基于时空克里格的土壤重金属时空建模与预测

土壤重金属或其他生态环境属性在时间和空间上均存在连续性和变异性,而目前的研究忽略了它们在时间维的变异。为了在预测时使用多时期采样数据,该文提出使用时空克里格方法对土壤重金属进行时空建模及预测,着重介绍了经验半方差值的计算、理论变异模型的形式及参数拟合、时空克里格估值算法、估值方差和精度随邻近点数量的变化及时空克里格制图。以武汉市青山区土壤重金属为例介绍了时空克里格建模及预测的流程。结果表明,时空克里格方法能够很好地描述土壤重金属在空间、时间和时空上3个部分的变异特征,能够利用其他时期的数据对预测时间点的属性进行插值,而多时期的属性空间分布图能够很好地反映土壤重金属的分布变化规律。该研究可为资源环境生态时空建模及预测研究提供参考。

Spatio-temporal modeling and prediction of soil heavy metal based on spatio-temporal Kriging

Abstract: Soil plays a very important role in the food chain, and hence is a very important pathway through which humans come into contact with most pollutants. Therefore, there is considerable interest in the best way to monitor the quality of the soil to ensure that it is managed sustainably. However, when the need to monitor the status of soil heavy metals for one area continuously occurs, the sampling and analysis procedures are expensive and time-consuming. Therefore, space-time interpolation is necessary because we can use previous soil sampling points to predict present spatial distribution with fewer soil samples. In this paper, spatio-temporal kriging was utilized to model and predict the spatio-temporal distribution of soil heavy metals. The main objectives of this study were 1) to explore the methods of obtaining an experimental spatio-temporal semivariogram; 2) to fit models for experimental spatio-temporal semivariogram; 3) to perform the algorithm of spatio-temporal kriging interpolation; 4) to evaluate the accuracy and uncertainty of spatio-temporal kriging under the conditions of different neighborhoods; and 5) to predict the spatio-temporal distribution of soil heavy metals of a study area using spatio-temporal kriging. The study area was east of Qingshan district, Wuhan city, Hubei province, China. To monitor the degree of soil contamination, we collected topsoil samples from the study area every year from 2011 to 2014. The number of soil samples from 2011, 2012, 2013, and 2014 were 45, 48, 55, and 48, respectively. The concentrations of cadmium (Cd), copper (Cu), lead (Pb), and zinc (Zn) were analyzed and used as experimental data. For Cd, Cu, and Zn, soil concentrations showed a constant increase from 2010 to 2014. However, the concentrations of Pb showed an increase from 2010 to 2013, followed by a small decrease in 2014. The results of K-S tests showed that Cd, Pb, and Cu did not follow a normal distribution, however, Zn followed a normal distribution. Therefore, the data of Cd, Pb, and Cu were transformed to their common logarithms to achieve a normal distribution. As the results of experimental spatio-temporal semivariance, the T parts of semivariograms for LogCd, LogCu, and LogPb were modeled with a linear model, for Zn was modeled with an exponential model; The S and ST parts of semivariograms for LogCd, LogCu, LogPb, and Zn were modeled with a spherical model. The method of fitting models was the genetic algorithm proposed by the author in 2011. With the results of theoretical variation semivariogram models of LogCd, LogCu, LogPb, and Zn, spatio-temporal kriging were performed. To determine the influence created by the number of neighborhoods, we decided to predict the unmeasured ST point using 4 to 20 of the nearest ST sampling points around the predicted ST site. The results showed that including more neighborhoods could result in less prediction variance. However, more neighborhoods might not produce less RMSE. In addition, ordinary kriging was performed using the same year sampling points while generating a spatial distribution for one year. The results of comparison RMSE generated by ordinary kriging and spatio-temporal kriging showed that spatio-temporal kriging can produce higher prediction accuracy than ordinary kriging. The results of spatio-temporal distribution generally reveal a tendency of Cd, Cu, and Zn concentrations to spread from the south-western part to the whole study area over time, while Pb contamination tends to concentrate mostly on the northern and western parts. The paper showed the computational process of spatio-temporal kriging and its application to soil heavy metals. The results showed that spatio-temporal kriging can improve the prediction accuracy with the help of multi - temporal data.