Estimation of the temporal autocorrelation structure by the collocation technique with emphasis on soil moisture studies, Hydrolog

The collocation technique has become a popular tool in oceanography and hydrology for estimating the error variances of different data sources such as in-situ sensors, models and remote sensing products. It is also possible to determine calibration constants to account for e.g. an offset between the data sources. So far the temporal autocorrelation structure of the errors has not been studied, although it is known that it has detrimental effects on the results of the collocation technique, in particular when calibration constants are determined as well. In this paper it is shown how the (triple) collocation estimators can be adapted to retrieve the autocovariance functions and the statistical properties as well as the structural deficencies are described. The coupling between the autocorrelation of the error and the estimation of calibration constants is studied in detail, due to its importance for analyzing temporal changes. In soil moisture applications, such time variations can e.g. be induced by seasonal changes in the vegetation cover, which affect both models and remote sensing products. The limitations of the proposed technique associated with these considerations are analyzed using remote sensing and in-situ soil moisture data. The variability of the inter-sensor calibration and the autocovariance are shown to be closely related to temporal patterns of the data.