xref: /petsc/src/ts/tests/ex5.c (revision 40badf4fbc550ac1f60bd080eaff6de6d55b946d)
1 static char help[] = "Nonlinear, time-dependent. Developed from radiative_surface_balance.c \n";
2 /*
3   Contributed by Steve Froehlich, Illinois Institute of Technology
4 
5    Usage:
6     mpiexec -n <np> ./ex5 [options]
7     ./ex5 -help  [view petsc options]
8     ./ex5 -ts_type sundials -ts_view
9     ./ex5 -da_grid_x 20 -da_grid_y 20 -log_view
10     ./ex5 -da_grid_x 20 -da_grid_y 20 -ts_type rosw -ts_atol 1.e-6 -ts_rtol 1.e-6
11     ./ex5 -drawcontours -draw_pause 0.1 -draw_fields 0,1,2,3,4
12 */
13 
14 /*
15    -----------------------------------------------------------------------
16 
17    Governing equations:
18 
19         R      = s*(Ea*Ta^4 - Es*Ts^4)
20         SH     = p*Cp*Ch*wind*(Ta - Ts)
21         LH     = p*L*Ch*wind*B(q(Ta) - q(Ts))
22         G      = k*(Tgnd - Ts)/dz
23 
24         Fnet   = R + SH + LH + G
25 
26         du/dt  = -u*(du/dx) - v*(du/dy) - 2*omeg*sin(lat)*v - (1/p)*(dP/dx)
27         dv/dt  = -u*(dv/dx) - v*(dv/dy) + 2*omeg*sin(lat)*u - (1/p)*(dP/dy)
28         dTs/dt = Fnet/(Cp*dz) - Div([u*Ts, v*Ts]) + D*Lap(Ts)
29                = Fnet/(Cs*dz) - u*(dTs/dx) - v*(dTs/dy) + D*(Ts_xx + Ts_yy)
30         dp/dt  = -Div([u*p,v*p])
31                = - u*dp/dx - v*dp/dy
32         dTa/dt = Fnet/Cp
33 
34    Equation of State:
35 
36         P = p*R*Ts
37 
38    -----------------------------------------------------------------------
39 
40    Program considers the evolution of a two dimensional atmosphere from
41    sunset to sunrise. There are two components:
42                 1. Surface energy balance model to compute diabatic dT (Fnet)
43                 2. Dynamical model using simplified primitive equations
44 
45    Program is to be initiated at sunset and run to sunrise.
46 
47    Inputs are:
48                 Surface temperature
49                 Dew point temperature
50                 Air temperature
51                 Temperature at cloud base (if clouds are present)
52                 Fraction of sky covered by clouds
53                 Wind speed
54                 Precipitable water in centimeters
55                 Wind direction
56 
57    Inputs are are read in from the text file ex5_control.txt. To change an
58    input value use ex5_control.txt.
59 
60    Solvers:
61             Backward Euler = default solver
62             Sundials = fastest and most accurate, requires Sundials libraries
63 
64    This model is under development and should be used only as an example
65    and not as a predictive weather model.
66 */
67 
68 #include <petscts.h>
69 #include <petscdm.h>
70 #include <petscdmda.h>
71 
72 /* stefan-boltzmann constant */
73 #define SIG 0.000000056703
74 /* absorption-emission constant for surface */
75 #define EMMSFC   1
76 /* amount of time (seconds) that passes before new flux is calculated */
77 #define TIMESTEP 1
78 
79 /* variables of interest to be solved at each grid point */
80 typedef struct {
81   PetscScalar Ts,Ta; /* surface and air temperature */
82   PetscScalar u,v;   /* wind speed */
83   PetscScalar p;     /* density */
84 } Field;
85 
86 /* User defined variables. Used in solving for variables of interest */
87 typedef struct {
88   DM          da;        /* grid */
89   PetscScalar csoil;     /* heat constant for layer */
90   PetscScalar dzlay;     /* thickness of top soil layer */
91   PetscScalar emma;      /* emission parameter */
92   PetscScalar wind;      /* wind speed */
93   PetscScalar dewtemp;   /* dew point temperature (moisture in air) */
94   PetscScalar pressure1; /* sea level pressure */
95   PetscScalar airtemp;   /* temperature of air near boundary layer inversion */
96   PetscScalar Ts;        /* temperature at the surface */
97   PetscScalar fract;     /* fraction of sky covered by clouds */
98   PetscScalar Tc;        /* temperature at base of lowest cloud layer */
99   PetscScalar lat;       /* Latitude in degrees */
100   PetscScalar init;      /* initialization scenario */
101   PetscScalar deep_grnd_temp; /* temperature of ground under top soil surface layer */
102 } AppCtx;
103 
104 /* Struct for visualization */
105 typedef struct {
106   PetscBool   drawcontours;   /* flag - 1 indicates drawing contours */
107   PetscViewer drawviewer;
108   PetscInt    interval;
109 } MonitorCtx;
110 
111 /* Inputs read in from text file */
