| 1 |
C $Header: /u/gcmpack/MITgcm/pkg/thsice/thsice_step_fwd.F,v 1.20 2007/04/16 22:38:24 heimbach Exp $ |
| 2 |
C $Name: $ |
| 3 |
|
| 4 |
#include "THSICE_OPTIONS.h" |
| 5 |
|
| 6 |
CBOP |
| 7 |
C !ROUTINE: THSICE_STEP_FWD |
| 8 |
C !INTERFACE: |
| 9 |
SUBROUTINE THSICE_STEP_FWD( |
| 10 |
I bi, bj, iMin, iMax, jMin, jMax, |
| 11 |
I prcAtm, |
| 12 |
I myTime, myIter, myThid ) |
| 13 |
C !DESCRIPTION: \bv |
| 14 |
C *==========================================================* |
| 15 |
C | S/R THSICE_STEP_FWD |
| 16 |
C | o Step Forward Therm-SeaIce model. |
| 17 |
C *==========================================================* |
| 18 |
C \ev |
| 19 |
|
| 20 |
C !USES: |
| 21 |
IMPLICIT NONE |
| 22 |
|
| 23 |
C === Global variables === |
| 24 |
#include "SIZE.h" |
| 25 |
#include "EEPARAMS.h" |
| 26 |
#include "PARAMS.h" |
| 27 |
#include "FFIELDS.h" |
| 28 |
#include "THSICE_SIZE.h" |
| 29 |
#include "THSICE_PARAMS.h" |
| 30 |
#include "THSICE_VARS.h" |
| 31 |
#include "THSICE_TAVE.h" |
| 32 |
#include "THSICE_2DYN.h" |
| 33 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 34 |
# include "tamc.h" |
| 35 |
# include "tamc_keys.h" |
| 36 |
#endif |
| 37 |
|
| 38 |
INTEGER siLo, siHi, sjLo, sjHi |
| 39 |
PARAMETER ( siLo = 1-OLx , siHi = sNx+OLx ) |
| 40 |
PARAMETER ( sjLo = 1-OLy , sjHi = sNy+OLy ) |
| 41 |
|
| 42 |
C !INPUT/OUTPUT PARAMETERS: |
| 43 |
C === Routine arguments === |
| 44 |
C- input: |
| 45 |
C bi,bj :: tile indices |
| 46 |
C iMin,iMax :: computation domain: 1rst index range |
| 47 |
C jMin,jMax :: computation domain: 2nd index range |
| 48 |
C prcAtm :: total precip from the atmosphere [kg/m2/s] |
| 49 |
C myTime :: current Time of simulation [s] |
| 50 |
C myIter :: current Iteration number in simulation |
| 51 |
C myThid :: my Thread Id number |
| 52 |
C-- Use fluxes hold in commom blocks |
| 53 |
C- input: |
| 54 |
C icFlxSW :: net short-wave heat flux (+=down) below sea-ice, into ocean |
| 55 |
C icFlxAtm :: net Atmospheric surf. heat flux over sea-ice [W/m2], (+=down) |
| 56 |
C icFrwAtm :: evaporation over sea-ice to the atmosphere [kg/m2/s] (+=up) |
| 57 |
C- output |
| 58 |
C icFlxAtm :: net Atmospheric surf. heat flux over ice+ocean [W/m2], (+=down) |
| 59 |
C icFrwAtm :: net fresh-water flux (E-P) from the atmosphere [m/s] (+=up) |
| 60 |
INTEGER bi,bj |
| 61 |
INTEGER iMin, iMax |
| 62 |
INTEGER jMin, jMax |
| 63 |
_RL prcAtm(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 64 |
