Estimating biases and error variances through the comparison of coincident satellite measurements

A framework for the statistical comparison of six coincident remote sounding measurements is presented, which distinguishes between additive and multiplicative biases. The relationship between multiplicative bias and error variance is explored, and three methods are proposed for producing sets of values for three comparison variables: the multiplicative bias, and the error variance for each of two instruments. We illustrate and compare the three methods through the comparison of coincident measurements of the relatively long‐lived stratospheric species O3, N2O, and HNO3 from two independent measurement sets: version 2.2 retrievals (with updated O3) from the Atmospheric Chemistry Experiment‐Fourier transform spectrometer onboard SCISAT‐1, and version 1.51 retrievals from the Earth Observing System Microwave Limb Sounder onboard Aura. We find that multiplicative bias between the two measurement sets, compared on a common vertical grid, is significant at some heights for O3 and N2O, and for all heights tested for HNO3. The most realistic estimates of measurement error are produced by a method which incorporates a third correlative data set into the analysis. Using this method, estimated error standard deviations (SDs) are comparable between the two instruments for O3 measurements, and are less than 10% of the mean measurement value between approximately 100 and 1 hPa. ACE N2O measurements are consistent with a 10% error SD at all heights tested, although the uncertainty of the estimates is large at heights above 5 hPa. Estimated MLS N2O error SDs are comparable with those for ACE in the lower stratosphere, but increase steeply with height. For HNO3, estimated error SDs are approximately 10% between 70 and 10 hPa for both instruments. At heights above 10 hPa and below 100 hPa, estimated ACE errors are significantly smaller than those for MLS.