乔学瑾(1989-), 男, 山西应县人, 博士研究生, 主要从事干旱区水土资源利用与土壤水盐运移研究。Email:
明晰土壤盐渍化空间分布特征是盐碱地改良的基础。与单一尺度相比,嵌套多尺度研究可更好地分析土壤盐分的空间变异结构特征,更精确地表达盐渍化程度的自相关随尺度的变化情况。采用传统统计学和地统计学相结合的方法,通过野外实地分层采集土样,分析了4 km、500 m和100 m三个嵌套尺度条件下,新疆安集海灌区膜下滴灌棉田根系层土壤含盐量的空间分布规律及其变异特性。结果表明,灌区棉田各尺度根系层土壤含盐量整体水平较低(平均1.52~1.87 g·kg-1),属中等变异,具有明显的连续变化和底聚特征。轻度盐化土和非盐化土在整个灌区占主导地位并主要分布于地表水矿化度较低、地势较高、排水相对通畅的灌区东南侧,盐渍化相对较重区域主要位于地下水埋深较浅的泉水溢出带,以及受平原水库和干渠渗漏影响的区域。受地形地貌等结构性因素与人为活动等随机性因素共同影响,土壤含盐量呈强空间自相关性:随尺度加大,地统计模型的块基比减小,相关距离增加,自相关性增强,结构性因素影响增强,随机因素影响减弱;反之随尺度减小,空间分布更加清晰明确,随机因素的影响则逐渐增强。对于盐渍化严重区域,有必要针对整个根系层采用嵌套方式在更小尺度上加密采样,以充分了解土壤盐分的空间分布规律与变异特性。
The knowledge about the spatial distribution characteristics of salinization is the basis for amelioration of saline-alkali soils. Compared with research based on a single scale, nested multi-scale research can be more effectively applied to analyzing structural characteristics of the spatial variation of soil salinity with higher accuracy in describing scale-dependent self-correlated variation of salinization.
In the Anjihai Irrigation Zone of Xinjiang, soil samples were collected by soil layer in the film-mulched cotton fields for analysis of rules and variabilities of the spatial distribution of salt content in the root zone of the drip-irrigated cotton field under film mulch with the method combining conventional statistics and geo-statistics, as affected by nested scales of 4 km, 500 m and 100 m.
Results show that, for any scale, soil salinity in the root-zone of the cotton fields in the zone is generally low, with the mean being in the range of 1.52-1.87 g·kg-1, moderate in variability, and characterized by continuous variation and accumulation at the bottom of the root zone. Non- and mildly-salinized soils dominate the irrigation zone and are mainly located in the south-east part of the zone, where the surface water is low in salinity and the ground is quite high with unobstructed drainage, while relatively seriously salinized soils are mainly distributed in areas where the ground water is shallow and overflows, and in areas that are affected by the leakage from reservoirs in the plains and trunk canals. As influenced by some structural factors (e.g. terrain landform) and stochastic factors (e.g. artificial activities), soil salt content in this area shows a significant spatial self-correlation in distribution. With increasing scale, nugget-to-sill ratio of the geo-statistical analysis model decreases, and related distance, self-correlation and impact of structural factors increase, but the influence of random factors weakens. On the contrary with declining research scale, spatial distribution becomes more explicit, and the impact of random factors intensifies.
For those relatively seriously salinized areas, it is advisable to employ the nested multi-scale root-zone sampling strategy so as to get a full knowledge about characteristics of the spatial distribution and variability of soil salinity in the drip-irrigated cotton fields under film mulch.
