/*****************************************************************************
Function name: IceEnergyBalance()
Purpose : Calculate the surface energy balance for the snow pack
Required :
double TSurf - new estimate of effective surface temperature
Returns :
double RestTerm - Rest term in the energy balance
Modifies :
double *RefreezeEnergy - Refreeze energy (W/m2)
double *VaporMassFlux - Mass flux of water vapor to or from the
intercepted snow (m/s)
Comments :
Reference: Bras, R. A., Hydrology, an introduction to hydrologic
science, Addisson Wesley, Inc., Reading, etc., 1990.
Modifications:
16-Jul-04 Renamed VaporMassFlux to vapor_flux to denote fact that its
units are m/timestep rather than kg/m2s. Created new variable
VaporMassFlux with units of kg/m2s. After VaporMassFlux is
computed, vapor_flux is derived from it by unit conversion.
vapor_flux is the variable that is passed in/out of this
function. TJB
24-Aug-04 Added logic to handle blowing_flux and vapor_flux. TJB
28-Sep-04 Added Ra_used to store the aerodynamic resistance used in flux
calculations. TJB
04-Oct-04 Merged with Laura Bowling's updated lake model code. Now
blowing snow sublimation is calculated for lakes. TJB
2006-Sep-23 Replaced redundant STEFAN constant with STEFAN_B. TJB
2006-Nov-07 Removed LAKE_MODEL option. TJB
*****************************************************************************/
double IceEnergyBalance::calculate(double TSurf)
{
const char *Routine = "IceEnergyBalance";
double Density; /* Density of water/ice at TMean (kg/m3) */
double EsSnow; /* saturated vapor pressure in the snow pack
(Pa) */
double Ls; /* Latent heat of sublimation (J/kg) */
double NetRad; /* Net radiation exchange at surface (W/m2) */
double RestTerm; /* Rest term in surface energy balance
(W/m2) */
double TMean; /* Average temperature for time step (C) */
double qnull;
double VaporMassFlux; /* Total mass flux of water vapor to or from
snow (kg/m2s) */
double BlowingMassFlux; /* Mass flux of water vapor to or from
blowing snow (kg/m2s) */
double SurfaceMassFlux; /* Mass flux of water vapor to or from
snow pack (kg/m2s) */
/* Calculate active temp for energy balance as average of old and new */
/* TMean = 0.5 * (OldTSurf + TSurf); */
TMean = TSurf;
Density = RHO_W;
/* Correct aerodynamic conductance for stable conditions
Note: If air temp >> snow temp then aero_cond -> 0 (i.e. very stable)
velocity (vel_2m) is expected to be in m/sec */
/* Apply the stability correction to the aerodynamic resistance
NOTE: In the old code 2m was passed instead of Z-Displacement. I (bart)
think that it is more correct to calculate ALL fluxes at the same
reference level */
if (Wind > 0.0)
*Ra_used = Ra / StabilityCorrection(Z, 0.f, TMean, Tair, Wind, Z0);
/* *Ra_used = Ra / StabilityCorrection(2.f, 0.f, TMean, Tair, Wind, Z0);*/
else
*Ra_used = HUGE_RESIST;
/* Calculate longwave exchange and net radiation */
*LongRadOut = LongRadIn - STEFAN_B * (TMean+273.15) * (TMean+273.15)
* (TMean+273.15) * (TMean+273.15);
NetRad = ShortRad + *LongRadOut;
/* Calculate the sensible heat flux */
*SensibleHeat = AirDens * CP_PM * (Tair - TMean) / *Ra_used;
/* Calculate the mass flux of ice to or from the surface layer */
/* Calculate the saturated vapor pressure in the snow pack,
(Equation 3.32, Bras 1990) */
EsSnow = svp(TMean) /* * 1000. */;
/* EsSnow = 610.78 * exp((double)((17.269 * TMean) / (237.3 + TMean))); */
/* if (TMean < 0.0) */
/* EsSnow *= 1.0 + .00972 * TMean + .000042 * pow((double)TMean,(double)2.0); */
/* Calculate sublimation terms and latent heat flux */
/* blowing_flux was calculated outside of the root_brent iteration */
BlowingMassFlux = *blowing_flux * Density / (Dt * SECPHOUR);
latent_heat_from_snow(AirDens, EactAir, Lv, Press, Ra, TMean, Vpd,
LatentHeat, LatentHeatSub, &VaporMassFlux, &BlowingMassFlux,
&SurfaceMassFlux);
/* Convert sublimation terms from kg/m2s to m/timestep */
*vapor_flux = VaporMassFlux * Dt * SECPHOUR / Density;
*surface_flux = SurfaceMassFlux * Dt * SECPHOUR / Density;
/* Calculate advected heat flux from rain
WORK IN PROGRESS: Should the following read (Tair - Tsurf) ?? */
// Temporary fix for lake model.
