基于地理加权回归克里格的日平均气温插值

气温是大量农业、水文、气候、生态模型的输入变量.在地形复杂的区域,考虑气温与环境变量的线性回归关系和残差的自相关性的方法(如回归克里格法,regression Kriging,RK)是目前气温插值的主要方法.但此类方法多使用基于普通最小二乘的全局回归技术,没有顾及回归关系的空间非平稳性.地理加权回归克里格(geographically weighted regression-Kriging,GWRK)是一种既能顾及回归关系的空间非平稳性、又能考虑残差的自相关性的一种插值方法.本文用RK和GWRK对海南岛2013年12月18日的日平均气温进行插值并进行比较研究.依相关性分析和逐步回归分析的结果,采用RK1(以海拔为辅助变量)、GWRK1(以海拔为辅助变量)、RK2(以纬度、海拔、海陆距离为辅助变量)和GWRK2(以海拔、海陆距离为辅助变量)4种模型进行研究,并用80个验证站评估4种模型的精度.结果表明:GWRK1模型的最大正误差、最大负误差、平均绝对误差、均方根误差均最接近于0.从最大正误差、平均绝对误差、均方根误差3个指标看,考虑更多辅助变量的RK2、GWRK2模型反而不及只考虑海拔的RK1、GWRK1模型,表明RK2、GWRK2模型中辅助变量之间的相关性对插值结果有较大影响.     

基于协同克里格的橡胶园土壤速效钾空间变异性

选取有效变量的协同克里格方法能够提高县域尺度橡胶园土壤速效钾的空间预测精度,对橡胶树精准施肥管理具有重要意义。本研究以海南省白沙县橡胶园0～20 cm耕层土壤为对象,采用地统计学分析土壤速效钾的空间变异特征,运用相关分析筛选显著的特征变量,并比较不同变量的协同克里格(COK)空间插值精度。结果表明: 研究区土壤速效钾平均含量为44.65 g·kg^-1,总体处于缺乏状态;变异系数为52.6%,属中等变异强度;块金效应为12.5%,存在较强的空间自相关。有机质、高程与土壤速效钾含量关系密切,均呈极显著相关;有机质(COK₁)、高程(COK₂)、有机质+高程(COK₃)3种协变量的COK空间插值预测精度均高于普通克里格法(OK),交叉验证模型拟合精度为COK₁>COK₃> COK₂>OK;拟合精度与协变量选取的数量不呈正比,选取相关性更高的协变量更有利于反映区域土壤属性的空间异质性。研究区土壤速效钾含量具有西北部较高、中偏东部地区较低的分布特点。研究结果为今后开展橡胶园土壤钾素管理提供了理论依据。     

基于回归和地理加权回归Kriging的土壤有机质空间插值

基于地形因子与土壤有机质的相关分析,选取相对高程和汇流动力指数作为辅助变量.以普通克里格(OK)作对照,比较地理加权回归克里格(GWRK)与回归克里格(RK)在土壤有机质空间插值及制图上的精度与效果.结果表明:土壤有机质含量与相对高程呈显著正相关,与汇流动力指数呈显著负相关;经半方差分析,土壤有机质及其插值残差具有强烈的空间自相关;对验证集中98个样点的精度加以分析,RK法插值结果的平均误差(ME)、平均绝对误差(MAE)、均方根误差(RMSE)较OK法分别降低39.2％、17.7％和20.6％,相对提高度(RI)为20.63,GWRK法插值结果的ME、MAE、RMSE较OK法分别降低60.6％、23.7％、27.6％,RI为59.79.与OK相比,考虑了辅助变量的RK和GWRK明显提高了插值精度;GWRK考虑了样点位置,成图效果更加精细,对土壤有机质的局部模拟效果优于RK.     

河北省年均降水量插值方法比较

以河北省及临近区域120个气象观测站点1971～2000年均降水量数据为基础,选择其中的40个作为检验站点,其余站点分别取80、40、20个作为插值站点,采用局部插值、整体插值、多元线性回归、综合模拟等多种插值模型讨论了降水空间插值问题,主要结论如下:插值站点数、模型类型、模型参数都会影响插值精度.局部插值模型相对误差最小值出现在Spline、IDW模型中,其次为Kridging模型,而整体模型Trend、多元线性回归模型误差均较大,但综合了局部插值模型和统计模型的综合模型一定程度上能改善插值精度及误差分布.河北省80和40个站点的最优插值模型为综合模型,20个站点的最优插值模型为IDW2.     

