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Maps of erosivity, which are also commonly referred to as isoerodent maps, have played a critical role in soil conservation efforts in the United States and around the world. Currently available erosivity maps for the United States are either outdated, conflict with erosivity benchmarking studies, or utilized less advanced spatial mapping methods. Furthermore, it is possible that the same underlying issues with US maps are impacting global maps as well. In this study, we used more than 3400 15-min, fixed-interval precipitation gauges to update the isoerodent map of the conterminous United States. Erosivity values were interpolated using universal kriging under several spatial model configurations and resolutions. The optimal spatial model was selected based on which result had the lowest sample variogram error. Rainfall, erosivity, and erosivity density maps were compared to existing products. Some average annual and annual erosivity results were compared to high-quality erosivity benchmarking publications. Erosivity values from both RUSLE2 and Panagos et al. (2017) were generally lower in the eastern United States and mixed in the western United States compared to our results. Topographic effects resulted in much greater erosivity differences in this study as compared to prior maps. Benchmark comparisons revealed that erosivity maps from this study and others were lower than the benchmark by 14% or more (up to 38%). These findings suggest current practices of storm omission and intensity dampening correction need to be revisited, especially in locations with relatively low-to-moderate rainfall erosivity such as the Midwest or Northeast United States, for example.

Since the first investment in mining operations is very high, so, it is absolutely important to model the field in three dimensions for appropriate planning and cost analysis. The whole data set belonging to the geological, geophysical and drilling exploration studies carried out in the field should be evaluated as a package. In the modelling phase, the computer-aided tri-dimensional mining software has been used instead of the classical reserve calculation methods being utilized in previous years. Thus, more realistic and shorter results are achieved. In the present work, three-dimensional seam modelling of the Adana-Tufanbeyli (Turkey) lignite field was carried out. In modelling, the coal horizon of the field was examined. Then, the sub-seam levels in the horizon were determined and after examining their geometric relationships with each other, three sub-seams were defined. Seam composites were prepared by the downhole method to make the analysis results of different sizes uniform. It is possible to make block quality estimations, which will be the basis for reserve calculations, by creating variograms in different directions. Variograms are first created in the vertical direction and then in the horizontal direction respectively, to obtain the necessary parameters. The nugget effect and structural distance parameters were obtained from the created variogram models. To assign quality estimation values on the block model, the Kriging method was used when the number of data was sufficient, and the inverse distance method was applied, when it was insufficient. As a result of this modelling study, a total of 355.617.194 tons of lignite reserves with an average calorific value of 1.153 Kcal/kg were determined in the field.

Ground-mounted photovoltaic (PV) arrays of an agrivoltaic system (AVS) creates shade in the interspace areas as well as below PV areas of the AVS. Therefore, availability of photosynthetic photon flux density (PPFD) and daily light integral (DLI) in the AVS is negatively affected, which restricts optimum crop growth and yield. Therefore, in this study, spatial and temporal variation of PPFD and DLI in the AVS (105 kWp) developed at Jodhpur, India were quantified. Among three designs of PV arrays in the AVS, the proportion of shaded area in interspace was found highest in single row design and lowest in triple row design. The amount of PPFD varied widely in the AVS and even within the shaded area. Following semivariogram and kriging approach, spatial variation of PPFD and DLI was quantified within the AVS. Highest amount of PPFD was observed near noon in unshaded areas (1295 μmol m−2 s−1) whereas lowest amount was observed during morning at below PV array (24 μmol m−2 s−1). Based on the maps of PPFD and DLI, three distinct zones in the AVS were identified: (i) below PV array (DLI = 0–5 mol m−2 d−1), (ii) interspace area with partial shade (DLI = 5–20 mol m−2 d−1) and (iii) interspace areas with no shade (DLI = 20–30 mol m−2 d−1). Knowledge of spatial and temporal variation of PPFD and DLI may help in selection of suitable crops for the AVS.

