/******************************************************************************
* @brief Calculate sublimation from blowing snow
*****************************************************************************/
double
CalcBlowingSnow(double Dt,
double Tair,
unsigned LastSnow,
double SurfaceLiquidWater,
double Wind,
double Ls,
double AirDens,
double EactAir,
double ZO,
double Zrh,
double snowdepth,
double lag_one,
double sigma_slope,
double Tsnow,
int iveg,
int Nveg,
double fe,
double displacement,
double roughness,
double *TotalTransport)
{
extern parameters_struct param;
extern option_struct options;
/* Local variables: */
double Age;
double U10, Uo, prob_occurence;
double es, Ros, F;
double SubFlux;
double Diffusivity;
double ushear;
double Tk;
double utshear;
int p;
double upper, lower, Total;
double area;
double sigma_w;
double Zo_salt;
double ratio, wind10;
double Uveg, hv, Nd;
double Transport;
/*******************************************************************/
/* Calculate some general variables, that don't depend on wind speed. */
/* Age in hours */
Age = LastSnow * Dt / SEC_PER_HOUR;
/* Saturation density of water vapor, Liston A-8 */
es = svp(Tair);
Tk = Tair + CONST_TKFRZ;
Ros = CONST_EPS * es / (CONST_RDAIR * Tk);
/* Diffusivity in m2/s, Liston eq. A-7 */
Diffusivity = (2.06e-5) * pow(Tk / 273., 1.75);
// Essery et al. 1999, eq. 6 (m*s/kg)
F = (Ls / (param.BLOWING_KA * Tk)) * (Ls * Tk / CONST_RDAIR - 1.);
F += 1. / (Diffusivity * Ros);
/* grid cell 10 m wind speed = 50th percentile wind */
/* Wind speed at 2 m above snow was passed to this function. */
wind10 = Wind * log(10. / ZO) / log((2 + ZO) / ZO);
/* Check for bare soil case. */
if (iveg == Nveg) {
fe = 1500;
sigma_slope = .0002;
}
// sigma_w/uo:
ratio = (2.44 - (0.43) * lag_one) * sigma_slope;
sigma_w = wind10 * ratio;
Uo = wind10;
/*********** Parameters for roughness above snow. *****************/
hv = (3. / 2.) * displacement;
Nd = (4. / 3.) * (roughness / displacement);
/*******************************************************************/
/** Begin loop through wind probability function. */
Total = 0.0;
*TotalTransport = 0.0;
area = 1. / (double) param.BLOWING_NUMINCS;
if (snowdepth > 0.0) {
if (options.BLOWING_SPATIAL_WIND && sigma_w != 0.) {
for (p = 0; p < param.BLOWING_NUMINCS; p++) {
SubFlux = lower = upper = 0.0;
/* Find the limits of integration. */
if (p == 0) {
lower = -9999;
upper = Uo + sigma_w * log(2. * (p + 1) * area);
}
else if (p > 0 && p < param.BLOWING_NUMINCS / 2) {
lower = Uo + sigma_w * log(2. * (p) * area);
upper = Uo + sigma_w * log(2. * (p + 1) * area);
}
else if (p < (param.BLOWING_NUMINCS - 1) && p >=
(double) param.BLOWING_NUMINCS / 2) {
lower = Uo - sigma_w * log(2. - 2. * (p * area));
upper = Uo - sigma_w * log(2. - 2. * ((p + 1.) * area));
}
else if (p == param.BLOWING_NUMINCS - 1) {
lower = Uo - sigma_w * log(2. - 2. * (p * area));
upper = 9999;
}
if (lower > upper) { /* Could happen if lower > Uo*2 */
lower = upper;
log_err("Error with probability boundaries");
}
/* Find expected value of wind speed for the interval. */
U10 = Uo;
if (lower >= Uo) {
U10 = -0.5 *
((upper +
sigma_w) * exp((-1. / sigma_w) * (upper - Uo)) -
(lower +
sigma_w) *
exp((-1. / sigma_w) * (lower - Uo))) / area;
}
else if (upper <= Uo) {
U10 = 0.5 *
((upper -
sigma_w) * exp((1. / sigma_w) * (upper - Uo)) -
(lower -
sigma_w) *
exp((1. / sigma_w) * (lower - Uo))) / area;
}
else {
log_err("Problem with probability ranges: Increment = %d, "
"integration limits = %f - %f", p, upper, lower);
}
if (U10 < 0.4) {
U10 = .4;
}
if (U10 > 25.) {
U10 = 25.;
}
/*******************************************************************/
/* Calculate parameters for probability of blowing snow occurence. */
/* ( Li and Pomeroy 1997) */
if (snowdepth < hv) {
Uveg = U10 / sqrt(1. + 170 * Nd * (hv - snowdepth));
}
else {
Uveg = U10;
}
prob_occurence = get_prob(Tair, Age, SurfaceLiquidWater, Uveg);
/*******************************************************************/
