A User's Guide for SCRIP: A Spherical Coordinate
Contents
1. 3 JJ tua 3 2 where Ang is the area of the source grid cell n covered by the destination grid cell k and fn is the local value of the flux in the source grid cell see Figure 3 1 Note that 3 2 is normalized by the destination area Az corre sponding to the normalize_opt value of destarea The sum of the weights for a destination cell k in this case would be between 0 and 1 and would be the area fraction if f were identically 1 everywhere on the source grid Fy 14 The normalization option fracarea would actually divide by the area of the source grid overlapped by cell k gt J f dA 3 3 For this normalization option remapping a function f which is 1 everywhere on the source grid would result in a function F that is exactly one wherever the destination grid overlaps a non masked source grid cell and zero other wise A normalization option of none would result in the actual angular area participating in the remapping Assuming fn is constant across a source grid cell 3 2 would lead to the first order area weighted schemes used in current coupled models A more accurate form of the remapping is obtained by using where V f is the gradient of the flux in cell n and F is the centroid of cell n defined by P 1 Such a distribution satisfies the conservation constraint and is equivalent to the first terms of a Taylor series expansion of f around ra The remapping is thus second order accurate if V f is2. 22 RIME ELE Uw hee Si one how ER Sethe GAP ea 2 2 1 Namelist Input cis ae SA se BA BS 2 2 2 Grid Input Bless Sn ee ee Ee Ek BS 2 2 3 Outp t Bales se ay ria donante eee ECS 2a Lestmez i ah es Sk Meet oS densa aa pak a eld bible 3 Conservative Remapping 3 1 Search algorithms fa e Bw te daa A oe Intersections n a e pole red RS O era 3 3 PIMIENTOS es a arena Boe Lea 3 4 Spherical coordinates AAA A o Si CONCISO 6140 2482 2 aud a A A 4 Bilinear Remapping 5 Bicubic Remapping 6 Distance weighted Average Remapping 7 Bugs 14 16 18 19 19 20 21 24 26 27 Chapter 1 Introduction SCRIP is a software package used to generate interpolation weights for remap ping fields from one grid to another in spherical geometry The package currently supports four types of remappings The first is a conservative remapping scheme that is ideally suited to a coupled model context where the area integrated field e g water or heat flux must be conserved The sec ond type of mapping is a basic bilinear interpolation which has been slightly generalized to perform a local bilinear interpolation A third method is a bicubic interpolation similar to the bilinear method The last type of remap ping is a distance weighted average of nearest neighbor points The bilinear and bicubic schemes can only be used with logically rectangular grids the other two methods can be used for any grid in spherical coordinates SCRIP is available via the web
3. cos 4 cos cos dg cos s sin gasin ds sin 4sin0 6 2 where 0 is latitude is longitude and the subscripts d s denote destination and source grids respectively When finding nearest neighbors the distance is not computed between the destination grid point and every source grid point Instead the search is narrowed by sorting the two grids into latitude bins Only those source grid cells lying in the same latitude bin as the destination grid cell are checked to find the nearest neighbors 26 Chapter 7 Bugs A file called bugs is included in the distribution which lists current out standing bugs as well as a version history Any further bugs comments or suggestions should be sent to me at pwjones lanl gov The code does not have very useful error messages to help diagnose prob lems so feel free to pester me with any problems you encounter The package has also not been extensively tested on a variety of machines It works fine on SGI machines and IBM machines but has not been run on other machines It is pretty vanilla Fortran so should be ok on machines with standard compliant F90 compilers 27
4. 1 B 3 28 o2 a 1 B03 28 a2 a 1 2 Thus num_wts is set to four 2a f i j Ia i 1 j 1 4 di BB 2B a a Dia B 1 1 02 3 2a 2 B 1 20 3 20 1 a 3 2 i EJA Ct aI F 1 3 vB n PE D 1 0 3 2a 2 24 2 Of ala PASEA ola DAA PREGL a a 1818 vst i 1 3 1 4 ala PSI 5 1 where a and 8 are identical to those found in the bilinear case and are found using an identical algorithm Note that unlike the conservative remappings the gradients here are gradients with respect to the logical variable and not latitude or longitude Lastly the four weights corresponding to each address pair correspond to the weight multiplying the field value at the point the weight multiplying the gradient with respect to i the weight multiplying the gradient with respect to j and the weight multiplying the cross gradient in that order 25 Chapter 6 Distance weighted Average Remapping This scheme for remapping is probably the simplest in this package The code simply searches for the num_neighbors nearest neighbors and computes the weights using 7 1 d e A de Da a where e is a small number to prevent dividing by zero the sum is for normal ization and d is the distance from the destination grid point to the source grid point The distance is the angular distance w 6 1 d cos
