Mixed Layer Potential Temperature and Height Calculator

Introduction : This calculator calculates the height and potential temperature in a mixed layer in a PBL. In this calculator, you have three input values:
  1. the potential temperature at the surface in degrees Celsius
  2. the lapse rate in the layer, in degrees Kelvin per kilometer
  3. the cumulative daytime heating, in degrees Kelvin meter.

A sample problem is provided by Stull:

Given an early morning sounding with surface temperature of 5 degC and a lapse rate of 3 K/km, find the mixed layer potential temperature and depth at 10 am, when the cumulative heating is 500 K-m (0.5 K-km).

The algorithm for the mixed layer height is:

Mathematical equation for mixed layer depth

This calculator also determines the potential temperature for the mixed layer. The algorithm for the potential temperature is:

Mathematical equation for potential temperature in the mixed layer

Mixed Layer Potential Temperature and Height Calculator

NOTE: Pay attention to units!

Input Values:

Potential temperature at the surface (degC)
Lapse rate in the layer (K/km)
Cumulative daytime heating (K-km)

Results:

Height of the mixing layer (meters)
Potential temperature of the mixing layer (degC)