Table 3.

Prediction errors of the different methods for the independent validation points. MAE, mean absolute error; RMSE, root mean square error; MRE, mean relative error; OK, ordinary kriging; RK, regression kriging; HASM_RBFNN, the combined method (HASM_RBFNN) developed using high-accuracy surface modelling (HASM) and radial basis function neural network (RBFNN) modelling, taking into account the spatial non-stationarity of the relationships between soil Cd and the auxiliary variables; HASM_ RBFNNs, the combined method (HASM_RBFNN), without taking into account the spatial non-stationarity of the relationships.

Methods	Sample number	MAE	RMSE	MRE
HASM_RBFNN	66	0.034	0.042	15.715
HASM_RBFNNs	66	0.036	0.045	16.622
RK	66	0.037	0.046	17.746
OK	66	0.040	0.051	18.083