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1.
喀斯特地区春季土壤水分空间插值方法对比   总被引：1，自引：0，他引：1  
以杨眉河小流域为研究区,通过土壤水分采样,选取辅助变量,采用普通克里金、协同克里金、回归克里金3种地统计学方法对土壤水分数据进行空间插值。结果表明：1）回归克里金对研究区土壤水分估算误差最小,其次为协克里金,普通克里金的误差最大;2）普通克里金生成的土壤水分表面最为平滑,而回归克里金最大程度反映了研究区实际的土壤水分空间变化;3）对于协同克里金,以湿度指数（WI）样点数据作为辅助变量的估算误差小于将WI栅格数据作为辅助变量的估算误差。总之,在可获得有效辅助变量的条件下,回归克里金对研究区土壤水分估算的效果优于协同克里金与普通克里金。  相似文献   

2.
秦岭中部山地降水的垂直变化研究   总被引：1，自引：0，他引：1  
明确秦岭高海拔山区降水的变化规律,是深入理解秦岭作为中国南北地理过渡带特征、认识秦岭水资源在南水北调中线工程中重要作用的前提。但秦岭高海拔地区长期缺乏有效的降水观测数据,导致对其降水变化缺乏了解。利用2018年6月1日—2019年5月31日秦岭太白山海拔3760 m实测降水数据,发现在秦岭海拔3760 m处年降水量可达1300 mm,远高于汉江盆地和关中平原600~800 mm的年降水量。在此基础上,检验了克里金（Kriging）、反距离加权（IDW）和薄盘样条（ANUSPLIN）插值方法,以及GPM修正数据（GPM-cal）和ERA5再分析资料对秦岭中部山地年和季节降水空间模态的再现效果,各方案均能揭示秦岭高山区是降水高值中心,且降水随海拔的升高而增大,但利用克里金、反距离加权插值方案不能得到准确的高海拔降水值,与此相比,GPM-cal数据、薄盘样条插值与ERA5资料能较准确刻画秦岭中部山地年降水量随地形的变化。水汽通量分析显示,秦岭凭借高大地形对600 hPa高度以下的南来湿润气流具有明显的阻挡、强迫和拦截作用,使其南坡成为区域降水高值中心。结合高山区降水观测、薄盘样条插值、多源格点资料和数据修正方法,是认识秦岭山地降水形成和变化的有效途径。  相似文献   

3.
Generally, multiple variables are sampled in addition to the one used to quantify the main phenomenon under study. In some situations, this secondary information is sampled exhaustively for the study area and can be incorporated for helping in estimating the variable of interest. There are several methodologies available for incorporating densely sampled secondary information. Collocated cokriging is one of these methodologies and has the advantage to other methodologies, of accounting for spatial correlation. However, one drawback in its application comes from the difficulty in modeling the coregionalization. Simplified models of coregionalization were developed specifically for the collocated cokriging case. This paper presents, through a case study, the incorporation of dense secondary information using collocated cokriging. The watertable above a coal underground mine is mapped using water-level readings at monitoring piezometers complemented by highly correlated topographic data. The incorporation of dense secondary information through the utilization of a linear model of coregionalization and Markov models is comparatively evaluated in various aspects such as mathematical quality, coherence with the natural phenomena and the ease of utilization and modeling. Simple kriging with local varying means also is evaluated as it accounts for nonstationarity and is easily implemented. All these methods that incorporate topography as secondary information for mapping the watertable provided maps more in accordance with the natural phenomena than ordinary kriging using the principal attribute solely. Among these methods, strictly collocated cokriging using a linear model of coregionalization showed overall superior performance.  相似文献   

4.
王红  刘高焕  宫鹏 《地理学报》2005,60(3):511-518
估算土壤中化学物质的含量与空间分布是了解多孔介质中水盐运移规律并进而因地制宜地提出盐渍土改良措施的关键。大面积的实地采样分析费时费力且耗资巨大。通过地统计分析, 使用有限的采样数据可获得土壤溶质的准确变异。本文探讨和比较了Ordinary kriging (OK) 与Cokriging (COK) 这两种内插方法。结果显示一半的采样点数据的COK较之全部采样点数据的OK精度更高, 相对均方根误差降幅为130.83%;采用同样的协同变量 (239个全盐量数据), 一半的采样点数据的COK较之全部采样点数据的COK精度更高, 相对均方根误差降幅为20.10%。协同变量与主变量的相关度决定了COK的预测精度, 当相关系数由77%升高为99%时, 相对均方根误差降低了48.30%。  相似文献   

