Filtering a statistically exactly solvable test model for turbulent tracers from partial observations

B. Gershgorin, A. J. Majda

Research output: Contribution to journalArticle

Abstract

A statistically exactly solvable model for passive tracers is introduced as a test model for the authors' Nonlinear Extended Kalman Filter (NEKF) as well as other filtering algorithms. The model involves a Gaussian velocity field and a passive tracer governed by the advection-diffusion equation with an imposed mean gradient. The model has direct relevance to engineering problems such as the spread of pollutants in the air or contaminants in the water as well as climate change problems concerning the transport of greenhouse gases such as carbon dioxide with strongly intermittent probability distributions consistent with the actual observations of the atmosphere. One of the attractive properties of the model is the existence of the exact statistical solution. In particular, this unique feature of the model provides an opportunity to design and test fast and efficient algorithms for real-time data assimilation based on rigorous mathematical theory for a turbulence model problem with many active spatiotemporal scales. Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization. The role of partial and sparse observations, the frequency of observations and the observation noise strength in recovering the true signal, its spectrum, and fat tail probability distribution are the central issues discussed here. The results of our study provide useful guidelines for filtering realistic turbulent systems with passive tracers through partial observations.

Original languageEnglish (US)
Pages (from-to)1602-1638
Number of pages37
JournalJournal of Computational Physics
Volume230
Issue number4
DOIs
StatePublished - Feb 20 2011

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tracers
Extended Kalman filters
Kalman filters
Probability distributions
contaminants
greenhouses
turbulence models
fats
assimilation
Advection
climate change
linearization
Oils and fats
advection
Turbulence models
Linearization
Greenhouse gases
Climate change
carbon dioxide
Carbon dioxide

Keywords

  • Data assimilation
  • Exactly solvable model
  • Nonlinear Kalman filter
  • Turbulent advection-diffusion equation

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Filtering a statistically exactly solvable test model for turbulent tracers from partial observations. / Gershgorin, B.; Majda, A. J.

In: Journal of Computational Physics, Vol. 230, No. 4, 20.02.2011, p. 1602-1638.

Research output: Contribution to journalArticle

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