Comparison of ordinary and lognormal kriging on skewed data of total cadmium in forest soils of Sweden

Spatial statistical analysis of georeferenced data of total cadmium (TCd) in forest soils of Sweden was assumed to providemore advantageous maps than traditional interpolated maps. However, 264 measurements of TCd in O-horizon of forest soils displayed skewed frequency distribution. Since atypicalobservations affect badly the variogram, outliers wereidentified, different data transformations were tested andordinary (OK) and lognormal kriging (LK) scenarios werecompared based on cross-validation. Results were comparedusing overall measures of predictors, e.g. traditionalmean squared prediction error (MSPE), mean of krigingvariances, variance ratio, median of internallystandardised residuals, and assessments of classificationaccuracy, such as percentage of correctly predictedsamples and within-class MSPE.One outlier was identified based on the absolute value of skewness of value differences less or equal to one in data pairs separated at certain lag classes. Mapping categories characterised by percentage of correct classification and within-class MSPE were found to be essential in comparison of kriging results additionally to the overall measures. In comparison of kriging methods, OK predicted high values moreaccurately and LK was more effective to predict low and mediumvalues. Thus, OK was suggested for mapping high concentration of TCd and other pollutants. Percentage of correctly predictedsamples and within-class MSPE were found to be dependent on kriging method, as well as on the number and limits of categories.     

Kriging for estimating spatial pattern of contaminants: Potential and problems

This paper discusses and illustrates the use of kriging techniques for estimating the spatial pattern of contaminants in environmental media, particularly soil. The assumptions underlying kriging are reviewed as are some advantages and disadvantages of the method. Lognormal kriging (kriging applied to logarithmic-transformed data) is illustrated using a set of radionuclide soil concentrations at a nuclear testing area on the Nevada Test Site. This example shows how lognormal kriging can be used to estimate average concentrations at points or for blocks of land, concentration contours over space, confidence bands about these contours, and radionuclide inventory in soil. The validity of kriging estimates depends on the accurate estimation and modeling of the spatial correlation structure of the phenomenon. Accuracy is especially important when lognormal kriging is used and estimates of means and their standard deviations are required in the original, untransformed scale. This paper illustrates the bias that can result when a changing correlation structure over space is ignored.Operated for the U.S. Department of Energy by Battelle Memorial InstituteWork supported by Nevada Applied Ecology Group, U.S. Department of Energy, Nevada Operations Office under Contract DE-AC06-76RLO 1830.     

Geostatistical Analysis of Spatial and Temporal Variations of Groundwater Level

Groundwater and water resources management plays a key role in conserving the sustainable conditions in arid and semi-arid regions. Applying management tools which can reveal the critical and hot conditions seems necessary due to some limitations such as labor and funding. In this study, spatial and temporal analysis of monthly groundwater level fluctuations of 39 piezometric wells monitored during 12 years was carried out. Geostatistics which has been introduced as a management and decision tool by many researchers has been applied to reveal the spatial and temporal structure of groundwater level fluctuation. Results showed that a strong spatial and temporal structure existed for groundwater level fluctuations due to very low nugget effects. Spatial analysis showed a strong structure of groundwater level drop across the study area and temporal analysis showed that groundwater level fluctuations have temporal structure. On average, the range of variograms for spatial and temporal analysis was about 9.7 km and 7.2 months, respectively. Ordinary and universal kriging methods with cross-validation were applied to assess the accuracy of the chosen variograms in estimation of the groundwater level drop and groundwater level fluctuations for spatial and temporal scales, respectively. Results of ordinary and universal krigings revealed that groundwater level drop and groundwater level fluctuations were underestimated by 3% and 6% for spatial and temporal analysis, respectively, which are very low and acceptable errors and support the unbiasedness hypothesis of kriging. Although, our results demonstrated that spatial structure was a little bit stronger than temporal structure, however, estimation of groundwater level drop and groundwater level fluctuations could be performed with low uncertainty in both space and time scales. Moreover, the results showed that kriging is a beneficial and capable tool for detecting those critical regions where need more attentions for sustainable use of groundwater. Regions in which were detected as critical areas need to be much more managed for using the current water resources efficiently. Conducting water harvesting systems especially in critical and hot areas in order to recharge the groundwater, and altering the current cropping pattern to another one that need less water requirement and applying modern irrigation techniques are highly recommended; otherwise, it is most likely that in a few years no more crop would be cultivated.     

