Data archive strategy for computing the long-term means of nonlinear functions in geophysical problems

Abstract

An algorithm for computing the temporal mean of a nonlinear function using the temporal means, covariances and higher order statistical moments of the variables involved in the function is revisited. Furthermore, a pyramidal algorithm is derived, which hierarchically stores the statistical moments of a longer interval of a variable from those of its shorter subintervals. The 2 methodologies together presented here show a systematic way of data storage and show that the long-term mean of a nonlinear process can be analyzed by decomposing it into various shorter subtime scales such as diurnal and seasonal cycles. For example, the long-term mean of horizontal moisture flux can be decomposed into the product of the means of wind speed and humidity observations, plus the covariance of daily means of the 2 variables, and plus the mean of the daily covariances, of the 2 variables on each day, where the 3 mean values and the covariance are Suggested for storage The results are exactly the same as those directly calculated from their hourly data. Since only 4 statistical moments are needed, significant data reduction for data distribution can be achieved The error associated with the data archive replica has been discussed for a highly nonlinear function of which the statistical moments of its variables are only available up to a finite order. A case study using 41 yr of data taken on an urbanizing site on a Subtropical island is illustrated.