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dispersion.f90
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dispersion.f90
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!----------------------------------------------------------------------
SUBROUTINE ALPHA_CALC (LO,LA)
!......................................................................
!DESCRIPTION:
! #. CALL SUBROUTINE ALPHA() TO DETERMINE HIDDEN GRIDS FOR THE
! PURPOSE OF DISPERSION IMPROVEMENT
! #. LO%LAYGOV:
! 2 - LINEAR SWE WITH DISPERSION-IMPROVED SCHEME;
! 3 - NONLINEAR SWE WITH DISPERSION-IMPROVED SCHEME;
!NOTES:
! #. CREATED ON JAN 22 2009 (XIAOMING WANG, GNS)
! #. UPDATED ON JAN.27 2009 (XIAOMING WANG, GNS)
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: LO
TYPE (LAYER), DIMENSION(NUM_GRID) :: LA
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
IF (LO%LAYGOV .EQ. 2 .OR. LO%LAYGOV .EQ. 3) THEN
WRITE (*,*) ' CALCULATING COEFICIENTS FOR DISPERSION-IMPROVED SCHEME......'
ENDIF
IF (LO%LAYSWITCH .EQ. 0) THEN
IF (LO%LAYGOV .GE. 2) CALL ALPHA (LO)
END IF
DO I=1,NUM_GRID
IF (LA(I)%LAYSWITCH .EQ. 0) THEN
IF (LA(I)%LAYGOV .GE. 2) CALL ALPHA (LA(I))
END IF
END DO
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE ALPHA (LO)
!.....REF: YOON, S.B. (2002), JOURNAL OF GEOPHYSICAL RESEARCH, VOL.107,
! NO.C10,3140
!.....DETERMINE COEFFICIENT ALPHA SO AS TO IMPROVE NUMERICAL DISPERSION
! SUBROUTINE IS DESIGNED TO INCLUDE DISPERSION EFFECT IN SWE
! ASSUME 'SQUARE' GRID CELLS (I.E., DX=DY)
!.....CREATED ON DEC 2007 (XIAOMING WANG, CORNELL UNIVERSITY)
! UPDATED ON DEC 15, 2008 (XIAOMING WANG, GNS)
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: LO
REAL DX, DY, DT, DXS, DYS
REAL H(LO%NX,LO%NY)
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DX = LO%DX
DY = LO%DY
DT = LO%DT
H = LO%H
DO I = 1,LO%NX
DO J = 1,LO%NY
IF (H(I,J) .GT. GX) THEN
!ADJUSTED GRID SIZE IN METERS
DELTA = SQRT(4.0*H(I,J)**2+GRAV*H(I,J)*(DT**2))
IF (LO%LAYCORD .EQ. 0) THEN
LO%ALPHA(I,J) = DELTA/(R_EARTH*COS(LO%Y(J) &
*RAD_DEG)*LO%DX*RAD_MIN)
ELSE
LO%ALPHA(I,J) = DELTA/LO%DX
ENDIF
ELSE
LO%ALPHA(I,J) = 1.0
ENDIF
!SETUP LIMIT ON ALPHA
A_LIMIT = 10.0
IF (LO%ALPHA(I,J) .GT. A_LIMIT) LO%ALPHA(I,J) = A_LIMIT
!CALCULATE THE SIZE OF HIDDEN GRIDS
IF (LO%LAYCORD.EQ.0) THEN
!* DYS = LO%DEL_Y(J)*RAD_MIN*LO%ALPHA(I,J)
!* DXS = LO%DX*RAD_MIN*LO%ALPHA(I,J)
DXS = LO%DX*LO%ALPHA(I,J)
DYS = LO%DEL_Y(J)*LO%ALPHA(I,J)
ELSE
DXS = LO%DX*LO%ALPHA(I,J)
DYS = LO%DY*LO%ALPHA(I,J)
ENDIF
!CALCULATE COEF. OF 4-PTS LAGRANGE CUBIC INTERPOLATION
A = LO%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
N = FLOOR(SHIFT)
BETA = SHIFT - N
B1 = 1.0-BETA
B2 = BETA
DX = LO%DX
XF = DX+BETA*DX
XB = DX+(1.0-BETA)*DX
X1 = 0.0*DX
X2 = 1.0*DX
X3 = 2.0*DX
X4 = 3.0*DX
LO%CF(I,J,1) = ((XF-X2)*(XF-X3)*(XF-X4)) &
/((X1-X2)*(X1-X3)*(X1-X4))
LO%CF(I,J,2) = ((XF-X1)*(XF-X3)*(XF-X4)) &
/((X2-X1)*(X2-X3)*(X2-X4))
LO%CF(I,J,3) = ((XF-X1)*(XF-X2)*(XF-X4)) &
/((X3-X1)*(X3-X2)*(X3-X4))
LO%CF(I,J,4) = ((XF-X1)*(XF-X2)*(XF-X3)) &
/((X4-X1)*(X4-X2)*(X4-X3))
LO%CB(I,J,1) = ((XB-X2)*(XB-X3)*(XB-X4)) &
/((X1-X2)*(X1-X3)*(X1-X4))
LO%CB(I,J,2) = ((XB-X1)*(XB-X3)*(XB-X4)) &
/((X2-X1)*(X2-X3)*(X2-X4))
LO%CB(I,J,3) = ((XB-X1)*(XB-X2)*(XB-X4)) &
/((X3-X1)*(X3-X2)*(X3-X4))
LO%CB(I,J,4) = ((XB-X1)*(XB-X2)*(XB-X3)) &
/((X4-X1)*(X4-X2)*(X4-X3))
!CREATE MASK FOR DISPERSION CALCULATION:
! 1 - WITH DISPERSION-IMPROVED SCHEME;
! 0 - WITHOUT DISPERSION-IMPROVED SCHEME;
LO%MASK(:,:) = 0
N_LIMIT = NINT(A_LIMIT)
IF (I.GT.N_LIMIT .AND. I.LT.LO%NX-N_LIMIT) THEN
IF (J.GT.N_LIMIT .AND. J.LT.LO%NY-N_LIMIT) THEN
LO%MASK(I,J) = 1
ENDIF
ENDIF
N_LIMIT = NINT(2.0*A_LIMIT)
IF (I.GT.N_LIMIT .AND. I.LT.LO%NX-N_LIMIT) THEN
IF (J.GT.N_LIMIT .AND. J.LT.LO%NY-N_LIMIT) THEN
IF (LO%H(I,J) .LT. GX) THEN
DO KI = I-N_LIMIT,I+N_LIMIT
DO KJ = J-N_LIMIT,J+N_LIMIT
LO%MASK(KI,KJ) = 0
ENDDO
ENDDO
ENDIF
ENDIF
ENDIF
!......................................................................