SPATIAL ANALYSIS AND EUTROPHICATION ASSESSMENT FOR CHLOROPHYLL a IN TAIHU LAKE

Spatial structure analysis and kriging analysis have been identified to be useful tools in illustrating the spatial patterns of variables. Taihu Lake is one of the largest fresh water lakes in China, and has suffered serious eutrophication in recent years due to the rapid economic development and growing environmental pollution in the Taihu Catchment. In this paper, spatial structural analysis, kriging interpolation and eutrophication assessment were carried out for chlorophyll a in the lake. Studies show that spherical model could be applied to fit all experimental variograms. Positive nuggets were observed for three directions except NE–SW direction. The variograms show some anisotropy with anisotropic ratio falling within 1.76. The spatial structural patterns of chlorophyll a in the lake were affected by factors such as distribution of pollution sources, water flow and wind. Two-dimensional ordinary block kriging was applied for interpolation process. An eutrophication assessment map was also made based on a water-quality evaluation standard. Results show that the content of chlorophyll a in Taihu Lake was quite high. The whole lake has suffered serious eutrophication. However, the eutrophic situation varied in space. Higher contents of chlorophyll a appeared mainly in the northern part of the lake.     

An approach for land suitability evaluation using geostatistics, remote sensing, and geographic information system in arid and semiarid ecosystems

This study was undertaken to incorporate geostatistics, remote sensing, and geographic information system (GIS) technologies to improve the qualitative land suitability assessment in arid and semiarid ecosystems of Arsanjan plain, southern Iran. The primary data were obtained from 85 soil samples collected from tree depths (0–30, 30–60, and 60–90 cm); the secondary information was acquired from the remotely sensed data from the linear imaging self-scanner (LISS-III) receiver of the IRS-P6 satellite. Ordinary kriging and simple kriging with varying local means (SKVLM) methods were used to identify the spatial dependency of soil important parameters. It was observed that using the data collected from the spectral values of band 1 of the LISS-III receiver as the secondary variable applying the SKVLM method resulted in the lowest mean square error for mapping the pH and electrical conductivity (ECe) in the 0–30-cm depth. On the other hand, the ordinary kriging method resulted in a reliable accuracy for the other soil properties with moderate to strong spatial dependency in the study area for interpolation in the unstamped points. The parametric land suitability evaluation method was applied on the density points (150 × 150 m²) instead of applying on the limited representative profiles conventionally, which were obtained by the kriging or SKVLM methods. Overlaying the information layers of the data was used with the GIS for preparing the final land suitability evaluation. Therefore, changes in land characteristics could be identified in the same soil uniform mapping units over a very short distance. In general, this new method can easily present the squares and limitation factors of the different land suitability classes with considerable accuracy in arbitrary land indices.     

Soil gas radon analysis in some areas of Northern Punjab, India

The radon concentration levels in soil samples from 39 locations of Northern Punjab are measured using AlphaGUARD (PQ 2000 PRO Model) of Genitron instruments, Germany. The radon concentration in soil varies from 0.3 to 35.8 kBq/l. The minimum value of radon is observed in Talwandi Choudhrian and is maximum for Nushera Dhala. The soil gas radon is correlated with soil temperature, pressure, and humidity to observe the effect of these parameters on radon release. The soil gas radon values in the study area are compared with that obtained in groundwater. The results are also compared with the available radon data for other parts of Punjab and Himachal Pradesh.     

Spatial evaluation of the risk of groundwater quality degradation. A comparison between disjunctive kriging and geostatistical simulation

In some previous papers a probabilistic methodology was introduced to estimate a spatial index of risk of groundwater quality degradation, defined as the conditional probability of exceeding assigned thresholds of concentration of a generic chemical sampled in the studied water system. A crucial stage of this methodology was the use of geostatistical techniques to provide an estimation of the above-mentioned probability in a number of selected points by crossing spatial and temporal information. In this work, spatial risk values were obtained using alternatively stochastic conditional simulation and disjunctive kriging. A comparison between the resulting two sets of spatial risks, based on global and local statistical tests, showed that they do not come from the same statistical population and, consequently, they cannot be viewed as equivalent in a statistical sense. At a first glance, geostatistical conditional simulation may appear to represent the spatial variability of the phenomenon more effectively, as the latter tends to be smoothed by DK. However, a close examination of real case study results suggests that disjunctive kriging is more effective than simulation in estimating the spatial risk of groundwater quality degradation. In the study case, the potentially ‘harmful event’ considered, threatening a natural ‘vulnerable groundwater system,’ is fertilizer and manure application.     

