基于协同克里格插值和地理加权回归模型的土壤属性空间预测比较

选取宜昌市红花套镇作为研究区域,研究土壤pH、有机质、有效磷、速效钾、碱解氮与土壤属性指标变量之间的关系,选择与预测变量之间具有较高相关性的变量作为辅助变量用以提高预测精度,本文试图将地理加权回归模型应用于土壤属性空间模拟中,以此与协同克里格插值的预测结果进行对照,从而比较它们的预测精度以提出更适合土壤属性预测的模型。结果表明:协同克里格插值和地理加权回归模型对土壤属性的空间模拟均有较高的预测精度,在辅助变量较多的情况下地理加权回归模型具有比协同克里格插值更为简单的算法,并且比较预测值相对误差的范围跨度和标准差以及均方根误差等方面,地理加权回归模型在土壤属性指标预测方面具有更高的预测精度,也具有更大的优势。     

基于混合地理加权回归与克里格的区域降水量空间插值方法

基于四川省区域范围内144个气象站点的实测降水数据,在综合考虑空间位置、地形等影响因素的基础上,采用改进的回归克里格模型,即混合地理加权回归克里格模型（MGWRK）对四川省年降水量的空间分布进行空间插值,并与普通克里格（OK）、全局回归克里格（GRK）和地理加权回归克里格（GWRK）等模型的插值效果进行对比分析。结果表明：（1）应用逐步回归法筛选确定的用于回归分析的影响因子组合为经度、纬度和坡度,可有效消除解释变量间的多重共线性,为后续的空间插值奠定基础;（2）同一回归变量在地理加权回归（GWR）与全局回归（GR）两种回归模型中的AICc（修正的赤池信息量准则,Corrected Akaike Information Criterion）值之差（ΔAICc）可用于定量判定各回归变量的空间非平稳性类型,据此将变量坡度设为全局变量,经度和纬度设为局部变量进行处理。在此基础上,通过MGWRK模型对四川省年降水量进行空间插值;（3）MGWRK插值模型综合考虑了空间位置、地形等多个影响因素及其与降水相互关系的空间非平稳性特征,相对于传统的OK和GRK法具有更高的插值精度。     

基于GIS和地理加权回归的砂田土壤阳离子交换量空间预测

土壤阳离子交换量(CEC)反映土壤保水保肥能力,研究CEC空间分布可为土壤改良和田间施肥提供理论依据。本文以宁夏香山地区砂田淡灰钙土为研究对象,在土壤CEC和理化性质相关分析基础上以普通克里格(OK)为对照,探索回归克里格(RK)和地理加权回归克里格(GWRK)在CEC空间插值上的应用,并对三者的插值精度及制图效果进行评价。描述统计表明研究区土壤CEC含量均值为10.145cmol/kg,CEC与有机质含量呈显著正相关,与砂粒含量呈显著负相关;地统计分析表明CEC实测值、OLS残差和GWR残差块金系数分别为8.50%、6.36%和7.02%,比值均小于25%,具有强烈空间自相关;对验证点进行插值精度分析,RK和GWRK的相对模型改进值(RI)分别为40.49%、41.50%,插值精度GWRK>RK>OK;从成图效果看,GWRK中辅助变量参与了局部回归,成图效果更加精细,揭示了更多空间变化细节。本研究结论可为土壤CEC空间预测研究提供可靠的方法借鉴。     

基于回归克里格和遥感的紫色土区土壤有机质含量空间预测

精确预测紫色土区土壤有机质含量的空间分布,对于指导紫色土区农业生产和培肥土壤具有重要意义。以杜家沟小流域为研究区,以遥感影像作辅助变量,采用回归克里格法,预测土壤有机质含量的空间分布,并与参照方法的预测精度进行比较。结果表明:(1)Landsat ETM+影像的波段2和波段5是土壤有机质含量多元线性回归预测的最佳辅助变量,回归残差的最优半方差函数模型为球状模型,模型的拟合精度较高;(2)土壤有机质含量呈由沟谷逐渐向坡顶递减的趋势,空间变异的细节信息表达较好;(3)回归克里格法在验证点的预测值与实测值的拟合能力更好,预测结果更倾向于无偏的,MAE、RMSE和R2均优于参照方法。因此,回归克里格法是紫色土区土壤有机质含量高精度空间预测的有效方法。     

