| 1 |
jmc |
1.4 |
C $Header: /u/gcmpack/MITgcm/pkg/thsice/thsice_solve4temp.F,v 1.3 2004/05/07 21:33:34 jmc Exp $ |
| 2 |
jmc |
1.1 |
C $Name: $ |
| 3 |
|
|
|
| 4 |
|
|
#include "THSICE_OPTIONS.h" |
| 5 |
|
|
|
| 6 |
|
|
CBOP |
| 7 |
|
|
C !ROUTINE: THSICE_SOLVE4TEMP |
| 8 |
|
|
C !INTERFACE: |
| 9 |
|
|
SUBROUTINE THSICE_SOLVE4TEMP( |
| 10 |
|
|
I useBlkFlx, flxExcSw, Tf, hi, hs, |
| 11 |
|
|
U flxSW, Tsf, qicen, |
| 12 |
|
|
O Tice, sHeating, flxCnB, |
| 13 |
|
|
O dTsf, flxAtm, evpAtm, |
| 14 |
|
|
I i,j,bi,bj, myThid) |
| 15 |
|
|
C !DESCRIPTION: \bv |
| 16 |
|
|
C *==========================================================* |
| 17 |
|
|
C | S/R THSICE_SOLVE4TEMP |
| 18 |
|
|
C *==========================================================* |
| 19 |
|
|
C | Solve (implicitly) for sea-ice and surface temperature |
| 20 |
|
|
C *==========================================================* |
| 21 |
|
|
C \ev |
| 22 |
|
|
|
| 23 |
|
|
C !USES: |
| 24 |
|
|
IMPLICIT NONE |
| 25 |
|
|
|
| 26 |
|
|
C == Global variables === |
| 27 |
|
|
#include "THSICE_SIZE.h" |
| 28 |
|
|
#include "THSICE_PARAMS.h" |
| 29 |
|
|
|
| 30 |
|
|
C !INPUT/OUTPUT PARAMETERS: |
| 31 |
|
|
C == Routine Arguments == |
| 32 |
|
|
C useBlkFlx :: use surf. fluxes from bulk-forcing external S/R |
| 33 |
|
|
C flxExcSw :: surf. heat flux (+=down) except SW, function of surf. temp Ts: |
| 34 |
|
|
C 0: Flx(Ts=0) ; 1: Flx(Ts=Ts^n) ; 2: d.Flx/dTs(Ts=Ts^n) |
| 35 |
|
|
C Tf :: freezing temperature (oC) of local sea-water |
| 36 |
|
|
C hi :: ice height |
| 37 |
|
|
C hs :: snow height |
| 38 |
|
|
C flxSW :: net Short-Wave flux (+=down) [W/m2]: input= at surface |
| 39 |
|
|
C :: output= at the sea-ice base to the ocean |
| 40 |
|
|
C Tsf :: surface (ice or snow) temperature |
| 41 |
|
|
C qicen :: ice enthalpy (J m-3) |
| 42 |
|
|
C Tice :: internal ice temperatures |
| 43 |
|
|
C sHeating :: surf heating left to melt snow or ice (= Atmos-conduction) |
| 44 |
|
|
C flxCnB :: heat flux conducted through the ice to bottom surface |
| 45 |
|
|
C dTsf :: surf. temp adjusment: Ts^n+1 - Ts^n |
| 46 |
|
|
C flxAtm :: net flux of energy from the atmosphere [W/m2] (+=down) |
| 47 |
|
|
C without snow precip. (energy=0 for liquid water at 0.oC) |
| 48 |
|
|
C evpAtm :: evaporation to the atmosphere (kg/m2/s) (>0 if evaporate) |
