Drainage formula (Water Overlay)

Depending on whether the drainage is passive or active, the formula for either passive or active drainage is used.

Drainage passive

First the flow capacity is calculated

$Q_{p}=\Delta t\cdot q_{t}$

$Q_{b}=A_{d}\cdot f_{s}\cdot {\frac {||w_{d}-w_{w}||\cdot A_{w}}{A_{d}\cdot f_{s}+A_{w}}}$

if $w_{d}>w_{w}$ then:

$Q_{d}=A_{d}\cdot (w_{d}-z_{d})\cdot f_{s}$

$Q_{t}=min(Q_{p},Q_{b},Q_{d})$

else:

$Q_{w}=A_{w}\cdot (w_{w}-z_{w})$

$Q_{t}=min(Q_{p},Q_{b},Q_{w})$

Where:

q_{t}

is the DRAINAGE_Q of the Drainage at time t.

\Delta t

is the computational timestep.

w_{d}

is the ground water level, above the drainage, in meters.

w_{w}

is the water level in the waterway.

z_{d}

is the drainage datum height in meters.

z_{w}

is the max waterway height.

A_{d}

is the drainage area size in square meters.

A_{w}

is the waterway area size in square meters.

f_{s}

is the average storage percentage of the ground above the drainage.

Q_{p}

is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.

Q_{b}

is the amount transferred for a balanced ground and surface water level.

Q_{d}

is the amount of water available in the ground above the drainage.

Q_{w}

is the amount of water available in the waterway.

Q_{t}

is the actual drained, or infiltrated backwards, volume at time t.

Drainage active

Case 1: Active Draining:

If a positive DRAINAGE_Q is defined:

Q_{p}=\Delta t\cdot q_{t}

Q_{d}=(w_{d}-z_{d})\cdot f_{s}

If an overflow threshold $T_{o,t}$ is defined as well:

Q_{o}=max(0,T_{o,t}-w_{w})

The actual water pumped out of the drainage system is calculated. If any of the terms are undefined, they are not included.

Q_{t}=max(0,min(Q_{d},Q_{o},Q_{p}))

Case 2: Active Reverse Draining:

If a negative DRAINAGE_Q is defined:

Q_{p}=\Delta t\cdot q_{t}

Q_{w}=min(0,z_{w}-w_{t,w})

If an overflow threshold $T_{o,t}$ is defined as well:

Q_{o}=min(0,T_{o,t}-w_{t,w})

The actual water pumped into the drainage system is calculated. If any of the terms are undefined, they are not included.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_t = max( 0 , max( Q_p, Q_w , Q_o) ) }

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q_t} is the DRAINAGE_Q of the Drainage at time t.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta t} is the computational timestep.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_p} is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_d} is the ground water level, above the drainage, in meters.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_w} is the water level in the waterway.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_d} is the drainage datum height in meters.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_w} is the waterway's datum height.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_s} is the average storage percentage of the ground above the drainage.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_d} is the amount of water available in the ground above the drainage.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{o,t}} is the overflow threshold in meters at time t.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_o} is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_w} is the amount of water available in the waterway.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{t}} is the actual drained (or pumped) volume at time t.