4 Some but not all files contain comment lines These are actually text data strings which are read by the model and discarded 5 The maximum length of a comment line is 128 characters 6 Itis good practice but not necessary to remove white space from the end of lines 7 Comments cannot be appended to the end of lines of data If these are included the model will crash 8 Comments can be appended to the ends of files 9 The names of all files are fixed except those defined in the input file zoomq3d dat 10 For some data sets one file is required per model layer In this case the layer number is appended as a two digit integer number to the end of the file name before the file extension For example hydcond0O1 dat hydcond02 dat etc when defining hydraulic conductivity distributions The list of input files required by ZOOMQ3D is presented in Tables 1 2 and 3 In Table 1 the files are listed in alphabetical order whereas in Table 2 they are grouped into categories Though there are thirty nine files listed not all of these are required for all simulations For example if no rivers are included the model only one of the files is required from the group of four that relate to rivers Table 3 lists the minimum set of data files required to run ZOOMQ3D when rivers and VKD are not included in the model Each of the ZOOMQ3D input files is described in the following section
101. nstall ZOOMQ3D on a Windows PC copy the executable zoomq3d exe into suitable directory such as c Program Files ZOOM Then add this directory to the Windows system PATH variable Control Panel System Advanced Tab Environment Variables No installation procedure is run in which ZOOMQ3D program files are added to the system registry All the input files required by ZOOMQ3D must be located in a single directory All the output files produced by ZOOMQ3D will be created in the same directory It is strongly recommended that ZETUP and ZOOMQ3D are never run using the same working directory and that their files are kept within separate folders ZOOMQ3D should be run from the command line in a console window and not started from Windows Explorer In the event that an error occurs messages are written to the screen If ZOOMQ3D is run from Explorer it may terminate before the user is able to read error messages To start a command window select Run from the Windows start menu and type cmd in the drop down list box Figure 2 The user should then change directory to that of the working directory where the ZOOMQ3D input files are located For help on the commands used to change directory type help cd within the console window Figure 3 To run the model type zoomq3d followed by the path to the working directory on the command line e g zoomgq3d_ c myZOOMQ3D_project Alternatively this string can be placed in a batch file
102. ntly only two parameter values must be assigned in the code file for this grid This relationship is the same for the final two grids in 30 the map file Re iterating because eight letters are defined on the base grid in the map file eight corresponding parameter values must be defined in the code file for this grid The first integer number in each block of data between the comment lines in the code file is the number of zones or letters specified in the character array After this integer value an equivalent number of parameter values must be specified Therefore for example if twenty six letters were used in the map file for a specific grid i e the letters a to z twenty six parameters values must defined within the code file for the corresponding grid In the above description it is stated that there must be an equivalent number of parameter values specified in the code file to the number of letters used in the corresponding character array in the map file However this is not strictly the case In fact there must be at least the same numbers of parameters specified in the code file as are used in the map file for the corresponding grid Therefore it is allowable for example to specify parameter values for all fifty two characters in the range a b y z A B Y Z but only use a subset of these letters in the map file The final rule to follow when editing the map and code files is that the minimum number of parameters t
103. o enter in the code file is determined by the highest letter in the range a b y z A B Y Z For example if C is the highest letter used then twenty nine parameters values must be defined in the code file Similarly if m is the highest letter used then thirteen parameters values are required This means that if only the two letters a and z are used to define a grid character array in a map file at least twenty six parameters values must still be defined in the corresponding code file for the corresponding grid This is because the parameter values defined in code files must be listed in the order a to z then A to Z i e in alphabetical order with the lower case alphabet preceding the upper case alphabet in the fifty two character scheme fOr grid i Bottom i right 700 700 for grid A Bottom left 100 100 Top right 300 300 for grid Bottom left 400 400 Top right 600 600 for grid Bottom left 150 150 Top right 250 250 Figure 16 Example code file for the entry of spatial data within a layer 31 7 3 3 Specifying spatial data using numeric data files Instead of using a pair of map and code files to specify the spatial variation of a parameter within a model layer a single data file can be used containing raw numeric data This has the same name as the map and code files but has the dat extension For example the file specstor04 dat could b
104. of the point of inflection Zp VKD profile data must be entered into the model using either 1 a pair of map and code files for each profile level for each VKD parameter or 2 anumeric data file for each profile level for each VKD parameter As shown in Figure 43 profiles can be on the same level but represent cross different model layers Reiterating VKD profile data is input for each profile level and not for each model layer For the example shown in Figure 43 either four pairs of map and codes or four numeric data files are required for each of the four VKD parameters K K VKDGrad Z This is because the maximum number of profiles in the vertical is four An example set of map and code files is shown in Figure 45a for the first profile level and an example set of numeric data files is shown in Figure 45b 73 vkdkx01 cod vkdkx01 map vkdkx01 dat vkdky01 cod vkdky01 map vkdky01 dat vkdgrad01 cod vkdgrad01 map vkdgrad01 dat vkdzp01 cod vkdzp01 map vkdzp01 dat Figure 45 Example set of a code and map file and b numeric data files for VKD parameters on first profile level The number in the file name relates to the profile level and not model layer Hence for the example shown in Figure 43 three additional sets of files are required with names containing 02 03 and 04 instead of 01 This is because in this example the maximum number of profiles in the vertical is four The user specifies whether map and code files
105. ons at the start of a time step Ac involves transmissivity and mesh spacing values together with storage and time step size The terms A to A contain only transmissivity and mesh spacing information while A and A are related to vertical hydraulic conductivity values and layer thicknesses A involves only the storage coefficent and time step size In all members of the family of methods leading to SOR the format of the iterative formula is similar and is based on the above equation The first of the series is Jacobi iteration which uses the basic finite difference equation without change The unknown heads on the right hand side are treated as known for the duration of a single iteration and the relationship is used to update the central unknown groundwater head h An iteration cycle is complete after all the nodes have acted as the central node At this point a check for convergence to the corrrect solution is conducted and iteration continues until the convergence criterion is satisfied An important feature of the method is that updated values are not used until the next iteration As the mesh is scanned one updated value is available to be used immediately in progressing to the next node in sequence This produces an alternative formulation known as Gauss Seidel iteration which is superior in terms of its rate of convergence The Jacobi method does converge to the correct solution but it is much slower than Gauss Seidel iteration As there