基于辅助环境变量的土壤有机碳空间插值——以黄土丘陵区小流域为例

利用普通克里格法(OK)、反距离加权法(IDW)、径向基函数法(RBF)、基于土地利用类型修正的普通克里格法(OK_LU)4种插值方法,对黄土丘陵羊圈沟小流域的土壤有机碳含量进行空间插值。预测结果的准确性通过Pearson相关系数(R),平均绝对误差(MAE),均方根误差(RMSE),准确度(AC)来评价。研究结果表明:(1)在前3种常规空间插值方法中,OK对刻画区域土壤有机碳的空间分布趋势效果最佳,其预测MAE值和RMSE值均为最小,Pearson相关系数(R)和准确度(AC)最大,说明其预测结果的准确性最好、预测的极端误差也最小;其次为RBF;IDW预测的效果最差。(2)OK_LU在空间特征表达方面能够更好地反映复杂地形区的局部变异,其插值结果的精度相比OK有一定程度的提高,其平均绝对误差(MAE)从0.900%降到了0.567%,均方根误差(RMSE)从1.101%降到了0.777%,Pearson相关系数(R)从0.4026提高到0.5589,准确度(AC)从0.9081提高到0.9505。综合比较,在黄土丘陵地区,OK_LU能使插值结果的精度有较大提高,是土壤有机碳空间制图的有效途径。     

不同干扰程度下土壤有机质空间最优插值法研究

选择最优空间插值方法对明确不同干扰程度下干旱区土壤有机质空间分布规律具有重要意义。通过对新疆阜康市土壤采样分析,分别运用普通克里格法(Ordinary Kriging, OK)、反距离权重法(inverse distance weight, IDW)、径向基函数法(radial basis function, RBF)、局部多项式法(local polynomial, LPI)4种插值方法,描述不同人为干扰程度下干旱区土壤有机质空间分布特征,以探讨其最优空间插值方法。结果表明:①随干扰程度增加,土壤有机质含量降低,空间变异性由弱到中等,变异系数由9.27%增加至28.7%;同时,土壤有机质空间自相关性逐渐降低,从无人为干扰区、人为干扰区到重度人为干扰区分别呈强烈、中等、弱相关关系,即干扰程度越强受随机因素作用越大。②虽然4种方法的插值精度均随干扰程度的增强而降低。但OK法在空间结构性较强的无人为干扰区插值效果最好,R~2为0.625;在人为干扰区及重度人为干扰区RBF法的插值精度均最高,R~2分别为0.562和0.434。该结果为寻找适合于不同干扰程度下干旱区土壤有机质的空间插值方法提供一定的科学参考。     

海洋浮游植物丰度的空间插值优化

在探索性空间数据分析(Exploratory spatial data analysis)和数据转化的基础上,利用反距离加权(Inverse distance weighting,IDW)、径向基函数(Radial basis functions,RBF)、普通克里格(Ordinary Kriging,OK),3种插值方法,对2003年8月获得的珠江口浮游植物丰度数据进行插值运算,并对插值准确度进行交叉验证。结果显示,珠江口浮游植物丰度数据具有离散性大、存在极大和极小值、呈正偏分布等特点。而对数转化能大大减小数据的离散性和不对称性,有效消除插值结果图中各类插值噪音。交叉验证显示,插值精确度OK最高,RBF次之,IDW最低。观察插值结果等值面图,发现3种方法均能较客观地模拟出浮游植物丰度的总体分布趋势,在对局部趋势的模拟上,OK的表现最好。综合评定,OK为最适合珠江口浮游植物丰度数据的插值方法。半变异模型的选择对OK的插值结果影响不明显。在四种半变异模型中,圆形模型的拟合效果最好。     

