Abstract
This article presents the comparison of two algorithms for data assimilation of two dimensional shallow water flows. The first algorithm is based on a linearization of the model equations and a quadratic programming (QP) formulation of the problem. The second algorithm uses Ensemble Kalman Filtering (EnKF) applied to the non-linear two dimensional shallow water equations. The two methods are implemented on a scenario in which boundary conditions and Lagrangian measurements are available. The performance of the methods is evaluated using twin experiments with experimentally measured bathymetry data and boundary conditions from a river located in the Sacramento Delta. The sensitivity of the algorithms to the number of drifters, low or high discharge and time sampling frequency is studied.
Highlights
The modeling and monitoring of river hydraulics are increasingly important as they provide drinkable water for populations as well as irrigation for a variety of crops
We present two data assimilation methods applied to river flows, namely, a novel algorithm based on Quadratic Programming (QP), and an algorithm using Ensemble Kalman Filtering (EnKF)
Two data assimilation methods were applied to a river in the Sacramento Delta and their respective performances were compared
Summary
The modeling and monitoring of river hydraulics are increasingly important as they provide drinkable water for populations as well as irrigation for a variety of crops. The notations for the EnKF algorithm presented in the rest of section 4 are as follows: θn: Vector of state variables, namely the velocity components (u, v), the water height h for each mesh point and the positions of the drifters xD, yD at a time instant tn. Lagrangian drifter positions are embedded in the state vector in discretized form and the new state vector θn at time tn is written as θn = This approach makes it possible to take the Lagrangian nature of observations into account in a way which does not require deriving Eulerian quantities from Lagrangian measurements as was done in the previous section in equations (18) and (19). For the state space model (20)–(21), the EnKF algorithm can be summarized as in [15, 12]: Algorithm
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