几种地统计学方法在县域土壤空间信息处理上的应用与研究
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摘要
地统计学,自从诞生的那一刻开始,就和应用学科(如探矿)紧密结合,共同发展,已取得累累硕果。特别是近些年来,它越来越深入地渗透到了诸如土壤、环境、生态、气象、经济和人文等领域,具有越来越重要的应用前景。当然,通过这种应用,地统计学在理论方法上也找到了新的增长点,出现了新的有意义的问题和崭新的思维,这些新思想反过来又可以促进其应用在广度和深度上进一步拓展。虽然本研究没有涉及,但值得指出的是,近些年来还出现了一些克里格框架之外的地统计学理论和方法,尚待发展和广泛认可。
在土壤和环境科学领域,许多研究者已经对地统计学算法的特点进行了深入研究,并针对结合软数据、空间不确定性评估等现实问题提出了许多改进方法。然而,无论从理论算法还是应用实践层面仍有很多极具挑战性的问题亟待解决,如：
·在土壤属性的地统计学制图领域,是否存在较以前的残差克里格更好的结合范畴数据的方法?
·能否结合范畴数据进行随机模拟,进而减小模拟结果的不确定性?
·在重金属污染源解析中,除了能够利用样本观测数据定性推测排放源的数目及其性质,能否进一步定量计算各个污染源所排放重金属的空间分布格局?
·是否随机模拟前一定需要对样本观测数据进行转换?如何利用直接顺序模拟的结果来评估土壤属性的空间不确定性?
·由于克里格的平滑效应以及指示克里格中污染概率阈值的确定通常比较主观,故直接采用克里格法和指示克里格法对污染物区域划定是不合理的。那么是否存在一种较为客观的污染范围划定方案?
·如何在生态风险评价中考虑污染物的空间异质性和空间不确定性?
·如何利用地统计学研究土壤主要营养元素的有效性比率?有鉴于此,本文以探索新的理论和方法、解决应用实际问题为目的,围绕地统计学理论及其在土壤和环境科学中的应用问题做了多方面的研究,取得了如下七个方面的新成果：
(1)将面点克里格引入土壤属性制图领域,为精准农业和环境管理提供了一个更为适合的土壤属性制图方法。
近十多年来,使用样本观测数据来对土壤养分进行空间分布的制图引起了广泛的关注。但为提高制图质量而在大尺度上进行大量高密度田间取样在经济和劳力花费等方面都是不现实的,对于地形复杂和偏远地区尤其如此。土地利用类型通常对局部土壤养分含量存在影响,那么对土地利用类型和土壤养分含量之间的这种关系加以利用,则可以达到以有限稀疏样本数据进行较高质量土壤和环境属性制图的目的。最近出现的面点克里格(AAPK:area-and-point kriging)为结合范畴信息提供了一个新的插值技术。本研究结合402个点样本数据和土地利用信息,利用面点克里格制作了中国汉川县土壤全氮(TN:total nitrogen)含量的空间分布图。同时普通克里格(OK:ordinary kriging)和残差克里格(RK:residual kriging)被用于参照方法,用来评价面点克里格的效果。结果表明：(1)土地利用类型对土壤全氮的空间分布有重要影响；(2)135个验证位的实测值与AAPK预测值之间相比与RK和OK预测值之间具有更强的相关性、更低的平均误差和均方根误差；(3)AAPK较RK和OK产生更小的误差方差。这意味着AAPK为增加土壤全氮插值精度的有效方法。
(2)提出了一种新的结合范畴数据的随机模拟方法,并运用于实际的案例研究,丰富和发展了随机模拟理论。
地统计学经常被用来描述土壤属性含量的空间变异。然而,由地统计学随机算法产生的模拟实现图能够更好的代表实际的空间分布状况。土地利用类型通常会影响局部土壤氮的含量水平,故将土地利用类型结合进土壤氮的地统计学随机模拟中是可取的。据此,作者提出了sequential Gaussian simulation incorporating land use information (SGSLU)的随机模拟算法。在这项研究中,402个采样点的土壤全氮观测数据与土地利用范畴信息相结合,利用作者提出的SGSLU算法来模拟了土壤全氮的空间分布,并将SGSLU与OK和顺序高斯模拟(SGS:sequential Gaussian simulation)的预测结果做了比较。其中135个验证数据被用来评估SGSLU在提高预测精度和减小预测不确定性方面的改善程度。结果表明,验证数据与SGSLU的最佳预测(即E-type估计)的相关性更大,且平均误差和均方根误差更小。而且根据精确图和最佳统计量G, SGUSLU在减小预测结果的不确定性方面优于SGS。故SGSLU在提高预测的准确性和减少土壤全氮预测的不确定性方面,是一种行之有效的方法,同时模拟实现之间的差异代表了土壤全氮预测的空间不确定性。这些知识为土壤全氮缺乏和丰富区域的划定提供了定量信息。
(3)将主成份分析／绝对主成分分数(PCA/APCS)模型引入土壤污染源解析领域,同时将其与地统计学结合,提出了一个土壤重金属污染源解析的综合方法。
目前在土壤污染源确定方面,主成份分析(PCA)是最常用的工具。源解析是在源确定方面进一步的定量化。PCA/APCS不需要事先了解源的个数及其特点,也就是说可以在源未知的情况下进行源解析,因此该模型被广泛应用。源解析技术已被广泛应用于大气环境和水环境研究中,但目前在土壤重金属污染领域运用该技术的研究还鲜有报道。PCA的结果与源贡献相关,但是并不成比例,故其结果只能定性的推测潜在的污染源而不能直接用于源解析。应用PCA/APCS受体模型不但可以定量地确定每个变量对每个源的载荷,还可以定量确定源对其重金属的平均贡献量和在每个采样点的贡献量。但受体模型源解析的结果仍缺乏直观视觉效果,不利于在源未知的情况下利用源解析结果进行源识别(如隐蔽性污染源)。为了便于直观理解每个污染源的贡献量的空间分布和在源未知的情况下推测具体的污染源,我们在本文中将地统计学和受体模型结合起来,利用普通克里格法对由PCA/APCS受体模型获得的采样点的源绝对贡献量插值。因此该研究的目的是提出一个土壤重金属污染源解析的综合方法。同时我们根据污染数据集所能提取的信息的不同,如是否能直接从PCA推断污染源的性质,单个重金属污染物的源解析是否需要多元数据集的源解析技术等问题,用两个案例加以展示说明。
