Waterway level change benchmark (Water Module)

Initially, the ground water table is the same as the water level in the waterway. Suddenly the level in the waterway rises with h0 meters. This causes water to infiltrate into the ground, raising the ground water table.

Formulas

When the water level in the water way changes, the water table level will also change over time. The relation between water level in the waterway and the ground water table at distance x from the water way is described by the following formulas: Water level raised: ${\frac {h(x)}{h_{0}}}=erfc(x{\sqrt {\frac {S}{4kDt}}})$

Water level lowered: ${\frac {h(x)}{h_{0}}}=erf(x{\sqrt {\frac {S}{4kDt}}})$

The formula erf is the complementary error function. 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 erf(z) = \frac{2}{\sqrt{\pi}}\int\limits_{0}^{z}e^(-t^2)dt}

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 erfc(z) = 1 - erf(z)}

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 h(x)} : change in freatic groundwater table (m)

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 h0} : change in water level in the waterway(m)

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 x} : distance to the water way (m)

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} : time since the water level change

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 kD} : transmissivity of the aquifer (m2 / day)

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 S} : freatic water storage fraction.