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Mathematical Challenges in Measuring Variability Patterns for Precipitation Analysis

  • Maria EmelianenkoEmail author
  • Viviana Maggioni
Chapter
Part of the Mathematics of Planet Earth book series (MPE, volume 5)

Abstract

This chapter addresses some of the mathematical challenges associated with current experimental and computational methods to analyze spatiotemporal precipitation patterns. After a brief overview of the various methods to measure precipitation from in situ observations, satellite platforms, and via model simulations, the chapter focuses on the statistical assumptions underlying the most common spatiotemporal and pattern-recognition techniques: stationarity, isotropy, and ergodicity. As the variability of Earth’s climate increases and the volume of observational data keeps growing, these assumptions may no longer be satisfied, and new mathematical methodologies may be required. The chapter discusses spatiotemporal decorrelation measures, a nonstationary intensity-duration-function, and 2-dimension reduction methodologies to address these challenges.

Keywords

Centroidal Voronoi tessellation Data reduction Decorrelation Empirical orthogonality functions Ergodicity Isotropy Precipitation patterns Stationarity Statistical assumptions 

Notes

Acknowledgements

This work was instigated at the Mason Modeling Days workshop held at George Mason University, generously supported by the National Science Foundation grant DMS-1056821. The authors are grateful to Paul Houser for stimulating discussions at the initial stages of this collaboration. ME also wishes to thank Hans Engler and Hans Kaper for their encouragement over the years, and for introducing this research group to the MPE community.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA
  2. 2.Sid and Reva Dewberry Department of Civil, Environmental, and Infrastructure EngineeringGeorge Mason UniversityFairfaxUSA

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