Using rank-order geostatistics for spatial interpolation of highly skewed data in a heavy-metal contaminated site

The spatial distribution of a pollutant in contaminated soils is usually highly skewed. As a result, the sample variogram often differs considerably from its regional counterpart and the geostatistical interpolation is hindered. In this study, rank-order geostatistics with standardized rank transformation was used for the spatial interpolation of pollutants with a highly skewed distribution in contaminated soils when commonly used nonlinear methods, such as logarithmic and normal-scored transformations, are not suitable. A real data set of soil Cd concentrations with great variation and high skewness in a contaminated site of Taiwan was used for illustration. The spatial dependence of ranks transformed from Cd concentrations was identified and kriging estimation was readily performed in the standardized-rank space. The estimated standardized rank was back-transformed into the concentration space using the middle point model within a standardized-rank interval of the empirical distribution function (EDF). The spatial distribution of Cd concentrations was then obtained. The probability of Cd concentration being higher than a given cutoff value also can be estimated by using the estimated distribution of standardized ranks. The contour maps of Cd concentrations and the probabilities of Cd concentrations being higher than the cutoff value can be simultaneously used for delineation of hazardous areas of contaminated soils.     

Decision making under uncertainty in case of soil remediation

Decisions on soil remediation are one of the most difficult management issues of municipal and state agencies. The assessment of contamination is uncertain, the costs of remediation are high, and the impacts on the environment are multiple. This paper presents a general, transparent, and consistent method for decision making among the remediation alternatives. Soil washing, phytoremediation, and no remediation are exemplarily considered. Multi-criteria utility functions including (a) the cost of remediation (b) the impact on human health and agricultural productivity, and (c) the economic gain after remediation are constructed using probability density functions representing contamination for all site coordinates. Herewith, the probability of different types of (i) correct decisions such as a hit or a true rejection and (ii) erroneous decisions such as a false alarm or miss are examined. The decision theoretic model is applied to a case study on heavy metal contaminated soil. This case study reveals the non-linear structure of multi-criteria-decision making. The case study shows that the geostatistical uncertainties of the log-normal distributed soil contamination must be taken into account: When uncertainties are not considered and the utilities are assessed according to the estimated value for a spatial unit, only few (N=26) spatial units result where the utility score of the alternative soil washing are higher than the utility score to the no remediation alternative. However, when taking into account geostatistical uncertainties of the log-normal soil distribution this number is about ten times greater (N=237). Furthermore, the use of 'maximizing expected utility' as decision rule is critical in that it may lead to a high probability of misses.     

Mapping residual pyrite after a mine spill using non co-located spatiotemporal observations

Monitoring of soil chemical properties for pollution assessment generally requires destructive soil sampling and results in spatiotemporal datasets where data from different sampling dates are non co-located. The objective of this study was to assess the spatial distribution of residual pyrite sludge at a reclaimed site, using temporally non co-located data on pH; soil oxidizable fraction (SOF); and EDTA-extractable Fe, Zn, and Cu from six different sampling dates over a period of 2 yr. During this period spatially averaged pH and Zn concentrations ranged, respectively, from 4.4 to 6.6 and from 60 to 140 mg kg(-1), with minimum pH values of below 2.7. The data were merged into a single dataset for each chemical property after applying a normal score (ns) transform. Normal score pH was significantly negatively correlated with the ns metal concentrations. A principal component analysis (PCA) showed that normal score pH, Zn, and Fe were associated with the residual contamination, while ns Cu, SOF, and elevation were related with historic contamination. The spatial dependence between the properties was found to be scale-dependent. The best ns estimates were produced by ordinary kriging with an anisotopic variogram model, for the properties related with Principal Component (PC) I, while those associated with PC II were best estimated using simple kriging with varying local means. A classified ns pH map showed that 33% of the study area reached at least once values of below 4 during the 2-yr period. This part of the area should be excluded to ensure successful revegetation.     