!CALCULATE COEF FOR YOON'S METHOD (2002)
A = LO%ALPHA(I,J)
IF (A .GT. 3.0) A = 3.0
IF (LO%LAYCORD .EQ. 0) THEN
LO%A1X(I,J) = (A**2-1)/(24.*LO%DX*RAD_MIN)
LO%A2X(I,J) = 3.*(9.-A**2)/(24.*LO%DX*RAD_MIN)
LO%A1Y(I,J) = (A**2-1)/(24.*LO%DEL_Y(J)*RAD_MIN)
LO%A2Y(I,J) = 3.*(9.-A**2)/(24.*LO%DEL_Y(J)*RAD_MIN)
ELSE
LO%A1X(I,J) = (A**2-1)/(24.*LO%DX)
LO%A2X(I,J) = 3.*(9.-A**2)/(24.*LO%DX)
LO%A1Y(I,J) = (A**2-1)/(24.*LO%DEL_Y(J))
LO%A2Y(I,J) = 3.*(9.-A**2)/(24.*LO%DEL_Y(J))
ENDIF
ENDDO
ENDDO
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE UVW (U,U0,V,V0,WX,WY,WX0,WY0,LO)
!.....REF: YOON, S.B. (2002), JOURNAL OF GEOPHYSICAL RESEARCH, VOL.107,
! NO.C10,3140
!.....DETERMINE COEFFICIENT ALPHA SO AS TO IMPROVE NUMERICAL DISPERSION
! SUBROUTINE DESIGNED TO INCLUDED DISPERSION IN SWE
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: LO
REAL DX, DY, DT, DXS, DYS, G
REAL H(LO%NX,LO%NY)
REAL U(LO%NX,LO%NY),U0(LO%NX,LO%NY) !0 MEANS VALUE AT TIME STEP N-1
REAL V(LO%NX,LO%NY),V0(LO%NX,LO%NY)
REAL WX0(LO%NX,LO%NY),WY0(LO%NX,LO%NY) !PQ AT CELL CORNERS
REAL WX(LO%NX,LO%NY),WY(LO%NX,LO%NY) !PQ AT CELL EDGES
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DATA RAD/0.01745329252/
G = GRAV
DX = LO%DX
DY = LO%DY
DT = LO%DT
H = LO%H
DO I = 1,LO%NX
IP1 = I + 1
IM1 = I - 1
IF(IP1.GE.LO%NX) IP1 = LO%NX
IF(IM1.LE.1) IM1 = 1
DO J = 1,LO%NY
JP1 = J + 1
JM1 = J - 1
IF(JP1.GE.LO%NY) JP1 = LO%NY
IF(JM1.LE.1) JM1 = 1
IF (LO%HP(I,J).GT.0.0 .AND. LO%HP(IP1,J).GT.0.0) THEN
IF (LO%HQ(I,J).GT.0.0 .AND. LO%HQ(I,JP1).GT.0.0) THEN
HP = LO%HP(I,J)
HQ = LO%HQ(I,J)
HPQ = (LO%HP(I,J) + LO%HP(I,JP1) + LO%HQ(I,J) &
+ LO%HQ(IP1,J))/4.0
U(I,J) = LO%M(I,J,1)**2/HP
U0(I,J) = LO%M0(I,J)**2/HP
V(I,J) = LO%N(I,J,1)**2/HQ
V0(I,J) = LO%N0(I,J)**2/HQ
WX(I,J) = (LO%N(I,J,1)+LO%N(IP1,J,1) &
+LO%N(I,JM1,1)+LO%N(IP1,JM1,1)) &
*(LO%M(I,J,1))/(4.0*HP)
WY(I,J) = (LO%M(I,J,1)+LO%M(IM1,J,1) &
+LO%M(I,JP1,1)+LO%M(IM1,JP1,1)) &
*(LO%N(I,J,1))/(4.0*HQ)
WX0(I,J) = (LO%N0(I,J)+LO%N0(IP1,J)+LO%N0(I,JM1) &
+LO%N0(IP1,JM1))*(LO%M0(I,J))/(4.0*HP)
WY0(I,J) = (LO%M0(I,J)+LO%M0(IM1,J)+LO%M0(I,JP1) &
+LO%M0(IM1,JP1))*(LO%N0(I,J))/(4.0*HQ)
ENDIF
ENDIF
ENDDO
ENDDO
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE MASS_S_D (L)
! ....SOLVE CONTINUITY EQUATION IN SPHERICAL COORD.
!.....ADOPT DISPERSION-IMPROVED NUMERICAL SCHEME
!.....CREATED ON DEC 2007 (XIAOMING WANG, CORNELL UNIVERSITY)
! UPDATED ON DEC.15 2008 (XIAOMING WANG, GNS)
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: L
REAL ALPHA, DPDX, DQDY, A1, A2
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DATA UB/99.0/
DATA OSIXTY/0.016666666667/
!
IS = 2
JS = 2
!.....DIMENSIONALITY INCLUDED IN THE COMPUTATION
IDIM = 2
!.....INTERPOLATION METHOD.
