c c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c . . c . copyright (c) 1998 by UCAR . c . . c . University Corporation for Atmospheric Research . c . . c . all rights reserved . c . . c . . c . SPHEREPACK . c . . c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c c c c ... file dives.f c c this file includes documentation and code for c subroutine dives i c c ... files which must be loaded with dives.f c c sphcom.f, hrfft.f, vhaes.f,shses.f c c c subroutine dives(nlat,nlon,isym,nt,dv,idv,jdv,br,bi,mdb,ndb, c + wshses,lshses,work,lwork,ierror) c c given the vector spherical harmonic coefficients br and bi, precomputed c by subroutine vhaes for a vector field (v,w), subroutine dives c computes the divergence of the vector field in the scalar array dv. c dv(i,j) is the divergence at the colatitude c c theta(i) = (i-1)*pi/(nlat-1) c c and east longitude c c lambda(j) = (j-1)*2*pi/nlon c c on the sphere. i.e. c c dv(i,j) = 1/sint*[ d(sint*v(i,j))/dtheta + d(w(i,j))/dlambda ] c c where sint = sin(theta(i)). w is the east longitudinal and v c is the colatitudinal component of the vector field from which c br,bi were precomputed. required associated legendre polynomials c are stored rather than recomputed as they are in subroutine divec. c c c input parameters c c nlat the number of colatitudes on the full sphere including the c poles. for example, nlat = 37 for a five degree grid. c nlat determines the grid increment in colatitude as c pi/(nlat-1). if nlat is odd the equator is located at c grid point i=(nlat+1)/2. if nlat is even the equator is c located half way between points i=nlat/2 and i=nlat/2+1. c nlat must be at least 3. note: on the half sphere, the c number of grid points in the colatitudinal direction is c nlat/2 if nlat is even or (nlat+1)/2 if nlat is odd. c c nlon the number of distinct londitude points. nlon determines c the grid increment in longitude as 2*pi/nlon. for example c nlon = 72 for a five degree grid. nlon must be greater than c 3. the efficiency of the computation is improved when nlon c is a product of small prime numbers. c c c isym a parameter which determines whether the divergence is c computed on the full or half sphere as follows: c c = 0 c c the symmetries/antsymmetries described in isym=1,2 below c do not exist in (v,w) about the equator. in this case the c divergence is neither symmetric nor antisymmetric about c the equator. the divergence is computed on the entire c sphere. i.e., in the array dv(i,j) for i=1,...,nlat and c j=1,...,nlon. c c = 1 c c w is antisymmetric and v is symmetric about the equator. c in this case the divergence is antisymmetyric about c the equator and is computed for the northern hemisphere c only. i.e., if nlat is odd the divergence is computed c in the array dv(i,j) for i=1,...,(nlat+1)/2 and for c j=1,...,nlon. if nlat is even the divergence is computed c in the array dv(i,j) for i=1,...,nlat/2 and j=1,...,nlon. c c = 2 c w is symmetric and v is antisymmetric about the equator c in this case the divergence is symmetyric about the c equator and is computed for the northern hemisphere c only. i.e., if nlat is odd the divergence is computed c in the array dv(i,j) for i=1,...,(nlat+1)/2 and for c j=1,...,nlon. if nlat is even the divergence is computed c in the array dv(i,j) for i=1,...,nlat/2 and j=1,...,nlon. c c c nt nt is the number of scalar and vector fields. some c computational efficiency is obtained for multiple fields. c can be three dimensional corresponding to an indexed multiple c vector field. in this case multiple scalar synthesis will c be performed to compute the divergence for each field. the c third index is the synthesis index which assumes the values c k=1,...,nt. for a single synthesis set nt = 1. the c description of the remaining parameters is simplified by c assuming that nt=1 or that all the arrays are two dimensional. c c idv the first dimension of the array dv as it appears in c the program that calls dives. if isym = 0 then idv c must be at least nlat. if isym = 1 or 2 and nlat is c even then idv must be at least nlat/2. if isym = 1 or 2 c and nlat is odd then idv must be at least (nlat+1)/2. c c jdv the second dimension of the array dv as it appears in c the program that calls dives. jdv must be at least nlon. c c br,bi two or three dimensional arrays (see input parameter nt) c that contain vector spherical harmonic coefficients c of the vector field (v,w) as computed by subroutine vhaes. c *** br and bi must be computed by vhaes prior to calling c dives. c c mdb the first dimension of the arrays br and bi as it c appears in the program that calls dives. mdb must be at c least min0(nlat,nlon/2) if nlon is even or at least c min0(nlat,(nlon+1)/2) if nlon is odd. c c ndb the second dimension of the arrays br and bi as it c appears in the program that calls dives. ndb must be at c least nlat. c c c wshses an array which must be initialized by subroutine shsesi c once initialized, c wshses can be used repeatedly by dives as long as nlon c and nlat remain unchanged. wshses must not be altered c between calls of dives. wdives is identical to the saved c work space initialized by subroutine shsesi and can be c set by calling that subroutine instead of divesi. c c c lshses the dimension of the array wshses as it appears in the c program that calls dives. define c c l1 = min0(nlat,(nlon+2)/2) if nlon is even or c l1 = min0(nlat,(nlon+1)/2) if nlon is odd c c and c c l2 = nlat/2 if nlat is even or c l2 = (nlat+1)/2 if nlat is odd c c then lshses must be at least c c (l1*l2*(nlat+nlat-l1+1))/2+nlon+15 c c c work a work array that does not have to be saved. c c lwork the dimension of the array work as it appears in the c program that calls dives. define c c l1 = min0(nlat,(nlon+2)/2) if nlon is even or c l1 = min0(nlat,(nlon+1)/2) if nlon is odd c c and c c l2 = nlat/2 if nlat is even or c l2 = (nlat+1)/2 if nlat is odd c c if isym = 0 then lwork must be at least c c nlat*((nt+1)*nlon+2*nt*l1+1) c c if isym > 0 then lwork must be at least c c (nt+1)*l2*nlon+nlat*(2*nt*l1+1) c c ************************************************************** c c output parameters c c c dv a two or three dimensional array (see input parameter nt) c that contains the divergence of the vector field (v,w) c whose coefficients br,bi where computed by subroutine c vhaes. dv(i,j) is the divergence at the colatitude point c theta(i) = (i-1)*pi/(nlat-1) and longitude point c lambda(j) = (j-1)*2*pi/nlon. the index ranges are defined c above at the input parameter isym. c c c ierror = 0 no errors c = 1 error in the specification of nlat c = 2 error in the specification of nlon c = 3 error in the specification of isym c = 4 error in the specification of nt c = 5 error in the specification of idv c = 6 error in the specification of jdv c = 7 error in the specification of mdb c = 8 error in the specification of ndb c = 9 error in the specification of lshses c = 10 error in the specification of lwork c ********************************************************************** c c