Use of ecosystem information to improve soil organic carbon mapping of a Mediterranean island

Detailed maps of soil C are needed to guide sustainable soil uses and management decisions. The quality of soil C maps of Italian Mediterranean areas may be improved and the sampling density reduced using secondary data related to the nature of the ecosystem. The current study was conducted to determine: (i) the improvements obtainable in mapping soil C over a Mediterranean island by using ecosystem features and (ii) the effect of different sampling densities on the map accuracy. This work relied on field sampling (n=164) of soil properties measured over the island of Pianosa (Central Italy). Statistical analysis assessing the relationship between soil properties and ecosystem features revealed that the conceptual model of ecosystems defined on the basis of environmental features such as vegetation cover, land use, and soil type was mainly related to the variation of soil organic carbon (OC) content and to the type of Mediterranean environment. The distribution of ecosystems was used to improve the accuracy of soil OC maps obtainable by a simple interpolation approach (ordinary kriging). Substantial improvement was obtained by: (i) stratification into ecosystem types and (ii) applying locally calibrated regressions to satellite imagery that introduced both inter-ecosystem and intra-ecosystem information linked to vegetation features. This study showed that interpolation methods using information on ecosystem distribution can produce accurate maps of soil OC in Mediterranean environments, mostly because of the linkage between soil OC and vegetation types, which are spatially fragmented and heterogeneous.     

Zonal management of arsenic contaminated ground water in Northwestern Bangladesh

This paper used ordinary kriging to spatially map arsenic contamination in shallow aquifers of Northwestern Bangladesh (total area  35,000 km²). The Northwestern region was selected because it represents a relatively safer source of large-scale and affordable water supply for the rest of Bangladesh currently faced with extensive arsenic contamination in drinking water (such as the Southern regions). Hence, the work appropriately explored sustainability issues by building upon a previously published study (Hossain et al., 2007; Water Resources Management, vol. 21: 1245–1261) where a more general nation-wide assessment afforded by kriging was identified. The arsenic database for reference comprised the nation-wide survey (of 3534 drinking wells) completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) of Bangladesh. Randomly sampled networks of zones from this reference database were used to develop an empirical variogram and develop maps of zonal arsenic concentration for the Northwestern region. The remaining non-sampled zones from the reference database were used to assess the accuracy of the kriged maps. Two additional criteria were explored: (1) the ability of geostatistical interpolators such as kriging to extrapolate information on spatial structure of arsenic contamination beyond small-scale exploratory domains; (2) the impact of a priori knowledge of anisotropic variability on the effectiveness of geostatistically based management. On the average, the kriging method was found to have a 90% probability of successful prediction of safe zones according to the WHO safe limit of 10 ppb while for the Bangladesh safe limit of 50 ppb, the safe zone prediction probability was 97%. Compared to the previous study by Hossain et al. (2007) over the rest of the contaminated country side, the probability of successful detection of safe zones in the Northwest is observed to be about 25% higher. An a priori knowledge of anisotropy was found to have inconclusive impact on the effectiveness of kriging. It was, however, hypothesized that a preferential sampling strategy that honored anisotropy could be necessary to reach a more definitive conclusion in regards to this issue.     

CO-KRIGING TO INCORPORATE SCREENING DATA: HUDSON RIVER SEDIMENT PCBs1

ABSTRACT: Kriging methods of geostatistical analysis provide valuable techniques for analysis of sediment contamination problems, including interpolation of concentration maps from point data and estimation of global mean concentrations. Sample collection efforts frequently include preliminary screening data of considerably more extensive coverage than the laboratory analyses on which estimation is usually based. How should these be incorporated in kriging? Screening and laboratory analysis constitute two separate estimates of the same spatial field but of very different characteristics. A modified version of co-kriging is developed to include the imprecise screening information in the analysis of contaminant distribution. Use of the method is demonstrated on a data set of sediment PCB samples from the Upper Hudson River, for which preliminary categorical mass spectrometry screening was used to select a smaller set of samples for gas chromatograph analysis. The method is widely applicable to many situations of contaminant and natural resource estimation.     

