ARIANE User Manual - Espace d'authentification univ
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1. A 7 3 13 22 September 2005 ARIANE User Manual 1 Spirit of the Lagrangian approach A crossing time in the zonal direction can only be obtained if F 1 and F 0 have the same sign and this implies F 0 in the cell If this condition is not verified for F the three dimensional non divergence of the velocity field ensures that at least one other direction satisfies it One can assume that this condition is checked in the zonal direction The pseudo time s is then related to the transport F by s AF In F Fy A 8 The crossing time in this direction corresponds to the moment when the transport reaches the exit face value F 1 As AF In Fo AF Fo A 9a or if AF 0 its limit when AF 0 As 1 Fo A 9b As previously mentioned at least one of the three crossing times is to be defined through such a formulation The shortest one defines the traveling time in the considered cell Thus if the particle first attains the zonal extremity of the cell its positions on the meridional and vertical axes are deduced from the equations of the trajectories using s As Computations are done for the next cell with a starting point equal to the exit point of the previous one and the age of the particle is regularly updated summing the expressions A 9 obtained for As e Quantitative diagnostics Quantitative results are obtained by increasing considerably the number of particles possibly up to several millions2. etc We assume now that the three components of the transport vary linearly between two opposite faces of one individual cell This hypothesis respects the local three dimensional non divergence of the flow It means that within a given cell F depends linearly on i G depends linearly on j and H depends linearly on k where i j and k are considered as fractional within the cell i e as non integer In the cell extending from i 0 to i 1 one can write for instance for F F r Fo r AP A 3 with r 0 1 and F 0 Fo and where AF stands for F 1 F 0 One can also write the equation linking position and velocity namely dx dt U for the transport drids F A 4 with s e1 amp e3 l tand x e r With some adequate initial conditions for example r 0 for s 0 one can combine A 3 and A 4 and find the time dependency of r within the considered cell r Fo AF exp AF s 1 A 5a If AF 0 only the limit of A 5a for AF gt 0 is to be considered r Fos A 5b Similar relationships are of course obtained along both other directions Since these expressions only apply in one individual cell one also has to determine the time when a given particle switches to another cell or equivalently the time when r is equal to its exit value here r 1 Time dependency is obtained from a different writing of A 4 ds F dr A 6 Using A 3 one obtains the following expression for ds ds F AF dF
3. following the technique developed by D s 1995 and Blanke and Raynaud 1997 Due to water incompressibility one given particle with an infinitesimal section is to conserve its infinitesimal mass along its trajectory As a current can be entirely determined by the particles that compose it with well defined characteristics position velocity and other scalars the transport of a given water mass can be calculated from its own particles and their associated infinitesimal transport For most of the quantitative diagnostics run with ARIANE the area of each grid cell for a given instant and with a given transport 7 is described with particles whose N initial positions are homogeneously distributed in space and time with lagged departure times The number of subdivisions along each direction N satisfies T N lt To A 10 where To is the prescribed maximum transport associated with a single particle The total number of particles used to describe the water mass is the sum of the N s over the relevant grid points of the section and the total number of instants as for instance the 12 months of a climatological year knowing that a homogeneous space time distribution of particles is used in each sub gridcell Blanke et al 1999 The best positioning of the particles over an initial section is indeed the one that gives the highest accuracy in the computation of the transports associated with the circulation for a reasonable number
