xref: /petsc/src/ts/tests/ex5.c (revision ffa8c5705e8ab2cf85ee1d14dbe507a6e2eb5283)
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   PetscInt       time;           /* amount of loops */
149   struct in      put;
150   PetscScalar    rh;             /* relative humidity */
151   PetscScalar    x;              /* memory varialbe for relative humidity calculation */
152   PetscScalar    deep_grnd_temp; /* temperature of ground under top soil surface layer */
153   PetscScalar    emma;           /* absorption-emission constant for air */
154   PetscScalar    pressure1 = 101300; /* surface pressure */
155   PetscScalar    mixratio;       /* mixing ratio */
156   PetscScalar    airtemp;        /* temperature of air near boundary layer inversion */
157   PetscScalar    dewtemp;        /* dew point temperature */
158   PetscScalar    sfctemp;        /* temperature at surface */
159   PetscScalar    pwat;           /* total column precipitable water */
160   PetscScalar    cloudTemp;      /* temperature at base of cloud */
161   AppCtx         user;           /*  user-defined work context */
162   MonitorCtx     usermonitor;    /* user-defined monitor context */
163   TS             ts;
164   SNES           snes;
165   DM             da;
166   Vec            T,rhs;          /* solution vector */
167   Mat            J;              /* Jacobian matrix */
168   PetscReal      ftime,dt;
169   PetscInt       steps,dof = 5;
170   PetscBool      use_coloring  = PETSC_TRUE;
171   MatFDColoring  matfdcoloring = 0;
172   PetscBool      monitor_off = PETSC_FALSE;
173 
174   PetscCall(PetscInitialize(&argc,&argv,(char*)0,help));
175 
176   /* Inputs */
177   PetscCall(readinput(&put));
178 
179   sfctemp   = put.Ts;
180   dewtemp   = put.Td;
181   cloudTemp = put.Tc;
182   airtemp   = put.Ta;
183   pwat      = put.pwt;
184 
185   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial Temperature = %g\n",(double)sfctemp)); /* input surface temperature */
186 
187   deep_grnd_temp = sfctemp - 10;   /* set underlying ground layer temperature */
188   emma           = emission(pwat); /* accounts for radiative effects of water vapor */
189 
190   /* Converts from Fahrenheit to Celsuis */
191   sfctemp        = fahr_to_cel(sfctemp);
192   airtemp        = fahr_to_cel(airtemp);
193   dewtemp        = fahr_to_cel(dewtemp);
194   cloudTemp      = fahr_to_cel(cloudTemp);
195   deep_grnd_temp = fahr_to_cel(deep_grnd_temp);
196 
197   /* Converts from Celsius to Kelvin */
198   sfctemp        += 273;
199   airtemp        += 273;
200   dewtemp        += 273;
201   cloudTemp      += 273;
202   deep_grnd_temp += 273;
203 
204   /* Calculates initial relative humidity */
205   x        = calcmixingr(dewtemp,pressure1);
206   mixratio = calcmixingr(sfctemp,pressure1);
207   rh       = (x/mixratio)*100;
208 
209   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial RH = %.1f percent\n\n",(double)rh));   /* prints initial relative humidity */
210 
211   time = 3600*put.time;                         /* sets amount of timesteps to run model */
212 
213   /* Configure PETSc TS solver */
214   /*------------------------------------------*/
215 
216   /* Create grid */
217   PetscCall(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,20,20,PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da));
218   PetscCall(DMSetFromOptions(da));
219   PetscCall(DMSetUp(da));
220   PetscCall(DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
221 
222   /* Define output window for each variable of interest */
223   PetscCall(DMDASetFieldName(da,0,"Ts"));
224   PetscCall(DMDASetFieldName(da,1,"Ta"));
225   PetscCall(DMDASetFieldName(da,2,"u"));
226   PetscCall(DMDASetFieldName(da,3,"v"));
227   PetscCall(DMDASetFieldName(da,4,"p"));
228 
229   /* set values for appctx */
230   user.da             = da;