_RL myTime |
| 65 |
INTEGER myIter |
| 66 |
INTEGER myThid |
| 67 |
CEOP |
| 68 |
|
| 69 |
#ifdef ALLOW_THSICE |
| 70 |
C !LOCAL VARIABLES: |
| 71 |
C === Local variables === |
| 72 |
C iceFrac :: fraction of grid area covered in ice |
| 73 |
C flx2oc :: net heat flux from the ice to the ocean (+=down) [W/m2] |
| 74 |
C frw2oc :: fresh-water flux from the ice to the ocean |
| 75 |
C fsalt :: mass salt flux to the ocean |
| 76 |
C frzmltMxL :: ocean mixed-layer freezing/melting potential [W/m2] |
| 77 |
C tFrzOce :: sea-water freezing temperature [oC] (function of S) |
| 78 |
C isIceFree :: true for ice-free grid-cell that remains ice-free |
| 79 |
C ageFac :: snow aging factor [1] |
| 80 |
C snowFac :: snowing refreshing-age factor [units of 1/snowPr] |
| 81 |
LOGICAL isIceFree(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 82 |
_RL iceFrac (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 83 |
_RL flx2oc (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 84 |
_RL frw2oc (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 85 |
_RL fsalt (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 86 |
_RL tFrzOce (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 87 |
_RL frzmltMxL(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 88 |
_RL ageFac |
| 89 |
_RL snowFac |
| 90 |
_RL cphm |
| 91 |
_RL opFrac, icFrac |
| 92 |
#ifdef ALLOW_DIAGNOSTICS |
| 93 |
_RL tmpFac |
| 94 |
#endif |
| 95 |
INTEGER i,j |
| 96 |
LOGICAL dBugFlag |
| 97 |
|
| 98 |
C- define grid-point location where to print debugging values |
| 99 |
#include "THSICE_DEBUG.h" |
| 100 |
|
| 101 |
1010 FORMAT(A,1P4E14.6) |
| 102 |
|
| 103 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 104 |
|
| 105 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 106 |
act1 = bi - myBxLo(myThid) |
| 107 |
max1 = myBxHi(myThid) - myBxLo(myThid) + 1 |
| 108 |
act2 = bj - myByLo(myThid) |
| 109 |
max2 = myByHi(myThid) - myByLo(myThid) + 1 |
| 110 |
act3 = myThid - 1 |
| 111 |
max3 = nTx*nTy |
| 112 |
act4 = ikey_dynamics - 1 |
| 113 |
iicekey = (act1 + 1) + act2*max1 |
| 114 |
& + act3*max1*max2 |
| 115 |
& + act4*max1*max2*max3 |
| 116 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 117 |
|
| 118 |
C- Initialise |
| 119 |
dBugFlag = debugLevel.GE.debLevB |
| 120 |
DO j = 1-OLy, sNy+OLy |
| 121 |
DO i = 1-OLx, sNx+OLx |
| 122 |
isIceFree(i,j) = .FALSE. |
| 123 |
saltFlux(i,j,bi,bj) = 0. _d 0 |
