altitude_derivative_on_pressure_level#
- rojak.turbulence.calculations.altitude_derivative_on_pressure_level(function: DataArray, geopotential: DataArray, level_coord_name: str = 'pressure_level') DataArray[source]#
Derivative w.r.t. altitude for data on pressure level
Using the definition of geopotential,
\[\Phi = gz \implies \frac{ \partial \Phi }{ \partial z } = g\]Express derivative w.r.t. altitude in terms of pressure. For example, for the function \(f\),
\[\frac{ \partial f }{ \partial z } = \frac{ \partial f }{ \partial p } \frac{ \partial p }{ \partial \Phi } \frac{ \partial \Phi }{ \partial z } = g \frac{ \partial f }{ \partial p } \left( \frac{ \partial \Phi }{ \partial p } \right)^{-1}\]