106. or numeric data files are being used in the input file entry_method dat see Section 7 3 1 The part of the file name preceding the number is defined by the user in the input file vkd dat which has the format shown in Figure 46 The ability to specify the name of the VKD parameter files is implemented to simplify the management of different data sets vkd dat File format vkdkx Name prefix of files containing K data X vkdky Name prefix of files containing K data vkdgrad Name prefix of files containing VKDGrad data vkdzp Name prefix of files containing Zp data Figure 46 Format of vkd dat input file The format of the map and code files is described in detail in Section 7 3 2 Each of these pairs of code cod and map map files is used to input the values of one of the VKD profile parameters on a particular profile level For example considering the first pair vkdkx01 cod and vkdkx01 map for which examples are shown in Figure 47 The first line of each file is a comment line On the second line of the code file the number of codes or factors N is defined For each of the N codes one value of K is entered per line The first value corresponds to the letter a the second to b etc Consequently where the letter a is defined in the map file the hydraulic conductivity K of the profile will be assigned a value of 1 7 Where the letter b is specifi
107. or type 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 Rate for each stress period for type 1971 k number for block 0 81 1 04 0 73 0 80 0 31 0 12 0 00 0 00 0 00 0 5 Rate for each stress period for type O05 OLS 0s L5 015 04 05 0 225 0 25 0 15 0 15 05 s Rate for each stress period for type 1972 k number for block 1 43 1 05 0 71 0 64 0 10 0 00 0 00 0 00 0 00 O 5 g Rate for each stress period for type 0223 0 423 0 223 0423 0 2 3 0423 105 2 3 0 23 0 s Rate for each stress period for type one or any number of blank lines SECT Comment line must start SECTION Comment line which must start SECTION Data for numeric recharge files Comment line Name of numeric recharge data file Comment line rech_rates dat Name of numeric recharge data entry file Set all numeric recharge rates to first months recharge y n Comment line n Using rates for 1 stress period only flag S OO N 0 U n aN CR a A S a 10 11 12 13 14 15 16 17 18 Figure 38 Example recharge dat file 64 10 2 ABSTRACTION AND OBSERVATION WELLS 10 2 1 Abstraction wells Groundwater can be abstracted from or injected into the aquifer at specific model nodes The position of boreholes and rates of pumping are specified in a file with the structure defined in Figure 40 The name of this file for example pumping
108. ossessi sasos sons LO 5 1 The process of constructing a model sseesessessseesessresressessresressersresresseeseesrersreseeseresre 15 PART 2 Model input seeseseesseseecesseseesesseseescesecoesoeseecosseseesorseecesoeseecesoesoesorseccesoeseesesoeseesesseseesees LO 6 Summary of input files required by ZOQOMQSD cccccsssccssssscsssscesssscssssscsssscsssscssees LO 6 1 The philosophy of model mputsc6c 6 cde teen iaciivs Bede ee oo iad ee Ba ees 16 Model Structure ceistesceniee cettenicanecsacaecaehied sacusncetace vaseescguicanuausaetnhecsececnuciuschbussetvbecseceenaesuscbtauays 20 FE Model SU HAT Ce seas esos cates e A Aa A E ora E aR 20 7 2 Confined unconfined conditions sssssseseseeeesseessresseesseressessstesseesseresseesseeessseessees 24 7 3 File formats for inputting Spatial datascc 5 a t ciuecdah eccosade onde Matedeal meus ds eaead aged es 28 7A Representation of layers 24 ne25 cee ia hae a Gate ee ee Betas ae ae ie 33 Tid Hydraulic parameters osiensa neasi n Eear EES EE E Ea a EEES eea 35 Time discretisation and initial conditions ssesssssssssssssssssssssssssesosososesesososesesesesese JD Sak SEIMeSISCTES Atl on naeun n a a a eee a 38 8 2 Initial groundwater heads 2 cc sccssisdieiavascccevsnseaisasvaeaies lesscesanesead aves sdaceaasnens es lecdgaaanestase 42 Boundary conditions coos ssc ccescesscdevs sieeceoess sade veasdoeseodss gees vesdoecevess esebesiaccedeave deen sou
109. oving node 9250 0 3000 0 9500 0 3000 0 9750 0 3000 0 Number of years of elevation data For each block year no then 1 line of nSP elevations m for each moving leakage node 0 6 0 6 0 6 0 0 6 0 6 0 6 0 0 5 0 5 0 5 0 Figure 24 Example leakage dat file 9 3 1 Monitoring flow through leakage nodes over time The flows into and out of leakage nodes are monitored over time by specifying data in a file with the following structure The name of this file for example obsleak dat is specified by the user in the input file zoomq3d dat see Section 14 2 The file has the format n start_block end_block Layer x y one for each of n leakage nodes where n is the number of leakage nodes at which the flow is monitored start _block is the block number when monitoring starts end_block is the block number when monitoring ends Layer is the layer in which the leakage node has been created x is the x co ordinate of the leakage node and y is the y co ordinate of the leakage node 46 9 4 SPRINGS 9 4 1 Conceptualisation Springs are usually simulated in models using a head dependent leakage mechanism This mechanism is incorporated in the model however the conceptualisation of a spring in this way in which the outflow from the aquifer is based on a bed conductance could be argued to be simplistic Consequently a spring mechanism has been developed in which spring flows are dependent on the groundwa
110. ow eo oV 0 CODCOD COCONWNHOBN OQananannnnk DDDDDKR CODDCOCCOKR INWNFPOBDND SPCODTODCODRCDCCOQDAHHEHENNNNNQAODCONKBEHEE GQaOanannnnnnoryrynrnynnodc cCCCOCOCONWNHEOCANOO OO OO OOo ao UUAN A a O GeO OGO OQ O O a O O0 OO 0G O O a O GeO OO OG O O oOoOOCCOCOOC oO a O Ger OO O O OW UUAA A a O a CO Q O UnAn A Figure 17 Example numeric data file for the entry of spatial data within a layer 7 3 4 Definition of data at coincident points on multiple grids It is apparent from the example model and input files described above that parameters values at particular finite difference nodes are specified more than once in an input file when the model mesh is locally refined This occurs at those nodes on a refined grid that are coincident with the nodes on a coarser grid Where this occurs the data defined on the refined grid will always override that defined on the coarse mesh 32 7 4 REPRESENTATION OF LAYERS Vertical discretisation of the model grid is incorporated through the inclusion of layers of finite difference nodes which are continuous across the model domain The vertical discretisation is implemented by specifying the number of layers and the conductance between them Because the vertical conductance term embodies the layer thickness they are not explicitly included in the finite difference equations However the elevations of the layers are required by other model mechanisms for example the de watering and re wetting of model nod