Environmental monitoring of radon in soil during a very seismically active period occurred in South West Greece

This paper focuses on the environmental monitoring of radon in soil as a potential trace gas in the search of earthquake precursors. The paper reports the following: (a) Pre-monitoring experiments. (b) Set-up of methods and devices. (c) Active and passive monitoring results concentrating on two extremely-strong radon anomalies (~ 500 kBq m(-3)). (e) Discussion regarding the employed ± 2σ technique for identifying radon disturbances. (f) Application of wavelet-power-spectrum fractal analysis for detecting power-law behaviour. The strong anomalies exhibited anti-persistent power-law-beta-values (b = (1.8 ± 0.2), b = (1.8 ± 0.3)) significantly higher than those of the baseline. Persistent b-values were also detected. The findings comply with a self-organised-critical pre-earthquake state. (h) Discussion on models that interpret the radon anomalies focusing on the recently-proposed asperity-model. (i) Application of a recent technique which showed that the two strong disturbances were proportional to the strain change. It was concluded that the strong radon disturbances may be linked to the strong earthquake of 8/6/2008, M = 6.5, occurred 29 km away from the installed instrumentation.     

The geostatistic-based spatial distribution variations of soil salts under long-term wastewater irrigation

The purpose of this study was to determine and evaluate the spatial changes in soil salinity by using geostatistical methods. The study focused on the suburb area of Beijing, where urban development led to water shortage and accelerated wastewater reuse to farm irrigation for more than 30 years. The data were then processed by GIS using three different interpolation techniques of ordinary kriging (OK), disjunctive kriging (DK), and universal kriging (UK). The normality test and overall trend analysis were applied for each interpolation technique to select the best fitted model for soil parameters. Results showed that OK was suitable for soil sodium adsorption ratio (SAR) and Na⁺ interpolation; UK was suitable for soil Cl^? and pH; DK was suitable for soil Ca²⁺. The nugget-to-sill ratio was applied to evaluate the effects of structural and stochastic factors. The maps showed that the areas of non-saline soil and slight salinity soil accounted for 6.39 and 93.61 %, respectively. The spatial distribution and accumulation of soil salt were significantly affected by the irrigation probabilities and drainage situation under long-term wastewater irrigation.     

Spatial assessment of soil salinity in the Harran Plain using multiple kriging techniques

The Harran Plain is located in the southeastern part of Turkey and has recently been developed for irrigation agriculture. It already faces soil salinity problems causing major yield losses. Management of the problem is hindered by the lack of information on the extent and geography of the salinization problem. A survey was carried out to delineate the spatial distribution of salt-affected areas by randomly selecting 140 locations that were sampled at two depths (0 to 30 and 30 to 60 cm) and analyzed for soil salinity variables: soil electrical conductivity (EC), soluble cations (Ca^2+, Mg²⁺, Na⁺, and K⁺), soluble anions (SO ₄ ^2? , Cl^?), exchangeable Na⁺ (me 100 g^?1) and exchangeable sodium percentage. Terrain attributes (slope, topographical wetness index) were extracted from the digital elevation model of the study area. Variogram analyses after log transformation and ordinary kriging (OK) were applied to map spatial patterns of soil salinity variables. Multivariate geostatistical methods—regression kriging (RK) and kriging with external drift (KED)—were used using elevation and soil electrical conductivity data as covariates. Performances of the three estimation methods (OK, RK, and KED) were compared using independent validation samples randomly selected from the main dataset. Soils were categorized into salinity classes using disjunctive kriging (DK) and ArcGIS, and classification accuracy was tested using the kappa statistic. Results showed that soil salinity variables all have skewed distribution and are poorly correlated with terrain indices but have strong correlations among each other. Up to 65 % improvement was obtained in the estimations of soil salinity variables using hybrid methods over OK with the best estimations obtained with RK using EC_0–30 as covariate. DK–ArcGIS successfully classified soil samples into different salinity groups with overall accuracy of 75 % and kappa of 0.55 (p?<?0.001).     

