Snow reservoir
In Rameau, the snow reservoir produces snow melting \(q_{sm}\) (mm) and snow runoff \(q_{sr}\) (mm) according to the values of rainfall \(R\) (mm), PET \(E_P\) (mm), temperature \(T\) (°C) and, if available, snow \(R_S\) (mm). \(q_{sm}\) and \(q_{sr}\) are then added to the effective rainfall produced by the soil reservoir.
The SWE \(H_n\) (mm) determines how much water the snowpack in the reservoir contains. The liquid water retention \(r\) (%) corresponds to the fraction of \(H_n\) bounded by capillarity to the snowpack.
During a time step, snow melting occurs according to a succession of physical processes:
Snow melting by soil calories \(M_s\) (mm),
Snow melting using a degree day model \(M_d\) (mm),
If \(R > E_P\), snow melting by rainfall calories \(M_r\) (mm).
If \(R < E_P\), PET may not be fully satisfied by rainfall and the rest may be taken from the snow by sublimation, leading to the calculation of an AET from the snow \(E_S\) (mm) and an UPET \(E_U\).
\(M_s\) participates in feeding the soil reservoir while \(M_d + M_r\) are partitioned between storage in the snow pack, \(q_{sm}\) and \(q_{sr}\).
Activate snow
To activate snow in the model, the user needs to provide at least a temperature input data file.
[files]
temperature = "temperature.csv"
In this case, snow is produced if \(T < 0\). Alternatively, a snow input data file can directly been provided in addition to the temperature data file.
[files]
temperature = "temperature.csv"
snow = "snow.csv"
Physical parameters
Temperature correction
Additive temperature correction \(T_c\) (°C). Before proceeding with snow melting processes, \(T\) is potentially corrected by \(T_c\) in order to correct the possible discrepancies affecting the model input temperature:
Should be optimised. Default value is 0 °C.
[watershed.1]
snow.correction.temperature = { value = 0.0, lower = -3.0, upper = 3.0, opti = false, sameas = 0 }
Snow melting by soil calories
Amount of SWE likely to melt under the action of the calories released by the soil \(C_s\) (1/10 \(\mathrm{mm.day^{-1}}\)).
Should be optimised. Default value is 5 1/10 \(\mathrm{mm.day^{-1}}\).
[watershed.1]
snow.melting = { value = 5.0, lower = 0.001, upper = 20.0, opti = false, sameas = 0 }
Degree day model coefficient
Degree day coefficient of the degree day model \(C_d\) (\(\mathrm{mm.°C^{-1}.day^{-1}}\)).
Should be optimised. Default value is 4 \(\mathrm{mm.°C^{-1}.day^{-1}}\).
[watershed.1]
snow.degree_day.coefficient = { value = 4.0, lower = 0.001, upper = 7.0, opti = false, sameas = 0 }
Degree day model temperature threshold
Temperature threshold of the degree day model \(T_d\) (°C).
Should be optimised. Default value is 0 °C.
[watershed.1]
snow.degree_day.temperature = { value = 0.0, lower = -2.0, upper = 2.0, opti = false, sameas = 0 }
Correction factor of snow melting by rain
Correction factor \(F_m\) (%) applied to the amount of snow that will melt under the action of rainfall.
Should not be optimised in most cases. Default value is 0%.
[watershed.1]
snow.correction.rainfall = { value = 0.0, lower = -20, upper = 20.0, opti = false, sameas = 0 }
Correction factor of PET
Correction factor \(F_s\) (%) applied to \(E_P\) for calculating the amount of SWE that will evaporate by sublimation. \(F_s\) corrects \(E_p\) since the evaporation rate is not necessarily the same between the soil reservoir and the snowpack.
Should not be estimated in most cases. Default value is 0%.
[watershed.1]
snow.correction.pet = { value = 0.0, lower = -20.0, upper = 20.0, opti = false, sameas = 0 }
Maximum snow retention
The maximum snow retention of the snow pack \(r_m\) (%).
Should be optimised. Default value is 5%.
[watershed.1]
snow.maximum_retention = { value = 5.0, lower = 0.001, upper = 30.0, opti = false, sameas = 0 }
Calculating snow melting
In the following section, \(H_0\) and \(r_0\) designate the initial SWE and retention values, respectively, at the beginning of the time step of duration \(\Delta t\) (s).
Snow melting by soil calories
If \(H_n > 0\), snow can melt daily under the action of the calories released by the soil. The SWE likely to melt in this way is noted as \(C_s\) (1/10 \(\mathrm{mm.day^{-1}}\)):
Degree day model
A degree day model assumes that, for each 1°C over 0°C, a certain depth of snow will be melted. The degree day parameters are the degree day factor \(C_d\) (\(\mathrm{mm.°C^{-1}.day^{-1}}\)) and the temperature threshold \(T_d\) (°C) above which melting occurs. If \(T > 0\):
Snow melting by rainfall calories
If \(R > E_p\) and \(T > 0\), snow can melt under the action of the rainfall calories:
The latent heat of fusion of water is 79.7 calories per gram.
Sublimation of snow
If \(R < E_p\), \(E_a\) and \(E_u\) (mm) are calculated as follows:
Snow melting and runoff calculation
Assuming that \(M_s\) feeds directly the soil reservoir, the free liquid water in the snowpack \(W_r\) (mm) is:
The total available liquid water in the snowpack is equal to the addition of the bounded water \(r_0H_0\) and the free water \(W_f\). If \(r_0 < r_m\), a part of this total available liquid water, denoted \(W_d\), will replenish the snowpack in order for \(r\) to reach the maximum snow retention \(r_m\) (%):
\(1 - \frac{W_d}{W_f}\) is the fraction of the total liquid water available that contribute either to \(q_{sm}\) or to \(q_{sr}\):