## Water available for infiltration and direct runoff

In the permeable fraction of each pixel $(1- f_{dr})$, the **amount of water** that is **available for infiltration**, $W_{av}$ $[mm]$ equals (Supit *et al.*,1994):

where:

- $R$: Rainfall $[\frac{mm}{day}]$,

- $M$: Snow melt $[mm]$,

- $D_{int}$: Leaf drainage $[mm]$,

- $Int$: Interception $[mm]$, and

- $\Delta t$: time step $[days]$.

Since no infiltration can take place in each pixel’s ‘direct runoff fraction’, **direct runoff** is calculated as:

where $R_d$ is in $mm$ per time step and $IntercSealed$ is the water in $mm$ retained by the depressions of the impervious surfaces and not immediately available to generate direct runoff. More specifically, $IntercSealed$ is equal to the total of raifall and snow melt until all the depressions have been filled, that is until the $AvailableStorageSealed$ is larger than 0. The computation is shown by the following equations:

\[IntercSealed = R \cdot \Delta t + M\]when

\[AvailableStorageSealed= SMAXsealed - StorageSealed > 0\]where $SMAXsealed$ is the maximum depression storage in $mm$ (provided as input data), and $StorageSealed$ is the volume already filled by water in $mm$. The computation of the latter accounts for the volume already used at the initial time step ($StorageSealedInit$, provided as input data) and the water volume loss due to evaporation:

\[StorageSealed = StorageSealedInit + IntercSealed - EW0\]Direct runoff $R_d$ is added to surface runoff.

Note here that $W_{av}$ is valid for the permeable fraction only, whereas $R_d$ is computed for the full pixel (permeable + direct runoff areas).