CE 374K Homework on Evaporation and Precipitation

Hydrology Spring 2001

This assignment uses a 24 hour period of climatic and energy balance data recorded at the Southern Great Plains Atmospheric Radiation Measurement site in Washita Oklahoma for July 29, 1998. Download the Excel comma delimited files: energy.csv and climate.csv or get them from the LRC Class server: /class/maidment/ce374k/evap.

1. The Energy Balance worksheet shows in half-hourly intervals, the Net radiation (R_n), Latent heat flux (lE), Sensible heat flux (H), and Ground heat flux (G), all in W/m², and the Bowen ratio measured by climatology apparatus at the site. Note that the signs on the tabulated energy fluxes are positive when the flux is downward, negative when the flux is upward. Verify that the energy balance is closed at each time interval.

2. Make a plot showing the time distribution over the day of Net radiation (R_n), Latent heat flux (lE), Sensible heat flux (H), and Ground heat flux (G), all in W/m². Make a table showing for R_n, lE, H, G, and R_n - G:

• daily average value in W/m²
• amount of energy received in MJ/m²-day
• equivalent amount of water evaporation in mm/day, assuming l = 2.5 MJ/kg of water, and density of water = 1000 kg/m³

3. The Climate worksheet shows Wind Speed in m/s (u), Air Temperature in °C (T), Relative Humidity in % (R_h), and Atmospheric Pressure in kPa (p). These variables are measured at 2m above the ground. Make a plot showing Wind Speed and Air Temperature as a function of time during the day. Make a second plot showing Relative Humidity and Air Pressure as a function of time during the day. What can you conclude by inspection of these plots about the diurnal variation of these quantities? What are the average values of these quantities for the day?

4. Calculate the value of the Saturated Vapor Pressure (e_s), Vapor Pressure (e), and the Vapor Pressure Deficit (D), all in kPa for each half-hourly interval, and make a plot of these quantities. When does the main period of vapor pressure deficit occur during the day? Calculate the daily average values of these quantities.

5. Calculate the value of the specific humidity, q_v, and the density of moist air, r_a, for each half-hourly interval and make a plot of these quantities. Use equation (3.2.8) in Applied Hydrology to get the value of the gas constant for moist air R_a. What is the average value and the range of these quantities during the day? When do the maxima and minima occur?

6. Using the tabulated Latent Heat fluxes in the Energy Balance worksheet, calculate the time distribution of the evaporation rate expressed in mm/day for each half-hourly interval. Assume that evaporation upward is positive. Allow for the variation of the latent heat of vaporization with temperature in this calculation. What is the average evaporation rate for the day? How does it compare with the value you obtained in (2)? What are the maximum and minimum rates of evaporation during the day and when do they occur?

7. Using the daily average values of R_n - G, and the climate variables that you’ve computed previously in this exercise, estimate the daily average evaporation using the combination equation (3.5.26) in Applied Hydrology, in which the aerodynamic component of evaporation, E_a, is determined using the wind function for B given by equation (3.6.1). Compare the value you’ve determined with the actual daily evaporation measured at the site. By what percentage do they differ? The values of D (DeltaEs) and g (Gamma) in the combination equation (3.5.26) can be taken from the table evapcoeff.csv, which is attached to this homework.

8. Do Problem 3.4.3 in Applied Hydrology

This problem set is due in on Tues Feb 13.