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Extension of annual streamflow record by correlation with precipitation subject to heterogeneous errors
Author(s) -
Clarke R. T.
Publication year - 1979
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr015i005p01081
Subject(s) - streamflow , precipitation , bivariate analysis , variance (accounting) , environmental science , regression , rain gauge , statistics , climatology , meteorology , mathematics , drainage basin , geography , geology , cartography , accounting , business
Mean annual streamflow, μ Y , from a basin must frequently be estimated from short streamflow records. Where longer precipitation records are available, regression methods are commonly used to ‘extend’ the record of annual streamflow with the objective of improving the precision of the estimate of μ Y . However, the longer record of annual precipitation consists of mean areal estimates derived from a network of gages, and each year's estimate will be subject to a within‐year sampling error with a variance that is a function of the density of the rain gage network used in calculating it. This paper examines the consequences of neglecting to take account of heterogeneous variance of mean areal precipitation where regression of annual streamflow on annual precipitation is used to improve the precision of . Two correlation models are used; in the first, it is assumed that annual streamflow and estimated mean areal annual precipitation are bivariate‐normally distributed, and that the rain gage network increased from g 2 to g 1 gages at the time when streamflow records began. If spatial correlation in rain gage catch is neglected, and if Δ = 1/ g 2 − 1/ g 1 , then it is shown that the bias in which results from neglecting to take account of change in gage density, is of the order of Δ 2 ; the large‐sample variance var , neglecting change in network density, underestimates the true variance, although the extent of the underestimation is not large for the typical situations that are evaluated numerically. The second correlation model assumes a bivariate gamma distribution of annual precipitation and runoff; this distribution has advantages over the bivariate Normal, but is not without its own drawbacks. For this correlation model, a qualitative assessment of the effect on var that results from neglect of variation in network density shows that this effect is also small for typical situations.