4. input output files I will have also to familiarize myself with the fact that the quantity Ak is defined as negative in the core of the calculations done by ARIANE but that fk the initial vertical position is positive Having modified the FORTRAN code I need to recompile it Then I run the new experiment go EXPERO4 I look at the results given by file stats qt Destinations 0 and 1 present now distinct values of transport Destination 0 sums up the transport which recirculates towards the initial section in the same hydrological range as the one introduced in criter0O h hence the name meanders Destination 1 on the contrary accounts on the same section for the transport transmitted converted into another hydrological class I see finally that another destination is mentioned It has the name Criter1 with an index equal to my total number of control sections plus 1 This is the hydrological interception carried out by ARIANE on the particles that encountered temperatures larger than 16 C before reaching any of the final sections The statistics minimal and maximum values for each field and each destination for initial and final positions enable me to check that my hydrological criteria were indeed respected by ARIANE 16 Although I may test only the parameter of time positioning this process is not at all easy and may even be tricky 17 The surface of the ocean thus corresponds to the value hk while th
5. jt lt j 1 e for a reference on the U V grids i lt iu lt i 1 andj 1 lt jv lt j The decimal coordinates then satisfy it iu 0 5 and jt jv 0 5 7 13 22 September 2005 ARIANE User Manual 2 Things I should know before I compile ARIANE Wijk jkt 1 Wiijik 2 Indexation system used on the vertical Decimal coordinates of the star satisfy e for a reference on the T grid k lt kt lt k 1 e for a reference on the U V grids k 1 lt kw lt k 2 The decimal coordinates then satisfy kt kw 0 5 e key_sigma should be used if I want ARIANE to calculate its own density field at reference level zsigma from the temperature and salinity read on file Otherwise ARIANE will have in central memory the density field that is read on file e key_approximatesigma must be used only if I want ARIANE to use the density array in central memory for density interpolations Indeed ARIANE prefers by default not to interpolate directly density but to recalculate it from locally interpolated values of temperature and salinity using its own density equation and reference level zsigma e key_nointerpolstats is used only if I prefer to use of the nearest tracer gridpoint value in tracer statistics for initial and final positions instead of a quadri linear interpolation of several neighboring gridpoints e key_partialsteps is to be used to accommodate partial steps the way they are implemented in OPA e key_unitm3 replaces the st
6. should know before I compile ARIANE 2 Things I should know before I compile ARIANE I must edit the namelist and adjust each variable to my specific needs Here are the most important variables e imt jmt kmt and Imt the dimensions of the grid three space dimensions one time dimension must be correct and consistent with the fields prepared for ARIANE e tunit defines a convenient unit of time in seconds usually one day 86400 e ntfic is the sampling time in number of tunit for the available velocity and tracer fields Therefore the product ntficxtunit must give in seconds the period covered by each velocity and tracer time sample e zsigma gives the reference immersion in meters used by ARIANE in particular in the output files for the recalculation if needed of density The unit is Oon where n corresponds to the depths expressed in thousands of meters nmax maxsegm and maxsect allow the maximum dimensioning of arrays used by ARIANE in its Lagrangian calculations An error message in the course of execution will normally inform me of their possible bad calibration and I will then have to increase their value Some boolean keys can be used to activate a few additional ARIANE functionalities e key_alltracers should be used true value if I want to activate diagnostics related to tracers Otherwise the Lagrangian tracing will only deal with kinematics e key_periodic and key_jfold allow me to inform ARIANE about
7. that the destination 0 corresponds geographically to the destination 1 namely to my initial section 14 The coordinates given for the particles are not geographical coordinates but grid indices expressed on the mesh of my domain just like what I used for the initial positioning of my particles in my first qualitative experiment 15 As I need here to use two distinct immersions to define my density criteria I cannot work directly with the model array rr corresponding to the density field recomputed by ARIANE from the parameter zsigma given in param I note that the function sigma enables me to define specific hydrological tests in criter 012 h while the parameter zsigma will condition the whole set of density diagnostics provided by ARIANE at the end of the execution in files stats qt final _pos gt andinit pos qt 12 13 22 September 2005 ARIANE User Manual 3 After a successful compilation reaching any of the geographical sections defined in segments I edit criter1 h and replace the instruction criter FALSE with t zinter tt hi hj hk hl criterl t gt 16 It is also possible to introduce in one of both criteria criter0 horcriter1 h a test on the geographical position of the particle I will use parameters hi hj and hk being careful that they are defined on the model velocity grid whatever the convention I could adopt on the format of the coordinates used for ARIANE
