Wind setup

Observation of wind setup in Vlissingen in 1953

In lakes, water level fluctuations are typically attributed to wind setup. This effect is particularly noticeable in lakes with well-regulated water levels, where the wind setup can be clearly observed. By comparing this with the wind over the lake, the relationship between wind speed, water depth, and fetch length can be accurately determined. This is especially feasible in lakes where water depth remains fairly consistent, such as the IJsselmeer.[4]

At sea, wind setup is usually not directly observable, as the observed water level is a combination of both the tide and the wind setup. To isolate the wind setup, the (calculated) astronomical tide must be subtracted from the observed water level. For example, during the North Sea flood of 1953 at the Vlissingen tidal station (see image), the highest water level along the Dutch coast was recorded at 2.79 metres, but this was not the location of the highest wind setup, which was observed at Scheveningen with a measurement of 3.52 metres.

Notably, the highest wind setup ever recorded in the Netherlands (3.63 metres) was in Dintelsas, Steenbergen in 1953, a location approximately 40 km from the sea along the Haringvliet estuary.

Based on the equilibrium between the shear stress due to the wind on the water and the hydrostatic back pressure, the following equation is used: [5]

${\displaystyle {\frac {dh}{dx}}={\frac {\kappa u^{2}\cos \phi }{gh}}}$

in which:

h = water depth

x = distance

u= wind speed

${\displaystyle \kappa =c_{w}{\frac {\rho _{air}}{\rho _{water}}}}$, Ippen [5] suggests ${\displaystyle \kappa }$ = 3.3*10⁻⁶

${\displaystyle \phi }$ = angle of the wind relative to the coast

g = acceleration of gravity

c_w has a value between 0.8*10⁻³ and 3.0*10⁻³

Application at (shallow) lakes

Graph showing result of using modified value κ=1.7*10-7 for the calculation of wind setup, after Feij (2015).[4]

To calculate the wind setup in a lake, the following solution for the differential equation is used:

${\displaystyle \Delta h=0.5\kappa {\frac {u^{2}}{gh}}F\cos \phi }$

In 1966 the Delta Works Committee recommended using a value of 3.8*10⁻⁶ for ${\displaystyle \kappa }$ under Dutch conditions. However, an analysis of measurement data from the IJsselmeer between 2002 and 2013 led to a more reliable value for ${\displaystyle \kappa }$, specifically ${\displaystyle \kappa }$ = 2.2*10⁻⁶.[4]

This study also found that the formula underestimated wind setup at higher wind speeds. As a result, it has been suggested to increase the exponent of the wind speed from 2 to 3 and to further adjust ${\displaystyle \kappa }$ to ${\displaystyle \kappa }$=1.7*10⁻⁷. This modified formula can predict the wind setup on the IJsselmeer with an accuracy of approximately 15 centimetres.

Wind setup should not be mistaken for wave run-up, which refers to the height which a wave reaches on a slope, or wave setup which is the increase in water level caused by breaking waves.

• Storm surge
• Coastal flooding
• Coastal Engineering