空间回归分析在土壤属性预测制图中的应用

以河南省孟津县为研究区,选取坡度、高程、地面曲率和复合地形指数(CTI)作为表层土壤缓效钾含量空间预测的环境协变量,系统探讨了空间回归分析技术在土壤属性预测制图中的应用.结果表明:土壤缓效钾的空间自相关距离阈值约为10 000 m,与坡度、高程和地面曲率存在显著相关性;尽管空间回归模型的预测精度和普通回归模型相近,但前者可以更加准确地表征土壤缓效钾的空间分布格局及空间分异细节特征.     

西南典型岩溶区土壤硒空间分布预测

土壤硒精准预测和制图是富硒土壤资源开发利用和环境规划管理的基础。该文以西南典型岩溶区桂林永福百寿河流域为例,在分析影响土壤硒化学行为因子的基础上,通过野外样品采集和室内化学分析以及Arc GIS空间分析,获取了研究区相关地理环境因子和土壤属性因子数据。利用逐步回归方法选择土壤硒空间分布预测的辅助变量,使用协同克里格模型对非连续分布的辅助变量进行插值。在此基础上利用地理加权回归模型对土壤硒空间分布进行预测,同时以普通克里格插值结果作为参照。研究结果表明:使用地理环境因子和影响土壤硒化学行为的土壤属性因子可以提高土壤硒预测精度;协同克里格插值解决了辅助变量数据连续分布的问题;土壤硒的空间分布与地形和影响土壤硒化学行为的因子有关。     

基于地理加权回归的地形平缓区土壤有机质空间建模

气候变化效应评估、土壤固碳潜力和肥力管理等,迫切需要详尽的土壤有机质（soil organic matter, SOM）空间分布信息。该文以江苏省第二次土壤普查的1 519个典型土壤剖面的表层（0～20 cm）SOM含量为例,选择1 217个样本为建模集,302个为验证集,选取年均温度、年均降雨、物理性黏粒和土壤pH值等因子进行SOM的地理加权回归（geographically weighted regression, GWR）建模。从建模集中分别随机抽取100%（1 217个）、80%（973个）、60%（730个）、40%（486个）,20%（243个）的样点,对比不同样点数量下GWR和传统全局回归模型的精度差异,并选择最优模型进行SOM空间预测制图。结果表明：1）江苏省SOM含量在不同空间尺度上存在极显著的空间自相关性。不同样点数量的建模集的全局自相关性和局部空间自相关聚类图结果相似。全局Moran’s I值介于0.25～0.61（P<0.001）。SOM含量空间分布以空间聚集特征为主,“高-高”聚集区主要分布在苏中和苏南地区,“低-低”聚集区主要分布在苏北地区。2）GWR建模结果均优于传统的全局回归建模,其残差在不同的空间尺度上均不存在空间自相关性。不同建模集的GWR的R2adj较全局建模均提高0.15～0.20,其AIC和RSS均比全局模型有大幅降低,为56.08～360.19和17.40～76.67。不同建模样本数量的GWR模型对SOM的解释能力差异较小。3）建模样点数量（除建模样本n=243）对GWR预测制图结果的精度影响不大,RMSE介于5.56～5.75 g/kg之间,MAE介于3.87～4.05 g/kg之间,R2介于0.52～0.48之间,均优于全部建模样点的普通克里格插值验证结果。该研究可为样点数较少的省级尺度地区SOM空间建模与制图提供借鉴。     

江西多年平均降水量空间插值模型的选取与比较

为了探究江西省多年平均降水量的空间分布格局,本文选取81个时间序列完整的气象站30 a(1976-2005年)降水数据,运用泛克里格中不同半变异模型对降水数据进行拟合.分别采用65个建模站点交叉验证和16个验证站点的检验,证实了该研究区域多年平均降水量存在较强的空间相关性.通过不同半变异函数模型的对比发现,球面和指数模型在建模站点交叉验证结果中的标准均方根预测误差分别为1.024和1.023,较为接近1,表明其误差较小;其在验证站点检验结果中的标准均方根预测误差分别为1.105和1.104,表明这两种模型的拟合效果较优,能较为真实地反映江西省多年平均降水量的空间分布情况,其中以指数模型拟合效果最优.     

