Efficient Data Assimilation in High-Dimensional Hydrologic Modeling through Optimal Spatial Clustering

While high-resolution models have the potential of advancing the frontier of forecasting in the geosciences, their initialization through data assimilation is computationally challenging because of the huge number of interactions between state variables. This article introduces a method to reduce the dimensionality of state vectors to improve existing assimilation algorithms. The method couples model elements that behave similarly using optimized $k$-means clustering with the goal of making covariance matrices more manageable, and of allowing for smaller errors when dependencies are ignored for efficiency reasons. An experiment using a highly-distributed hydrologic model showed that an intermediate level of compression, with optimized clustering parameters, improved the probabilistic performance of streamflow forecasts. While higher levels of compression could be achieved more efficiently and lower levels offer more realistic representations, an intermediate level yielded the best balance between the degree of cell coupling and the preservation of the spatial heterogeneity of the watershed.