111. p and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 7 5 4 Specific yield Input files containing specific yield data must be defined for the top model layer and each of the lower layers which are defined as containing convertible model nodes see Section 7 2 Specific yield data is dimensionless and permissible values are between O and 1 0 i e the values are not read in as percentages The storage applied at a node only incorporates the specific yield if it is an unconfined node or if the node is defined as convertible and the groundwater level is below its top elevation Input file names and format Specific yield data must be entered into the model using either 1 pairs of map and code files with the names syield map and syield cod or 2 numeric data files with the names syield dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described
112. p of the upper layer is now ignored if it is unconfined and the transmissivity is calculated based on the difference between the groundwater head and the base of the layer The transmissivity was calculated correctly in version 1 01 when the groundwater head was below the top of the upper layer e One comment line and one data line have been added to the clock input file to allow the specification of a start time in year month day hh mm ss format This has been implemented because the model has been made OpenMI compliant See www openmi org for more information e An additional column has been added to the time series output files e g gauging stations out between the third and the fourth column of the output files produced by the previous version of the model This contains the time in Modified Julian Day format starting from the time specified on the new line in clock dat e All executables should now be placed in a suitable directory e g c Program Files ZOOM and this folder should be added to the Windows system PATH variable The models can then be run from any working directory containing the data files by typing the name of the executable followed by the path of the working directory e g ZOOMQ3D c myZoomModel Alternatively this string can be placed in a batch file and the batch file run from the command line iii Contents A FORO WOLO PEE SE ET A sceedeescesasscecueaucescaccacesocecceascadcssoeccsscesseasas
113. pressions used to calculate transmissivity are T K h z for h gt Z T 0 for h lt z The expressions used to calculate total storage are S S h z S for h gt Zg S 0 for h lt Z 7 2 1 Defining the spatial distribution of confined unconfined conditions Different types of aquifer nodes can be defined within different areas of the top model layer layer 01 The file aquifer map is used to specify whether nodes are confined convertible or unconfined in layer 01 This map file contains a single array or multiple arrays if grid refinement is incorporated which is are composed of the characters c v or u The letters relate to confined convertible or unconfined conditions respectively These character arrays are listed in grid level order and are separated by a comment line The comment lines contain information required to identify to which grid each array relates ZETUP the set up program for ZOOMQ3D produces this file and writes the co ordinates of the bottom left and top right hand corners of the mesh within the comment lines Consequently the user need only adjust the letters in the arrays in order to modify the representation of the aquifer An example of a simple map file is presented in Figure 10 This shows an aquifer which is unconfined towards the left hand boundary and confined along the right hand edge of the model A number of convertible nodes are used to represent the transition from u
114. r each of the parameters that can vary spatially across the model domain To specify which data entry method is to be used the user must adjust the input file entry_method dat The format of this file is shown in Figure 13 It consists of a series of integers each of which is preceded by a comment line There is also an additional comment line at the top of the file Each comment line except for the first notifies the user of the related parameter e g specific yield The entry mode of the specified parameter is entered on the next line as an integer value If this integer is equal to 1 a pair of map and code files is required for each model layer If the integer is equal to 2 one numeric data file with the dat extension is required for each layer 28 Entry method 1 Map and codes files 2 Raw data Base elevations Top elevations Specific storage Specific yield Hydraulic conductivity Anisotropy VKD Vertical conductance Wetting thresholds Post wetting heads Porosity Figure 13 entry_method dat file format 7 3 2 Specifying spatial data using map and code files In this method the spatial distribution of parameter values is defined using maps These maps are contained in files with the map extension For example hydcond02 map would be used to define hydraulic conductivity in layer 02 of the model i e one layer down from the top layer The map files contain one character array for each grid in the
115. recharge data 00 0 eee eeeeeeeeeeeeee 59 Figure 34 Example aquifer modelled using two recharge types ceesseeeeseeeeeeeeeeeteeeees 60 Figure 35 Example model mesh used to simulate aquifer shown in Figure 34 seess 60 Figure 36 Example recharge time series recharge code file and recharge map file used to define two different recharge types s555a0t asc teuck sigs Synaniautest cadantendedeceasaacdevs ts atanineeteeee ook 61 Figure 37 Format of numeric recharge data file cess cesceseeeseecseecnseeeseeesneecsaecseensees 62 Figure 38 Example recharge dat file wicdcvsunvatat len elves eee ew ive 64 Figure 39 Conceptualisation of multi layer well pumping from layers 1 3 and 5 66 Figure 40 Example pumping dat file and format of input elles eeseeceeceeeeeeeeeenees 67 Figure 41 Hypothetical hydraulic conductivity transmissivity versus depth profile 68 Figure 42 Parameters used to define VKD profiles in ZOOMQ3D 0 cee eeeeeeeeeeeeeeenees 70 Figure 43 Specification of VKD schemes in ZOOMQ3D 00 eee eeeceeeceeeeeseeeeneenteetseeeenees 71 Figure 44 Example a VKD scheme map file and b associated model grid eee 73 Figure 45 Example set of a code and map file and b numeric data files for VKD PaLaineters OM first Promle TEVvel2 55sesc0 sses aurscetanntnade de ceaunasdveeiessieaeaataegute Joie a aE 74 Figure 46 Format of vkd dat input file ee ee ceeseeceeeeceeececeeeeeceeeeeceeeeece
116. ric data files with the names hydcond dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 7 5 2 Anisotropy Hydraulic conductivity in the y direction is calculated by the model as the product of the hydraulic conductivity in the x direction and the anisotropy ratio K K All values greater than or equal to zero are valid as input Input file names and format Anisotropy ratio data must be entered into the model using either 1 pairs of map and code files with the names anisotropy map and anisotropy cod or 2 numeric data files with the names anisotropy dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The forma
117. rids dat osnsonneoensseesseeeesseesseessesssesesseessseessersseessee 34 Figure 20 Division of time into time steps stress periods and blocks 1 0 ceeeeeeeeeeeeeeeeee 38 Figure 21 Example clok dat ile ni cten cain a nile nau E reads aaa Qe 41 Figure 22 Format of numeric initial groundwater head data file eee eee eeseeeseeeeeeeeneee 42 Figure 23 Format of leakag dat 22s d2incsin itiwiiud iii asiiiendiui alias 45 Figure 24 Example leakage da file ge sisin ccc ccc tte toate lat ta luctte sl mrataie lak aeimieetane neat 46 Figure 25 Example springs da input file a i2 443 0486256 2a R AAS 48 Figure 26 Numbering schemes in ZOOMQ3D for a river branches and b river nodes foran example THOCE TIVE siansa S OOSA RS 50 Figure 27 Schematic representation of connections between river and grid nodes 51 Figure 28 Formulation of river aquifer interaction under influent and effluent conditions A AEE E E E E a Sica Guede E E E ssaive 53 Figure 29 Specification of flow along or discharge into river at specific river nodes 55 Figure 30 Format of file rivers dat i c2c ci 2c tegyeenetanienenccdiecs nacelle neta eeendeeion 56 vi Figure 31 Format of input file initialflow dat oo eee eeceeeseecsseceseeeseeesaeecnaeeseeseeeeeaees 57 Figure 32 Format of input file river_inputs dat 20 0 0 ce eeeceeccecesececssececeeececseeeeeeeeeenseeees 58 Figure 33 Example code and map file for the entry of
