Review of the Kriging Technique Applications to Groundwater Quality

Kriging, a geostatistical technique, has been used for many years to evaluate groundwater quality. The best estimation data for unsampled points were determined by using this method depending on measured variables for an area. The groundwater contaminants assessment worldwide was found through many kriging methods. The present paper shows a review of the most known methods of kriging that were used in estimating and mapping the groundwater quality. Indicator kriging, simple kriging, cokriging, ordinary kriging, disjunctive kriging and lognormal kriging are the most used techniques. In addition, the concept of the disjunctive kriging method was explained in this work to be easily understood.

Pollution Characteristics, Spatial Patterns, and Sources of Toxic Elements in Soils from a Typical Industrial City of Eastern China

Soil pollution due to toxic elements (TEs) has been a core environmental concern globally, particularly in areas with developed industries. In this study, we sampled 300 surface (0–0.2 m) soil samples from Yuyao City in eastern China. Initially, the geo-accumulation index, potential ecological risk index, single pollution index, and Nemerow composite pollution index were used to evaluate the soil contamination status in Yuyao City. Ordinary kriging was then deployed to map the distribution of the soil TEs. Subsequently, indicator kriging was utilized to identify regions with high risk of TE pollution. Finally, the positive matrix factorization model was used to apportion the sources of the different TEs. Our results indicated that the mean content of different TEs kept the order: Zn > Cr > Pb > Cu > Ni > As > Hg ≈ Cd. Soil pollution was mainly caused by Cd and Hg in the soil of Yuyao City, while the content of other TEs was maintained at a safe level. Regions with high TE content and high pollution risk of TEs are mainly located in the central part of Yuyao City. Four sources of soil TEs were apportioned in Yuyao City. The Pb, Hg, and Zn contents in soil were mainly derived from traffic activities, coal combustion, and smelting. Meanwhile, Cu was mainly sourced from industrial emissions and atmospheric deposition, Cr and Ni mainly originated from soil parental materials, and Cd and As were produced by industrial and agricultural activities. Our study provides important implications for improving the soil environment and contributes to the development of efficient strategies for TE pollution control and remediation.

Facies and Petrophysical Modeling of Triassic Chang 6 Tight Sandstone Reservoir, Heshui Oil Field, Ordos Basin, China

Tight sandstone reservoirs are widely distributed worldwide. The Upper Triassic Chang 6 member of the Yanchang Formation is characterized by low permeability and porosity. The facies model offers a unique approach for understanding the characteristics of various environments also heterogeneity, scale, and control of physical processes. The role of subsurface facies features and petrophysical properties was unclear. Notable insufficient research has been conducted based on facies and petrophysical modeling and that demands to refine the role of reservoir properties. To tackle this problem, a reservoir model is to be estimated using various combinations of property modeling algorithms for discrete (facies) and continuous (petrophysical) properties. Chang 6 member consists of three main facies, i.e., channel, lobe main body, and lobe margin facies. The current research is aimed at comparing the applicability and competitiveness of various facies and petrophysical modeling methods. Further, well-log data was utilized to interpret unique facies and petrophysical models to better understand the reservoir architecture. Methods for facies modeling include indicator kriging, multiple-point geostatistics, surface-based method, and sequential indicator simulation. Overall, the indicator kriging method preserved the local variability and accuracy, but some facies are smoothed out. The surface-based method showed far better results by showing the ability to reproduce the geometry, extent, connectivity, and facies association. The multiple-point geostatistics (MPG) model accurately presented the facies profiles, contacts, geometry, and geomorphological features. Sequential indicator simulation (SIS) honored the facies spatial distribution and input statistical parameters. The porosity model built using sequential Gaussian simulation (SGS) showed low porosity (74% values <2%). Gaussian random function simulation (GRFS) models showed very low average porosity (8%-10%) and low permeability (less than 0.1 mD). These methods indicate that Chang 6 member is a typical unconventional tight sandstone reservoir with ultralow values of petrophysical properties.

Assessment of the Spatial Distribution and Risk Associated with Fruit Rot Disease in Areca catechu L.

Phytophthora meadii (McRae) is a hemibiotrophic oomycete fungus that infects tender nuts, growing buds, and crown regions, resulting in fruit, bud, and crown rot diseases in arecanut (Areca catechu L.), respectively. Among them, fruit rot disease (FRD) causes serious economic losses that are borne by the growers, making it the greatest yield-limiting factor in arecanut crops. FRD has been known to occur in traditional growing areas since 1910, particularly in Malnad and coastal tracts of Karnataka. Systemic surveys were conducted on the disease several decades ago. The design of appropriate management approaches to curtail the impacts of the disease requires information on the spatial distribution of the risks posed by the disease. In this study, we used exploratory survey data to determine areas that are most at risk. Point pattern (spatial autocorrelation and Ripley’s K function) analyses confirmed the existence of moderate clustering across sampling points and optimized hotspots of FRD were determined. Geospatial techniques such as inverse distance weighting (IDW), ordinary kriging (OK), and indicator kriging (IK) were performed to predict the percent severity rates at unsampled sites. IDW and OK generated identical maps, whereby the FRD severity rates were higher in areas adjacent to the Western Ghats and the seashore. Additionally, IK was used to identify both disease-prone and disease-free areas in Karnataka. After fitting the semivariograms with different models, the exponential model showed the best fit with the semivariogram. Using this model information, OK and IK maps were generated. The identified FRD risk areas in our study, which showed higher disease probability rates (>20%) exceeding the threshold level, need to be monitored with the utmost care to contain and reduce the further spread of the disease in Karnataka.