231   user.Ts             = sfctemp;
232   user.fract          = put.fr;          /* fraction of sky covered by clouds */
233   user.dewtemp        = dewtemp;         /* dew point temperature (mositure in air) */
234   user.csoil          = 2000000;         /* heat constant for layer */
235   user.dzlay          = 0.08;            /* thickness of top soil layer */
236   user.emma           = emma;            /* emission parameter */
237   user.wind           = put.wnd;         /* wind spped */
238   user.pressure1      = pressure1;       /* sea level pressure */
239   user.airtemp        = airtemp;         /* temperature of air near boundar layer inversion */
240   user.Tc             = cloudTemp;       /* temperature at base of lowest cloud layer */
241   user.init           = put.init;        /* user chosen initiation scenario */
242   user.lat            = 70*0.0174532;    /* converts latitude degrees to latitude in radians */
243   user.deep_grnd_temp = deep_grnd_temp;  /* temp in lowest ground layer */
244 
245   /* set values for MonitorCtx */
246   usermonitor.drawcontours = PETSC_FALSE;
247   PetscCall(PetscOptionsHasName(NULL,NULL,"-drawcontours",&usermonitor.drawcontours));
248   if (usermonitor.drawcontours) {
249     PetscReal bounds[] = {1000.0,-1000.,  -1000.,-1000.,  1000.,-1000.,  1000.,-1000.,  1000,-1000, 100700,100800};
250     PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer));
251     PetscCall(PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds));
252   }
253   usermonitor.interval = 1;
254   PetscCall(PetscOptionsGetInt(NULL,NULL,"-monitor_interval",&usermonitor.interval,NULL));
255 
256   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
257      Extract global vectors from DA;
258    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
259   PetscCall(DMCreateGlobalVector(da,&T));
260   PetscCall(VecDuplicate(T,&rhs)); /* r: vector to put the computed right hand side */
261 
262   PetscCall(TSCreate(PETSC_COMM_WORLD,&ts));
263   PetscCall(TSSetProblemType(ts,TS_NONLINEAR));
264   PetscCall(TSSetType(ts,TSBEULER));
265   PetscCall(TSSetRHSFunction(ts,rhs,RhsFunc,&user));
266 
267   /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
268   PetscCall(DMSetMatType(da,MATAIJ));
269   PetscCall(DMCreateMatrix(da,&J));
270   PetscCall(TSGetSNES(ts,&snes));
271   if (use_coloring) {
272     ISColoring iscoloring;
273     PetscCall(DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring));
274     PetscCall(MatFDColoringCreate(J,iscoloring,&matfdcoloring));
275     PetscCall(MatFDColoringSetFromOptions(matfdcoloring));
276     PetscCall(MatFDColoringSetUp(J,iscoloring,matfdcoloring));
277     PetscCall(ISColoringDestroy(&iscoloring));
278     PetscCall(MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts));
279     PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring));
280   } else {
281     PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL));
282   }
283 
284   /* Define what to print for ts_monitor option */
285   PetscCall(PetscOptionsHasName(NULL,NULL,"-monitor_off",&monitor_off));
286   if (!monitor_off) {
287     PetscCall(TSMonitorSet(ts,Monitor,&usermonitor,NULL));
288   }
289   PetscCall(FormInitialSolution(da,T,&user));
290   dt    = TIMESTEP; /* initial time step */
291   ftime = TIMESTEP*time;
292   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"time %D, ftime %g hour, TIMESTEP %g\n",time,(double)(ftime/3600),(double)dt));
293 
294   PetscCall(TSSetTimeStep(ts,dt));
295   PetscCall(TSSetMaxSteps(ts,time));
296   PetscCall(TSSetMaxTime(ts,ftime));
297   PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));
298   PetscCall(TSSetSolution(ts,T));
299   PetscCall(TSSetDM(ts,da));
300 
301   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302      Set runtime options