| 124 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 125 |
iceFrac(i,j) = 0. |
| 126 |
#endif |
| 127 |
ENDDO |
| 128 |
ENDDO |
| 129 |
|
| 130 |
ageFac = 1. _d 0 - thSIce_deltaT/snowAgTime |
| 131 |
snowFac = thSIce_deltaT/(rhos*hNewSnowAge) |
| 132 |
|
| 133 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 134 |
CADJ STORE iceMask(:,:,bi,bj) = comlev1_bibj, key=iicekey, byte=isbyte |
| 135 |
#endif |
| 136 |
DO j = jMin, jMax |
| 137 |
DO i = iMin, iMax |
| 138 |
IF (iceMask(i,j,bi,bj).GT.0. _d 0) THEN |
| 139 |
C-- Snow aging : |
| 140 |
snowAge(i,j,bi,bj) = thSIce_deltaT |
| 141 |
& + snowAge(i,j,bi,bj)*ageFac |
| 142 |
IF ( snowPrc(i,j,bi,bj).GT.0. _d 0 ) |
| 143 |
& snowAge(i,j,bi,bj) = snowAge(i,j,bi,bj) |
| 144 |
& * EXP( - snowFac*snowPrc(i,j,bi,bj) ) |
| 145 |
c & * EXP( -(thSIce_deltaT*snowPrc(i,j,bi,bj)/rhos) |
| 146 |
c & /hNewSnowAge ) |
| 147 |
C------- |
| 148 |
C note: Any flux of mass (here fresh water) that enter or leave the system |
| 149 |
C with a non zero energy HAS TO be counted: add snow precip. |
| 150 |
icFlxAtm(i,j,bi,bj) = icFlxAtm(i,j,bi,bj) |
| 151 |
& - Lfresh*snowPrc(i,j,bi,bj) |
| 152 |
C-- |
| 153 |
ENDIF |
| 154 |
ENDDO |
| 155 |
ENDDO |
| 156 |
|
| 157 |
#ifdef ALLOW_DIAGNOSTICS |
| 158 |
IF ( useDiagnostics ) THEN |
| 159 |
tmpFac = 1. _d 0 |
| 160 |
CALL DIAGNOSTICS_FRACT_FILL( |
| 161 |
I snowPrc, iceMask,tmpFac,1,'SIsnwPrc', |
| 162 |
I 0,1,1,bi,bj,myThid) |
| 163 |
CALL DIAGNOSTICS_FRACT_FILL( |
| 164 |
I siceAlb, iceMask,tmpFac,1,'SIalbedo', |
| 165 |
I 0,1,1,bi,bj,myThid) |
| 166 |
ENDIF |
| 167 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 168 |
DO j = jMin, jMax |
| 169 |
DO i = iMin, iMax |
| 170 |
siceAlb(i,j,bi,bj) = iceMask(i,j,bi,bj)*siceAlb(i,j,bi,bj) |
| 171 |
ENDDO |
| 172 |
ENDDO |
| 173 |
|
| 174 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 175 |
C part.2 : ice-covered fraction ; |
| 176 |
C change in ice/snow thickness and ice-fraction |
| 177 |
C note: can only reduce the ice-fraction but not increase it. |
| 178 |
C------- |
| 179 |
DO j = jMin, jMax |
| 180 |
DO i = iMin, iMax |
| 181 |
|
| 182 |
tFrzOce(i,j) = -mu_Tf*sOceMxL(i,j,bi,bj) |
| 183 |
cphm = cpwater*rhosw*hOceMxL(i,j,bi,bj) |
| 184 |
frzmltMxL(i,j) = ( tFrzOce(i,j)-tOceMxL(i,j,bi,bj) ) |
| 185 |
& * cphm/ocean_deltaT |
| 186 |
iceFrac(i,j) = iceMask(i,j,bi,bj) |
| 187 |
flx2oc(i,j) = icFlxSW(i,j,bi,bj) |
| 188 |
C------- |
| 189 |
#ifdef ALLOW_DBUG_THSICE |
| 190 |