5. at http climate acl lanl gov software SCRIP NOTE This location has changed since the 1 2 release The next chapter describes how to compile and run SCRIP while the following sections describe the remapping methods in more detail Chapter 2 Compiling and Running The distribution file is a gzipped tarfile so you must uncompress the file using gunzip and then extract SCRIP from the tar file using tar xvf scripl 4 tar The extraction process will create a directory called SCRIP with two subdirectories named source and grids The source directory contains all the source files and the makefile for building the package The grids directory contains some sample grid files and routines for creating or converting other grid files to the proper format 2 1 Compiling In order to compile SCRIP you need access to a Fortran 90 compiler and a netCDF library version 3 or later In the source directory you must edit the makefile to insert the appropriate compiler and compiler options for whatever machine you happen to work on The makefile currently only has SGI compiler options In addition you must edit the paths in the makefile to find the proper netCDF library if netCDF is in your default path you may delete the path altogether Once the makefile has been edited to reflect your local environment type make and let it build By default the makefile builds two executables in the main SCRIP directory the first
6. must be added to the appropriate cells The pole contribution can be computed analytically The pole also creates problems for the search and intersection algorithms described above For example a grid cell that overlaps the pole can result 19 in a nonconvex cell in latitude longitude coordinates The cross product test described above will fail in this case In addition segments near the pole typically exhibit large changes in longitude even for very short segments In such a case the linear parametrizations used above result in inaccuracies for determining the correct intersections To avoid these problems a coordinate transformation can be used pole ward of a given threshold latitude typically within one degree of the pole A possible transformation is the Lambert equivalent azimuthal projection m 0 X 2sin sin 3 3 coso of OY Y 2sin 5 2 sin 3 17 for the North Pole The transformation for the South Pole is similar This transformation is only used to compute intersections line integrals are still computed in latitude longitude coordinates Because intersections computed in the transformed coordinates can be different from those computed in latitude longitude coordinates line segments which cross the latitude thresh old must be treated carefully To compute the intersections consistently for such a segment intersections with the threshold latitude are detected and used as a normal grid intersection to pro
7. the weights consistent with internal model computed areas which may differ somewhat from the SCRIP computed areas 2 2 2 Grid Input Files The grid input files are in netCDF format as shown by the sample nc dump grid output in Fig 2 2 If you re unfamiliar with ncdump output it s important to not that ncdump shows the array dimensions in C or dering In Fortran the order is reversed e g arrays are dimensioned grid_corners grid_size In the grids subdirectory of the distribution there are some fortran source codes for creating these grid files for some special cases See the README file in that subdirectory for details The name of the grid is given as the title and will be used to specify the grid name throughout the remapping process The grid_size dimension is the total size of the grid grid_rank refers to the number of dimensions the grid array would have when used in a model code The number of corners vertices in each grid cell is given by grid_corners Note that if your grid has a variable number of corners on grid cells then you should set grid_corners to be the highest value and use redundant points on cells with fewer corners The integer array grid_dims gives the length of each grid axis when used in a model code Because the remapping routines read the grid properties as a linear list of grid cells the grid_dims array is necessary for reconstructing the grid particularly for a bilinear mapping where a logically rectang
