Multi-scale analysis framework for bias characterisation, bias correction and de-noising

Abstract:

Global environmental monitoring requires measurements from a variety of disparate sources (in situ probes, remote sensing and models) to be appropriately combined to generate complete gridded fields with quality commensurate with or better than that of each of the individual sources. To achieve this, unbiased characterisation of systematic errors (i.e., biases) and random errors (noise) are needed. Triple collocation analysis (TCA) enables unbiased estimation of their additive and multiplicative biases, and additive noise variance, conditional on the validity of an affine model that relates three coincident estimates. However this linearity assumption has yet been properly examined. Since the dynamics of a geophysical variable and its representations at variable supports are generally influenced by different physical processes operating at characteristic spatiotemporal scales, it may be conceivable to decompose its time series into multiple temporal scales for individual analyses. Here we propose a new analysis framework of combining TCA with wavelet-based multi-resolution analysis (MRA) to develop a time-scale dependent linear bias model, where the conventional TCA is its special case. We illustrate the applications of the new analysis on soil moisture observational and modelled data sets, without the loss of generality, in three areas: (1) characterization scale-dependent biases and noise; (2) investigation of the influence of conventional bias correction schemes on these biases and noise; and (3) implementation of a new scheme for multi-scale bias correction and nonlinear de-noising.