Calculating Mixing Heights

Overview

Two of the critical pieces of calculations needed for the EKMA/OZIP model are the 0800 mixing height and the maximum mixing height. Mixing heights are a meteorological calculation that determine the height of the column of air that moves in search of a peak ozone value. In the OZIP model, the rate of dilution of atmospheric pollutants is controlled by the diurnal (daytime) change in mixing height. Mixing height is defined as the top of a surface-based layer of air which is well-mixed due to mechanical and thermal turbulence. Given the mixing height at 0800, the maximum mixing height, and the time of the maximum height, the model computes the rate of rise internally.

[Note: The meteorologist/modeler has a choice of using the online mixing height calculator or some other computing tool, such as a spreadsheet. Complete online documentation for the use of the calculator and steps for calculating morning and maximum mixing heights are available, and should be read carefully. This document only provides a brief overview.] The meteorologist must determine the 0800 and the maximum mixing heights. In order to do so, the meteorologist must use National Weather Service (NWS) temperature or radiosonde (temperature, pressure, and humidity samples taken by balloon) samplings from one of various locations in the United States (or go to an alternate site).

Site Selection

In selecting a NWS site as the basis for mixing height estimation, care should be taken to insure that the site is meteorologically representative of the city of interest. A list of primary and secondary sites is provided. Backup sites are listed for those cases in which radiosonde data may not be available for a given day, or if the site has significantly different meteorological conditions. Examples of the latter are the case in which a surface front lies between the sounding site and the city or the city is clear but cloudiness or precipitation occurs at the sounding site.

Selection of Day Specific Data

The daily morning mixing height for the mode is normally estimated using the 1200 GMT (0800 EDT) sounding, while the maximum mixing height is estimated using the 0000 GMT (2000 EDT) sounding. In some cases, these soundings may not be available or appropriate or alternate soundings will be necessary.

In addition to the sounding data, surface temperature and pressure data are also needed for each day modeled. The urban surface temperature at 0800 LCT (or the average temperature between 0800-0900 LCT) and the maximum temperature occurring prior to 1800 LCT are needed to estimate the morning and maximum mixing height, respectively. The surface temperature data should be measured to the nearest 0.1 degree at a well-ventilated site. The site should be located near the center of the urban center. Surface atmospheric pressure measurements are needed at the same time and location of the urban surface temperature measurements, if at all possible.

If the elevation of the pressure reading and the elevation of the modeling site are different, an adjustment should be made to the pressure measurement using this equation:

P_sfc = P_obs +[0.11 mb/m * (Z_obs - Z_sfc)]

where:

Z_obs =: the elevation, in meters above sea level (mASL), of the pressure observation
Z_sfc =: the elevation (mASL) of the modeling site temperature measurement
P_obs =: the pressure, in millibars, at Z_obs
Psfc =: the pressure, in millibars, at the modeling site

You can use the online Javascript converter to make this conversion.

Data selection should use values chosen in this order:

Morning Mixing Height Estimate

1200 GMT sounding at primary site
0600 GMT sounding at primary site
1200 GMT sounding at backup site
0600 GMT sounding at backup site

Maximum Mixing Height Estimate

0000 GMT sounding at primary site
1800 GMT sounding at primary site
1200 GMT sounding at primary site
0000 GMT sounding at backup site
1800 GMT sounding at backup site
1200 GMT sounding at backup site

The value of P_sfc is an approximate value and can be rounded to the nearest millibar.

Mixing Height Estimation

In order to calculate the mixing heights, you need to obtain the hourly surface temperatures, the heights and pressures for the day of interest, and the climatological mixing heights for the modeling station. Note that you may need to approximate the climatological mixing height based on the height of the nearest or most meteorologically-similar city.

Once you have collected the appropriate data, you can then use the online form to do the appropriate calculations for you. You should never use an 0800 mixing height of less than 150 mAGL, regardless of what the calculations tell you. In fact, the output of the online form will in all likelihood remind you of this fact!

Likewise, if the city's maximum mixing height is greater than twice the climatological maximum value from the table, the surface temperature and pressure used and the choice of sounding site should be checked for representativeness. If no backup data is available, twice the climatological value should be used as the maximum. Also, a maximum mixing height less than the morning mixing height, or less than one-third the climatological maximum mixing height value is suspect.

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