Stable Boundary Layer Temperature Calculator

Introduction : This calculator calculates the potential temperature and height of a the stable boundary layer in the planetary boundary level (PBL). In this calculator, you have two input values:
  1. the accumulated heat QAk
  2. the accumulated amount of time (in seconds). For example, if you were calculating the heating for the daytime (defined as 0800 to 1600 (4 pm), the accumulated time would be 8 hours x 60 minutes x 60 seconds = 28,800 seconds. For the night time, the total amount of night time is 16 hours.
  3. the wind in the stable boundary layer in meters per second

The algorithm for the the potential temperature is:

Mathematical equation for the potential temperature of the stable layer

The algorithm for the height of the stable boundary layer is:

Mathematical equation for the height of the stable layer

Once we have determined these values, we can calculate the potential temperature at a given height z:

Mathematical equation for the potential temperaature of the stable layer at a given height

Cumulative Heat Calculator

Input Values:

Time (in hours, example shows two hours of daytime (10 am)
Accumulated heating (negative for night-time cooling
Wind speed (m/s)
Height (z) in the atmosphere (meters)

Results:

efolding eight of the stable layer (He, in meters)
Depth of the stable layer (in meters)
Strength of the stable layer (in degrees C)
Potential temperature at elevation (z)