Calculation of Divergence

[Bill Schintler]

How is divergence calculated - such that displayed on the SPC 300 mb mesoanalysis plot? Is it as simple as applying the definition of divergence (in two dimensions using Cartesian coordinates) to the *velocity* field over the isobaric surface? For example, divergence (of a velocity field) is defined as the sum of the derivatives of the X and Y components of the velocity with respect to X and Y. Consider X (zonal Component, for example) and Y (meridional component) coordinates. Define U and V as the X and Y components of the velocity vector, respectively: U = delta(X)/delta(t) and V = delta (Y)/delta(t).

Divergence D = delta(U)/delta(X) + delta(V)/delta(Y) (units = 1/time)

*OR*, does one need to calculate the divergence of the mass flow field, since the isobaric surface is not necessarily an isentropic surface? I would assume that in practice it wouldn't make much of a difference. Are there other subtleties that I need to consider?

A side question: what are the units on the SPC 300 mb divergence plot.

- bill

 

[Glen Romine]

How is divergence calculated - such that displayed on the SPC 300 mb mesoanalysis plot?

Divergence D = delta(U)/delta(X) + delta(V)/delta(Y) (units = 1/time)

A side question: what are the units on the SPC 300 mb divergence plot.

- bill

Certainly you could calculate it either way - yet since the divergence product is overlayed on a constant pressure surface plot - it would be most intuitive for the divergence calculation to be done on a constant pressure surface. The normal units for divergence is 10^-5 s^-1, so that is what I suspect is used there.

Glen