NWC REU 2008
May 27 - August 1



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Estimating Correlations from a Coastal Ocean Model for Localizing an Ensemble Transform Kalman Filter

Jonathan Poterjoy, Ross Hoffman, and Mark Leidner



Data assimilation is the process of using past and present data to estimate the current synoptic state of a dynamical system. Current data is merged with a previous model forecast or “background” field to produce the best estimate of a system’s state called an “analysis”. For cases where the probability distribution of observation and background errors are normally distributed, a Kalman filter can be shown to produce the best estimate of a variable and its uncertainty. A type of data assimilation system called the Ensemble Kalman Filter (EnKF) approximates the background covariance field using only a small ensemble of forecasts. Since a limited number of samples are used, many spurious correlations exist between an observation at one point and forecast errors at various locations within the model domain. To limit spurious relationships the Local Ensemble Transform Kalman filter (LETKF) limits the region considered in a process called “localization”. But a question arises regarding the optimal localization size for analyses within complex model domains. Using the Estuarine Coastal Ocean Model (ECOM) coupled with the LETKF, we examined correlations between simulated state variables on various locations and depths within a domain that spans the New York Harbor region. Distributions of correlation coefficients surrounding an analysis point were used to determine the optimal localization domain for each particular relationship. Since spurious correlations tend to diminish after 1 to 2 days of simulation, results observed during days 3 and 4 of this experiment were taken to be a good estimate of true relationships between variables. Given the large amount of dynamical and bathymetric variability within this model domain, correlation structures of mixed shapes and sizes were observed. In many instances, the parameterized localization domain was either too small or too large to capture the actual correlations. Results from this study provide incentive to pursue an automated solution to optimal localization within the LETKF/ECOM that tailors a unique localization volume for each analysis. If successful this solution can be applied to various other prediction systems that rely on ensemble data assimilation.

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