8. A User s Guide for SCRIP A Spherical Coordinate Remapping and Interpolation Package Version 1 4 Philip W Jones Theoretical Division Los Alamos National Laboratory COPYRIGHT NOTICE Copyright 1997 1998 the Regents of the University of California This software and ancillary information herein called SOFTWARE called SCRIP is made available under the terms described here The SOFTWARE has been approved for release with associated LA CC Number 98 45 Unless otherwise indicated this SOFTWARE has been authored by an employee or employees of the University of California operator of Los Alamos National Laboratory under Contract No W 7405 ENG 36 with the United States Department of Energy The United States Government has rights to use reproduce and distribute this SOFTWARE The public may copy distribute prepare derivative works and publicly display this SOFTWARE without charge provided that this Notice and any statement of authorship are reproduced on all copies Neither the Government nor the University makes any warranty express or implied or assumes any liability or respon sibility for the use of this SOFTWARE If SOFTWARE is modified to produce derivative works such modified SOFTWARE should be clearly marked so as not to confuse it with the version available from Los Alamos National Laboratory Contents 1 Introduction 2 Compiling and Running DAs SUOMI eolie ey En id is 2 1 1 Compile time Parameters
9. are common lines e g the Equator When this is the case the method described above will double count the contribution of these line segments Coincidences can be detected when computing cross products for the search algorithm described above If the cross product is zero in this case the endpoint lies on the cell side A second cross product between the line segment and the cell side can then be computed If the second cross product is also zero the lines are coincident Once a coincidence has been detected the contribution of the coincident segment can be computed during the first sweep and ignored during the second sweep 3 4 Spherical coordinates Some aspects of the spherical coordinate system introduce additional prob lems for the method described above Longitude is multiple valued on one line on the sphere and this branch cut may be chosen differently by different grids Care must be taken when calculating intersections and line integrals to ensure that the proper longitude values are used A simple method is to always check to make sure the longitude is in the same interval as the source grid cell center Another problem with computing weights in spherical coordinates is the treatment of the pole First note that although the pole is physically a point it is a line in latitude longitude space and has a nonzero contribution to the weight integrals If a grid does not contain the pole explicitly as a grid vertex the pole contribution
10. at least a first order approximation to the gradient The remapping can now be expanded in spherical coordinates as N F gt atin ne Es Wank 5 3 6 n 1 where 0 is latitude is longitude and the three remapping weights are 1 sit A ma alt 3 7 Wonk JJ 0 00 J f oda En ip dA 3 8 15 and 1 Wank DN cos 0 dn dA DI 1 Wink al f es 0dA x f 6008 0dA 3 9 Again if the gradient is zero 3 6 reduces to a first order area weighted remapping The area integrals in equations 3 7 3 9 are computed by converting the area integrals into line integrals using the divergence theorem Com puting line integrals around the overlap regions is much simpler one simply integrates first around every grid cell on the source grid keeping track of in tersections with destination grid lines and then one integrates around every grid cell on the destination grid in a similar manner After the sweep of each grid all overlap regions have been integrated Choosing appropriate functions for the divergence the integrals in equa tions 3 7 3 9 become J f _dA sin d 3 10 yon dA E cos 8 sin do 3 11 a cos ddA e S ising cos 0 Odd 3 12 where Cy is the counterclockwise path around the region Ang Computing these three line integrals during the sweeps of each grid provides all the information necessary for computing the remapping weights 3 1 Search al
11. buted memory context however The scrip test code shows an example of how the remappings can be implemented 2 3 Testing In order to test the weights computed by the SCRIP package a simple test code is provided This code reads in the weights and remaps analytic fields Three choices for the analytic field are provided The first is a cosine bell function f 2 cos rr L where r is the distance from the center of the hill and L is a length scale Such a function is useful for determining the effects of repeated applications The other two fields are representative of spherical harmonic wavefunctions A relatively smooth function f 2 cos 6 cos 2 is similar to a spherical harmonic with 2 and m 2 where is the spherical harmonic order and m is the azimuthal wave number The function f 2 sin 20 cos 16 is similar to a spherical harmonic with 32 and m 16 and is useful for testing a field with relatively high spatial frequency and rapidly changing gradients The choice of which field is remapped in determined by the input namelist scrip_test_in For conservative remappings the test code tests three different remap pings the first is a first order remapping the second is a second order remap ping using only latitude gradients and the third is a full second order remap ping The second is performed in order to determine which weights are caus ing problems when errors occur The code prints out three diagnostics to stan