112 struct in {
113   PetscScalar Ts;     /* surface temperature  */
114   PetscScalar Td;     /* dewpoint temperature */
115   PetscScalar Tc;     /* temperature of cloud base */
116   PetscScalar fr;     /* fraction of sky covered by clouds */
117   PetscScalar wnd;    /* wind speed */
118   PetscScalar Ta;     /* air temperature */
119   PetscScalar pwt;    /* precipitable water */
120   PetscScalar wndDir; /* wind direction */
121   PetscScalar lat;    /* latitude */
122   PetscReal   time;   /* time in hours */
123   PetscScalar init;
124 };
125 
126 /* functions */
127 extern PetscScalar emission(PetscScalar);                           /* sets emission/absorption constant depending on water vapor content */
128 extern PetscScalar calc_q(PetscScalar);                             /* calculates specific humidity */
129 extern PetscScalar mph2mpers(PetscScalar);                          /* converts miles per hour to meters per second */
130 extern PetscScalar Lconst(PetscScalar);                             /* calculates latent heat constant taken from Satellite estimates of wind speed and latent heat flux over the global oceans., Bentamy et al. */
131 extern PetscScalar fahr_to_cel(PetscScalar);                        /* converts Fahrenheit to Celsius */
132 extern PetscScalar cel_to_fahr(PetscScalar);                        /* converts Celsius to Fahrenheit */
133 extern PetscScalar calcmixingr(PetscScalar, PetscScalar);           /* calculates mixing ratio */
134 extern PetscScalar cloud(PetscScalar);                              /* cloud radiative parameterization */
135 extern PetscErrorCode FormInitialSolution(DM,Vec,void*);            /* Specifies initial conditions for the system of equations (PETSc defined function) */
136 extern PetscErrorCode RhsFunc(TS,PetscReal,Vec,Vec,void*);          /* Specifies the user defined functions                     (PETSc defined function) */
137 extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);     /* Specifies output and visualization tools                 (PETSc defined function) */
138 extern PetscErrorCode readinput(struct in *put);                              /* reads input from text file */
139 extern PetscErrorCode calcfluxs(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*); /* calculates upward IR from surface */
140 extern PetscErrorCode calcfluxa(PetscScalar, PetscScalar, PetscScalar, PetscScalar*);                           /* calculates downward IR from atmosphere */
141 extern PetscErrorCode sensibleflux(PetscScalar, PetscScalar, PetscScalar, PetscScalar*);                        /* calculates sensible heat flux */
142 extern PetscErrorCode potential_temperature(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*);  /* calculates potential temperature */
143 extern PetscErrorCode latentflux(PetscScalar, PetscScalar, PetscScalar, PetscScalar, PetscScalar*);             /* calculates latent heat flux */
144 extern PetscErrorCode calc_gflux(PetscScalar, PetscScalar, PetscScalar*);                                       /* calculates flux between top soil layer and underlying earth */
145 
146 int main(int argc,char **argv)
147 {
148   PetscErrorCode ierr;
149   PetscInt       time;           /* amount of loops */
150   struct in      put;
151   PetscScalar    rh;             /* relative humidity */
152   PetscScalar    x;              /* memory varialbe for relative humidity calculation */
153   PetscScalar    deep_grnd_temp; /* temperature of ground under top soil surface layer */
154   PetscScalar    emma;           /* absorption-emission constant for air */
155   PetscScalar    pressure1 = 101300; /* surface pressure */
156   PetscScalar    mixratio;       /* mixing ratio */
157   PetscScalar    airtemp;        /* temperature of air near boundary layer inversion */
158   PetscScalar    dewtemp;        /* dew point temperature */
159   PetscScalar    sfctemp;        /* temperature at surface */
160   PetscScalar    pwat;           /* total column precipitable water */
161   PetscScalar    cloudTemp;      /* temperature at base of cloud */
162   AppCtx         user;           /*  user-defined work context */
163   MonitorCtx     usermonitor;    /* user-defined monitor context */
164   TS             ts;
165   SNES           snes;
166   DM             da;
167   Vec            T,rhs;          /* solution vector */
