Problem 2.1. 

This exercise consists of working with a data set collected at a typical Bowen Ratio/Energy Budget meteorological station to construct a water budget for a 1-dimesnional column of soil on the basis of estimated ET and measured precipitation.

An experiment was conducted to estimate the change in subsurface water storage and drainage for a one-dimensional soil column within a meadow in the mountain foothills west of Denver, Colorado USA. Details of the study are contained in Bossong et al. (2003) (http://pubs.usgs.gov/wri/wri03-4034).

The file meadowSite.xls contains a week's worth of data from the site.  The data consist of half-hour measurements of precipitation (P) in mm, net radiation (Rn) in W/m², soil-heat flux (G) in W/m², temperature in ºC at heights of 1m (T₁) and 2m (T₂), and relative humidity at heights of 1m (RH₁) and 2m (RH₂). ET is to be calculated with the Bowen-ratio method (Equation 2.16 with the latent heat of vaporizaiton, L, equal to 2.45e6 J/kg water). The Bowen ratio, B, is the ratio of sensible to latent heat flux (H/LET) and can be determined from the ratio of the vertical gradient in air temperature divided by the vertical gradient in water vapor pressure:

B = H/LET = g(T₂-T₁)/(e_a2-e_a1)                                              (P2.1.1)

where g is the psychrometric constant (equal to about 0.0515 kPa/ ºC at the study site elevation of 2370 m) and e_a2 and e_a1 are water vapor pressure at 2m and 1m heights. Water vapor pressure is calculated as the product of relative humidity and saturated water vapor pressure (e_s):

e_a= RH*e_s                                                                             (P2.1.2)

Saturated water vapor pressure varies with temperature, T, and can be estimated by the following equation from (Smithsonian Tables, 1984):

      e_s  = 0.1x10**[-7.90298 (373.16/T-1)                                        

                          + 5.02808 Log₁₀(373.16/T)

                          - 1.3816x10^-7 (10^{11.344 (1-T/373.16)} -1)

                         + 8.1328x10^-3 (10^{-3.49149 (373.16/T-1)} -1)

                         + Log₁₀(1013.246)]                                     (P2.1.3)

      with T in [K] and e and e_s in [kPa]

A) Calculate B, H, LE, and ET for each half hour period (dividing LE (W/m²) by the latent heat of vaporization, L, (J/kg) produces an ET rate in units of mm/s - demonstrate this). How do B and ET vary on a diurnal basis? 

Calculate average daily and weekly values for B, H, LE, and ET on the basis of the half hour calculations.

Equation 2.6 is unstable when B is close to -1.  At what parts of the day is this most likely to occur?  Why?

Some kind of correction is typically made for these times. Assume that ET=0 when -1.3 < B < -0.7; how does this assumption affect daily ET estimates?

B) Uncertainties in measurements of the vertical gradients of temperature and relative humidity are an important concern when applying the Bowen ratio/energy budget method for estimating ET.  Conduct a simple uncertainty analysis. How does an uncertainty of +/- 0.1 ºC in air temperature affect estimated ET rates? 

How does an uncertainty of +/- 0.01 in relative humidity affect estimated ET rates?  How can this sensitivity be over come?

C) Calculate daily averages for all measured data; then apply Equation P2.1.2 and 2.16 to determine daily and weekly estimates of B, H, LE, and ET on the basis of these daily averages.

Calculate a daily Bowen ratio on the basis of temperature and relative humidity during daylight hours only; use this value of B along with the daily average of Rn and G to estimate daily and weekly ET.

How do the different estimates of daily and weekly values compare?  Discuss reasons for any differences.

D) Apply the following water budget equation:

DS + D = P - ET                                                                   (P2.1.4)

where DS is storage within the soil zone and D is drainage beneath the soil zone.  Discuss the assumptions that are inherent in Equation (P2.1.4) and the possible ramifications of those assumptions under different climate, soil, vegetation, and land use scenarios. By using the precipitation data and the half hour estimates of ET from (A) calculate cumulative estimates of DS + D for the one-week period.

How will uncertainties in ET calculated in (B) affect estimates of DS + D?

What approaches might be used to separate drainage estimates from the sum of change in storage and drainage?  What additional information would be required?

Problem 2.2

A number of meteorological and hydrological monitoring sites across the US and other countries provide data that can be used to construct water budgets of 1-dimensional columns of soil.  Identify sources of data that could be used in a water budget study within your state or province. Explain how these data could be used to provide preliminary estimates of drainage beneath the root zone.

Problem 2.3

SNOTEL (U.S. Bureau of Reclamation) and SCAN (Natural Resources Conservation Service) are two sources of water budget data within the United States. Dry Lake, Colorado (http://www.wcc.nrcs.usda.gov/nwcc/site?sitenum=457) is the location of one SNOTEL site.  Summarize the data that are available at this site. 

Construct a water-budget equation that can be used to estimate drainage below the root zone.  What is the control volume for the water-budget equation?

Describe the assumptions upon which the water-budget equation is based. 

What climatological methods can be used to estimate ET? 

What storage compartments should be considered?

Determine estimates of all components of the water budget equation for a one-year period.  Discuss trends in drainage below the root zone.

References

Bossong, C.R., et al.  (2003) Hydrologic conditions and assessment of water resources in the Turkey Creek watershed, Jefferson County, Colorado. U.S. Geological Survey Water-Resources Report 2003-4263.