! 1 - YOON 2002;
! 2 - LAGRANGE 4 POINTS (CUBIC)
INTP = 2
IF (L%ID .EQ. 1) THEN
IE = L%NX-1 !FOR OUTEST LAYER
JE = L%NY-1
ELSE
IE = L%NX !FOR INNER LAYER
JE = L%NY
END IF
DO J=JS,JE
JM1 = J-1
JM2 = J-2
JP1 = J+1
JP2 = J+2
IF (JM1.LE.1) JM1 = 1
IF (JM2.LE.1) JM2 = 1
IF (JP1.GE.L%NY) JP1 = L%NY
IF (JP2.GE.L%NY) JP2 = L%NY
DO I=IS,IE
IM1 = I-1
IM2 = I-2
IP1 = I+1
IP2 = I+2
IF (IM1.LE.1) IM1 = 1
IF (IM2.LE.1) IM2 = 1
IF (IP1.GE.L%NX) IP1 = L%NX
IF (IP2.GE.L%NX) IP2 = L%NX
IF (L%H(I,J) .GT. GX) THEN
A = L%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*RAD_MIN*L%ALPHA(I,J)
DYS = L%DEL_Y(J)*RAD_MIN*L%ALPHA(I,J)
IF (L%MASK(I,J) .EQ. 1) THEN
IF (INTP.EQ.1) THEN
ALPHA = L%ALPHA(I,J)
A1X = L%A1X(I,J) !(ALPHA**2-1)/(24.*L%DX)
A1Y = L%A1Y(I,J)
A2X = L%A2X(I,J) !3.*(9.-ALPHA**2)/(24.*L%DX)
A2Y = L%A2Y(I,J)
DPDX = A1X*(L%M(IP1,J,1)-L%M(IM2,J,1)) &
+A2X*(L%M(I,J,1)-L%M(IM1,J,1))
DQDY = A1Y*(L%N(I,JP1,1)*L%R6(JP1)-L%N(I,JM2,1) &
*L%R6(J-2))+A2Y*(L%N(I,J,1)*L%R6(J) &
-L%N(I,JM1,1)*L%R6(JM1))
ZZ = L%Z(I,J,1)-L%R1(I,J)*DXS*DPDX &
-L%R11(I,J)*DYS*DQDY
ENDIF
IF (INTP.EQ.2) THEN
PF = L%CF(I,J,1)*L%M(IM1+NN,J,1) &
+ L%CF(I,J,2)*L%M(I+NN,J,1) &
+ L%CF(I,J,3)*L%M(IP1+NN,J,1) &
+ L%CF(I,J,4)*L%M(IP2+NN,J,1)
PB = L%CB(I,J,1)*L%M(IM1-NN,J,1) &
+ L%CB(I,J,2)*L%M(I-NN,J,1) &
+ L%CB(I,J,3)*L%M(IP1-NN,J,1) &
+ L%CB(I,J,4)*L%M(IP2-NN,J,1)
QF = L%CF(I,J,1)*L%N(I,JM1+NN,1)*L%R6(JM1+NN) &
+ L%CF(I,J,2)*L%N(I,J+NN,1)*L%R6(J+NN) &
+ L%CF(I,J,3)*L%N(I,JP1+NN,1)*L%R6(JP1+NN) &
+ L%CF(I,J,4)*L%N(I,JP2+NN,1)*L%R6(JP2+NN)
QB = L%CB(I,J,1)*L%N(I,JM1-NN,1)*L%R6(JM1-NN) &
+ L%CB(I,J,2)*L%N(I,J-NN,1)*L%R6(J-NN) &
+ L%CB(I,J,3)*L%N(I,JP1-NN,1)*L%R6(JP1-NN) &
+ L%CB(I,J,4)*L%N(I,JP2-NN,1)*L%R6(JP2-NN)
DPDX = (PF-PB)
DQDY = (QF-QB)
!* ZZ = L%Z(I,J,1)-L%R1(I,J)*DPDX-L%R0(I,J)*DQDY
ZZ = L%Z(I,J,1)-L%R1(I,J)*DPDX-L%R11(I,J)*DQDY
ENDIF
ELSE
ZZ = L%Z(I,J,1)-L%R1(I,J)*(L%M(I,J,1)-L%M(IM1,J,1)) &
-L%R11(I,J)*(L%N(I,J,1)*L%R6(J) &
-L%N(I,JM1,1)*L%R6(JM1))
ENDIF
IF (L%INI_SWITCH .EQ. 3 .OR. L%INI_SWITCH.EQ.4) THEN
ZZ = ZZ-(L%HT(I,J,2)-L%HT(I,J,1))
ENDIF
IF (ABS(ZZ) .LT. EPS) ZZ = ZERO
! IF (ABS(ZZ) .GT. UB) ZZ=SIGN(UB,ZZ)
!DEPRESSION CANNOT BE LESS THAN BOTTOM ELEVATION
IF ( (ZZ+L%H(I,J)) .LE. ZERO ) ZZ = -L%H(I,J)
L%Z(I,J,2) = ZZ
ELSE
L%Z(I,J,2) = 0.0
ENDIF
END DO
END DO
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE MASS_C_D (L)
! ....SOLVE CONTINUITY EQUATION (LINEAR) IN CARTESIAN COORD.
! LAYID = 1, OUTEST LAYER
! OTHERWISE, INNER LAYER
!
!NOTES:
! #. ADD SUPPORT FOR DX\=DY (FOR HIGH-LATITUDE, 05/04/2007)
! RX = L%R
! RY = L%DT/L%DY
! SUBROUTINE DESIGNED TO INCCLUDE DISPERSION IN SWE
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: L
REAL ALPHA, DPDX, DQDY, A1, A2
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DATA UB/99.0/
RX = L%RX
RY = L%RY
GRT = L%DT*GRAV
!.....DIMENSIONALITY INCLUDED IN THE COMPUTATION
IDIM = 2
!.....INTERPOLATION METHOD.