12. d weights An example ncdump of the output files is shown in Fig 2 3 The grid information is simply echoing the input grid file information and adding grid_area and grid frac arrays The grid_area array currently is only computed by the conservative remapping option the others will write arrays full of zeros for this field The grid_frac array for the conservative remapping returns the area fraction of the grid cell which participates in the remapping based on the source grid mask For the other two remapping options the grid frac array is one where the grid point participates in the remapping and zero otherwise based again on the source grid mask and not on the grid_imask for that grid The remapping data itself is written as if for a sparse matrix multiplica tion Again the Fortran array must be dimensioned num_wgts num links rather than the C order shown in the ncdump The dimension num_wgts refers to the number of weights for a given remapping and is one for bi linear and distance weighted remappings For the conservative remapping num_wgts is 3 as it contains two additional weights for a second order remap ping The bicubic remappings require four weights as for gradients in each direction plus a term for the cross gradient The dimension num links is the number of unique address pairs in the remapping and is therefore the number of entries in a sparse matrix for the remapping The integer address arrays contain the source and destina
13. dard output and writes many quantities to a netCDF output file First it prints out the minimum and maximum of the source and desti nation remapped fields This is a test for monotonicity although only the first order conservative remapping is monotone by default Second the test code prints out the maximum and average relative error e Fast Fanatytic Fanatytic Where Fanalytic 18 the source function evaluated at the destination grid points and Fs is the destination remapped field LA The errors here can sometimes be misleading For example if a conservative remapping is performed from a fine grid to a coarse grid the destination array will contain the field averaged over many source cells while Fanalytic 18 the analytic field evaluated at the cell center point Another instance which leads to relatively large errors is near mask boundaries where the remapped field is correctly returning values indicative of the edge of a grid cell while Fanalytie 18 again computing cell center values To avoid the latter problem the error is only computed where the destination grid fraction is greater than 0 999 Lastly the test code prints out the area integrated field on the source and destination grids in order to test conservation This diagnostic returns zeros for all but conservative remappings For a first order conservative remap ping these numbers should agree to machine accuracy For a second order conservative remapping they w
14. e in radians above which a coordinate transformation is used to perform intersection calculation remap_conserv f south_thresh 2 00 same for south pole remap conserv f max subseg 10000 maximum number of sub segments allowed to prevent infinite loop remap_bilinear f max_iter 100 max number of iterations to determine local i j remap_bilinear f converge 1 x 1071 convergence criterion for bilinear iteration remap_bicubic f max_iter 100 max number of iterations to determine local i j remap_bicubic f converge 1 x 1071 convergence criterion for bicubic iteration remap_distwgt f num_neighbors 4 number of nearest neighbors to use for distance weighted average iounits f stdin 5 I O unit reserved for standard input iounits f stdout 6 I O unit reserved for standard output iounits f stderr 6 I O unit reserved for standard error output timers f max timers 99 max number of CPU timers The num_maps variable determines the number of mappings to be com puted If you d like mappings only from a source grid grid 1 to a destination grid grid 2 then num _maps should be set to one If you d also like weights for a remapping in the opposite direction grid 2 to grid 1 then num_maps should be set to two The map_method variable determines the method to be used for the map ping A conservative remapping is map_method conservative a bilinear mapping is map method bilinear a distance weighted av
