Estimation of time averages from irregularly spaced observations: With application to coastal zone color scanner estimates of chlorophyll concentration

Abstract

A formalism is presented for quantifying the sampling error of an arbitrary linear estimate of a time‐averaged quantity constructed from a time series of irregularly spaced observations at a fixed location. The method is applicable to any irregularly sampled time series; it is applied here to satellite observations of chlorophyll from the coastal zone color scanner (CZCS). The two specific linear estimates considered here are the composite average formed from the simple average of all observations within the averaging period and the optimal estimate formed by minimizing the mean squared error of the temporal average based on all of the observations in the time series. The formalism requires a priori knowledge of the variances and correlation functions of the chlorophyll signal and CZCS measurement error. In the usual absence of the necessary detailed information on these parameters, values obtained here from in situ measurements of chlorophyll and fluorescence off the coast of southern California can be used. The resulting estimates are referred to here as “suboptimal estimates,” which are optimal only if the assumed values for the parameters are correct. Suboptimal estimates are shown to be much more accurate than composite averages. Moreover, suboptimal estimates are also shown to be nearly as accurate as optimal estimates obtained using the correct signal and measurement error variances and correlation functions for realistic ranges of these parameters. Suboptimal estimation is thus a very useful and practical alternative to the composite average method generally used at present.