降水稀少、蒸发强烈使得水资源短缺和土壤盐渍化成为制约新疆等干旱区绿洲农业的主要障碍因子。新疆作为我国最主要的产棉区,平均每年因干旱缺水、土壤盐渍化损失近5万t棉花[
短期而言,高频率、低定额的膜下滴灌可使表层土壤脱盐;但就长期变化而言,由于其淋溶作用微弱,随着时间的推移,下部根系层盐分含量可能会明显升高,致使根系层整体含盐量逐渐增加[
土壤盐分的空间分布及变异规律具有地质结构特性和统计学的随机特性,可利用地统计学进行研究[
安集海灌区(85°09′E~85°36′E,44°19′N~44°38′N)位于天山北麓、准噶尔盆地南缘、玛纳斯河流域西北部(
安集海灌区多尺度样点与地类分布
Distributions of multi-scale sampling points and land use classification for the Anjihai Irrigation Zone
本研究主要针对当地长期膜下滴灌棉田,涉及的野外调查采样工作包括两项:遥感影像地物分类(棉田识别)的地面验证和不同尺度膜下滴灌棉田根系层土壤采样,分别在2017年和2018年7-8月间开展。
合理采样数量目前多采用Cochran[
式中,
Ⅰ级网格:对灌区尺度作物识别(比例
Ⅱ级网格:对于多尺度条件下土壤特性的采样布局,应根据研究区特点进行相应的设计[
Ⅲ级网格:最小嵌套尺度(Ⅲ级网格)样点间距按地统计常采用的最小样点间距选择为100 m[
基于以上规则,按空间等间距分别布设拟定的Ⅰ、Ⅱ、Ⅲ级网格,间距分别为4 km、500 m和100 m(
受灌区东南侧安集海水库影响,Ⅰ级网格的样点个数调整为57;因Ⅱ级网格组的四个顶角与Ⅰ级网格点重合,故Ⅱ级网格实际采样点数为77;为提高测量精度,采用GPS定位与100 m皮尺测距相结合的方法来确定Ⅲ级网格组的36个点。最终全区的采样点位共170个(如
将采集的土样自然风干、研磨,过1 mm筛后备用,按1︰5土水质量比浸提,测定其电导率EC1︰5(梅特勒-托利多S230型电导率仪,瑞士)。此外,为了准确标定研究区土壤可溶性全盐含量SSC(g∙kg–1)与EC1:5(dS∙m–1)的关系,从采集的土样中随机选择灌区南部、中部和北部共60个样点、360个土样,采用残渣烘干--质量法测定其SSC[
其他未直接测定SSC的土样,则通过浸提液的EC1:5经式(2)换算获得。由于本研究主要关注研究区膜下滴灌棉田根系层整体含盐量的空间分布特性,尽管棉田中膜下与膜间以及不同层次土壤的含盐量不同,但研究过程中不再考虑这些细微差异,每个样点(包括膜下与膜间两个位置及各自相应的6个土层)均取为一个统一的SSC值,即做整体均一化处理,具体方法如下:对每个样点膜间与膜下根系层含盐量先分别根据6层土样的含盐量实测值按采样深度加权平均;之后,每个样点根系层的含盐量SSC则根据所获得的膜间与膜下含盐量按照当地覆膜棉田膜间裸地(60 cm,占比22.64%)和覆膜宽度(205 cm超宽膜,占比77.36%)[
式中,SSC膜间
分别采用传统统计学和地统计学方法来分析不同尺度根系层含盐量的空间分布特征。其中传统统计分析选用SPSS23软件完成,应用单样本K-S(Kolomogorov-Semirnov)方法检验数据是否呈正态分布,对于不服从正态分布的数据集,经对数变换或博克斯-考克斯(Box-Cox)变换转换为正态分布,供地统计分析进一步使用。
地统计研究采用地统计学软件GS+9.0进行半方差函数分析:以决定系数
安集海灌区三个采样尺度下根系层土壤含盐量的统计特征参数差异明显(
不同尺度根系层土壤含盐量统计特征
Statistics of soil salt content in the root-zone layer relative to scale
尺度 |
样点数 |
最小值 |
最大值 |
平均值 |
标准差SD |
变异系数CV |
注*:其中4个(Ⅱ级)网格角点与4 km尺度(Ⅰ级)网格实测样点重合。Note:In the graph,the four corners of a grid(Grade Ⅱ)coincide with the actual sampling points in a grid on the 4 km scale(Ⅰ grid). | ||||||
4 km | 57 | 0.15 | 5.01 | 1.52 | 1.24 | 81.58 |
500 m | 81* | 0.10 | 6.38 | 1.87 | 1.54 | 82.35 |
100 m | 36 | 0.21 | 5.56 | 1.60 | 1.45 | 90.63 |
变异系数(CV)反映了土壤特性的变异程度。就变异系数而言,三个采样尺度下根系层土壤含盐量均为中等强度变异(CV介于10%~100%,
经比较优化,最终确定4 km和100 m尺度的半方差函数为高斯模型(
不同尺度根系层土壤含盐量的半方差函数图
Semivariogram of soil salt content in the root-zone layer relative to scales
不同尺度根系层土壤含盐量的半方差函数模型
Semivariogram models for soil salt content in the root-zone layer relative to scale
尺度 |
模型 |
