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Scaling Limits and Self‐Similarity in Precipitation Fields
Author(s) -
Waymire Ed
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i008p01271
Subject(s) - scaling , statistical physics , limiting , similarity (geometry) , precipitation , scale (ratio) , cluster (spacecraft) , mathematics , environmental science , computer science , meteorology , physics , artificial intelligence , geometry , image (mathematics) , engineering , mechanical engineering , quantum mechanics , programming language
It has been recognized in the literature on rainfall models in hydrology that the exact calculations of probabilities for models which incorporate cluster structure is typically not possible. Consequently, one is led to considerations of limiting approximations. However, because of the presence of dependencies and/or fat tails in several of the current models, the nature of the approximations involves some important issues for both theoretical as well as experimental consideration in precipitation research. The objective of the present paper is to systematically describe these issues as they pertain to rainfall models. Some specific large‐scale approximations are given for models of the type currently in the literature.