! 1 - YOON2002;
! 2 - LAGRANGE 4 POINTS (CUBIC)
INTP = 2
!
IS = 2
JS = 2
IF(L%ID .EQ. 1)THEN !OUTTEST LAYER
IE = L%NX -1
JE = L%NY -1
ELSE ! INNER LAYER
IE = L%NX
JE = L%NY
ENDIF
IF (IDIM.EQ.2) THEN
DO J=JS,JE
JM1 = J-1
JM2 = J-2
JP1 = J+1
JP2 = J+2
IF (JM1.LE.1) JM1 = 1
IF (JM2.LE.1) JM2 = 1
IF (JP1.GE.L%NY) JP1 = L%NY
IF (JP2.GE.L%NY) JP2 = L%NY
DO I=IS,IE
IM1 = I-1
IM2 = I-2
IP1 = I+1
IP2 = I+2
IF (IM1.LE.1) IM1 = 1
IF (IM2.LE.1) IM2 = 1
IF (IP1.GE.L%NX) IP1 = L%NX
IF (IP2.GE.L%NX) IP2 = L%NX
IF (L%H(I,J) .GT. GX) THEN
A = L%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*L%ALPHA(I,J)
DYS = L%DY*L%ALPHA(I,J)
IF (L%MASK(I,J).EQ.1) THEN
IF (INTP.EQ.1) THEN
A1X = L%A1X(I,J) !(ALPHA**2-1)/(24.*L%DX)
A1Y = L%A1Y(I,J)
A2X = L%A2X(I,J) !3.*(9.-ALPHA**2)/(24.*L%DX)
A2Y = L%A2Y(I,J)
DPDX = A1X*(L%M(IP1,J,1)-L%M(IM2,J,1)) &
+A2X*(L%M(I,J,1)-L%M(IM1,J,1))
DQDY = A1Y*(L%N(I,JP1,1)-L%N(I,JM2,1)) &
+A2Y*(L%N(I,J,1)-L%N(I,JM1,1))
ZZ = L%Z(I,J,1)-L%DT*(DPDX+DQDY)
ENDIF
IF (INTP.EQ.2) THEN
PF = L%CF(I,J,1)*L%M(IM1+NN,J,1) &
+ L%CF(I,J,2)*L%M(I+NN,J,1) &
+ L%CF(I,J,3)*L%M(IP1+NN,J,1) &
+ L%CF(I,J,4)*L%M(IP2+NN,J,1)
PB = L%CB(I,J,1)*L%M(IM1-NN,J,1) &
+ L%CB(I,J,2)*L%M(I-NN,J,1) &
+ L%CB(I,J,3)*L%M(IP1-NN,J,1) &
+ L%CB(I,J,4)*L%M(IP2-NN,J,1)
QF = L%CF(I,J,1)*L%N(I,JM1+NN,1) &
+ L%CF(I,J,2)*L%N(I,J+NN,1) &
+ L%CF(I,J,3)*L%N(I,JP1+NN,1) &
+ L%CF(I,J,4)*L%N(I,JP2+NN,1)
QB = L%CB(I,J,1)*L%N(I,JM1-NN,1) &
+ L%CB(I,J,2)*L%N(I,J-NN,1) &
+ L%CB(I,J,3)*L%N(I,JP1-NN,1) &
+ L%CB(I,J,4)*L%N(I,JP2-NN,1)
DP = (PF-PB)
DQ = (QF-QB)
ZZ = L%Z(I,J,1) - (L%DT/DXS*DP+L%DT/DYS*DQ)
ENDIF
ELSE
ZZ = L%Z(I,J,1) - RX*(L%M(I,J,1)-L%M(IM1,J,1)) &
- RY*(L%N(I,J,1)-L%N(I,JM1,1))
ENDIF
IF (L%INI_SWITCH.EQ.3 .OR. L%INI_SWITCH.EQ.4) THEN
ZZ = ZZ-(L%HT(I,J,2)-L%HT(I,J,1))
ENDIF
IF (ABS(ZZ) .LT. EPS) ZZ = ZERO
!* IF (ABS(ZZ) .GT. UB) ZZ=SIGN(UB,ZZ)
!DEPRESSION CANNOT BE LESS THAN BOTTOM ELEVATION
IF ( (ZZ+L%H(I,J)) .LE. ZERO ) ZZ = -L%H(I,J)
L%Z(I,J,2) = ZZ
ELSE
L%Z(I,J,2) = 0.0
ENDIF
END DO
END DO
ENDIF
!.....CODE FOR 1-D STUDY
IF (IDIM.EQ.1) THEN
L%N(:,:,:) = 0.0
J = FLOOR(L%NY/2.)