块金值 |
基台值 |
块基比 |
变程 |
决定系数 |
残差平方和 |
分形维数 |
① Gaussian,②Exponential. | ||||||||
4 km | 高斯① | 0.001 | 0.957 | 0.10 | 9 734 | 96.20 | 8.99×10–3 | 1.21 |
500 m | 指数② | 0.103 | 1.337 | 7.70 | 2 352 | 90.30 | 0.04 | 1.06 |
100 m | 高斯① | 0.004 | 0.266 | 1.50 | 198 | 99.99 | 3.82×10–6 | 1.85 |
本研究三种尺度条件下根系层土壤含盐量的变程分别为:9 734 m、2 352 m和198 m,均高于相应的采样间隔(4 km、500 m和100 m),表明空间内插和制图是有效的[
本研究中土壤含盐量存在局部自相关性结构,分形维数(
半方差函数模型及其参数是否合适通常可依据交叉验证结果予以评价[
不同尺度条件下根系层土壤含盐量普通克里格插值的交叉验证结果
Cross validation of the Ordinary Kriging interpolation of soil salt content in the root-zone layer relative to scale
误差指标 |
尺度 Scale | ||
4 km | 500 m | 100 m | |
注:注,多尺度条件下土壤特性的采样布局,ME:平均误差;RMSE:均方根误差;|MSE|:标准化平均误差;RMSSE:标准均方根误差;ASE:平均标准误差。Note:ME:Mean error;RMSE:Root-mean-square error;|MSE|:Mean standardized error;RMSSE:Root-mean-square standardized error;ASE:Average standard error. | |||
ME | 0.0055 | 0.0159 | 0.0121 |
RMSE | 0.4889 | 0.4872 | 0.4864 |
|MSE| | 0.0094 | 0.0275 | 0.0206 |
RMSSE | 0.9970 | 1.0152 | 1.0242 |
ASE | 0.4919 | 0.4812 | 0.4764 |
|RMSE-ASE| | 0.0030 | 0.0060 | 0.0100 |
基于随机森林模型提取的棉田分布情况(
不同尺度根系层土壤各盐渍化等级所占面积及比例
Areas and percentages of salinized root-zone soil relative to grade and scale
尺度 |
非盐化土 |
轻度盐化土 |
中度盐化土 |
合计 |
||||||||
棉田面积 |
比例 |
棉田面积 |
比例 |
棉田面积 |
比例 |
棉田面积 |
网格面积 |
棉田占比 |
||||
注*:因采样过程不可避免出现样点偏移,而内插和制图需覆盖全部样点,故500 m和100 m网格合计面积略大于16 km2和0.25 km2的设计值。Note:The total area of the 500 m and 100 m grids are slightly larger than the 16 km2 and 0.25 km2,the designed area,as during sampling it was inevitable to have the sampling points deviating slightly,while all samples needed to be covered in interpolation and mapping. | ||||||||||||
4 km | 315.8 | 70.45 | 131.4 | 29.31 | 1.06 | 0.24 | 448.2 | 880.1 | 50.93 | |||
500 m | 6.13 | 59.78 | 3.94 | 38.43 | 0.18 | 1.79 | 10.25 | 16.39* | 62.58 | |||
100 m | 0.182 3 | 74.26 | 0.054 4 | 22.15 | 0.008 8 | 3.59 | 0.245 5 | 0.255 8* | 95.98 |
4 km尺度(
不同尺度根系层土壤含盐量空间分布
Spatial distributions of soil salt content in the root-zone layer relative to scale
与4 km尺度相比,500 m尺度(
由于选择的是棉田占比最大的Ⅱ级网格单元,故100 m尺度(
总体而言,4 km尺度从整体上反映了根系层土壤含盐量在区域上的空间分布趋势,随着膜下滴灌技术的不断推广应用,除少部分有潜在盐渍化危险的区域外,安集海灌区膜下滴灌棉田根系层土壤的盐渍化已得到较好的控制(
以上分析针对的是根系层整体,而以往相关研究多数关注的仅是表层(常取为0~20 cm)土壤[
不同尺度不同深度层次根系层土壤含盐量空间分布
Spatial distributions of soil salt content in the root-zone layer relative to scale and layer
