Stories of a water-table: anomalous depressions, aquitard breaches and seasonal implications, Shelby County, Tennessee, USA

An extensive water level survey of the water-table aquifer (i.e., shallow aquifer) within Shelby County, Tennessee, was conducted in the dry (fall 2020) and wet (spring 2021) seasons. Water-table surfaces were generated using cokriging to observe seasonal differences to identify anomalous water-table depressions, indicative of an underlying aquitard breach. Seasonal differences were attributed to non-coincident control and timing between the surveys and when optimum dry (fall) and wet (spring) conditions existed, as observed through comparisons with continuous historical water levels from 12 shallow monitoring wells. Additionally, data from fall 2020 were compared to previous studies in 2005 and 2015 to determine decadal changes in levels and shape of the water-table surface which were mostly attributed to changes in data control and potential climate variations. A prediction error map was generated from the 2020 dataset to identify areas of the county with high-prediction error (>7.0 m) to offer guidance on where future well control would be optimal.

An iterative optimization scheme to accommodate inequality constraints in air quality geostatistical estimation of multivariate PM

The kriging-based estimation of the different types of atmospheric particulate matter (PM) pollutions defined in the air quality regulation raises some operational problems because the (co)kriging equations are obtained by minimizing a linear combination of the estimation variances subject to unbiasedness constraints. As a consequence, the estimation process can result in total PM₁₀ concentrations that are less than the PM_2.5 concentrations which would be physically impossible. In a previous publication, it was shown that a convenient external drift modeling can reduce the number of spatial locations where the inequality constraint is not satisfied, without completely solving the problem. In this work, the formulation of the cokriging system is modified, inspired by previous works focusing on positive kriging. The introduction of additional constraints on the cokriging weights are presented, leading to a unique and optimal solution to the problem of cokriging under inequality constraints between two variables. Some computational and algorithmic details are introduced. An evaluation of the penalized cokriging is provided by using the European PM monitoring sites dataset: some maps and performance scores are given to assess the relevance of our iterative optimization scheme.

Effectiveness of predicting the spatial distributions of target contaminants of a coking plant based on their related pollutants

The prediction accuracy of the spatial distribution of soil pollutants at a site is relatively low. Related pollutants can be used as auxiliary variables to improve the prediction accuracy. However, little relevant research has been conducted on site soil pollution. To analyze the prediction accuracy of target pollutants combined with auxiliary pollutants, Cu, toluene, and phenanthrene were selected as the target pollutants for this study. Based on geostatistical analysis and spatial analysis, the following results were obtained. (1) The reduction in the root mean square errors (RMSEs) for Cu, toluene, and phenanthrene with multivariable cokriging was 68.4%, 81.6%, and 81.2%, respectively, which are proportional to the correlation coefficient of the relationship between the auxiliary pollutants and the target pollutants. (2) The RMSEs calculated for the multivariable cokriging were lower than those obtained by only combining one related pollutants, and two co-variables should be better. (3) The predicted results for Cu, phenanthrene, and toluene and their corresponding related pollutants are more accurate than the results obtained not using the related pollutants. (4) In the interpolation process, the RMSEs for Cu, toluene, and phenanthrene with multivariable cokriging basically increase as the neighborhood sample data increases, and then they become stable. (5) When 84, 61, and 34 sample points were removed, the RMSEs for Cu, toluene, and phenanthrene, respectively, with multivariable cokriging were close to the RMSEs of the target pollutants based on the total samples. The results are of great significance to improving the prediction accuracy of the spatial distribution of soil pollutants at coking plant sites.