/* Calculate threshold shear stress. Send 0 for constant or */
/* 1 for variable threshold after Li and Pomeroy (1997) */
utshear =
get_thresh(Tair, SurfaceLiquidWater, ZO);
/* Iterate to find actual shear stress during saltation. */
shear_stress(U10, ZO, &ushear, &Zo_salt, utshear);
if (ushear > utshear) {
SubFlux = CalcSubFlux(EactAir, es, Zrh, AirDens, utshear,
ushear, fe, Tsnow,
Tair, U10, Zo_salt, F, &Transport);
}
else {
SubFlux = 0.0;
Transport = 0.0;
}
Total += (1. / (double) param.BLOWING_NUMINCS) * SubFlux *
prob_occurence;
*TotalTransport += (1. / (double) param.BLOWING_NUMINCS) *
Transport * prob_occurence;
}
}
else {
U10 = Uo;
/*******************************************************************/
/* Calculate parameters for probability of blowing snow occurence. */
/* ( Li and Pomeroy 1997) */
if (snowdepth < hv) {
Uveg = U10 / sqrt(1. + 170 * Nd * (hv - snowdepth));
}
else {
Uveg = U10;
}
prob_occurence = get_prob(Tair, Age, SurfaceLiquidWater, Uveg);
/*******************************************************************/
/* Calculate threshold shear stress. Send 0 for constant or */
/* 1 for variable threshold after Li and Pomeroy (1997) */
utshear = get_thresh(Tair, SurfaceLiquidWater, ZO);
/* Iterate to find actual shear stress during saltation. */
shear_stress(Uo, ZO, &ushear, &Zo_salt, utshear);
if (ushear > utshear) {
SubFlux = CalcSubFlux(EactAir, es, Zrh, AirDens, utshear,
ushear, fe, Tsnow,
Tair, Uo, Zo_salt, F, &Transport);
}
else {
SubFlux = 0.0;
Transport = 0.0;
}
Total = SubFlux * prob_occurence;
*TotalTransport = Transport * prob_occurence;
}
}
if (Total < -.00005) {
Total = -.00005;
}
return Total;
}
/*****************************************************************************
Function name: CalcBlowingSnow()
Purpose : Calculate sublimation from blowing snow
Required : double Dt; Model time step (hours)
double Tair; Air temperature (C)
int LastSnow; Time steps since last snowfall.
double SurfaceLiquidWater; Liquid water in the surface layer (m)
double Wind; Wind speed (m/s), 2 m above snow
double Ls; Latent heat of sublimation (J/kg)
double AirDens; Density of air (kg/m3)
double Lv; Latent heat of vaporization (J/kg3)
double Press; Air pressure (Pa)
double EactAir; Actual vapor pressure of air (Pa)
double ZO; Snow roughness height (m)
Returns : BlowingMassFlux
Modifies :
Comments : Called from SnowPackEnergyBalance
Reference:
*****************************************************************************/
double CalcBlowingSnow( double Dt,
double Tair,
int LastSnow,
double SurfaceLiquidWater,
double Wind,
double Ls,
double AirDens,
double Press,
double EactAir,
double ZO,
double Zrh,
double snowdepth,
float lag_one,
float sigma_slope,
double Tsnow,
int iveg,
int Nveg,
float fe,
double displacement,
double roughness,
double *TotalTransport)
{
/* Local variables: */
double Age;
double U10, Uo, prob_occurence;
double es, Ros, F;
double SubFlux;
double Diffusivity;
double ushear, Qsalt, hsalt, phi_s, psi_s;
double Tk;
double Lv;
double T, ztop;
double ut10, utshear;
int p;
double upper, lower, Total;
double area;
double sigma_w;
double undersat_2;
double b, temp2; /* SBSM scaling parameter. */
double temp, temp3;
double Zo_salt;
double ratio, wind10;
double Uveg, hv, Nd;
double Transport;
int count=0;
Lv = (2.501e6 - 0.002361e6 * Tsnow);
/*******************************************************************/
/* Calculate some general variables, that don't depend on wind speed. */
/* Age in hours */
Age = LastSnow*(Dt);
/* Saturation density of water vapor, Liston A-8 */
es = svp(Tair);
Tk = Tair + KELVIN;
Ros = 0.622*es/(287*Tk);
/* Diffusivity in m2/s, Liston eq. A-7 */
Diffusivity = (2.06e-5) * pow(Tk/273.,1.75);
// Essery et al. 1999, eq. 6 (m*s/kg)
F = (Ls/(Ka*Tk))*(Ls*MW/(R*Tk) - 1.);
F += 1./(Diffusivity*Ros);
/* grid cell 10 m wind speed = 50th percentile wind */
/* Wind speed at 2 m above snow was passed to this function. */
wind10 = Wind*log(10./ZO)/log((2+ZO)/ZO);
