BACKGROUND

Cumulus clouds are caused by convection, during which a parcel of warm, moist air rises and cools until the air temperature equals the dew point temperature and invisible water vapor condenses to become liquid cloud droplets or solid ice crystals. When air rises, it cools at a lapse rate of approximately 10 degrees Celsius per kilometer. The dew point temperature also decreases, but at the lower lapse rate of 1.7 degrees Celsius per kilometer. To predict the approximate height at which cumulus clouds will form, known as the Convective Condensation Level (CCL), write an algebraic equation to calculate the altitude at which the air temperature equals the dew point temperature.

Solution:

A = T_g - DP_g / 8.3

where:
A = CCL (in kilometers)
T_g = air temperature at ground level (in degrees Celsius)
DP_g = dew point temperature at ground level (in degrees Celsius)

ACTIVITY EXTENSION

Use the Texas Instruments TI-82 (or TI-83) graphing calculator to plot a graph that can be used to determine the CCL (given the air temperature and dew point temperature at ground level).

PROCEDURE

1. Randomly select five pairs of ground level air temperatures and dew point temperatures, e.g., 30 & 25, 30 & 20, 30 & 15, 30 & 10, and 30 & 5. Use the algebraic equation (above) to solve for the CCL. On the graphing calculator, enter the resulting altitudes as List 2 (L2).
2. Using the same five pairs of numbers (as in Step 1 above), calculate the ground level Dew Point Depression (DPD), e.g., 30 - 25 = 5, 30 - 20 = 10, 30 - 15 = 15, 30 - 10 = 20, and 30 - 5 = 25. On the graphing calculator, enter the ground level DPDs in List 1 (L1); be sure to enter the DPDs in the same order as List 2 (L2).
3. Using L1 as the "x" value, and L2 as the "y" value, graph the data. (For step-by-step instructions, refer to TI-83 Help.)
4. Use the "TRACE" function to determine the CCL for other combinations of ground level air temperature and dew point temperature. Note the X and Y coordinates at the bottom of the screen--the "Y" value is the CCL (in km) for a given DPD (X value).