Cost effective policies for alternative distributions of stochastic water pollution

This study investigates the role for cost effective coastal water management with regard to different assumptions of probability distributions (normal and lognormal) of pollutant transports to coastal waters. The analytical results indicate a difference in costs for a given probability of achieving a certain pollutant load target whether a normal or lognormal distribution is assumed. For low standard deviations and confidence intervals, the normal distribution implies a lower cost while the opposite is true for relatively high standard deviations and confidence intervals. The associated cost effective charges and permit prices are higher for lognormal distributions than for normal distributions at relatively high confidence intervals and probabilities of achieving the target. An application to Himmerfj?rden--an estuary south of Stockholm, Sweden--shows that the minimum costs of achieving a 50 per cent reduction in nitrogen load to the coast varies more for a lognormal than normal probability distribution. At high coefficient of variation and chosen probability of achieving the target, the minimum cost under a lognormal assumption can be three times as high as for a normal distribution.     

THE FLEXIBLE TOLERANCE METHOD FOR ESTIMATING HYDROLOGIC PARAMETERS IN THE ROOT ZONE1

In this study, a constrained minimization method, the flexible tolerance method, was used to solve the optimization problems for determining hydrologic parameters in the root zone: water uptake rate, spatial root distribution, infiltration rate, and evaporation. Synthetic soil moisture data were first generated using the Richards' equation and its associated initial and boundary conditions, and these data were then used for the inverse analyses. The results of inverse simulation indicate the following. If the soil moisture data contain no noise, the rate of estimated water uptake and spatial root distribution parameters are equal to the true values without using constraints. If there is noise in the observed data, constraints must be used to improve the quality of the estimate results. In the estimation of rainfall infiltration and surface evaporation, interpolation methods should be used to reduce the number of unknowns. A fewer number of variables can improve the quality of inversely estimated parameters. Simultaneous estimation of spatial root distribution and water uptake rate or estimation of evaporation and water uptake rate is possible. The method was used to estimate the water uptake rate, spatial root distribution, infiltration rate, and evaporation using long‐term soil moisture data collected from Nebraska's Sand Hills.     

Spatial distributions and potential risk analysis of total soil selenium in Guangdong Province, China

A total of 260 soil profiles were examined to investigate the spatial distribution of total soil selenium (Se) in Guangdong province, China. In the investigated area, the soil Se concentrations follow an approximately lognormal distribution. The soil Se geometric mean concentration of 0.23 mg kg(-1) is higher than that of Chinese soils; however, Se concentration varies over the study area. The baseline concentration of 0.13 to 0.41 mg kg(-1) indicates that the soil Se concentration is mostly in the range of deficiency to medium level for surface soils in Guangdong province. In A-, B-, and C-horizon, soil Se spatial distribution is correlated with the nature of the parent material, with high Se concentration mainly located in limestone and sandshale areas and low Se concentration associated with purple shale and granite areas. The spatial distribution pattern of soil Se concentrations suggests that potential Se deficiency may be an issue for human health in this province. Moreover, due to soil degradation and erosion, calculated soil Se exported into surrounding waters could reach approximately 23,000 kg yr(-1) in the study area.     

Soil water repellency induced by long-term irrigation with treated sewage effluent

This study describes soil water repellency developed under prolonged irrigation with treated sewage effluent in a semiarid environment. Soil surface layer (0-5 cm) and soil profile (0-50 cm) transects were sampled at a high resolution at the close of the irrigation season and rainy winter season. Samples from 0- to 5-cm transects were subdivided into 1-cm slices to obtain fine scale resolution of repellency and organic matter distribution. Extreme to severe soil water repellency in the 0- to 5-cm soil surface layer persisted throughout the 2-yr study period in the effluent-irrigated Shamouti orange [Citrus sinensis (L.) Osbeck cv. Shamouti] orchard plot. Nearby Shamouti orange plots irrigated with tap water were either nonrepellent or only somewhat repellent. Repellency was very variable spatially and with depth, appearing in vertically oriented "repellency tongues." Temporal and spatial variability in repellency in the uppermost 5-cm soil surface layer was not related to seasonality, soil moisture content, or soil organic matter content. Nonuniform distribution of soil moisture and fingered flow were observed in the soil profile after both seasons, demonstrating that the repellent layer had a persistent effect on water flow in the soil profile. A lack of correlation between bulk density and volumetric water content in the soil profile demonstrates that the observed nonuniform spatial distribution of moisture results from preferential flow and not heterogeneity in soil properties. Soil water repellency can adversely affect agricultural production, cause contamination of underlying ground water resources, and result in excessive runoff and soil erosion.     

