Question

Below you are given temperature data at several heights above the ground on a sunny day, acquired from a radiosonde launch.

Height Above Ground (m)	Temperature (°C)
0	28
500	22
1000	18
1500	14.5
2000	15.5
2500	13
3000	9

1. Calculate the environmental lapse rate for each of the five lowest layers, expressing your answer in °C/km. Remember that the lapse rate is defined as the rate of decrease of temperature with altitude. Thus, if temperature decreases with altitude, the lapse rate will be positive. As an example, we compute the environmental lapse rate in the uppermost layer:

   Layer Lapse rate=Temperature at bottom of layer - Temperature at top of layerThickness of layerLayer Lapse rate=Temperature at bottom of layer - Temperature at top of layerThickness of layer

   Layer Lapse rate=(13∘C−9∘C)/(500 m)=4∘C/500m=8∘C/kmLayer Lapse rate=(13∘C−9∘C)/(500 m)=4∘C/500m=8∘C/km

2. Now that you know the environmental lapse rate of each layer, determine the stability of each layer (stable, unstable, or conditionally unstable) simply by comparing your answers to the dry adiabatic and moist adiabatic lapse rates (use 10°C/km and 6°C/km, respectively). Explain your reasoning in each case.
3. We can also directly test the stability of a layer by lifting parcels of air from the bottom of the layer to the top of the layer and comparing the parcel’s temperature at the top of the layer to the environmental temperature there.

   As an example, we test the stability of the uppermost layer by lifting a parcel of air initially at 2500 m to 3000 m. We assume the parcel’s temperature at the bottom of the layer is the same as the environmental temperature there. Thus, a parcel at 2500 m will have a temperature of 13°C. First, we lift the parcel dry adiabatically. In this case, the parcel’s temperature decreases 5°C during its 500-m ascent, so its temperature at 3000 m is 8°C (cooler than the environment, so the parcel is negatively buoyant). Next, we lift the parcel moist adiabatically, in which case it cools 3°C during its 500-m ascent. At 3000 m, the parcel’s temperature is 10°C (warmer than the environment, so the parcel is positively buoyant). Thus, because the parcel’s buoyancy at the top of the layer depends on whether ascent was dry adiabatic or moist adiabatic, the layer is conditionally unstable.

   Following this procedure, determine the stability of the 0 to 500 m layer, 500 to 1000 m layer, and 1500 to 2000 m layer.

Answer 1

Environmental lapse rate of each layer -

1. 0 -500m = 28-22/500 m = 6/ 500m or 12 degree Celsius per 1km

2. 500 to 1000 m = 8 degree per 1km

3. 1000 to 1500 =7 degrees per 1km

4. 1500 to 2000 = 14.5-15.5/500m = it would be negative as -2 degrees per 1km I.e temperatures increase with increasing altitude or negative lapse rate

5. 2000 to 2500 = 5 per 1km

6. 2500 to 3000m = 8 per 1km

Stability of 0 to 500 m layer = surface temperatures is same 28 degrees .and temperatures at 500m of air is 22 degrees . As per dry adabatic lapse rate 10 per 1km temperatures of air parcel at 500m would be 28-5= 23 degrees. Warmer than surrounding air so air will ascent. Thus it is unstable. Same as moist lapse rate 6 per 1km temperatures at 500m of moist air parcel is 28-3 = 25 warm air . So unstable

500 to 1000m layer - Temperatures at 1000m of air = 18 degrees

​​​​​​ dry air parcel temperatures would be28-10 = 18 degrees same as surrounding air so Stable moist air parcel temperatures would be = 28-6= 22 degrees which is warmer than surrounding air so it is unstable. Thus this layer is conditional Unsatable provided which air parcel is.

1500 to 2000 layer - Temperatures at 1500m is 14.5 and at 2000 15.5 degrees . Dry air parcel temperatures at 2000 m would be 28- 20 = 8 degrees cooler than surrounding air so Stable. For moist air parcel temperatures would be 28- 12 = 16 degrees at 2000m warmer than surrounding air. Thus it is conditional unstable. Dry air parcel = stable . Moist = unstable