15. erage is map_method distwgt a bicubic mapping is map_method bicubic The restrict_type variable and num_srch_bins determines how the software restricts the range of grid points to search to avoid a full N search There are currently two options for restrict_type latitude and latlon The first was used in all previous versions of SCRIP and restricts the search by dividing the grid points into num srch _bins latitude bins The latlon choice divides the spherical domain into latitude longitude boxes and thus provides a way to restrict the longitude range as well Note that for the latlon option the domain is divided by num_srch_bins in each direction so that the total number of bins is the square of num srch bins Generally the larger the number of bins the more the search can be restricted However if the number of bins is too large more time will be taken restricting the search than the search itself For coarse grids choosing the latitude option with 90 bins one degree bins is sufficient The normalize opt variable is used to choose the normalization of the remappings for the conservative remapping method By default normal ize_opt is set to be fracarea and will include the destination area fraction in the output weights other options are none and destarea see chapter on the conservative remapping method The latter two are useful when deal ing with masks that are dynamic e g variable ice
16. executable is called scrip and computes all the necessary weights for a remapping The second executable is a simple test code scrip_test which will test the weights output by scrip Figure 2 1 Required input namelist amp remap_inputs num_maps 2 gridi_file grid_i_file_name grid2_file grid_2_file_name interp_filei map_i_output_file_name interp_file2 map_2_output_file_name mapi_name name_for_mapping_1 map2_name name_for_mapping_2 map_method conservative normalize_opt frac output_opt scrip restrict_type latitude num_srch_bins 90 luse_gridi_area false luse_grid2_area false 2 1 1 Compile time Parameters There are a few compile time parameters that can be changed before com piling see Table 2 1 For the most part the defaults are adequate but you may wish to change these at some point The use of these parameters will become clear in the chapters describing the remapping algorithms 2 2 Running Once the code is compiled a few input files are needed The first is a namelist input file and the other two required files are grid description files 2 2 1 Namelist Input The namelist input file must be called scrip_in and contain a namelist as shown in Fig 2 1 Table 2 1 Compile time parameters Routine Parameter Default Description Name Value remap_conserv f north_thresh 1 42 threshold latitud
17. fraction Keep in mind that in such a case the area fractions must be computed explicitly by the remapping routine at the time the remappings are actually computed see the example in Fig 2 4 The grid file are names with relative paths of the grid input files The first grid file gridl file must be the source grid if num_maps 1 If this mapping uses the conservative remapping method the first grid file must also be the grid with the master mask e g a land mask grid fractions on the second grid will be determined by this mask Names of the output files for the remapping weights are determined by the interp_filex filenames again with paths Map 1 refers to a mapping from 6 grid 1 to grid 2 map 2 is in the opposite direction A descriptive name for the remappings are determined by the mapx name variables These should be descriptive enough to know exactly which grids and methods were used The output_opt variable determines the format of the netCDF output file The two currently supported options are scrip and ncar csm The latter is to generate files for use in the NCAR CSM Flux Coupler for coupled climate modeling The primary difference between the formats is the choice of variable names The two logical flags luse_gridx_area are for using an input area to nor malize the conservative weights If these are set to true the input grid files must contain the grid areas This option is provided primarily for making
18. gorithms As mentioned in the previous section the algorithm for computing the remap ping weights is relatively simple The process amounts to finding the location of the endpoint of a segment and then finding the next intersection with the other grid The line integrals are then computed and summed according to which grid cells are associated with that particular subsegment The most time consuming portion of the algorithm is finding which cell on one grid 16 Figure 3 1 An example of a triangular destination grid cell k overlapping a quadrilateral source grid The region Ag is where cell k overlaps the quadrilateral cell n Vectors used by search and intersection routines are also labelled 17 contains an endpoint from the other grid Optimal search algorithms can be written when the grid is well structured and regular However if one requires a search algorithm that will work for any general grid a hierarchy of search algorithms appears to work best In SCRIP each grid cell address is assigned to one or more latitude bins When the search begins only those cells belonging to the same latitude bin as the search point are used The second stage checks the bounding box of each grid cell in the latitude bin The bounding box is formed by the cells minimum and maximum latitude and longitude This process further restricts the search to a small number of cells Once the search has been restricted a robust algorithm that works for m
