Changes between Version 5 and Version 6 of EnsembleGeneration
 Timestamp:
 Jan 29, 2021, 10:00:55 AM (4 weeks ago)
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EnsembleGeneration
v5 v6 7 7 To start ensemblebased data assimilation one has to generate an ensemble of model states that represents both the state estimate (provided by the ensemble mean state) and the uncertainty of the state estimate, given by the ensemble spread. In case of ensemble Kalman filters, the uncertainty is estimate by the sample covariance matrix of the ensemble, i.e. the covariance matrix of the deviations of the ensemble states from the ensemble mean state. 8 8 9 There are different possibilities to generate an ensemble. With PDAF we currently provide support for one sampling method, the cocalled secondorder exact sampling from a model trajectory. This method was introduced by Pham et al. (see e.g. Pham, Monthly Weather Review 129 (2001) 11941207). The method is as follows:9 There are different possibilities to generate an ensemble. With PDAF we currently provide support for one sampling method, the socalled secondorder exact sampling from a model trajectory. This method was introduced by Pham et al. (see e.g. Pham, Monthly Weather Review 129 (2001) 11941207). The method is as follows: 10 10 1. Run the model with which the data assimilation will be performed and write a trajectory of model snapshots into files. 11 11 1. In a separate program read the model snapshots. Compute the temporal mean state and subtract it from all snapshots. Now compute the singular value decomposition of the resulting matrix. This is known as the EOFdecomposition. It provides the singular vectors (EOFS, empirical orthogonal functions) and singular values (EOF coefficients). The number of EOFs is usually '''r''' if the trajectory contains '''r+1''' model snapshots. Store the singular vectors and singular values in a file.