# Peterson#

class Peterson[source]#

Recharge to the groundwater calculated based on Peterson and Western (2014).

The water balance for the unsaturated zone reservoir is written as:

$\frac{dS}{dt} = P_e - E_a - R$

where the fluxes $P_e$, $E_a$ and $R$ are calculated as:

$P_e = P \left(1 - \frac{S}{\hat{S_{cap}}}\right)^\alpha$
$E_a = E_p \left(\frac{S}{\hat{S_{cap}}}\right)^\gamma$
$R = \hat{k_{sat}}\left(\frac{S}{\hat{S_{cap}}}\right)^{\hat{\beta}}$

with the parameters:

$\hat{S_{cap}} = 10^{S_{cap}}; \hat{k_{sat}} = 10^{k_{sat}}; \hat{\beta} = 10^{\beta}$

Note that the method currently uses forward Euler method to solve the ODE so significant water balance errors can occur.

## Methods#

 __init__ get_init_parameters Method to obtain the initial parameters. get_recharge Internal method used for the recharge calculation. get_water_balance simulate Simulate the recharge flux. to_dict Method to export the recharge model object.