19. ill be very close but may not exactly agree due to mask boundary effects where it is not possible to perform the exact area integral The netCDF output file from the test code contains the source and des tination arrays as well as the error arrays so the error can be examined at every grid point to pinpoint problems The arrays in the netCDF file are written out in arrays with rank grid_rank e g two dimensional grids are written as proper 2 d arrays rather than vectors of values These arrays can then be viewed using any visualization package 13 Chapter 3 Conservative Remapping The SCRIP package implements a conservative remapping scheme described in detail in a separate paper Jones P W 1999 Monthly Weather Review 127 2204 2210 A brief outline will be given here to aid the user in under standing what this portion of the package does To compute a flux on a new destination grid which results in the same energy or water exchange as a flux f on an old source grid the destination flux F at a destination grid cell k must satisfy i 2 faa 3 1 where F is the area averaged flux and Ax is the area of cell k Because the integral in 3 1 is over the area of the destination grid cell only those cells on the source grid that are covered at least partly by the destination grid cell contribute to the value of the flux on the destination grid If cell k overlaps N cells on the source grid the remapping can be written as
20. ost cases is a cross product test In this test a cross product is computed between the vector corresponding to a cell side 732 in Figure 3 1 and a vector extending from the beginning of the cell side to the search point 715 If To X Tip gt 0 3 13 the point lies to the left of the cell side If 3 13 holds for every cell side the point is enclosed by the cell This test is not completely robust and will fail for grid cells that are non convex 3 2 Intersections Once the location of an initial endpoint is found it is necessary to check to see if the segment intersects with the cell side If the segment is parametrized as 0 0 s1 0e 04 Q sile dp 3 14 and the cell side as di 0 sa 02 01 Q1 s2 d2 1 3 15 where 61 1 02 2 0 and Oe are endpoints as shown in Figure 3 1 the in tersection of the two lines occurs when 0 and are equal The linear system 0 0 01 02 Sy 01 0 de T Pb 7 2 s2 Ta dv 18 3 16 is then solved to determine s and sa at the intersection point If s and s are between zero and one an intersection occurs with that cell side It is important also to compute identical intersections during the sweeps of each grid To ensure that this will occur the entire line segment is used to compute intersections rather than using a previous or next intersection as an endpoint 3 3 Coincidences Often pairs of grids will sh
21. ral quadrilateral grid 3 i 1 j 1 22 a solution Differentiating 4 2 results in 90 da 1 81 o 02 01 T 0 0 03 05 8 04 01 0 0 03 02 a da d1 01 G4 63 09 8 da d1 01 Pa 63 dojo 4 4 where A Inverting this system 00 94 7 91 T 0 04 03 02 a Ra 0A 56 ba th ta UA 9 and 02 01 01 0a 03 02 6 00 PEL do 1 bi datos a A 8 Starting with an initial guess for a and 8 say a 8 0 equations 4 5 and 4 6 can be iterated until da and 08 are suitably small The weights can then be computed from 4 1 Note that for simple latitude longitude grids this iteration will converge in the first iteration In order to compute the weights using this general bilinear iteration it must be determined in which box the point P resides For this the search algorithms outlined in the previous chapter are used with the exception that instead of using cell corners the relevant box is formed by neighbor cell centers as shown in Fig 4 1 23 Chapter 5 Bicubic Remapping The bicubic remapping exactly follows the bilinear remapping except that four weights for each corner point are required for this option The bicubic remapping is fp 1 63 28 1 a 3 1 6 3 28 0 8 20 f 6 1 3 8 3 2B a 3 2a f i 1 j 1 PB A 3 20 fli 5 1 1 8 3 28 a a 1 94 of di
