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<br />335
<br />
<br />JOURNAL OF APPLIED METEOROLOGY
<br />
<br />VOLUME J 2
<br />
<br />TABLE 9. Optimal combinations of stations in the target (San Juan Mountains) and the control (Maroon Peak),
<br />
<br /> Number of
<br /> existing years
<br /> of record Gage Drainage Weight
<br />CSU Location within elevation area factor
<br />number Station name (Basins) (1939-68) (ft) (mi2) X
<br /> Stations in target
<br />1078000 East Fork San Juan River San Juan 30 7597,63 86,9 1.0 .1,
<br /> above Sand Creek near
<br /> Pagosa Springs ,.
<br />1073448 IIermosa Creek near Animas 29 6705,0 172.0 1.0
<br /> IIermosa
<br /> Stations in control
<br />1377200 Tomichi Creek at Tomichi Creek 30 8420,0 155,0 9,755
<br /> , Sargen ts
<br />1590000 Roaring Fork at Roaring Fork 30 5720,7 1460,0 -0,110
<br /> Glenwood Springs
<br />
<br />Number of years with optimal weights in the combination is 3,8",,4 years,
<br />Number of years with all X's= 1 is 33 years,
<br />
<br />listed in Table 8) and total control runoff, i.e., for the
<br />case where all the Xi are a priori given the value 1.
<br />Fig. 11 shows the corresponding regression line when
<br />optimal weights are used.
<br />Comparison of the two figures explains the reason
<br />for the efficiency of the technique.
<br />
<br />b. Only zone 1 is seeded (zones 3 and 4 are used as controls)
<br />
<br />Table 10 summarizes the results for this case. It is
<br />somewhat disappointing that in this case the minimum
<br />number of years is 6 which exceeds the planned 4-5
<br />years duration of the project. Note that an 11%
<br />increase in precipitation (rather than 10%) would
<br />suffice to return the power of the test to 50% for the
<br />5-year period.
<br />
<br />c. Zones 1 and 2 are both seeded (zones 3 and 4 are used as
<br />controls)
<br />
<br />Table 11 summarizes the resul ts for this case. In this
<br />instance for the 5-year period the power of the test is
<br />
<br />4,5
<br />
<br />
<br /> 4,0
<br />" 3,5
<br />'"
<br />0
<br />c~ 30
<br />'- ~
<br />~ "
<br />0 "
<br />51 '" 2,5
<br />~ 0;
<br />o ,~
<br />.::
<br />" ,~ 2,0
<br />en 2:-
<br />0
<br />0 1.5
<br />....
<br />
<br />12 16 20 24 2B 3,2 3,6
<br />
<br />Total Sum of Runoff in Control
<br />(Million Acre-Ft)
<br />
<br />FIG, 10. Regression line between total target runoff and total
<br />control runoff for stations listed in Table 8,
<br />
<br />slightly better than 50%. For this case the optimal X's
<br />were rounded off to simpler values to see if the calculated
<br />number of years would change appreciably. For the
<br />set of X's; 1.6, 0.1, 2.0, -0.3, 0.7, 0.9, 4.5 (compare
<br />with the last column of Table 11), the calculated value
<br />was again 4.9, indicating that this number of years is
<br />not overly sensitive to small changes in the X's around
<br />the optimal point.
<br />
<br />7. Conclusions
<br />
<br />From a theoretical point of view this paper shows
<br />the value of grouping stations both in the target and
<br />the control areas in an optimized manner to maximize
<br />the power of the detection test for a given significance
<br />level. From a practical point of view, the study shows
<br />that this new technique of testing yields a power for
<br />the test over a 5-year period of experimentation which
<br />is slightly better than 50% if only zones 1 and 2 in
<br />the target are seeded. It is better than 50% if the entire
<br />target area were seeded (which it is not, currently).
<br />
<br />.~
<br />0.
<br />o
<br />
<br />
<br /> 38
<br /> 3,6
<br />v 34
<br />'"
<br />"
<br />~ 3,2
<br />....
<br />'. 3,0
<br />
<br />~
<br />~
<br />~ ':' 2.8
<br />P:: ~ 2.6
<br />~ v
<br />; ~ 2.4
<br />~ ~ 2.2
<br />~:: 2.0
<br />.~~
<br />'" 18
<br />
<br />16
<br />14
<br />
<br />1.5
<br />
<br />2,5
<br />
<br />3,5
<br />
<br />FIG, 11. Regression line between optimal grouped target runoff
<br />and optimal grouped control runoff for stations listed in Table
<br />8,
<br />
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