Calculating Adiabatic Temperature Changes.

Without a doubt, the topic of lapse rates and stability is a difficult one. Here we'll learn how to calculate and graph (like this) the temperature of a parcel of air as it rises from the surface. After graphing the temperatures changes, we'll investigate the effect of temperature on air density and stability. We'll take a very simplified approach. We will not consider any changes in the dew point of the air as it rises. Though a slight deviation from the real situation, this discussion is appropriate for our introductory approach here.

Before starting....

 Please review "Adiabatic Temperature Change and Stability".

Determining condensation level

To chart the adiabatic temperature changes of a parcel of air one essentially needs three points, 1) ground level temperature, the condensation level and 3) a location of interest aloft. In most cases you know the ground level temperature of the air. So you then have to determine the condensation level. 

The condensation level is the elevation where the rising air reaches saturation, condensation begins, and clouds start to form. The dew point temperature of the air can be estimated from a saturation curve if you know the air's humidity. In this case, we'll use the mixing ratio for our measure of humidity. Thus the graph below shows us the relationship between temperature and humidity as measured by the mixing ratio.

If you are given the mixing ratio, find its value on the Y-axis and move horizontally over to the saturation curve. Once you reach the curve, move vertically down to the X-axis and you get is the dew point temperature (temperature the air has to be for the air to be saturated at the given humidity). For instance, if the humidity is  5 g/kg find 5 gm/kg on the Y-axis then move horizontally to the saturation curve, and then down to the X-axis. The temperature you find is the dew point temperature of about 4^oC.

Once you have the dew point temperature you can calculate the condensation level.  Given that condensation requires the air to be saturated, we will force the air to rise upwards, allow it to expand and cool adiabatically until the air reaches its dew point temperature. Once the air achieves its dew point temperature it will be fully saturated, condensation occurs and a cloud will start to form. So, from the surface up to the condensation level the air is considered "dry" and above the condensation level it will be considered "saturated". 

If the air parcel has a ground level temperature of 13^oC and a dew point temperature of 4^oC,  the air temperature needs to cool by 9^o C to bring it to saturation. If the air is rising and cooling at the dry adiabatic rate (DAR) of 1^o C/100 meters and it decreases its temperature by 9^oC, then multiplying the DAR by 9^oC will gives us the condensation level. But not so fast.... We have to set up the DAR so that when we multiply it by 9^oC we end up with the right units for the condensation level, that is, meters:

OK, now comes the fun part ....

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