Abstract/Summary

Fundamental and thematic climate data records derived from satellite observations provide unique information for climate monitoring and research. Since any satellite operates over a limited period of time only, creating a climate data record requires the combination of space-borne measurements from a series of several (often similar) satellite sensors. A simple combination of calibrated measurements from several sensors, however, can produce an inconsistent climate data record. This is particularly true of older, historic sensors whose behavior in space was often different from their behavior during pre-launch calibration in the laboratory. More scientific value can be derived from considering the series of historical and present satellites as a whole. Here we consider harmonisation as a process that obtains new calibration coefficients for revised sensor calibration models by comparing calibrated measurements over appropriate satellite-to-satellite match-ups, such as simultaneous nadir overpasses. When we perform a comparison of two sensors, however, we must consider that those sensors are not observing exactly the same Earth radiance. This is in part due to differences in exact location and time tolerated by the match-up process itself, but also due to differences in the spectral response functions of the two instruments, even when nominally observing the same spectral band. To derive a harmonised data set we do not aim to correct for spectral response function differences, but to reconcile the calibration of different sensors given their estimated spectral response function differences. Here we present the concept of a framework that establishes calibration coefficients and their uncertainty and error covariance for an arbitrary number of sensors in a metrologically-rigorous manner. We describe harmonisation and its mathematical formulation as an inverse problem. Solving this problem is challenging when some hundreds of millions of match-ups are involved and the errors of fundamental sensor measurements are correlated. We solve the harmonisation problem as marginalised errors in variables regression. The algorithm involves computation of first and second order partial derivatives, for which the corresponding computer source code is generated by Automatic Differentiation. Finally we present re-calibrated AVHRR radiances from a series of 10 sensors. It is shown that the new time series have much less match-up differences while being consistent with uncertainty statistics.