(4)将直接顺序模拟技术引入土壤和环境属性的不确定性评估中,扩展了直接顺序模拟的应用范围。
最常用的随机模拟方法为顺序高斯模拟和顺序指示模拟,这两种模拟方法使用前必须进行数据转换,而数据转换必然伴随着模拟结果精度的降低。最近出现的直接顺序模拟克服了这一弱点。本研究采用直接顺序模拟这一新的模拟技术模拟了土壤全氮的空间分布。利用模拟的结果,定量评估了土壤全氮的空间不确定性。同时普通克里格被用于参照方法,用于说明直接顺序模拟技术在不确定性评估方面的优点。
(5)使用顺序高斯模拟和传递函数模拟了由划定土壤镍污染范围所引起的健康风险损失和补救风险损失,并提出了一个基于最小化期望损失标准的污染区域划定方案。
由于克里格插值的平滑效应,采用克里格插值的结果作为污染范围的划定是不恰当的。而超概率阈值方案中,由于概率阈值的设定通常比较主观,故这一划定方案也缺乏客观的科学依据。地统计学模拟实现值因克服了插值的平滑效应,故较克里格最佳预测值更能准确的代表所研究变量的空间异质性。模拟实现之间的差异代表了空间的不确定性。这些实现可以作为传递函数的输入数据,以进一步评估产生的因变量的不确定性。本研究将研究区域的镍模拟实现值输入传递函数,以计算健康风险损失(低估其含量而未补救)和补救风险损失(高估其含量,采取补救措施)。模拟的镍含量的不确定性通过传递函数传播,导致不确定性的健康风险损失和补救风险损失。这样,两种风险损失就可以通过镍的反应值来评估。同时在该研究中,由于不同的土地利用类型中镍的危害程度不同,本研究也在传递函数中加以考虑。最后作者依据最小化风险损失为标准,划定了重金属镍污染的范围。这样为污染的划定提供了一个新的思路。
(6)结合地统计学随机模拟模型和Hakanson潜在生态风险指数法,提出了一种生态风险空间分析的综合方法。
Hakanson潜在生态风险指数法不但考虑了土壤沉积物中重金属的毒性、重金属在沉积物中普遍的迁移转化规律以及评价区域对重金属污染的敏感性,而且利用重金属总量分析测试结果与区域背景值进行比较,消除了区域差异及异源污染影响。目前该方法已被国内外广泛接受,已成为生态风险评价方面最常使用的方法之一。地统计学在生态风险评估领域是个被忽视的方法。本研究以结合地统计学随机模拟和Hakanson (?)替在生态风险指数法,提出了一种综合的空间分析生态风险的方法。本研究先对各个重金属元素含量进行地统计学随机模拟,然后将模拟实现值输入Hakanson潜在生态风险指数法,得到每个重金属元素所引起的生态风险系数,这样由各个重金属元素所引起的生态风险的空间不确定性被量化。而且由所有重金属元素引起的生态风险指数的最佳估计可由各个重金属元素的生态风险系数的期望值之和得到。
(7)地统计学在土壤主要营养元素有效性比率分布格局上的一个应用。
全氮(TN)、全磷(TP)、全钾(TK)、AN、AP和AK的含量及土壤各主要元素的有效性比率(即氮、磷和钾元素的有效量与全量之比)为土壤系统主要营养的重要指标。对于农业生产和环境保护至关重要。土壤营养元素中,比较高的有效性比率意味着该元素更加有利于植物的吸收,同时也暗示该元素更加容易进入水体。因此,为了更加有效的对农作物施肥和环境进行管理,了解主要营养物质的有效量、全量和有效性比率的空间分布格局显得非常必要。在过去的几十年内,很多研究者研究了氮、磷和钾各中形态的空间分布格局。但这些研究主要是关注这些主要营养元素的全量或有效量,缺少对其有效性比率的研究记录。本研究采用多元统计分析土壤有效性比率与土壤属性之间的关系,找出了影响有效性比率的控制因子；同时利用地统计学分别对主要营养元素的全量和有效量分布进行插值,最后得到有效性比率的空间分布格局。
Geostatistics has been evovling with applied sciences such as mining. In two recent decades, it has become more and more popular in soil science, environmental science, ecology, meteorology and even in economics and human science. It is through these applications that geostatistics obtained many new ideas for its futher development. Indeed, scientists in the fields of soil and environmental sciences have investigated geostatistics for various application perspectives, for example, soft data integration, stochastic simulation and spatial uncertainty assessment. However, further study is needed to address some important issues in both methodology and applications in soil and environmental sciences. This study explored the following seven subtopics:
■Whether this is an effective geostatistical method better than previously used residual kriging to integrating categorical information into the geostatistical mapping of soil properties.