303    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
304   PetscCall(TSSetFromOptions(ts));
305 
306   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307      Solve nonlinear system
308      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
309   PetscCall(TSSolve(ts,T));
310   PetscCall(TSGetSolveTime(ts,&ftime));
311   PetscCall(TSGetStepNumber(ts,&steps));
312   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %D steps\n",(double)(ftime/3600),steps));
313 
314   if (matfdcoloring) PetscCall(MatFDColoringDestroy(&matfdcoloring));
315   if (usermonitor.drawcontours) {
316     PetscCall(PetscViewerDestroy(&usermonitor.drawviewer));
317   }
318   PetscCall(MatDestroy(&J));
319   PetscCall(VecDestroy(&T));
320   PetscCall(VecDestroy(&rhs));
321   PetscCall(TSDestroy(&ts));
322   PetscCall(DMDestroy(&da));
323 
324   PetscCall(PetscFinalize());
325   return 0;
326 }
327 /*****************************end main program********************************/
328 /*****************************************************************************/
329 /*****************************************************************************/
330 /*****************************************************************************/
331 PetscErrorCode calcfluxs(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar fract, PetscScalar cloudTemp, PetscScalar *flux)
332 {
333   PetscFunctionBeginUser;
334   *flux = SIG*((EMMSFC*emma*PetscPowScalarInt(airtemp,4)) + (EMMSFC*fract*(1 - emma)*PetscPowScalarInt(cloudTemp,4)) - (EMMSFC*PetscPowScalarInt(sfctemp,4)));   /* calculates flux using Stefan-Boltzmann relation */
335   PetscFunctionReturn(0);
336 }
337 
338 PetscErrorCode calcfluxa(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar emma, PetscScalar *flux)   /* this function is not currently called upon */
339 {
340   PetscScalar emm = 0.001;
341 
342   PetscFunctionBeginUser;
343   *flux = SIG*(-emm*(PetscPowScalarInt(airtemp,4)));      /* calculates flux usinge Stefan-Boltzmann relation */
344   PetscFunctionReturn(0);
345 }
346 PetscErrorCode sensibleflux(PetscScalar sfctemp, PetscScalar airtemp, PetscScalar wind, PetscScalar *sheat)
347 {
348   PetscScalar density = 1;    /* air density */
349   PetscScalar Cp      = 1005; /* heat capicity for dry air */
350   PetscScalar wndmix;         /* temperature change from wind mixing: wind*Ch */
351 
352   PetscFunctionBeginUser;
353   wndmix = 0.0025 + 0.0042*wind;                               /* regression equation valid for neutral and stable BL */
354   *sheat = density*Cp*wndmix*(airtemp - sfctemp);              /* calculates sensible heat flux */
355   PetscFunctionReturn(0);
356 }
357 
358 PetscErrorCode latentflux(PetscScalar sfctemp, PetscScalar dewtemp, PetscScalar wind, PetscScalar pressure1, PetscScalar *latentheat)
359 {
360   PetscScalar density = 1;   /* density of dry air */
361   PetscScalar q;             /* actual specific humitity */
362   PetscScalar qs;            /* saturation specific humidity */
363   PetscScalar wndmix;        /* temperature change from wind mixing: wind*Ch */
364   PetscScalar beta = .4;     /* moisture availability */
365   PetscScalar mr;            /* mixing ratio */
366   PetscScalar lhcnst;        /* latent heat of vaporization constant = 2501000 J/kg at 0c */
367                              /* latent heat of saturation const = 2834000 J/kg */
368                              /* latent heat of fusion const = 333700 J/kg */
369 
370   PetscFunctionBeginUser;
371   wind   = mph2mpers(wind);                /* converts wind from mph to meters per second */
372   wndmix = 0.0025 + 0.0042*wind;           /* regression equation valid for neutral BL */
373   lhcnst = Lconst(sfctemp);                /* calculates latent heat of evaporation */
374   mr     = calcmixingr(sfctemp,pressure1); /* calculates saturation mixing ratio */
