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Detection of Non‐Gaussian Behavior Using Machine Learning Techniques: A Case Study on the Lorenz 63 Model
Author(s) -
Goodliff Michael,
Fletcher Steven,
Kliewer Anton,
Forsythe John,
Jones Andrew
Publication year - 2020
Publication title -
journal of geophysical research: atmospheres
Language(s) - English
Resource type - Journals
eISSN - 2169-8996
pISSN - 2169-897X
DOI - 10.1029/2019jd031551
Subject(s) - gaussian , skewness , computer science , log normal distribution , artificial intelligence , artificial neural network , machine learning , probability density function , support vector machine , data assimilation , random variable , algorithm , mathematics , statistics , physics , meteorology , quantum mechanics
An important assumption made in most variational, ensemble, and hybrid‐based data assimilation systems is that all minimized errors are Gaussian random variables. A theory developed at the Cooperative Institute for Research in the Atmosphere enables for the Gaussian assumption for the different types of errors to be relaxed to a lognormally distributed random variable. While this is a first step toward using more consistent distributions to model the errors involved in numerical weather/ocean prediction, we still need to be able to identify when we need to assign a lognormal distribution in a mixed Gaussian‐lognormal approach. In this paper, we present some machine learning techniques and experiments with the Lorenz 63 model. Using these machine learning techniques, we show detection of non‐Gaussian distributions can be done using two methods: a support vector machine and a neural network. This is done by training past data to classify (1) differences with the distribution statistics (means and modes) and (2) the skewness of the probability density function.