Beyond triple collocation: Applications to soil moisture monitoring

Abstract

Triple collocation (TC) is routinely used to resolve approximated linear relationships between different measurements (or representations) of a geophysical variable that are subject to errors. It has been utilized in the context of calibration, validation, bias correction, and error characterization to allow comparisons of diverse data records from various direct and indirect measurement techniques including in situ remote sensing and model-based approaches. However, successful applications of TC require sufficiently large numbers of coincident data points from three independent time series and, within the analysis period, homogeneity of their linear relationships and error structures. These conditions are difficult to realize in practice due to infrequent spatiotemporal sampling of satellite and ground-based sensors. TC can, however, be generalized within the framework of instrumental variable (IV) regression theory to address some of the conceptual constraints of TC. We review the theoretics of IV and consider one possible strategy to circumvent the three-data constraint by use of lagged variables (LV) as instruments. This particular implementation of IV is suitable for circumstances where multiple data records are limited and the geophysical variable of interest is sampled at time intervals shorter than its temporal correlation length. As a demonstration of utility, the LV method is applied to microwave satellite soil moisture data sets to recover their errors over Australia and to estimate temporal properties of their relationships with in situ and model data. These results are compared against standard two-data linear estimators and the TC estimator as benchmark.

Multi-scale analysis of bias correction of soil moisture

“…These effects can give rise to temporal autocorrelation in errors and undermine the linearity assumption between coincident measures. Finally, the non-stationary characteristic of noise in satellite SM (Loew and Schlenz , 2011;Zwieback et al, 2013;Su et al, 2014a) due to e.g. dynamical land surface characteristics such as soil moisture (Su et al, 2014b), is not treated here.…”

“…Su et al, 2013a). But these methods can induce artificial biases in the signal component of the corrected data as the error statistics were ignored; this also suggests a connection that the issue of bias correction is inseparable from that of error characterisation (Su et al, 2014a).…”

“…Thus, the biases are likely to be non-systematic across short and long timescales on different spatial scales and errors are non-white, undermining the utility of the affine model. One possible remedy is to apply bias correction, either TC or statistical-moment matching, only to anomaly time series (Miralles et al, 2011;Liu et al, 2012;Su et al, 2014a), but it remains unclear how these methods affect the signal and noise components in the corrected data. Alternatively a moving time window can be used to examine the time-varying statistics of time series (Loew and Schlenz , 2011;Zwieback et al, 2013;Su et al, 2014a).…”

An assessment of the performance of global rainfall estimates without ground-based observations

“…The first applications of TC concerned geophysical variables such as ocean wind speed and wave height (Stoffelen, 1998). More recently, it has been used extensively to estimate errors in soil moisture (SM) products (Crow and Van Den Berg, 2010;Miralles et al, 2010;Dorigo et al, 2010;Draper et al, 2013;Su et al, 2014;Gruber et al, 2016). Given three estimates of the same variable, the main assumptions of the method are the (i) stationarity of the statistics, (ii) linearity between the three estimates (vs. the same target) across all timescales and (iii) existence of uncorrelated error between the three estimates.…”

Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe?

“…However, even if an optimal RT can be theoretically found, its application to reality might not be straightforward. For instance, the successful application of TC requires sufficiently large numbers of coincident data points from three independent time series and, within the analysis period, homogeneity of their linear relationships and error structures [39]-two requirements not always fulfilled.…”