长期膜下滴灌的结果使得含盐量在不同层次土层中呈现出较大差异,表层土壤受滴灌水分的不断淋洗,绝大部分处于非盐化状态(
本文以安集海灌区为研究区,采用经典统计学和地统计学相结合的方法,探索了4 km、500 m和100 m三个不同尺度条件下膜下滴灌棉田根系层(0~100 cm)土壤含盐量的空间变异特征与分布规律,得到主要结果如下:(1)灌区根系层土壤含盐量分布不均,变幅较大(含盐量介于0.10~6.38 g·kg–1),但总体水平较低,主要为非盐化土和轻度盐化土,仅少部分区域达中度水平,无重度盐化土分布;(2)灌区土壤盐渍化是自然条件(结构性因素)和人为活动(随机性因素)综合作用的产物,不同研究尺度根系层的土壤含盐量均具有明显的空间结构特征,可用半方差函数模型较好地表征,相应半方差函数的变程均大于采样间距,样点内插和制图有效,伴随尺度的增大,根系层土壤含盐量的变异程度减弱、空间自相关性和结构性因素影响增强;(3)不同研究尺度下根系层土壤含盐量的统计特征与空间分布规律差异明显,大尺度(4 km)可较好地展现土壤盐渍化在灌区上的整体分布状况,中、小尺度则可观测到大尺度不能观测到的细微变化,由于较小尺度采样网格主要选在盐渍化相对更为严重区域,因而较4 km尺度而言,两个较小尺度(500 m和100 m)的土壤盐渍化稍显严重。此外,以往常采用的表层土壤采样无法真实表征膜下滴灌棉田根系层土壤的盐渍化状况。因此,针对盐渍化严重区域,应结合不同嵌套尺度并进行完整根系层采样,以更加清晰准确地阐明膜下滴灌棉田根系层土壤含盐量的空间分布规律和变异特性。土壤盐分演变是众多影响因素在空间和时间上相互作用的结果,本研究仅探讨了土壤含盐量在空间上的分布规律和变异特性,有必要充分利用遥感技术和手段,进一步开展长期膜下滴灌棉田根系层土壤含盐量的时空演变规律研究,从而为当地区域性水土资源管理和生态环境建设及可持续发展提供合理可靠的依据。
Chen X B, Yang J S, Zhang F D, et al. Control of soil water-salinity variations based on crop-saltwater production functionin Tarim irrigation area[J]. Journal of Irrigation and Drainage, 2007, 26(4): 75-78.
陈小兵, 杨劲松, 张奋东, 等. 基于水盐生产函数的绿洲灌区水盐调控研究[J]. 灌溉排水学报, 2007, 26(4): 75-78.
Meng C R, Yan L, Zhang S J, et al. Variation of soil salinity in plow layer of farmlands under long-term mulched drip irrigation in arid region[J]. Acta Pedologica Sinica, 2017, 54(6): 1386-1394.
孟超然, 颜林, 张书捷, 等. 干旱区长期膜下滴灌农田耕层土壤盐分变化[J]. 土壤学报, 2017, 54(6): 1386-1394.
Wang Z H, Yang P L, Zheng X R, et al. Variation characteristics of soil salinity and ion in root zone by long-term drip irrigation under mulch in typical oasis irrigation area[J]. Journal of Soil and Water Conservation, 2014, 28(3): 158-165.
王振华, 杨培岭, 郑旭荣, 等. 典型绿洲灌区长期膜下滴灌棉田根区土壤盐分及离子变化特征[J]. 水土保持学报, 2014, 28(3): 158-165.
Ning S R, Zuo Q, Shi J C. Advances in studying soil water and salt transport in the cotton filed with drip irrigation under film in Xinjiang[J]. Journal of Irrigation and Drainage, 2014, 33(2): 121-125.
宁松瑞, 左强, 石建初. 新疆膜下滴灌棉田水盐运移特征研究进展[J]. 灌溉排水学报, 2014, 33(2): 121-125.
Cheng W M, Zhou C H, Liu H J, et al. Oasis 50-year expansion and evolution of the ecological environment in Manas River basin[J]. Science in China, Series D: Earth Science, 2005, 35(11): 1074-1086.
程维明, 周成虎, 刘海江, 等. 玛纳斯河流域50年绿洲扩张及生态环境演变研究[J]. 中国科学: D辑: 地球科学, 2005, 35(11): 1074-1086.