黄土高原年均降水量空间插值及其方法比较

采用不同空间插值方法(普通克里格法OK、反距离权重法IDW和径向基函数法RBF),对黄土高原地区85个气象站点1957—2013年逐日降水数据进行年均降水量空间插值分析,采用平均绝对误差(MAE)、均方根误差(RMSE)、Pearson相关系数(R)以及准确度(AC)对插值结果进行对比,研究不同方法对该地区年均降水量插值结果的影响.结果表明:研究期间,黄土高原地区年均降水量的Moran I值为0.67,各站点年均降水量存在较强的空间自相关性.63个预测站点和22个检验站点的验证结果显示,3种方法的实测值和预测值均显著相关,但反距离权重法和径向基函数法的平均绝对误差(MAEIDW=38.98,MAERBF=34.61)和均方根误差(RMSEIDW=51.49,RMSERBF=43.79)均高于普通克里格法.通过普通克里格法的不同半变异函数模型(环形模型、球体模型、指数模型、高斯模型)对比发现,环形模型的平均绝对误差最小(MAE=32.34),准确度最高(AC=0.976),指数模型平均绝对误差最大(MAE=33.24).综合对比不同插值方法实测值与估算值的验证结果表明,采用半变异函数为环形模型的普通克里格法是进行黄土高原年均降水量插值较好的方法.     

利用辅助变量对污染土壤锌分布的克里格估值

采用协同克里格及与回归相结合的克里格方法,以36个下层(10～20 cm)土壤锌数据为目标变量、另36个下层土壤锌数据为校验数据、72个上层(0～10 cm)土壤锌为辅助变量,对沈阳市南郊某有色金属加工厂附近农田0.1 mol·L^-1 HCl浸提态土壤锌进行插值分析,并对这两种利用辅助变量的克里格方法在土壤锌空间分布研究中的适用性进行评价.结果表明,与回归相结合的克里格的估值效果明显优于协同克里格及普通克里格法.结合回归模型的变异函数理论模型决定系数较大、残差较小,估值精度比普通克里格法提高4%,且基于回归克里格的土壤锌分布图与利用72个样点普通克里格插值图具有高度的相似性.而协同克里格与普通克里格相比未表现出明显优势.借助辅助变量,采用基于回归模型的克里格方法是进行土壤重金属空间分布估值的一种有效方法.     

西双版纳热带山地雨林枯落物及其土壤水文功能

研究了云南西双版纳热带不同海拔梯度山地雨林枯落物层及土壤层水文功能.结果表明: 土壤容重随着海拔的增加而降低,土壤总孔隙度、非毛管孔隙度、毛管孔隙度、土壤最大持水率、最大持水量、有效持水量和土壤含水量随海拔的增加而增加,局部有所波动;雨季前期含水量、饱和含水量和有效调蓄水空间随海拔的增加而增加,其中,饱和含水量和土壤有效调蓄水空间在不同海拔区差异均显著(P<0.05).土壤渗透性能与总孔隙度和非毛管孔隙度均呈极显著正相关关系(P<0.01),其中,非毛管孔隙对土壤渗透性的影响更为显著.不同海拔枯落物未分解层厚度均占总厚度的一半以上,枯落物厚度均表现为未分解层＞半分解层;枯落物总蓄积量和半分解层蓄积量占枯落物总蓄积量的比例均随海拔的增加而增加,说明低海拔枯落物分解速度较慢,高海拔枯落物分解速度较快.不同海拔枯落物半分解层和未分解层最大持水量、最大持水率、自然含水率、有效拦蓄率和有效拦蓄量均随海拔的增加而增加,并且各海拔未分解层均高于半分解层,而有效拦蓄量深度随海拔的增加而降低,局部有所波动.综合未分解层和半分解层的变化规律可知,高海拔拦蓄能力较强,低海拔较弱.不同海拔枯落物持水量随着浸泡时间增加而增加;枯落物吸水速率随着浸泡时间增加而降低,12 h后枯落物吸水速率逐渐趋于饱和.不同海拔枯落物持水量与浸水时间可用对数方程表示;吸水速率与浸泡时间可用冥函数方程表示.综合分析各项因子,低海拔热带山地雨林水源涵养能力普遍低于高海拔.     