118. ronts It incorporates a mesh refinement procedure which aids the solution of problems related to scale This is the first of its contributions The second is that it uses object oriented techniques as the basis for the program Whilst this is well established in the development of general commercial software it represents a novel approach to groundwater model structure It is of considerable value in maintaining the code but it is in changing model behaviour that it holds most promise for modellers Further the direct correspondence between computer based objects and real world features makes the link between numerical and conceptual models very easy to see even to those with no programming expertise 2 Physics of flow ZOOMQ3D is a quasi three dimensional groundwater flow model To understand the implications of its quasi three dimensionality it is convenient to begin with a general three dimensional groundwater flow equation cfc aaa eae Ox dx dy dy l a ot x y Z t is the groundwater head value at a point x y z and at time L where k x y z k x y z k x y z are the hydraulic conductivity values in the x y and z directions respectively LT S x y z is the specific storage at x y z L N x y z t is a source flow term as a flow per unit volume T This equation is derived by considering a flow balance for an infinitesimally small volume element located anywhere within a body of saturat
119. s shown in bold should be modified by the user These flows will determine how much water can leak into the aquifer during the first time step if sections of the river run dry for example due to groundwater abstraction 9 5 4 Time variant inflows or discharges to rivers To specify time variant discharges to a river for example from a sewage treatment works or to specify the baseflow in a river as it comes onto a model as illustrated in Figure 29 the following file is used The name of this file for example river_inputs dat is specified by the user in the input file zoomq3d dat see Section 14 2 It contains data specifying which river nodes receive baseflow and how these flows vary over time An example file and a description of the file format is given in Figure 32 The user enters the following data e The number of river nodes at which an inflow is specified e The location of each of the river nodes defined by the river number and river node number e The number of time blocks for which flow rates are read e The inflow at each of the river nodes for each stress period in each time block 54 Ji Specification y of flow onto model at upstream river N node aa A s a a lt eo o e Py o o ET Specification of discharge to river at specific river node
120. s point methods where the algorithm is applied one node at a time or as block methods where a group of nodes is treated together Successive over relaxation SOR is an iterative point method which is very convenient for dealing with the equations in a model with grid refinement where the number of unknowns varies between nodes The basis of all iterative methods is to find a relationship which will change an initial estimate of the solution so that it converges on the required value after a finite number of applications Successive over relaxation SOR represents the most efficient of a series of related methods which all rely on making use of the basic finite difference equation In the case of ZOOMQ3D the structure of the finite difference equation can be expressed as follows Ah Ah A h A h A h A h Ah F where hc is the unknown groundwater head at the central node h hn are the unknown groundwater heads at surrounding nodes on the same layer ha and h are the unknown groundwater heads on layers above and below the central node he is the known groundwater head at the central node Ac Ac Ay An Aa and Ap are coefficients F is acollection of terms involving known flow rates due to recharge and abstraction n is the number of surrounding nodes on the layer containing the central node which will be 4 or 5 depending on presence of mesh refinement The various coefficients are calculated on the basis of conditi
121. s the number of times when groundwater head data will be saved in a format for contouring An equivalent number of lines of data must be specified after the second comment line These data lines must contain three integers numbers the time step the stress period and the block number At each of these specified times one output file will be produced named contour_TS_SP_B txt with TS SP and B replaced by the corresponding time step stress period and block numbers These output files can be used to produce groundwater head contours in each model layer Their format is described in Section 16 2 Number of times at which to output heads in format for contouring 4 Times at which to output contour heads time step stress period block 4 1975 1983 4 4 1988 4 1995 Figure 54 Example contour_times dat file 81 14 2 SELECTING WHICH DATA INPUT FILES TO USE The names of many of the ZOOMQ3D input files are fixed and invariable However some file names can be specified by the user in the input file zoomq3d dat These files are distinguished in Table 6 ZOOMQ3D reads the file names and opens the corresponding input data files Consequently it is easy to modify a model by using an input file that contains the same type of data but which has a different name The format of the file zoomq3d dat is shown in Table 6 It must contain eighteen text strings representing the input file names in the order shown in the figure
122. s within ZOOMQ3D However the data input files are not themselves complex The spatial and temporal distribution of recharge can be specified using two methods 1 The use of map and code files similar to those described in Section 7 3 2 The use of a single numeric data file containing arrays of recharge rates in mm day In fact both of these methods can be implemented simultaneously 10 1 1 Applying recharge using map and code files The formats of the recharge map and code files are identical to those described in Section 7 3 An example code file is shown in Figure 33 for a hypothetical model which contains a coarse base grid and no grid refinement If this code file was related to the specification of hydraulic conductivity a value of 0 9 m day would be applied where an a is located in the corresponding map file and a value of 1 2 m day applied where a b is defined If this was a recharge code file the values would not represent recharge rates of 0 9 and 1 2 mm day but rather multipliers of a recharge rate defined in a file for example named recharge dat The values in the code files are multipliers and not actual values of recharge because recharge varies both spatially and temporally The spatial variation is defined using the map and code file and the temporal variation is defined within the file recharge dat Code file Map file aaaaaaaabbbbb aaaaaaaabbbbb 9 22 aaaaaaaabbbbb