375   qs     = calc_q(mr);                     /* calculates saturation specific humidty */
376   mr     = calcmixingr(dewtemp,pressure1); /* calculates mixing ratio */
377   q      = calc_q(mr);                     /* calculates specific humidty */
378 
379   *latentheat = density*wndmix*beta*lhcnst*(q - qs); /* calculates latent heat flux */
380   PetscFunctionReturn(0);
381 }
382 
383 PetscErrorCode potential_temperature(PetscScalar temp, PetscScalar pressure1, PetscScalar pressure2, PetscScalar sfctemp, PetscScalar *pottemp)
384 {
385   PetscScalar kdry;     /* poisson constant for dry atmosphere */
386   PetscScalar pavg;     /* average atmospheric pressure */
387   /* PetscScalar mixratio; mixing ratio */
388   /* PetscScalar kmoist;   poisson constant for moist atmosphere */
389 
390   PetscFunctionBeginUser;
391   /* mixratio = calcmixingr(sfctemp,pressure1); */
392 
393 /* initialize poisson constant */
394   kdry   = 0.2854;
395   /* kmoist = 0.2854*(1 - 0.24*mixratio); */
396 
397   pavg     = ((0.7*pressure1)+pressure2)/2;     /* calculates simple average press */
398   *pottemp = temp*(PetscPowScalar((pressure1/pavg),kdry)); /* calculates potential temperature */
399   PetscFunctionReturn(0);
400 }
401 extern PetscScalar calcmixingr(PetscScalar dtemp, PetscScalar pressure1)
402 {
403   PetscScalar e;        /* vapor pressure */
404   PetscScalar mixratio; /* mixing ratio */
405 
406   dtemp    = dtemp - 273;                                /* converts from Kelvin to Celsuis */
407   e        = 6.11*(PetscPowScalar(10,((7.5*dtemp)/(237.7+dtemp)))); /* converts from dew point temp to vapor pressure */
408   e        = e*100;                                      /* converts from hPa to Pa */
409   mixratio = (0.622*e)/(pressure1 - e);                  /* computes mixing ratio */
410   mixratio = mixratio*1;                                 /* convert to g/Kg */
411 
412   return mixratio;
413 }
414 extern PetscScalar calc_q(PetscScalar rv)
415 {
416   PetscScalar specific_humidity;        /* define specific humidity variable */
417   specific_humidity = rv/(1 + rv);      /* calculates specific humidity */
418   return specific_humidity;
419 }
420 
421 PetscErrorCode calc_gflux(PetscScalar sfctemp, PetscScalar deep_grnd_temp, PetscScalar* Gflux)
422 {
423   PetscScalar k;                       /* thermal conductivity parameter */
424   PetscScalar n                = 0.38; /* value of soil porosity */
425   PetscScalar dz               = 1;    /* depth of layer between soil surface and deep soil layer */
426   PetscScalar unit_soil_weight = 2700; /* unit soil weight in kg/m^3 */
427 
428   PetscFunctionBeginUser;
429   k      = ((0.135*(1-n)*unit_soil_weight) + 64.7)/(unit_soil_weight - (0.947*(1-n)*unit_soil_weight)); /* dry soil conductivity */
430   *Gflux = (k*(deep_grnd_temp - sfctemp)/dz);   /* calculates flux from deep ground layer */
431   PetscFunctionReturn(0);
432 }
433 extern PetscScalar emission(PetscScalar pwat)
434 {
435   PetscScalar emma;
436 
437   emma = 0.725 + 0.17*PetscLog10Real(PetscRealPart(pwat));
438 
439   return emma;
440 }
441 extern PetscScalar cloud(PetscScalar fract)
442 {
443   PetscScalar emma = 0;
444 
445   /* modifies radiative balance depending on cloud cover */
446   if (fract >= 0.9)                     emma = 1;
447   else if (0.9 > fract && fract >= 0.8) emma = 0.9;
448   else if (0.8 > fract && fract >= 0.7) emma = 0.85;
449   else if (0.7 > fract && fract >= 0.6) emma = 0.75;
450   else if (0.6 > fract && fract >= 0.5) emma = 0.65;
451   else if (0.4 > fract && fract >= 0.3) emma = emma*1.086956;
452   return emma;
453 }
454 extern PetscScalar Lconst(PetscScalar sfctemp)
455 {
456   PetscScalar Lheat;
457   sfctemp -=273;                               /* converts from kelvin to celsius */