5.
“Krige”空间内插技术在地理学中的应用   总被引：24，自引：1，他引：24  
称为“Krige”技术的内插稀疏观测资料的随机方法是Matheron(1970年)提出的,D.R.Krige首先将这一方法应用于找矿上,因而命名于“Krige”技术。本文首先定义和说明了空间协方差曲线,基于无偏估计和最优原理导出了“Krige”内插权重系数的代数方程组,最后给出实例说明该方法如何应用到地理学和水文学中。  相似文献   

6.
Five decades of geostatistical development are reviewed to summarize the state of the art for spatial interpolation vis-à-vis kriging or a form thereof. Although a search of the literature reveals a variety of kriging methods, there are but two infrastructures for geostatistical interpolation: simple cokriging, for estimating a single variable using two variables, and generalized cokriging, for estimating one or more variables using the same number of variables that are estimated. The many forms of kriging are varieties of these two interpolation infrastructures. This notion is emphasized to aid the selection of an appropriate interpolation model for a nonrenewable resource. These models are discussed, and literature for the models and for applicable software is cited. Additionally, all aspects of spatial interpolation are discussed, including the adequacy of spatial sampling, distribution characteristics of spatial samples, semivariograms, search parameters, and selection of interpolation models in conformance with spatial data characteristics. Finally, the relationship between interpolation and raster-based geographic information systems is emphasized.  相似文献   

7.
A series of rainfalls observed in central Japan from noon on the 13th to midnight on the 14th, August 1999 (36 h), has been analyzed by spatiotemporal variograms in order to reveal the continuity of rain precipitation in a 3-D space defined by geographic coordinates and time. All instances of zero precipitation are considered, but have been treated as four different cases: case 0 excludes all zero data, case 1 includes a zero datum neighboring to each finite value, case 2 includes a zero neighboring to each finite value and the next neighboring zero, and a fourth case (termed case A) includes all zeros. Hourly precipitation has a statistical distribution best approximated by a Weibull model, and somewhat less well by a normal distribution, in all four cases. A rectangular variogram of measured values of total precipitation shows that the best continuity appears approximately along the N-S direction (the ranges given by directional variograms are 500 and 80 km in the N-S and W-E directions, respectively). In contrast, temporally stacked rectangular variograms of hourly precipitation shows that the best continuity direction is W-E in all cases (the ranges in case A are 50 and 100 km along the N-S and W-E directions, respectively). A spatial variogram gives a spatial range independently of time, whereas a temporal variogram gives a temporal range. When geographic coordinates are normalized by the spatial range (here 80 km given by the temporally stacked omnidirectional variogram in case A), and time is normalized by the temporal range (here 7 h given by the spatially stacked temporal variogram), geographic coordinates and time can be treated as equivalent variables. Consequently, a spatiotemporal variogram can be calculated along a given direction in 3-D space using the normalized coordinates. The continuity direction of a series of rainfalls can be best understood by display on a Wulff net, where each range value is written at a point corresponding to the direction. The direction of the best continuity is N0°W+20° in the normalized space. A rectangular variogram in the normalized space, in which the horizontal and vertical axes represent N-S direction and time, respectively, suggests that the series of heavy rainfalls examined here had a continuity pattern that was elongated from west to east (the range values are 20–30 km and 100 km along N-S and W-E, respectively), and that migrated from south to north with a speed of 30 km/h.  相似文献   

8.
Small-sized housing samples and price predictions at nonobserved locations require geostatistical approaches, particularly the kriging estimator. Nevertheless, geostatistics has thus far received little attention in real estate economics. The article’s objective is to empirically compare the prediction accuracy of univariate kriging variants, namely detrended kriging (DK) and universal kriging (UK), and multivariate extensions, including detrended cokriging (DCK) and universal cokriging (UCK). Both latter methods consider structural and neighborhood characteristics as auxiliary variables. While the price surfaces of DK and UK show nearly identical cross-validated accuracies, the cross-validation-based prediction accuracy of DCK and UCK differ in favor of the latter. If real estate agencies are faced with a univariate sample of property prices, either DK or UK can be used, while in the multivariate case, UCK is recommended, although numerically more complex.  相似文献   

