A correlation procedure for augmenting hydrologic data

A linear regression for a short and long sequence of hydrologic events is used to lengthen the short sequence. The lengthened sequence consists of the original observations and regressed values plus noise, where the noise is a random variable with zero mean and variance proportional to the variance of the observations for the short sequence about the line of regression. Estimates of the mean and variance for the lengthened sequence are shown to be unbiased. If the correlation coefficient, which measures the strength of the linear regression, exceeds about 0.5, then the estimates of the mean and variance based on the lengthened sequence are better estimators of the population values of the mean and variance than the estimates based on the observations for the short sequence. If noise is not added to the regressed values, the correlation coefficient must exceed about 0.8 to obtain improvement in the estimates by use of correlated values.