458   Lheat    = 4186.8*(597.31 - 0.5625*sfctemp); /* calculates latent heat constant */
459   return Lheat;
460 }
461 extern PetscScalar mph2mpers(PetscScalar wind)
462 {
463   wind = ((wind*1.6*1000)/3600);                 /* converts wind from mph to meters per second */
464   return wind;
465 }
466 extern PetscScalar fahr_to_cel(PetscScalar temp)
467 {
468   temp = (5*(temp-32))/9; /* converts from farhrenheit to celsuis */
469   return temp;
470 }
471 extern PetscScalar cel_to_fahr(PetscScalar temp)
472 {
473   temp = ((temp*9)/5) + 32; /* converts from celsuis to farhrenheit */
474   return temp;
475 }
476 PetscErrorCode readinput(struct in *put)
477 {
478   int    i;
479   char   x;
480   FILE   *ifp;
481   double tmp;
482 
483   PetscFunctionBegin;
484   ifp = fopen("ex5_control.txt", "r");
485   PetscCheck(ifp,PETSC_COMM_SELF,PETSC_ERR_FILE_OPEN,"Unable to open input file");
486   for (i=0; i<110; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
487   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
488   put->Ts = tmp;
489 
490   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
491   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
492   put->Td = tmp;
493 
494   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
495   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
496   put->Ta = tmp;
497 
498   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
499   PetscCheck(fscanf(ifp, "%lf", &tmp)== 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
500   put->Tc = tmp;
501 
502   for (i=0; i<43; i++) { PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
503   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
504   put->fr = tmp;
505 
506   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
507   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
508   put->wnd = tmp;
509 
510   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
511   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
512   put->pwt = tmp;
513 
514   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
515   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
516   put->wndDir = tmp;
517 
518   for (i=0; i<43; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
519   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
520   put->time = tmp;
521 
522   for (i=0; i<63; i++) {PetscCheck(fscanf(ifp, "%c", &x) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");}
523   PetscCheck(fscanf(ifp, "%lf", &tmp) == 1,PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Unable to read file");
524   put->init = tmp;
525   PetscFunctionReturn(0);
526 }
527 
528 /* ------------------------------------------------------------------- */
529 PetscErrorCode FormInitialSolution(DM da,Vec Xglobal,void *ctx)
530 {
531   PetscErrorCode ierr;
532   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
533   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
534   Field          **X;
535 
536   PetscFunctionBeginUser;
537   ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
538                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);PetscCall(ierr);
539 
540   /* Get pointers to vector data */
541   PetscCall(DMDAVecGetArray(da,Xglobal,&X));
542 
543   /* Get local grid boundaries */
544   PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));
545 
546   /* Compute function over the locally owned part of the grid */
547 
548   if (user->init == 1) {
549     for (j=ys; j<ys+ym; j++) {
550       for (i=xs; i<xs+xm; i++) {
551         X[j][i].Ts = user->Ts - i*0.0001;
552         X[j][i].Ta = X[j][i].Ts - 5;
553         X[j][i].u  = 0;
554         X[j][i].v  = 0;
555         X[j][i].p  = 1.25;
556         if ((j == 5 || j == 6) && (i == 4 || i == 5))   X[j][i].p += 0.00001;
557         if ((j == 5 || j == 6) && (i == 12 || i == 13)) X[j][i].p += 0.00001;
