Does spatial auto-correlation call for a revision of latest heavy metal and nitrogen deposition maps?

Background: Within the framework of the Convention on Long-range Transboundary Air Pollution atmospheric depositions of heavy metals and nitrogen as well as critical loads/levels exceedances are mapped yearly with a spatial resolution of 50 km by 50 km. The maps rely on emission data and are calculated by use of atmospheric modelling techniques. For validation, EMEP monitoring data collected at up to 70 sites across Europe are used. This spatially sparse coverage gave reason to test if the chemical and physical relations between atmospheric depositions and their accumulation in mosses collected at up to 7000 sites throughout Europe can be quantified in terms of statistical correlations which, if proven, could be used to calculate deposition maps with a higher spatial resolution. Indeed, combining EMEP maps on atmospheric depositions of cadmium, lead and nitrogen and the related maps of their concentrations in mosses by use of a Regression Kriging approach yielded deposition maps with a spatial resolution of 5 km by 5 km. Since spatial auto-correlation can make testing of statistical inference too liberal, the investigation at hand was to validate the 5 km by 5 km deposition maps by analysing if spatial auto-correlation of both EMEP deposition data and moss data impacted on the significance of their statistical correlation and, thus, the validity of the deposition maps. To this end, two hypotheses were tested: 1. The data on deposition and concentrations in mosses of heavy metals and nitrogen are not spatially auto-correlated significantly. 2. The correlations between the deposition and moss data lack statistical significance due to spatial autocorrelation. Results: As already published, the regression models corroborated significant correlations between the concentrations of heavy metals and nitrogen in atmospheric depositions on the one hand and respective concentrations in mosses on the other hand. This investigation proved that atmospheric deposition and bioaccumulation data are spatially auto-correlated significantly in terms of Moran’s I values and, thus, hypothesis 1 could be rejected. Accordingly, the degrees of freedom were reduced. Nevertheless, the results of the calculations regarding the reduced degrees of freedom indicate that the statistical relations between atmospheric depositions and bioaccumulations remained statistically significant so that hypothesis 2 could be rejected, too. Conclusions: The positive auto-correlation in data on atmospheric deposition and bioaccumulation does not call for a revision of the 5 km by 5 km deposition maps published in recent papers. Therefore we can conclude that the European moss monitoring yields data that support the validation of modelling and mapping of atmospheric depositions of heavy metals and nitrogen at a high spatial resolution compared to the 50 km x 50 km EMEP maps.