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Title: An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic modelmore » with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics and Department of Meteorology, the Pennsylvania State University, University Park, PA 16802, Unites States (United States)
  2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States)
  3. Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States)
Publication Date:
OSTI Identifier:
22230852
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 257; Journal Issue: Part A; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; DEGREES OF FREEDOM; DIFFERENTIAL EQUATIONS; FILTERS; GAUSS FUNCTION; JETS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; STATISTICS; STOCHASTIC PROCESSES; THREE-DIMENSIONAL CALCULATIONS