Spatial variability of soil phosphorus in relation to the topographic index and critical source areas: sampling for assessing risk to water quality

A measure of soil P status in agricultural soils is generally required for assisting with prediction of potential P loss from agricultural catchments and assessing risk for water quality. The objectives of this paper are twofold: (i) investigating the soil P status, distribution, and variability, both spatially and with soil depth, of two different first-order catchments; and (ii) determining variation in soil P concentration in relation to catchment topography (quantified as the "topographic index") and critical source areas (CSAs). The soil P measurements showed large spatial variability, not only between fields and land uses, but also within individual fields and in part was thought to be strongly influenced by areas where cattle tended to congregate and areas where manure was most commonly spread. Topographic index alone was not related to the distribution of soil P, and does not seem to provide an adequate indicator for CSAs in the study catchments. However, CSAs may be used in conjunction with soil P data for help in determining a more "effective" catchment soil P status. The difficulties in defining CSAs a priori, particularly for modeling and prediction purposes, however, suggest that other more "integrated" measures of catchment soil P status, such as baseflow P concentrations or streambed sediment P concentrations, might be more useful. Since observed soil P distribution is variable and is also difficult to relate to nationally available soil P data, any assessment of soil P status for determining risk of P loss is uncertain and problematic, given other catchment physicochemical characteristics and the sampling strategy employed.     

Kriging method evaluation for assessing the spatial distribution of urban soil lead contamination

Describing contaminant spatial distribution is an integral component of risk assessment. Application of geostatistical techniques for this purpose has been demonstrated previously. These techniques may provide both an estimate of the concentration at a given unsampled location, as well as the probability that the concentration at that location will exceed a critical threshold concentration. This research is a comparative study between multiple indicator kriging and kriging with the cumulative distribution function of order statistics, with both local and global variograms. The aim was to determine which of the four methods is best able to delineate between "contaminated" and "clean" soil. The four methods were validated with a subset of data values that were not used in the prediction. Method performance was assessed by calculating the root mean square error (RMSE), analysis of variance, the proportion of sites misclassified by each method as either "clean" when they were actually "contaminated" or vice versa, and the expected loss for each misclassification type. The data used for the comparison were 807 topsoil Pb concentrations from the inner-Sydney suburbs of Glebe and Camperdown, Australia. While there was very little difference between the four methods, multiple indicator kriging was found to produce the most accurate predictions for delineating "clean" from "contaminated" soil.     

Improving National-Scale Carbon Stock Inventories Using Knowledge on Land Use History

National-scale inventories of soil organic carbon (SOC) and forest floor carbon (FFC) stocks have a high uncertainty. Inventories are often based on the interpolation of sampled information, often using a number of covariables to help such interpolation. The rationale for the choice of these covariables is not always documented, despite the fact that many local-scale studies have identified the factors explaining spatial variability of SOC and FFC stocks. These studies indicate, among others the importance of long-term land use history. Despite this, information on the effects of land use history has never been used to explain variability of carbon stocks in national-scale inventories. We designed an alternative method to improve national-scale inventories of SOC and FCC for the Dutch sand area that takes stock of the findings of detailed case studies. Determinants for SOC and FFC stocks derived from landscape-scale case studies were used to map national-scale spatial variability and to calculate national totals. The resulting national-scale spatial distribution was compared with the SOC stock map from the current Dutch greenhouse gas inventory. Using land use history to explain SOC variability decreased the error of the SOC stock estimate in 60 % of the area. The error in FFC stocks decreased in half of the forest area after including soil fertility, tree species, and forest age as explanatory factors. Estimates with reduced uncertainty will make land use and land management a more attractive and acceptable mitigation option to reduce emissions of greenhouse gases for the LULUCF sector.     

