xref: /petsc/src/ts/tests/ex5.c (revision ebead697dbf761eb322f829370bbe90b3bd93fa3)
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   PetscFunctionBeginUser;
175   PetscCall(PetscInitialize(&argc,&argv,(char*)0,help));
176 
177   /* Inputs */
178   PetscCall(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   PetscCall(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   PetscCall(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   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));
219   PetscCall(DMSetFromOptions(da));
220   PetscCall(DMSetUp(da));
221   PetscCall(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   PetscCall(DMDASetFieldName(da,0,"Ts"));
225   PetscCall(DMDASetFieldName(da,1,"Ta"));
226   PetscCall(DMDASetFieldName(da,2,"u"));
227   PetscCall(DMDASetFieldName(da,3,"v"));
228   PetscCall(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   PetscCall(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     PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer));
252     PetscCall(PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds));
253   }
254   usermonitor.interval = 1;
255   PetscCall(PetscOptionsGetInt(NULL,NULL,"-monitor_interval",&usermonitor.interval,NULL));
256 
257   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
258      Extract global vectors from DA;
259    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
260   PetscCall(DMCreateGlobalVector(da,&T));
261   PetscCall(VecDuplicate(T,&rhs)); /* r: vector to put the computed right hand side */
262 
263   PetscCall(TSCreate(PETSC_COMM_WORLD,&ts));
264   PetscCall(TSSetProblemType(ts,TS_NONLINEAR));
265   PetscCall(TSSetType(ts,TSBEULER));
266   PetscCall(TSSetRHSFunction(ts,rhs,RhsFunc,&user));
267 
268   /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
269   PetscCall(DMSetMatType(da,MATAIJ));
270   PetscCall(DMCreateMatrix(da,&J));
271   PetscCall(TSGetSNES(ts,&snes));
272   if (use_coloring) {
273     ISColoring iscoloring;
274     PetscCall(DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring));
275     PetscCall(MatFDColoringCreate(J,iscoloring,&matfdcoloring));
276     PetscCall(MatFDColoringSetFromOptions(matfdcoloring));
277     PetscCall(MatFDColoringSetUp(J,iscoloring,matfdcoloring));
278     PetscCall(ISColoringDestroy(&iscoloring));
279     PetscCall(MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts));
280     PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring));
281   } else {
282     PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL));
283   }
284 
285   /* Define what to print for ts_monitor option */
286   PetscCall(PetscOptionsHasName(NULL,NULL,"-monitor_off",&monitor_off));
287   if (!monitor_off) {
288     PetscCall(TSMonitorSet(ts,Monitor,&usermonitor,NULL));
289   }
290   PetscCall(FormInitialSolution(da,T,&user));
291   dt    = TIMESTEP; /* initial time step */
292   ftime = TIMESTEP*time;
293   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"time %" PetscInt_FMT ", ftime %g hour, TIMESTEP %g\n",time,(double)(ftime/3600),(double)dt));
294 
295   PetscCall(TSSetTimeStep(ts,dt));
296   PetscCall(TSSetMaxSteps(ts,time));
297   PetscCall(TSSetMaxTime(ts,ftime));
298   PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));
299   PetscCall(TSSetSolution(ts,T));
300   PetscCall(TSSetDM(ts,da));
301 
302   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303      Set runtime options
304    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
305   PetscCall(TSSetFromOptions(ts));
306 
307   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308      Solve nonlinear system
309      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
310   PetscCall(TSSolve(ts,T));
311   PetscCall(TSGetSolveTime(ts,&ftime));
312   PetscCall(TSGetStepNumber(ts,&steps));
313   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %" PetscInt_FMT " steps\n",(double)(ftime/3600),steps));
314 
315   if (matfdcoloring) PetscCall(MatFDColoringDestroy(&matfdcoloring));
316   if (usermonitor.drawcontours) {
317     PetscCall(PetscViewerDestroy(&usermonitor.drawviewer));
318   }
319   PetscCall(MatDestroy(&J));
320   PetscCall(VecDestroy(&T));
321   PetscCall(VecDestroy(&rhs));
322   PetscCall(TSDestroy(&ts));
323   PetscCall(DMDestroy(&da));
324 
325   PetscCall(PetscFinalize());
326   return 0;
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   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   PetscCall(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));
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 %" PetscInt_FMT ", 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) PetscCall(VecView(T,viewer));
725   PetscFunctionReturn(0);
726 }
727 
728 /*TEST
729 
730    build:
731       requires: !complex !single
732 
733    test:
734       args: -ts_max_steps 130 -monitor_interval 60
735       output_file: output/ex5.out
736       requires: !complex !single
737       localrunfiles: ex5_control.txt
738 
739    test:
740       suffix: 2
741       nsize: 4
742       args: -ts_max_steps 130 -monitor_interval 60
743       output_file: output/ex5.out
744       localrunfiles: ex5_control.txt
745       requires: !complex !single
746 
747 TEST*/
748