基于地理权重回归模型的土壤有机质空间预测

准确了解土壤有机质的空间分布是合理施肥的重要前提,也是水土流失控制及保护环境的重要基础。利用113个土壤有机质样点数据,以海拔高度、土壤侵蚀强度、土地利用、比值植被指数、样点至河流的欧氏距离、亚铁矿物指数及坡度为参考因子,来尝试利用GWR(Geographically Weighted Regression)模型探索多重因素作用下的土壤有机质空间分布,并通过与普通线性回归(ordinary least squares,OLS)相比较,来了解GWR模型的精度,进而进行了土壤有机质的空间制图,并对其制图效果进行了评价。结果表明,与OLS模型相比,GWR预测模型它能显著降低AIC(Akaike Information Criterion)值,较大程度地提高模型的决定系数,并有效地减少模型的回归残差值。从制图的总体效果看,GWR模型的预测结果与实测值的吻合程度要优于OLS模型。文章还对利用GWR模型进行回归时的样点数量、因子筛选及因子定量化等方面进行了相应的讨论。     

克里格插值在区域土壤有机碳空间预测中的应用

基于河北省第二次全国土壤普查数据,对比了常用土壤有机碳相关因子土地利用和土壤类型与普通克里格插值结合前后对土壤有机碳密度空间预测精度的差异,探讨了普通克里格插值在区域土壤有机碳空间预测中的应用。研究结果表明,土地利用能够独立解释土壤有机碳密度总方差的19.0%,与普通克里格插值结合以后能够将对土壤有机碳密度总方差的解释程度显著提高到30.2%。低级土壤分类土属能够独立解释土壤有机碳密度总方差的45.0%,但与普通克里格插值结合以后对土壤有机碳密度总方差的解释程度为44.8%,两者相差不大。因此区域空间上能否进一步应用普通克里格插值优化土壤有机碳的空间预测与所选用的土壤有机碳相关因子有关。     

Prediction of soil salinity in the Yellow River Delta using geographically weighted regression

It is essential to determine the content and spatial distribution of soil salinity in a timely manner because soil salinization can cause land degradation on a regional scale. Geographically weighted regression (GWR) is a local regression method that can achieve the spatial extension of dependent variables based on the relationships between the dependent variables and environment variables and the spatial distances between the sample points and predicted locations. This study aimed to explore the feasibility of GWR in predicting soil salinity because the existing interpolation methods for soil salinity in the Yellow River Delta are still of low precision. Additionally, multiple linear regressions, cokriging and regression kriging were added to compare the accuracy of GWRs. The results showed that GWR predicted soil salinity with high accuracy. Furthermore, the accuracy was improved when compared to other methods. The root mean square error, correlation coefficient, regression coefficient and adjustment coefficients between the observed values and predicted values of the validation points were 0.31, 0.65, 0.57 and 0.42, respectively, which were better than that of other methods, indicating that GWR is an optimal method.     

Analysis on influence factors of soil Pb and Cd in agricultural soil of Changsha suburb based on geographically weighted regression model

为了定量分析土壤重金属含量的影响因素,以长沙城郊农田土壤Pb、Cd为例,采用传统回归模型（ordinary least squares, OLS）和地理加权回归模型（geographically weighted regression, GWR）分析比较了土壤Pb、Cd含量与影响因素间的相关关系。结果表明：长沙城郊农田土壤Pb、Cd含量存在空间自相关性,Pb、Cd的GWR模型拟合度较OLS模型高,残差不存在空间自相关,GWR模型能更好地解释土壤Pb、Cd与影响因素变量的空间异质性。土壤Pb与Cd含量呈极显著正相关;土壤pH值、有机质、氮磷含量是影响土壤Pb、Cd含量的重要因素;离河流、城镇、工矿建设用地的距离对于城郊农田土壤Pb、Cd含量也有一定影响,土壤Pb、Cd的"高-高"集聚区（土壤Pb或Cd含量高的区域被Pb或Cd含量高的其他区域所包围,区域土壤Pb或Cd含量水平较高,且空间差异程度较小）和离河流、城镇、工矿建设用地较近的农田是Pb、Cd污染风险防控的重点区域。该研究可为定量分析区域土壤重金属含量的空间结构与影响因素提供参考,为长沙城郊农田土壤重金属污染的防控提供参考。     

