A correlation procedure for augmenting hydrologic data

摘要: A linear regression for a short and long sequence of hydrologic events is used to lengthen the sequence. The lengthened consists original observations regressed values plus noise, where noise random variable with zero mean variance proportional about line regression. Estimates are shown be unbiased. If correlation coefficient, which measures strength regression, exceeds 0.5, then estimates based on better estimators population than not added values, coefficient must exceed 0.8 obtain improvement in by use correlated values. INTRODUCTION In statistical studies hydrology, assumption made that finite number observed represents sample from an infinite such events, outcome each event governed some probability distribution. Any change hi regime given associated reflected Although various parameters may describe distribution, mean, variance, skewness three provide information most useful properties any measure central tendency, value tend cluster, whereas dispersion or average spread mean. asymmetry distribution These cannot define uniquely, except special cases; nevertheless, they do characteristics compare phenomena. these generally unknown, but estimated observations. How reliable depends primarily upon period length total unbiased, their reliability increases increase length. To making additional time order more always operationaUy economically feasible. not, recourse had other procedures increasing One procedure, topic discussion this paper, utilize relations among relation concurrent can nonobserved correspond nonconcurrent portion manner lengthened. skewness. Whether greater only mainly between sequences. mathematical evaluation procedure has been several investigators under assumptions (1) independently distributed time, (2) two sequences have joint normal (3) defined (4) no changes occur regimes associated. measured productmoment coefficient. Under normality, need considered because uniquely For zero. El E2 STATISTICAL STUDIES IN HYDROLOGY H. A. Thomas, Jr. (written commun. 1956), showed yields unbiased estimate if product-moment lf-yNi 2 NI period, results also were obtained W. G. Cochran (1953) earlier independent study double sampling problem. J. R. Rosenblatt (1959) biased 0.8. M. B. Fiering (1963) somewhat similar when one related multiple cited above, estimates, is, yield smaller would real "preserve" inherent observations, component estimates. This component, often referred as normally paper reports investigation determine computed Noise effect However, addition lead MODEL pair phenomena denoted x y. general, same. If, example, y denotes streamflow, denote precipitation, temperature, geochronologic tree-ring widths. represented (Ni-+-Na) representation sequences, observation. practice, first sequence, nor consecutively. there loss generality above. assumed nx, ny, a2., a2,, p=ft