| 49 |
|
|
C i,j,bi,bj :: indices of current grid point |
| 50 |
|
|
C myThid :: Thread no. that called this routine. |
| 51 |
|
|
LOGICAL useBlkFlx |
| 52 |
|
|
_RL flxExcSw(0:2) |
| 53 |
|
|
_RL Tf |
| 54 |
|
|
_RL hi |
| 55 |
|
|
_RL hs |
| 56 |
|
|
|
| 57 |
|
|
_RL flxSW |
| 58 |
|
|
_RL Tsf |
| 59 |
|
|
_RL qicen(nlyr) |
| 60 |
|
|
|
| 61 |
|
|
_RL Tice (nlyr) |
| 62 |
|
|
_RL sHeating |
| 63 |
|
|
_RL flxCnB |
| 64 |
|
|
_RL dTsf |
| 65 |
|
|
_RL flxAtm |
| 66 |
|
|
_RL evpAtm |
| 67 |
|
|
INTEGER i,j, bi,bj |
| 68 |
|
|
INTEGER myThid |
| 69 |
|
|
CEOP |
| 70 |
|
|
|
| 71 |
|
|
#ifdef ALLOW_THSICE |
| 72 |
|
|
|
| 73 |
|
|
C ADAPTED FROM: |
| 74 |
|
|
C LANL CICE.v2.0.2 |
| 75 |
|
|
C----------------------------------------------------------------------- |
| 76 |
|
|
C.. thermodynamics (vertical physics) based on M. Winton 3-layer model |
| 77 |
|
|
C.. See Bitz, C. M. and W. H. Lipscomb, 1999: "An energy-conserving |
| 78 |
|
|
C.. thermodynamic sea ice model for climate study." J. Geophys. |
| 79 |
|
|
C.. Res., 104, 15669 - 15677. |
| 80 |
|
|
C.. Winton, M., 1999: "A reformulated three-layer sea ice model." |
| 81 |
|
|
C.. Submitted to J. Atmos. Ocean. Technol. |
| 82 |
|
|
C.. authors Elizabeth C. Hunke and William Lipscomb |
| 83 |
|
|
C.. Fluid Dynamics Group, Los Alamos National Laboratory |
| 84 |
|
|
C----------------------------------------------------------------------- |
| 85 |
|
|
Cc****subroutine thermo_winton(n,fice,fsnow,dqice,dTsfc) |
| 86 |
|
|
C.. Compute temperature change using Winton model with 2 ice layers, of |
| 87 |
|
|
C.. which only the top layer has a variable heat capacity. |
| 88 |
|
|
|
| 89 |
|
|
C == Local Variables == |
| 90 |
|
|
INTEGER k |
| 91 |
|
|
|
| 92 |
|
|
_RL frsnow ! fractional snow cover |
| 93 |
|
|
|
| 94 |
|
|
_RL fswpen ! SW penetrating beneath surface (W m-2) |
| 95 |
|
|
_RL fswdn ! SW absorbed at surface (W m-2) |
| 96 |
|
|
_RL fswint ! SW absorbed in ice (W m-2) |
| 97 |
|
|
_RL fswocn ! SW passed through ice to ocean (W m-2) |
| 98 |
|
|
|
| 99 |
|
|
_RL flxExceptSw ! net surface heat flux, except short-wave (W/m2) |
| 100 |
|
|
C evap :: evaporation over snow/ice [kg/m2/s] (>0 if evaporate) |
| 101 |
|
|
C dEvdT :: derivative of evap. with respect to Tsf [kg/m2/s/K] |
| 102 |
|
|