Application of geostatistical models to identify spatial distribution of groundwater quality parameters

Groundwater quality management is a priority in arid and semi-arid zones where water is scarce. Leachate from open dumping of municipal solid wastes may threaten groundwater quality. This research aimed at assessing groundwater quality of the aquifer of Shur river basin in Tehran province, Iran. The pollution potential of leachate from a landfill, located at the center of the basin, was estimated to assess its impact on the aquifer. Samples from 38 wells and 2 leachate ponds around the landfill were analyzed for their physico-chemical parameters and heavy metals. Leachate Pollution Index (LPI) and Water Quality Index (WQI) were calculated and multivariate statistical techniques were employed through geostatistical models to predict the spatial variability of groundwater quality and assess its contamination sources. The groundwater quality map was developed by GIS Interface. LPI indicated that leachate from the closed cell (LPI = 36) was more contaminating than that of the active site (LPI = 25). Kriging and cokriging geostatistical interpolation methods were applied to groundwater quality parameters. The best interpolation model was then identified through cross-validation with RMSE and GSD criteria. Cokriging yielded more accurate results than kriging. Spatial distribution maps showed high groundwater contamination and degraded water quality mainly in the central part of the basin, where the landfill was. Also, 293.7 ha of the study area possessed poor and very poor water quality, unsuitable for drinking. This study implicated multiple approaches for groundwater quality assessment and estimated its spatial structure as an effort toward effective groundwater quality management in Shur river basin.

Mercury spatiality and mobilization in roadside soils adjacent to a savannah ecological reserve

Mercury (Hg) is a persistent environmental pollutant of global concern. Recognized anthropic contributions to environmental Hg pollution include fuel fossil emissions, soil erosion, and industrial and mining activities. Environmental Hg that enters water bodies can be methylated before entering the food chain and contaminating man and wildlife. We used a kriging approach for sampling and X-ray crystallography to study the pressure of road-traffic Hg emissions on soil Hg concentrations in an ecological reserve (ESECAE) in Central Brazil' savannah. We took samples of organic (n = 144) and mineral (n = 144) layers from the road-side and from the undisturbed soils at 0.1, 1, and 2 km from traffic, inside the ESECAE. Overall, total mercury (THg) concentrations determined by atomic absorption spectrophotometry were significantly higher in the organic layer than in the mineral layer. The mean soil THg in the organic and mineral layers was highest at the roadside (respectively 19.77 ± 12.01 and 16.18 ± 11.54 μg g^-1), gradually decreasing with the distance from the road. At 2 km, the mean soil THg was 0.09 ± 0.30 and 0.029 ± 0.03 μg g^-1, respectively, for the organic and mineral layers. X-ray crystallography showed mineralogical similarity of the sampled soils, indicating Hg externality, i.e, it did not originate from existing soil minerals. Co-kriging analysis (n = 288) confirmed Hg hotspots on the roadsides and a faster mobilization occurring up to a distance of 1 km for both layers. The soil reception and retention of traffic Hg emissions are mainly in the organic layer and can impact subsoil and adjacent areas. Thus, traffic soil-Hg pollution is limited to the road proximities; THg concentrations are high up to 100 m with an inflection point at 1 km.

Hydrogeochemical characterizations and quality evaluation of groundwater in the major river basins of a geologically and anthropogenically driven semi-arid tract of India

Access to clean drinking water has been acknowledged as a human right and assessing the hydrogeochemistry and groundwater quality status plays an important role in proving cleaner and safer water for human consumption. This study evaluated the sources and driving factors of the groundwater facies in the five major river basins (viz. Ajay, Mayurakshi, Kopai, Brahmani and Dwarka) of an agroeconomic semi-arid Indian tract through hydrogeochemical and principal component analyses based on 2200 groundwater samples (N_s = 2200) obtained during the pre- and post-monsoon cycles from 1100 wells (N_w = 1100). The results revealed that minerals weathering, ion/reverse ion exchange, mixing and evaporation processes along with anthropogenic inputs are responsible for the deteriorated groundwater quality of the river basins. The study has considered the cokriging approach that uses geostatistical and multivariate statistical techniques to interpolate a dataset. To determine the spatio-seasonal variabilities of the groundwater facies more accurately, the estimation accuracies of different interpolation techniques viz. inverse distance weighting, kriging/cokriging and splines techniques were compared and kriging/cokriging was found to represent the variability more accurately. Shannon's entropy theory was employed to assess the groundwater quality of the river basins as it eliminates the subjective bias and inherent uncertainties of the groundwater systems. Groundwater in ~37.45-38.42% of the total area was moderate to extremely poor for human consumption where 10.40-12.14%, 9.09-12.40%, 21.18-22.35%, 15.20-19.93% and 6.48-8.80% samples from the Ajay (N_w = 175), Brahmani (N_w = 175), Dwarka (N_w = 180), Kopai (N_w = 350) and Mayurakshi (N_w = 220) river basins exhibited unfit to drink water quality. The sensitivity of the water quality model was analyzed to identify the influences of the individual parameters which revealed that the outcome does not depend solely on one parameter. The study recommends adaptation of the treatment techniques to ensure clean drinking water for the residents. Managed aquifer recharge techniques might also improve the groundwater quality in certain areas.