Combining geostatistical models and remotely sensed data to improve tropical tree richness mapping

Information on the spatial distribution and composition of biological communities is essential in designing effective strategies for biodiversity conservation and management. Reliable maps of species richness across the landscape can be useful tools for these purposes. Acquiring such information through traditional survey techniques is costly and logistically difficult. The kriging interpolation method has been widely used as an alternative to predict spatial distributions of species richness, as long as the data are spatially dependent. However, even when this requirement is met, researchers often have few sampled sites in relation to the area to be mapped. Remote sensing provides an inexpensive means to derive complete spatial coverage for large areas and can be extremely useful for estimating biodiversity. The aim of this study was to combine remotely sensed data with kriging estimates (hybrid procedures) to evaluate the possibility of improving the accuracy of tree species richness maps. We did this through the comparison of the predictive performance of three hybrid geostatistical procedures, based on tree species density recorded in 141 sampling quadrats: co-kriging (COK), kriging with external drift (KED), and regression kriging (RK). Reflectance values of spectral bands, computed NDVI and texture measurements of Landsat 7 TM imagery were used as ancillary variables in all methods. The R² values of the models increased from 0.35 for ordinary kriging to 0.41 for COK, and from 0.39 for simple regression estimates to 0.52 and 0.53 when using simple KED and RK, respectively. The R² values of the models also increased from 0.60 for multiple regression estimates to 0.62 and 0.66 when using multiple KED and RK, respectively. Overall, our results demonstrate that these procedures are capable of greatly improving estimation accuracy, with multivariate RK being clearly superior, because it produces the most accurate predictions, and because of its flexibility in modeling multivariate relationships between tree richness and remotely sensed data. We conclude that this is a valuable tool for guiding future efforts aimed at conservation and management of highly diverse tropical forests.     

Mapping soil organic matter using the topographic wetness index: A comparative study based on different flow-direction algorithms and kriging methods

Terrain attributes derived from digital elevation models have been used widely for mapping soil organic matter (SOM). Among these attributes, the topographic wetness index (TWI), an index for quantitatively indicating the balance between water accumulation and drainage conditions at the local scale, has been shown to correlate with SOM. However, TWIs used in most studies are calculated using a single-flow-direction (SFD) algorithm, which assumes that all water from a grid cell flows into only one neighboring cell. This assumption is not always valid, especially in areas with low relief where movement of water may be divergent. To overcome this SFD limitation, a multiple-flow-direction (MFD) algorithm has been developed, which distributes flow from a grid cell to several downslope neighbors. In this study we compared the effect of TWI calculations based on SFD and MFD in predictive mapping of SOM by incorporating them into different kriging methods over a 51.76 km² area in Nenjiang County of northeastern China. We found that the MFD-based TWI was better correlated with SOM than was the SFD-based index. We then compared the accuracies of SOM maps which were derived from MFD-based TWI and SFD-based TWI incorporated by ordinary kriging (OK), simple kriging with varying local means (SKlm), kriging with external drift (KED) and collocated cokriging (CC). The MFD-based TWI, used as a secondary variable in SKlm and CC, outperforms the SFD-based TWI. For the different kriging methods, CC (incorporating either MFD-based TWI or SFD-based TWI) showed the best performance, and OK generated a better result than SKlm and KED. Both the MFD-based TWI and SFD-based TWI proved to be incompatible with KED and SKlm due to their numerical instability caused by the rough TWI surfaces. Among all predictive methods, CC incorporating the MFD-based TWI produced the best results. This is because: (1) the MFD-based TWI is best able to indicate quantitatively soil moisture and therefore has the strongest correlation with SOM; (2) CC is capable of utilizing effectively the spatial auto-correlation of SOM and the cross-correlation between SOM and the MFD-based TWI.     