DO I=IS,IE
IM1 = I-1
IM2 = I-2
IP1 = I+1
IP2 = I+2
IF (IM1.LE.1) IM1 = 1
IF (IM2.LE.1) IM2 = 1
IF (IP1.GE.L%NX) IP1 = L%NX
IF (IP2.GE.L%NX) IP2 = L%NX
IF (L%H(I,J) .GT. GX) THEN
A = L%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*L%ALPHA(I,J)
BETA = SHIFT - NN
IF (L%MASK(I,J).EQ.1) THEN
IF (INTP.EQ.1) THEN
A1X = L%A1X(I,J) !(ALPHA**2-1)/(24.*L%DX)
A2X = L%A2X(I,J) !3.*(9.-ALPHA**2)/(24.*L%DX)
DPDX = A1X*(L%M(IP1,J,1)-L%M(IM2,J,1)) &
+A2X*(L%M(I,J,1)-L%M(IM1,J,1))
ZZ = L%Z(I,J,1)-L%DT*DPDX
ENDIF
IF (INTP.EQ.2) THEN
IM2 = IM1-1
PF = L%CF(I,J,1)*L%M(IM1+NN,J,1) &
+ L%CF(I,J,2)*L%M(I+NN,J,1) &
+ L%CF(I,J,3)*L%M(IP1+NN,J,1) &
+ L%CF(I,J,4)*L%M(IP2+NN,J,1)
PB = L%CB(I,J,1)*L%M(IM1-NN,J,1) &
+ L%CB(I,J,2)*L%M(I-NN,J,1) &
+ L%CB(I,J,3)*L%M(IP1-NN,J,1) &
+ L%CB(I,J,4)*L%M(IP2-NN,J,1)
DP = (PF-PB)
ZZ = L%Z(I,J,1)-L%DT/DXS*DP
ENDIF
ELSE
ZZ = L%Z(I,J,1)-RX*(L%M(I,J,1)-L%M(IM1,J,1))
ENDIF
IF (L%INI_SWITCH.EQ.3 .OR. L%INI_SWITCH.EQ.4) THEN
ZZ = ZZ-(L%HT(I,J,2)-L%HT(I,J,1))
ENDIF
IF (ABS(ZZ) .LT. EPS) ZZ = ZERO
! IF (ABS(ZZ) .GT. UB) ZZ=SIGN(UB,ZZ)
!DEPRESSION CANNOT BE LESS THAN BOTTOM ELEVATION
IF ( (ZZ+L%H(I,J)) .LE. ZERO ) ZZ = -L%H(I,J)
L%Z(I,:,2) = ZZ
ELSE
L%Z(I,:,2) = 0.0
ENDIF
ENDDO
ENDIF
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE MOMT_S_D (L)
! ....SOLVE MOMENTUM EQUATION (LINEAR) IN SPHERICAL COORD.
! LAYID = 1, OUTEST LAYER
! OTHERWISE, INNER LAYER
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: L
REAL MODSCM
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DATA TWLVTH/0.08333333333333/
DATA RAD/0.01745329252/
MODSCM = 0.0
!
GRT = GRAV*L%DT
!.....DIMENSIONALITY INCLUDED IN THE COMPUTATION
IDIM = 2
!.....INTERPOLATION METHOD.
! 1 - YOON2002;
! 2 - LAGRANGE 4 POINTS (CUBIC)
INTP = 2
IXM1 = L%NX-1
JYM1 = L%NY-1
IS = 2
JS = 2
IF (L%ID .EQ. 1) THEN
IS = 1
JS = 1
END IF
DO I=IS,IXM1
IP1 = I+1
DO J=JS,L%NY
IF ((L%H(I,J).GT.GX) .AND. (L%H(IP1,J).GT.GX)) THEN
JM1 = J-1
JM2 = J-2
JP1 = J+1
JP2 = J+2
IF (JM1 .LT. 1) JM1 = 1
IF (JM2 .LT. 1) JM2 = 1
IF (JP1 .GT. L%NY ) JP1 = L%NY
IF (JP2 .GT. L%NY ) JP2 = L%NY
HM = L%HP(I,J)
A = L%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*RAD_MIN*L%ALPHA(I,J)
DYS = L%DEL_Y(J)*RAD_MIN*L%ALPHA(I,J)
IPN = I+NN
IMN = I-NN
NS = NINT(A)
IF (NS.LT.1) NS = 1
JPNN = J+NS
JMNN = J-NS
IP1PN = IP1+NN
IM1PN = IM1+NN
IP1MN = IP1-NN
IM1MN = IM1-NN
IP2PN = IP2+NN
IP2MN = IP2-NN
IF (L%MASK(I,J) .EQ. 1) THEN
IF (INTP.EQ.1) THEN
ALPHA = L%ALPHA(I,J)
A1X = L%A1X(I,J) !(ALPHA**2-1)/(24.*L%DX)
A2X = L%A2X(I,J) !3.*(9.-ALPHA**2)/(24.*L%DX)
DZDX = A1X*(L%Z(I+2,J,2)-L%Z(I-1,J,2)) &
+ A2X*(L%Z(I+1,J,2)-L%Z(I,J,2))
TOT_N = L%N(I,J,1) + L%N(IP1,J,1) + L%N(I,JM1,1) &
+ L%N(IP1,JM1,1)
R2 = L%R2(I,J)*DXS
XM = L%M(I,J,1)-R2*DZDX + L%R3(I,J)*TOT_N
IF (L%MODSCM .EQ. 0) THEN
IF (ALPHA .LT. 1.732) THEN
GAMMA = ALPHA**2
DZFDX = A1X*(L%Z(I+2,J+1,2)-L%Z(I-1,J+1,2)) &
+A2X*(L%Z(I+1,J+1,2)-L%Z(I,J+1,2))
DZBDX = A1X*(L%Z(I+2,J-1,2)-L%Z(I-1,J-1,2)) &
+A2X*(L%Z(I+1,J-1,2)-L%Z(I,J-1,2))
ELSE
GAMMA = ALPHA**2/4.0
DZFDX = A1X*(L%Z(I+2,J+2,2)-L%Z(I-1,J+2,2)) &