168   Mat            J;              /* Jacobian matrix */
169   PetscReal      ftime,dt;
170   PetscInt       steps,dof = 5;
171   PetscBool      use_coloring  = PETSC_TRUE;
172   MatFDColoring  matfdcoloring = 0;
173   PetscBool      monitor_off = PETSC_FALSE;
174 
175   ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
176 
177   /* Inputs */
178   CHKERRQ(readinput(&put));
179 
180   sfctemp   = put.Ts;
181   dewtemp   = put.Td;
182   cloudTemp = put.Tc;
183   airtemp   = put.Ta;
184   pwat      = put.pwt;
185 
186   CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Initial Temperature = %g\n",(double)sfctemp)); /* input surface temperature */
187 
188   deep_grnd_temp = sfctemp - 10;   /* set underlying ground layer temperature */
189   emma           = emission(pwat); /* accounts for radiative effects of water vapor */
190 
191   /* Converts from Fahrenheit to Celsuis */
192   sfctemp        = fahr_to_cel(sfctemp);
193   airtemp        = fahr_to_cel(airtemp);
194   dewtemp        = fahr_to_cel(dewtemp);
195   cloudTemp      = fahr_to_cel(cloudTemp);
196   deep_grnd_temp = fahr_to_cel(deep_grnd_temp);
197 
198   /* Converts from Celsius to Kelvin */
199   sfctemp        += 273;
200   airtemp        += 273;
201   dewtemp        += 273;
202   cloudTemp      += 273;
203   deep_grnd_temp += 273;
204 
205   /* Calculates initial relative humidity */
206   x        = calcmixingr(dewtemp,pressure1);
207   mixratio = calcmixingr(sfctemp,pressure1);
208   rh       = (x/mixratio)*100;
209 
210   CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Initial RH = %.1f percent\n\n",(double)rh));   /* prints initial relative humidity */
211 
212   time = 3600*put.time;                         /* sets amount of timesteps to run model */
213 
214   /* Configure PETSc TS solver */
215   /*------------------------------------------*/
216 
217   /* Create grid */
218   CHKERRQ(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,20,20,PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da));
219   CHKERRQ(DMSetFromOptions(da));
220   CHKERRQ(DMSetUp(da));
221   CHKERRQ(DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
222 
223   /* Define output window for each variable of interest */
224   CHKERRQ(DMDASetFieldName(da,0,"Ts"));
225   CHKERRQ(DMDASetFieldName(da,1,"Ta"));
226   CHKERRQ(DMDASetFieldName(da,2,"u"));
227   CHKERRQ(DMDASetFieldName(da,3,"v"));
228   CHKERRQ(DMDASetFieldName(da,4,"p"));
229 
230   /* set values for appctx */
231   user.da             = da;
232   user.Ts             = sfctemp;
233   user.fract          = put.fr;          /* fraction of sky covered by clouds */
234   user.dewtemp        = dewtemp;         /* dew point temperature (mositure in air) */
235   user.csoil          = 2000000;         /* heat constant for layer */
236   user.dzlay          = 0.08;            /* thickness of top soil layer */
237   user.emma           = emma;            /* emission parameter */
238   user.wind           = put.wnd;         /* wind spped */
239   user.pressure1      = pressure1;       /* sea level pressure */
240   user.airtemp        = airtemp;         /* temperature of air near boundar layer inversion */
241   user.Tc             = cloudTemp;       /* temperature at base of lowest cloud layer */
242   user.init           = put.init;        /* user chosen initiation scenario */
243   user.lat            = 70*0.0174532;    /* converts latitude degrees to latitude in radians */
244   user.deep_grnd_temp = deep_grnd_temp;  /* temp in lowest ground layer */
245 
246   /* set values for MonitorCtx */
247   usermonitor.drawcontours = PETSC_FALSE;
248   CHKERRQ(PetscOptionsHasName(NULL,NULL,"-drawcontours",&usermonitor.drawcontours));
249   if (usermonitor.drawcontours) {
250     PetscReal bounds[] = {1000.0,-1000.,  -1000.,-1000.,  1000.,-1000.,  1000.,-1000.,  1000,-1000, 100700,100800};
251     CHKERRQ(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer));
252     CHKERRQ(PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds));
253   }
254   usermonitor.interval = 1;
255   CHKERRQ(PetscOptionsGetInt(NULL,NULL,"-monitor_interval",&usermonitor.interval,NULL));
256 
257   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
258      Extract global vectors from DA;
259    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
260   CHKERRQ(DMCreateGlobalVector(da,&T));