8. zonal grid periodicity and meridional grid folding respectively as introduced in the OPA model e key_computew asks ARIANE to diagnose the vertical velocity by the vertical integration of the horizontal divergence from the ocean floor where the vertical velocity is expected to be 0 to the surface In this case I may obtain a non zero vertical velocity residual and may need to use a horizontal lid to intercept evaporating particles see the discussion below If key_computew is false I understand that ARIANE will use the vertical velocity provided in the input velocity files and that this vertical velocity must balance exactly the convergence of the horizontal transport e key_ingridt and key_outgridt may be used to modify the convention used by ARIANE for reading and writing spatial coordinates respectively I must understand that ARIANE used by default its internal system of coordinates related to the velocity gridpoints of a C grid I may force the system of coordinates to be referenced to tracer gridpoints The latter system may be easier to master for me but it is not the standard ARIANE reference tvi j iji Iyi j JEGELj I I I I PELD TARD UG L fij I I I I E F i Lj Fi Witt Ire I I A onc TD IUD E DS Jie I 5 3 Indexation system used on the horizontal Decimal coordinates of the star satisfy e for a reference on the T grid i 1 lt it lt i 2 andj lt
9. ARIANE User Manual I am to work with ARIANE Here follow some indications which can make easier its implementation and use B BLANKE and N GRIMA Laboratoire de Physique des Oc ans Brest France Contact blanke univ brest fr 1 13 22 September 2005 ARIANE User Manual 1 Spirit of the Lagrangian approach 1 Spirit of the Lagrangian approach a Introduction The ARIANE utility developed at LPO makes it possible to describe from a Lagrangian point of view the dynamics simulated by an Ocean General Circulation Model OGCM as OPA Such diagnostics are based on the calculation of multiple trajectories in the modeled velocity field with an advection scheme particularly fitted to the three dimensional nature of the oceanic circulation Blanke and Raynaud 1997 and to an effective description of a water mass from the particles which form it D s 1995 Within the framework of the European program TRACMASS June 1998 May 2001 these analyses were applied to various classes of OGCM an isopycnic and three z coordinate models over distinct domains the Mediterranean Sea and the global ocean with various spatial resolutions One of the key problems of the Lagrangian tracing of ocean water masses is posed by the characteristic times of large scale advection The Lagrangian trajectories must be integrated for sufficiently a long time to describe the full range of the movements at a basin or global scale This means several
10. NE It is only a parameter used for graphic purposes 9 13 22 September 2005 ARIANE User Manual 3 After a successful compilation Thus on each line I find the following information index of the particle 0 stands for land gridpoints x y z time in number of cycles covered by the velocity field provided to ARIANE i e generally in years T S on I note that I have given to ARIANE initial coordinates on the model grid mesh indices but that the result of the qualitative experiment traj q1 is directly expressed in the form of geographical and time coordinates longitude latitude depth age Everything works perfectly for the time being and I choose to use the result of this first run to test backward calculations I will start from the final position obtained at the end of the first experiment and I will check if I succeed to go back to the same initial position as previously I use for this new experiment the binary archive full precision of the final position of the first experiment I copy the file final sav in another directory for example EXPERO2 under the name initial bin and I specify now the code BIN instead of NOBIN in param In this same file I use from now on the code BACKWARD As I did not modify the FORTRAN code itself I do not need to compile the code again and I use the script go directly by specifying the name of the new experiment i e the directory where I copied the initial bin fi
11. al position The file for final positions final pos qt has a similar structure and also shows the elapsed time in years followed by the index of the section of arrival according to the convention adopted in file segments Files prefixed with xy yz ou xz_ include the information necessary to the graphic representation of the mass transfers achieved towards each section I will be able to read these files with a utility like IDL and to use existing scripts for a fast and easy visualization of the results in the form of streamlines I can now determine tentatively a better value for parameter Tro The first experiment run with Tro 10 m s gives me a coarse estimate in sverdrups of the mass transfers between my initial section and my final sections I can thereafter take for Ti roa value roughly equal to the precision I wish to obtain on these transfers for example 10 Sv i e 10 m s I decide to run a new quantitative experiment and activate new functionalities in ARIANE I take the same domain of study but I choose to use a different section as a starting section Insofar as mk seg already did a clean work I only need to edit file segments to allocate number 1 initial section to the segments defining the new section I want to use for the initialization of the particles for example numbered 3 in the former experiment and to give number 3 to the former initial section simple swap of indices I also choose to refi