■Whether categorical data can be combined into stochastic simulation and thus reduce the spatial uncertainty of simulated results of soil attributes.
■Whether we can obtain the spatial distribution maps of the absolute contributions of pollutant sources from multiple data sets of samples in different spatial positions.
■Whether data transformation conducted in previous stochastic simulations can be avoid; and if it is feasible then how to assess the spatial uncertainty of soil properties using such method.
■Because kriging has the smoothing effect and the division of pollution probability thresholds is usually subjective, whether there is a more objective delineation method to map polluted areas.
■How to assess the spatial uncertainty of ecological risks that account for the spatial heterogeneity and uncertainty of pollutants in ecological risk assessment study.
■How to map effectively the spatial distribution of the availability of soil macronutrients.
We conducted some explorations in developing geostatistcs and expanding its application breadth and depth. This dissertation achieved the following major results:
(1) The area-and-point kriging was introduced to the field of predictive soil mapping, and it was proven to be a better method for precision agriculture and environmental management.
Mapping the spatial distribution of soil nutrient contents from sample data received much attention in recent decade. Accurately mapping soil nutrients purely based on sample data, however, is difficult due to the sparsity and high cost of samples. Land use types usually influence the contents of soil nutrients at local level and it is desirable to integrate such information into the predictive mapping. The area-and-point kriging (AAPK) method, which was proposed recently, may provide an interpolation technique for such purpose. This study mapped the soil total nitrogen (TN) distribution of Hanchuan County, China, using AAPK with402point sample data and land use information. Ordinary kriging (OK) and residual kriging (RK) were compared to evaluate the performance of AAPK. Results showed that:(1) land use types had important impacts on the spatial distribution of soil TN;(2) measured data at the135validation locations had stronger correlation with the predicted data by AAPK than with those by RK and OK, and the mean error and root mean square error with AAPK were lower than those with RK and OK; and (3) AAPK generated smaller error variances than RK and OK did. This means AAPK represents an effective method for increasing the interpolation accuracy of soil TN.
(2) We developed a new geostatistical stochastic simulation method by combining categorical land use data and sequential Gaussian simulation, and applied it to a case study. This may improve the application value of sequential Gausian simulation.
Geostatistics is often used to characterize the spatial variability of soil properties. However, simulated realization maps by stochastic geostatistical algorithms can represent the spatial distribution more realistically than the kriged optimal map. Because land use types usually influence the local content level of soil nitrogen, it is desirable to integrate land use information into the geostatistical stochastic simulation of soil nitrogen. In this study, the data of TN contents at402sampling sites and the categorical information of land use maps were integrated together for performing the sequential Gaussian simulation incorporating land use information (SGSLU). A comparison of SGSLU with ordinary kriging (OK) and sequential Gaussian simulation (SGS) in their performances was conducted, and135validation samples were used to assess the improvement of SGSLU over SGS in prediction quality and uncertainty reduction of soil TN contents. Results showed that the validation data were more correlated with the optimal prediction (i.e., E-type estimates) data of SGSLU than with those of OK and of SGS, and the mean error and root mean square error with the optimal prediction of SGSLU were lower than those with OK and SGS. Further, according to accuracy plots and the goodness statistic G, SGSLU performed better in uncertainty modeling than SGS did. We conclude that land use types have important impacts on the spatial distribution of soil TN, and SGSLU is an effective method for increasing the prediction accuracy and reducing the uncertainty in soil TN prediction. The differences among realizations represent the spatial uncertainty of soil TN prediction and such knowledge will be helpful to evaluate the delineation of soil TN deficiency and abundance areas for agricultural and environmental management.
(3) We introduced the principal component analysis/absolute principal component scores (PCA/APCS) model to the field of the source apportionment of pollution sources and developed a more effective method for source apportionment through combined gestatstics and PCA/APCS.
