Abstract. Remote sensing, in situ networks and models are now providing unprecedented information for environmental monitoring. To conjunctively use multi-source data nominally representing an identical variable, one must resolve biases existing between these disparate sources, and the characteristics of the biases can be non-trivial due to spatiotemporal variability of the target variable, inter-sensor differences with variable measurement supports. One such example is of soil moisture (SM) monitoring. Triple collocation (TC) based bias correction is a powerful statistical method that increasingly being used to address this issue but is only applicable to the linear regime, whereas nonlinear method of statistical moment matching is susceptible to unintended biases originating from measurement error. Since different physical processes that influence SM dynamics may be distinguishable by their characteristic spatiotemporal scales, we propose a multi-time-scale linear bias model in the framework of a wavelet-based multi-resolution analysis (MRA). The joint MRA-TC analysis was applied to demonstrate scale-dependent biases between in situ, remotely-sensed and modelled SM, the influence of various prospective bias correction schemes on these biases, and lastly to enable multi-scale bias correction and data adaptive, nonlinear de-noising via wavelet thresholding.
Multi-scale geometric methods for data sets II: Geometric Multi-Resolution Analysis