Evaluation of geostatistical techniques and their hybrid in modelling of groundwater quality index in the Marand Plain in Iran

In many parts of the world, groundwater is considered as one of the main sources of urban and rural drinking water. Over the past three decades, the qualitative and quantitative characteristics of aquifers have been negatively affected by different factors such as excessive use of chemical fertilizers in agriculture, indiscreet, and over-exploitation use of groundwater. Therefore, finding the effective method for mapping the water quality index (WQI) is important for locating suitable and non-suitable areas for urban and rural drinking waters. In the present paper, the best method to estimate the spatial distribution of WQI was assessed using the inverse distance weighted, kriging, cokriging, geographically weighted regression (GWR), and hybrid models. Creating hybrid models can increase modeling capabilities. Hybrid methods make use of a combination of estimated model capabilities. In addition, to improve the results of cokriging, GWR, and hybrid methods, the auxiliary parameters of land slope, groundwater table, and groundwater transmissibility were used. In order to assess the proposed methodology, 11 qualitative parameters obtained from 63 observation wells in Marand Plain (Iran) were utilized. Four statistical measures, namely the root mean square error (RMSE), the mean absolute error (MAE), the Akaike coefficient (AIC), and the correlation coefficient (R²) along with the Taylor diagram, have been done. Classification of the WQI index showed that the quality of a number of 1, 27, 18, and 17 wells was, respectively, in excellent, good, moderate, and poor grades. The results of modeling the WQI index based on IDW, kriging, cokriging, GWR, and hybrid methods showed that the best estimate of WQI was obtained by using hybrid GWR-kriging method with three input parameters of land slope, groundwater table, and groundwater transmissibility. Therefore, hybrid kriging and GWR methods have been fairly well able to simulate the WQI index.

Use of an epiphytic lichen and a novel geostatistical approach to evaluate spatial and temporal changes in atmospheric deposition in the Athabasca Oil Sands Region, Alberta, Canada

Temporal and spatial atmospheric deposition trends of elements to the boreal forest surrounding bitumen production operations in the Athabasca Oil Sands Region (AOSR), Alberta, Canada were investigated as part of a long-term lichen bioindicator study. The study focused on eight elements (sulfur, nitrogen, aluminum, calcium, iron, nickel, strontium, vanadium) that were previously identified as tracers for the major oil sand production sources. Samples of the in situ epiphytic lichen Hypogymnia physodes were collected in 2002, 2004, 2008, 2011, 2014, and 2017 within a ~150 km radius from the center of surface oil sand production operations in the AOSR. Site-specific time series analysis conducted at eight jack pine upland sites that were repeatedly sampled generally showed significant trends of increasing lichen concentrations for fugitive dust linked elements, particularly at near-field (<25 km from a major oil sands production operation) sample locations. Multiple regional scale geostatistical models were developed and evaluated to characterize broad-scale changes in atmospheric deposition based on changes in H. physodes elemental concentrations between 2008 and 2014. Empirical Bayesian kriging and cokriging lichen element concentrations with oil sands mining, bitumen upgrading, coke materials handling, and limestone quarry/crushing influence variables produced spatial interpolation estimates with the lowest validation errors. Gridded zonal mean lichen element concentrations were calculated for the two comprehensive sampling years (2008, 2014) and evaluated for spatial and temporal change. Lichen sulfur concentrations significantly increased in every grid cell within the domain with the largest increases (44-88%) in the central valley in close proximity to the major surface oil sand production operations, while a minor nitrogen concentration decrease (-20%) in a single grid cell was observed. The areal extent of fugitive dust element deposition generally increased with significantly higher deposition to lichens restricted to the outer grids of the enhanced deposition field, reflecting new and expanding surface mining activity.

