A multiscale ensemble filtering system for hydrologic data assimilation. Part I: Implementation and synthetic experiment

The multiscale autoregressive (MAR) framework was introduced in the last decade to process signals that exhibit multiscale features. It provides the method for identifying the multiscale structure in signals and a filtering procedure, and thus is an efficient way to solve the optimal estimation problem for many high-dimensional dynamic systems. Later, an ensemble version of this multiscale filtering procedure, the ensemble multiscale filter (EnMSF), was developed for estimation systems that rely on Monte Carlo samples, making this technique suitable for a range of applications in geosciences. Following the prototype study that introduced EnMSF, a strategy is devised here to implement the multiscale method in a hydrologic data assimilation system, which runs a land surface model. Assimilation experiments are carried out over the Arkansas-Red River basin, located in the central United States (∼645 000 km²), using the Variable Infiltration Capacity (VIC) model with a computing grid of 1062 pixels. A synthetic data assimilation experiment is performed, driven by meteorological forcing fields downscaled from the ensemble forecasts made by the NOAA/National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFS). The classic full-rank ensemble Kalman filter is used as the benchmark to evaluate the multiscale filter performance, and comparisons are also made with a horizontally uncoupled filter. It is demonstrated that the multiscale filter is able to closely approximate the full-rank solution with a low computational cost (∼1/20 of the full-rank filter) in an experiment in which the top-layer soil moisture is assimilated, whereas the horizontally uncoupled filter fails to approximate the full-rank solution.