Spatial-temporal distribution of marine fishes is strongly influenced by environmental factors. To obtain a more continuous distribution of these variables usually measured by stationary sampling designs, spatial interpolation methods (SIMs) is usually used. However, different SIMs may obtain varied estimation values with significant differences, thus affecting the prediction of fish spatial distribution. In this study, different SIMs were used to obtain continuous environmental variables (water depth, water temperature, salinity, dissolved oxygen (DO), pH, chlorophyll a and chemical oxygen demand (COD)) in the Changjiang River Estuary (CRE), including inverse distance weighted (IDW) interpolation, ordinary Kriging (OK) (semivariogram model: exponential (OKE), Gaussian (OKG) and spherical (OKS)) and radial basis function (RBF) (regularized spline function (RS) and tension spline function (TS)). The accuracy and effect of SIMs were cross-validated, and two-stage generalized additive model (GAM) was used to predict the distribution of Coilia nasus from 2012 to 2014 in CRE. DO and COD were removed before model prediction due to their autocorrelation coefficient based on variance inflation factors analysis. Results showed that the estimated values of environmental variables obtained by the different SIMs differed (i.e., mean values, range etc.). Cross-validation revealed that the most suitable SIMs of water depth and chlorophyll a was IDW, water temperature and salinity was RS, and pH was OKG. Further, different interpolation results affected the predicted spatial distribution of Coilia nasus in the CRE. The mean values of the predicted abundance were similar, but the differences between and among the maximum value were large. Studies showed that different SIMs can affect estimated values of the environmental variables in the CRE (especially salinity). These variations further suggest that the most applicable SIMs to each variable will also differ. Thus, it is necessary to take these potential impacts into consideration when studying the relationship between the spatial distribution of fishes and environmental changes in the CRE.

Phosphorus (P) is considered an indispensable and finite resource that limits crop yields, and soil P is distributed heterogeneously in space. However, a systematic analysis of previous studies indicates that there are large gaps in our knowledge regarding the spatial patterns of soil P due to the lack of sufficient field observations, especially at larger scales. Thus, we explored the spatial patterns of soil total P (TP) and Olsen-available P (AP) in the Hexi Corridor, which is an important commodity grain base for China where large quantities of chemical P fertilizers were applied. We analyzed the spatial variability of soil P using semivariogram and Anselin Local Moran’s I analysis at the regional and local scales. We explored the driving factors that influence the variances in soil P using principal component regression and Johnson’s relative weights. Overall, soil TP was at a “low” level (0.55 g/kg in 0–20 cm and 0.49 g/kg in 20–40 cm) and AP was at the “lowest” level (2.54 mg/kg in 0–20 cm and 1.73 mg/kg in 20–40 cm). The soil TP and AP levels tended to be similar within land use types and they varied according to the following decreasing order: farmland > grassland > forestland > bare land. The soil TP and AP both exhibited strong spatial dependence (nugget ratio = 4.4–8.0%) within large ranges (132.0–222.0 km). At the local scale, Anselin Local Moran’s I analysis indicated the existence of some clusters and outlier areas, and land use determined the local disparities in the soil P contents. Ordinary kriging (OK) interpolation was used to obtain unbiased estimates of the soil TP content (mean absolute error (MAE)

Sulfuris a concern in Ghorabi iron oreand it is an unwantedcomponent when the ore is chargedinto a blast furnace. The goal of this paper aims to track thesulfur contentin Ghorabi iron ore by using geostatistical modelling. Geologically, the ore is splitinto fourdistinct zones. The experimental variograms were created tohighlight the spatial variability of sulfur element within the deposit. The experimental variogramswere fitted with Gaussian, linear and exponentialvariogram models. Finally,the appropriate fitted models were utilized to create a distribution mapsfor the four separated zones using the ordinary kriging and indicator kriging in 0.7% cut-offs. يمثل الکبريت مشکلة في خام حديد منطقة غرابي ويعتبر مکونا غير مرغوب فيه عند شحن الخام للفرن العالي. تهدفهذه الورقة إلى رصد تباين الکبريت الموجود في خام حديد منطقة غرابي باستخدام النمذجة الجيوإحصائية. تم تقسيمالخام جيولوجي ا إلى أربع مناطق منفصلة. لإظهار التباين المکاني لعنصر الکبريت ، تم إنشاء المتغيرات التجريبيةداخل الرواسب. تم ترکيب نماذج التباين )جاوسيان – الخطية – الأسية( للمتغيرات التجريبية. أخيرا ، تم استخدا م النماذج المناسبة لإنشاء خرائط توزيع لعنصر الکبريت باستخدام الکريجنج العادي و الکريجنج المؤشر لحد قطع معين للمناطق الأربعة المختلفة.

