報告書番号

U03055

タイトル（和文）

特異値分解を用いた沿岸流動のデータ同化

タイトル（英文）

Data Assimilation of Coastal Currents with Singular Value Decomposition

概要 （図表や脚注は「報告書全文」に掲載しております）

特異値分解を用いて観測結果を沿岸流動モデルにデータ同化し，観測結果を再現する開境界の水位形状を推定した．観測結果には，汀線29km×沖合11kmの海域に疎らに設置された15地点の流速計の結果を用いた．沿岸流動モデルには，線形・定常な浅水方程式を用いた．モデルが線形であることを利用して特異値分解を行い，特異値，左右固有ベクトルを用いてデータ同化を行った.その結果，勾配法を用いた場合と比べて，データ同化にかかる計算時間を約3000倍程度短くすることが出来た.観測点を囲む4つの計算点の結果が観測結果であるとした出力モデルを用い，開境界の水位形状を構成する直交関数の係数を推定したデータ同化では，直交関数に多項式からなる関数を用いた場合でも，観測結果にほぼ一致した流動場を推定出来，さらにこの流速場を実現する開境界の水位形状を決定できた.

概要 （英文）

The distribution of the sea level on the open boundary was estimated by Data Assimilation Method to assimilate the observations into a coastal current model with Singular Value Decomposition. The observations available in this study were only the velocity data measured with current-meters at 15 stations sparsely located in the sea area with about 29km in the alongshore direction × about 11km in the offshore direction. The linear and steady shallow water equation was applied as the coastal current model. The sea levels of all calculation points on the open boundary and the coefficients of Legendre polynomials, of which linear sum was the distribution of the water level on the open boundary were respectively estimated to decide the open boundary condition. Two observation models were applied, which converted the computational results into the outputs to compare with the observations. The matrix of these models was decomposed into singular values and a right and left eigenvectors by SVD, because the numerical and observational models were linear matrix. These singular values and right and left eigenvectors were used for the data assimilation. The computational time of Data Assimilation with SVD was about 3000 times shorter than with the time with the gradient method. The calculated flow field agreed with the observed flow patterns, which suggested that the open boundary conditions were estimated appropriately.

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