123. sequent lines These comment lines or text strings must be included in the input file but are read and discarded by the program For reference purposes only a line number is shown in the first column of Figure 21 This column is not part of the input file The discretisation of time is specified between lines 1 and 18 The number of time steps per stress period stress periods per block and blocks are selected in addition to the length of each stress period On line 6 the user specifies the time at the start of the simulation which does not necessarily have to correspond to the stress period and block numbers If the user specifies that stress periods and blocks are equivalent to months and years line 10 the program checks that the length of each stress period is equal to the number of days in each month In this case the user must ensure that 1 there are twelve stress periods per block line 2 and that 2 the time at the end of the penultimate time step is less than 28 days i e less than the number of days in February if method 1 or 3 is selected for calculating the time step lengths line 14 or 18 The program automatically corrects for leap years Between lines 20 and 24 the block numbers are listed Blocks numbers can be listed out of sequence or repeated except when recharge data is input using the numeric data file discussed in Section 10 1 2 On line 26 an integer flag is entered which specifies the frequency of data output
124. simulation sesssssssesssesessesesseessseessresseessee 86 16 7 Dezwatenngiand Pewee iroot cinnara e a e a iS 88 16 8 Nodal flow Balances iii cisscaassseacaacidsg tacts siceedaatsg bacdisunead vs lessaata a E D s 88 16 9 Global flow balanc S suiti taaa aara E EEE eA 89 16 10 Monitoring leakages wcccscsceccescecseckcets ices iasdsvesaavasaceisasenssaee cdedna sg vend cansmeasedsdecndeadectaceeinteas 90 LG TVS OTH BLOWS nnna a A a tama tubs Reis a a a e a ai aa 91 16 12 Multi layer wells icccct ais isianieiaed heidi aniseed a E E aad 91 16 13 COMmVEFZENCS f solton estira i s te tas tuadsien shes e oaaao esastan 92 16 14 Variation in WANSMUISSIVICY scccsveccvesssbevsseessdeaesaaeaveisasegssdcassacceale jeaseauecaceesndeeconancosate tees 92 16 15 Output files required for particle tracking eeeeeesesseseesessseeseserssesrrrsreseresrersereresreesesse 92 Referent S sssini aseek essene osese aeneae eesse sesos eresi iaaeao passe 95 FIGURES Figure 1 Node numbering in the finite difference stencil eee eee eeeeeeneeceeeceseeeeeeeeneees 5 Figure2 Starting a command line window from the Windows start menu eee 13 Figure 3 Example of changing the working directory within a console window 14 Figure 4 Changing the properties of the console window eeseeseeceseceseeeeseecnaeenteeteees 14 Figure 5 Process of constructing and running a ZOOMQ3D model osses 15 Figure 6 Model mesh represented by e
125. smissivity at a node is calculated by integrating the hydraulic conductivity over the vertical saturated thickness of the node 10 4 1 7 Recharge Recharge can vary spatially and temporally Recharge is always applied to the upper most active node 4 1 8 Abstraction wells Pumped boreholes can be placed at any node within the model domain Abstraction rates can vary temporally and wells can both abstract water from the aquifer and inject water into it 4 1 9 Rivers Dendritic rivers basins are simulated using a series of interconnected river reaches The hydraulic parameters characterising a reach can vary along the river as can the degree of connection with the aquifer The transfer of water between the aquifer and rivers is simulated as is the accretion of baseflow along each river branch Discharges to the river can be specified in any reach for example to represent a sewage treatment works and the discharge rate can vary over time Both fully penterating and perched rivers can be simulated 4 1 10 Head dependent leakage nodes In addition to rivers a second head dependent leakage mechanism is included in ZOOMQ3D The flow through leakage nodes is proportional to the difference between its elevation and the groundwater head at the finite difference node to which it is connected Flow can occur in either direction i e into or out of the aquifer Leakage nodes can be used to model spring flows lakes or estuaries for example 4 1 11
126. sscocceel m Acknowledgements cess tesecacailadediatas ccailsbasigandacecaiescncuddsedsseadacnacgandoeceauessucuhissasceasuswecdaacasciezell Preface to the second CitiOn ccccccccssccsssssscsscscssscscscssscscscscscscscscscscscscscssscscscssscsssssesesssesssssese ll PART 1 DISCUSSION sess cscesces ca obeseeeseenckesSeceeckeestcaceaseactedscswcescatoaconsseswcsdsastastedvosweescatoasensbossseccasoastetoo lL 1 2 Introduction sicsccccscessccceciicidsessdcsctes se scccecnc cdedesdesieseseebectoake caai eaea sea oaea osoite sosoo d Physics OE OW Ciscunieasiebviestishssieasvetebebutysavecuby bunk dephaeseashyehekusp dei eas bytuch dasbsbUucupetvebas seussecbivenc tisewone The numerical solution PrOCess cssccsssccsesrssssssecsssecssssessssscsssssccsscssssscssessssssssssssscssssssees D Sol JPimite difference SquatiOns ssi nes i i a e R a ata eaa Oaa 5 3 2 SUCCESSIVE over Telakan n aa ia a aean 7 Capabilities of ZOOMQ3D eessesessocsssssssecesccesocesoosesocessccesocssocesoosesoesssecssocssoosssosessesssesssoesssse LO 4 1 Fe tures of ZOMG 1 rnein istna a a heats E A A R A R 10 4 2 Constructing models using ZETUP sesesesseeseeeesseeesssresseserssresseseresressessresresseesresresseeee 11 4 3 erminolos yatan enn a a r aaah sw ea ee 12 a e AE DATARO AENG i DORAE E EEEE E E T saat iagcae basuee syaasseespmeasobecass 12 Running th M d l sissssssssssssrossossssissssssvcssssoscessssssasst sss esssossotasoss
127. st be specified using either 1 pairs of map and code files with the names ztop map and ztop cod or 2 numeric data files with the names ztop dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of map and code files is required for each of the model layers or a single numeric data file is required for each of the layers The format of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 34 7 5 HYDRAULIC PARAMETERS The spatial distribution of a number of hydraulic parameters must be defined within the model Input files must be prepared for each of the parameters for each layer in the model The format of these input files is described in Section 7 3 7 5 1 Hydraulic conductivity Kx Only hydraulic conductivity values in the x direction are read directly by the model Hydraulic conductivity in the y direction is calculated as the product of the hydraulic conductivity in the x direction and an anisotropy ratio Input file names and format Hydraulic conductivity in the x direction must be entered into the model using either 1 pairs of map and code files with the names hydcond map and hydcond cod or 2 nume
128. subgrids on the first level of refinement and a third refined grid at the finest scale on the second level of grid refinement The format of this input file is described in the second column of Figure 7 The data on lines 1 to 6 of grids dat can be adjusted by the user however the remainder of the file should not be modified This data is generated by ZETUP and defines the structure of the model mesh If the user wishes to modify the mesh the model should be uploaded into ZETUP and altered using this tool 700 m 700 m Figure 6 Model mesh represented by example grids dat file 7 1 1 Lines 1 to 6 of grids dat The first three pairs of lines in the input file grids dat contain a comment line and a data line The parameter specified in the first of these three pairs of lines is the number of layers in the model This can be modified manually but this would then require the user to check the existence and structure of other ZOOMQ3D input files If the number of layers is increased additional input files must be produced because one file must be created for each layer for some file types Furthermore the structure of the file boundary dat would have to be altered The parameters specified in the second of these three pairs of lines are used to specify the type of aquifer conditions operating within each model layer Each layer can be specified as 20 confined c or convertible v dep
