Quadruple Collocation Analysis of In-Situ, Scatterometer, and NWP Winds

Triple collocation is an established technique for retrieving linear calibration coefficients
and observation error variances of a physical quantity observed simultaneously by three different
observation systems. The formalism is extended to an arbitrary number of systems, and representativeness
errors and associated cross-covariances are included in a natural way. It is applied to quadruple
collocations of ocean surface vector winds from two scatterometers (ASCAT-A, ASCAT-B, or ScatSat),
buoy measurements, and NWP model forecasts. There are 15 possible sets of quadruple collocation
equations, 12 of which are solvable for the essential variables (calibration coefficients, observation
error variances, and common variance) as well as two additional error covariances, each set leading to
a different solution. The quadruple collocation equations by themselves give little information on the
representativeness errors involved; these have to be estimated using other methods. The spreading in the
solutions is a measure of the accuracy of the underlying error model. Variation of the scale at which the
spatial variances are evaluated yields an optimal scale of 100–200 km. From triple collocation subsets the
error in the scatterometer error standard deviations is found to be 0.03–0.05 m s−1, more than expected on
statistical grounds. A more precise determination requires an error model that better describes the data
error properties.