IF ( dBug(i,j,bi,bj) ) THEN |
| 191 |
IF (frzmltMxL(i,j).GT.0. .OR. iceFrac(i,j).GT.0.) THEN |
| 192 |
WRITE(6,'(A,2I4,2I2)') 'ThSI_FWD: i,j=',i,j,bi,bj |
| 193 |
WRITE(6,1010) 'ThSI_FWD:-1- iceMask, hIc, hSn, Tsf =', |
| 194 |
& iceFrac(i,j), iceHeight(i,j,bi,bj), |
| 195 |
& snowHeight(i,j,bi,bj), Tsrf(i,j,bi,bj) |
| 196 |
WRITE(6,1010) 'ThSI_FWD: ocTs,tFrzOce,frzmltMxL,Qnet=', |
| 197 |
& tOceMxL(i,j,bi,bj), tFrzOce(i,j), |
| 198 |
& frzmltMxL(i,j), Qnet(i,j,bi,bj) |
| 199 |
ENDIF |
| 200 |
IF (iceFrac(i,j).GT.0.) |
| 201 |
& WRITE(6,1010) 'ThSI_FWD: icFrac,flxAtm,evpAtm,flxSnw=', |
| 202 |
& iceFrac(i,j), icFlxAtm(i,j,bi,bj), |
| 203 |
& icFrwAtm(i,j,bi,bj),-Lfresh*snowPrc(i,j,bi,bj) |
| 204 |
ENDIF |
| 205 |
#endif |
| 206 |
ENDDO |
| 207 |
ENDDO |
| 208 |
|
| 209 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 210 |
CADJ STORE iceMask(:,:,bi,bj) = comlev1_bibj, key=iicekey, byte=isbyte |
| 211 |
#endif |
| 212 |
|
| 213 |
CALL THSICE_CALC_THICKN( |
| 214 |
I bi, bj, siLo, siHi, sjLo, sjHi, |
| 215 |
I iMin,iMax, jMin,jMax, dBugFlag, |
| 216 |
I iceMask(siLo,sjLo,bi,bj), tFrzOce, |
| 217 |
I tOceMxL(siLo,sjLo,bi,bj), v2ocMxL(siLo,sjLo,bi,bj), |
| 218 |
I snowPrc(siLo,sjLo,bi,bj), prcAtm, |
| 219 |
I sHeating(siLo,sjLo,bi,bj), flxCndBt(siLo,sjLo,bi,bj), |
| 220 |
U iceFrac, iceHeight(siLo,sjLo,bi,bj), |
| 221 |
U snowHeight(siLo,sjLo,bi,bj), Tsrf(siLo,sjLo,bi,bj), |
| 222 |
U Qice1(siLo,sjLo,bi,bj), Qice2(siLo,sjLo,bi,bj), |
| 223 |
U icFrwAtm(siLo,sjLo,bi,bj), frzmltMxL, flx2oc, |
| 224 |
O frw2oc, fsalt, |
| 225 |
I myTime, myIter, myThid ) |
| 226 |
|
| 227 |
C-- Net fluxes : |
| 228 |
DO j = jMin, jMax |
| 229 |
DO i = iMin, iMax |
| 230 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 231 |
ikey_1 = i |
| 232 |
& + sNx*(j-1) |
| 233 |
& + sNx*sNy*act1 |
| 234 |
& + sNx*sNy*max1*act2 |
| 235 |
& + sNx*sNy*max1*max2*act3 |
| 236 |
& + sNx*sNy*max1*max2*max3*act4 |
| 237 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 238 |
C-- |
| 239 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 240 |
CADJ STORE icemask(i,j,bi,bj) = comlev1_thsice_1, key=ikey_1 |
| 241 |
#endif |
| 242 |
IF (iceMask(i,j,bi,bj).GT.0. _d 0) THEN |
| 243 |
C- weighted average net fluxes: |
| 244 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 245 |
CADJ STORE fsalt(i,j) = comlev1_thsice_1, key=ikey_1 |
| 246 |
CADJ STORE flx2oc(i,j) = comlev1_thsice_1, key=ikey_1 |
| 247 |
CADJ STORE frw2oc(i,j) = comlev1_thsice_1, key=ikey_1 |
