User guide for 1+1D Var shallow water model
Contents
1. code Source code for assimilation scheme exec Default directory where code is executed 3 Running an assimilation 3 1 Microsoft Once you have a project set up inside the compiler s development environment simply click build or compile and link then run 3 2 UNIX The script to run the assimilation is called Unix_Compilation_script txt and is found at the top of the new directory structure To run the script simply type Unix_Compilation_script txt from the command line It may on some systems be necessary to run the command dos2unix Unix_Compilation_script txt or a similar command first 4 Input Files Assimilation Variables and Namelists You are provided with two assimilation versions which use different input data and generate different output The input variables can be found in the files Case_1 vars_user_mod_test1 f90 and Case_2 vars_user_mod_test2 f90 The output from both of these examples has also been stored in these directories When a new version of the assimilation is run it is recommended that you edit a copy of one of these files and create a new directory to store it and the new output files in There are other input files found in the directory data_in but these should not be changed The vars_user_mod f90 files store all of the input data in namelists the variables are listed below a default value is in brackets Namelist amp general This n2. found in the directory plot There are four routines conv m This routine plots the cost function and gradient convergence for a given run using the costfn dat output file The user should set the variable data_dir at the top of the routine to the directory of where the output files of the run are held and the name of the costfn dat file to be read The routine is then called using the command conv N where N is the number of lines in the costfn dat file written out during the minimiza tion process This number is printed out at the end of the corresponding output dat file conv2 m This routine works in exactly the same way as conv m but allows the convergence of two runs to be compared for example one with a TLM and one with a PFM The user must now set two directory paths at the top of the routine data_dir and data_dir2 and the routine is called using the command conv M N where M and N are the numbers described above for the respective runs plotanal m This routine plots the truth background and analysis at various times throughout the run The user must set the following options at the top of the routine e number_of_times The number of output times to plot e times A vector consisting of the output times to plot Units time steps e data_dir Full pathname of data directory The name of the analysis file also needs to be specified The output consistes of two figures Figure 1 shows a comparison of the truth back
3. User guide for 1 1D Var shallow water model Amos S Lawless The University of Reading This document provides brief documentation to run simple variational assimila tion experiments on the 1D shallow water model with no rotation This system is essentially a simple 4D Var system but has just one space dimension plus a time dimension 1 Setting up the system 1 1 Microsoft You are given a compressed folder SW_norot zip copy it to the place you want your project to live right click on the file and select Extract All then follow the instructions in the WinZip wizard If you do not have WinZip then it needs to be downloaded and installed It is recomended that you use a compiler with an inter grated development environment for example Salford A free version of Salford F95 can be downloaded from www silverfrost com 32 ftn95 ftn95_personal_edition asp If you are using Salford then the Fortran project is already made for you simply open the file my_SW ftn95p in the top level of the new directory structure If you are using a different environment then you will have to select all f and f90 files in directories minim Model fort Model PFM Model PFM_Adj Model TLM and var code and add them to a new project 1 2 UNIX Copy the file SW_norot zip into the directory under which you want to create your shallow water assimilation and unzip the file with the unzip command Note that this will create a directory called SW_norot
4. amelist controls the timing information for the assimilation and forecast x_len Number of grid points in domain 1000 problem number Choice of initial set up 1 Erbes data 2 Houghton and Kasa hara data 3 Read in dataset 3 delta_x Model spatial step 0 01 timestep Model time step 9 2D 3 number_of_assim_timesteps Number of assimilation time steps 250 number_of forecast_timesteps Number of forecast time steps 250 model_error Include error in all model runs except the truth where the model error is given by halving the size of the orography 0O Perfect model 1 model error 0 Namelist amp model This namelist controls the running of the numerical model linear_model Linear model used in inner loop 1 Tangent linear model 2 Per turbation forecast model 1 sl iterations Number of iterations for departure point calculation 3 interp_scheme Interpolation for semi Lagrangian scheme 1 Cubic Lagrange 2 Lin ear 1 solver_diag_level Level of output diagnostics for solver 0 None 1 Residual norm 2 Maximum and minimum values 1 solver_max_iterations Maximum number of iterations for elliptic equation solver in model 50 solver_tolerance Tolerance for convergence of elliptic equation solver within model 1 0D 8 alpha_1 alpha_2 beta_1 beta_2 Time weighting parameters for semi implicit scheme 0 6 alpha_1p alpha 2p Extra time weighting paramteres for PF model 0 6 phi_bar Basic state in nume
5. dient is less than this tolerance 1 0d 6 mach_accuracy Estimate of machine accuracy used in CONMIN routine 10 D 20 Namelists amp diags and amp luns The variables in these namelists set up the output files and so in general should not be changed The only one which may be of use is the variable L_gradient_test in the namelist amp diags If this is set to true then the gradient test is run instead of the assimilation The default is false 5 Output Files The output data files used are found in the directory data_out and their apperance in the code is in the file main f you may wish to rename the outputs The output files are as follows outfile dat A text file which shows all of the standard output information as the code runs At the end of this file there is the number of points required for making the plots with the Matlab scripts costfn dat Iterations of the cost function and gradient for plotting using routines conu m and convt m analysis dat Analysis data file for plotting using routines plotanal m and plotanal2 m background dat Background data file truth dat Truth data file These files will be overwritten every time the code runs so if they are to be stored they should be renamed or moved elsewhere for example in the same directory where your edited input variable file vars_user_mod f90 lives 6 Plotting the output using Matlab 6 1 Plotting Routines The routines for plotting output can be
