Real-updating multivariate analysis for unsteady flows with ensemble Kalman filter

To reduce uncertainty in the forecast or analysis of unsteady flows,the ensemble Kalman filter technique(EnKF) is introduced based on the stochastic unsteady flow system with a stochastic state space model.The multivariate analysis scheme is proposedfor updating flow states when the water stage and the discharge measurements are both assimilated.Taking a single-wave flood event in open channel as an example,the performance of EnKF is investigated with the experiments of 13 groups.The investigation mainly focuses on the comparisons of the effects of water stage or discharge measurements with different order of the available accuracy on the EnKF analysis.Main results show that one can identify flow states well by assimilating the water stage measurements with less than Scm standard deviation alone.And the results using discharge measurement with 5%relative standard deviation are close to those using water stage with lOcm standard deviation.Further,when both kinds of measurements are assimilated,the appropriate variable transformation is required to remedy the truncation errors of the numerical computation.