A Multi-Objective Data Assimilation Filtering Method for Distributed High-Resolution Hydrologic Modeling

Abstract:

Operative hydrologic forecast models rely on accurate estimations of initial conditions which are represented by a number of state variables. Filtering-based data assimilation methods have been established as the most widespread alternatives to combine model results with sensor data to better estimate these state vectors. However, current state of the art filtering methods continue to struggle with two difficulties: the adequate balancing of the uncertainties associated with each of the data sources, and the estimation of high-dimensional state variable vectors used by modern distributed land-surface models.

In this work we introduce the Pareto Filter, a data assimilation algorithm based on the Particle Filter to address these two challenges. In the first place, this method explicitly formulates the filtering goals—to favor candidate particles whose states are consistent with the observations and with the preceding conditions—in a multi-objective optimization framework to sort the particles in a set of fronts according to a domination ordering. Each front contains a set of mutually non-dominated particles that balance the trade-offs between objectives.

Kernel smoothing is then used on the filtered particles to define a multivariate probability distribution from where states are sampled. Particles are given weights according to the rank of their front, with the highest values assigned to those in the non-dominated Pareto front. This probabilistic perspective helps in reducing the adverse effects of drifting particles and in enabling likelihood computations without the need of assuming a Gaussian distribution. Finally, two optimization algorithms are used to complement the random sampling of candidate states by exploiting the features of high-performing particles in order to accelerate the convergence rate.

The proposed Pareto Filter was tested with the Distributed Hydrology Soil Vegetation Model (DHSVM) applied to a real watershed with a state vector of over 30,000 variables. The forecasting accuracy of the model was measured after performing data assimilation using the Pareto Filter and a standard Sequential Importance Resampling Particle Filter. The results show a more robust performance by the Pareto Filter and a higher reduction in the uncertainty of the state variable estimates.