12.307 Weather and Climate Laboratory 

Yuma Convection Data Set Data consists of the vertical temperature profile (recorded every 2 hrs) and the incoming solar radiation (measured every 15 min). Since Yuma is in a desert, this is a great example of dry convection and a great analogue to the tank experiment lab. Explanation of data files (1) Altitude, Pressure, Temperature, and Dew Point data (Excel) (Matlab) There are six radiosonde profiles approximately every two hours with the first one starting at 1136Z. As the radiosonde ascends, pressure, dew point and temperature are recorded every 100m.
Time is given in GMT. To get local time, subtract 7 hours. (2) Station surface data including incoming solar radiation (Excel) (Matlab) Measurements are also taken at the surface. Among them, the incoming solar radiation (given in langleys) were recorded every 15 minutes. Note that the first column is in local time. What can be done with data (1) On one graph, create a vertical profiles of temperature for the six given times. (2) Calculate potential temperature (in Kelvin), and plot vertical profiles as in (1). (3) For each time period, identify the stable and unstable regions. Discuss the evolution of the temperature profile. How does the height of the boundary layer evolve with time? (4) Compare and contrast your results with your tank experiment. How is the heating supplied? How is the heat distributed upwards in the tank and the atmosphere? Why is it convenient to use temperature in the lab experiment and potential temperature in the atmosphere?
(5) We can also be quantitative about how the energy supplied by the sun is transferred into the energy in the boundary layer. Using the basic law that the heat supplied must equal the change in internal energy of the atmosphere yields
where H is the heating rate per unit area (W/m^{2}), ρ is the density of air, c_{p} is the specific heat of dry air, and T is temperature. The hydrostatic relationship is used to convert from height to pressure coordinates in the second step and the integral is only taken over the depth of the boundary layer where temperature appreciably changes.
Using the radiosonde dataset, we can calculate the the right hand side of the equation above, which is perhaps a bit clearer in a discretized form
where Δt is the time difference between radiosonde measurements (approx. 2 hours), ΔT_{i} is the temperature difference between radiosonde measurements at some level i, and δp_{i} is the "thickness" (e.g. p_{i+1}p_{i}). The summation is carried out from the ground through the top of the boundary layer at level N.
Next, we can use the surface dataset giving the solar radiation. Note that the units are given in Langleys accumulated over 15 minutes. You need to divide by 15 to get Langleys/min. Then to convert form Langleys/min to W/m^{2}, multiply by 697.3. Multiplying by (1albedo = 0.5) to account for only the portion of solar radiation absorbed by the ground and integrating the incoming solar radiation data over the two hours of interest, you can get a value for the left hand side of the equation above. Are your two calculations consistent with one another? 
