Mode Decomposition Methods for Soil Moisture Prediction

Abstract:

Lack of reliable, well-distributed, long-term datasets for model validation is a bottle-neck for most exercises in soil moisture analysis and prediction. Understanding what factors drive soil hydrological processes at different scales and their variability is very critical to further our ability to model the various components of the hydrologic cycle more accurately. For this, a comprehensive dataset with measurements across scales is very necessary. Intensive fine-resolution sampling of soil moisture over extended periods of time is financially and logistically prohibitive. Installation of a few long term monitoring stations is also expensive, and needs to be situated at critical locations. The concept of Time Stable Locations has been in use for some time now to find locations that reflect the mean values for the soil moisture across the watershed under all wetness conditions. However, the soil moisture variability across the watershed is lost when measuring at only time stable locations. We present here a study using techniques such as Dynamic Mode Decomposition (DMD) and Discrete Empirical Interpolation Method (DEIM) that extends the concept of time stable locations to arrive at locations that provide not simply the average soil moisture values for the watershed, but also those that can help re-capture the dynamics across all locations in the watershed. As with the time stability, the initial analysis is dependent on an intensive sampling history. The DMD/DEIM method is an application of model reduction techniques for non-linearly related measurements. Using this technique, we are able to determine the number of sampling points that would be required for a given accuracy of prediction across the watershed, and the location of those points. Locations with higher energetics in the basis domain are chosen first. We present case studies across watersheds in the US and India. The technique can be applied to other hydro-climates easily.