Site-specific management of salt affected soils: A case study from Egypt

In Egypt all agricultural practices are generally applied uniformly without taking spatial variability into consideration, which is not efficient and may be more expensive than site-specific management approach. This is based on accurate assessment of within-field variation and on field delineation into homogeneous zones to be submitted to differential management. Multivariate geostatistics allows to assess and model the spatial variation of a set of soil attributes influencing management. The objective of this paper was to propose an approach for determining spatially variable rate application (VRA) of leaching water, to control soil salinity, and of fertilizer to improve productivity while reducing environmental impact. The research was conducted in an experimental 3.1-ha field in Egypt and the following soil attributes were measured: electrical conductivity (ECe), available nitrogen (N), available phosphorus (P), available potassium (K) and organic matter content (OM). Ordinary cokriging was applied to produce thematic maps of soil attributes and the appropriateness of the linear model of coregionalization was evaluated with cross-validation. Spatial maps of the five soil variables were classified into three isofrequencies classes and the mean values were calculated for each class. These values were then compared with critical reference values to assess the local soil requirements for reducing soil salinity and/or improving soil fertility. The results showed that the estimations of soil attributes were unbiased and accurate. Only for ECe and available nitrogen site-specific management would be preferable because it would reduce the agricultural costs for both soil reclamation (saving water used to leach salts) and improvement of soil N fertility in comparison with the traditional uniform methods. The proposed approach, though producing encouraging results, would require improvements in the determination of the threshold values used to plan salt leaching and soil fertilization.

Comparison of IDW, cokriging and ARMA for predicting spatiotemporal variability of soil salinity in a gravel-sand mulched jujube orchard

Information about the spatiotemporal variability of soil salinity is important for managing salinization in gravel-sand mulched fields. We used inverse distance weighting (IDW) and cokriging to model the spatial variability of soil salinity from 2013 to 2016 and used an autoregressive moving-average (ARMA) model time series to analyze the temporal variability. The objectives of this paper are (a) to compare IDW and cokriging for predicting salinity in deep soil layers from surface data, thus finding a more appropriate method to model the spatial variability of soil salinity, and, using ARMA time series, (b) to identify one or a few sampling points, where soil salt content is the most temporally stable, to increase sampling efficiency or decrease cost and to estimate the overall soil salt content of a field. The IDW interpolation was more accurate than cokriging when using surface salt content to estimate the content in deep layers; so, we used IDW to interpolate the data and draw spatial distribution maps of salt content. Salinity in the 0-10 cm layer gradually decreased with the amount of gravel-sand mulching, from 1.02 to 0.7 g/kg over four years, and increased with depth. ARMA was accurate when using sample dates to predict soil salinity in the time series, and the model was more stable. The stability of the salt spatial patterns over time and along the soil profile allowed us to identify a location representative of the field-mean salt content, with mean relative error ranging between 0.56 and 2.19%. The monitoring of soil salt from a few observations is thus a valuable tool for practitioners and will aid the management of soil salt in gravel-sand-mulched fields in arid regions, with a range of potential applications beyond the framework of monitoring salinity.

