frostdepth
This module is defined in Classfrostdepth. The number of soil layers is defined by NLAY. The snow cover is handled as a separate layer whose depth is calculated from the SWE of the HRU using the function depthofsnow.
Observations
- none
Variables
- frostdepth (m) - frostdepth. State variable.
- snowdepth (mm) - calculated from SWE. State variable.
- Findex (°C) - cumulative degrees of frost in (day.°C). State variable.
- Tfreeze (d) - days of frost. State variable.
- Lacc (MJ/m3) - cumulative effective latent heat. State variable.
- Cacc (MJ/(m3.K)) - cumulative effective heat capacity. State variable.
- Kacc (W/(m K)) - cumulative effective thermal conductivity. State variable.
Parameters
- Ta (°C) - annual air temperature.
- soil_type () - 1/sand 2/loam 3/clay 4/organic (only used to differentiate between mineral and organic layers).
- por (m3/m3) - porosity.
- theta (m3/m3) - degree of saturation.
- d (m) - layer depths 1 ... NLAY.
- hru_lat (°) - latitude. Adjusts empirical Julian constants for Northern/Southern Hemisphere.
Variable Inputs
- hru_tmean (obs) (°C)
- SWE (pbsm) (mm)
Other Constants
- Lsnow = 0.35*Ci MJ/(m3) - latent heat of snow.
- csnow = 0.35*ki + 0.65*ka MJ/(m3.°C) - heat capacity of snow.
- ko = 0.21 W/(m K) organic material
- km = 0.27 W/(m K) mineral
- ka = 0.025 W/(m K) air
- ki = 2.24 W/(m K) ice
- kw = 0.57 W/(m K) water
- Cm = 2.000 MJ/(m3.K) mineral
- Cw = 4.185 MJ/(m3.K) water
- Ca = 0.001 MJ/(m3.K) air
- Co = 0.110 MJ/(m3.K) organic
- Ci = 1.950 MJ/(m3.K) organic
Returns
FrostDepth = sqrt((24*Kacc*Findex)/(Lacc + Cacc(Ta + Findex/(2.0*Tfreeze)))) - SnowDepth
where for individual layers
Ln = theta*por*333.0
Kn = (1.0 - por) * km + theta*por*kw + ( por - theta*por)*ka
Cn = (1.0 - por) * Cm + theta*por*Cw + ( por - theta*por)*Ca
for organic material use ko and Co instead of km and Cm.
For snow assuming a snowpack density of (250kg/m3) use
Ln = 0
Ks = 0.25*ki + 0.75*ka
Cs = 0.25*Ci
For the combined layers use
Lacc = (Ls*Ds + L1*D1 + L2*D2 ... Ln*Dn)/Dsum
Cacc = (Cs*Ds + C1*D1 + C2*D2 ... Cn*Dn)/Dsum
Kacc = Dsum/(Ds/Ks + D1/K1 + D2/K2 ... Dn/Kn)
where Ds (m) is SWE/250.0 assuming a snowpack density of (250kg/m3) and D1, D2 .. Dn, 1 ...NLAY are the respective layer thicknesses. The last layer only to the depth frozen.
Reference
Van Wijk W. R., (1963) Physics of Plant Environment. North-Holland Publishing Company - Amsterdam, pp.166