129. t of these files is described in Section 7 3 The user specifies whether map and code files or numeric data files are used in the input file entry_method dat 7 5 3 Specific storage Input files containing specific storage data must defined for each model layer Specific storage has units of m The confined storage coefficient of each finite difference node is calculated by multiplying the specific storage by a vertical saturated thickness The thickness used depends on whether the node is of the confined convertible or unconfined type The following expressions hold for each of the nodal types 35 Confined nodes Convertible node S S zt ia S S zm E Ze for h gt zP S S x h z for h lt Z Unconfined nodes where S S x n ze S is the confined storage coefficient S is the specific storage m h if the groundwater head m Z is the top elevation of the node m Z is the base elevation of the node m Input file names and format Specific storage data must be entered into the model using either 1 pairs of map and code files with the names specstor map and specstor cod or 2 numeric data files with the names specstor dat The symbols must be replaced by a two digit 01 to 99 number representing the layer to which the data files refer The upper layer is layer 01 and their numbers are incremented from the top to the bottom of the model Either a pair of ma
130. ter head in the aquifer but not governed by a conductance term Instead spring flows can only be adjusted by modifying the transmissivity of the aquifer in the region of the spring Consequently the general pattern of flow within the aquifer determines the outflow at a spring location Springs in ZOOMQ3D encapsulate a head dependent abstraction mechanism When simulating unconfined aquifers the transmissivity is updated within a cyclical procedure see Section 7 2 2 The solution for the current time step is computed a number of times within this cyclical process After each cycle the transmissivity is adjusted Spring flows are also adjusted at the end of each cycle A spring object is defined by an upper and lower elevation which for example represent the ground level and a level just below the ground surface e g 0 1 m below the ground surface If at the end of a cycle the groundwater head at this node is above the upper spring elevation then the spring is set to a fixed flow This flow rate is calculated using the specific yield and time step length so that the groundwater head is lowered to between the two elevations defined in the spring object It is given by the equation Q h Bt ia Ay i 2 At where Q is the specified spring flow rate m day h is the groundwater head at the spring node m Z is the elevation of the top of the spring m Z 1s the elevation of the base of the spring m Ax is the width of the node in th
131. the assistance of A G Hughes and M M Mansour of the British Geological Survey and P J Hulme of the Environment Agency for their help in reviewing the ZOOMQ3D software Additionally the authors would like to acknowledge the assistance of the following colleagues at the British Geological Survey for reviewing this document A G Hughes and D G Kinniburgh Preface to the second edition The production of the second edition of the ZOOMQ3D manual coincided with the release of version 1 01 of the groundwater modelling code This version of the model incorporates some minor adjustments to the original code and some additional functionality The changes that have been made are described in the following bulleted list To enable version 1 01 to run models developed using version 1 0 three data files need to be modified These are i the abstraction file Section 10 2 ii the main recharge input file Section 10 1 3 and iii the numeric recharge rate file Section 10 1 2 DIFFERENCES BETWEEN VERSION 1 0 AND 1 01 OF ZOOMQ3D e Multi layer wells have been added to the code This enables a pumped borehole to be connected to one or more layers The pumped well calculates how much water is abstracted from each model layer The pumped layers do not have to be contiguous Refer to Section 10 2 The particle tracking code ZOOPT has been updated for use with multi layer wells e All input parameters have been converted to use metres for the unit of lengt
132. the input file zoomq3d dat Consequently the output file can be used to start a simulation using the groundwater heads computed at the end of a previous run The format of this input and output file is shown in Figure 22 INITIAL GROUNDWATER HEADS KAKKKKKKKK LAYER Ol FERRER KKKEK kkk BASE GRID Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Base grid Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Grid 1 Layer 01 Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Subgrid 2 KAKKKKKKKK LAYER 02 ERR KKKKEK k k k BASE GRID Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Subgrid 1 Layer 02 Replace rectangle with an array of initial groundwater heads with the same number of rows and columns as this grid Subgrid 2 Figure 22 Format of numeric initial groundwater head data file 42 The first line of the file is a comment line Blocks of data follow this comment line for each model layer starting with the top layer Within each block of layer data blocks of data are defined for the
133. tin nodenn n ade ed alleen Stet adel A tee ae a 80 14 Additional model input files oi iissssesesssvcrevcnspecencdsvGuescevnsesvcebycevecsseceosceveeesvcceucedeccbyeedosconcevensye 1 14 1 Saving groundwater heads for COMtOULING 0 0 eee eeeeeseceececeeececeeeeeceteeeceeneecseeeeeeeeee 81 14 2 Selecting which data input files to use o s 05 sc descessencesieessedsdag hag gaseavevadedasandeasduaceuventenaea 82 PPA ROD SW ant pons aiaiiessscsdiivestcesacesscccavcncecnascneaytansaescancesnuzesnca cecaceccnecsiveaecegansoseacenecessaveneere 83 15 Summary of output files produced by ZOQOMOSD cccssccssssscssssccsssccssssccsssssssscsscoess 83 15 1 The philosophy of model ouput eeseeeeseseeseesesssesseeseesresersseessrserssressessresseeseesreeseeseee 83 13 2 Processing model gutp t Seer nena an A E E a TE 83 16 Description of output file formats ssosscooesooessoecssecesocesocesoocesocsssecssocesocssoosssoesssecssocesossee 84 16 1 Observation well datasenter eran E a EAE EE Sa eo 84 16 2 Contouring groundwater heads ees ceesseceesceceececeeneeceseececseceeceeeeceeeeceeeeeeseeeeeneees 84 16 3 Groundwater heads in format to re start a simulation ss sssssssessseessesessseesseesssresseessee 85 16 4 RIVER flow gauging inosine ee is ER E e EEE E EEI E e EE 85 16 5 River baseflow accretion profiles sesssssesseesseesseesseessstessstesseesseesseesssessseesseesseesset 85 16 6 River baseflows in a format to re start a
134. tion is represented by negative values Spring flow m day Positive values represent flow of the aquifer negative values not possible 88 16 9 GLOBAL FLOW BALANCES Global flow balance information for the model is written to the file global out This output file contains flow balance data for a single time step only and is over written periodically during the simulation The frequency with which the file is produced is defined in the input file clock dat It is created after either every time step stress period or block or only for the final time step in the simulation It is always re written at the end of the simulation This file gives a water balance for the whole model over a time step An example file is shown in Figure 56 Information includes the total recharge to the model the total flow across its boundary the total abstraction the total downstream flow and anthropogenic input to each river the total outflow to leakage nodes and fixed heads the total change in storage over the last time step and the total spring flow These flow rates are summed to give a global flow imbalance figure which is written on the last line of the file GLOBAL FLOW BALANCE AT END OF 4 12 1974 TS SP BLOCK Total recharge 188750 m3 d Total boundary inflow 0 m3 d Total abstraction 32900 m3 d River 1 Downstream flow 7421 12 m3 d nthropogenic input 5000 m3 d 2 tream flow 40684 7 m3 d hropogenic input 32
