ABSTRACT
The objective of the present study is to compare and to test the application of two different data assimilation techniques on a 2D shallow water equation model under different conditions. The main differences between the filters (Madsen [44]) are the following:
Calculation of the model forecast. The RRSQRT uses a deterministic model forecast while the EnKF calculates the model forecast as the mean (or median, mode) of the ensemble of states.
Error propagation. The EnKF propagates the ensemble using the full model dynamics while the RRSQRT propagates the error covariance matrix using a tangent linear model operator.
The model error forcing is introduced in the EnKF as part of the ensemble propagation. In the RRSQRT some matrix algebra is needed for this purpose.
With regards to the representation of the error covariance matrix, the RRSQRT uses a reduced rank approximation of the square root of the error covariance matrix and the EnKF uses an ensemble estimate of the error covariance.
The EnKF has a computational cost expressed in terms of the number of model integrations of the order of the ensemble size. In the case of the RRSQRT the greatest part of the computational cost is taken up by a number of model integrations equal to the number of leading eigenvalues plus the cost associated with the matrix algebra including the eigenvalue decomposition, which can be very costly.