9.
Tropical laterite-type bauxite deposits often pose a unique challenge for resource modelling and mine planning due to the extreme lateral variability at the base of the bauxite ore unit within the regolith profile. An economically viable drilling grid is often rather sparse for traditional prediction techniques to precisely account for the lateral variability in the lower contact of a bauxite ore unit. However, ground-penetrating radar (GPR) offers an inexpensive and rapid method for delineating laterite profiles by acquiring fine-scale data from the ground. These numerous data (secondary variable) can be merged with sparsely spaced borehole data (primary variable) through various statistical and geostatistical techniques, provided that there is a linear relation between the primary and secondary variables. Four prediction techniques, including standard linear regression, simple kriging with varying local means, co-located cokriging and kriging with an external drift, were used in this study to incorporate exhaustive GPR data in predictive estimation the base of a bauxite ore unit within a lateritic bauxite deposit in Australia. Cross-validation was used to assess the performance of each technique. The most robust estimates are produced using ordinary co-located cokriging in accordance with the cross-validation analysis. Comparison of the estimates against the actual mine floor indicates that the inclusion of ancillary GPR data substantially improves the quality of the estimates representing the bauxite base surface.  相似文献   

10.
The object of this study is to build a three-dimensional (3D) geometric model of the stratigraphicunits of the margin of the Rhone River on the basis of geophysical investigations by a networkof seismic profiles at sea. The geometry of these units is described by depth charts of eachsurface identified by seismic profiling, which is done by geostatistics. The modeling starts bya statistical analysis by which we determine the parameters that enable us to calculate thevariograms of the identified surfaces. After having determined the statistical parameters, wecalculate the variograms of the variable Depth. By analyzing the behavior of the variogramwe then can deduce whether the situation is stationary and if the variable has an anisotropicbehavior. We tried the following two nonstationary methods to obtain our estimates: (a) Themethod of universal kriging if the underlying variogram was directly accessible. (b) Themethod of increments if the underlying variogram was not directly accessible. After havingmodeled the variograms of the increments and of the variable itself, we calculated the surfacesby kriging the variable Depth on a small-mesh estimation grid. The two methods then arecompared and their respective advantages and disadvantages are discussed, as well as theirfields of application. These methods are capable of being used widely in earthsciences forautomatic mapping of geometric surfaces or for variables such as a piezometricsurface or aconcentration, which are not stationary, that is, essentially, possess a gradient or a tendencyto develop systematically in space.  相似文献   

11.
空间软数据及其插值方法研究进展   总被引：7，自引：0，他引：7  
罗明  裴韬 《地理科学进展》2009,28(5):663-672
由于对地观测技术的迅速发展,空间数据的种类和数量增长迅猛,由空间数据反演得到的各种信息日趋膨胀,这些反演结果中的信息不少以软数据的形式出现。在实际应用中,这些软数据往往与空间插值的目标变量具有一定的相关性,甚至成为控制目标变量空间分布特征的重要因素。然而,由于这些数据通常表示为非数值形式,在计算和处理上存在着一定困难,以致被传统的插值方法所忽视,从而造成信息浪费。近来出现的空间软插值方法是一种利用空间软数据作为辅助信息并以改善插值效果的方法,能够较好的处理并利用软数据所隐含的信息,具有较好的应用发展前景。本文根据空间软数据的特点及其分类,系统综述了空间软插值方法及其应用领域。首先分析了空间数据软硬性质的根本区别,论述了软数据的分类和“硬化”方法,然后介绍空间插值模型中对空间软数据的集成方法和原理,最后对空间软插值方法及其应用研究领域进行了展望。  相似文献   

12.
Spatial interpolation of marine environment data using P-MSN   总被引：1，自引：0，他引：1  
ABSTRACT

When a marine study area is large, the environmental variables often present spatially stratified non-homogeneity, violating the spatial second-order stationary assumption. The stratified non-homogeneous surface can be divided into several stationary strata with different means or variances, but still with close relationships between neighboring strata. To give the best linear-unbiased estimator for those environmental variables, an interpolated version of the mean of the surface with stratified non-homogeneity (MSN) method called point mean of the surface with stratified non-homogeneity (P-MSN) was derived. P-MSN distinguishes the spatial mean and variogram in different strata and borrows information from neighboring strata to improve the interpolation precision near the strata boundary. This paper also introduces the implementation of this method, and its performance is demonstrated in two case studies, one using ocean color remote sensing data, and the other using marine environment monitoring data. The predictions of P-MSN were compared with ordinary kriging, stratified kriging, kriging with an external drift, and empirical Bayesian kriging, the most frequently used methods that can handle some extent of spatial non-homogeneity. The results illustrated that for spatially stratified non-homogeneous environmental variables, P-MSN outperforms other methods by simultaneously improving interpolation precision and avoiding artificially abrupt changes along the strata boundaries.  相似文献   