Lü N N, Luo G P, Ding J L, et al. Spatio-temporal variation of soil salinity in wastelands inside and outside of oasis in Manas River watershed in the context of dripping irrigation[J]. Journal of Natural Resources, 2017, 32(9): 1542-1553.
吕娜娜, 罗格平, 丁建丽, 等. 滴灌背景下玛纳斯流域绿洲内外荒地土壤盐分时空变化趋势分析[J]. 自然资源学报, 2017, 32(9): 1542-1553.
Mu H C, Hudan·Tumaerbai, Su L T, et al. Salt transfer law for cotton field with drip irrigation under mulch in arid region[J]. Transactions of the Chinese Society of Agricultural Engineering, 2011, 27(7): 18-22.
牟洪臣, 虎胆·吐马尔白, 苏里坦, 等. 干旱地区棉田膜下滴灌盐分运移规律[J]. 农业工程学报, 2011, 27(7): 18-22.
Ji L, Liu B, He X L, et al. Changing characteristics and influencing causes of groundwater depth in irrigation areas in the lower reaches of the Manas River[J]. Journal of Irrigation and Drainage, 2015, 34(9): 59-65.
吉磊, 刘兵, 何新林, 等. 玛纳斯河下游灌区地下水埋深变化特征及成因分析[J]. 灌溉排水学报, 2015, 34(9): 59-65.
Florinsky I, Eilers R, Manning G, et al. Prediction of soil properties by digital terrain modelling[J]. Environmental Modelling & Software, 2002, 17(3): 295-311.
Goovaerts P. Geostatistics in soil science: State-of-the-art and perspectives[J]. Geoderma, 1999, 89(1/2): 1-45.
Yang Q Y, Yang J S, Yao R J. Evaluation on spatial distribution of soil salinity by indicator Kriging at two sampling scales[J]. Soils, 2011, 43(6): 998-1003.
杨奇勇, 杨劲松, 姚荣江. 不同尺度下土壤盐分空间变异的指示克里格评价[J]. 土壤, 2011, 43(6): 998-1003.
Yao R J, Yang J S, Liu G M, et al. Spatial variability of soil salinity in characteristic field of the Yellow River Delta[J]. Transactions of the Chinese Society of Agricultural Engineering, 2006, 22(6): 61-66.
姚荣江, 杨劲松, 刘广明, 等. 黄河三角洲地区典型地块土壤盐分空间变异特征研究[J]. 农业工程学报, 2006, 22(6): 61-66.
Liu G M, Lü Z Z, Yang J S, et al. Spatial variation characteristics of soil salinity in typical oasis region[J]. Transactions of the Chinese Society of Agricultural Engineering, 2012, 28(16): 100-107.
刘广明, 吕真真, 杨劲松, 等. 典型绿洲区土壤盐分的空间变异特征[J]. 农业工程学报, 2012, 28(16): 100-107.
Yan A, Jiang P A, Sheng J D, et al. Spatial variability of surface soil salinity in Manas River basin[J]. Acta Pedologica Sinica, 2014, 51(2): 410-414.
颜安, 蒋平安, 盛建东, 等. 玛纳斯河流域表层土壤盐分空间变异特征研究[J]. 土壤学报, 2014, 51(2): 410-414.
Blöschl G, Sivapalan M. Scale issues in hydrological modelling: A review[J]. Hydrological Processes, 1995, 9(3/4): 251-290.
Gao C Y. The cause of high mineralization of diving water quality in Anjihai irrigation area[J]. Xinjiang Water Resources, 1996(2): 26-29.
高长远. 安集海灌区潜水水质高矿化成因[J]. 新疆水利, 1996(2): 26-29.
Luo J X. Amelioration of saline-alkali soil in Xinjiang irrigation district[M]. Beijing: Press of Water Conservancy and Electric Power, 1985.
罗家雄. 新疆垦区盐碱地改良[M]. 北京: 水利电力出版社, 1985.
Cochran WG. Sampling techniques[M]. 3rd ed. New York: John Wiley, 1977.
Li M, Zhang X L, Wu J C. Sampling point arrangement based on GIS in eastern Henan Province[J]. Soils, 2011, 43(3): 459-465.
李梅, 张学雷, 武继承. GIS支持下豫东地区土壤野外采样布点方法探索[J]. 土壤, 2011, 43(3): 459-465.
Xu J H. Mathematical methods in contemporary geography[[M]. Beijing: Higher Education Press, 1996.
