Reservoir balance
Represented system
The model represents the regulated Sau–Susqueda–Pasteral system in an aggregated manner.
For each month, storage is updated using a volume balance:
\[ V_{m+1} = V_m + Q^{in}_m S_m - Q^{rel}_m S_m - V^{evap}_m - V^{overflow}_m \]
where:
- \(V_m\): volume stored at the start of the month;
- \(Q^{in}_m\): inflow;
- \(Q^{rel}_m\): controlled release;
- \(S_m\): duration of the month in seconds;
- \(V^{evap}_m\): evaporation loss;
- \(V^{overflow}_m\): overflow volume.
Initial volume
The initial volume specified by the user is used in the first month. In subsequent months, the final volume from the previous month is used.
Evaporation
Evaporation is calculated from:
- potential evapotranspiration at the reservoir node;
- estimated inundated area;
- stored volume.
The monthly loss is:
\[ V^{evap}_m = \frac{ E_m A^{res}_m }{ 10^9 } \]
where \(E_m\) is evaporation in mm and \(A^{res}_m\) is the inundated area in \(\mathrm{m^2}\). The result is expressed in \(\mathrm{hm^3}\).
Automatic release
When the user does not set a release, the model estimates the water required to:
- meet downstream demands;
- maintain environmental flows;
- compensate for losses that occur during routing along the river.
User-defined release
The user can specify an annual volume or monthly values. The model always applies the physical constraint:
\[ V^{release}_m \leq V_m+V^{in}_m-V^{evap}_m \]
Therefore, no more water can be released than is available.
Overflow
When the resulting volume exceeds the maximum system capacity, the excess becomes overflow:
\[ V^{overflow}_m = \max(0,V^{provisional}_{m+1}-V^{max}) \]
The stored volume is limited to \(V^{max}\).