261   CHKERRQ(VecDuplicate(T,&rhs)); /* r: vector to put the computed right hand side */
262 
263   CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts));
264   CHKERRQ(TSSetProblemType(ts,TS_NONLINEAR));
265   CHKERRQ(TSSetType(ts,TSBEULER));
266   CHKERRQ(TSSetRHSFunction(ts,rhs,RhsFunc,&user));
267 
268   /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
269   CHKERRQ(DMSetMatType(da,MATAIJ));
270   CHKERRQ(DMCreateMatrix(da,&J));
271   CHKERRQ(TSGetSNES(ts,&snes));
272   if (use_coloring) {
273     ISColoring iscoloring;
274     CHKERRQ(DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring));
275     CHKERRQ(MatFDColoringCreate(J,iscoloring,&matfdcoloring));
276     CHKERRQ(MatFDColoringSetFromOptions(matfdcoloring));
277     CHKERRQ(MatFDColoringSetUp(J,iscoloring,matfdcoloring));
278     CHKERRQ(ISColoringDestroy(&iscoloring));
279     CHKERRQ(MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts));
280     CHKERRQ(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring));
281   } else {
282     CHKERRQ(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL));
283   }
284 
285   /* Define what to print for ts_monitor option */
286   CHKERRQ(PetscOptionsHasName(NULL,NULL,"-monitor_off",&monitor_off));
287   if (!monitor_off) {
288     CHKERRQ(TSMonitorSet(ts,Monitor,&usermonitor,NULL));
289   }
290   CHKERRQ(FormInitialSolution(da,T,&user));
291   dt    = TIMESTEP; /* initial time step */
292   ftime = TIMESTEP*time;
293   CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"time %D, ftime %g hour, TIMESTEP %g\n",time,(double)(ftime/3600),(double)dt));
294 
295   CHKERRQ(TSSetTimeStep(ts,dt));
296   CHKERRQ(TSSetMaxSteps(ts,time));
297   CHKERRQ(TSSetMaxTime(ts,ftime));
298   CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));
299   CHKERRQ(TSSetSolution(ts,T));
300   CHKERRQ(TSSetDM(ts,da));
301 
302   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303      Set runtime options
304    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
305   CHKERRQ(TSSetFromOptions(ts));
306 
307   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308      Solve nonlinear system
309      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
310   CHKERRQ(TSSolve(ts,T));
311   CHKERRQ(TSGetSolveTime(ts,&ftime));
312   CHKERRQ(TSGetStepNumber(ts,&steps));
313   CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %D steps\n",(double)(ftime/3600),steps));
314 
315   if (matfdcoloring) CHKERRQ(MatFDColoringDestroy(&matfdcoloring));
316   if (usermonitor.drawcontours) {
317     CHKERRQ(PetscViewerDestroy(&usermonitor.drawviewer));
318   }
319   CHKERRQ(MatDestroy(&J));
320   CHKERRQ(VecDestroy(&T));
321   CHKERRQ(VecDestroy(&rhs));
322   CHKERRQ(TSDestroy(&ts));
323   CHKERRQ(DMDestroy(&da));
324 
325   ierr = PetscFinalize();
326   return ierr;
327 }
328 /*****************************end main program********************************/
329 /*****************************************************************************/
330 /*****************************************************************************/
331 /*****************************************************************************/
332 PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
333 {
334   PetscFunctionBeginUser;
335   *flux = SIG*((EMMSFC*emma*PetscPowScalarInt(airtemp,4)) + (EMMSFC*fract*(1 - emma)*PetscPowScalarInt(cloudTemp,4)) - (EMMSFC*PetscPowScalarInt(sfctemp,4)));   /* calculates flux using Stefan-Boltzmann relation */
336   PetscFunctionReturn(0);
337 }
338 
339 PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux)   /* this function is not currently called upon */
340 {
341   PetscScalar emm = 0.001;
342 
343   PetscFunctionBeginUser;
344   *flux = SIG*(-emm*(PetscPowScalarInt(airtemp,4)));      /* calculates flux usinge Stefan-Boltzmann relation */
345   PetscFunctionReturn(0);
346 }
347 PetscErrorCode sensibleflux(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar wind, PetscScalar *sheat)
348 {
349   PetscScalar density = 1;    /* air density */
350   PetscScalar Cp      = 1005; /* heat capicity for dry air */
351   PetscScalar wndmix;         /* temperature change from wind mixing: wind*Ch */
352 
353   PetscFunctionBeginUser;
354   wndmix = 0.0025 + 0.0042*wind;                               /* regression equation valid for neutral and stable BL */
355   *sheat = density*Cp*wndmix*(airtemp - sfctemp);              /* calculates sensible heat flux */