At present, principal component analysis is the most often used method in the field of identifying pollution sources. Source apportionment is further quantitative at the basis of PCA. PCA/APCA has the advantage of not requiring the knowledge in the number of sources and source characteristics in advance, thus being widely used in source apportionment studies. Source apportionment is an underutilized technique in soil science. The application of PCA to environmental data has experienced significant setbacks because its outcomes are correlated with but not proportional to source contributions. Consequently, PCA results can detect latent sources only qualitatively and cannot be used directly for source apportionment. With the PCA/APCA method, it is possible to determine quantitatively the loading of each variable from each source, and the contribution of that source to the total pollutant concentration. However, the results of the PCA/APCA lack visual effect, and are not conductive to identification of the locations of the pollution sources (such as hidden pollution source). In order to facilitate understanding the spatial distribution of the absolute contribution of each pollution source and identifying the specific pollution sources, geostatistics and PCA/APCS were combined together, that us, kriging is used to interpolate the absolute contribution of each source obtained from PCA/APCS. The purpose of this study is to propose an integrated approach for source appointment of soil pollution source. At the same time, two case studies were conducted according to the different characters of the data set and whether multiple data sets should be used in source apportionment of a single pollution matter.
(4) Direct sequential simulation (DSS) was introduced for uncertainty assessment of soil properties, which may help to expand the application scope of DSS.
Sequential Gaussian simulation and sequential indicator simulation are the most often used method to simulate the soil and environmental properties. A data transformation process must be carried out in advance when using the two simulation technologies; this process will inevitably lead to the reduction of simulation accuracy. The recently emerged direct sequential simulation (DSS) method overcomes this weakness. In this study, the spatial uncertainty assessment of the soil total nitrogen was performed. Ordinary kriging was used as a reference method to illustrate the advantages of the DSS method in uncertainty assessment.
(5) We simulated the risk costs of delineating pollution areas by combing the method of sequential Gaussian simulation with transfer functions, and at the meantime a method of delineating pollution areas based on the standard of minimum expected costs was proposed.
As kriging interpolation has the smoothing effect, it is not appropriate to use the kriged results as the standard data for delineating pollution areas. In addition, as the setup of probability thresholds is usually subjective in estimating threshold exceedance probabilities, such delineation scheme lacks scientific basis. Geostatistical simulated realization maps can represent the spatial heterogeneity of the studied spatial variable more realistically than the kriged optimal map because they overcome the smoothing effect of interpolation. The difference among realizations indicates spatial uncertainty. These realizations may serve as input data to transfer functions to further evaluate the resulting uncertainty in impacted dependent variables. In this study, sequential Gaussian simulation was used to simulate the spatial distribution of soil nickel (Ni) in the study area. Simulated realizations were then imported into transfer functions to calculate the health risk costs caused by Ni polluted areas being ignored in remediation due to underestimation of the Ni contents and the remediation risk costs caused by unnecessary remediation of unpolluted areas due to overestimation of the Ni contents. The uncertainty about the input Ni content values thus propagated through these transfer functions, leading to uncertain responses in health risk costs and remediation risk costs. The spatial uncertainties of the two forms of risk costs were assessed based on the response realizations. Because the risk of exposure of soil Ni to humans and animals is generally greater in contaminated arable lands than in industrial and residential lands, the effect of land use types was also taken into account in risk cost estimation. Most of the south part of the study area was delineated as contaminated according to the minimum expected cost standard. This study shows that sequential Gaussian simulation and transfer functions are valuable tools for assessing risk costs of soil contamination delineation and associated spatial uncertainty.
(6) An integrated approach was proposed by combing sequential Gaussian simulation and Hakanson potential ecological risk index.
Potential ecological risk index was introduced to assess the degree of heavy metal pollution in soils, which was originally introduced by Hakanson (1980), according to the toxicity of heavy metals and the response of the environment. At present, potential ecological risk index (RI) is one of the most commonly used tools for ecological risk assessment. However, while the spatial distribution of heavy metals is heterogeneous the spatial heterogeneity was seldomly accounted for in previous literature related to ecological risk study. In this study, a comprehensive method for spatial analysis of ecological risks was proposed through combining stochastic simulation and Hakanson potential ecological risk index. Sequential Gaussian simulation (SGS) is usually used to describe joint realizations of pollutants. The objective of this study is to generate a number of realizations in the studied region, which can effectively reflect the uncertainty resulting from heterogeneity, and feed them into the model of the potential ecological risk index, so that the spatial uncertainty of the ecological risks resulting from the spatial uncertainty of pollutants could be quantified. The E-type estimates of the Hakanson potential ecological risk indexes could be obtained through summing the E-type estimates of the potential ecological risk factors for signal metals.
(7) An application of geostatistics in the spatial distribution pattern of N, P and K availability ratios was performed.
