Dealing with spatial heterogeneity in pointwise-to-griddeddata comparisons

Most studies on validation of satellite trace gas retrievals or atmospheric chemical transport models assume that pointwise measurements, which roughly represent the element of space, should compare well with satellite (model) pixels (grid box). This assumption implies that the field of interest must possess a high degree of spatial homogeneity within the pixels (grid box), which may not hold true for species with short atmospheric lifetimes or in the proximity of plumes. Results of this assumption often lead to a perception of a nonphysical discrepancy between data, resulting from different spatial scales, potentially making the comparisons prone to overinterpretation. Semivariogram is a mathematical expression of spatial variability in discrete data. Modeling the semivariogram behavior permits carrying out spatial optimal linear prediction of a random process field using kriging. Kriging can extract the spatial information (variance) pertaining to a specific scale, which in turn translates pointwise data to a gridded space with quantified uncertainty such that a grid-to-grid comparison can be made. Here, using both theoretical and real-world experiments, we demonstrate that this classical geostatistical approach can be well adapted to solving problems in evaluating model-predicted or satellite-derived atmospheric trace gases. This study suggests that satellite validation procedures using the present method must take kriging variance and satellite spatial response functions into account. We present the comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2 columns against 11 Pandora spectrometer instrument (PSI) systems during the DISCOVER-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 , r 2 = 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 , r 2 = 0.72), illustrating that OMI possibly has a constant systematic bias over the area. To avoid gross errors in comparisons made between gridded data vs. pointwise measurements, we argue that the concept of semivariogram (or spatial autocorrelation) should be taken into consideration, particularly if the field exhibits a strong degree of spatial heterogeneity at the scale of satellite and/or model footprints.