12. ample 10 for 10 days and the total number of positions I want for example 20 if I want the calculation of a 200 day trajectory As I want to include in the output file the surface mask of the model land gridpoints I use the code MASK Lastly I do not take care of the last parameter of file param since it deals only with quantitative experiments I run the program with script go providing the name of the experiment which will denote also the name of the directory in which the results will be stored lt prompt gt go EXPERO1 The result land gridpoints and successive positions for particles is in the ASCII file traj ql where one line represents one position I am careful not to let truncated lined at the end of this file There must be as many lines not starting with as initial positions Not more nor less This fifth parameter appears only for consistency with the format used in the quantitative experiments run with ARIANE I initialize it with an arbitrary value typically 1 0 while being conscious that it will absolutely not be used in qualitative calculations 4I do not initialize my particles exactly on the corner of a temperature gridcell insofar as the velocity is imperfectly defined there An initial positioning exactly at the center of T gridpoints often proves judicious gt As the calculations are analytical this parameter does not affect the precision of the trajectories calculated by ARIA
13. andard output unit used for transports sverdrups by m s e key_eco reduces a lot some calculations made by ARIANE and should be used every time I am not interested in plotting separate streamfunctions for separate final sections I must understand that it does not modify the trajectory calculations but that it has an impact on the information stored on some of the output files that will be used for subsequent diagnostics 8 13 22 September 2005 ARIANE User Manual 3 After a successful compilation 3 After a successful compilation a Qualitative experiments Everything seems ready for a first experiment I will thus try first the calculation of an individual trajectory I add the initial coordinates of my particle to the end of file initial positions Not less than five values three spatial indices one temporal index and a fifth parameter that I can choose right now equal to 1 0 define an initial position The format of the spatial indices must respect the convention I may modify with key_ingridt By default the frame of reference uses the three velocity grids U V and W I am aware that lines of comments starting with in file initial positions refer to this coordinate system For a spatial frame organized on the tracer grid 7 the positioning strategy is intuitive integer coordinates correspond to a position at the center of the tracer gridcell bearing the same indices i j and k I will use non integer float indi
14. ces to introduce any shift with respect to this central position A spatial frame organized on the velocity grids matches the internal calculations performed by ARIANE but requires use of three references one along each direction The format used to position my initial particle in time is also described in the comments of file initial positions An integer value corresponds to the center of the period covered by the corresponding sample Thus if I have a monthly velocity speed mt 12 a value 4 0 of the time parameter will initialize the particle at the date of April 15 On the other hand I would specify the date of December 31 by using the value 12 5 or 0 5 I can require constant depth calculations for trajectories i e without using the vertical component of the velocity by putting a minus sign before the initial vertical index In file param I specify that I want a qualitative experiment full monitoring of the successive positions of one or several particles code QUALITATIVE for the study of their fate code FORWARD I do not use for the moment the possibility to restart from the results of a former experiment and my initial positions are actually provided by file initial positions Therefore I thus use the code NOBIN After having defined a convenient unit of time in seconds for example 86400 for a day I indicate the interval I want between two successive position outputs on file for my particles for ex
