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jahn |
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C $Header: /u/gcmpack/MITgcm_contrib/darwin2/pkg/monod/monod_radtrans_direct.F,v 1.2 2012/08/24 19:45:36 jahn Exp $ |
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jahn |
1.2 |
C $Name: $ |
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jahn |
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#include "DARWIN_OPTIONS.h" |
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CBOP |
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C !ROUTINE: MONOD_RADTRANS_DIRECT |
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C !INTERFACE: ========================================================== |
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subroutine MONOD_RADTRANS_DIRECT( |
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I H,rmud,Edsf,Essf,a_k,bt_k,bb_k,kmax, |
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O Edbot,Esbot,Eubot,Estop,Eutop, |
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O tirrq,tirrwq, |
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O amp1, amp2, |
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I myThid) |
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C !DESCRIPTION: |
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c |
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c Model of irradiance in the water column. Accounts for three |
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c irradiance streams [Ackleson, Balch, Holligan, JGR, 1994], |
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c |
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c Edbot = direct downwelling irradiance in W/m2 per waveband |
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c Esbot = diffuse downwelling irradiance in W/m2 per waveband |
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c Eubot = diffuse upwelling irradiance in W/m2 per waveband |
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c |
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c all defined at the bottom of each layer. Also computed are Estop, |
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c Eutop at the top of each layer which should be very close to Esbot, |
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c Eubot of the layer above. |
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c |
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c The Ed equation is integrated exactly, Es and Eu are computed by |
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c solving a set of linear equation for the amplitudes in the exact |
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c solution [see, e.g., Kylling, Stamnes, Tsay, JAC, 1995]. |
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c The boundary condition in the deepest wet layer is |
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c downward-decreasing modes only (i.e., zero irradiance at infinite |
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c depth, assuming the optical properties of the last layer). |
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c |
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c Also computed are scalar radiance and PAR at the grid cell center |
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c (both in uEin/m2/s). |
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c |
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C !USES: =============================================================== |
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IMPLICIT NONE |
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#include "SIZE.h" /* Nr */ |
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#include "EEPARAMS.h" |
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#include "MONOD_SIZE.h" |
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#include "SPECTRAL_SIZE.h" /* tlam */ |
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#include "SPECTRAL.h" /* WtouEin */ |
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#include "WAVEBANDS_PARAMS.h" /* darwin_PAR_ilamLo/Hi |
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darwin_radmodThresh |
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darwin_rmus darwin_rmuu */ |
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C !INPUT PARAMETERS: =================================================== |
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C H :: layer thickness (including hFacC!) |
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C rmud :: inv.cosine of direct (underwater solar) zenith angle |
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C Edsf :: direct downwelling irradiance below surface per waveband |
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C Essf :: diffuse downwelling irradiance below surface per waveband |
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C a_k :: absorption coefficient per level and waveband (1/m) |
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C bt_k :: total scattering coefficient per level and waveband (1/m) |
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C = forward + back scattering coefficient |
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C bb_k :: backscattering coefficient per level and waveband (1/m) |
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C kmax :: maximum number of layers to compute |
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_RL H(Nr) |
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_RL rmud |
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_RL Edsf(tlam), Essf(tlam) |
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_RL a_k(Nr,tlam), bt_k(Nr,tlam), bb_k(Nr,tlam) |
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INTEGER kmax |
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INTEGER myThid |
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C !OUTPUT PARAMETERS: ================================================== |
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C Edbot :: direct downwelling irradiance at bottom of layer |
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C Esbot :: diffuse downwelling irradiance at bottom of layer |
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C Eubot :: diffuse upwelling irradiance at bottom of layer |
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C Estop :: diffuse downwelling irradiance at top of layer |
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C Eutop :: diffuse upwelling irradiance at top of layer |