| 248 |
CADJ STORE icemask(i,j,bi,bj) = comlev1_thsice_1, key=ikey_1 |
| 249 |
#endif |
| 250 |
icFrac = iceMask(i,j,bi,bj) |
| 251 |
opFrac= 1. _d 0-icFrac |
| 252 |
icFlxAtm(i,j,bi,bj) = icFrac*icFlxAtm(i,j,bi,bj) |
| 253 |
& - opFrac*Qnet(i,j,bi,bj) |
| 254 |
icFrwAtm(i,j,bi,bj) = icFrac*icFrwAtm(i,j,bi,bj) |
| 255 |
& + opFrac*rhofw*EmPmR(i,j,bi,bj) |
| 256 |
Qnet(i,j,bi,bj) = -icFrac*flx2oc(i,j) + opFrac*Qnet(i,j,bi,bj) |
| 257 |
EmPmR(i,j,bi,bj)= -icFrac*frw2oc(i,j)/rhofw |
| 258 |
& + opFrac*EmPmR(i,j,bi,bj) |
| 259 |
saltFlux(i,j,bi,bj) = -icFrac*fsalt(i,j) |
| 260 |
|
| 261 |
#ifdef ALLOW_DBUG_THSICE |
| 262 |
IF (dBug(i,j,bi,bj)) WRITE(6,1010) |
| 263 |
& 'ThSI_FWD:-3- iceFrac, hIc, hSn, Qnet =', |
| 264 |
& iceFrac(i,j), iceHeight(i,j,bi,bj), |
| 265 |
& snowHeight(i,j,bi,bj), Qnet(i,j,bi,bj) |
| 266 |
#endif |
| 267 |
|
| 268 |
ELSEIF (hOceMxL(i,j,bi,bj).gt.0. _d 0) THEN |
| 269 |
icFlxAtm(i,j,bi,bj) = -Qnet(i,j,bi,bj) |
| 270 |
icFrwAtm(i,j,bi,bj) = rhofw*EmPmR(i,j,bi,bj) |
| 271 |
ELSE |
| 272 |
icFlxAtm(i,j,bi,bj) = 0. _d 0 |
| 273 |
icFrwAtm(i,j,bi,bj) = 0. _d 0 |
| 274 |
ENDIF |
| 275 |
ENDDO |
| 276 |
ENDDO |
| 277 |
|
| 278 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 279 |
C part.3 : freezing of sea-water |
| 280 |
C over ice-free fraction and what is left from ice-covered fraction |
| 281 |
C------- |
| 282 |
CALL THSICE_EXTEND( |
| 283 |
I bi, bj, siLo, siHi, sjLo, sjHi, |
| 284 |
I iMin,iMax, jMin,jMax, dBugFlag, |
| 285 |
I frzmltMxL, tFrzOce, |
| 286 |
I tOceMxL(siLo,sjLo,bi,bj), |
| 287 |
U iceFrac, iceHeight(siLo,sjLo,bi,bj), |
| 288 |
U snowHeight(siLo,sjLo,bi,bj), Tsrf(siLo,sjLo,bi,bj), |
| 289 |
U Tice1(siLo,sjLo,bi,bj), Tice2(siLo,sjLo,bi,bj), |
| 290 |
U Qice1(siLo,sjLo,bi,bj), Qice2(siLo,sjLo,bi,bj), |
| 291 |
O flx2oc, frw2oc, fsalt, |
| 292 |
I myTime, myIter, myThid ) |
| 293 |
|
| 294 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 295 |
CADJ STORE snowHeight(:,:,bi,bj) = |
| 296 |
CADJ & comlev1_bibj, key=iicekey, byte=isbyte |
| 297 |
#endif |
| 298 |
DO j = jMin, jMax |
| 299 |
DO i = iMin, iMax |
| 300 |
IF (frzmltMxL(i,j).GT.0. _d 0) THEN |
| 301 |
C-- Net fluxes : |
| 302 |
Qnet(i,j,bi,bj) = Qnet(i,j,bi,bj) - flx2oc(i,j) |
| 303 |
EmPmR(i,j,bi,bj)= EmPmR(i,j,bi,bj)- frw2oc(i,j)/rhofw |
| 304 |
saltFlux(i,j,bi,bj)=saltFlux(i,j,bi,bj) - fsalt(i,j) |
| 305 |
|
| 306 |
#ifdef ALLOW_DBUG_THSICE |
| 307 |
IF (dBug(i,j,bi,bj)) WRITE(6,1010) |