Mapping The Distribution of Iron Content in Nickel Laterite Deposits Using Indicator Kriging and Ordinary Kriging Interpolation Method

Beside containing nickel (Ni), nickel laterite deposits also contain other elements, including iron (Fe) which have varying levels in each layer. In this study, the distribution of Fe content in the limonite layers was carried out using the indicator kriging method to analyze the probability distribution of iron levels and ordinary kriging to analyze the variability of iron levels spatially. Fitting the variogram was undertaken by using spherical, exponential and gaussian models. The selection of the best variogram model was carried out based on the smallest root mean square error (RMSE) value, while the estimation of resource potential was calculated by the polygon extended area method. The results of the interpolation show that the distribution of iron anomaly occupies ± 83,3% of the research area with a potential resource of ±64.522.110 ton of iron. The evaluation of the interpolation results base on the root mean square standardized prediction error (RMSP) indicates that the estimation results of iron content using the ordinary kriging method are underestimated.

Assessing local and spatial uncertainty with nonparametric geostatistics

Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore how HER can be used for estimating threshold-exceeding probabilities, it is applied to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in the literature. For the analyzed dataset, IK and HER predictions achieve the best performance and exhibit comparable accuracy and precision. Compared to IK, advantages of HER for uncertainty estimation in a fine resolution are that it does not require modeling of multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distributions. Finally, to avoid the well-known smoothing effect when using point estimations (as is the case with both kriging and HER), and to provide maps that reflect the spatial fluctuation of the observed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

Uso da krigagem indicatriz na avaliação de regiões para produção de feijão-caupi no estado da Bahia / Indicator kriging in the evaluation of regions for the production of bean/cowpea in the state of Bahia

O feijão-caupi constitui-se em um dos principais componentes da dieta alimentar nas regiões Nordeste e Norte do Brasil. A deficiência de água é um dos fatores mais limitantes para a obtenção de elevadas produtividades; portanto, recomenda-se sua implantação em regiões com índices de precipitação que satisfaçam as necessidades da cultura. Objetivou-se analisar a estrutura da dependência espacial de dados de precipitação pluvial anual no estado da Bahia e a construção do mapa de probabilidade utilizando-se a técnica de krigagem indicadora com vista na localização de regiões de risco com altas e baixas probabilidades de precipitação inferiores a 500 mm. Os dados em estudo referem-se às informações de precipitação pluvial anual coletadas no ano 2014 no estado de Bahia; foram ajustados e comparados os modelos Gaussiano, exponencial e esférico. Os resultados mostram que o modelo Gaussiano se ajusta melhor aos dados, os quais apresentam dependência espacial forte, A técnica de krigagem indicadora mostra-se eficiente no mapeamento da probabilidade de precipitação em relação ao valor de corte estabelecido. Não é recomendado produzir feijão-caupi na região nordeste e no centro norte do estado da Bahia.

Geostatistics as a tool to reduce the sampling effort in forest inventories

Geostatistics is one of the tools applied to investigate the spatial variability of forests to reduce costs and recognize the best productivity areas for planning. This study aimed to test the performance of geostatistical techniques in reducing the sampling effort in forest inventories. For this purpose, we used the height of dominant trees as a discriminator of the homogeneous strata to obtain a better representation of the productivity within the forest stands. We carried out the study in Pinus taeda L. stands in the Center-South of Paraná, Brazil, by using plots from a forest inventory allocated with the systematic process. Then, we tested three models to determine the site curves (Schumacher, Chapman-Richards 2, and 3 coefficients) with the thirty-seventh year being the reference age. To model the spatial patterns of the dominant height, we used the ordinary kriging, and, after that, we generated the thematic maps of the site classes. Similarly, we used the indicator kriging which allowed obtaining the probabilities of high, medium, and low productivity sites. The processing of the stratified sampling, with the support of the visual interpretation of the images, allowed us to define five strata according to productivity. Results showed that ordinary kriging is effective in defining the productivity classes. Along with geostatistical techniques, it produces more homogeneous strata and reduces the errors of the forest inventory. Moreover, the best-selected model was the Chapman-Richards (3 coefficients) for the site curves. The exponential model was the best model to identify the best areas of the probability of occurrence of sites with higher productivity. The efficiency of indicative kriging generated thematic maps to delimit the likely locations of the most promising sites. Overall, geostatistics proved to be efficient concerning error when compared to simple random sampling.

Integration of Dual Border Effects in Resource Estimation: A Cokriging Practice on a Copper Porphyry Deposit

Hierarchical or cascade resource estimation is a very common practice when building a geological block model in metalliferous deposits. One option for this is to model the geological domains by indicator kriging and then to estimate (by kriging) the grade of interest within the built geodomains. There are three problems regarding this. The first is that sometimes the molded geological domains are spotty and fragmented and, thus, far from the geological interpretation. The second is that the resulting estimated grades highly suffer from a smoothing effect. The third is related to the border effect of the continuous variable across the boundary of geological domains. The latter means that the final block model of the grade shows a very abrupt transition when crossing the border of two adjacent geological domains. This characteristic of the border effect may not be always true, and it is plausible that some of the variables show smooth or soft boundaries. The case is even more complicated when there is a mixture of hard and soft boundaries. A solution is provided in this paper to employ a cokriging paradigm for jointly modeling grade and geological domains. The results of modeling the copper in an Iranian copper porphyry deposit through the proposed approach illustrates that the method is not only capable of handling the mixture of hard and soft boundaries, but it also produces models that are less influenced by the smoothing effect. These results are compared to an independent kriging, where each variable is modeled separately, irrespective of the influence of geological domains.