558       }
559     }
560   } else {
561     for (j=ys; j<ys+ym; j++) {
562       for (i=xs; i<xs+xm; i++) {
563         X[j][i].Ts = user->Ts;
564         X[j][i].Ta = X[j][i].Ts - 5;
565         X[j][i].u  = 0;
566         X[j][i].v  = 0;
567         X[j][i].p  = 1.25;
568       }
569     }
570   }
571 
572   /* Restore vectors */
573   PetscCall(DMDAVecRestoreArray(da,Xglobal,&X));
574   PetscFunctionReturn(0);
575 }
576 
577 /*
578    RhsFunc - Evaluates nonlinear function F(u).
579 
580    Input Parameters:
581 .  ts - the TS context
582 .  t - current time
583 .  Xglobal - input vector
584 .  F - output vector
585 .  ptr - optional user-defined context, as set by SNESSetFunction()
586 
587    Output Parameter:
588 .  F - rhs function vector
589  */
590 PetscErrorCode RhsFunc(TS ts,PetscReal t,Vec Xglobal,Vec F,void *ctx)
591 {
592   AppCtx         *user = (AppCtx*)ctx;       /* user-defined application context */
593   DM             da    = user->da;
594   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
595   PetscReal      dhx,dhy;
596   Vec            localT;
597   Field          **X,**Frhs;                            /* structures that contain variables of interest and left hand side of governing equations respectively */
598   PetscScalar    csoil          = user->csoil;          /* heat constant for layer */
599   PetscScalar    dzlay          = user->dzlay;          /* thickness of top soil layer */
600   PetscScalar    emma           = user->emma;           /* emission parameter */
601   PetscScalar    wind           = user->wind;           /* wind speed */
602   PetscScalar    dewtemp        = user->dewtemp;        /* dew point temperature (moisture in air) */
603   PetscScalar    pressure1      = user->pressure1;      /* sea level pressure */
604   PetscScalar    airtemp        = user->airtemp;        /* temperature of air near boundary layer inversion */
605   PetscScalar    fract          = user->fract;          /* fraction of the sky covered by clouds */
606   PetscScalar    Tc             = user->Tc;             /* temperature at base of lowest cloud layer */
607   PetscScalar    lat            = user->lat;            /* latitude */
608   PetscScalar    Cp             = 1005.7;               /* specific heat of air at constant pressure */
609   PetscScalar    Rd             = 287.058;              /* gas constant for dry air */
610   PetscScalar    diffconst      = 1000;                 /* diffusion coefficient */
611   PetscScalar    f              = 2*0.0000727*PetscSinScalar(lat); /* coriolis force */
612   PetscScalar    deep_grnd_temp = user->deep_grnd_temp; /* temp in lowest ground layer */
613   PetscScalar    Ts,u,v,p;
614   PetscScalar    u_abs,u_plus,u_minus,v_abs,v_plus,v_minus;
615 
616   PetscScalar sfctemp1,fsfc1,Ra;
617   PetscScalar sheat;                   /* sensible heat flux */
618   PetscScalar latentheat;              /* latent heat flux */
619   PetscScalar groundflux;              /* flux from conduction of deep ground layer in contact with top soil */
620   PetscInt    xend,yend;
621 
622   PetscFunctionBeginUser;
623   PetscCall(DMGetLocalVector(da,&localT));
624   PetscCall(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));
625 
626   dhx = (PetscReal)(Mx-1)/(5000*(Mx-1));  /* dhx = 1/dx; assume 2D space domain: [0.0, 1.e5] x [0.0, 1.e5] */
627   dhy = (PetscReal)(My-1)/(5000*(Mx-1));  /* dhy = 1/dy; */
628 
629   /*
630      Scatter ghost points to local vector,using the 2-step process
631         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
632      By placing code between these two statements, computations can be
633      done while messages are in transition.
634   */
635   PetscCall(DMGlobalToLocalBegin(da,Xglobal,INSERT_VALUES,localT));
636   PetscCall(DMGlobalToLocalEnd(da,Xglobal,INSERT_VALUES,localT));
637 
638   /* Get pointers to vector data */
639   PetscCall(DMDAVecGetArrayRead(da,localT,&X));
640   PetscCall(DMDAVecGetArray(da,F,&Frhs));
641 
642   /* Get local grid boundaries */
643   PetscCall(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));
644 
645   /* Compute function over the locally owned part of the grid */
646   /* the interior points */
647   xend=xs+xm; yend=ys+ym;
648   for (j=ys; j<yend; j++) {
649     for (i=xs; i<xend; i++) {
650       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; */
651 
652       sfctemp1 = (double)Ts;
653       PetscCall(calcfluxs(sfctemp1,airtemp,emma,fract,Tc,&fsfc1));        /* calculates surface net radiative flux */