135. tualisation of the multi layer well is shown in Figure 39 which shows a well pumping from layers 1 3 and 5 The aquifer nodes are linked to a single node that represents the borehole via a very high conductance connection This conductance should be set to a high value e g 10 tol0 m day a value of 10 m day is specified in the input file shown in Figure 40 The magnitude of this parameter can affect the rate of convergence of the solution Higher values will generally slow convergence but if too low a value is defined a satisfactory flow balance may not be achieved The flow balance can be checked by examining the output files zoomq3d out and multi_wells out The vertical connection between the aquifer nodes is unaffected by the implementation of multi layer wells and depends on the vertical conductance of the aquifer as specified by the user 65 pm Abstraction Multi layer well water p gt ae i s level ho Y Layer 2 tes Udy Cha QC Very high conductance o amp a bd er S s Qs Layer 4 Layer 5 Figure 39 Conceptualisation of multi layer well pumping from layers 1 3 and 5 10 2 2 Observation wells Groundwater heads are monitored over time by creating a file with the following structure The name of this file for example obswells dat is specified by the user in the input file zoomq3d dat see Section 14 2 The file has the format n start_block end_block Layer x y one for
136. turated thickness Finally the storage coefficient is set equal to the aquifer specific yield These features add to the approximations to which the model is subject While a quasi three dimensional model has numerous theoretical limitations for many practical problems it represents an acceptable solution There is a compromise between representing the complexity of real flow systems and the data and computational demands which a three dimensional model imposes 3 The numerical solution process 3 1 FINITE DIFFERENCE EQUATIONS ZOOMQ3D uses implicit finite difference approximations as the basis for its representation of the layered aquifer flow equation 7 4 as a T a S a q Dees F Lictow Ox ox Oy dy Ot To allow the approximation the aquifer is divided into grid of nodal points at which the groundwater head will be calculated The calculation proceeds from a known pattern of head values the initial condition through a series of discrete time steps The nodal groundwater head values at the end of a time step are all unknown Each term in the equation has a corresponding finite difference approximation with those involving flow through the aquifer using groundwater head values at the end of a time step By applying the finite difference approximations at each node a set of simultaneous algebraic equations is formed The solution to the equations provides the head values at the end of the time step The newly calculated values form t
137. undary of a refined grid Nodes of type 15 or Oxf in hexadecimal are conventional nodes based on a five point finite difference stencil Data on the third line of a node block relates to the position of the node with respect to the boundary If the first parameter is a b the node is located on the model boundary Otherwise it is inside the model domain and represented by an i The second parameter is the boundary node type shown in Figure 9 The third parameter is the relative area of the node For nodes inside the model boundary this is always 1 0 however this value can be either 0 25 0 5 or 0 75 if it is located on the boundary see Figure 9 21 T 5 grids dat Format of data Number of layers Comment line Number of model layers Layer types confined c or convertible v From top to bottom Comment line Layer type for each layer from top to bottom of model Read layer top elevations y n Comment line Character variable specifying if reading layer top elevations GRID DATA Comment line Number of grid levels followed by number of grids on each level Comment line start of grid data block separator Grid level number of subgrids number of nodes in grid i j of start point on boundary Number intervals in x amp y directions co ords of SW amp NE corners of grid Comment line node block separator i j x and y co ords of node node type Boundary node flag boundary node type nodal
138. ver bed thickness m All of the parameters can be altered by the user However the reach length should be considered fixed as it is defined by the distance between adjacent river nodes 52 Figure 28 a Influent river I o kwit n b Effluent river Groundwater head above the base of the river bed Z zor B but below river stage E Q S2 W L h h c Effluent river Groundwater head below base of the river bed Zs B Q E W Zen B h is the flow rate m day from the aquifer to the river is the vertical hydraulic conductivity of the river bed m day under effluent river conditions is the vertical hydraulic conductivity of the river bed m day under influent river conditions is the elevation of the bed of the river is the thickness of the river bed m is the width of the river m is the length of the river reach m is the head in the aquifer m and is the river stage m Formulation of river aquifer interaction under influent and effluent conditions 53 9 5 3 Initial river flows This file is created by ZETUP and referred to as initialflow dat in this manual It may be given any name providing this is entered into the input file zoomq3d dat The file contains information relating to the initial flow in the rivers at each of their nodes The format of the file is shown in Figure 31 based on the river shown in Figure 26 Only the parameter value
139. ware which can be used to produce river baseflow hydrographs 16 5 RIVER BASEFLOW ACCRETION PROFILES River flow accretion data is written to the output file named in zoomq3d dat for example accretion out The data is in a form suitable for the rapid production of accretion profiles using spreadsheet software This output file contains flow data for a single time step only and is Over written periodically during the simulation The frequency with which the file is produced is defined in the input file clock dat It is created after either every time step 85 stress period or block or only for the final time step in the simulation Each time it is written the previous data set is lost Accretion profiles at different times can be saved by specifying each node along the river section of interest as a gauging station in the relevant input file see Section 9 5 5 The output file is space delimited and has a simple format An example output file is shown in Figure 55 The number of rivers in the model is written on the first line A block of data then follows for each river Eleven columns of data are defined within each block which are separated by comment lines composed of a series of dashes Each row represents one node of the river The eleven columns contain the following data 1 River branch number River node number x co ordinate of river node m y co ordinate of river node m Distance downstream from upper
140. ween influent and effluent conditions The difference reflects the seepage force applied to the bed material and the associated increase in permeability when groundwater is discharging to the river The hydraulic conductivities are defined by the user in input file rivers dat The different relative positions of the river stage and groundwater head are shown in Figure 28 The appropriate vertical flow equation representing the interaction is presented next to each scenario 9 5 2 River input file This file is created by ZETUP as rivers out For input into ZOOM2D is must be renamed rivers dat It contains parameter information for the river nodes which make up each river in the model The file format is shown in Figure 30 This figure is based on the start of the rivers dat file used to construct the river shown in Figure 26 Each river node is described by a four line block of data The first line of the block is a series of dashes which are used to separate each group of river node information The second and fourth lines of the block should not be altered The following parameters are listed on the third line of the block i the river stage m il the river bed elevation m iii the channel width m iv the reach length m v the hydraulic conductivity of the river bed under effluent conditions m day vi the hydraulic conductivity of the river bed under influent conditions and m day vii the ri
