Catchment models describe how the inputted water leaves the subcatchment.
Currently only one is implemented:
Comola Catchment Model
SWIFlow is a two layer streamflow model. There is an upper storage and a lower
storage that interact. The model uses three state variables to model streamflow.
The are storage of a layer, infiltration rate into the layer, and the flowrate
from the layer.
This model was introduced by Comola et. al 2015 and implemented the same in swiflow
as it was originally described.
Equations
Below are the definitions used in the model equations:
- Q - Flowrate in \(\frac{m^3}{s}\)
- S - Storage in units of meters of water height over subbasin area.
- I - Infiltration rate in units of \(\frac{m}{s}\)
- \(\bar{\tau}\) - Residence time, (calibrated term) in units of seconds
- \(R_{max}\) - Maximum infiltration rate to the lower layer (calibrated)
- A - Surface area of either the subbasin or the total watershed in \(m^2\).
The model is described by the following equations:
\[ \begin{align}\begin{aligned}I_{res_L} = min(I_{swi}, R_{max})\\I_{res_U} = I_{swi} - I_{res_L}\end{aligned}\end{align} \]
For change in storage in the upper and lower layer:
\[\frac{d S_{res_{L,U}}}{dt} = I_{res_{L,U}} - \frac{Q}{A_{subbasin}}\]
The Residence time for each layer for each subbasin is:
\[\tau = \left(\frac{A_{subbasin}}{A_{total}}\right) ^ {\frac{1}{3}} \bar{\tau}\]
The flowrate out of a layer is defined by:
\[ \begin{align}\begin{aligned}Q_{res_{L,U}} = A_{subbasin} \frac{S_{res_{L,U}}}{\tau_{res_{L,U}}}\\Q_{subbasin} = Q_{res_U} + Q_{res_L}\end{aligned}\end{align} \]
Discretization
Spatially the model is split up by subwatersheds or sometimes called HRUs prior
to running SWIFlow. This can be performed by
basin_setup . Temporally, the change in storage equation is split up
explicitly which is implemented as follows:
\[S_{res_{t+1}} = \left(I_{res_t} - \frac{Q_t}{A_{subbasin}}\right) \Delta t + S_{res_t}\]
Algorithm
At the beginning of the run, SWIFlow the initial conditions for
\(Q_{res_{L,U}}\) and \(S_{res_{L,U}}\), S are all zero. SWIFlow computes
the state variables in the following order for each timestep.
- Calculate lower then upper infiltration rates (\(I_{res_{L,U}}\))
- Calculate upper and lower flowrates (\(Q_{res_{L,U}}\))
- Calculate future storage using discretized change in storage equation (\(S_{res_{t+1}}\))
Comola Catchment Model¶
SWIFlow is a two layer streamflow model. There is an upper storage and a lower storage that interact. The model uses three state variables to model streamflow. The are storage of a layer, infiltration rate into the layer, and the flowrate from the layer.
This model was introduced by Comola et. al 2015 and implemented the same in swiflow as it was originally described.
Equations¶
Below are the definitions used in the model equations:
The model is described by the following equations:
For change in storage in the upper and lower layer:
The Residence time for each layer for each subbasin is:
The flowrate out of a layer is defined by:
Discretization¶
Spatially the model is split up by subwatersheds or sometimes called HRUs prior to running SWIFlow. This can be performed by basin_setup . Temporally, the change in storage equation is split up explicitly which is implemented as follows:
Algorithm¶
At the beginning of the run, SWIFlow the initial conditions for \(Q_{res_{L,U}}\) and \(S_{res_{L,U}}\), S are all zero. SWIFlow computes the state variables in the following order for each timestep.