At ground level the temperature is 15.3 ^oC. The lapse rate up to 800m is 1.1^oC/100m at 1000m there is an inversion and the lapse rate is -1^oC/100m up to 1200m. Above this the lapse rate is equal to the dry adiabatic lapse rate. Estimate the ventilation coefficient if the 10m wind speed is 5m/s. Assume that you are on smooth terrain. The sky is not overcast and it is daytime.

SOLUTION

This solution has been calculated using an Excel spreadsheet but it is relatively simple and can be calculated manually using graph paper. However if you are not familiar with Spreadsheets you should do the calculation in the questions section below using a spreadsheet. It will be essential that you are up to speed with this later.

Remember that the dry adiabatic lapse rate is around 1^oC/100m and that a negative lapse rate indicates the temperature is increasing with altitude.

First we produce plots of temperature against altitude. In this case the temperature at 100m intervals was calculated using a logic function but a much simpler device could be used. We see from the graph below that the maximum mixing depth is about 1100m.

We now need to calculate the average wind speed over the mixing depth.

We estimate this by calculating the wind speed at 550m. If we look at the actual lapse rate we see it is slightly higher than the dry adiabatic lapse rate. Looking at the table above wee see that the exponent p will be either based on a table value of 0.15 or 0.2. If we look at the table for daytime conditions we see that for wind speeds of 5m/s in sunny conditions the exponent we use will be based on 0.2 we multiply this by 0.6 to account for smooth terrain to get an exponent of 0.12.

Using we find that the wind speed at 550m is about 8.1m/s (about 7.2m/s if we use the 200m limit).

The ventilation coefficient is therefore 8.1m/s x 1100m = 8910m²/s and thus we see a low pollution potential (or 7920 m²/s if we use the 200m wind speed limit).

This example has been given for the purposes of demonstrating the principles. In fact such a combination of wind speed and inversion would be rare. Task 1is more realistic.

Task 1: This should be completed using Excel or a similar spreadsheet.

At ground level the temperature is 15.3 ^oC. The lapse rate up to 400m is 3^oC/100m at 400m there is an inversion and the lapse rate is -1^oC/100m up to 900m.