Kriging methods with auxiliary nighttime lights data to detect potentially toxic metals concentrations in soil

The spatial distribution of potentially toxic metals (PTMs) has been shown to be related to anthropogenic activities. Several auxiliary variables, such as those related to remote sensing data (e.g. digital elevation models, land use, and enhanced vegetation index) and soil properties (e.g. pH, soil type and cation exchange capacity), have been used to predict the spatial distribution of soil PTMs. However, these variables are mostly focused on natural processes or a single aspect of anthropogenic activities and cannot reflect the effects of integrated anthropogenic activities. Nighttime lights (NTL) images, a representative variable of integrated anthropogenic activities, may have the potential to reflect PTMs distribution. To uncover this relationship and determine the effects on evaluation precision, the NTL was employed as an auxiliary variable to map the distribution of PTMs in the United Kingdom. In this study, areas with a digital number (DN) ≥ 50 and an area > 30 km² were extracted from NTL images to represent regions of high-frequency anthropogenic activities. Subsequently, the distance between the sampling points and the nearest extracted area was calculated. Barium, lead, zinc, copper, and nickel concentrations exhibited the highest correlation with this distance. Their concentrations were mapped using distance as an auxiliary variable through three different kriging methods, i.e., ordinary kriging (OK), cokriging (CK), and regression kriging (RK). The accuracy of the predictions was evaluated using the leave-one-out cross validation method. Regardless of the elements, CK and RK always exhibited lower mean absolute error and root mean square error, in contrast to OK. This indicates that using the NTL as the auxiliary variable indeed enhanced the prediction accuracy for the relevant PTMs. Additionally, RK showed superior results in most cases. Hence, we recommend RK for prediction of PTMs when using the NTL as the auxiliary variable.

Geostatistical prediction of water lead levels in Flint, Michigan: A multivariate approach

Despite several environmental crises, little research has been conducted on citywide geospatial modeling of water lead levels (WLL) in public distribution systems. This paper presents the first application of multivariate geostatistics to lead in drinking water within a distribution system, specifically in Flint, Michigan. One of the key features of the Flint data is their collection through two different sampling initiatives: (i) voluntary or homeowner-driven sampling whereby concerned citizens decided to acquire a testing kit and conduct sampling on their own (10,717 sites), and (ii) State-administered sampling where data were collected bi-weekly at 809 selected sites after training of residents by technical teams (sentinel sites). These two datasets were first averaged over the 41-week sampling period and each tax parcel to attenuate sampling fluctuations and create a set of 420 tax parcels sampled by both protocols. Both variables displayed a correlation of 0.62 while their direct and cross-semivariograms showed substantial nugget effect and a long range of 7.5 km. WLLs recorded at sentinel sites and deemed more reliable by city officials were then interpolated using cokriging to account for the more densely sampled voluntary data and information on service line composition (lead, other, or unknown) available for each of 51,045 residential tax parcels. Cross-validation demonstrated the greater prediction accuracy of the multivariate geostatistical approach relative to kriging and inverse square distance weighting interpolation using only sentinel data. This general procedure is applicable to other cities with aging infrastructure where lead in drinking water is a concern.

Geospatial estimation of the impact of Deepwater Horizon oil spill on plant oiling along the Louisiana shorelines

Stranded oil covering soil and plant stems in fragile Louisiana marshes was one of the most visible impacts of the 2010 Deepwater Horizon (DWH) oil spill. As part of the assessment of marsh injury after the DWH spill, plant stem oiling was broken into five categories (0%, 0-10%, 10-50%, 50-90%, 90-100%) and used as the independent variable for estimating death of vegetation, accelerated erosion, and other metrics of injury. The length of shoreline falling into each of these stem oiling categories was therefore a key measure of the total extent of marsh injury, and its accurate estimation is the focus of this paper. First, we used geographically-weighted logistic regression (GWR) to explore and model spatially varying relationships between stem oiling field data and secondary information (oiling exposure category) collected during shoreline surveys. We then combined GWR probability estimates with field data using indicator cokriging to predict the probability of exceeding four stem oiling thresholds (0, 10, 50, and 90%) at 50 m intervals along the Louisiana shoreline. Cross-validation using Receiver Operating Characteristic (ROC) Curves demonstrate the greater prediction accuracy of the multivariate geostatistical approach relative to either aspatial regression or indicator kriging that ignores secondary information.

