The stochastic view used in climate sciences: (some) perspectives from (some of) mathematical statistics

TL;DR

This paper discusses statistical methodologies relevant to climate science, emphasizing model selection, prediction, uncertainty quantification, and the analysis of extreme events, with a focus on the stochastic approaches used in the field.

Contribution

It highlights key statistical themes and methodologies pertinent to climate science, integrating perspectives from mathematical statistics and emphasizing their application to climate data analysis.

Findings

Improved modeling and model selection strategies for meteorological time series.

Methods for predicting trend crossings and assessing uncertainties.

Analysis of probabilities and uncertainties related to extreme climate events.

Abstract

Climate statistics is of course a very broad field, along with the many connections and impacts for yet other areas, with a history as long as mankind has been recording temperatures, describing drastic weather events, etc. The important work of Klaus Hasselmann, with crucial contributions to the field, along with various other connected strands of work,is being reviewed and discussed in other chapters. The aim of the present chapter is to point to a few statistical methodology themes of relevance for and joint interest with climate statistics. These themes, presented from a statistical methods perspective, include (i) more careful modelling and model selection strategies for meteorological type time series; (ii) methods for prediction, not only for future values of a time series, but for assessing when a trend might be crossing a barrier, along with relevant measures of uncertainty for these; (iii) climatic influence on marine biology; (iv) monitoring processes to assess whether and then to what extent models and their parameters have stayed reasonably constant over time; (v) combination of outputs from different information sources; and (vi) analysing probabilities and their uncertainties related to extreme events.