Inlet formula (Water Overlay)

Inlets are hydraulic structures that 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:

$Q_{lth}=max(0,T_{l,t}-w_t)$

If a positive inlet $Q_t$ is defined:

$Q_t=\Delta t\cdot Q_t$

If a capacity $Q_{total}$ is defined:

$Q_c=Q_{total}-\sum _{\mathrm{0..}t-1}{Q}_i$

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

$\Delta w=\frac{max(0,min(Q_{lth},Q_t,Q_c))}{A}$

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

If an upper threshold T_u,t is defined:

$Q_{uth}=min(0,T_{u,t}-w_t)$

If a negative inlet $Q_t$ is defined:

$Q_t=\Delta t\cdot Q_t$

If a capacity $Q_{total}$ is defined:

$Q_c=-Q_{total}-\sum _{\mathrm{0..}t-1}{Q}_i$

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

$\Delta w=\frac{min(0,max(Q_{uth},Q_t,Q_c))}{A}$

Where:

• $w_t$ = The water level on the surface relative to datum, at time t.
• $T_{l,t}$ = The LOWER_THRESHOLD of the Inlet at time t.
• $T_{u,t}$ = The UPPER_THRESHOLD of the Inlet at time t.
• $q_t$ = The INLET_Q of the Inlet at time t.
• $\Delta t$ = Computational timestep.
• $Q_{total}$ = The INLET_CAPACITY of the Inlet.

• $Q_{\mathrm{0..}n}$ = The calculated previous amounts of flow.
• $Q_{lth}$ = The desired lower water level at the Inlet's location, based on the LOWER_THRESHOLD of the Inlet.
• $Q_{uth}$ = 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 $\Delta t$.
• $Q_c$ = 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.
• $\Delta w$ = The amount of water flow which takes place.

Related

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