Comparison of spatial interpolation methods for soil moisture and its application for monitoring drought

Soil moisture data can reflect valuable information on soil properties, terrain features, and drought condition. The current study compared and assessed the performance of different interpolation methods for estimating soil moisture in an area with complex topography in southwest China. The approaches were inverse distance weighting, multifarious forms of kriging, regularized spline with tension, and thin plate spline. The 5-day soil moisture observed at 167 stations and daily temperature recorded at 33 stations during the period of 2010–2014 were used in the current work. Model performance was tested with accuracy indicators of determination coefficient (R ²), mean absolute percentage error (MAPE), root mean square error (RMSE), relative root mean square error (RRMSE), and modeling efficiency (ME). The results indicated that inverse distance weighting had the best performance with R ², MAPE, RMSE, RRMSE, and ME of 0.32, 14.37, 13.02%, 0.16, and 0.30, respectively. Based on the best method, a spatial database of soil moisture was developed and used to investigate drought condition over the study area. The results showed that the distribution of drought was characterized by evidently regional difference. Besides, drought mainly occurred in August and September in the 5 years and was prone to happening in the western and central parts rather than in the northeastern and southeastern areas.     

A Quantile Regression Approach to Evaluate Factors Influencing Residential Indoor Radon Concentration

Indoor radon concentrations depend on building characteristics such as building materials, ventilation and water supply. In this paper, a quantile regression approach is proposed to evaluate the effect of some buildings factors potentially influencing indoor radon concentration. Many of the considered factors, such as soil connection, age of construction and being a single family building, are found to have a statistically significant effect; however, this is far from being constant across the entire support of indoor radon concentration. A potential impact due to geological and geo-physical reasons is also found using the altitude of building locations as a surrogate variable. In addition, a clear local spatial effect is detected by a spatial autoregression approach.     

灵宝市金矿选冶区土壤汞的地统计分析及污染评价

利用数理统计、地统计方法和地理信息系统(GIS)技术研究了灵宝市的金矿选冶区土壤汞的空间分布特性和污染程度评价。Hg和Cu、Zn、Pb、Cd重金属元素存在较大的偏度和峰度,为了使这些元素的数据服从正态分布并降低其偏度和峰度,采用了Box-Cox变换。地统计分析认为研究区内土壤Hg元素具有空间结构特性。用普通克里格插值绘制的研究区Hg含量地球化学图体现了其空间分布特征。结合地累积指数法评价指标得出的研究区Hg污染等级分布图为土壤恢复治理提供了一定科学依据。     

Mapping the Spatial Variability of Plant Diversity in a Tropical Forest: Comparison of Spatial Interpolation Methods

Knowledge of the spatial distribution of plant species is essential to conservation and forest managers in order to identify high priority areas such as vulnerable species and habitats, and designate areas for reserves, refuges and other protected areas. A reliable map of the diversity of plant species over the landscape is an invaluable tool for such purposes. In this study, the number of species, the exponent Shannon and the reciprocal Simpson indices, calculated from 141 quadrat sites sampled in a tropical forest were used to compare the performance of several spatial interpolation techniques used to prepare a map of plant diversity, starting from sample (point) data over the landscape. Means of mapped classes, inverse distance functions, kriging and co-kriging, both, applied over the entire studied landscape and also applied within vegetation classes, were the procedures compared. Significant differences in plant diversity indices between classes demonstrated the usefulness of boundaries between vegetation types, mapped through satellite image classification, in stratifying the variability of plant diversity over the landscape. These mapped classes, improved the accuracy of the interpolation methods when they were used as prior information for stratification of the area. Spatial interpolation by co-kriging performed among the poorest interpolators due to the poor correlation between the plant diversity variables and vegetation indices computed by remote sensing and used as covariables. This indicated that the latter are not suitable covariates of plant diversity indices. Finally, a within-class kriging interpolator yielded the most accurate estimates of plant diversity values. This interpolator not only provided the most accurate estimates by accounting for the indices' intra-class variability, but also provided additional useful interpretations of the structure of spatial variability of diversity values through the interpretation of their semi-variograms. This additional role was found very useful in aiding decisions in conservation planning.     