356   PetscFunctionReturn(0);
357 }
358 
359 PetscErrorCode latentflux(PetscScalar sfctemp, PetscScalar dewtemp, PetscScalar wind, PetscScalar pressure1, PetscScalar *latentheat)
360 {
361   PetscScalar density = 1;   /* density of dry air */
362   PetscScalar q;             /* actual specific humitity */
363   PetscScalar qs;            /* saturation specific humidity */
364   PetscScalar wndmix;        /* temperature change from wind mixing: wind*Ch */
365   PetscScalar beta = .4;     /* moisture availability */
366   PetscScalar mr;            /* mixing ratio */
367   PetscScalar lhcnst;        /* latent heat of vaporization constant = 2501000 J/kg at 0c */
368                              /* latent heat of saturation const = 2834000 J/kg */
369                              /* latent heat of fusion const = 333700 J/kg */
370 
371   PetscFunctionBeginUser;
372   wind   = mph2mpers(wind);                /* converts wind from mph to meters per second */
373   wndmix = 0.0025 + 0.0042*wind;           /* regression equation valid for neutral BL */
374   lhcnst = Lconst(sfctemp);                /* calculates latent heat of evaporation */
375   mr     = calcmixingr(sfctemp,pressure1); /* calculates saturation mixing ratio */
376   qs     = calc_q(mr);                     /* calculates saturation specific humidty */
377   mr     = calcmixingr(dewtemp,pressure1); /* calculates mixing ratio */
378   q      = calc_q(mr);                     /* calculates specific humidty */
379 
380   *latentheat = density*wndmix*beta*lhcnst*(q - qs); /* calculates latent heat flux */
381   PetscFunctionReturn(0);
382 }
383 
384 PetscErrorCode potential_temperature(PetscScalar temp, PetscScalar pressure1, PetscScalar pressure2, PetscScalar sfctemp, PetscScalar *pottemp)
385 {
386   PetscScalar kdry;     /* poisson constant for dry atmosphere */
387   PetscScalar pavg;     /* average atmospheric pressure */
388   /* PetscScalar mixratio; mixing ratio */
389   /* PetscScalar kmoist;   poisson constant for moist atmosphere */
390 
391   PetscFunctionBeginUser;
392   /* mixratio = calcmixingr(sfctemp,pressure1); */
393 
394 /* initialize poisson constant */
395   kdry   = 0.2854;
396   /* kmoist = 0.2854*(1 - 0.24*mixratio); */
397 
398   pavg     = ((0.7*pressure1)+pressure2)/2;     /* calculates simple average press */
399   *pottemp = temp*(PetscPowScalar((pressure1/pavg),kdry)); /* calculates potential temperature */
400   PetscFunctionReturn(0);
401 }
402 extern PetscScalar calcmixingr(PetscScalar dtemp, PetscScalar pressure1)
403 {
404   PetscScalar e;        /* vapor pressure */
405   PetscScalar mixratio; /* mixing ratio */
406 
407   dtemp    = dtemp - 273;                                /* converts from Kelvin to Celsuis */
408   e        = 6.11*(PetscPowScalar(10,((7.5*dtemp)/(237.7+dtemp)))); /* converts from dew point temp to vapor pressure */
409   e        = e*100;                                      /* converts from hPa to Pa */
410   mixratio = (0.622*e)/(pressure1 - e);                  /* computes mixing ratio */
411   mixratio = mixratio*1;                                 /* convert to g/Kg */
412 
413   return mixratio;
414 }
415 extern PetscScalar calc_q(PetscScalar rv)
416 {
417   PetscScalar specific_humidity;        /* define specific humidity variable */
418   specific_humidity = rv/(1 + rv);      /* calculates specific humidity */
419   return specific_humidity;
420 }
421 
422 PetscErrorCode calc_gflux(PetscScalar sfctemp, PetscScalar deep_grnd_temp, PetscScalar* Gflux)
423 {
424   PetscScalar k;                       /* thermal conductivity parameter */
425   PetscScalar n                = 0.38; /* value of soil porosity */
426   PetscScalar dz               = 1;    /* depth of layer between soil surface and deep soil layer */
427   PetscScalar unit_soil_weight = 2700; /* unit soil weight in kg/m^3 */
428 
429   PetscFunctionBeginUser;
430   k      = ((0.135*(1-n)*unit_soil_weight) + 64.7)/(unit_soil_weight - (0.947*(1-n)*unit_soil_weight)); /* dry soil conductivity */
431   *Gflux = (k*(deep_grnd_temp - sfctemp)/dz);   /* calculates flux from deep ground layer */
432   PetscFunctionReturn(0);
433 }
434 extern PetscScalar emission(PetscScalar pwat)
435 {
436   PetscScalar emma;
437 
438   emma = 0.725 + 0.17*PetscLog10Real(PetscRealPart(pwat));
439 
440   return emma;
