Surface wind from gradient wind

Cyclonic : knots
Anticyclonic : knots
Direction : °
This utility allows you to calculate the expected surface wind speed and direction for a given geostrophic wind. Initially gradient wind speed is calculated for cyclonic (sub-geostrophic) and anticyclonic (super-geostrophic) flow as follows; if r is the radius of flow curvature (nautical miles), Φ the latitude (degrees), f the coriolis parameter (s-1) and Vg the geostrophic wind velocity (ms-1):
$$V_{sub-geostr} = \frac{1}{2} \left(-rf + \sqrt{r^2f^2 + 4rfv_g} \right)$$ $$V_{super-geostr} = \frac{1}{2} \left(rf - \sqrt{r^2f^2 - 4rfv_g} \right)$$ $$f = 2\Omega sin\phi$$ Note: If there's an error in calculating the super geostrophic wind, remember there is, dynamically a limit to the strength of winds around an anticyclone. Pressure gradient force acts outwards so closer isobars fight against circular motion, in effect the expression within the square root section of the super geostrophic equation must be positive or zero. The resultant speeds are then reduced and the direction backed for the selected atmospheric stability profile and surface type as follows:

Calculating surface wind from the gradient wind

Stability and surface Speed reduction factor Direction backed (degs)
Land - clear night 0.2 -40
Land - average 0.4 -30
Land - unstable 0.5 -20
Sea - stable 0.8 -10
Sea - unstable 0.9 -5