+A2X*(L%Z(I+1,J+2,2)-L%Z(I,J+2,2))
DZBDX = A1X*(L%Z(I+2,J-2,2)-L%Z(I-1,J-2,2)) &
+A2X*(L%Z(I+1,J-2,2)-L%Z(I,J-2,2))
ENDIF
SCM = GAMMA*R2*TWLVTH &
*(DZFDX-2*DZDX+DZBDX)
XM = XM - SCM
ENDIF
ENDIF
IF (INTP.EQ.2) THEN !4-PTS LAGRANGE INTERPOLATION
ZMF = L%CF(I,J,1)*L%Z(IM1PN,J,2) &
+ L%CF(I,J,2)*L%Z(IPN,J,2) &
+ L%CF(I,J,3)*L%Z(IP1PN,J,2) &
+ L%CF(I,J,4)*L%Z(IP2PN,J,2)
ZMB = L%CB(I,J,1)*L%Z(IM1MN,J,2) &
+ L%CB(I,J,2)*L%Z(IMN,J,2) &
+ L%CB(I,J,3)*L%Z(IP1MN,J,2) &
+ L%CB(I,J,4)*L%Z(IP2MN,J,2)
DZMDX = (ZMF-ZMB)
TOT_N = L%N(I,J,1)+L%N(IP1,J,1)+L%N(I,JM1,1) &
+L%N(IP1,JM1,1)
XM = L%M(I,J,1)-L%R2(I,J)*DZMDX + L%R3(I,J)*TOT_N
IF (L%MODSCM .EQ. 0) THEN
ZUF = L%CF(I,J,1)*L%Z(IM1PN,JPNN,2) &
+ L%CF(I,J,2)*L%Z(IPN,JPNN,2) &
+ L%CF(I,J,3)*L%Z(IP1PN,JPNN,2) &
+ L%CF(I,J,4)*L%Z(IP2PN,JPNN,2)
ZUB = L%CB(I,J,1)*L%Z(IM1MN,JPNN,2) &
+ L%CB(I,J,2)*L%Z(IMN,JPNN,2) &
+ L%CB(I,J,3)*L%Z(IP1MN,JPNN,2) &
+ L%CB(I,J,4)*L%Z(IP2MN,JPNN,2)
ZLF = L%CF(I,J,1)*L%Z(IM1PN,JMNN,2) &
+ L%CF(I,J,2)*L%Z(IPN,JMNN,2) &
+ L%CF(I,J,3)*L%Z(IP1PN,JMNN,2) &
+ L%CF(I,J,4)*L%Z(IP2PN,JMNN,2)
ZLB = L%CB(I,J,1)*L%Z(IM1MN,JMNN,2) &
+ L%CB(I,J,2)*L%Z(IMN,JMNN,2) &
+ L%CB(I,J,3)*L%Z(IP1MN,JMNN,2) &
+ L%CB(I,J,4)*L%Z(IP2MN,JMNN,2)
DZUDX = (ZUF-ZUB)
DZLDX = (ZLF-ZLB)
ZADD = DZUDX-2.0*DZMDX+DZLDX
GAMMA = L%ALPHA(I,J)**2/(NS**2)
SCM = GAMMA*L%R2(I,J)*TWLVTH*ZADD
XM = XM - SCM
ENDIF
ENDIF
ELSE
TOT_N = L%N(I,J,1) + L%N(IP1,J,1) + L%N(I,JM1,1) &
+ L%N(IP1,JM1,1)
XM = L%M(I,J,1)-L%R2(I,J)*(L%Z(IP1,J,2)-L%Z(I,J,2)) &
+L%R3(I,J)*TOT_N
IF (L%MODSCM .EQ. 0) THEN
SCM = L%R2(I,J)*TWLVTH*((L%Z(IP1,JP1,2) &
-2*L%Z(IP1,J,2)+L%Z(IP1,JM1,2)) &
-(L%Z(I,JP1,2)-2*L%Z(I,J,2) &
+L%Z(I,JM1,2)))
XM = XM - SCM
ENDIF
ENDIF
IF (ABS(XM) .LT. EPS) XM = ZERO
L%M(I,J,2) = XM
ELSE
L%M(I,J,2) = 0.0
ENDIF
END DO
END DO
!
DO J=JS,JYM1
JP1 = J+1
DO I=IS,L%NX
IF ((L%H(I,J).GT.ZERO) .AND. (L%H(I,JP1).GT.ZERO)) THEN
IP1 = I+1
IP2 = I+2
IM1 = I-1
IM2 = I-2
IF (IP1 .GE. L%NX) IP1 = L%NX
IF (IP2 .GE. L%NX) IP2 = L%NX
IF (IM1 .LE. 1) IM1 = 1
IF (IM2 .LE. 1) IM2 = 1
HN = L%HQ(I,J)
A = L%ALPHA(I,J)
SHIFT = 0.5*(A+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*RAD_MIN*L%ALPHA(I,J)
DYS = L%DEL_Y(J)*RAD_MIN*L%ALPHA(I,J)
JPN = J+NN
JMN = J-NN
JP1PN = JP1+NN
JM1PN = JM1+NN
JP1MN = JP1-NN
JM1MN = JM1-NN
JP2PN = JP2+NN
JP2MN = JP2-NN
NS = NINT(A)
IF (NS.LT.1) NS = 1
IPNN = I+NS
IMNN = I-NS
GAMMA = L%ALPHA(I,J)**2
SCM = 0.0
IF (L%MASK(I,J) .EQ. 1) THEN
IF (INTP.EQ.1) THEN
ALPHA = L%ALPHA(I,J)
A1Y = L%A1Y(I,J) !(ALPHA**2-1)/(24.*L%DY)
A2Y = L%A2Y(I,J) !3.*(9.-ALPHA**2)/(24.*L%DY)
DZDY = A1Y*(L%Z(I,JP2,2)-L%Z(I,J-1,2)) &
+A2Y*(L%Z(I,JP1,2)-L%Z(I,J,2))
TOT_M = L%M(IM1,J,1)+L%M(IM1,JP1,1)+L%M(I,J,1) &
+L%M(I,JP1,1)
R4 = L%R4(I,J)*DYS
XN = L%N(I,J,1)-R4*DZDY -L%R5(I,J)*TOT_M
IF (L%MODSCM .EQ. 0) THEN
IF (ALPHA .LT. 1.732) THEN
GAMMA = ALPHA**2
DZUDY = A1Y*(L%Z(IP1,JP2,2)-L%Z(IP1,JM1,2)) &
+A2Y*(L%Z(IP1,JP1,2)-L%Z(IP1,J,2))
DZLDY = A1Y*(L%Z(IM1,JM2,2)-L%Z(IM1,JM1,2)) &
+A2Y*(L%Z(IM1,JP1,2)-L%Z(IM1,J,2))
ELSE
GAMMA = ALPHA**2/4.0