_RL evap, dEvdT |
| 103 |
|
|
_RL flx0 ! net surf heat flux, from Atmos. to sea-ice (W m-2) |
| 104 |
|
|
_RL fct ! heat conducted to top surface |
| 105 |
|
|
|
| 106 |
|
|
_RL df0dT ! deriv of flx0 wrt Tsf (W m-2 deg-1) |
| 107 |
|
|
|
| 108 |
|
|
_RL k12, k32 ! thermal conductivity terms |
| 109 |
|
|
_RL a10, b10 ! coefficients in quadratic eqn for T1 |
| 110 |
|
|
_RL a1, b1, c1 ! coefficients in quadratic eqn for T1 |
| 111 |
|
|
c _RL Tsf_start ! old value of Tsf |
| 112 |
|
|
|
| 113 |
|
|
_RL dt ! timestep |
| 114 |
|
|
|
| 115 |
|
|
INTEGER iceornot |
| 116 |
|
|
LOGICAL dBug |
| 117 |
|
|
|
| 118 |
|
|
1010 FORMAT(A,I3,3F8.3) |
| 119 |
|
|
1020 FORMAT(A,1P4E11.3) |
| 120 |
|
|
|
| 121 |
|
|
dt = thSIce_deltaT |
| 122 |
|
|
dBug = .FALSE. |
| 123 |
jmc |
1.3 |
c dBug = ( bi.EQ.3 .AND. i.EQ.15 .AND. j.EQ.11 ) |
| 124 |
jmc |
1.1 |
c dBug = ( bi.EQ.6 .AND. i.EQ.18 .AND. j.EQ.10 ) |
| 125 |
jmc |
1.4 |
IF (dBug) WRITE(6,'(A,2I4,2I2)') 'ThSI_SOLVE4T: i,j=',i,j,bi,bj |
| 126 |
jmc |
1.1 |
|
| 127 |
|
|
if ( hi.lt.himin ) then |
| 128 |
|
|
C If hi < himin, melt the ice. |
| 129 |
jmc |
1.3 |
STOP 'THSICE_SOLVE4TEMP: should not enter if hi<himin' |
| 130 |
jmc |
1.1 |
endif |
| 131 |
|
|
|
| 132 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 133 |
|
|
|
| 134 |
|
|
C fractional snow cover |
| 135 |
|
|
frsnow = 0. _d 0 |
| 136 |
|
|
if (hs .gt. 0. _d 0) frsnow = 1. _d 0 |
| 137 |
|
|
|
| 138 |
|
|
C Compute SW flux absorbed at surface and penetrating to layer 1. |
| 139 |
|
|
fswpen = flxSW * (1. _d 0 - frsnow) * i0 |
| 140 |
|
|
fswocn = fswpen * exp(-ksolar*hi) |
| 141 |
|
|
fswint = fswpen - fswocn |
| 142 |
|
|
|
| 143 |
|
|
fswdn = flxSW - fswpen |
| 144 |
|
|
|
| 145 |
|
|
C Compute conductivity terms at layer interfaces. |
| 146 |
|
|
|
| 147 |
|
|
k12 = 4. _d 0*kice*ksnow / (ksnow*hi + 4. _d 0*kice*hs) |
| 148 |
|
|
k32 = 2. _d 0*kice / hi |
| 149 |
|
|
|
| 150 |
|
|
C compute ice temperatures |
| 151 |
|
|
a1 = cpice |
| 152 |
|
|
b1 = qicen(1) + (cpwater-cpice )*Tmlt1 - Lfresh |
| 153 |
|
|
c1 = Lfresh * Tmlt1 |
| 154 |
|
|
Tice(1) = 0.5 _d 0 *(-b1 - sqrt(b1*b1-4. _d 0*a1*c1))/a1 |
| 155 |
|
|
Tice(2) = (Lfresh-qicen(2)) / cpice |
| 156 |
|
|
|
| 157 |
|
|
if (Tice(1).gt.0. _d 0 .or. Tice(2).gt.0. _d 0) then |
| 158 |
|
|
write (6,*) 'BBerr Tice(1) > 0 = ',Tice(1) |