Application of Likelihood Ratio and Logistic Regression Models to Landslide Susceptibility Mapping Using GIS

For landslide susceptibility mapping, this study applied and verified a Bayesian probability model, a likelihood ratio and statistical model, and logistic regression to Janghung, Korea, using a Geographic Information System (GIS). Landslide locations were identified in the study area from interpretation of IRS satellite imagery and field surveys; and a spatial database was constructed from topographic maps, soil type, forest cover, geology and land cover. The factors that influence landslide occurrence, such as slope gradient, slope aspect, and curvature of topography, were calculated from the topographic database. Soil texture, material, drainage, and effective depth were extracted from the soil database, while forest type, diameter, and density were extracted from the forest database. Land cover was classified from Landsat TM satellite imagery using unsupervised classification. The likelihood ratio and logistic regression coefficient were overlaid to determine each factors rating for landslide susceptibility mapping. Then the landslide susceptibility map was verified and compared with known landslide locations. The logistic regression model had higher prediction accuracy than the likelihood ratio model. The method can be used to reduce hazards associated with landslides and to land cover planning. Note: This version was published online in June 2005 with the cover date of August 2004.     

Assessment of spatial variation of cesium-137 in small catchments

Surface contamination by bomb-derived and Chernobyl-derived 137Cs has been subject to changes due to physical decay and lateral transport of contaminated soil particles, which have resulted in an on-going transfer of radionuclides from terrestrial ecosystems to surface water, river bed sediments, and flood plains. Knowledge of the different sources of spatial variation of 137Cs is particularly essential for estimating 137Cs transfer to fluvial systems and for successfully applying 137Cs as an environmental tracer in soil erosion studies. This study combined a straightforward sediment redistribution model and geostatistical interpolation of point samples of 137Cs activities in soil to distinguish the effects of sediment erosion and deposition from other sources of variation in 137Cs in the small Mochovce catchment in Slovakia. These other sources of variation could then be interpreted. Besides erosion and deposition processes, the initial pattern of 137Cs deposition, floodplain sedimentation, and short-range spatial variation were identified as the major sources of spatial variation of the 137Cs inventory.     

Spatial Pattern of Ecosystem Function and Ecosystem Conservation

The spatial pattern of ecosystem function can affect ecosystem conservation. Ecosystem functions are often heterogeneous spatially due to physical and biological factors. We can influence ecosystem functions by changing the spatial patterns of the physical and biological elements of an ecosystem and regulating their combinations. The variation–position effect highlights a phenomenon resulting from the spatial pattern of ecosystem function. The effect shows that the identical variation of a factor may produce different effects on the overall situation when this variation occurs in a different spatial position. In a watershed of the Yangtze River, water retention is a primary ecosystem function. The variation–position effect for water retention capacity occurs in the watershed because of the spatial heterogeneity in vegetation, soil, and slope. The change of vegetation that occurs in a complex can affect the overall situation of water retention, and the effect can be different due to the change occurring in the position holding different vegetation-soil-slope complex. To improve the ecosystem in the watershed and to meet the social needs for the ecosystem function of water retention, a strategy called ecosystem function and spatial pattern-based forest extension was proposed to conserve forests. The implementation of the strategy enables the watershed to attain the maximum effective increase in water retention capacity.     

