Inlet formula (Water Overlay)

Inlets are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.

The amount flowing in or out of Inlets is calculated for the cell the Inlet resides on.

Case 1: Inlet:
When calculating Inlets, first the capacities are calculated.

If a lower threshold $T_{l, t}$ is defined:

Q_{l t h} = m a x (0, T_{l, t} - w_{t})

If a positive inlet q Q_t is defined:

Q_{t} = Δ t \cdot Q_{t}

If a capacity Q_total is defined:

Q_{c} = Q_{t o t a l} - \sum_{0 . . t - 1} Q_{i}

After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.

Δ w = \frac{m a x (0, m i n (Q_{l t h}, Q_{t}, Q_{c}))}{A}

Case 2 Outlets:
When calculating outlets, first the capacities are calculated.

If an upper threshold T_u,t is defined:

Q_{u t h} = m i n (0, T_{u, t} - w_{t})

If a negative inlet q Q_t is defined:

Q_{t} = Δ t \cdot Q_{t}

If a capacity Q_total is defined:

Q_{c} = - Q_{t o t a l} - \sum_{0 . . t - 1} Q_{i}

After calculating the capacities, the actual water ouflow is calculated. If any of the terms are undefined, they are not included.

Δ w = \frac{m i n (0, m a x (Q_{u t h}, Q_{t}, Q_{c}))}{A}

Where:

$Q_{0 . . n}$ = The calculated previous amounts of flow.
$Q_{l t h}$ = The desired lower water level at the Inlet's location, based on the LOWER_THRESHOLD of the Inlet.
$Q_{u t h}$ = The desired upper water level at the outlet's location, based on the outlet's UPPER_THRESHOLD of the Inlet.
$Q_{t}$ = The amount of water inflow (or outflow when negative) possible based on the INLET_Q of the Inlet and timestep $Δ t$ .
$Q_{c}$ = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the Inlet.

$A$ = Size of the Inlet/outlet area in m², based on the amount of cells and cell size. Current implementation only has one cell.
$Δ w$ = The amount of water flow which takes place.

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