农田土壤铅、镉含量影响因素地理加权回归模型分析

为了定量分析土壤重金属含量的影响因素,以长沙城郊农田土壤Pb、Cd为例,采用传统回归模型(ordinary least squares,OLS)和地理加权回归模型(geographically weighted regression,GWR)分析比较了土壤Pb、Cd含量与影响因素间的相关关系。结果表明:长沙城郊农田土壤Pb、Cd含量存在空间自相关性,Pb、Cd的GWR模型拟合度较OLS模型高,残差不存在空间自相关,GWR模型能更好地解释土壤Pb、Cd与影响因素变量的空间异质性。土壤Pb与Cd含量呈极显著正相关;土壤pH值、有机质、氮磷含量是影响土壤Pb、Cd含量的重要因素;离河流、城镇、工矿建设用地的距离对于城郊农田土壤Pb、Cd含量也有一定影响,土壤Pb、Cd的"高-高"集聚区(土壤Pb或Cd含量高的区域被Pb或Cd含量高的其他区域所包围,区域土壤Pb或Cd含量水平较高,且空间差异程度较小)和离河流、城镇、工矿建设用地较近的农田是Pb、Cd污染风险防控的重点区域。该研究可为定量分析区域土壤重金属含量的空间结构与影响因素提供参考,为长沙城郊农田土壤重金属污染的防控提供参考。     

Predicting soil organic matter content in a plain-to-hill transition belt using geographically weighted regression with stratification

ABSTRACT

In contrasting landscapes, the ignorance of diverse relationships between environmental covariates and soil organic matter (SOM) will likely lead to a great deal of prediction uncertainty. To deal with this issue, this study aimed to develop a method to predict SOM in a plain-to-hill transition belt through defining a landform-based stratified model (i.e., separate estimation for different landforms). Initially, the area was split into two strata based on landform types (low-relief areas and hill areas). And then in each stratum the dominant environmental variables were determined. Finally, geographically weighted regression (GWR) was applied to explore the relationships between SOM and environmental variables for the whole study area as well as for each stratum. The results showed that the dominant variables for each stratum were different. The model with stratification outperformed the model without stratification with regards to mean error (0.1 vs. 1.0, respectively), mean absolute error (3.1 vs. 3.8, respectively) and root mean square error (4.1 vs. 5.4, respectively). We conclude that the developed strategy that based on landscape stratification and GWR will be useful for predicting SOM in areas with high variation in topography.     

Uncertainty in the spatial prediction of soil texture: Comparison of regression tree and Random Forest models

Within the southern Ecuadorian Andes, landslides have an impact on landscape development. Landslide risk estimation as well as hydrological modelling requires physical soil data. Statistical models were adapted to predict the spatial distribution of soil texture from terrain parameters. For this purpose, 56 soil profiles were analysed horizon-wise by pipette and laser method. Results by pipette compared to laser method showed the expected shift to higher silt and lower clay contents. Linear regression equations were adapted. The performance of regression tree (RT) and Random Forest (RF) models was compared by hundredfold model runs on random Jackknife partitions. Digital soil maps of sand, silt and clay percentage mean and standard deviation indicate model variability and prediction uncertainty.RF models performed better than RT models. All terrain factors considered in the analysis influenced soil texture of the surface horizon, but altitude a.s.l. was assigned the highest variable importance during model construction. Shallow subsurface flow is considered responsible for increasing sand/clay ratios with increasing altitude, on steep slopes and with overland flow distance to the channel network by removing clay particles downslope. Deeper soil layers are not influenced by this process and therefore, did not show the same texture properties. However, the influence of parent material and landslides on the spatial distribution of soil texture cannot be neglected. Model performance, most probably, could be improved by a bigger dataset.     