22. rea map_method Conservative remapping history Created 07 19 1999 conventions SCRIP source_grid POP 4 3 Displaced Pole T grid dest_grid T42 Gaussian Grid 10 gt Figure 2 4 Sample Fortran code for performing a first order conservative remap dst_array 0 0 select case normalize_opt case fracarea do n 1 num_links dst_array dst_address n dst_array dst_address n remap_matrix 1 n src_array src_address n end do case destarea do n 1 num_links dst_array dst_address n dst_array dst_address n remap_matrix 1 n src_array src_address n dst_frac dst_address n end do case none do n 1 num_links dst_array dst_address n dst_array dst_address n remap_matrix 1 n src_array src_address n dst_area dst_address n dst_frac dst_address n end do end select 11 The address arrays are sorted by destination address and are linear ad dresses that assume standard Fortran ordering They can therefore be con verted to logical address space if necessary For example a point on a two dimensional grid with logical coordinates i j will have a linear address n given by n j 1 grid_dims 1 7 Alternatively if the code is run on a se rial machine the multi dimensional arrays can be passed into linear dummy arrays and the addresses can be used directly Such a storage sequence as sociation may not be valid in a distri
23. tion address for each link So a Fortran code to complete the conservative remappings might look like that shown in Fig 2 4 Figure 2 3 A sample output file for mapping data in scrip format netcdf rmp_POP43_to_T42_cnsrv dimensions src_grid_size 24576 dst_grid_size 8192 src_grid_corners 4 dst_grid_corners 4 src_grid_rank 2 dst_grid_rank 2 num_links 42461 num_wgts 3 variables long src_grid_dims src_grid_rank long dst_grid_dims dst_grid_rank double src_grid_center_lat src_grid_size double dst_grid_center_lat dst_grid_size double src_grid_center_lon src_grid_size double dst_grid_center_lon dst_grid_size long src_grid_imask src_grid_size long dst_grid_imask dst_grid_size double src_grid_corner_lat src_grid_size src_grid_corners double src_grid_corner_lon src_grid_size src_grid_corners double dst_grid_corner_lat dst_grid_ size dst_grid_corners double dst_grid_corner_lon dst_grid_size dst_grid_corners double src_grid_area src_grid_ src_grid_area units double dst_grid_area dst_grid_ dst_grid_area units double src_grid_frac src_grid_ double dst_grid_frac dst_grid_ long src_address num_links long dst_address num_links double remap_matrix num_links global attributes size square radians size square radians size size num_wgts title POP 4 3 to T42 Conservative Mapping normalization fraca
24. ular structure is needed Figure 2 2 A sample input grid file netcdf remap_grid_T42 dimensions grid_size 8192 grid_corners 4 grid_rank 2 variables long grid_dims grid_rank double grid_center_lat grid_size grid_center_lat units radians double grid_center_lon grid_size grid_center_lon units radians long grid_imask grid_size grid_imask units unitless double grid_corner_lat grid_size grid_corners grid_corner_lat units radians double grid_corner_lon grid_size grid_corners grid_corner_lon units radians global attributes title T42 Gaussian Grid The integer array grid_imask is used to mask out grid cells which should not participate in the remapping The array should by zero for any points e g land points that do not participate in the remapping and one for all other points Coordinate arrays provide the latitudes and longitudes of cell centers and cell corners Although the above reports the units as radians the code happily accepts degrees as well The grid corner coordinates must be written in an order which traces the outside of a grid cell in a counterclockwise sense That is when moving from corner 1 to corner 2 to corner 3 etc the grid cell interior must always be to the left 2 2 3 Output Files The remapping output files are also in netCDF format and contain some grid information from each grid as well as the remapping addresses an
25. vide a clean break between the two coordinate systems 3 5 Conclusion The implementation in the SCRIP code follows closely the description above The user should be able to follow and understand the process based on this description 20 Chapter 4 Bilinear Remapping Standard bilinear interpolation schemes can be found in many textbooks Here we present a more general scheme which uses a local bilinear approxima tion to interpolate to a point in a quadrilateral grid Consider the grid points shown in Fig 4 1 labelled with logically rectangular indices e g i 7 Let the latitude longitude coordinates of point 1 be 0 i j d i j the coordinates of point 2 be 0 1 1 3 i 1 7 etc Now let a and 8 be continuous local coordinates such that the coordinates a 8 of point 1 are 0 0 point 2 are 1 0 point 3 are 1 1 and point 4 are 0 1 If point P lies inside the cell formed by the four points above the function f at point P can be approximated by fp 1 a 1 0 f i J a 1 0 f i 1 3 aBf i 1 3 1 1 0f i j 1 4 1 The remapping weights must therefore be computed by finding a and at point P The latitude longitude coordinates 0 of point P are known and can also be approximated by 0 1 a 1 0 0 a 1 B 02 0803 1 a 364 1 a 1 p a 1 B d2 a8G3 1 a Bos 4 2 Because 4 2 is nonlinear in a and 8 we must linearize and iterate toward 21 Figure 4 1 A gene
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