Quadratic programming based data assimilation with passive drifting sensors for shallow water flows

We present a method for assimilating Lagrangian sensor measurement data into a shallow water equation model. The underlying estimation problem (in which the dynamics of the system are represented by a system of partial differential equations) relies on the formulation of a minimisation of an error functional, which represents the mismatch between the estimate and the measurements. The corresponding so-called variational data assimilation problem is formulated as a quadratic programming problem with linear constraints. For the hydrodynamics application of interest, data is obtained from drifting sensors that gather position and velocity. The data assimilation method refines the estimate of the initial conditions of the hydrodynamic system. The method is implemented using a new sensor network hardware platform for gathering flow information from a river, which is presented in this article for the first time. Validation of the results is performed by comparing them to an estimate derived from an independent set of static sensors, some of which were deployed as part of our field experiments.