|
<br />precipitation data p, 's corresponding to Q are
<br />J
<br />collected, as many as possible, in the basin in question
<br />Equation (8) is then modified as
<br />
<br />Q = f (P l' P 2' . . .)
<br />
<br />In the case of precipitation management in the
<br />Upper Colorado River Basin, it is the spring runoff,
<br />(Q ), caused mainly by winter precipitation, (P .),
<br />s WJ
<br />and partially by spring precipitation, (P .), which is
<br />SJ
<br />of concern. The relationship is represented more pre-
<br />cisely'by the following equation:
<br />
<br />Qs = f(Pwl,Psl,Pw2,Ps2"")
<br />
<br />(10)
<br />
<br />Multiple linear regression analysis is applied to
<br />find the approximate relationship. Finally,
<br />
<br />Qs = a + blPwl + clsl + blw2 + cls2+'" (11)
<br />
<br />where the a, b., c, are coefficients determined from
<br />J J
<br />available data.
<br />
<br />Then, the increase of spring runoff, (~Qs)' caused
<br />
<br />by the increase of winter precipitation, (~Pw)' is
<br />given by
<br />
<br />~Qs = (Qs + ~Qs) - Qs
<br />
<br />{a+bl (Pwl+~Pwl) + cIPsl+b2(Pw2+~Pw2) + c2Ps2+"}
<br />
<br />{a + blPwl + clPsl + b2Pw2 + c2Ps2 + ..}
<br />
<br />= bl~Pwl + b2~Pw2 + .,.
<br />
<br />(12)
<br />
<br />Substituting equation (7) into (12), and averaging
<br />
<br />~Qs blklPwl + b2k2Pw2 + ....
<br />
<br />(13)
<br />
<br />From a water resource point of view, the greater
<br />the EQ calculated from equation (13), the more suita-
<br />ble th~ basin.
<br />
<br />3. Suitability of basins for,evaluation.
<br />
<br />a. Two-sample u-test. One of the goals of the
<br />precipitation management program has been the rigorous
<br />establishment of the statistical significance of its
<br />attainment. For this purpose, various methods of
<br />evaluation were devised. Indeed, a great deal is al-
<br />ready known about methods of evaluation of attainment
<br />[6] .
<br />
<br />Of course, the criteria of suitability of basins
<br />for evaluation depend upon the choice of the variable
<br />selected to test the hypothesis or the type of statis-
<br />tical test and upon the design of the experiments.
<br />
<br />Assuming that the end result of seeding is to in-
<br />crease the natural mean, but that everything else stays
<br />the same, the criteria are derived from the two-sample
<br />u-test [6] in the following way. The two-sample u-test
<br />is a test of the hypothesis that assumes that the popu-
<br />lation mean is equal to a given value while the
<br />
<br />population standard deviation is known and stationary
<br />[25]. The statistic used in testing this hypothesis
<br />is
<br />
<br />(9)
<br />
<br />u = x - 11
<br />o/In
<br />
<br />(14)
<br />
<br />where x is the sample mean,
<br /> 11 is the population mean,
<br /> 0 is the standard deviation, and
<br /> n is the sample size
<br />
<br />with the critical region lul > 1.96 if the 5 percent
<br />significance level is used. The significance of the
<br />increase in spring runoff is achieved if the observed
<br />statistic u, in equation (15), is greater than 1.96
<br />at the 95 percent confidence level, i.e.,
<br />
<br />u
<br />
<br />LlQs
<br />
<br />oQ /IN
<br />s
<br />
<br />(15)
<br />
<br />.::. 1.96
<br />
<br />where ~Qs is the expected increase in spring runoff,
<br />
<br />N
<br />
<br />is the number of years necessary to estab-
<br />lish the significance of the increase
<br />wi th a 50% power, and
<br />is the standard deviation of the natural
<br />spring runoff.
<br />
<br />OQ
<br />S
<br />
<br />b. A criterion to determine the relative suita-
<br />bility of an individual basin. The number of years,
<br />N, necessary for evaluation is derived from equation
<br />(15)
<br />
<br />N
<br />
<br />3.84 OQ2
<br />s
<br />
<br />(~Q ) 2
<br />s
<br />
<br />(16)
<br />
<br />A low value of N in equation (16) provides a
<br />criterion to determine the relative suitability of
<br />many potential basins.
<br />
<br />c. A criterion to determine the suitability of
<br />grouped basins. In the major basins there are sets of
<br />gaged sub-basins that are not, in part or in full, a
<br />tributary of any other member sub-basin of the set.
<br />Suppose that in a major basin there exist m such sub-
<br />basins. The spring runoff for each of these individual
<br />sub-basins is denoted Qsi (i=1,2,.. .m). Now suppose one
<br />
<br />wants to choose n of the m sub-basins for a pilot
<br />program (n < m). Construct a linear combination of
<br />Qsi' s, i. e. ,
<br />
<br />Q*
<br />s
<br />
<br />n
<br />l: ctiQsi'
<br />i=l
<br />
<br />(17)
<br />
<br />ctlQsl + ct2Qs2+"'+ ctnQsn
<br />
<br />The variance of Q* is given by
<br /> s
<br /> n n
<br />2 l: l: a. .ct.ct.
<br /> OQ* i=l j=l ~J ~ J
<br />s
<br />
<br />(18)
<br />
<br />where
<br />
<br />15
<br />
|