Spatiotemporal analysis of olive flowering using geostatistical techniques

Analysis of flowering patterns in the olive (Olea europaea L.) are of considerable agricultural and ecological interest, and also provide valuable information for allergy-sufferers, enabling identification of the major sources of airborne pollen at any given moment by interpreting the aerobiological data recorded in pollen traps. The present spatiotemporal analysis of olive flowering in central Spain combined geostatistical techniques with the application of a Geographic Information Systems, and compared results for flowering intensity with airborne pollen records. The results were used to obtain continuous phenological maps which determined the pattern of the succession of the olive flowering. The results show also that, although the highest airborne olive-pollen counts were recorded during the greatest flowering intensity of the groves closest to the pollen trap, the counts recorded at the start of the pollen season were not linked to local olive groves, which had not yet begin to flower. To detect the remote sources of olive pollen several episodes of pollen recorded before the local flowering season were analysed using a HYSPLIT trajectory model and the findings showed that western, southern and southwestern winds transported pollen grains into the study area from earlier-flowering groves located outside the territory.

SGPP: spatial Gaussian predictive process models for neuroimaging data

The aim of this paper is to develop a spatial Gaussian predictive process (SGPP) framework for accurately predicting neuroimaging data by using a set of covariates of interest, such as age and diagnostic status, and an existing neuroimaging data set. To achieve a better prediction, we not only delineate spatial association between neuroimaging data and covariates, but also explicitly model spatial dependence in neuroimaging data. The SGPP model uses a functional principal component model to capture medium-to-long-range (or global) spatial dependence, while SGPP uses a multivariate simultaneous autoregressive model to capture short-range (or local) spatial dependence as well as cross-correlations of different imaging modalities. We propose a three-stage estimation procedure to simultaneously estimate varying regression coefficients across voxels and the global and local spatial dependence structures. Furthermore, we develop a predictive method to use the spatial correlations as well as the cross-correlations by employing a cokriging technique, which can be useful for the imputation of missing imaging data. Simulation studies and real data analysis are used to evaluate the prediction accuracy of SGPP and show that SGPP significantly outperforms several competing methods, such as voxel-wise linear model, in prediction. Although we focus on the morphometric variation of lateral ventricle surfaces in a clinical study of neurodevelopment, it is expected that SGPP is applicable to other imaging modalities and features.

Use of generalized additive models and cokriging of spatial residuals to improve land-use regression estimates of nitrogen oxides in Southern California

Land-use regression (LUR) models have been developed to estimate spatial distributions of traffic-related pollutants. Several studies have examined spatial autocorrelation among residuals in LUR models, but few utilized spatial residual information in model prediction, or examined the impact of modeling methods, monitoring site selection, or traffic data quality on LUR performance. This study aims to improve spatial models for traffic-related pollutants using generalized additive models (GAM) combined with cokriging of spatial residuals. Specifically, we developed spatial models for nitrogen dioxide (NO(2)) and nitrogen oxides (NO(x)) concentrations in Southern California separately for two seasons (summer and winter) based on over 240 sampling locations. Pollutant concentrations were disaggregated into three components: local means, spatial residuals, and normal random residuals. Local means were modeled by GAM. Spatial residuals were cokriged with global residuals at nearby sampling locations that were spatially auto-correlated. We compared this two-stage approach with four commonly-used spatial models: universal kriging, multiple linear LUR and GAM with and without a spatial smoothing term. Leave-one-out cross validation was conducted for model validation and comparison purposes. The results show that our GAM plus cokriging models predicted summer and winter NO(2) and NO(x) concentration surfaces well, with cross validation R(2) values ranging from 0.88 to 0.92. While local covariates accounted for partial variance of the measured NO(2) and NO(x) concentrations, spatial autocorrelation accounted for about 20% of the variance. Our spatial GAM model improved R(2) considerably compared to the other four approaches. Conclusively, our two-stage model captured summer and winter differences in NO(2) and NO(x) spatial distributions in Southern California well. When sampling location selection cannot be optimized for the intended model and fewer covariates are available as predictors for the model, the two-stage model is more robust compared to multiple linear regression models.