Geostrophic covariances

Assume pressure-pressure correlations are isotropic

where is the correlation of pressure at position and pressure at position , is the distance between positions and ,

and is the length scale (approx. 750 km).

State geostrophic relations

where is pressure, is density, is Corriolis parameter , is the Earth's angular velocity, is latitude, is zonal wind, and is meridional wind.

Need first and second spatial derivatives of p-p correlations

Derive covariances for winds and pressure

Pressure - pressure covariances

is the pressure standard deviation (assume homogeneous)

Pressure - zonal wind covariances

Pressure - meridional wind covariances

Zonal wind - pressure covariances

Zonal - zonal wind covariances

Zonal - meridional wind covariances

Meridional wind - pressure covariances

Meridional - zonal wind covariances

Meridional - meridional wind covariances

Covariance maps

The above covariances are plotted with the colour scheme: red (positive) and blue (negative) covariances.

	p	u	v
p
u
v