Mapping forest vegetation patterns in an Atlantic-Mediterranean transitional area by integration of ordination and geostatistical techniques

Aims Forest vegetation variability may be explained by the complex interplay among several spatial structuring factors, including climate and topography. We modelled the spatial variability of forest vegetation assemblages and significant environmental variables along a complex environmental gradient or coenocline to produce a detailed cartographic database portraying the distribution of forests along it.Methods We combined an analysis of ordination coenoclines with kriging over 772 field data plots from the third Spanish National Forest Inventory in an Atlantic–Mediterranean transitional area (northern Spain).Important findings The best fitted empirical semivariogram revealed a strong spatial structure of forest species composition along the complex environmental gradient considered (the climatic–topographic gradient from north to south). The steady and gradual increase of semivariance with a marked lag distance indicates a gradual turnover of forest assemblages according to the climatic–topographic variations (regional or local). Two changes in the slope of the semivariogram suggest the existence of two different scales of spatial variation. The interpolation map by Kriging of forest vegetation assemblages along the main coenocline shows a clear spatial distribution pattern of trees and shrubs in accordance with the spatial variation of significant environmental variables. We concluded that the multivariate geostatistical approach is a suitable technique for spatial analysis of forest systems employing data from national forest inventories based on a regular network of field plots. The development of an assortment of maps describing changes in vegetation assemblages and variation in environmental variables is expected to be a suitable tool for an integrated forest management and planning.     

典型亚热带森林生态系统碳密度及储量空间变异特征

以浙江省森林生态系统为研究对象,基于GIS网格布点,采集了838个森林样地样本(土壤、枯落物等),结合浙江省森林资源监测中心相关数据,利用地统计学和Moran's I相结合的方法系统研究了浙江省森林生态系统碳密度及碳储量空间变异特征。结果表明:浙江省森林生态系统平均碳密度为145.22 t/hm~2,其中森林植被、土壤、枯落物和枯死木层碳密度分别为27.34、108.89、1.79、1.38 t/hm~2。克里格空间插值和局部Moran's I指数结果表明碳密度空间分布规律呈现从西南向东北方向逐渐递减的趋势,与浙江省地形、地势较为一致,受海拔、树龄、森林类型、台风气候等自然因素和人类活动共同影响。浙江省森林生态系统碳储量为877.19 Tg C,森林植被、土壤、枯落物和枯死木层碳储量分别为203.88、656.20、10.84、6.27 Tg C,分别占总碳储量的23%、75%、1.3%、0.7%。在浙江省森林生态系统碳储量空间分布格局中,土壤层是森林生态系统中最大的碳库,约是森林植被层的3.22倍,是整个浙江省森林生态系统碳储量最主要的贡献者。浙江省森林资源丰富,大多数森林仍处于中幼龄林阶段,碳密度水平较低,但是中幼龄林生长速度较快,加强对全省中幼龄林的健康管理,是未来整体提升浙江省森林生态系统固碳潜力的关键。     

长白山低山区森林土壤有机碳及养分空间异质性

以吉林延边汪清林业局金仓林场境内森林土壤为对象,采用多元线性回归方法和地统计学回归克里格方法,研究了土壤有机碳及养分的垂直分布规律,预测了其空间分布,并对预测结果进行插值.结果表明: 0～60 cm深度土壤有机碳密度为(16.14±4.58) kg·m^-2.随土壤深度增加,土壤有机碳含量、有机碳密度以及土壤全N、全P、全K、有效P及速效K含量都呈减小趋势,其中不同土层间土壤有机碳含量、有机碳密度差异显著(P<0.01).0～60 cm土层土壤有机碳含量和碳密度的拟合方程中,地形因子中高程和坡向余弦值是最优的拟合因子,方程的决定系数分别为0.34和0.39(P<0.01).0～20和0～60 cm土层的半方差函数模型分别为高斯模型和指数模型,利用回归克里格插值方法得到土壤有机碳的空间分布图.与普通克里格法相比,回归克里格法的空间预测精度改进了18%～58%.利用回归克里格插值方法预测了土壤全N的空间分布特征.     

Bioclimatic and vegetation mapping of a topographically complex oceanic island applying different interpolation techniques