15. e first tracer levels correspond to hk 5 hk 2 5 and hk 3 5 respectively This minus sign appears only in ARIANE internal calculations and thus in the portions of code related to interception criteria but not in the input output files 13 13 22 September 2005
16. e various internal and surface forcing functions proved to be necessary for the development of reliable Lagrangian analyses b Advantages of a C grid The equations of the OPA model are discretized on a C type grid Arakawa 1972 This mesh system proves to be ideal for the analytical calculation of successive streamline segments Blanke and Raynaud 1997 from a time sampled velocity field with period AT This Lagrangian integration scheme respects the local conservation of mass and thus defines a judicious tool to carry out water mass tracing The technique lies on the insemination of a given water mass considered on a geographical section by tens or hundreds of thousands of individual particles D s 1995 Blanke and Raynaud 1997 and by assigning to each of them an infinitesimal fraction of the incoming transport For a selected set of final destinations other geographical sections or the satisfaction of a hydrological criterion infinitesimal transports can be combined and allow the evaluation of directional transports water flow between two given sections c Individual trajectories The analytical calculation of streamlines on the model grid for successive AT periods over which the velocity speed is assumed to remain constant offers several advantages This method for computing trajectories is both fast and accurate it only calculates positions on the edge of individual grid cells and it fully respects the local three dimen
17. ean mass transfers Journal of Physical Oceanography 31 1623 1642 Blanke B S Speich G Madec and R Maug 2002 A global diagnostic of interior ocean ventilation Geophysical Research Letters 29 10 1029 2001GL013727 Blanke B M Arhan A Lazar and G Pr vost 2002 A Lagrangian numerical investigation of the origins and fates of the salinity maximum water in the Atlantic Journal of Geophysical Research 107 10 1029 2002JC001318 Blanke B M Arhan S Speich and K Pailler 2002 Diagnosing and picturing the North Atlantic segment of the global conveyor belt by means of an ocean general circulation model Journal of Physical Oceanography 32 1430 1451 Blanke B S Speich A Bentamy C Roy and B Sow 2005 Modeling the structure and variability of the southern Benguela upwelling using QuikSCAT wind forcing Journal of Geophysical Research 110 doi 10 1029 2004JC002529 Friocourt Y S Drijfhout B Blanke and S Speich 2005 Water mass export from Drake Passage to the Atlantic Indian and Pacific Oceans A Lagrangian model analysis Journal of Physical Oceanography 35 1206 1222 Izumo T J Picaut and B Blanke 2002 Tropical pathways equatorial undercurrent variability and the 1998 La Nifia Geophysical Research Letters 29 10 1029 2002GL015073 Radenac M H Y Dandonneau and B Blanke 2005 Displacements and transformations of nitrate rich and nitrate poor water masses in the tropical Pacific durin
18. g the 1997 El Ninfio Ocean Dynamics 55 34 46 Rodgers K B B Blanke G Madec O Aumont P Ciais and J C Dutay 2003 Extratropical sources of equatorial Pacific upwelling in an OGCM Geophysical Research Letters 30 10 1029 2002GL016003 Rodgers K B O Aumont G Madec C Menkes B Blanke P Monfray J C Orr and D P Schrag 2004 Radiocarbon as a thermocline proxy for the eastern equatorial Pacific Geophysical Research Letters 31 Speich S B Blanke and G Madec 2001 Warm and cold water routes of a GCM thermohaline conveyor belt Geophysical Research Letters 28 311 314 Speich S B Blanke P De Vries K D s S Drijfhout A Ganachaud and R Marsh 2002 Tasman leakage a new route in the global ocean conveyor belt Geophysical Research Letters 29 doi 10 1029 2001GL014586 Valdivieso Da Costa M and B Blanke 2004 Lagrangian methods for flow climatologies and trajectory error assessment Ocean Modelling 6 335 358 h Cited references 5 13 22 September 2005 ARIANE User Manual 1 Spirit of the Lagrangian approach D s K 1995 Inter ocean exchange of water masses Journal of Geophysical Research 100 13499 13514 Arakawa A 1972 Design of the UCLA general circulation model Numerical simulation of weather and climate Tech Rep 7 Dept of Meteorology University of California Los Angeles 116 pp 6 13 22 September 2005 ARIANE User Manual 2 Things I