13.
This article describes a proposed work-sequence to generate accurate reservoir-architecture models, describing the geometry of bounding surfaces (i.e., fault locations and extents), of a structurally complex geologic setting in the Jeffara Basin (South East Tunisia) by means of geostatistical modeling. This uses the variogram as the main tool to measure the spatial variability of the studied geologic medium before making any estimation or simulation. However, it is not always easy to fit complex experimental variograms to theoretical models. Thus, our primary purpose was to establish a relationship between the geology and the components of the variograms to fit a mathematically consistent and geologically interpretable variogram model for improved predictions of surface geometries. We used a three-step approach based on available well data and seismic information. First, we determined the structural framework: a seismo-tectonic data analysis was carried out, and we showed that the study area is cut mainly by NW–SE-trending normal faults, which were classified according to geometric criteria (strike, throw magnitude, dip, and dip direction). We showed that these normal faults are at the origin of a large-scale trend structure (surfaces tilted toward the north-east). At a smaller scale, the normal faults create a distinct compartmentalization of the reservoirs. Then, a model of the reservoir system architecture was built by geostatistical methods. An efficient methodology was developed, to estimate the bounding faulted surfaces of the reservoir units. Emphasis was placed on (i) elaborating a methodology for variogram interpretation and modeling, whereby the importance of each variogram component is assessed in terms of probably geologic factor controlling the behavior of each structure; (ii) integrating the relevant fault characteristics, which were deduced from the previous fault classification analysis, as constraints in the kriging estimation of bounding surfaces to best reflect the geologic structure of the study area. Finally, the estimated bounding surfaces together with seismic data and variogram interpretations were used to obtain further insights into the tectonic evolution of the study area that has induced the current reservoirs configuration.  相似文献   

14.
ABSTRACT

Recently developed urban air quality sensor networks are used to monitor air pollutant concentrations at a fine spatial and temporal resolution. The measurements are however limited to point support. To obtain areal coverage in space and time, interpolation is required. A spatio-temporal regression kriging approach was applied to predict nitrogen dioxide (NO2) concentrations at unobserved space-time locations in the city of Eindhoven, the Netherlands. Prediction maps were created at 25 m spatial resolution and hourly temporal resolution. In regression kriging, the trend is separately modelled from autocorrelation in the residuals. The trend part of the model, consisting of a set of spatial and temporal covariates, was able to explain 49.2% of the spatio-temporal variability in NO2 concentrations in Eindhoven in November 2016. Spatio-temporal autocorrelation in the residuals was modelled by fitting a sum-metric spatio-temporal variogram model, adding smoothness to the prediction maps. The accuracy of the predictions was assessed using leave-one-out cross-validation, resulting in a Root Mean Square Error of 9.91 μg m?3, a Mean Error of ?0.03 μg m?3 and a Mean Absolute Error of 7.29 μg m?3. The method allows for easy prediction and visualization of air pollutant concentrations and can be extended to a near real-time procedure.  相似文献   

15.
The service seNorge ( http://senorge.no ) provides gridded temperature and precipitation for mainland Norway. The products are provided as interpolated station measurements on a 1 × 1 km grid. Precipitation gauges are predominantly located at lower elevations such as coastal areas and valleys. Therefore, there are large uncertainties in extrapolating precipitation data to higher altitudes, both due to sparsity of observations as well as the large spatial variability of precipitation in mountainous regions. Using gridded temperature and precipitation data from seNorge, surface mass balance was modeled for five Norwegian glaciers of different size and climate conditions. The model accounts for melting of snow and ice by applying a degree‐day approach and considers refreezing assuming a snow depth depended storage. Calculated values are compared to point measurements of glacier winter mass balance. On average for each glacier, modeled and measured surface mass‐balance evolutions agree well, but results at individual stake locations show large variability. Two types of problems were identified: first, grid data were not able to capture spatial mass balance variability at smaller glaciers. Second, a significant increase in the bias between model and observations with altitude for one glacier suggested that orographic enhancement of precipitation was not appropriately captured by the gridded interpolation.  相似文献   

