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REGIONAL ANALYSES OF STREAMFLOW CHARACTERISTICS 11 the erroneous assumption that the structure of the model is revealed by a particular :::et of data. The contribution that prior knowledge can make to under~ standing of the present problem or process is ex_ cluded by this practice, which also is inefficient and the frequent cause of incorrect conclusions. By such a practice man abdicates much of his responsibility and the research process loses the crucial elements of intelligence and logic that only man can contribute. In general the extent of a region encom. passed by a regional analysis should be limit. ed to that in which the same variables are considered effective throughout, For example, Benson (1964) found it necessary to separate the western Gulf of Mexico basins into two parts, one dominated by thunderstorms and widespread tropical storms, and another in which snowmelt is the principal flood pro- ducer, Reliability of a regionalization The reliability of a regional frequency re. lation cannot be determined precisely but can be approximated, Suppose we have thirty 10. year flood records, that we define the 10.year flood from each, that we relate these 10-year floods to drainage area by regression, and that the standard error of the regression is 0,2 log unit, Now let us estimate the 10.year flood from this regression for a drainage area that is the mean of all the drainage areas used, What are the confidence limits of that estimate? If we consider that we are estimat- ing the 10.year flood that we would expect to define from 10 years of record, then the 67 percent confidence limits would be one stand- ard error of regression, plus the standard error of the mean, above and below the esti- mate, But we assume the regression performs a regionalization function; ideally that the differences due to basin characteristics are I removed by drainage area and that the reo maining variability is due to random errors in defining the 10-year floods at each site, If these assumptions are met, the estimate of the true 10.year flood defined would have a standard error of s / V N = 0.2 / V 30 = 0,037 log units, equivalent to about 9 percent. The standard error, based on regression, of an estimated 10.year flood in the above exam- pie would be much greater than 9 percent because (1) the 30 individual 10.year floods used to define the regression are not entirely independent, (2) the differences among 10. year floods due to basin characteristics are not completely explained by drainage area (nor would they be by any group of basin variables), and (3) estimates for drainage areas other than the mean drainage area would have a larger theoretical error than the estimate for the mean drainage area, Even though the samples are random, it is possible that they are also biased because the weather experience in one 10.year period may not represent long.term conditions. This addi- tional source of error due to bias cannot be stated statistically, The above discussion should lead to the conclusion that the standard error of an esti- mate from a regional analysis lies somewhere between the standard errol', S, and S IvN. That the error is substantially less than S is indicated by comparing Benson's (1960) reo suits with Irza's (1966), Benson drew 100 samples of 10 years each from one distribu. tion and found that about 80 percent of the 10.year floods defined by those 10.year rec- ords were within 25 percent of the true value (actually Benson showed that 80 percent of 10-yr floods estimated from 8.yr records would be within 25 percent of correct), Irza related the 10.year flood, defined from 8 years of record, to several basin characteristics and found the standard error of regression to be + 100 percent and -49 percent, that is, 67 percent of the items were within that range, Benson's 100.sample study and Irza's reo gional analysis are analogous if the regional analysis is assumed to have removed the variability of floods due to differences in basin characteristics; that is, the standard error of the 10.year flood (not the 10.yr flood defined from 10 yr of record) from Irza's equation is less than the computed standard error. Regionalizing Flood Stages Flood stages corresponding to selected re- currence intervals are needed for planning ~