{ "item_title" : "Wavelet Approximation in Data Assimilation", "item_author" : [" Nasa Technical Reports Server (Ntrs)", "Andrew Tangborn "], "item_description" : " Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation. ", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/1/28/928/973/1289289735_b.jpg", "price_data" : { "retail_price" : "15.75", "online_price" : "15.75", "our_price" : "15.75", "club_price" : "15.75", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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