Comparison of Point Estimation Techniques in the Spatial Analysis of Radium-226, Radium-228 and Potassium-40 in Soil

Many environmental surveys require the implementation of estimation techniques to determine the spatial distribution of the variable being investigated. Traditional methods of interpolation and estimation, for example, inverse distance squared and triangulation often ignore features of the data set such as anisotropy which may have a significant impact on the quality of the estimates produced. Geostatistical techniques may offer an improved method of estimation by modelling the spatial continuity of the variable using semi-variogram analysis. The theoretical model fitted to the semi-variogram is then used in the assignation of weighting factors to the samples surrounding the location to be estimated. This paper outlines the results of a comparison between three common estimation methods, polygonal, triangulation and inverse distance squared and a geostatistical method, in the estimation of soil radionuclide activities. The geostatistical estimation method known as kriging performed best over a range of parameters used to test the performance of the methods. Kriging exhibited the best correlation between actual and estimated values, the narrowest error distribution and the lowest overall estimation error. Polygonal estimation was best at reproducing the data set distribution. Conditional bias was evident in all the methods, low values being over-estimated and high values being under-estimated.     

Spatial Prediction of Stream Temperatures Using Top-Kriging with an External Drift

Top-kriging is a method for estimating stream flow and stream flow-related variables on a river network. Top-kriging treats these variables as emerging from a two-dimensional spatially continuous process in the landscape. The top-kriging weights are estimated by a family of variogram models (regularisations) for different catchment areas (kriging support), which accounts for the different scales and the nested nature of the catchments. This assures that kriging weights are distributed to both hydrologically connected and unconnected sites of the stream network according to the data situation: top-kriging gives most weight to close-by sites at the same river system, but when the next hydrologically connected site is far away, more weight is given to a close-by site at an adjacent river system. The distribution of weights is in contrast to ordinary kriging and stream distance-based kriging which does not account for both spatial proximity and network connectivity. We extend the top-kriging method by incorporating an external drift function to account for the deterministic patterns of the spatial variable. We test the method for a comprehensive Austrian stream temperature dataset. The drift is modelled by exponential regression with catchment altitude. Top-kriging is then applied to the regression residuals. The variogram used in top-kriging is fitted by a semiautomatic optimisation procedure. A leave-one-out cross-validation analysis shows that the model performs well for the study domain. The residual mean squared error (cross-validation) decreases by 20 % when using top-kriging in addition to the regression model. For regions where the observed stream temperatures deviate from the expected value of the drift model, top-kriging corrects these regional biases. By exploiting the topological information of the stream network, top-kriging is able to improve the local adjustment of the drift model for the main streams and the tributaries.     

Indicator and probability kriging methods for delineating Cu, Fe, and Mn contamination in groundwater of Najafgarh Block, Delhi, India

Two non-parametric kriging methods such as indicator kriging and probability kriging were compared and used to estimate the probability of concentrations of Cu, Fe, and Mn higher than a threshold value in groundwater. In indicator kriging, experimental semivariogram values were fitted well in spherical model for Fe and Mn. Exponential model was found to be best for all the metals in probability kriging and for Cu in indicator kriging. The probability maps of all the metals exhibited an increasing risk of pollution over the entire study area. Probability kriging estimator incorporates the information about order relations which the indicator kriging does not, has improved the accuracy of estimating the probability of metal concentrations in groundwater being higher than a threshold value. Evaluation of these two spatial interpolation methods through mean error (ME), mean square error (MSE), kriged reduced mean error (KRME), and kriged reduced mean square error (KRMSE) showed 3.52% better performance of probability kriging over indicator kriging. The combined result of these two kriging method indicated that on an average 26.34%, 65.36%, and 99.55% area for Cu, Fe, and Mn, respectively, are coming under the risk zone with probability of exceedance from a cutoff value is 0.6 or more. The groundwater quality map pictorially represents groundwater zones as ??desirable?? or ??undesirable?? for drinking. Thus the geostatistical approach is very much helpful for the planners and decision makers to devise policy guidelines for efficient management of the groundwater resources so as to enhance groundwater recharge and minimize the pollution level.     

