No abstract

Summary Existing predictive soil mapping (PSM) methods often require soil sample data to be sufficient to represent soil–environment relationships throughout the study area. However, in many parts of the world with only a limited quantity of soil sample data to represent the study area, this is still an issue for PSM application. This paper presents a method, named ‘individual predictive soil mapping’ (iPSM), which can make use of limited soil sample data for PSM. With the assumption that similar environmental conditions have similar soils, iPSM uses the soil–environment relationship at each individual soil sample location to predict soil properties at unvisited locations and estimate prediction uncertainty. Specifically, the environmental similarities of an unvisited location to a set of soil sample locations are used in a weighted average method to integrate the soil–environment relationships at sample locations for prediction and uncertainty estimation. As a case study, iPSM was applied to map soil organic matter (SOM) content (%) in the topsoil layer using two sets of soil samples. Compared with multiple linear regression (MLR), iPSM produced a more accurate SOM map (root mean squared error (RMSE) 1.43, mean absolute error (MAE) 1.16) than MLR (RMSE 8.54, MAE 7.34) the ability of the sample set to represent the study area is limited and achieved a comparable accuracy (RMSE 1.10, MAE 0.69) with MLR (RMSE 1.01, MAE 0.73) when the sample set could represent the study area better. In addition, the prediction uncertainty estimated by iPSM was positively related to prediction residuals in both scenarios. This study demonstrates that iPSM is an effective alternative when existing soil samples are limited in their ability to represent the study area and the prediction uncertainty in iPSM can be used as an indicator of its prediction accuracy.

Information System (LREIS), the Institute of Geographic Sciences and Natural Resources Research (IGSNRR), the Chinese Academy of Sciences; the University of Chinese Academy of Sciences (UCAS) in Beijing, China; and the Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application in Nanjing, China. Hui-Ran Gao is a graduate student at the LREIS, the IGSNRR, the Chinese Academy of Sciences; and the UCAS in Beijing, China. Liang-Jun Zhu (corresponding author) is a doctoral student at the LREIS, the IGSNRR, the Chinese Academy of Sciences; and the UCAS in Beijing, China. AXing Zhu is a professor at the Key Laboratory of Virtual Geographic Environment (VGE),

Current methods of spatial prediction are based on either the First Law of Geography or the statistical principle or the combination of these two. The Second Law of Geography contributes to the revision of these methods so they are adaptive to local conditions but at the cost of increasing demand for samples. This paper presents a new thinking about spatial prediction based on the Third Law of Geography which focuses on the similarity of geographic configuration of locations. Under the Third Law of Geography, spatial prediction can be made on the basis of the similarity of geographic configurations between a sample and a prediction point. This allows the representativeness of a single sample to be used in prediction. A case study in predicting spatial variation of soil organic matter content was used to compare the spatial prediction based the Third Law of Geography with those based on the First Law and the statistical principle. It is concluded that spatial prediction based on the Third Law of Geography does not require samples to be over certain size nor to be of a particular spatial distribution to achieve a high quality prediction. The prediction uncertainty associated with spatial prediction based on the Third Law of Geography is more indicative to quality of the prediction, thus more effective in allocating error reduction efforts. These properties make spatial prediction based on the Third Law of Geography more suitable for prediction over large and complex geographic areas.