DZUDY = A1Y*(L%Z(IP2,JP2,2)-L%Z(IP2,JM1,2)) &
+A2Y*(L%Z(IP2,JP1,2)-L%Z(IP2,J,2))
DZLDY = A1Y*(L%Z(IM2,JP2,2)-L%Z(IM2,JM1,2)) &
+A2Y*(L%Z(IM2,JP1,2)-L%Z(IM2,J,2))
ENDIF
MODSCM = GAMMA*R4*TWLVTH &
*(DZUDY-2*DZDY+DZLDY)
XN = XN - MODSCM
ENDIF
ENDIF
IF (INTP.EQ.2) THEN
ZMF = L%CF(I,J,1)*L%Z(I,JM1PN,2) &
+ L%CF(I,J,2)*L%Z(I,JPN,2) &
+ L%CF(I,J,3)*L%Z(I,JP1PN,2) &
+ L%CF(I,J,4)*L%Z(I,JP2PN,2)
ZMB = L%CB(I,J,1)*L%Z(I,JM1MN,2) &
+ L%CB(I,J,2)*L%Z(I,JMN,2) &
+ L%CB(I,J,3)*L%Z(I,JP1MN,2) &
+ L%CB(I,J,4)*L%Z(I,JP2MN,2)
DZMDY = (ZMF-ZMB)
TOT_M = L%M(IM1,J,1)+L%M(IM1,JP1,1)+L%M(I,J,1) &
+L%M(I,JP1,1)
XN = L%N(I,J,1)-L%R4(I,J)*DZMDY-L%R5(I,J)*TOT_M
IF (L%MODSCM.EQ.0) THEN
ZRF = L%CF(I,J,1)*L%Z(IPNN,JM1PN,2) &
+ L%CF(I,J,2)*L%Z(IPNN,JPN,2) &
+ L%CF(I,J,3)*L%Z(IPNN,JP1PN,2) &
+ L%CF(I,J,4)*L%Z(IPNN,JP2PN,2)
ZRB = L%CB(I,J,1)*L%Z(IPNN,JM1MN,2) &
+ L%CB(I,J,2)*L%Z(IPNN,JMN,2) &
+ L%CB(I,J,3)*L%Z(IPNN,JP1MN,2) &
+ L%CB(I,J,4)*L%Z(IPNN,JP2MN,2)
ZLF = L%CF(I,J,1)*L%Z(IMNN,JM1PN,2) &
+ L%CF(I,J,2)*L%Z(IMNN,JPN,2) &
+ L%CF(I,J,3)*L%Z(IMNN,JP1PN,2) &
+ L%CF(I,J,4)*L%Z(IMNN,JP2PN,2)
ZLB = L%CB(I,J,1)*L%Z(IMNN,JM1MN,2) &
+ L%CB(I,J,2)*L%Z(IMNN,JMN,2) &
+ L%CB(I,J,3)*L%Z(IMNN,JP1MN,2) &
+ L%CB(I,J,4)*L%Z(IMNN,JP2MN,2)
DZRDY = (ZRF-ZRB)
DZLDY = (ZLF-ZLB)
ZADD = DZRDY-2.0*DZMDY+DZLDY
GAMMA = L%ALPHA(I,J)**2/NS**2
SCM = GAMMA*L%R4(I,J)*TWLVTH*ZADD
XN = XN - SCM
ENDIF
ENDIF
ELSE
TOT_M = L%M(IM1,J,1)+L%M(IM1,JP1,1)+L%M(I,J,1) &
+L%M(I,JP1,1)
XN = L%N(I,J,1)-L%R4(I,J)*(L%Z(I,JP1,2)-L%Z(I,J,2)) &
-L%R5(I,J)*TOT_M
IF (L%MODSCM .EQ. 0) THEN
SCM = L%R4(I,J)*TWLVTH*((L%Z(IP1,JP1,2) &
-2*L%Z(I,JP1,2)+L%Z(IM1,JP1,2)) &
-(L%Z(IP1,J,2)-2*L%Z(I,J,2) &
+L%Z(IM1,J,2)))
XN = XN - SCM
ENDIF
ENDIF
IF (ABS(XN) .LT. EPS) XN = ZERO
L%N(I,J,2) = XN
ELSE
L%N(I,J,2) = 0.0
ENDIF
END DO
END DO
!
RETURN
END
!----------------------------------------------------------------------
SUBROUTINE MOMT_C_D (L)
!.....SOLVE MOMENTUM EQUATION (LINEAR) IN CARTESIAN COORD.
! LAYID = 1, OUTEST LAYER
! OTHERWISE, INNER LAYER
! SUBROUTINE DESIGNED TO INCCLUDE DISPERSION IN SWE
! OPTION L%LAYGOV ==
! 2, LINEAR EQUATION WITH DISPERSION CORRECTION
! 3, NONLINEAR EQUATION WITH DISPERSION CORRECTION
!.....CREATED ON DEC 2007 (XIAOMING WANG, CORNELL UNIVERSITY)
! UPDATED ON DEC 15, 2008 (XIAOMING WANG, GNS)
!----------------------------------------------------------------------
USE LAYER_PARAMS
TYPE (LAYER) :: L
REAL SCM, GRX,GRY,FF,FM
REAL U(L%NX,L%NY),U0(L%NX,L%NY) !0 MEANS VALUE AT TIME STEP N-1
REAL V(L%NX,L%NY),V0(L%NX,L%NY)
REAL W(L%NX,L%NY),W0(L%NX,L%NY)
REAL WX0(L%NX,L%NY),WY0(L%NX,L%NY) !PQ AT CELL CORNERS
REAL WX(L%NX,L%NY),WY(L%NX,L%NY) !PQ AT CELL EDGES
COMMON /CONS/ ELMAX,GRAV,PI,R_EARTH,GX,EPS,ZERO,ONE,NUM_GRID, &
NUM_FLT,V_LIMIT,RAD_DEG,RAD_MIN
DATA TWLVTH/0.08333333333333/
SCM = 0.0
CONST = 0.5*L%DT*GRAV
FM = L%FRIC_COEF
FF = 0.0
DX = L%DX
DY = L%DY
DT = L%DT
GRT = GRAV*L%DT
RX = L%RX
RY = L%RY
GRX = L%GRX
GRY = L%GRY
!.....DIMENSIONALITY OF COMPUTATION. 1 - 1D; 2 - 2D
IDIM = 2
IF (IDIM .EQ. 1) L%N = 0.0
!.....INTERPOLATION METHOD.