Many studies on soil N, P and K. were conducted in the past several decades. Most of them, however, were focused on the total contents or available contents of these elements in agricultural fields, and few characterized their variability in soils. In this study, the controlling factors on the spatial variability of soil N, P and K availability ratios were determined using multivariate statistics;and geostatistcs were adopted to map the spatial distribution patterns of the soil available contents and total contents of the macronutrients, and then N, P and K availability ratios were obtained from the result of the geostatistics analysis.
在土壤和环境科学领域,许多研究者已经对地统计学算法的特点进行了深入研究,并针对结合软数据、空间不确定性评估等现实问题提出了许多改进方法。然而,无论从理论算法还是应用实践层面仍有很多极具挑战性的问题亟待解决,如：
·在土壤属性的地统计学制图领域,是否存在较以前的残差克里格更好的结合范畴数据的方法?
·能否结合范畴数据进行随机模拟,进而减小模拟结果的不确定性?
·在重金属污染源解析中,除了能够利用样本观测数据定性推测排放源的数目及其性质,能否进一步定量计算各个污染源所排放重金属的空间分布格局?
·是否随机模拟前一定需要对样本观测数据进行转换?如何利用直接顺序模拟的结果来评估土壤属性的空间不确定性?
·由于克里格的平滑效应以及指示克里格中污染概率阈值的确定通常比较主观,故直接采用克里格法和指示克里格法对污染物区域划定是不合理的。那么是否存在一种较为客观的污染范围划定方案?
·如何在生态风险评价中考虑污染物的空间异质性和空间不确定性?
·如何利用地统计学研究土壤主要营养元素的有效性比率?有鉴于此,本文以探索新的理论和方法、解决应用实际问题为目的,围绕地统计学理论及其在土壤和环境科学中的应用问题做了多方面的研究,取得了如下七个方面的新成果：
(1)将面点克里格引入土壤属性制图领域,为精准农业和环境管理提供了一个更为适合的土壤属性制图方法。
近十多年来,使用样本观测数据来对土壤养分进行空间分布的制图引起了广泛的关注。但为提高制图质量而在大尺度上进行大量高密度田间取样在经济和劳力花费等方面都是不现实的,对于地形复杂和偏远地区尤其如此。土地利用类型通常对局部土壤养分含量存在影响,那么对土地利用类型和土壤养分含量之间的这种关系加以利用,则可以达到以有限稀疏样本数据进行较高质量土壤和环境属性制图的目的。最近出现的面点克里格(AAPK:area-and-point kriging)为结合范畴信息提供了一个新的插值技术。本研究结合402个点样本数据和土地利用信息,利用面点克里格制作了中国汉川县土壤全氮(TN:total nitrogen)含量的空间分布图。同时普通克里格(OK:ordinary kriging)和残差克里格(RK:residual kriging)被用于参照方法,用来评价面点克里格的效果。结果表明：(1)土地利用类型对土壤全氮的空间分布有重要影响；(2)135个验证位的实测值与AAPK预测值之间相比与RK和OK预测值之间具有更强的相关性、更低的平均误差和均方根误差；(3)AAPK较RK和OK产生更小的误差方差。这意味着AAPK为增加土壤全氮插值精度的有效方法。
(2)提出了一种新的结合范畴数据的随机模拟方法,并运用于实际的案例研究,丰富和发展了随机模拟理论。
地统计学经常被用来描述土壤属性含量的空间变异。然而,由地统计学随机算法产生的模拟实现图能够更好的代表实际的空间分布状况。土地利用类型通常会影响局部土壤氮的含量水平,故将土地利用类型结合进土壤氮的地统计学随机模拟中是可取的。据此,作者提出了sequential Gaussian simulation incorporating land use information (SGSLU)的随机模拟算法。在这项研究中,402个采样点的土壤全氮观测数据与土地利用范畴信息相结合,利用作者提出的SGSLU算法来模拟了土壤全氮的空间分布,并将SGSLU与OK和顺序高斯模拟(SGS:sequential Gaussian simulation)的预测结果做了比较。其中135个验证数据被用来评估SGSLU在提高预测精度和减小预测不确定性方面的改善程度。结果表明,验证数据与SGSLU的最佳预测(即E-type估计)的相关性更大,且平均误差和均方根误差更小。而且根据精确图和最佳统计量G, SGUSLU在减小预测结果的不确定性方面优于SGS。故SGSLU在提高预测的准确性和减少土壤全氮预测的不确定性方面,是一种行之有效的方法,同时模拟实现之间的差异代表了土壤全氮预测的空间不确定性。这些知识为土壤全氮缺乏和丰富区域的划定提供了定量信息。
(3)将主成份分析／绝对主成分分数(PCA/APCS)模型引入土壤污染源解析领域,同时将其与地统计学结合,提出了一个土壤重金属污染源解析的综合方法。
目前在土壤污染源确定方面,主成份分析(PCA)是最常用的工具。源解析是在源确定方面进一步的定量化。PCA/APCS不需要事先了解源的个数及其特点,也就是说可以在源未知的情况下进行源解析,因此该模型被广泛应用。源解析技术已被广泛应用于大气环境和水环境研究中,但目前在土壤重金属污染领域运用该技术的研究还鲜有报道。PCA的结果与源贡献相关,但是并不成比例,故其结果只能定性的推测潜在的污染源而不能直接用于源解析。应用PCA/APCS受体模型不但可以定量地确定每个变量对每个源的载荷,还可以定量确定源对其重金属的平均贡献量和在每个采样点的贡献量。但受体模型源解析的结果仍缺乏直观视觉效果,不利于在源未知的情况下利用源解析结果进行源识别(如隐蔽性污染源)。为了便于直观理解每个污染源的贡献量的空间分布和在源未知的情况下推测具体的污染源,我们在本文中将地统计学和受体模型结合起来,利用普通克里格法对由PCA/APCS受体模型获得的采样点的源绝对贡献量插值。因此该研究的目的是提出一个土壤重金属污染源解析的综合方法。同时我们根据污染数据集所能提取的信息的不同,如是否能直接从PCA推断污染源的性质,单个重金属污染物的源解析是否需要多元数据集的源解析技术等问题,用两个案例加以展示说明。