| 159 |
|
|
write (6,*) 'BBerr Tice(2) > 0 = ',Tice(2) |
| 160 |
|
|
endif |
| 161 |
jmc |
1.4 |
IF (dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k, Ts, Tice=',0,Tsf,Tice |
| 162 |
jmc |
1.1 |
|
| 163 |
|
|
C Compute coefficients used in quadratic formula. |
| 164 |
|
|
|
| 165 |
|
|
a10 = rhoi*cpice *hi/(2. _d 0*dt) + |
| 166 |
|
|
& k32 * (4. _d 0*dt*k32 + rhoi*cpice *hi) |
| 167 |
|
|
& / (6. _d 0*dt*k32 + rhoi*cpice *hi) |
| 168 |
|
|
b10 = -hi* |
| 169 |
|
|
& (rhoi*cpice*Tice(1)+rhoi*Lfresh*Tmlt1/Tice(1)) |
| 170 |
|
|
& /(2. _d 0*dt) |
| 171 |
|
|
& - k32 * (4. _d 0*dt*k32*Tf+rhoi*cpice *hi*Tice(2)) |
| 172 |
|
|
& / (6. _d 0*dt*k32 + rhoi*cpice *hi) - fswint |
| 173 |
|
|
c1 = rhoi*Lfresh*hi*Tmlt1 / (2. _d 0*dt) |
| 174 |
|
|
|
| 175 |
jmc |
1.4 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 176 |
jmc |
1.1 |
C Compute new surface and internal temperatures; iterate until |
| 177 |
|
|
C Tsfc converges. |
| 178 |
|
|
|
| 179 |
|
|
C ----- begin iteration ----- |
| 180 |
|
|
do 100 k = 1,nitMaxTsf |
| 181 |
|
|
|
| 182 |
|
|
C Save temperatures at start of iteration. |
| 183 |
|
|
c Tsf_start = Tsf |
| 184 |
|
|
|
| 185 |
|
|
IF ( useBlkFlx ) THEN |
| 186 |
|
|
C Compute top surface flux. |
| 187 |
|
|
if (hs.gt.3. _d -1) then |
| 188 |
|
|
iceornot=2 |
| 189 |
|
|
else |
| 190 |
|
|
iceornot=1 |
| 191 |
|
|
endif |
| 192 |
|
|
CALL THSICE_GET_BULKF( |
| 193 |
|
|
I iceornot, Tsf, |
| 194 |
|
|
O flxExceptSw, df0dT, evap, dEvdT, |
| 195 |
|
|
I i,j,bi,bj,myThid ) |
| 196 |
|
|
flx0 = fswdn + flxExceptSw |
| 197 |
|
|
ELSE |
| 198 |
|
|
flx0 = fswdn + flxExcSw(1) |
| 199 |
|
|
df0dT = flxExcSw(2) |
| 200 |
|
|
ENDIF |
| 201 |
jmc |
1.4 |
IF ( dBug ) WRITE(6,1020) 'ThSI_SOLVE4T: flx0,df0dT,k12,D=', |
| 202 |
|
|
& flx0,df0dT,k12,k12-df0dT |
| 203 |
jmc |
1.1 |
|
| 204 |
|
|
C Compute new top layer and surface temperatures. |
| 205 |
|
|
C If Tsfc is computed to be > 0 C, fix Tsfc = 0 and recompute T1 |
| 206 |
|
|
C with different coefficients. |
| 207 |
|
|
|
| 208 |
|
|
a1 = a10 - k12*df0dT / (k12-df0dT) |
| 209 |
|
|
b1 = b10 - k12*(flx0-df0dT*Tsf) / (k12-df0dT) |
| 210 |
|
|
Tice(1) = -(b1 + sqrt(b1*b1-4. _d 0*a1*c1))/(2. _d 0*a1) |
| 211 |
|
|
dTsf = (flx0 + k12*(Tice(1)-Tsf)) / (k12-df0dT) |
| 212 |
|
|
Tsf = Tsf + dTsf |