// fprintf(stderr,"wind=%f, Uo=%f\n",Wind, Uo);
/* Check for bare soil case. */
if(iveg == Nveg) {
fe = 1500;
sigma_slope = .0002;
}
// sigma_w/uo:
ratio = (2.44 - (0.43)*lag_one)*sigma_slope;
// sigma_w = wind10/(.69+(1/ratio));
// Uo = sigma_w/ratio;
sigma_w = wind10*ratio;
Uo = wind10;
/*********** Parameters for roughness above snow. *****************/
hv = (3./2.)*displacement;
Nd = (4./3.)*(roughness/displacement);
/*******************************************************************/
/** Begin loop through wind probability function. */
Total = 0.0;
*TotalTransport = 0.0;
area = 1./NUMINCS;
if(snowdepth > 0.0) {
if(SPATIAL_WIND && sigma_w != 0.) {
for(p= 0; p< NUMINCS; p++) {
SubFlux = lower = upper = 0.0;
/* Find the limits of integration. */
if(p==0) {
lower = -9999;
upper = Uo + sigma_w*log(2.*(p+1)*area);
}
else if(p > 0 && p < NUMINCS/2) {
lower = Uo + sigma_w*log(2.*(p)*area);
upper = Uo + sigma_w*log(2.*(p+1)*area);
}
else if(p < (NUMINCS-1) && p >= NUMINCS/2) {
lower = Uo - sigma_w*log(2.-2.*(p*area));
upper = Uo - sigma_w*log(2.-2.*((p+1.)*area));
}
else if(p == NUMINCS-1) {
lower = Uo - sigma_w*log(2.-2.*(p*area));
upper = 9999;
}
if(lower > upper) {/* Could happen if lower > Uo*2 */
lower = upper;
fprintf(stderr,"Warning: Error with probability boundaries in CalcBlowingSnow()\n");
}
/* Find expected value of wind speed for the interval. */
U10 = Uo;
if(lower >= Uo )
U10 = -0.5*((upper+sigma_w)*exp((-1./sigma_w)*(upper - Uo))
- (lower+sigma_w)*exp((-1./sigma_w)*(lower - Uo)))/area;
else if(upper <= Uo )
U10 = 0.5*((upper-sigma_w)*exp((1./sigma_w)*(upper - Uo))
- (lower-sigma_w)*exp((1./sigma_w)*(lower - Uo)))/area;
else {
fprintf(stderr,"ERROR in CalcBlowingSnow.c: Problem with probability ranges\n");
fprintf(stderr," Increment = %d, integration limits = %f - %f\n",p,upper, lower);
return ( ERROR );
}
if(U10 < 0.4)
U10 = .4;
if(U10 > 25.) U10 = 25.;
/*******************************************************************/
/* Calculate parameters for probability of blowing snow occurence. */
/* ( Li and Pomeroy 1997) */
if(snowdepth < hv) {
Uveg = U10/sqrt(1.+ 170*Nd*(hv - snowdepth));
}
else
Uveg = U10;
// fprintf(stderr, "Uveg = %f, U10 = %f\n",Uveg, U10);
prob_occurence = get_prob(Tair, Age, SurfaceLiquidWater, Uveg);
// printf("prob=%f\n",prob_occurence);
/*******************************************************************/
/* Calculate threshold shear stress. Send 0 for constant or */
/* 1 for variable threshold after Li and Pomeroy (1997) */
utshear = get_thresh(Tair, SurfaceLiquidWater, ZO, VAR_THRESHOLD);
/* Iterate to find actual shear stress during saltation. */
shear_stress(U10, ZO, &ushear, &Zo_salt, utshear);
if(ushear > utshear) {
SubFlux = CalcSubFlux(EactAir, es, Zrh, AirDens, utshear,ushear, fe, Tsnow,
Tair, U10, Zo_salt, F, &Transport);
}
else {
SubFlux=0.0;
Transport = 0.0;
}
Total += (1./NUMINCS)*SubFlux*prob_occurence;
*TotalTransport += (1./NUMINCS)*Transport*prob_occurence;
}
}
else {
U10=Uo;
/*******************************************************************/
/* Calculate parameters for probability of blowing snow occurence. */
/* ( Li and Pomeroy 1997) */
if(snowdepth < hv)
Uveg = U10/sqrt(1.+ 170*Nd*(hv - snowdepth));
else
Uveg = U10;
prob_occurence = get_prob(Tair, Age, SurfaceLiquidWater, Uveg);
/*******************************************************************/
/* Calculate threshold shear stress. Send 0 for constant or */
/* 1 for variable threshold after Li and Pomeroy (1997) */
utshear = get_thresh(Tair, SurfaceLiquidWater, ZO, VAR_THRESHOLD);
/* Iterate to find actual shear stress during saltation. */
shear_stress(Uo, ZO, &ushear, &Zo_salt, utshear);
if(ushear > utshear) {
SubFlux = CalcSubFlux(EactAir, es, Zrh, AirDens, utshear,ushear, fe, Tsnow,
Tair, Uo, Zo_salt, F, &Transport);
}
else {
SubFlux=0.0;
Transport = 0.0;
}
Total = SubFlux*prob_occurence;
*TotalTransport = Transport*prob_occurence;
}
}
if(Total < -.00005)
Total = -.00005;
return Total;
}