(4)将直接顺序模拟技术引入土壤和环境属性的不确定性评估中,扩展了直接顺序模拟的应用范围。
最常用的随机模拟方法为顺序高斯模拟和顺序指示模拟,这两种模拟方法使用前必须进行数据转换,而数据转换必然伴随着模拟结果精度的降低。最近出现的直接顺序模拟克服了这一弱点。本研究采用直接顺序模拟这一新的模拟技术模拟了土壤全氮的空间分布。利用模拟的结果,定量评估了土壤全氮的空间不确定性。同时普通克里格被用于参照方法,用于说明直接顺序模拟技术在不确定性评估方面的优点。
(5)使用顺序高斯模拟和传递函数模拟了由划定土壤镍污染范围所引起的健康风险损失和补救风险损失,并提出了一个基于最小化期望损失标准的污染区域划定方案。
由于克里格插值的平滑效应,采用克里格插值的结果作为污染范围的划定是不恰当的。而超概率阈值方案中,由于概率阈值的设定通常比较主观,故这一划定方案也缺乏客观的科学依据。地统计学模拟实现值因克服了插值的平滑效应,故较克里格最佳预测值更能准确的代表所研究变量的空间异质性。模拟实现之间的差异代表了空间的不确定性。这些实现可以作为传递函数的输入数据,以进一步评估产生的因变量的不确定性。本研究将研究区域的镍模拟实现值输入传递函数,以计算健康风险损失(低估其含量而未补救)和补救风险损失(高估其含量,采取补救措施)。模拟的镍含量的不确定性通过传递函数传播,导致不确定性的健康风险损失和补救风险损失。这样,两种风险损失就可以通过镍的反应值来评估。同时在该研究中,由于不同的土地利用类型中镍的危害程度不同,本研究也在传递函数中加以考虑。最后作者依据最小化风险损失为标准,划定了重金属镍污染的范围。这样为污染的划定提供了一个新的思路。
(6)结合地统计学随机模拟模型和Hakanson潜在生态风险指数法,提出了一种生态风险空间分析的综合方法。
Hakanson潜在生态风险指数法不但考虑了土壤沉积物中重金属的毒性、重金属在沉积物中普遍的迁移转化规律以及评价区域对重金属污染的敏感性,而且利用重金属总量分析测试结果与区域背景值进行比较,消除了区域差异及异源污染影响。目前该方法已被国内外广泛接受,已成为生态风险评价方面最常使用的方法之一。地统计学在生态风险评估领域是个被忽视的方法。本研究以结合地统计学随机模拟和Hakanson (?)替在生态风险指数法,提出了一种综合的空间分析生态风险的方法。本研究先对各个重金属元素含量进行地统计学随机模拟,然后将模拟实现值输入Hakanson潜在生态风险指数法,得到每个重金属元素所引起的生态风险系数,这样由各个重金属元素所引起的生态风险的空间不确定性被量化。而且由所有重金属元素引起的生态风险指数的最佳估计可由各个重金属元素的生态风险系数的期望值之和得到。
(7)地统计学在土壤主要营养元素有效性比率分布格局上的一个应用。
全氮(TN)、全磷(TP)、全钾(TK)、AN、AP和AK的含量及土壤各主要元素的有效性比率(即氮、磷和钾元素的有效量与全量之比)为土壤系统主要营养的重要指标。对于农业生产和环境保护至关重要。土壤营养元素中,比较高的有效性比率意味着该元素更加有利于植物的吸收,同时也暗示该元素更加容易进入水体。因此,为了更加有效的对农作物施肥和环境进行管理,了解主要营养物质的有效量、全量和有效性比率的空间分布格局显得非常必要。在过去的几十年内,很多研究者研究了氮、磷和钾各中形态的空间分布格局。但这些研究主要是关注这些主要营养元素的全量或有效量,缺少对其有效性比率的研究记录。本研究采用多元统计分析土壤有效性比率与土壤属性之间的关系,找出了影响有效性比率的控制因子；同时利用地统计学分别对主要营养元素的全量和有效量分布进行插值,最后得到有效性比率的空间分布格局。
Geostatistics has been evovling with applied sciences such as mining. In two recent decades, it has become more and more popular in soil science, environmental science, ecology, meteorology and even in economics and human science. It is through these applications that geostatistics obtained many new ideas for its futher development. Indeed, scientists in the fields of soil and environmental sciences have investigated geostatistics for various application perspectives, for example, soft data integration, stochastic simulation and spatial uncertainty assessment. However, further study is needed to address some important issues in both methodology and applications in soil and environmental sciences. This study explored the following seven subtopics:
■Whether this is an effective geostatistical method better than previously used residual kriging to integrating categorical information into the geostatistical mapping of soil properties.
