Spatial sampling is an important and frequently used method in investigating spatially distributed physical attributes, such as regional temperature, environmental pollution, cultivated land, organic material in soil, and so on. Traditional sampling methods, e.g., simple random sampling, systematic sampling and stratified sampling, have played a significant role in different spatial investigations. However, spatial correlation between spatial locations is not often taken account in practice, which affects not only the estimated results, but also the number and density of spatial samples.

Prof. WANG Jinfeng, Institute of Geographic Sciences and Natural Resources Research (IGSNRR) and his team have been engaged in the research of spatial statistic inference and optimization. Kriging is a mature spatial statistic method and often used to optimize spatial samples. But in practice, the second-order stationary assumption is hard to be guaranteed, especially for a large research area. A method named Mean of Surface with Non-homogeneity (MSN) was proposed to estimate the mean and its variance of complicated surfaces. It combines the merits of spatial stratification and Kriging based on the assumption that a non-homogeneous surface could be converted to several small homogeneous surfaces by stratification, which is possible in most cases. The estimated result of MSN is proven to be the best linear unbiased estimator (BLUE) of the true value.

Furthermore, the MSN method was applied to spatial sampling optimization due to its good merits. The density and distribution of spatial samples heavily affect the precision and reliability of estimated population attributes. An ideal spatial sampling scheme should consist of a minimal number of samples while can provide maximum estimated accuracy. Variance of the estimated mean is such an important indicator to assess the estimated result. In MSN, when some a priori information (semivariogram) of the global surface and strata are determined, the estimated variance only depends on the spatial samples’ position. For an expected variance given by user or research, the best configuration, including number and location, of spatial samples can be founded by a Monte Carlo - Particle Swarm optimization method. A software package is developed with the proposed method, and it can be downloaded freely from http://www.sssampling.org/msn .

The researches have been published in IEEE Transactions on Geoscience and Remote Sensing, 2009, 47(12): 4167-4174, and Environmental Modelling & Software (2010), doi:10.1016/j.envsoft.2010.10.006.