141. wo data lines for each node in the grid Blank lines do not exist SUBGRID LEVEL 3 etc for nodes on this refined grid Figure 7 Example grids dat file and format of data 22 Direction Binary node type Decimal node type Hex node type Nodal location Figure 8 Node type parameter values used in ZOOMQ3 defined within grids dat a B Relative areas of 0 25 oe ed JL Relative areas of 0 75 a ne a L Relative areas of 0 5 K Figure 9 Values of character flag used in ZOOMQS3D to the specify boundary node type defined within grids dat 23 7 2 CONFINED UNCONFINED CONDITIONS Both confined and unconfined conditions can be simulated within each layer of the model This is achieved by specifying whether each node in the upper model layer is confined convertible or unconfined and whether each lower layer is composed of confined or convertible nodes The definitions of these three terms is as follows Confined nodes At a confined node the transmissivity and storage are fixed and independent of groundwater head Transmissivity is calculated using the expression T K z Zp T 0 for h lt z and the storage is defined as S S zr Zs S 0 for h lt Z where T is the transmissivity in the x or y direction K is the horizontal hydraulic conductivity in the x or y direction S is the storage coefficient L S is the speci
142. xample grids dat file eee eeeeeeeseeeeeteeeenteeees 20 Figure 7 Example grids dat file and format of data 0 ee eeceseceseeeeeecneecnteeeseeeenees 22 Figure 8 Node type parameter values used in ZOOMQ3 defined within grids dat 23 Figure 9 Values of character flag used in ZOOMQ3D to the specify boundary node type defined within OTIS dat sisien a a TE E S 23 Figure 10 Example aquifer map file for defining aquifer conditions in the top model layer falas see A EE E E Gussie E E E E 25 Figure 11 Lines 3 and 4 of input file grids dat for a two layer model eens 26 Figure 12 Flow chart of the cyclical transmissivity updating process when simulating unconfined AGUILe PS iieri sna a ait teas EEAS a E O gece ean sa ade bees 27 Figure 13 entry method dat file format ccc hogenccstestyer asaeesteensbeapienennsaiaeeteenteagieneanesceieest 29 Figure 14 a Example mesh composed of four grids and b representation of the grid hierarehyn 05 pide vats cas wcren seas inne a Oasis Bs Dena eases 9 ts ete Ses Aca an ads us ao Re 29 Figure 15 Example map file for the entry of spatial data within a layer oes 30 Figure 16 Example code file for the entry of spatial data within a layer oes 31 Figure 17 Example numeric data file for the entry of spatial data within a layer 32 Figure 18 Calculation of the vertical conductance between layers eescescceceeeerreeeeee 33 Figure 19 Lines 5 and 6 of input file g
143. y if simulations are long or many options are being explored 4 Capabilities of ZOOMQ3D 4 1 FEATURES OF ZOOMQ3D This section summarises the capabilities of ZOOMQ3D Each of these features is discussed in detail in the following sections of this manual 4 1 1 Multiple layers ZOOMQ3D can incorporate multiple layers of finite difference nodes The elevation of these layers can vary across the model and the base elevation of one layer can be higher than the top of the layer below it The separation of model layers simplifies the representation of groundwater systems that contain aquifers separated aquitards This because the flow through low permeability layers which is assumed to be vertical is represented by the vertical leakage term connecting two finite difference nodes within the upper and lower aquifer 4 1 2 Local grid refinement ZOOMQ3D incorporates a mesh refinement procedure which aids the solution of problems related to scale The density of finite difference nodes can be increased by adding successively finer rectangular grids in discrete areas of the model domain The mesh can be refined in separate areas and grids can be refined multiple times in the same location in order to zoom into a specific model feature for example an abstraction borehole or a river reach 4 1 3 Confined unconfined conditions Both confined and unconfined aquifers can be modelled At confined finite difference nodes transmissivity and storage are ind
144. ysically based model which can be compared with field information If there is a high degree of similarity between physical model and reality then the conceptual model can be treated with some confidence Numerical models provide information based on the physics of the supposed processes and are therefore the best approximation to a physical model Fundamental difficulties arise in constructing a numerical model which is going to be able to be close to the real aquifer Amongst them are recognising the true mechanisms and finding an acceptable numerical implementation The ability to look at behaviour on different scales is also important While a relatively coarse approximation based on a grid spacing of hundreds of metres may be acceptable for regional flow through a large expanse of relatively homogeneous aquifer this will not be adequate for small scale local behaviour Examples such as the response of an abstraction well or the representation of a small stream will not be dealt with accurately on a coarse mesh The process of model development and construction is iterative Components of the conceptual model are frequently found to be inadequate and require changes The inability to reproduce features from the real aquifer brings these inadequacies to light Change and the introduction of new processes are fundamental to the development process ZOOMQ3D is a numerical model which advances the art of model development on two vitally important f
145. zero under influent conditions i e when the groundwater head is below the elevation of the leakage node and to set it to a non zero value under effluent conditions An additional feature of leakage nodes is that is possible to adjust their vertical elevation during the simulation period Leakage nodes are defined in the model using the input data file leakage dat The format of this file is shown in Figure 23 The number of leakage nodes and their associated parameter values are defined first After this set of information data are entered to specify which leakage nodes move vertically during the simulation and how their elevations vary over time An example leakage dat file is shown in Figure 24 in which five leakage nodes are created of which the elevations of three move during the simulation Number of leakage nodes Layer X Y Elevation Cz Effluent Cz Influent One line per leakage node Comment line Number of leakage nodes for which elevation changes over time Comment line Layer X Y One line per moving leakage node Comment line Number of blocks of elevation data Comment line For each block block no then 1 line of nSP elevations m for each moving leakage node Figure 23 Format of leakage dat 45 8000 3250 10 9000 3000 10 9250 3000 10 9500 3000 TOs 9750 0 3000 0 EO 0 0 Number of nodes for which elevation changes during simulation Layer X and Y co ordinate of each m

Download Pdf Manuals

Related Search

Related Contents

広報きつき 平成23年7月号 [PDFファイル／3.41MB]  Fungicida Concentrado emulsionable (EC)  PNY All in One Reader  Caméra couleur numérique  Benutzerhandbuch TC7200  Training Syllabus to Instruct/Prepare for the ASE Transit Bus Diesel    ISTRUZIONI PER L`USO per i plotter da taglio Secabo mini  un peu de volumes dans ce monde de brutes  docass247-12-manuel - Saint-Cricq  

Copyright © All rights reserved. Failed to retrieve file