| 213 |
|
|
if (Tsf .gt. 0. _d 0) then |
| 214 |
jmc |
1.4 |
IF(dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k,ts,t1,dTs=', |
| 215 |
jmc |
1.1 |
& k,Tsf,Tice(1),dTsf |
| 216 |
|
|
a1 = a10 + k12 |
| 217 |
|
|
b1 = b10 ! note b1 = b10 - k12*Tf0 |
| 218 |
|
|
Tice(1) = (-b1 - sqrt(b1*b1-4. _d 0*a1*c1))/(2. _d 0*a1) |
| 219 |
|
|
Tsf = 0. _d 0 |
| 220 |
|
|
IF ( useBlkFlx ) THEN |
| 221 |
|
|
if (hs.gt.3. _d -1) then |
| 222 |
|
|
iceornot=2 |
| 223 |
|
|
else |
| 224 |
|
|
iceornot=1 |
| 225 |
|
|
endif |
| 226 |
|
|
CALL THSICE_GET_BULKF( |
| 227 |
|
|
I iceornot, Tsf, |
| 228 |
|
|
O flxExceptSw, df0dT, evap, dEvdT, |
| 229 |
|
|
I i,j,bi,bj,myThid ) |
| 230 |
|
|
flx0 = fswdn + flxExceptSw |
| 231 |
|
|
dTsf = 0. _d 0 |
| 232 |
|
|
ELSE |
| 233 |
|
|
flx0 = fswdn + flxExcSw(0) |
| 234 |
|
|
dTsf = 1000. |
| 235 |
|
|
df0dT = 0. |
| 236 |
|
|
ENDIF |
| 237 |
|
|
Tsf = 0. _d 0 |
| 238 |
|
|
endif |
| 239 |
|
|
|
| 240 |
|
|
C Check for convergence. If no convergence, then repeat. |
| 241 |
|
|
C |
| 242 |
|
|
C Convergence test: Make sure Tsfc has converged, within prescribed error. |
| 243 |
|
|
C (Energy conservation is guaranteed within machine roundoff, even |
| 244 |
|
|
C if Tsfc has not converged.) |
| 245 |
|
|
C If no convergence, then repeat. |
| 246 |
|
|
|
| 247 |
jmc |
1.4 |
IF ( dBug ) WRITE(6,1010) 'ThSI_SOLVE4T: k,ts,t1,dTs=', |
| 248 |
jmc |
1.1 |
& k,Tsf,Tice(1),dTsf |
| 249 |
|
|
IF ( useBlkFlx ) THEN |
| 250 |
|
|
if (abs(dTsf).lt.Terrmax) then |
| 251 |
|
|
goto 150 |
| 252 |
|
|
elseif (k.eq.nitMaxTsf) then |
| 253 |
|
|
write (6,*) 'BB: thermw conv err ',i,j,bi,bj,dTsf |
| 254 |
|
|
write (6,*) 'BB: thermw conv err, iceheight ', hi |
| 255 |
|
|
write (6,*) 'BB: thermw conv err: Tsf, flx0', Tsf,flx0 |
| 256 |
|
|
if (Tsf.lt.-70. _d 0) stop !QQQQ fails |
| 257 |
|
|
endif |
| 258 |
|
|
ELSE |
| 259 |
|
|
goto 150 |
| 260 |
|
|
ENDIF |
| 261 |
|
|
|
| 262 |
|
|
100 continue ! surface temperature iteration |
| 263 |
|
|
150 continue |
| 264 |
|
|
C ------ end iteration ------------ |
| 265 |
|
|
|
| 266 |
|
|
c if (Tsf.lt.-70. _d 0) then |
| 267 |
|
|
cQQ print*,'QQQQQ Tsf =',Tsf |
| 268 |
|
|
cQQ stop !QQQQ fails |
| 269 |
|
|
c endif |
| 270 |
|
|
|
| 271 |
|
|
C Compute new bottom layer temperature. |
| 272 |
|
|
|
| 273 |
|
|
