Enhancing spatial estimates of metal pollutants in raw wastewater irrigated fields using a topsoil organic carbon map predicted from aerial photography

Various approaches have been used to estimate metal pollutant element (TE) contents at unsampled locations in a 15-ha contaminated site located in the plain of Pierrelaye–Bessancourt (about 24 km Northwest of Paris). 87 samples of soil plough layer were randomly sampled at each mesh of a regular square grid over the whole study area and the total contents of Cd, Cr, Cu, Ni, Pb, and Zn were measured. A first set of 50 measurements, randomly selected from the 87 samples, was used for the prediction and another set of 37 measurements was kept for the validation. Topsoil organic carbon contents (SOC) were measured at 75 sites with 50 measurements sharing the same locations as TE. An aerial photography of the study area showing bare soils was selected for relating brightness intensities and SOC. Mapping procedures used were ordinary kriging (OK), cokriging (COK), collocated cokriging (CC), and kriging with external drift (KED). SOC maps used as exhaustively sampled information in KED and CC of TE were obtained by KED and CC procedures, respectively, accounting for 75 SOC measurements and the brightness intensities of numerical counts provided by the visible bands of the aerial photograph bare soils. Consequently, for each TE, four maps were generated: two maps resulting from KED and CC procedures (KED-SOC75P, CC-SOC75P), another one provided by standard cokriging (COK-TE50SOC75) accounting for TE prediction set plus 75 SOC measurements, and the last one corresponding to that estimated by ordinary kriging from only prediction set measurements (OK50). Three indices: (1) the mean prediction error (ME) and the mean absolute prediction error (|ME|); (2) the root mean square error (RMSE); and (3) the relative improvement (RI) of accuracy, as well as residuals analysis, were computed from the validation set (observed data) and predicted values. On the 37 test data, the results showed that the more accurate predictions were systematically those obtained by kriging accounting for SOC map predicted by KED from 75 SOC measurements and brightness values of the aerial photo (KED-SOC75P) followed closely by CC-SOC75P procedure, except for Cu and Zn where CC-SOC75P appeared to be slightly more accurate than KED-SOC75P. In regard to the RI of accuracy between prediction methods, the results confirmed once for all the benefit of accounting for SOC data set plus the exhaustively sampled information provided by the aerial photography regardless of the considered TE. Nevertheless, for Cd, Pb, and Zn, the RI of accuracy was less than 20% between the two most accurate methods (KED-SOC75P and CC-SOC75P) and standard cokriging in which the information provided by the aerial photography is ignored when mapping.
The sensitivity of KED-SOC75P and CC-SOC75P approaches to the sampling density of the target variables (TE) was assessed using 10 random subsets of different sizes (25 and 33 observations) drawn from a prediction set that includes 50 data.
Results have shown that the TE estimates by KED-SOC75P and CC-SOC75P approaches using only 25 TE samples were much more accurate than the estimates performed by OK50 and COK-TE50SOC75 approaches that use the whole samples of the prediction set. Moreover, the RI of accuracy was reduced by less than 15% if the original sampling density was reduced by a third.