16.
High accuracy surface modeling(HASM) is a method which can be applied to soil property interpolation.In this paper,we present a method of HASM combined geographic information for soil property interpolation(HASM-SP) to improve the accuracy.Based on soil types,land use types and parent rocks,HASM-SP was applied to interpolate soil available P,Li,pH,alkali-hydrolyzable N,total K and Cr in a typical red soil hilly region.To evaluate the performance of HASM-SP,we compared its performance with that of ordinary kriging(OK),ordinary kriging combined geographic information(OK-Geo) and stratified kriging(SK).The results showed that the methods combined with geographic information including HASM-SP and OK-Geo obtained a lower estimation bias.HASM-SP also showed less MAEs and RMSEs when it was compared with the other three methods(OK-Geo,OK and SK).Much more details were presented in the HASM-SP maps for soil properties due to the combination of different types of geographic information which gave abrupt boundary for the spatial varia-tion of soil properties.Therefore,HASM-SP can not only reduce prediction errors but also can be accordant with the distribution of geographic information,which make the spatial simula-tion of soil property more reasonable.HASM-SP has not only enriched the theory of high accuracy surface modeling of soil property,but also provided a scientific method for the ap-plication in resource management and environment planning.  相似文献   

17.
无定河流域降雨量空间变异性研究   总被引：28，自引：4，他引：28  
李丽娟  王娟  李海滨 《地理研究》2002,21(4):434-440
运用地质统计学中的普通KRIGING方法 ,对 1 990～ 1 997年无定河流域 67个雨量站的年降雨量进行了插值及空间场变异分析。分析发现降雨量的频率分布符合对数正态分布 ,采用对数克立格方法为计算工具进行分析 ,结果显示实验半变异函数符合一般的球状模型。从获得的参数可知 ,1 990～ 1 997年期间 ,变程各不相同 ,甚至差异很大。 1 991年最小 ,为2 0 1 7km ,1 994年最大 ,为 68 65km ,说明了该年无定河流域的降雨量空间变化在所分析的时间序列中是最缓和的 ,这与 1 994年的变异系数最小也相吻合。同时各个年份计算结果均显示有块金值 ,说明在小于变程的空间尺度上仍然存在随机效应。最后运用克立格方法对该流域的部分区域降雨量进行了空间插值成图。  相似文献   

18.

Experimental variograms are crucial for most geostatistical studies. In kriging, for example, the variography has a direct influence on the interpolation weights. Despite the great importance of variogram estimators in predicting geostatistical features, they are commonly influenced by outliers in the dataset. The effect of some randomly spatially distributed outliers can mask the pattern of the experimental variogram and produce a destructuration effect, implying that the true data spatial continuity cannot be reproduced. In this paper, an algorithm to detect and remove the effect of outliers in experimental variograms using the Mahalanobis distance is proposed. An example of the algorithm’s application is presented, showing that the developed technique is able to satisfactorily detect and remove outliers from a variogram.

  相似文献   

19.
利用吐哈盆地2011-2015年逐时FY-2E静止气象卫星红外云图资料,吐鲁番市1976-2015年5个国家气象站和2013-2015年26个区域气象站降水资料,采用卫星资料反演和统计分析方法,首次定义TK（地面气温与云顶亮温的差值）来规避地面辐射对卫星接收辐射的影响,分析吐鲁番盆地各级别TBB（-10~-20℃、-20~-30℃、-30~-40℃、-40~-50℃）云的分布状况及其与降水的关系、降水的时空分布特征和变化趋势。结果表明,吐鲁番盆地TBB各级别云覆盖度与海拔高度显著正相关,云量从盆地平原区向山区递增;TK的月变化同月降水具有较好的正相关性,TK正值时段4~8月与盆地汛期相对应,TK极大值对应月降水量最大的6月;降水与海拔高度显著正相关,降水先随海拔高度增加而增多,1 400~1 900 m区域是降水量和降水垂直变率最大的区域,之后降水随海拔高度增加而减少;降水高度集中在夏季与秋季,6月降水最多（占3~4成）;降水集中出现在白天,平原地区集中在早晨至中午,山区集中在下午至傍晚。综合分析得出吐鲁番盆地人工增水作业区域、作业月份、作业"时间窗"选择的参考依据,其中最佳作业区域在1 400~1 900 m,最佳作业月份为6月,最佳作业"时间窗"为上午的06~10时与下午的14~18时。  相似文献   

20.
The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60° north latitude and 56° south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc‐second (～30 m) for areas within the USA and at 3 arc‐second (～90 m) resolution for the rest of the world. A resolution of 90 m can be considered suitable for the small or medium‐scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3” to 1”. We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1” model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1” NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1” surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline‐interpolated surface still presented some noise and linear artifacts, which were removed by kriging.  相似文献   

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