19. hundreds even thousands of years whereas direct OGCM simulations seldom exceed a few tens of years because of CPU time constraints or drift problems One way to by pass this difficulty is the development of diagnostics run from the archive of the model fields and associated tracers with repeated loops over the archived period usually a climatological year This offline approach is tempting because of its flexibility but it raises nevertheless two major questions e What is the impact of unresolved frequencies in the archived output on the subsequent offline trajectory calculations and other Lagrangian diagnostics e Can one be satisfied with such an approach in the case of an archive limited to a fraction of a simulation presenting signs of drift i e an imperfect adjustment to the surface forcing or with strong interannual variability This last point could be addressed by our TRACMASS collaborators and does not concern this presentation The contribution of LPO to the methodological section of the same TRACMASS project allowed us to study the first point in a model with a coarse horizontal resolution the ORCA2 version of the OPA model with a 2 zonal resolution and without drift as it was run a in robust diagnostic mode Valdivieso Da Costa and Blanke 2003 We could show that within this framework of climatological modeling at coarse space resolution a monthly archive of the velocity field sampling appropriately the seasonality th
20. ion either 4 13 22 September 2005 ARIANE User Manual 1 Spirit of the Lagrangian approach the vertical zonal or meridional axis we obtain a two dimensional non divergent field that we study by means of a streamfunction For a vertically integrated transport or a zonally integrated transport we define y and Yz respectively with Oi Xk T OW dy Ty OP 2k Tz Op 2 T A 12 and contours of p or py provide an adequate view of the movement in projection onto the selected plane As contours cannot cross each other by construction of a streamfunction the more accurately and selectively we define the initial conditions of the particles the more similar the contours are to actual projections of trajectories The choice of a horizontal projection usually turns out judicious but an additional plane of projection or plots of selected individual trajectories may be helpful in plotting the precise movement of the water mass g LPO publications related to the use of ARIANE Blanke B and S Raynaud 1997 Kinematics of the Pacific Equatorial Undercurrent a Eulerian and Lagrangian approach from GCM results Journal of Physical Oceanography 27 1038 1053 Blanke B M Arhan G Madec and S Roche 1999 Warm water paths in the equatorial Atlantic as diagnosed with a general circulation model Journal of Physical Oceanography 29 2753 2768 Blanke B S Speich G Madec and K D s 2001 A global diagnostic of oc
21. le lt prompt gt go EXPERO2 With a precision within my machine accuracy I check that I find the same trajectory than previously in traj q1 but calculated backward The code BIN forces the restarting of all the particles present in initial bin IfI have several positions in this file for example if initial bin is taken equal to the file final sav of a qualitative experiment using several particles I can go on with a qualitative experiment starting from only a subset of these positions by using the code SUBBIN instead of BIN in param and by listing line after line in an additional file named subset the indices of the particles that I want indeed to re use b Quantitative experiments Since the qualitative experiments do not pose specific problems I will run now a first quantitative experiment I activate the code QUANTITATIVE in param instead of QUALITATIVE and I go back to mode FORWARD I reactivate the code NOBIN insofar as my quantitative experiment will not use the result of an experiment previously carried out The time parameters in param control only the sampling of the individual trajectories and will not be used by ARIANE unlike in the qualitative mode Consequently I ignore them and I jump directly to the last parameter it defines the precision of the quantitative experiments In order to limit the computing time I use the lowest possible precision by inflating artificially the maximum value of transpo
22. ne the definition of the initial positions by asking ARIANE to keep only the initial particles corresponding to a temperature warmer than 15 5 C a density o4 lower than 45 9 and a density o2 larger than 45 84 Therefore I edit the piece of code criter0 h and I replace the default criterion criter0 TRUE by the following FORTRAN lines t zinter tt hi hj hk hl s zinter ss hi hj hk hl r2 sigma 2000 s t t gt 15 5 AND r2 gt 45 840 AND r4 le 45 900 r4 sigma 4000 s t criter0 I notice the use of the function zinter that allows a fine interpolation trilinear in space and linear in time of the tracer fields onto the position of the particle given by hi hj hk and hl and of function sigma that calculates density at a given reference level from known salinity and temperature values I also want to intercept during the Lagrangian integration the particles that will see their temperature warming beyond 16 C This hydrological interception will be done if necessary before 13 I check that the transfers to each final section are expressed in sverdrups and use the same numerical labeling as the numbering that I used to define my sections in file segments A code 0 meanders appears next to a code 1 section I will discover soon when I use of a hydrological criterion on the initial positions the reason for this distinction I remember for the moment