Different spatial interpolation techniques have been applied to construct objective bioclimatic maps of La Palma, Canary Islands. Interpolation of climatic data on this topographically complex island with strong elevation and climatic gradients represents a challenge. Furthermore, meteorological stations are not evenly distributed over the island, with few stations at high elevations. We carried out spatial interpolations of the compensated thermicity index (Itc) and the annual ombrothermic Index (Io), in order to obtain appropriate bioclimatic maps by using automatic interpolation procedures, and to establish their relation to potential vegetation units for constructing a climatophilous potential natural vegetation map (CPNV). For this purpose, we used five interpolation techniques implemented in a GIS: inverse distance weighting (IDW), ordinary kriging (OK), ordinary cokriging (OCK), multiple linear regression (MLR) and MLR followed by ordinary kriging of the regression residuals. Two topographic variables (elevation and aspect), derived from a high-resolution digital elevation model (DEM), were included in OCK and MLR. The accuracy of the interpolation techniques was examined by the results of the error statistics of test data derived from comparison of the predicted and measured values. Best results for both bioclimatic indices were obtained with the MLR method with interpolation of the residuals showing the highest R ² of the regression between observed and predicted values and lowest values of root mean square errors. MLR with correction of interpolated residuals is an attractive interpolation method for bioclimatic mapping on this oceanic island since it permits one to fully account for easily available geographic information but also takes into account local variation of climatic data.     

Spatial analysis of marine categorical information using indicator kriging applied to georeferenced video mosaics of the deep-sea Håkon Mosby Mud Volcano

The exact area calculation of irregularly distributed data is in the focus of all territorial geochemical balancing methods or definition of protection zones. Especially in the deep-sea environment the interpolation of measurements into surfaces represents an important gain of information, because of cost- and time-intensive data acquisition. The geostatistical interpolation method indicator kriging therefore is applied for an accurate mapping of the spatial distribution of benthic communities following a categorical classification scheme at the deep-sea submarine Håkon Mosby Mud Volcano. Georeferenced video mosaics were obtained during several dives by the Remotely Operated Vehicle Victor6000 in a water depth of 1260 m. Mud volcanoes are considered as significant source locations for methane indicated by unique chemoautotrophic communities as Beggiatoa mats and pogonophoran tube worms. For the detection and quantification of their spatial distribution 2840 georeferenced video mosaics were analysed by visual inspection. Polygons, digitised on the georeferenced images within a GIS, build the data basis for geostatistically interpolated mono-parametric surface maps. Indicator kriging is applied to the centroids of the polygons calculating surface maps. The quality assessment of the surface maps is conducted by leave-one-out cross-validation evaluating the fit of the indicator kriging variograms by using statistical mean values. Furthermore, the estimate was evaluated by a validation dataset of the visual inspection of 530 video mosaics not included within the interpolation, thus, proving the interpolated surfaces independently. With regard to both validating mechanisms, we attained satisfying results and we provided each category applied for the identification of biogeochemical habitats with a percentage probability value of occurrence.     

Geostatistical approaches and optimal additional sampling schemes for spatial patterns and future sampling of bird diversity

Aim To evaluate geostatistical approaches, namely kriging, co‐kriging and geostatistical simulation, and to develop an optimal sampling design for mapping the spatial patterns of bird diversity, estimating their spatial autocorrelations and selecting additional samples of bird diversity in a 2450 km² basin. Location Taiwan. Methods Kriging, co‐kriging and simulated annealing are applied to estimate and simulate the spatial patterns of bird diversity. In addition, kriging and co‐kriging with a genetic algorithm are used to optimally select further samples to improve the kriging and co‐kriging estimations. The association between bird diversity and elevation, and bird diversity and land cover, is analysed with estimated and simulated maps. Results The Simpson index correlates spatially with the normalized difference vegetation index (NDVI) within the micro‐scale and the macro‐scale in the study basin, but the Shannon diversity index only correlates spatially with NDVI within the micro‐scale. Co‐kriging and simulated annealing simulation accurately simulate the statistical and spatial patterns of bird diversity. The mean estimated diversity and the simulated diversity increase with elevation and decrease with increasing urbanization. The proposed optimal sampling approach selects 43 additional sampling sites with a high spatial estimation variance in bird diversity. Main conclusions Small‐scale variations dominate the total spatial variation of the observed diversity due to a lack of spatial information and insufficient sampling. However, simulations of bird diversity consistently capture the sampling statistics and spatial patterns of the observed bird diversity. The data thus accumulated can be used to understand the spatial patterns of bird diversity associated with different types of land cover and elevation, and to optimize sample selection. Co‐kriging combined with a genetic algorithm yields additional optimal sampling sites, which can be used to augment existing sampling points in future studies of bird diversity.