Abstract
We present a general theory of estimation of analysis error covariances based on cross-validation as well as a geometric interpretation of the method. In particular, we use the variance of passive observation-minus-analysis residuals and show that the true analysis error variance can be estimated, without relying on the optimality assumption. This approach is used to obtain near optimal analyses that are then used to evaluate the air quality analysis error using several different methods at active and passive observation sites. We compare the estimates according to the method of Hollingsworth-Lönnberg, Desroziers et al., a new diagnostic we developed, and the perceived analysis error computed from the analysis scheme, to conclude that, as long as the analysis is near optimal, all estimates agree within a certain error margin.
Highlights
At Environment and Climate Change Canada (ECCC) we have been producing hourly surface pollutants analyses covering North America [1,2,3] using an optimum interpolation scheme which combines the operational air quality forecast model GEM-MACH output [4] with real-time hourly observations of O3, PM2.5, PM10, NO2, and SO2 from the AirNow gateway with additional observations from Canada
As we changed the ratio of observation error to background error variances γ = σo2 /σb2, while keeping the sum σo2 + σb2 equal to var(O − B), we found a minimum in var(O − A) in the passive observation space
We showed that analysis error variance can be estimated and optimized, without using a model forecast, by partitioning the original observation data set into a training set, to create the analysis, and an independent set, used to evaluate the analysis
Summary
At Environment and Climate Change Canada (ECCC) we have been producing hourly surface pollutants analyses covering North America [1,2,3] using an optimum interpolation scheme which combines the operational air quality forecast model GEM-MACH output [4] with real-time hourly observations of O3 , PM2.5 , PM10 , NO2 , and SO2 from the AirNow gateway with additional observations from Canada These analyses are not used to initialize the air quality model and we wish to evaluate them by cross-validation, that is by leaving out a subset of observations from the analysis to use them for verification. In this second-part paper, we formalize this result, develop the principles of estimation of the analysis error covariance by cross-validation, and apply it to estimate and optimize the analysis error covariance of ECCC’s surface analyses of O3 and PM2.5
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