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. Most studies on validation of satellite trace gas retrievals or atmosphericchemical transport models assume that pointwise measurements, which roughlyrepresent the element of space, should compare well with satellite (model)pixels (grid box). This assumption implies that the field of interest mustpossess a high degree of spatial homogeneity within the pixels (grid box),which may not hold true for species with short atmospheric lifetimes or inthe proximity of plumes. Results of this assumption often lead to aperception of a nonphysical discrepancy between data, resulting fromdifferent spatial scales, potentially making the comparisons prone tooverinterpretation. Semivariogram is a mathematical expression of spatialvariability in discrete data. Modeling the semivariogram behavior permitscarrying out spatial optimal linear prediction of a random process fieldusing kriging. Kriging can extract the spatial information (variance)pertaining to a specific scale, which in turn translates pointwise data toa gridded space with quantified uncertainty such that a grid-to-gridcomparison can be made. Here, using both theoretical and real-worldexperiments, we demonstrate that this classical geostatistical approach canbe well adapted to solving problems in evaluating model-predicted orsatellite-derived atmospheric trace gases. This study suggests thatsatellite validation procedures using the present method must take krigingvariance and satellite spatial response functions into account. We presentthe comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2columns against 11 Pandora spectrometer instrument (PSI) systems during theDISCOVER-AQ campaign over Houston. The least-squares fit to the paired data shows a low slope (OMI=0.76×PSI+1.18×1015 molecules cm−2, r2=0.66), which is indicative of varying biases in OMI. This perceived slope, induced by the problem of spatial scale, disappears in the comparison of the convolved kriged PSI and OMI (0.96×PSI+0.66×1015 molecules cm−2,r2=0.72), illustrating that OMI possibly has a constant systematicbias over the area. To avoid gross errors in comparisons made betweengridded data vs. pointwise measurements, we argue that the concept ofsemivariogram (or spatial autocorrelation) should be taken intoconsideration, particularly if the field exhibits a strong degree of spatialheterogeneity at the scale of satellite and/or model footprints.

Dealing with spatial heterogeneity in pointwise-to-gridded- data comparisons