441 }
442 extern PetscScalar cloud(PetscScalar fract)
443 {
444   PetscScalar emma = 0;
445 
446   /* modifies radiative balance depending on cloud cover */
447   if (fract >= 0.9)                     emma = 1;
448   else if (0.9 > fract && fract >= 0.8) emma = 0.9;
449   else if (0.8 > fract && fract >= 0.7) emma = 0.85;
450   else if (0.7 > fract && fract >= 0.6) emma = 0.75;
451   else if (0.6 > fract && fract >= 0.5) emma = 0.65;
452   else if (0.4 > fract && fract >= 0.3) emma = emma*1.086956;
453   return emma;
454 }
455 extern PetscScalar Lconst(PetscScalar sfctemp)
456 {
457   PetscScalar Lheat;
458   sfctemp -=273;                               /* converts from kelvin to celsius */
459   Lheat    = 4186.8*(597.31 - 0.5625*sfctemp); /* calculates latent heat constant */
460   return Lheat;
461 }
462 extern PetscScalar mph2mpers(PetscScalar wind)
463 {
464   wind = ((wind*1.6*1000)/3600);                 /* converts wind from mph to meters per second */
465   return wind;
466 }
467 extern PetscScalar fahr_to_cel(PetscScalar temp)
468 {
469   temp = (5*(temp-32))/9; /* converts from farhrenheit to celsuis */
470   return temp;
471 }
472 extern PetscScalar cel_to_fahr(PetscScalar temp)
473 {
474   temp = ((temp*9)/5) + 32; /* converts from celsuis to farhrenheit */
475   return temp;
476 }
477 PetscErrorCode readinput(struct in *put)
478 {
479   int    i;
480   char   x;
481   FILE   *ifp;
482   double tmp;
483 
484   PetscFunctionBegin;
485   ifp = fopen("ex5_control.txt", "r");
486   PetscCheck(ifp,PETSC_COMM_SELF,PETSC_ERR_FILE_OPEN,"Unable to open input file");
487   for (i=0; i<110; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
488   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
489   put->Ts = tmp;
490 
491   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
492   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
493   put->Td = tmp;
494 
495   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
496   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
497   put->Ta = tmp;
498 
499   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
500   PetscCheck(fscanf(ifp, "%lf", &tmp)== 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
501   put->Tc = tmp;
502 
503   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
504   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
505   put->fr = tmp;
506 
507   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
508   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
509   put->wnd = tmp;
510 
511   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
512   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
513   put->pwt = tmp;
514 
515   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
516   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
517   put->wndDir = tmp;
518 
519   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
520   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
521   put->time = tmp;
522 
523   for (i=0; i<63; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
524   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
525   put->init = tmp;
526   PetscFunctionReturn(0);
527 }
528 
529 /* ------------------------------------------------------------------- */
530 PetscErrorCode FormInitialSolution(DM da,Vec Xglobal,void *ctx)
531 {
532   PetscErrorCode ierr;
533   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
534   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
535   Field          **X;
536 
537   PetscFunctionBeginUser;
538   ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
539                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
540 
541   /* Get pointers to vector data */
542   CHKERRQ(DMDAVecGetArray(da,Xglobal,&X));
543 
544   /* Get local grid boundaries */
545   CHKERRQ(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));
546 
547   /* Compute function over the locally owned part of the grid */
548 
549   if (user->init == 1) {
550     for (j=ys; j<ys+ym; j++) {
551       for (i=xs; i<xs+xm; i++) {
552         X[j][i].Ts = user->Ts - i*0.0001;
553         X[j][i].Ta = X[j][i].Ts - 5;
554         X[j][i].u  = 0;
555         X[j][i].v  = 0;
556         X[j][i].p  = 1.25;
557         if ((j == 5 || j == 6) && (i == 4 || i == 5))   X[j][i].p += 0.00001;
558         if ((j == 5 || j == 6) && (i == 12 || i == 13)) X[j][i].p += 0.00001;