654       PetscCall(sensibleflux(sfctemp1,airtemp,wind,&sheat));              /* calculate sensible heat flux */
655       PetscCall(latentflux(sfctemp1,dewtemp,wind,pressure1,&latentheat)); /* calculates latent heat flux */
656       PetscCall(calc_gflux(sfctemp1,deep_grnd_temp,&groundflux));         /* calculates flux from earth below surface soil layer by conduction */
657       PetscCall(calcfluxa(sfctemp1,airtemp,emma,&Ra));                    /* Calculates the change in downward radiative flux */
658       fsfc1    = fsfc1 + latentheat + sheat + groundflux;                               /* adds radiative, sensible heat, latent heat, and ground heat flux yielding net flux */
659 
660       /* convective coefficients for upwinding */
661       u_abs   = PetscAbsScalar(u);
662       u_plus  = .5*(u + u_abs); /* u if u>0; 0 if u<0 */
663       u_minus = .5*(u - u_abs); /* u if u <0; 0 if u>0 */
664 
665       v_abs   = PetscAbsScalar(v);
666       v_plus  = .5*(v + v_abs); /* v if v>0; 0 if v<0 */
667       v_minus = .5*(v - v_abs); /* v if v <0; 0 if v>0 */
668 
669       /* Solve governing equations */
670       /* P = p*Rd*Ts; */
671 
672       /* du/dt -> time change of east-west component of the wind */
673       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) */
674                      - v_plus*(u - X[j-1][i].u)*dhy - v_minus*(X[j+1][i].u - u)*dhy       /* - v(du/dy) */
675                      -(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)] */
676 /*                     -(1/p)*(X[j][i+1].P - X[j][i-1].P)*dhx */
677                      + f*v;
678 
679       /* dv/dt -> time change of north-south component of the wind */
680       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) */
681                      - v_plus*(v - X[j-1][i].v)*dhy - v_minus*(X[j+1][i].v - v)*dhy       /* - v(dv/dy) */
682                      -(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)] */
683 /*                     -(1/p)*(X[j+1][i].P - X[j-1][i].P)*dhy */
684                      -f*u;
685 
686       /* dT/dt -> time change of temperature */
687       Frhs[j][i].Ts = (fsfc1/(csoil*dzlay))                                            /* Fnet/(Cp*dz)  diabatic change in T */
688                       -u_plus*(Ts - X[j][i-1].Ts)*dhx - u_minus*(X[j][i+1].Ts - Ts)*dhx  /* - u*(dTs/dx)  advection x */
689                       -v_plus*(Ts - X[j-1][i].Ts)*dhy - v_minus*(X[j+1][i].Ts - Ts)*dhy  /* - v*(dTs/dy)  advection y */
690                       + diffconst*((X[j][i+1].Ts - 2*Ts + X[j][i-1].Ts)*dhx*dhx               /* + D(Ts_xx + Ts_yy)  diffusion */
691                                    + (X[j+1][i].Ts - 2*Ts + X[j-1][i].Ts)*dhy*dhy);
692 
693       /* dp/dt -> time change of */
694       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) */
695                      -v_plus*(p - X[j-1][i].p)*dhy - v_minus*(X[j+1][i].p - p)*dhy;    /* - v*(dp/dy) */
696 
697       Frhs[j][i].Ta = Ra/Cp;  /* dTa/dt time change of air temperature */
698     }
699   }
700 
701   /* Restore vectors */
702   PetscCall(DMDAVecRestoreArrayRead(da,localT,&X));
703   PetscCall(DMDAVecRestoreArray(da,F,&Frhs));
704   PetscCall(DMRestoreLocalVector(da,&localT));
705   PetscFunctionReturn(0);
706 }
707 
708 PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec T,void *ctx)
709 {
710   const PetscScalar *array;
711   MonitorCtx        *user  = (MonitorCtx*)ctx;
712   PetscViewer       viewer = user->drawviewer;
713   PetscReal         norm;
714 
715   PetscFunctionBeginUser;
716   PetscCall(VecNorm(T,NORM_INFINITY,&norm));
717 
718   if (step%user->interval == 0) {
719     PetscCall(VecGetArrayRead(T,&array));
720     PetscCall(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]));
721     PetscCall(VecRestoreArrayRead(T,&array));
722   }
723 
724   if (user->drawcontours) {
725     PetscCall(VecView(T,viewer));
726   }
727   PetscFunctionReturn(0);
728 }
729 
730 /*TEST
731 
732    build:
733       requires: !complex !single
734 
735    test:
736       args: -ts_max_steps 130 -monitor_interval 60
737       output_file: output/ex5.out
738       requires: !complex !single
739       localrunfiles: ex5_control.txt
740 
741    test:
742       suffix: 2
743       nsize: 4
744       args: -ts_max_steps 130 -monitor_interval 60
745       output_file: output/ex5.out
746       localrunfiles: ex5_control.txt
747       requires: !complex !single
748 
749 TEST*/
750