Effect of the Spatial Variability of Land Use,Soil Type,and Precipitation on Streamflows in Small Watersheds1

Abstract: The spatial variability of the data used in models includes the spatial discretization of the system into subsystems, the data resolution, and the spatial distribution of hydrologic features and parameters. In this study, we investigate the effect of the spatial distribution of land use, soil type, and precipitation on the simulated flows at the outlet of “small watersheds” (i.e., watersheds with times of concentration shorter than the model computational time step). The Soil and Water Assessment Tool model was used to estimate runoff and hydrographs. Different representations of the spatial data resulted in comparable model performances and even the use of uniform land use and soil type maps, instead of spatially distributed, was not noticeable. It was found that, although spatially distributed data help understand the characteristics of the watershed and provide valuable information to distributed hydrologic models, when the watershed is small, realistic representations of the spatial data do not necessarily improve the model performance. The results obtained from this study provide insights on the relevance of taking into account the spatial distribution of land use, soil type, and precipitation when modeling small watersheds.     

Spatial and temporal patterns of Campylobacter contamination underlying public health risk in the Taieri River, New Zealand

New Zealand's freshwater ecosystems are subject to microbial contamination from a predominantly agricultural landscape. This study examines the spatial and temporal distribution of the human pathogen Campylobacter in the lower Taieri River, South Island (New Zealand). Enumeration of thermophilic Campylobacter from river samples was performed using a most probable number (MPN) method. Seasonal variation in Campylobacter levels was evident, with higher median levels detected in summer, when human exposure through recreational water use is maximal. Campylobacter levels varied significantly among the 10 sampling sites, increasing below a major tributary entering the river and then showing a downstream decrease. These changes probably resulted from inputs from adjacent farms and instream Campylobacter losses (settling, death). Two main peaks in the flux of Campylobacter were observed, one in winter and one in summer. A decrease in notified cases of campylobacteriosis in the human population was observed when levels of Campylobacter at the main recreational bathing site on the river were low. Continuing land use change and intensification in New Zealand may lead to further increases in microbial contamination of freshwaters, and an associated increase in waterborne enteric diseases such as campylobacteriosis.     

Relationship between water repellency and native and petroleum-derived organic carbon in soils

Some soils develop severe and persistent water repellency following contamination with crude oil. This study was conducted to characterize and compare the spatial distribution of soil water repellency and residual oil contamination at 12 such sites. The molarity of ethanol droplet (MED) test was used to assess soil water repellency and the content of dichloromethane-extractable organics (DEO) was used to quantify residual oil in soil. We found a relatively strong positive correlation between MED and DEO in soil (r2 = 0.74). Both variables tended to decrease abruptly with depth at 11 of the 12 study sites. Dichloromethane-extractable organics similarly decreased with depth in control adjacent soil (MED = 0 M), but from an average concentration one to two orders of magnitude lower than in water-repellent soil. Using data from corresponding control adjacent and water-repellent soils, we determined that approximately 29 and 10% of measured total organic carbon in water-repellent A- and B-horizon soil, respectively, consists of dichloromethane-insoluble organic carbon of petroleum origin. We propose that this fraction contains most of the causative agents of soil water repellency at the studied sites.     

Hydrogeological relationships of sandy deposits: modeling of two-dimensional unsaturated water and pesticide transport

Prediction of the movement of water and solutes in the vadose zone requires information on the distribution of spatial trends and heterogeneities in porous media. The present study describes different lithofacies origination mainly from glaciofluvial deposits. Among different lithofacies, hydrological relationships were investigated. By means of a two-dimensional hydrological model it was evaluated how the flow of water and leaching of metribuzin (4-amino-6-tert-butyl-4,5-dihydro-3-methylthio-1,2,4-triazin-5-one) was affected. Two selected large outcrop sections consisting of glacial outwash deposits were used in the modeling study. Eleven different lithofacies were distinguished and described in terms of texture distribution, sorting, bedding style, and external boundaries based on excavated soil profiles from 27 locations representing seven predominantly sandy landforms in Denmark. Undisturbed soil columns were sampled from each of the lithofacies and brought to the laboratory to be analyzed. With respect to their soil hydraulic properties, the different lithofacies formed four different hydrofacies having relatively homogeneous, hydrogeological properties. Two large outcrop sections from one of the locations (a gravel pit) located near the terminal moraine of the former Weichsel glacier were used for the HYDRUS-2D modeling. Modeling results revealed that the spatial distribution of sedimentary bodies affected water flow and the leaching of metribuzin.