Overview of mathematical background of homogenization, summary of method MASH and comments on benchmark validation

Abstract

AbstractThere are several methods and software for the homogenization of climate data series but there is not any exact mathematical theory of homogenization. As we see, the basic problem of homogenization is the unreasonable dominance of the practical procedures over the theory. Therefore we try to formulate some questions of homogenization in accordance with the mathematical conventions. The topics to be discussed are as follows. (a) Themes and systems—meteorological, mathematical and software links. (b) Mathematical formulation of climate data series homogenization and special case of normal distribution. (c) Additive and multiplicative spatiotemporal models for climate data series homogenization. (d) Mathematical overview of methodological questions as, spatial comparison of series, inhomogeneity detection and adjustment of series, in accordance with the WMO Guidelines on Homogenisation (2020). (e) The last topic is the new version of MASH for homogenization of mean and standard deviation. The earlier versions of our method MASH (Multiple Analysis of Series for Homogenization; Szentimrey) were developed formerly at the Hungarian Meteorological Service. These procedures aimed to homogenize the daily and monthly data series in the mean, that is, the first order moment. The new version MASHv4.01 has been developed for joint homogenization of mean and standard deviation using some mathematical results. Theoretically, in case of normal distribution, the homogenization of mean and standard deviation is sufficient since if the first two moments are homogenous then the higher order moments are also homogeneous. An interactive automatic algorithm also was developed in this new version in order to make the homogenization easier for the users. We will present a summary of the software MASH where our intention was to develop a flexible, interactive automatic, artificial intelligence (AI) system. We finish the paper with some comments connected to the theoretical evaluation and benchmark validation of the methods.