23. of initial positions A measurement of the accuracy is the difference between section to section transports computed for a stationary velocity field with both forward and backward integrations as both transports are virtually equal Constant number of particles by grid cell and spatially homogeneous distributions are not satisfactory because they may use too few many particles to describe regions of weak slow currents A sophisticated approach would distribute particles so that they have the same transport thus grouping them in regions where the velocity is the highest f Lagrangian mass streamfunctions We compute trajectories for all the particles and sum algebraically the 7 on each junction of two model gridcells on the velocity grid points of the staggered C grid Arakawa 1972 Northward and eastward movements are counted positive while southward or westward movements are counted negative We obtain a three dimensional transport field that corresponds to the flow of the water mass in study within the domain of integration of the trajectories As one particle entering one model grid cell through one of its six faces has to leave it by another face the transport field exactly satisfies 0 T 0 7 OT 0 A 11 where T T and T designate the directional flows in sverdrups in the three directions and where i j or k refers to the grid index for the three axes Integrating this field along a selected direct
24. or discretizations in the OPA model to compute analytically trajectories from model outputs The algorithm calculates true trajectories for a given stationary velocity field through the exact computation of three dimensional streamlines Under the assumption of stationarity such streamlines indeed represent trajectories of particles advected by the given velocity field The three components of the velocity are known over the six faces of each cell The nondivergence of the velocity field then ensures continuous trajectories within this cell We develop here some equations with the tensorial formalism used in the OPA model Marti et al 1992 which allows a more general approach than a simple Cartesian view with for instance the description of a distorted grid over the sphere Using the same notations as Marti et al 1992 the divergence of the threedimensional velocity field V U V W is expressed as AV b Kez e3 U dfe es V Axle e W A 1 where n i j or k refers to the grid index for the three axes n refers to the corresponding finite difference e1 e2 and e are the scale factors in the three directions computed at each velocity grid point and b is the product e e2 e3 computed at the center of a given cell temperature grid point For any choice of the grid the non divergence of the flow now simply writes as F 0 G 0 H 0 A 2 where F G and H designate the transports in the three directions with F ez e U
25. r in the immediate vicinity of a problem that is found I must redo the construction of this file by correcting it the best I can With determination I end up with a clean output no more error messages and I copy the result namely the coordinates of the segments calculated by mk seq after the lines of comments of file Sseqments I introduce an explicit label for each section instead of section 2section and possibly add a lid as an additional horizontal section of control in order to intercept the particles feeling a vague desire to evaporate in the atmosphere For this last section I vary i from 1 to imt j from 1 to jmt and I choose kt and kt2 equal to kt0 0 Lastly I check in criter0O h and criterl1 h that the activated hydrological criteria are those I want For a first test I may find easier to activate standard values criter0 TRUE and criterl FALSE I will discover later how to use these criteria more cleverly My quantitative experiment is ready to run I type go EXPEROS after compiling the code if ever I modified the FORTRAN code In result I find the usual files init sav and final sav containing in a binary format the initial and final positions of all the particles used in this quantitative experiment I look immediately at the contents of the ASCII file stats qt to find the intensity of the mass transfers diagnosed from the initial section towards each final section as well as elementary sta
26. rt Tro in m s that may be associated with each particle I use 10 as recommended I will be able to refine my results thereafter by reducing this value I can obtain a trajectory shorter than what I explicitly asked in param if ever my particle is intercepted by ARIANE on the edges or at the surface of the domain covered by the grid In this case I will not have any binary archive of the initial and final positions of this particle files init sav and final sav 7 Insofar as I use the code BIN the content of the file initial positions will be ignored as ARIANE will use the position given in intial bin to start the calculation of the trajectories 8 In a SUBBIN configuration I must introduce the indices in subset by order ascending using for example the UNIX command sort n Otherwise I am likely to see ARIANE blunder badly in the selection of my particles 10 13 22 September 2005 ARIANE User Manual 3 After a successful compilation The usual purpose of a quantitative experiment is the evaluation of the mass transport established between an initial section of the domain and final interception sections For this reason I must define for ARIANE a closed sub volume within my domain of study whose simplest formulation is that of a right angled parallelepiped Such sections are defined in the form of segments forming vertical planes in the Ox i it to ib j jto k kt to kt or Oy i ito j jt to jt k kt