Comparison of stochastic and deterministic methods for mapping groundwater level spatial variability in sparsely monitored basins

In sparsely monitored basins, accurate mapping of the spatial variability of groundwater level requires the interpolation of scattered data. This paper presents a comparison of deterministic interpolation methods, i.e. inverse distance weight (IDW) and minimum curvature (MC), with stochastic methods, i.e. ordinary kriging (OK), universal kriging (UK) and kriging with Delaunay triangulation (DK). The study area is the Mires Basin of Mesara Valley in Crete (Greece). This sparsely sampled basin has limited groundwater resources which are vital for the island’s economy; spatial variations of the groundwater level are important for developing management and monitoring strategies. We evaluate the performance of the interpolation methods with respect to different statistical measures. The Spartan variogram family is applied for the first time to hydrological data and is shown to be optimal with respect to stochastic interpolation of this dataset. The three stochastic methods (OK, DK and UK) perform overall better than the deterministic counterparts (IDW and MC). DK, which is herein for the first time applied to hydrological data, yields the most accurate cross-validation estimate for the lowest value in the dataset. OK and UK lead to smooth isolevel contours, whilst DK and IDW generate more edges. The stochastic methods deliver estimates of prediction uncertainty which becomes highest near the southeastern border of the basin.     

Delineation of Environmental Units by Multivariate Techniques in the Duero River Watershed,Michoacán,Mexico

Environmental or hydrological landscape units can integrate various environmental characteristics to support proper management of natural resources. To delineate these units, quantitative methods such as ordination, clustering, and classification of abiotic factor information are used. In the present work, environmental units were delineated in the Duero River watershed of Michoacán, Mexico. This will enhance understanding of the hydrologic landscape, which is a fundamental to natural resource management. A digital elevation model was used to generate sub-basins. Climatic data were obtained from 16 meteorological stations. Sixty-nine soil and 150 water samples were collected and analyzed in the laboratory. Geostatistical methods for spatial prediction of the environmental variables were used. Mean data for each sub-basin were obtained from the environmental variable grids, generating an abiotic factor data matrix. A multivariate analysis was conducted. Exponential, linear, spherical, and Gaussian models were fit to an empirical variogram. Spatial prediction of the environmental data was done via universal and ordinary kriging. Based on principal component analysis, abiotic factors evaporation, total nitrogen, soil pH, and sodium absorption ratio of water were selected for cluster analysis. Five environmental units were delineated in the Duero watershed. One environmental unit (number 4) provided greater than 50 % of the payment for ecosystem services. The general trend is an increase of urban area. The urban surface in 1983 and 2014 was 1724 and 4750 ha, respectively, an increase of 275 %. Environmental unit 1 showed the greatest urban area growth (1336 ha) during the latter period.     

Mapping the organic carbon stocks of surface soils using local spatial interpolator

The largest uncertainties are associated with estimating the soil organic carbon (SOC) stock because of natural soil variability and data scarcity. Thus, a local spatial geostatistical hybrid approach, the geographically weighted regression kriging (GWRK), was used in the present study to overcome some of these uncertainties. This study was designed to estimate the SOC stock (kg C m(-2)) for the surface 0 to 15 cm depth using the state of Pennsylvania as the study region. A total of 920 soil profiles were extracted from the National Soil Survey Center database and were divided into calibration (80%) and validation (20%) periods. Some soil parameters that include clay content, bulk density (ρ(b)), total nitrogen (TN) content, pH, Ca(2+), Na(+), extractable acidity (EXACID), and cation exchange capacity (CEC) were used as covariates for estimating the SOC stock. These covariates exhibited spatial autocorrelation (Moran's Index, I = 0.62 to 0.89). Further, residuals of geographically weighted regression were spatially autocorrelated, and hence support the use of the GWRK approach. Validation results concluded that the performance of the GWRK approach was the best with the lowest values of root mean square error, mean estimation error and mean absolute estimation error. The estimated SOC stock for the surface 0 to 15 cm depth ranged from 1.41 to 3.94 kg m(-2). Results from this study show that the GWRK captures spatial dependent relationships, and addresses spatial non-stationarity issues, hence this approach improves the estimations of SOC stock.