Statistical upscaling of dynamic terrain state properties using a Symbolic Aggregate approXimation (SAX) approach

The current method for predicting terrain state properties such as soil moisture and temperature at the resolution and spatial scales needed for applications such as route planning and infrared sensor performance is computationally expensive due to the highly nonlinear physics involved. Areas of interest are not homogeneous and like pieces of ground over which representative terrain state information is calculated may, or may not be, contiguous. The complexity of the spatial and temporal variability of natural systems combined with the inherent nonlinear interactions in these systems makes it difficult to scale the problem. Not representing the heterogeneity, or representing the heterogeneity at a scale not commensurate with the model physics, can increase the uncertainty of the model predicted geophysical information. SAX (Symbolic Aggregate approXimation) of a data series has been successfully used to look for anomalies, changes and patterns in behavior.. SAX is based on the concept of piecewise aggregate approximation in which the data is divided into a user determined number of segments, “w”, having equal length, each of which is represented by its mean. The size of the symbolic alphabet, “k”, is such that the distribution of segment means is Gaussian. The original time series is now represented by a “word” of length “w”. Before assigning alphabets and word lengths, the different soil moisture and temperature time series are divided into subsections using Adaptive Piecewise Constant Approximation (APCA). A representative APCA curve is chosen then used to determine the SAX parameters from which the terrain state at other locations are predicted. No one has tried to use the SAX approach in this manner before. The all-season, dynamic 1-D state of the ground model FASST (Fast All-season Soil STrength) is used to provide the terrain response to predictive weather forcing. Being able to identify the spatial and temporal relationships in this fashion will help to account for the variability and enhance the fidelity (reduce the uncertainty) of the model predicted parameters.