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Unformatted text preview: Intro to Hydrogeology Homework 3 Due: Feb. 3, 2012
Evapotranspiration and runoff A. The average monthly air temperature in F0 for Miami is given in the table below. Using the
Thronthwaite method and the attached tables estimate the potential evapotranspiration for each
month. Averae Monthl air temperature F0) in Miami 77.0 79.2 83.5 85.6 90.4 87. La. Provide the monthly ET values in cm/month and in inches/month in a table (preferably in
Excel). 1.'o. Sum the monthly values to estimate the annual potential ET (cm/year and inches/year) and
include on the table. 10. The following table has the average monthly precipitation (in inches) at Miami Airport. Za. Plot on a graph (preferably in Excel) the monthly Potential ET you calculated in problem 1
in inches per month in one black and the average monthly rainfall in inches per month in grey on the same graph. 2b. Mark the areas on the graph were you would expect a gain of water storage in Miami and
areas that you would expect a loss in water Storage. 59 EXAMPLE 2.2 the potential evapotranspiration from an area. The Thornthwaite equation (see Gray et a]: 1970) is:
10T' a
E = a! ‘.
r 1.62( I ) (2.4)
12 1.5
T .
I = J2
i=1 ( 5 ) a = 0.492 + 0.01791 — 0. 0000771!2 + 0. 00000067513 (2.6) ., ..,,,[,, 2.22721 . . . 1 a "I: where E; is the potential evapotranspiration in cm/rnonth, Ta, is the mean monthly air
temperature in 0’ for month i, I is the annual heat index, and a is constant. It is assumed
that each day has 12 hours of sunshine with 30 days in a month. Table 2.3 lists the correction
factors to adjust the hours of sunshine in each day for various latitudes. Temperature may
also be in F°(C° = [P  32}_x 5/9, or F° = C° x 9/5 + 32). The second column of Table 2.4 lists the monthly temperatures between April and October in (from Gray et a]_, 1970) 1961 at Saskatoon, Canada. Calculate the potential evapotranspiration for an alfalfa crop using the Thornthwaite method. SOLUTION Temperature needs to be converted from F ° to c1. Next, the heat index is calculated
using Eq. (2.5). Each term is calculated and listed in the fourth column of Table 2.4. The heat index
is the summation of all the terms. 12 T_ 1.5
I=Z(?m) =0.21.+3.56+7.92+7.68+8.90+2.32+0.89=31.48 i=1 TABLE 2.3 NRC mean hours of bright sunshine expressed in units of 30 days of 12 hours each day North Lat. J F M  A M J J A S O N D
0 r N 1.04 0.94 1.04 1.01 1.04 1.01 1.04 1.04 1.01 1.04 1.01 1.04
10 1.00 0.91 1.03 1.03 1.08 1.06 1.08 1.07 1.02 1.02 0.98 0.99
%0 0.95 0. 90 1.03 1.05 1.13 1.11 1.14 1.11 1.02 1.00 0.93 0.94
0 0.90 0.87 1.03 1.08 1.18 1.17 1.20 1.14 1.03 0.98 0.89 0.88
35 0.87 0.85 1.03 1.09 1.21 1.21 1.23 1.16 1.03 0.97 0.86 0. 85
4011'. 0.84 0.83 1.03 1.11 1.24 1.25 1.27 1.18 1.04 0.96 0.83 0.81
45 0.80 0.81 1.02 1.13 1.28 1.29 1.31 1.21 1.04 0. 94 0.79 0.75
50 0.74 0.78 1.02 1.15 1.33 1.36 1.37 1.25 1.06 0.92 0.76 0.70 Source: Gray et.aI., 1970. Handbook on the principles of hydrology. Reprinted by permission of the National
Research Council of Canada. ...
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