Mass balance

Water mass balance error

For model types sbm and sbm_gwf water mass balance error computations are supported, and can be enabled by setting the following model setting in the TOML file:

[model]
water_mass_balance__flag = true

The water balance error \(\epsilon\) and relative error \(\epsilon_{\mathrm{r}}\) can be written as:

\[ \begin{aligned} \epsilon = \frac{S^{k+1} - S^{k}}{\Delta{t}} - Q^{k+1}_{\mathrm{total, in}} + Q^{k+1}_{\mathrm{total, out}}\\ \epsilon_{\mathrm{r}} = \frac{\epsilon}{0.5(Q^{k+1}_{\mathrm{total, in}} + Q^{k+1}_{\mathrm{total, out}})} \end{aligned} \]

where \(k\) refers to model time step, \(S\) is storage and \(Q_{\mathrm{total, in}}\) and \(Q_{\mathrm{total, out}}\) are total inflow and total outflow, respectively. Water balance (relative) errors are computed separately for:

  • the Land Hydrology SBM model
  • different routing concepts.

For the local inertial model for 1D river and 2D overland flow that includes subgrid channels for the 1D river routing, water balance errors are computed for each land cell (total storage) considering both river and overland flow. For this routing type output standard names that refer to land surface water should be used, for example:

[output.netcdf_grid.variables]
land_surface_water_mass_balance_error__volume_flow_rate = "balance_error"

For the local inertial river routing including 1D floodplains, water balance errors are computed considering both river and floodplain flow and total storage (river and floodplain), and output standard names that refer to river water should be used, for example:

[output.netcdf_grid.variables]
river_water_mass_balance_error__volume_flow_rate = "balance_error"

The list of water balance (relative) error output parameters that can be provided through the TOML file can be found here.

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