559       }
560     }
561   } else {
562     for (j=ys; j<ys+ym; j++) {
563       for (i=xs; i<xs+xm; i++) {
564         X[j][i].Ts = user->Ts;
565         X[j][i].Ta = X[j][i].Ts - 5;
566         X[j][i].u  = 0;
567         X[j][i].v  = 0;
568         X[j][i].p  = 1.25;
569       }
570     }
571   }
572 
573   /* Restore vectors */
574   CHKERRQ(DMDAVecRestoreArray(da,Xglobal,&X));
575   PetscFunctionReturn(0);
576 }
577 
578 /*
579    RhsFunc - Evaluates nonlinear function F(u).
580 
581    Input Parameters:
582 .  ts - the TS context
583 .  t - current time
584 .  Xglobal - input vector
585 .  F - output vector
586 .  ptr - optional user-defined context, as set by SNESSetFunction()
587 
588    Output Parameter:
589 .  F - rhs function vector
590  */
591 PetscErrorCode RhsFunc(TS ts,PetscReal t,Vec Xglobal,Vec F,void *ctx)
592 {
593   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
594   DM             da    = user->da;
595   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
596   PetscReal      dhx,dhy;
597   Vec            localT;
598   Field          **X,**Frhs;                            /* structures that contain variables of interest and left hand side of governing equations respectively */
599   PetscScalar    csoil          = user->csoil;          /* heat constant for layer */
600   PetscScalar    dzlay          = user->dzlay;          /* thickness of top soil layer */
601   PetscScalar    emma           = user->emma;           /* emission parameter */
602   PetscScalar    wind           = user->wind;           /* wind speed */
603   PetscScalar    dewtemp        = user->dewtemp;        /* dew point temperature (moisture in air) */
604   PetscScalar    pressure1      = user->pressure1;      /* sea level pressure */
605   PetscScalar    airtemp        = user->airtemp;        /* temperature of air near boundary layer inversion */
606   PetscScalar    fract          = user->fract;          /* fraction of the sky covered by clouds */
607   PetscScalar    Tc             = user->Tc;             /* temperature at base of lowest cloud layer */
608   PetscScalar    lat            = user->lat;            /* latitude */
609   PetscScalar    Cp             = 1005.7;               /* specific heat of air at constant pressure */
610   PetscScalar    Rd             = 287.058;              /* gas constant for dry air */
611   PetscScalar    diffconst      = 1000;                 /* diffusion coefficient */
612   PetscScalar    f              = 2*0.0000727*PetscSinScalar(lat); /* coriolis force */
613   PetscScalar    deep_grnd_temp = user->deep_grnd_temp; /* temp in lowest ground layer */
614   PetscScalar    Ts,u,v,p;
615   PetscScalar    u_abs,u_plus,u_minus,v_abs,v_plus,v_minus;
616 
617   PetscScalar sfctemp1,fsfc1,Ra;
618   PetscScalar sheat;                   /* sensible heat flux */
619   PetscScalar latentheat;              /* latent heat flux */
620   PetscScalar groundflux;              /* flux from conduction of deep ground layer in contact with top soil */
621   PetscInt    xend,yend;
622 
623   PetscFunctionBeginUser;
624   CHKERRQ(DMGetLocalVector(da,&localT));
625   CHKERRQ(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
626 
627   dhx = (PetscReal)(Mx-1)/(5000*(Mx-1));  /* dhx = 1/dx; assume 2D space domain: [0.0, 1.e5] x [0.0, 1.e5] */
628   dhy = (PetscReal)(My-1)/(5000*(Mx-1));  /* dhy = 1/dy; */
629 
630   /*
631      Scatter ghost points to local vector,using the 2-step process
632         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
633      By placing code between these two statements, computations can be
634      done while messages are in transition.
635   */
636   CHKERRQ(DMGlobalToLocalBegin(da,Xglobal,INSERT_VALUES,localT));
637   CHKERRQ(DMGlobalToLocalEnd(da,Xglobal,INSERT_VALUES,localT));
638 
639   /* Get pointers to vector data */
640   CHKERRQ(DMDAVecGetArrayRead(da,localT,&X));
641   CHKERRQ(DMDAVecGetArray(da,F,&Frhs));
642 
643   /* Get local grid boundaries */
644   CHKERRQ(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));
645 
646   /* Compute function over the locally owned part of the grid */
647   /* the interior points */
648   xend=xs+xm; yend=ys+ym;
649   for (j=ys; j<yend; j++) {
650     for (i=xs; i<xend; i++) {
651       Ts = X[j][i].Ts; u = X[j][i].u; v = X[j][i].v; p = X[j][i].p; /*P = X[j][i].P; */
652 
653       sfctemp1 = (double)Ts;
654       CHKERRQ(calcfluxs(sfctemp1,airtemp,emma,fract,Tc,&fsfc1));        /* calculates surface net radiative flux */
655       CHKERRQ(sensibleflux(sfctemp1,airtemp,wind,&sheat));              /* calculate sensible heat flux */
656       CHKERRQ(latentflux(sfctemp1,dewtemp,wind,pressure1,&latentheat)); /* calculates latent heat flux */