■Whether categorical data can be combined into stochastic simulation and thus reduce the spatial uncertainty of simulated results of soil attributes.
■Whether we can obtain the spatial distribution maps of the absolute contributions of pollutant sources from multiple data sets of samples in different spatial positions.
■Whether data transformation conducted in previous stochastic simulations can be avoid; and if it is feasible then how to assess the spatial uncertainty of soil properties using such method.
■Because kriging has the smoothing effect and the division of pollution probability thresholds is usually subjective, whether there is a more objective delineation method to map polluted areas.
■How to assess the spatial uncertainty of ecological risks that account for the spatial heterogeneity and uncertainty of pollutants in ecological risk assessment study.
■How to map effectively the spatial distribution of the availability of soil macronutrients.
We conducted some explorations in developing geostatistcs and expanding its application breadth and depth. This dissertation achieved the following major results:
(1) The area-and-point kriging was introduced to the field of predictive soil mapping, and it was proven to be a better method for precision agriculture and environmental management.
Mapping the spatial distribution of soil nutrient contents from sample data received much attention in recent decade. Accurately mapping soil nutrients purely based on sample data, however, is difficult due to the sparsity and high cost of samples. Land use types usually influence the contents of soil nutrients at local level and it is desirable to integrate such information into the predictive mapping. The area-and-point kriging (AAPK) method, which was proposed recently, may provide an interpolation technique for such purpose. This study mapped the soil total nitrogen (TN) distribution of Hanchuan County, China, using AAPK with402point sample data and land use information. Ordinary kriging (OK) and residual kriging (RK) were compared to evaluate the performance of AAPK. Results showed that:(1) land use types had important impacts on the spatial distribution of soil TN;(2) measured data at the135validation locations had stronger correlation with the predicted data by AAPK than with those by RK and OK, and the mean error and root mean square error with AAPK were lower than those with RK and OK; and (3) AAPK generated smaller error variances than RK and OK did. This means AAPK represents an effective method for increasing the interpolation accuracy of soil TN.
(2) We developed a new geostatistical stochastic simulation method by combining categorical land use data and sequential Gaussian simulation, and applied it to a case study. This may improve the application value of sequential Gausian simulation.
Geostatistics is often used to characterize the spatial variability of soil properties. However, simulated realization maps by stochastic geostatistical algorithms can represent the spatial distribution more realistically than the kriged optimal map. Because land use types usually influence the local content level of soil nitrogen, it is desirable to integrate land use information into the geostatistical stochastic simulation of soil nitrogen. In this study, the data of TN contents at402sampling sites and the categorical information of land use maps were integrated together for performing the sequential Gaussian simulation incorporating land use information (SGSLU). A comparison of SGSLU with ordinary kriging (OK) and sequential Gaussian simulation (SGS) in their performances was conducted, and135validation samples were used to assess the improvement of SGSLU over SGS in prediction quality and uncertainty reduction of soil TN contents. Results showed that the validation data were more correlated with the optimal prediction (i.e., E-type estimates) data of SGSLU than with those of OK and of SGS, and the mean error and root mean square error with the optimal prediction of SGSLU were lower than those with OK and SGS. Further, according to accuracy plots and the goodness statistic G, SGSLU performed better in uncertainty modeling than SGS did. We conclude that land use types have important impacts on the spatial distribution of soil TN, and SGSLU is an effective method for increasing the prediction accuracy and reducing the uncertainty in soil TN prediction. The differences among realizations represent the spatial uncertainty of soil TN prediction and such knowledge will be helpful to evaluate the delineation of soil TN deficiency and abundance areas for agricultural and environmental management.
(3) We introduced the principal component analysis/absolute principal component scores (PCA/APCS) model to the field of the source apportionment of pollution sources and developed a more effective method for source apportionment through combined gestatstics and PCA/APCS.