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C tirrq :: total scalar irradiance at cell center (uEin/m2/s) |
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C tirrwq :: total scalar irradiance at cell center per waveband |
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C amp1 :: amplitude of downward increasing mode |
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C amp2 :: amplitude of downward decreasing mode |
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_RL Edbot(tlam,Nr),Esbot(tlam,Nr),Eubot(tlam,Nr) |
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_RL Estop(tlam,Nr),Eutop(tlam,Nr) |
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_RL tirrq(Nr) |
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_RL tirrwq(tlam,Nr) |
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_RL amp1(tlam,Nr), amp2(tlam,Nr) |
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CEOP |
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#ifdef DAR_RADTRANS |
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C !LOCAL VARIABLES: ==================================================== |
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INTEGER k, nl, kbot |
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_RL Edtop(tlam,Nr) |
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_RL Etopwq, Ebotwq |
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_RL zd |
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_RL rmus,rmuu |
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_RL cd,au,Bu,Cu |
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_RL as,Bs,Cs,Bd,Fd |
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_RL bquad,D |
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_RL kappa1,kappa2,denom |
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_RL c1,c2 |
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_RL r2(Nr),r1(Nr),x(Nr),y(Nr) |
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_RL ed(Nr),e2(Nr),e1(Nr) |
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_RL a3d(2*Nr), b3d(2*Nr), c3d(2*Nr), y3d(2*Nr) |
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_RL rd, ru |
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data rd /1.5 _d 0/ !these are taken from Ackleson, et al. 1994 (JGR) |
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data ru /3.0 _d 0/ |
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rmus = darwin_rmus |
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rmuu = darwin_rmuu |
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c find deepest wet layer |
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jahn |
1.3 |
kbot = MIN(kmax, Nr) |
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DO WHILE (H(kbot).EQ.0 .AND. kbot.GT.1) |
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kbot = kbot - 1 |
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ENDDO |
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jahn |
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IF (H(kbot).EQ.0) kbot = kbot - 1 |
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jahn |
1.1 |
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DO nl = 1,tlam |
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DO k=1,Nr |
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Edtop(nl,k) = 0.0 |
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Estop(nl,k) = 0.0 |
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Eutop(nl,k) = 0.0 |
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Edbot(nl,k) = 0.0 |
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Esbot(nl,k) = 0.0 |
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Eubot(nl,k) = 0.0 |
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amp1(nl,k) = 0.0 |
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amp2(nl,k) = 0.0 |
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ENDDO |
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ENDDO |
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IF (kbot.GT.0) THEN |
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DO nl=1,tlam |
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IF (Edsf(nl) .GE. darwin_radmodThresh .OR. |
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& Essf(nl) .GE. darwin_radmodThresh) THEN |
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DO k=1,kbot |
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zd = H(k) |
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cd = (a_k(k,nl)+bt_k(k,nl))*rmud |
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au = a_k(k,nl)*rmuu |
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Bu = ru*bb_k(k,nl)*rmuu |
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Cu = au+Bu |
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as = a_k(k,nl)*rmus |
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Bs = rd*bb_k(k,nl)*rmus |
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Cs = as+Bs |
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Bd = bb_k(k,nl)*rmud |
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Fd = (bt_k(k,nl)-bb_k(k,nl))*rmud |
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bquad = Cs + Cu |
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D = 0.5*(bquad + SQRT(bquad*bquad - 4.0*Bs*Bu)) |
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kappa1 = D - Cs |
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kappa2 = Cs - Bs*Bu/D ! == D - Cu |
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r1(k) = Bu/D |
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r2(k) = Bs/D |
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denom = (cd-Cs)*(cd+Cu) + Bs*Bu |
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x(k) = -((cd+Cu)*Fd+Bu*Bd)/denom |
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y(k) = (-Bs*Fd+(cd-Cs)*Bd)/denom |
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ed(k) = EXP(-cd*zd) |
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e1(k) = EXP(-kappa1*zd) |
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e2(k) = EXP(-kappa2*zd) |
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ENDDO |
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C integrate Ed equation first |
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Edtop(nl,1) = Edsf(nl) |
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DO k=1,kbot-1 |
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Edbot(nl,k) = Edtop(nl,k)*ed(k) |
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Edtop(nl,k+1) = Edbot(nl,k) |
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ENDDO |
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Edbot(nl,kbot) = Edtop(nl,kbot)*ed(kbot) |
