Calculating Mixing Heights: Step-by-Step

Step 1

If the morning mixing height is to be calculated, the 0800 LCT surface data are used. If the maximum mixing height is to be determined, the data corresponding to the time of the maximum temperature (between 0800-1800 LCT) are used. In the first row of data, enter:

the elevation of the urban surface temperature in meters above sea level
the surface pressure in millibars (P_sfc)
the value of the surface temperature in degrees Celsius

Convert the surface temperature to degrees by adding 273.2. This value is T_sfc.

Use the equation below to calculate the potential temperature (called "theta") to the nearest 0.1 degrees Kelvin:

Step 2

Using the temperature sounding data, find the highest pressure level that is less than the pressure at the surface. For example, if the urban surface pressure is 985.0 mb, and the sounding presures are: 1005, 1000, 963, and 850 mb, then 963 is the highest pressure that is less than the surface pressure. The data associated with 963 mb should be entered next in the program. The data associated with 850 mb are needed in Step 4.

Step 3

Convert the temperature at this level to the Kelvin scale and convert it to a potential temperature using the equation below:

Step 4

If the potential temperature of the last row entered is greater than the potential temperature at the surface, then do Step 5. If it is less than or equal to the potential temperature at the surface, then read in the height (if known), pressure and temperature of the next lowest pressure level from the sounding data.

Step 5

The mixing height is defined as the point on the sounding where the potential temperature is equal to the urban surface potential temperature plus 0.1 degrees K. If the interval between the given height values or the sounding is less than 500 meters, go to Step 6. Otherwise, use linear interpolation from the pressure values of the last two rows read in to find the pressure (in millibars) at the value of theta at the mixing height.

Step 6

From the two levels where height is given on the sounding surrounding the mixing height level, use linear interpolation to find the height (in meters ASL) at the value of theta-surface plus 0.1 degree K.

Step 7

Use linear interpolation to find the height above sea level of the mixing height using the pressure at the mixing height from Step 5 and the pressure levels or the sounding above and below the mixing height presure that have both pressure and height values. These are the values to be used for the final mixing height calculations.

Step 8

Subtract the elevation of the urban site (mASL) from the height (mASL) of the mixing height. The result is the height of the mixing height in meters above the surface of the city (mAGL). This is the mixing height to be used in the OZIP model.

A screen snapshot of spreadsheet implementation of these steps is available. You can also obtain a graphical flowchart of the mixing height calculation program.

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