Triple collocation

The triple collocation method, introduced by Stoffelen [1998] offers the possibility to simultaneously calculate linear calibration coefficients and measurement error variances from collocated triplets of measurements. The method has been developed for scatterometer wind measurements made by the European remote Sensing satellite (ERS) with buoy winds and ECMWF model predictions as additional data sources.

Since then, the method has been used only few times: for ocean wave heights [Janssen et al., 2007], for ocean wind stress [Portabella and Stoffelen, 2009], and for ASCAT and SeaWinds scatterometer wind products [Vogelzang et al., 2011]. One reason for this relatively modest use may be the fact that three independent measurement systems are needed that must deliver simultaneous collocated measurements. This is in practice often hard to establish, and in the examples mentioned above the requirements of collocation in space and time must be relaxed a bit. Even then, it takes typically one year to gather enough data for successful application of the method.

Another reason may be that the triple collocation method is considered too difficult for practical application by the scientific community. The method has been described in the scientific literature [Stoffelen, 1998], but such a presentation must necessarily be very concise. Implementation of the method is tedious, since a more detailed description on text book level is missing. This report is intended to fill that gap.

The report gives a full description of the triple collocation error model, the derivation of the calibration coefficients and the measurement error variances, the assumptions needed in the triple collocation method, and its numerical implementation.