657       CHKERRQ(calc_gflux(sfctemp1,deep_grnd_temp,&groundflux));         /* calculates flux from earth below surface soil layer by conduction */
658       CHKERRQ(calcfluxa(sfctemp1,airtemp,emma,&Ra));                    /* Calculates the change in downward radiative flux */
659       fsfc1    = fsfc1 + latentheat + sheat + groundflux;                               /* adds radiative, sensible heat, latent heat, and ground heat flux yielding net flux */
660 
661       /* convective coefficients for upwinding */
662       u_abs   = PetscAbsScalar(u);
663       u_plus  = .5*(u + u_abs); /* u if u>0; 0 if u<0 */
664       u_minus = .5*(u - u_abs); /* u if u <0; 0 if u>0 */
665 
666       v_abs   = PetscAbsScalar(v);
667       v_plus  = .5*(v + v_abs); /* v if v>0; 0 if v<0 */
668       v_minus = .5*(v - v_abs); /* v if v <0; 0 if v>0 */
669 
670       /* Solve governing equations */
671       /* P = p*Rd*Ts; */
672 
673       /* du/dt -> time change of east-west component of the wind */
674       Frhs[j][i].u = - u_plus*(u - X[j][i-1].u)*dhx - u_minus*(X[j][i+1].u - u)*dhx       /* - u(du/dx) */
675                      - v_plus*(u - X[j-1][i].u)*dhy - v_minus*(X[j+1][i].u - u)*dhy       /* - v(du/dy) */
676                      -(Rd/p)*(Ts*(X[j][i+1].p - X[j][i-1].p)*0.5*dhx  + p*0*(X[j][i+1].Ts - X[j][i-1].Ts)*0.5*dhx) /* -(R/p)[Ts(dp/dx)+ p(dTs/dx)] */
677 /*                     -(1/p)*(X[j][i+1].P - X[j][i-1].P)*dhx */
678                      + f*v;
679 
680       /* dv/dt -> time change of north-south component of the wind */
681       Frhs[j][i].v = - u_plus*(v - X[j][i-1].v)*dhx - u_minus*(X[j][i+1].v - v)*dhx       /* - u(dv/dx) */
682                      - v_plus*(v - X[j-1][i].v)*dhy - v_minus*(X[j+1][i].v - v)*dhy       /* - v(dv/dy) */
683                      -(Rd/p)*(Ts*(X[j+1][i].p - X[j-1][i].p)*0.5*dhy + p*0*(X[j+1][i].Ts - X[j-1][i].Ts)*0.5*dhy) /* -(R/p)[Ts(dp/dy)+ p(dTs/dy)] */
684 /*                     -(1/p)*(X[j+1][i].P - X[j-1][i].P)*dhy */
685                      -f*u;
686 
687       /* dT/dt -> time change of temperature */
688       Frhs[j][i].Ts = (fsfc1/(csoil*dzlay))                                            /* Fnet/(Cp*dz)  diabatic change in T */
689                       -u_plus*(Ts - X[j][i-1].Ts)*dhx - u_minus*(X[j][i+1].Ts - Ts)*dhx  /* - u*(dTs/dx)  advection x */
690                       -v_plus*(Ts - X[j-1][i].Ts)*dhy - v_minus*(X[j+1][i].Ts - Ts)*dhy  /* - v*(dTs/dy)  advection y */
691                       + diffconst*((X[j][i+1].Ts - 2*Ts + X[j][i-1].Ts)*dhx*dhx               /* + D(Ts_xx + Ts_yy)  diffusion */
692                                    + (X[j+1][i].Ts - 2*Ts + X[j-1][i].Ts)*dhy*dhy);
693 
694       /* dp/dt -> time change of */
695       Frhs[j][i].p = -u_plus*(p - X[j][i-1].p)*dhx - u_minus*(X[j][i+1].p - p)*dhx     /* - u*(dp/dx) */
696                      -v_plus*(p - X[j-1][i].p)*dhy - v_minus*(X[j+1][i].p - p)*dhy;    /* - v*(dp/dy) */
697 
698       Frhs[j][i].Ta = Ra/Cp;  /* dTa/dt time change of air temperature */
699     }
700   }
701 
702   /* Restore vectors */
703   CHKERRQ(DMDAVecRestoreArrayRead(da,localT,&X));
704   CHKERRQ(DMDAVecRestoreArray(da,F,&Frhs));
705   CHKERRQ(DMRestoreLocalVector(da,&localT));
706   PetscFunctionReturn(0);
707 }
708 
709 PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec T,void *ctx)
710 {
711   const PetscScalar *array;
712   MonitorCtx        *user  = (MonitorCtx*)ctx;
713   PetscViewer       viewer = user->drawviewer;
714   PetscReal         norm;
715 
716   PetscFunctionBeginUser;
717   CHKERRQ(VecNorm(T,NORM_INFINITY,&norm));
718 
719   if (step%user->interval == 0) {
720     CHKERRQ(VecGetArrayRead(T,&array));
721     CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"step %D, time %8.1f,  %6.4f, %6.4f, %6.4f, %6.4f, %6.4f, %6.4f\n",step,(double)time,(double)(((array[0]-273)*9)/5 + 32),(double)(((array[1]-273)*9)/5 + 32),(double)array[2],(double)array[3],(double)array[4],(double)array[5]));
722     CHKERRQ(VecRestoreArrayRead(T,&array));
723   }
724 
725   if (user->drawcontours) {
726     CHKERRQ(VecView(T,viewer));
727   }
728   PetscFunctionReturn(0);
729 }
730 
731 /*TEST
732 
733    build:
734       requires: !complex !single
735 
736    test:
737       args: -ts_max_steps 130 -monitor_interval 60
738       output_file: output/ex5.out
739       requires: !complex !single
740       localrunfiles: ex5_control.txt
741 
742    test:
743       suffix: 2
744       nsize: 4
745       args: -ts_max_steps 130 -monitor_interval 60
746       output_file: output/ex5.out
747       localrunfiles: ex5_control.txt
748       requires: !complex !single
749 
750 TEST*/
751