土壤质地空间预测方法比较

土壤质地作为成分数据（compositional data）的一种,其空间插值需满足非负、定和、误差最小和无偏估计4个条件。采用成分克里格法（compositional Kriging）和基于对数比转换的普通克里格法对土壤质地各颗粒组成进行空间预测,均方根误差（root mean squared errors,RMSE）和标准化克里格方差（mean squared deviation ratio,MSDR）分别被用来衡量不同方法的预测精度及模型拟合效果。研究结果表明：对数比转换的普通克里格法和成分克里格法能够保证插值结果满足成分数据插值的4个条件;成分克里格法预测的各土壤颗粒组成的RMSE最小,预测精度最高,其黏粒RMSE值相对于非对称对数比转换的普通克里格法提高将近17%;成分克里格法的变异函数拟合效果总体上好于其他两种预测方法,预测结果极差更宽,更能反映土壤质地各颗粒组成与高程、母质和水域分布的关系。     

Comparison of several spatial prediction methods for soil pH

A survey of topsoil pH has been designed specifically to compare the performance of several two-dimensional spatial prediction methods. These methods have been classified as global or local, and interpolating or non-interpolating, and smooth or non-smooth predictors. The techniques tested were global means and medians, moving averages, inverse squared distance interpolation, Akima's interpolation, natural neighbour interpolation, quadratic trend surface, Laplacian smoothing splines and ordinary kriging. All methods showed some deficiencies; for example, prediction sums-of-squares were higher than expected for all methods. Interpolating methods either were very poor predictors, or suffered from theoretical drawbacks, or both. Of the non-interpolating methods, Laplacian smoothing splines and kriging generally performed best. Estimates of variance derived from models which assume independent errors were greater than estimates of variance derived from neighbouring pairs of data sites, suggesting that short range correlations definitely exist, and should be taken into account in any predictive modelling.     

Modeling crop yield potential of Eastern Anatolia by using geographically weighted regression

Wheat is a very important cereal crop in Eastern Anatolia in terms of acreage and production. It is a staple food and plays an important role in people's livelihood. Drought often occurs in the region and it dramatically influences wheat yield. The yield also depends upon prevailing climatic conditions, rainfall, temperature and humidity. Crop-modeling studies to forecast crop yield are important not only for people now but for planning studies and precautionary measures for the future. Traditional decision support systems based on crop simulation models are normally site-specific. In order to address the effect of spatial variability of weather variables on crop production, we modeled wheat yield potential on certain climatic conditions by using Geographically Weighted Regression and Geographical Information Systems in Eastern Anatolia in Turkey.     

地理加权回归模型结合高光谱反演盐生植物叶片盐离子含量

快速、无损地估算盐生植物叶片盐离子含量在植物生长监测、耐盐植物筛选和土壤盐渍化监测等方面有实用价值。该研究以新疆艾比湖保护区内盐生植物为研究对象,通过分析植物叶片盐离子(K~+、Na~+、Ca~(2+)、Mg~(2+))含量与冠层高光谱数据的光谱变换和二维植被指数(比值型植被指数(ratiovegetationindex,RVI)、差值型植被指数(difference vegetation index,DVI)、归一化型植被指数(normalized difference vegetation index,NDVI))的相关性选取特征波段,构建基于地理加权回归模型(geographically weighted regression,GWR)的叶片盐离子含量估算模型,并与BP神经网络模型(back propagation neural network)进行对比,研究基于GWR模型估算干旱区盐生植物叶片盐离子的可行性。结果表明,选取特征波段集中表现在红及短波红外波段:K~+含量在反射率倒数的对数选取的红光区域内波段使用GWR估算效果最佳;Na~+的特征波段在光谱变换下集中于短波红外区域,二维植被指数集中在近红外、短波近红外及黄、橙、红区域,各种波段选取下GWR对Na~+的含量估算均有较好效果,但反射率对数的一阶估算效果最好;Ca~(2+)含量在反射率平方根的一阶微分下选取的短波红外波段通过GWR模型估算效果最好;Mg~(2+)含量在DVI选取的位于红光区域特征波段估算效果最佳,但使用GWR模型对Mg~(2+)的估算精度不及BP模型。分析基于GWR盐离子模型估算模型发现,含量较高的离子估算效果更好,K~+、Na~+的模型精度优于Ca~(2+)、Mg~(2+)。在使用GWR模型估算植物叶片盐离子含量时,特征波段均指向红及短波红外波段,符合植被光谱机理的响应。