Precipitation Partitioning#

The aim of this section is to present the partitioning of the precipitation into liquid and solid components.

Denote \(P\) the precipitation, \(S\) the snow, \(T_e\) the temperature, \(x\in\Omega\) a given cell and \(t\in]0 .. T]\) a time step.

First, the precipitation \(P\) and the snow \(S\) are summed to give the total precipitation \(P_T\)

\[P_T(x, t) = P(x, t) + S(x, t) \;\;\; \forall (x, t) \in \Omega \times ]0 .. T]\]

Then, the liquid ratio \(l_r\) splits the total precipitation \(P_T\) into liquid part (precipitation) \(P\) and solid part (snow) \(S\).

\begin{eqnarray} &P(x, t)& &=& &l_r(x, t) \times P_T(x, t)\\ &S(x, t)& &=& &(1 - l_r(x, t)) \times P_T (x, t) \;\;\; \forall (x, t) \in \Omega \times ]0 .. T] \end{eqnarray}

where the liquid ratio \(l_r\) is derived from a classical parametric S-shaped curve [Garavaglia et al., 2017].

\[l_r(x, t) = 1 - \left( 1 + \exp\left( \frac{10}{4}T_e(x, t) - 1\right)\right)^{-1} \;\;\; \forall (x, t) \in \Omega \times ]0 .. T]\]

Note

  • If no snow \(S\) is provided, the total precipitation \(P_T\) is simply the precipitation \(P\) on which a liquid ratio \(l_r\) will be calculated.

  • If snow \(S\) is provided, the default liquid ratio \(l_r\) is overwritten.

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