! 0 - USING FIXED GRIDS;
! 1 - LINEAR;
! 2 - LAGRANGE 4-POINTS (CUBIC)
INTP = 2
!.....CONTROL IF NONLINEAR TERMS USE HIDDEN GRIDS.
! 0 - NO NONLINEAR;
! 1 - HIDDEN GRIDS,
! 2 - FIXED GRIDS;
! 3 - FIXED GRIDS (V. COEF.)
NL = 2
!.....CONTROL IF 5TH-ORDER DERIVATIVES ARE SOLVED.
! 0 - NO;
! 1 - YES;
IT4 = 0
IF (L%LAYGOV.EQ.2) NL = 0
IF (L%LAYGOV.EQ.3) NL = 2
IF (NL.NE.0) CALL UVW (U,U0,V,V0,WX,WY,WX0,WY0,L)
!
IXM1 = L%NX-1
JYM1 = L%NY-1
IF (L%ID .EQ. 1) THEN
IS = 1
JS = 1
ELSE
IS = 2
JS = 2
END IF
IF (IDIM.EQ.2) THEN
! MOMENTUM IN X DIRECTION
DO I=IS,IXM1
IP1 = I+1
IP2 = I+2
IM1 = I-1
IM2 = I-2
IF (IP1 .GE. L%NX) IP1 = L%NX
IF (IP2 .GE. L%NX) IP2 = L%NX
IF (IM1 .LE. 1) IM1 = 1
IF (IM2 .LE. 1) IM2 = 1
DO J=JS,L%NY
IF ((L%H(I,J).GT.GX) .AND. (L%H(IP1,J).GT.GX)) THEN
JM1 = J-1
JM2 = J-2
JP1 = J+1
JP2 = J+2
IF (JM1 .LT. 1) JM1 = 1
IF (JM2 .LT. 1) JM2 = 1
IF (JP1 .GT. L%NY ) JP1 = L%NY
IF (JP2 .GT. L%NY ) JP2 = L%NY
HM = L%HP(I,J)+0.5*(L%Z(I,J,2)+L%Z(IP1,J,2))
!USE BOTTOM FRICTION
IF (L%FRIC_SWITCH.NE.1) THEN
IF (L%FRIC_SWITCH .EQ. 2) FM = L%FRIC_VCOEF(I,J)
XQQ = 0.25*(L%N(I,J,1)+L%N(IP1,J,1)+L%N(I,JM1,1) &
+L%N(IP1,JM1,1))
! DF = 0.5*(L%H(I,J)+L%H(IP1,J))
IF (HM.GE.1.0E-3) THEN
FF = CONST*FM*FM*SQRT(L%M(I,J,1)**2+XQQ**2) &
/HM**(2.3333333)
ELSE
FF = 0.0
ENDIF
ENDIF !END OF APPLYING BOTTOM FRICTION
ALPHA = L%ALPHA(I,J)
SHIFT = 0.5*(ALPHA+1.0)
NN = FLOOR(SHIFT)
DXS = L%DX*ALPHA
DYS = L%DY*ALPHA
IF (NL.EQ.1) THEN
BETA = SHIFT - NN
B1 = (1.0-BETA)/DXS
B2 = BETA/DXS
ENDIF
IPN = I+NN
IMN = I-NN
NS = NINT(A)
IF (NS.LT.1) NS = 1
JPNN = J+NS
JMNN = J-NS
IP1PN = IP1+NN
IM1PN = IM1+NN
IP1MN = IP1-NN
IM1MN = IM1-NN
IP2PN = IP2+NN
IP2MN = IP2-NN
ISPANS = MAX(NN+5,10)
!* ISPANS = 10
ISPANE = L%NX-ISPANS
JSPANS = ISPANS
JSPANE = L%NY-JSPANS
IF (L%MASK(I,J) .EQ. 1) THEN
!CALCULATE DISPERSION CORRECTION
IF (INTP.EQ.0) THEN !FIXED POINT MULTIPLIED BY COEF.
ZMF = L%CF(I,J,1)*L%Z(IM1PN,J,2) &
+ L%CF(I,J,2)*L%Z(IPN,J,2) &
+ L%CF(I,J,3)*L%Z(IP1PN,J,2) &
+ L%CF(I,J,4)*L%Z(IP2PN,J,2)
ZMB = L%CB(I,J,1)*L%Z(IM1MN,J,2) &
+ L%CB(I,J,2)*L%Z(IMN,J,2) &
+ L%CB(I,J,3)*L%Z(IP1MN,J,2) &
+ L%CB(I,J,4)*L%Z(IP2MN,J,2)
DZMDX = (ZMF-ZMB)
XM = (1.-FF)*L%M(I,J,1)-GRX/ALPHA*HM*DZMDX
IF (L%MODSCM .EQ. 0) THEN
!TERM TO CORRECT DIAGNAL DIFFERENTIATION
ZADD = ((L%Z(IP1,JP1,2) &
-2*L%Z(IP1,J,2)+L%Z(IP1,JM1,2)) &
-(L%Z(I,JP1,2)-2*L%Z(I,J,2) &
+L%Z(I,JM1,2)))
GAMMA = L%ALPHA(I,J)**2
SCM = GAMMA*GRX*TWLVTH*HM*ZADD