At present, principal component analysis is the most often used method in the field of identifying pollution sources. Source apportionment is further quantitative at the basis of PCA. PCA/APCA has the advantage of not requiring the knowledge in the number of sources and source characteristics in advance, thus being widely used in source apportionment studies. Source apportionment is an underutilized technique in soil science. The application of PCA to environmental data has experienced significant setbacks because its outcomes are correlated with but not proportional to source contributions. Consequently, PCA results can detect latent sources only qualitatively and cannot be used directly for source apportionment. With the PCA/APCA method, it is possible to determine quantitatively the loading of each variable from each source, and the contribution of that source to the total pollutant concentration. However, the results of the PCA/APCA lack visual effect, and are not conductive to identification of the locations of the pollution sources (such as hidden pollution source). In order to facilitate understanding the spatial distribution of the absolute contribution of each pollution source and identifying the specific pollution sources, geostatistics and PCA/APCS were combined together, that us, kriging is used to interpolate the absolute contribution of each source obtained from PCA/APCS. The purpose of this study is to propose an integrated approach for source appointment of soil pollution source. At the same time, two case studies were conducted according to the different characters of the data set and whether multiple data sets should be used in source apportionment of a single pollution matter.
(4) Direct sequential simulation (DSS) was introduced for uncertainty assessment of soil properties, which may help to expand the application scope of DSS.
Sequential Gaussian simulation and sequential indicator simulation are the most often used method to simulate the soil and environmental properties. A data transformation process must be carried out in advance when using the two simulation technologies; this process will inevitably lead to the reduction of simulation accuracy. The recently emerged direct sequential simulation (DSS) method overcomes this weakness. In this study, the spatial uncertainty assessment of the soil total nitrogen was performed. Ordinary kriging was used as a reference method to illustrate the advantages of the DSS method in uncertainty assessment.
(5) We simulated the risk costs of delineating pollution areas by combing the method of sequential Gaussian simulation with transfer functions, and at the meantime a method of delineating pollution areas based on the standard of minimum expected costs was proposed.
As kriging interpolation has the smoothing effect, it is not appropriate to use the kriged results as the standard data for delineating pollution areas. In addition, as the setup of probability thresholds is usually subjective in estimating threshold exceedance probabilities, such delineation scheme lacks scientific basis. Geostatistical simulated realization maps can represent the spatial heterogeneity of the studied spatial variable more realistically than the kriged optimal map because they overcome the smoothing effect of interpolation. The difference among realizations indicates spatial uncertainty. These realizations may serve as input data to transfer functions to further evaluate the resulting uncertainty in impacted dependent variables. In this study, sequential Gaussian simulation was used to simulate the spatial distribution of soil nickel (Ni) in the study area. Simulated realizations were then imported into transfer functions to calculate the health risk costs caused by Ni polluted areas being ignored in remediation due to underestimation of the Ni contents and the remediation risk costs caused by unnecessary remediation of unpolluted areas due to overestimation of the Ni contents. The uncertainty about the input Ni content values thus propagated through these transfer functions, leading to uncertain responses in health risk costs and remediation risk costs. The spatial uncertainties of the two forms of risk costs were assessed based on the response realizations. Because the risk of exposure of soil Ni to humans and animals is generally greater in contaminated arable lands than in industrial and residential lands, the effect of land use types was also taken into account in risk cost estimation. Most of the south part of the study area was delineated as contaminated according to the minimum expected cost standard. This study shows that sequential Gaussian simulation and transfer functions are valuable tools for assessing risk costs of soil contamination delineation and associated spatial uncertainty.
(6) An integrated approach was proposed by combing sequential Gaussian simulation and Hakanson potential ecological risk index.
Potential ecological risk index was introduced to assess the degree of heavy metal pollution in soils, which was originally introduced by Hakanson (1980), according to the toxicity of heavy metals and the response of the environment. At present, potential ecological risk index (RI) is one of the most commonly used tools for ecological risk assessment. However, while the spatial distribution of heavy metals is heterogeneous the spatial heterogeneity was seldomly accounted for in previous literature related to ecological risk study. In this study, a comprehensive method for spatial analysis of ecological risks was proposed through combining stochastic simulation and Hakanson potential ecological risk index. Sequential Gaussian simulation (SGS) is usually used to describe joint realizations of pollutants. The objective of this study is to generate a number of realizations in the studied region, which can effectively reflect the uncertainty resulting from heterogeneity, and feed them into the model of the potential ecological risk index, so that the spatial uncertainty of the ecological risks resulting from the spatial uncertainty of pollutants could be quantified. The E-type estimates of the Hakanson potential ecological risk indexes could be obtained through summing the E-type estimates of the potential ecological risk factors for signal metals.
(7) An application of geostatistics in the spatial distribution pattern of N, P and K availability ratios was performed.
Many studies on soil N, P and K. were conducted in the past several decades. Most of them, however, were focused on the total contents or available contents of these elements in agricultural fields, and few characterized their variability in soils. In this study, the controlling factors on the spatial variability of soil N, P and K availability ratios were determined using multivariate statistics;and geostatistcs were adopted to map the spatial distribution patterns of the soil available contents and total contents of the macronutrients, and then N, P and K availability ratios were obtained from the result of the geostatistics analysis.
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