Multi-objective optimization sampling based on Pareto optimality for soil mapping

Abstract

Precise mapping based on sampling data is meaningful for efficient soil quality management. The distributions of sampling sites in feature space and geographical space, as well as the distribution of point pairs at different distances, all significantly impact mapping precision, and these three aspects should all be considered in a sampling design. Although optimizing the spread of sampling sites in the above three aspects has been realized and addressed in previous studies, their tradeoff relationship and influence on mapping accuracy have not been comprehensively investigated, partly due to the limitations of weighting-based optimization way. In this article, we proposed a sampling strategy based on Pareto optimality to examine the tradeoff relationship among the three aspects and their influence on interpolation precision. Based on soil organic matter data from Yi’an district, we applied this approach to generate sampling schemes and analyze their distributions and prediction errors. Single-objective optimization of these three aspects was also conducted for comparison. The results revealed that: (1) the sampling strategy that simultaneously optimizes the distributions of sampling sites in the three aspects was able to obtain sampling designs with higher mapping accuracy than the method that only optimizes one aspect. (2) There was an apparent synergistic relationship between the distributions of sampling sites in feature space and geographical space. However, these objectives had antagonistic relationships with the distribution of point pairs at different distances. (3) When considering the tradeoff among the three aspects, the more even the distribution in geographical space was, the higher the mapping accuracy they produced. Furthermore, more even distribution in feature space improved the mapping accuracy, but the benefit faded after a certain degree, whereas the mapping accuracy initially increased as the distance distribution of point pairs in different intervals became more even but subsequently declined beyond a certain point. Attention should be given to the tradeoff relationship and impact on interpolation when sampling for mapping. In similar scenarios like the study case, it is recommended that sampling sites should be distributed in feature space with more than 45% evenness of the optimal state and then distributed in geographical space as evenly as possible, while the distribution of point pairs should not exceed 65% evenness of its optimal state when the sample size range is approximately 50 to 150. This study provides helpful references for scientific sampling with the goal of precise mapping.