C**E
394K.2 Homework Assignment on
Energy Balance and Evaporation**

**Surface
Water 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

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/m^{2}, and the Bowen ratio
measured by climatology apparatus at the site. Verify that the energy balance is closed at each time
interval. The values for Latent heat
flux and Sensible heat flux at 19:30 hours are missing. Determine these values. Note that the signs on the tabulated energy
fluxes are positive when the flux is downward, negative when the flux is
upward.

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/m^{2}. Make a table showing for R_{n}, lE, H, G, and R_{n} - G:

- daily
average value in W/m
^{2} - amount
of energy received in MJ/m
^{2}-day - equivalent
amount of water evaporation in mm/day, assuming l = 2.5 MJ/kg of water, and density of water = 1000 kg/m
^{3}

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. 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?

6. 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 reference crop
evaporation, E_{rc}, at this site using the Penman-Monteith equation as
described in the Handbook of Hydrology.
Compare the value you’ve determined with the actual daily evaporation
measured at the site. By what
percentage do they differ?