徐建华. 现代地理学中的数学方法[M]. 北京: 高等教育出版社, 1996.
Thanh Noi P, Kappas M. Comparison of random forest, k-nearest neighbor, and support vector machine classifiers for land cover classification using Sentinel-2 imagery[J]. Sensors, 2017, 18(2): 18.
Wang W J, Zhang X, Zhao Y D, et al. Cotton extraction method of integrated multi-features based on multitemporal Landsat 8 images[J]. Journal of Remote Sensing, 2017, 21(1): 115-124.
王文静, 张霞, 赵银娣, 等. 综合多特征的Landsat 8时序遥感图像棉花分类方法[J]. 遥感学报, 2017, 21(1): 115-124.
Utset A, Ruiz M E, Herrera J, et al. A geostatistical method for soil salinity sample site spacing[J]. Geoderma, 1998, 86(1/2): 143-151.
Stenger R, Priesack E, Beese F. Spatial variation of nitrate-N and related soil properties at the plot-scale[J]. Geoderma, 2002, 105(3/4): 259-275.
Ning S R, Shi J C, Zuo Q, et al. Generalization of the root length density distribution of cotton under film mulched drip irrigation[J]. Field Crops Research, 2015, 177: 125-136.
Bao S D. Soil and agricultural chemistry analysis[M]. Beijing: China Agriculture Press, 2000.
鲍士旦. 土壤农化分析[M]. 北京: 中国农业出版社, 2000.
Wang Z Q. Geostatistics and its application in ecology[M]. Beijing: Science Press, 1999.
王政权. 地统计学及在生态学中的应用[M]. 北京: 科学出版社, 1999.
Xie Y F, Chen T B, Lei M, et al. Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: Accuracy and uncertainty analysis[J]. Chemosphere, 2011, 82(3): 468-476.
Wang Z Q, Zhu S Q, Yu R P, et al. Salt-affected soil in China[M]. Beijing: Science Press, 1993.
王遵亲, 祝寿泉, 俞仁培, 等. 中国盐渍土[M]. 北京: 科学出版社, 1993.
Xin M L, Lu T B, He X L, et al. Spatial variation of surface soil salinity in under-film drip irrigating of cotton field in irrigated areas of Manas River Basin[J]. Agricultural Research in the Arid Areas, 2017, 35(4): 74-79.
辛明亮, 吕廷波, 何新林, 等. 玛河灌区膜下滴灌棉田表层土壤盐分空间变异性[J]. 干旱地区农业研究, 2017, 35(4): 74-79.
Shen H, Jilili Abuduwaili. Spatial distribution of soil moisture and salinity and their influence factors in the farmland of Manas River catchment, Northwest China[J]. Chinese Journal of Applied Ecology, 2015, 26(3): 769-776.
沈浩, 吉力力·阿不都外力. 玛纳斯河流域农田土壤水盐空间分布特征及影响因素[J]. 应用生态学报, 2015, 26(3): 769-776.
Guo X D, Fu B J, Ma K M, et al. Spatial variability of soil nutrients based on geostatistics combined with GISA case study in Zunhua City of Hebei Province[J]. Chinese Journal of Applied Ecology, 2000, 11(4): 557-563.
郭旭东, 傅伯杰, 马克明, 等. 基于GIS和地统计学的土壤养分空间变异特征研究-以河北省遵化市为例[J]. 应用生态学报, 2000, 11(4): 557-563.
Cambardella C A, Moorman T B, Novak J M, et al. Field-scale variability of soil properties in central Iowa soils[J]. Soil Science Society of America Journal, 1994, 58(5): 1501-1511.
Zhang F S, Liu Z X. Fractal theory and its application in the analysis of soil spatial variability: A review[J]. Chinese Journal of Applied Ecology, 2011, 22(5): 1351-1358.
张法升, 刘作新. 分形理论及其在土壤空间变异研究中的应用[J]. 应用生态学报, 2011, 22(5): 1351-1358.
Hu K L, Li B G, Lü Y Z, et al. Comparison of various spatial interpolation methods for non-stationary regional soil mercury content[J]. Chinese Journal of Environmental Science, 2004, 25(3): 132-137.
胡克林, 李保国, 吕贻忠, 等. 非平稳型区域土壤汞含量的各种估值方法比较[J]. 环境科学, 2004, 25(3): 132-137.