Drainage-area contributions
Monthly water balance
Each drainage area generates a local contribution based on precipitation, evapotranspiration, snow and the drained area.
\[ Q^{contrib}_{i,m} = \frac{ A_i\,C \left( P_{i,m}-ET_{i,m}-r_m\Delta N_{i,m} \right) }{ 1000\,S_m } \]
where:
- \(Q^{contrib}_{i,m}\): flow contributed by area \(i\) during month \(m\), in \(\mathrm{m^3\,s^{-1}}\);
- \(A_i\): drainage area, in \(\mathrm{m^2}\);
- \(C\): runoff coefficient;
- \(P_{i,m}\): monthly precipitation, in mm;
- \(ET_{i,m}\): monthly actual evapotranspiration, in mm;
- \(\Delta N_{i,m}\): monthly change in snow storage;
- \(r_m\): conversion factor from snow to water equivalent;
- \(S_m\): duration of the month, in seconds;
- the factor \(1000\) converts millimetres to metres.
Evapotranspiration
Monthly potential evapotranspiration is calculated from mean monthly temperature using the Thornthwaite method:
\[ PET_m = 16 \left( \frac{10T_m}{I} \right)^a K_m \]
where:
\[ I=\sum_{m=1}^{12} \left( \frac{T_m}{5} \right)^{1.514} \]
and:
\[ a = 6.75\times10^{-7}I^3 - 7.71\times10^{-5}I^2 + 1.792\times10^{-2}I + 0.49239 \]
\(K_m\) corrects the result for day length and the number of days in the month.
PET represents the evaporative demand of the atmosphere if sufficient water were available. It is not necessarily the amount of water actually evapotranspired by the basin.
For each land use \(u\), actual evapotranspiration is calculated using a formulation based on precipitation, PET and a vegetation coefficient1:
\[ ET_{i,m} = \sum_u f_{i,u} \, P_{i,m} \, \frac{ 1+w_u\frac{PET_{i,m}}{P_{i,m}} }{ 1+w_u\frac{PET_{i,m}}{P_{i,m}} +\frac{P_{i,m}}{PET_{i,m}} } \]
where:
- \(f_{i,u}\): proportion of land use \(u\) within area \(i\);
- \(w_u\): evapotranspiration coefficient for the land use;
- \(P_{i,m}\): monthly precipitation;
- \(PET_{i,m}\): potential evapotranspiration.
Coefficients by land use
| Land use | \(w_u\) |
|---|---|
| Water | 0 |
| Urban land and impervious surfaces | 0 |
| Forest and tree plantations | 1.75 |
| Natural grassland and pasture | 1.00 |
| Rainfed crops | 0.75 |
| Irrigated crops | 1.50 |
Higher values represent a greater capacity of vegetation to use the available water.
The model represents the effect of land use on evapotranspiration in an aggregated manner. It does not explicitly simulate soil moisture, rooting or vegetation growth.
Footnotes
Mas-Pla, J. et al. (2016). “Recursos hidrològics”. In Tercer informe sobre el canvi climàtic a Catalunya, pp. 161–188↩︎