SUBROUTINE SATCOV(JCAP,NLATH,NLON,CSHAT,
     *  RLATS,PLN,WGTS,TRIGS,IFAX,RLKM,LMAD)
C$$$  SUBPROGRAM DOCUMENTATION BLOCK
C                .      .    .                                       .
C SUBPROGRAM:    SATCOV     SET UP ERROR FOR SATEMS
C   PRGMMR: PARRISH          ORG: W/NMC22    DATE: 90-10-06
C
C ABSTRACT: SET UP GRID ERROR AND CORRELATION SPECTRUM FOR SATEMS
C     (START WITH TRANSFORM OF SOAR FUNCTION)
C
C PROGRAM HISTORY LOG:
C   90-10-06  PARRISH
C
C   INPUT ARGUMENT LIST:
C     JCAP     - TRIANGULAR TRUNCATION
C     NLATH    - NUMBER OF GAUSSIAN LATS IN ONE HEMISPHERE
C     NLON     - NUMBER OF LONGITUDES
C     AP,BP    - RECURSION CONSTANTS FOR SPHERICAL HARMONICS
C     SLAT     - SIN(GAUSSIAN LATITUDES)
C     PE0      - STARTING FUNCTIONS FOR SPHERICAL HARMONICS
C     WGTS     - GAUSSIAN INTEGRATION WEIGHTS
C     TRIGS,IFAX - USED BY FFT
C     RLATS    - GRID LATITUDES (RADIANS)
C     RLKM     - SAT ERROR CORRELATION LENGTH SCALE
C     LMIX,LASTMIX,LPAIRS - USED FOR MULTITASKING
C
C   OUTPUT ARGUMENT LIST:
C     CSHAT    - SAT. CORRELATION FUNCTION ARRAY
C
C ATTRIBUTES:
C   LANGUAGE: CFT77
C   MACHINE:  CRAY YMP
C
C$$$
C
C-CRA          DIMENSION LMAD(0:JCAP,0:JCAP)
C-CRA          REAL CSHAT((JCAP+1)*(JCAP+2))
C-CRA          REAL CSN(0:JCAP),CST(0:JCAP)
C-CRA          REAL PLN((JCAP+1)*(JCAP+2),NLATH)
C-CRA          REAL WGTS(NLATH*2),TRIGS(2*NLON),RLATS(2*NLATH)
C-CRA          REAL CGRID(2*NLATH+1,NLON+2)
C-CRA          INTEGER IFAX(10)
 
          DIMENSION LMAD(0:62,0:62)
          REAL CSHAT((62+1)*(62+2))
          REAL CSN(0:62),CST(0:62)
          REAL PLN((62+1)*(62+2),48)
          REAL WGTS(48*2),TRIGS(2*192),RLATS(2*48)
          REAL CGRID(2*48+1,192+2)
          INTEGER IFAX(10)
C--------
C        RLKM=400.
C--------        RLKM IS LENGTH PARAMETER FOR SOAR (IN KM)
      NC=(JCAP+1)*(JCAP+2)
      RL=RLKM/6370.
      IF(RLKM .EQ. 0.)THEN
C-CRA                 CSN=1.
C       REAL CSN(0:JCAP),CST(0:JCAP)
          DO ITMP=0,JCAP
          CSN(ITMP)=1.
          ENDDO
      ELSE
C--------         RL IS LENGTH IN RADIANS
C--------
C-------- COMPUTE CORRELATION FUNCTION ON GRID.
C--------
       PIH=2.*ATAN(1.)
       DO J=1,NLATH*2
         ARG=(PIH-RLATS(J))/RL
         CORSAT=(1.+ARG)*EXP(-ARG)
C       PRINT *,J,CORSAT
        DO I=1,NLON
         CGRID(J,I)=CORSAT
        END DO
       END DO
       CALL G2S0(CSHAT,CGRID,JCAP,NLON,NLATH,WGTS,PLN,TRIGS,IFAX)
C--------
C-------- BEYOND WAVE 30, ERROR IS INFINITE
C--------
       DO N=31,JCAP
        CSHAT(LMAD(N,0))=CSHAT(LMAD(30,0))
       END DO
       DO N=0,JCAP
        CSN(N)=SQRT(2./(2.*N+1.))*CSHAT(LMAD(N,0))
        CSN(N)=MAX(CSN(N),5.E-4*CSN(0))
       END DO
      END IF
      WRITE(6,110)RLKM,JCAP
110   FORMAT(' SATEM ERROR COVAR SPECTRUM FOLLOWS FOR L=',F5.0,
     *    ' KM, JCAP=',I3)
      WRITE(6,120)(CSN(N),N=0,JCAP)
120   FORMAT(1H ,5E12.4)
      DO M=0,JCAP
       DO L=0,JCAP-M
        CSHAT(LMAD(M,L))=CSN(M+L)
        CSHAT(LMAD(M,L)+1)=CSN(M+L)
       END DO
      END DO
C--------
C-------- MULTIPLY L=0 PART OF SPECTRUM BY 2
C--------
      DO I=1,NC
       IF(CSHAT(I) .NE. 0.)CSHAT(I)=1./CSHAT(I)
      END DO
      DO M=0,JCAP
       CSHAT(LMAD(M,0))=2.*CSHAT(LMAD(M,0))
      END DO
C--------
C-------- COMPUTE DIAGONAL FOR NORMALIZATION
C--------
         CALL S2MG2X(CSHAT,CGRID,JCAP,NLATH,NLON,PLN)
         RNMAX=-1.E12
         RNMIN=1.E12
         DO 1150 I=1,NLON
          DO 1150 J=1,2*NLATH
           RNMAX=MAX(CGRID(J,I),RNMAX)
           RNMIN=MIN(CGRID(J,I),RNMIN)
1150     CONTINUE
         WRITE(6,1160)RLKM,JCAP,RNMAX,RNMIN
1160     FORMAT(' SATEM ERROR L= ',F5.0,' KM, JCAP= ',I3,
     *     ' MAX, MIN OF H*CHAT*HTRANS=',3E11.3)
         FACTOR=1./RNMAX
C-CRA                   CSHAT=FACTOR*CSHAT
C       REAL CSHAT((JCAP+1)*(JCAP+2))
          DO ITMP=1,(JCAP+1)*(JCAP+2)
          CSHAT(ITMP)=FACTOR*CSHAT(ITMP)
          ENDDO
C        CALL S2MG2X(CSHAT,CGRID,JCAP,NLATH,NLON,AP,BP,SLAT,PE0)
C        RNMAX=-1.E12
C        RNMIN=1.E12
C        DO 2150 I=1,NLON
C         DO 2150 J=1,2*NLATH
C          RNMAX=MAX(CGRID(J,I),RNMAX)
C          RNMIN=MIN(CGRID(J,I),RNMIN)
C150     CONTINUE
C        WRITE(6,2160)RNMAX,RNMIN
C160     FORMAT(' AFTER NORMALIZATION, MAX, MIN OF H*CHAT*HTRANS=',
C    *          2E11.3)
      RETURN
      END