Ensemble Kalman filters for dynamical systems with unresolved turbulence
Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarseresolution models are intended to predict the largescale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the largescale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein smallscale statistics can be used to estimate both the resolved and unresolved components of the solution. The onedimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the nonGaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in twothirds of the climatological variance being carried by the unresolved small scales.more »
 Authors:

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 Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)
 (United Arab Emirates)
 Publication Date:
 OSTI Identifier:
 22382110
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 273; Other Information: Copyright (c) 2014 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:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY SPECTRA; ERRORS; FILTERS; INCLUSIONS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; ONEDIMENSIONAL CALCULATIONS; RESOLUTION; STATISTICS; STOCHASTIC PROCESSES; TURBULENCE