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C setup tridiagonal matrix of continuity/boundary conditions |
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C variables: c2(1), c1(1), c2(2), ..., c1(kbot) |
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C a3d,b3d,c3d: lower, main and upper diagonal |
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C y3d: right-hand side |
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C |
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C top b.c.: c2(1) + e1(1)*r1(1)*c1(1) = Essf - x(1)*Edsf |
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a3d(1) = 0. _d 0 ! not used |
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b3d(1) = 1. ! A(1,1)*c2(1) |
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c3d(1) = e1(1)*r1(1) ! A(1,2)*c1(1) |
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y3d(1) = Essf(nl) - x(1)*Edsf(nl) |
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C continuity at layer boundaries |
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DO k=1, kbot-1 |
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a3d(2*k) = (1. - r2(k)*r1(k+1))*e2(k) ! A(2k,2k-1)*c2(k) |
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b3d(2*k) = r1(k) - r1(k+1) ! + A(2k,2k )*c1(k) |
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c3d(2*k) = -1. + r2(k+1)*r1(k+1) ! + A(2k,2k+1)*c2(k+1) |
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y3d(2*k)= (x(k+1) - x(k) - r1(k+1)*(y(k+1)-y(k)))*Edbot(nl,k) |
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a3d(2*k+1) = 1 - r1(k)*r2(k) ! A(2k+1,2k )*c1(k) |
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b3d(2*k+1) = r2(k) - r2(k+1) ! + A(2k+1,2k+1)*c2(k+1) |
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c3d(2*k+1) = (-1. + r1(k+1)*r2(k))*e1(k+1) ! + A(2k+1,2k+2)*c1(k+1) |
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y3d(2*k+1)= (y(k+1) - y(k) - r2(k)*(x(k+1)-x(k)))*Edbot(nl,k) |
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ENDDO |
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c bottom boundary condition: c1 = 0 |
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a3d(2*kbot) = 0. _d 0 ! A(2*kbot,2*kbot-1)*c2(kbot) |
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b3d(2*kbot) = 1. _d 0 ! + A(2*kbot,2*kbot )*c1(kbot) |
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c3d(2*kbot) = 0. _d 0 ! not used |
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y3d(2*kbot) = 0. _d 0 ! = 0 |
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CALL SOLVE_TRIDIAGONAL_PIVOT(a3d,b3d,c3d,y3d,2*kbot,myThid) |
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C compute irradiances |
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DO k=1,kbot |
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c2 = y3d(2*k-1) |
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c1 = y3d(2*k) |
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Estop(nl,k) = c2 + r1(k)*e1(k)*c1 + x(k)*Edtop(nl,k) |
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Esbot(nl,k) = e2(k)*c2 + r1(k)*c1 + x(k)*Edbot(nl,k) |
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Eutop(nl,k) = r2(k)*c2 + e1(k)*c1 + y(k)*Edtop(nl,k) |
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Eubot(nl,k) = r2(k)*e2(k)*c2 + c1 + y(k)*Edbot(nl,k) |
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amp1(nl,k) = c1 |
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amp2(nl,k) = c2 |
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ENDDO |
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IF (kbot .LT. Nr) THEN |
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Estop(nl,kbot+1) = Esbot(nl,kbot) |
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Eutop(nl,kbot+1) = Eubot(nl,kbot) |
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ENDIF |
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jahn |
1.1 |
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C endif thresh |
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ENDIF |
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DO k = 1,Nr |
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C convert to scalar irradiance in quanta |
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#ifdef DAR_RADTRANS_RMUS_PAR |
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C use rmus for all 3 components (?) |
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Etopwq = (Edtop(nl,k)+Estop(nl,k)+Eutop(nl,k))*WtouEins(nl) |
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Ebotwq = (Edbot(nl,k)+Esbot(nl,k)+Eubot(nl,k))*WtouEins(nl) |
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tirrwq(nl,k) = SQRT(Etopwq*Ebotwq)*rmus |
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#else |
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C use appropriate average cosine for each component |
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Etopwq = (rmud*Edtop(nl,k)+rmus*Estop(nl,k)+rmuu*Eutop(nl,k)) |
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& *WtouEins(nl) |
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Ebotwq = (rmud*Edbot(nl,k)+rmus*Esbot(nl,k)+rmuu*Eubot(nl,k)) |
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& *WtouEins(nl) |
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C and interpolate |
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tirrwq(nl,k) = SQRT(Etopwq*Ebotwq) |
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#endif |
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ENDDO |
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C enddo nl |
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ENDDO |
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C endif kbot.gt.0 |
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ENDIF |
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DO k = 1,Nr |
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C sum PAR range |
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tirrq(k) = 0.0 |
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DO nl = darwin_PAR_ilamLo,darwin_PAR_ilamHi |
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tirrq(k) = tirrq(k) + tirrwq(nl,k) |
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ENDDO |
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ENDDO |
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c |
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#endif /* DAR_RADTRANS */ |
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return |
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end |
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