27. sional non divergence of the flow The method is Tracing the water masses of the North Atlantic and the Mediterranean 2 13 22 September 2005 ARIANE User Manual 1 Spirit of the Lagrangian approach flexible too and backward integrations can be performed to track the origin of a given current insofar as calculations do not involve diffusive phenomena By making the assumption of a linear variation of each component of the velocity speed along each corresponding direction elementary relations are written to describe the trajectory equations along the three axes The integration in time of these equations allows binding each co ordinate x y or z to time inside each model gridcell Crossing times in each direction are evaluated independently by imposing as a possible final position each of the six sides of the gridcell The minimum of these estimates gives the exact crossing time and allows the accurate calculation of the final position on the exit side d Detailed calculations Blanke and Raynaud 1997 Usual ways to compute trajectories from GCM outputs involve first the interpolation of the three dimensional velocity at the location of a given particle then the advection of this particle in the direction of the current Such methods require accurate interpolation and advection schemes to minimize possible cumulative errors in the computation of the trajectories In the present study we take advantage of the C grid used f
28. tistics The initial section is also used as a section of interception in order to diagnose any possible recirculation 10 A correct orientation of the segments is imperative for the initial section and optional but recommended for the other final sections The convention for orientation a positive or negative sign of jto itoor kto is described in the comments given in file segments 1 Unlike ARIANE the mkseg utility does not handle currently the condition of meridional folding as activated for instance in the global version of the OPA model Like for the file initial positions I take care not to introduce truncated lines at the end of this file and I use as many lines as the number of segments I want to define 11 13 22 September 2005 ARIANE User Manual 3 After a successful compilation related to the initial and final positions participating in each transfer I do not pay too much attention to the very first line of file stats qt which informs me about a pseudo total transport before normalization by the time dimensioning parameter Imt I find in file init pos qt the whole set of initial positions with an ASCI format Each line corresponds to one particle and I recognize in that order spatial positioning on the grid tracer or velocity I chose time positioning with a convention identical to that defined in initial positions transport allotted by ARIANE and tracer values interpolated onto the initi
29. to kt2 directions or horizontal planes i it to ib j jt to jt k kto I will build my sections with such segments I will assign to each section a sequence number with 1 corresponding with the section where the particles will be initialized I will use a proper orientation for each of them to inform ARIANE about the localization of the interior and the outside of the domain of study I will put this information at the end of file segments I can use the utility mkseg to obtain a first fast and reliable definition of segments I run program mkseg0 I open the output file segrid with a suitable text editor so as to visualize in a convenient way the integrality of the domain I define by hand the sections I want to use by replacing ocean gridpoints by an appropriate section index I make sure that the segments related to a same section have a length larger or equal to 2 gridpoints I am careful to define a closed domain limited by section indices or by land gridpoints I end this step by putting a sign on an ocean gridpoint located inside the active domain This hot spot will allow mkseg to differentiate the interior and the outside of my active domain and to give a correct orientation to each segment Irunmkseg and I sort the output for a better legibility mkseg sort In the event of mistakes while editing segrid some error messages might be returned and in file segrid a star should appea
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