| 308 |
& 'ThSI_FWD:-4- iceFrac, hIc, hSn, Qnet =', |
| 309 |
& iceFrac(i,j), iceHeight(i,j,bi,bj), |
| 310 |
& snowHeight(i,j,bi,bj), Qnet(i,j,bi,bj) |
| 311 |
#endif |
| 312 |
ENDIF |
| 313 |
|
| 314 |
IF ( hOceMxL(i,j,bi,bj).GT.0. _d 0 ) |
| 315 |
& isIceFree(i,j) = iceMask(i,j,bi,bj).LE.0. _d 0 |
| 316 |
& .AND. iceFrac(i,j) .LE.0. _d 0 |
| 317 |
IF ( iceFrac(i,j) .GT. 0. _d 0 ) THEN |
| 318 |
iceMask(i,j,bi,bj)=iceFrac(i,j) |
| 319 |
IF ( snowHeight(i,j,bi,bj).EQ.0. _d 0 ) |
| 320 |
& snowAge(i,j,bi,bj) = 0. _d 0 |
| 321 |
ELSE |
| 322 |
iceMask(i,j,bi,bj) = 0. _d 0 |
| 323 |
iceHeight(i,j,bi,bj)= 0. _d 0 |
| 324 |
snowHeight(i,j,bi,bj)=0. _d 0 |
| 325 |
snowAge(i,j,bi,bj) = 0. _d 0 |
| 326 |
Tsrf(i,j,bi,bj) = tOceMxL(i,j,bi,bj) |
| 327 |
Tice1(i,j,bi,bj) = 0. _d 0 |
| 328 |
Tice2(i,j,bi,bj) = 0. _d 0 |
| 329 |
Qice1(i,j,bi,bj) = Lfresh |
| 330 |
Qice2(i,j,bi,bj) = Lfresh |
| 331 |
ENDIF |
| 332 |
ENDDO |
| 333 |
ENDDO |
| 334 |
|
| 335 |
#ifdef ATMOSPHERIC_LOADING |
| 336 |
# ifdef ALLOW_AUTODIFF_TAMC |
| 337 |
CADJ STORE snowHeight(:,:,bi,bj) = |
| 338 |
CADJ & comlev1_bibj, key=iicekey, byte=isbyte |
| 339 |
# endif |
| 340 |
DO j = jMin, jMax |
| 341 |
DO i = iMin, iMax |
| 342 |
C-- Compute Sea-Ice Loading (= mass of sea-ice + snow / area unit) |
| 343 |
sIceLoad(i,j,bi,bj) = ( snowHeight(i,j,bi,bj)*rhos |
| 344 |
& + iceHeight(i,j,bi,bj)*rhoi |
| 345 |
& )*iceMask(i,j,bi,bj) |
| 346 |
ENDDO |
| 347 |
ENDDO |
| 348 |
#endif |
| 349 |
|
| 350 |
IF ( thSIceAdvScheme.GT.0 ) THEN |
| 351 |
C-- note: those fluxes should to be added directly to Qnet, EmPmR & saltFlux |
| 352 |
DO j = jMin, jMax |
| 353 |
DO i = iMin, iMax |
| 354 |
IF ( hOceMxL(i,j,bi,bj).GT.0. _d 0 ) THEN |
| 355 |
Qnet(i,j,bi,bj) = Qnet(i,j,bi,bj) - oceQnet(i,j,bi,bj) |
| 356 |
EmPmR(i,j,bi,bj)= EmPmR(i,j,bi,bj)- oceFWfx(i,j,bi,bj)/rhofw |
| 357 |
saltFlux(i,j,bi,bj)=saltFlux(i,j,bi,bj) - oceSflx(i,j,bi,bj) |
| 358 |
ENDIF |
| 359 |
ENDDO |
| 360 |
ENDDO |
| 361 |
ENDIF |
| 362 |
|
| 363 |
#ifdef ALLOW_BULK_FORCE |
| 364 |
IF ( useBulkForce ) THEN |
| 365 |
CALL BULKF_FLUX_ADJUST( |
| 366 |
I bi, bj, iMin, iMax, jMin, jMax, |
| 367 |
I isIceFree, myTime, myIter, myThid ) |
| 368 |
ENDIF |
| 369 |
#endif /* ALLOW_BULK_FORCE */ |
| 370 |
|
| 371 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 372 |
#endif /* ALLOW_THSICE */ |
| 373 |
|
| 374 |
RETURN |
| 375 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph