{"product_id":"wavelet-approximation-in-data-assimilation-nasa-technical-reports-server-ntrs-9781289289737","title":"Wavelet Approximation in Data Assimilation","description":"\u003cbr\u003e 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. \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Nasa Technical Reports Server (Ntrs),Andrew Tangborn\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1289289735\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781289289737\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Bibliogov\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/07\/2013\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 38\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.19lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.69h x 7.44w x 0.08d","brand":"Nasa Technical Reports Server (Ntrs)","offers":[{"title":"Paperback","offer_id":47611436859647,"sku":"9781289289737","price":15.75,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_afb3fa79-839a-49ca-bc15-7480fbf0a88a.jpg?v=1764513867","url":"https:\/\/www.whiterainbookhouse.com\/products\/wavelet-approximation-in-data-assimilation-nasa-technical-reports-server-ntrs-9781289289737","provider":"WR Book House","version":"1.0","type":"link"}