Tice(2) = (2. _d 0*dt*k32*(Tice(1)+2. _d 0*Tf) |
| 274 |
|
|
& + rhoi*cpice *hi*Tice(2)) |
| 275 |
|
|
& /(6. _d 0*dt*k32 + rhoi*cpice *hi) |
| 276 |
jmc |
1.4 |
IF (dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k, Ts, Tice=',k,Tsf,Tice |
| 277 |
jmc |
1.1 |
|
| 278 |
|
|
|
| 279 |
|
|
C Compute final flux values at surfaces. |
| 280 |
|
|
|
| 281 |
|
|
fct = k12*(Tsf-Tice(1)) |
| 282 |
|
|
flxCnB = 4. _d 0*kice *(Tice(2)-Tf)/hi |
| 283 |
|
|
flx0 = flx0 + df0dT*dTsf |
| 284 |
|
|
IF ( useBlkFlx ) THEN |
| 285 |
|
|
evpAtm = evap |
| 286 |
|
|
C-- needs to update also Evap (Tsf changes) since Latent heat has been updated |
| 287 |
jmc |
1.2 |
evpAtm = evap + dEvdT*dTsf |
| 288 |
jmc |
1.1 |
C- energy flux to Atmos: use net short-wave flux at surf. and |
| 289 |
|
|
C use latent heat = Lvap (energy=0 for liq. water at 0.oC) |
| 290 |
|
|
flxAtm = flxSW + flxExceptSw + df0dT*dTsf |
| 291 |
|
|
& + evpAtm*Lfresh |
| 292 |
|
|
ELSE |
| 293 |
|
|
flxAtm = 0. |
| 294 |
|
|
evpAtm = 0. |
| 295 |
|
|
ENDIF |
| 296 |
|
|
sHeating = flx0 - fct |
| 297 |
|
|
|
| 298 |
|
|
C- SW flux at sea-ice base left to the ocean |
| 299 |
|
|
flxSW = fswocn |
| 300 |
|
|
|
| 301 |
jmc |
1.3 |
IF (dBug) WRITE(6,1020) 'ThSI_SOLVE4T: flx0,fct,Dif,flxCnB=', |
| 302 |
jmc |
1.1 |
& flx0,fct,flx0-fct,flxCnB |
| 303 |
|
|
|
| 304 |
|
|
C Compute new enthalpy for each layer. |
| 305 |
|
|
|
| 306 |
|
|
qicen(1) = -cpwater*Tmlt1 + cpice *(Tmlt1-Tice(1)) + |
| 307 |
|
|
& Lfresh*(1. _d 0-Tmlt1/Tice(1)) |
| 308 |
|
|
qicen(2) = -cpice *Tice(2) + Lfresh |
| 309 |
|
|
|
| 310 |
|
|
C Make sure internal ice temperatures do not exceed Tmlt. |
| 311 |
|
|
C (This should not happen for reasonable values of i0.) |
| 312 |
|
|
|
| 313 |
|
|
if (Tice(1) .ge. Tmlt1) then |
| 314 |
|
|
write (6,'(A,2I4,2I3,1P2E14.6)') |
| 315 |
|
|
& 'BBerr - Bug: IceT(1) > Tmlt',i,j,bi,bj,Tice(1),Tmlt1 |
| 316 |
|
|
endif |
| 317 |
|
|
if (Tice(2) .ge. 0. _d 0) then |
| 318 |
|
|
write (6,'(A,2I4,2I3,1P2E14.6)') |
| 319 |
|
|
& 'BBerr - Bug: IceT(2) > 0',i,j,bi,bj,Tice(2) |
| 320 |
|
|
endif |
| 321 |
|
|
|
| 322 |
|
|
#endif /* ALLOW_THSICE */ |
| 323 |
|
|
|
| 324 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 325 |
|
|
|
| 326 |
|
|
RETURN |
| 327 |
|
|
END |
Parent Directory
| 
Revision Log
| 
Revision Graph