6. field 25 A Cy 15 Figure 3 A comparison of the truth background and analysis for the u and fields for test case 1 Truth black solid line Background red solid line Analysis black dashed line ag u difference phi difference 2 a a Wyn 0 lah Figure 4 The error in the u and fields for test case 1 Truth black solid line Analysis black dashed line 10 u field phi field 0 5 100 150 200 0 50 100 150 200 u field 0 50100 150 200 Figure 5 A comparison of the truth background and analysis for the u and fields for test case 2 Truth black solid line Background red solid line Analysis black dashed line 11 u difference phi difference 0 4 ah Figure 6 The error in the u and fields for test case 2 Truth black solid line Analysis black dashed line
7. ground and analysis for the u and fields at the times requested The truth is shown by a black solid line the background by a red solid line and the analysis by a black dashed line Figure 2 shows the error in each of the fields truth analysis N B If you have set the background term to zero in your analysis cov B_matrix 1 then you should comment out the plotting of the background field plotanal2 m This routine works in exactly the same way as plotanal m but allows comparison from two different assimilations The only difference in the set up now is that the user must specify two data directories at the start of the routine The output is the same as previously with the extra analysis being indicated by a black dotted line 6 2 Example Plots The routines conv m and plotanal m are used to make example plots for the test cases 1 and 2 and can be found in the corresponding directories Convergence of cost function Function value So 2 4 6 8 0 2 14 16 lteration Convergence of gradient Gradient value Iteration Figure 1 The cost function convergence for input test case 1 Convergence of cost function Function value a C2 5 10 15 20 Iteration Convergence of gradient Gradient value Iteration Figure 2 The cost function convergence for input test case 2 u field 4 1 2 1 0 8 0 50 100 150 200 u field 1 4 1 2 1 0 8 0 50 100 150 200 phi field 25 i 0 50 100 150 200 phi
8. in the directory in which you unzip the file and then all other files will be under the SW_norot directory Hence you do not need to create a special directory first 2 Directory structure By following the instructions in the previous section you will automatically set up the following directory structure under the directory SW_norot Case_1 Contains the input variables file vars_user_mod_test1 f90 for example as similation 1 All output files are found here aswell Case_2 Contains the input variables file vars_user_mod_test2 f90 for example as similation 2 All output files are found here aswell data_in Directory from which any input files will be read By default this contains an example input data file nl_t25 dat and grid file grid for a domain of 200 points data_out Directory into which all output will be written doc Contains documentation of the system minim Contains the minimization routine conmin f No other minimization rou tines are presently provided Model Contains source code for the nonlinear linear and adjoint models with the following subdirectories fort Source code for nonlinear model PFM Source code for perturbation forecast model PFM_ Adj Adjoint routines for PFM TLM Source code for tangent linear model TLM Adj Adjoint routines for PFM plot Contains Matlab routines for viewing output var Contains code and scripts for running the assimilation with the following sub directories
9. rical model 1 5 Namelist amp sobservations This namelist controls when and where the observations are in the assimiliation The variables for observations of u are listed here Control of observations of are by means of similar variables with _u_ replaced by phi in the variable names eg first_u_ob_timestep becomes first_phi_ob_timestep first_u_ob_ timestep First time step on which observations of u are present 0 last_u_ob_timestep Last time step on which observations of u are present 1 indicates till the end of the assimilation window 1 time_frequency_of_u_obs Time frequency of u observations in number of time steps 1 first_u_ob_point First spatial point at which there are observations of u 1 last_u_ob_point Last spatial point at which there are observations of u 1 indicates till end of domain 1 space frequency of u obs Spatial frequency of u observations in number of grid points 1 variance_of_u_obs If non zero then add random noise to the observations with specified variance 0 0D0 Namelist amp var_control This namelist controls how the assimilation is performed assim_scheme Assimilation scheme to use 1 Incremental 4D Var 2 3D FGAT 3 Incremental 3D Var 1 background_setup Definition of background field 1 truth random noise 2 con stant 3 truth with phase error 4 zero everywhere 1 variance_of_u_background Variance of random noise to add to u to form back ground if background se
10. tup 1 Also used as variance if cov_B_matrix 3 0 0D0 variance_of_phi_background Variance of random noise to add to to form back ground if background_setup 1 Also used as variance if cov_B_matrix 3 0 0D0 corr_length Correlation length in number of grid points if cov _B_matrix 3 1 max_number_of_outer_loops Maximum number of outer loops to perform 1 minim_diag Controls output from minimization 0O No printed output from min imization gt 1 Values written out every minim_diag iterations 1 minim_max_iterations Maximum number of minimization iterations to perform in each inner loop Default 50 cov_B_matrix Specification of background error covariance matrix 1 Zero ie ignore this term 2 Identity 3 Laplace operator 2 cov_R_matrix Specification of observation error covariance matrix 1 Zero ie ignore this term 2 Identity 3 True error variance 2 filter_steps If gt 1 then the increment is added on to the linearization state over this number of time steps to provide a simple filter 1 stop_criteria Choose which criteria to stop the inner loop on 1 Relative gradient 2 Absolute gradient 3 Relative change in function 4 Gradient relative to initial gradient 1 low_res_factor Ratio of outer loop inner loop spatial resolution 1 inner_tolerance Stopping tolerance for inner loop 1 0D 6 outer_tolerance Stopping tolerance for outer loop Note that the outer loop stops when the absolute norm of the gra
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