An efficient optimum interpolation analysis scheme

Abstract

Abstract One of the characteristics of the optimum interpolation analysis scheme is that a matrix problem that depends on the number of observations has to be solved for each grid‐point value that is calculated. In data‐rich regions, this matrix can be quite large and in general, a limit on its size has to be imposed in order to avoid an excessive amount of computation. In the proposed univariate analysis scheme, the autocorrelation function has been approximated by the second‐order and fourth‐order Taylor series expansion of the Gaussian Hill function. It is shown that the weights given to the observations can then be evaluated analytically by resolving associated systems of order 4 and 9, respectively. When 24 pieces of data are used, the proposed schemes are, respectively, 6 and 3 times faster than an optimum interpolation analysis scheme using the Gaussian autocorrelation function. Furthermore, the analyses produced by those 3 schemes are almost identical. The search radius being limited, the proposed schemes are useful and worth while only over data‐dense areas.