*AdvectedEnergy = (CH_WATER * Tair * Rain) / (Dt*SECPHOUR);
//*AdvectedEnergy = 0.0;
/* Calculate change in cold content */
/* No change in cold content in lake model */
/* Changes for lake model start here. Actually, equals qo-Io (P&H eq. 7)*/
/* because Io (SWnet) is included in NetRad below. */
qnull = (1/AvgCond)*(Tfreeze - TMean + SWconducted);
*qf = qnull;
/* Changes for lake model end here. */
/* Calculate net energy exchange at the snow surface */
RestTerm = ( NetRad + *SensibleHeat + *LatentHeat + *LatentHeatSub + *AdvectedEnergy
+ qnull );
*RefreezeEnergy = (SurfaceLiquidWater * Lf * Density)/(Dt * SECPHOUR);
/* Melting, or partially refreeze surface water. */
if (TSurf == 0.0 && RestTerm > -(*RefreezeEnergy)) {
*RefreezeEnergy = -RestTerm; /* available energy input over cold content
used to melt, i.e. Qrf is negative value
(energy out of pack)*/
RestTerm = 0.0;
}
else { /* Pack is getting colder. */
RestTerm += *RefreezeEnergy; /* add this positive value to the pack */
}
return RestTerm;
}
void CSensibleHeatFlux::init(int y, int x, int Dt, float Ra, float ZRef,
float Displacement, float Z0, PIXMET * LocalMet,
float NetShort, float LongIn, float ETot,
int NSoilLayers, float *SoilDepth, SOILTABLE * SoilType,
float MeltEnergy, SOILPIX * LocalSoil)
{
float FluxDepth; /* Lower boundary for soil heat flux (m) */
float HeatCapacity; /* Soil heat capacity */
float MaxTSurf; /* Upper bracket for effective surface
temperature (C) */
float MinTSurf; /* Lower bracket for effective surface
temperature (C) */
float OldTSurf; /* Effective surface temperature at the end of
the last timestep (C) */
float KhEff; /* Thermal conductivity of the soil (W/(m*C)
*/
float TMean; /* Average surface temperature (C) */
float TSoilLower; /* Temperature os the soil at FluxDepth (C)
*/
float TSoilUpper; /* Temperature os the soil in top layer (C)
*/
double Tmp; /* Temporary value */
OldTSurf = LocalSoil->TSurf;
MaxTSurf = 0.5 * (LocalSoil->TSurf + LocalMet->Tair) + DELTAT;
MinTSurf = 0.5 * (LocalSoil->TSurf + LocalMet->Tair) - DELTAT;
/* WORK IN PROGRESS */
/* the lower boundary for the soil heat flux is currently fixed at a depth
of 1.0 m */
FluxDepth = 1.0;
TSoilLower = LocalSoil->Temp[NSoilLayers - 1];
TSoilUpper = LocalSoil->Temp[0];
/* Calculate the effective thermal conductivity of the soil above between
FluxDepth and DZ_TOP */
KhEff = CalcEffectiveKh(NSoilLayers, DZ_TOP, FluxDepth, SoilDepth,
SoilType->KhDry, SoilType->KhSol, LocalSoil->Moist,
SoilType->Porosity, LocalSoil->Temp);
/* KhEff = 1; */
/* Calculate the effective surface temperature that makes sure that the
sum of the terms of the energy balance equals 0 */
LocalSoil->TSurf =
RootBrent(y, x, MinTSurf, MaxTSurf, SurfaceEnergyBalance, Dt, Ra, ZRef,
Displacement, Z0, LocalMet->Wind, NetShort, LongIn,
LocalMet->AirDens, LocalMet->Lv, ETot, KhEff,
SoilType->Ch[0], SoilType->Porosity[0], LocalSoil->Moist[0],
FluxDepth, LocalMet->Tair, TSoilUpper,
TSoilLower, OldTSurf, MeltEnergy);
/* Calculate the terms of the energy balance. This is similar to the
code in SurfaceEnergyBalance.c */
TMean = 0.5 * (OldTSurf + LocalSoil->TSurf);
if (LocalMet->Wind > 0.0)
Ra /= StabilityCorrection(ZRef, Displacement, TMean, LocalMet->Tair,
LocalMet->Wind, Z0);
else
Ra = DHSVM_HUGE;
LocalSoil->Ra = Ra;
Tmp = TMean + 273.15;
LocalSoil->Qnet = NetShort + LongIn - STEFAN * (Tmp * Tmp * Tmp * Tmp);
LocalSoil->Qs = LocalMet->AirDens * CP * (LocalMet->Tair - TMean) / Ra;
LocalSoil->Qe = -(LocalMet->Lv * ETot) / Dt * WATER_DENSITY;
LocalSoil->Qg = KhEff * (TSoilLower - TMean) / FluxDepth;
HeatCapacity = (1 - SoilType->Porosity[0]) * SoilType->Ch[0];
if (TSoilUpper >= 0.0)
HeatCapacity += LocalSoil->Moist[0] * CH_WATER;
else
HeatCapacity += LocalSoil->Moist[0] * CH_ICE;
LocalSoil->Qst = (HeatCapacity * (OldTSurf - TMean) * DZ_TOP) / Dt;
LocalSoil->Qrest = LocalSoil->Qnet + LocalSoil->Qs + LocalSoil->Qe +
LocalSoil->Qg + LocalSoil->Qst + MeltEnergy;
}
