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Mathematics of Climate and Weather Forecasting

Ed. by Khouider, Boualem

Covered by MathSciNet and Zentralblatt Math (zbMATH)

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2353-6438
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Optimal Algorithms for Computing Average Temperatures

S. Foucart / M. Hielsberg / G. L. Mullendore / G. Petrova / P. Wojtaszczyk
Published Online: 2019-04-09 | DOI: https://doi.org/10.1515/mcwf-2019-0003

Abstract

A numerical algorithm is presented for computing average global temperature (or other quantities of interest such as average precipitation) from measurements taken at speci_ed locations and times. The algorithm is proven to be in a certain sense optimal. The analysis of the optimal algorithm provides a sharp a priori bound on the error between the computed value and the true average global temperature. This a priori bound involves a computable compatibility constant which assesses the quality of the measurements for the chosen model. The optimal algorithm is constructed by solving a convex minimization problem and involves a set of functions selected a priori in relation to the model. It is shown that the solution promotes sparsity and hence utilizes a smaller number of well-chosen data sites than those provided. The algorithm is then applied to canonical data sets and mathematically generic models for the computation of average temperature and average precipitation over given regions and given time intervals. A comparison is provided between the proposed algorithms and existing methods.

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About the article

Received: 2018-11-13

Accepted: 2019-03-24

Published Online: 2019-04-09


Citation Information: Mathematics of Climate and Weather Forecasting, Volume 5, Issue 1, Pages 34–44, ISSN (Online) 2353-6438, DOI: https://doi.org/10.1515/mcwf-2019-0003.

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© 2019 S. Foucart et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0

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