We examine how passive and active observations are useful to evaluate an air quality analysis. By leaving out observations from the analysis, we form passive observations, and the observations used in the analysis are called active observations. We evaluated the surface air quality analysis of O₃ and PM_2.5 against passive and active observations using standard model verification metrics such as bias, fractional bias, fraction of correct within a factor of 2, correlation and variance. The results show that verification of analyses against active observations always give an overestimation of the correlation and an underestimation of the variance. Evaluation against passive or any independent observations display a minimum of variance and maximum of correlation as we vary the observation weight, thus providing a mean to obtain the optimal observation weight. For the time and dates considered, the correlation between (independent) observations and the model is 0.55 for O₃ and 0.3 for PM_2.5 and for the analysis, with optimal observation weight, increases to 0.74 for O₃ and 0.54 for PM_2.5. We show that bias can be a misleading measure of evaluation and recommend the use of a fractional bias such as the modified normalized mean bias (MNMB). An evaluation of the model bias and variance as a function of model values also show a clear linear dependence with the model values for both O₃ and PM_2.5.

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.