Mapping soil organic carbon (SOC) and its uncertainty are essential for agricultural soil management. The current study was carried out to quantify and map the spatial variability of SOC in an Agro-Ecosystem region (~ 170 km2) in Northeast Iran using Ordinary Kriging (OK), Empirical Bayesian Kriging (EBK), and Inverse Distance Weighting (IDW) techniques. In the study area, a total of 288 soil surface samples (0–20 cm depth) were collected. Results showed that the mean SOC was 0.728% with high variability (CV = 44.78%), and also SOC was found to be deviant from a normal distribution as revealed by Kolmogorov–Smirnov (K-S) test, with positive skewness. Due to the deviation from the normal distribution, and for the purpose of modeling, the data were log-transformed to approximate a normal distribution. The best fit empirical variogram was the Exponential model. Among the various interpolation techniques, estimation with EBK approach was the fairly reliable (RMSE = 0.3156; ME = 0.004), followed by OK (RMSE = 0.3162; ME = 0.003), and IDW (RMSE = 0.3199; ME = 0.005). Moreover, results showed that the spatial analysis of SOC had a strong spatial dependency for this study. Thus, the results revealed that the simple interpolation approach was a fast method and highly suitable for the spatial prediction of SOC in this study.

Актуальность исследования обусловлена необходимостью повышения точности прогнозирования технологических показателей разработки месторождений углеводородного сырья. Это позволит подбирать оптимальное оборудование для подготовки сырья, сдвигать сроки ввода промышленных мощностей для достижения максимального экономического эффекта от разработки месторождений. Цель: определить точность расчета коэффициента пористости месторождения, принятую при подсчете запасов и проектировании разработки; оценить вариации коэффициента пористости во всем объеме месторождения; оценить степень снижения точности определения коэффициента пористости при переходе от этапа керновых исследований до трехмерной геологической модели; установить причины снижения точности определения коэффициента пористости при трехмерном геологическом моделировании. Объекты: сеноманская залежь нефтегазоконденсатного месторождения на севере Западной Сибири. Методы: вариограммный анализ, трехмерное геологическое моделирование, оценка точности определения коэффициента пористости. Результаты. Для корректного выполнения подсчета запасов и подготовки проектного документа требуется определить коэффициент пористости с погрешностью не более 5 %. В работе оценена вероятность достижения требуемого уровня точности расчета коэффициента пористости при подсчете запасов только по данным геофизических исследований скважин, по результатам данных геофизических исследований скважин, но с учетом расположения скважин по площади месторождения, а также с учетом пространственного распространения коэффициента пористости. Выполнена оценка границ изменения коэффициента пористости по всему объему породы-коллектора, что в дальнейшем может послужить основой для адаптации гидродинамической модели. Рассчитано снижение соотношения объемов исследованного керна к объему породы по геофизическим исследованием скважины, к общему объему породы-коллектора, а также проведена оценка точности определения коэффициента пористости при переходе от лабораторных исследований к среднему коэффициенту пористости по всему объему породы-коллектора. The relevance of the study is caused by the need to improve the accuracy of forecasting technological indicators of development of hydrocarbon deposits. This will allow us to select the optimal equipment for preparation of raw materials, to shift the timing of commissioning of industrial capacities, to achieve the maximum economic effect from the development of deposits. The aim of the research is to determine the accuracy of calculation of the porosity coefficient of the field, adopted in the calculation of reserves and design development; to estimate the variation of the porosity coefficient in the entire volume of the deposit; to assess the degree of decrease in the accuracy of determining the porosity coefficient during the transition from the stage of core studies to a threedimensional geological model; to establish the reasons of decrease in accuracy of determination of porosity coefficient at threedimensional geological modeling. Object: Cenomanian reservoir oil and gas condensate field located in the North of Western Siberia. Methods: variogram analysis, three-dimensional geological modeling, estimation of porosity coefficient determination accuracy. Results. For correct calculation of stocks and preparation of the project document it is required to define porosity coefficient with an error no more than 5 %. The authors have estimated the probability of achieving the required level of accuracy in calculation of porosity when assessing the reserves only according to geophysical researches of wells, the results of geophysical researches of wells data, but given the location of wells in the field area and also taking into account the spatial distribution of porosity. The boundaries of the porosity coefficient change in the entire volume of the deposit were estimated. This can serve as a basis for adaptation of the hydrodynamic model in the future. The ratio of the volume of the studied core to the volume of the studied geophysical researches of wells rock to the total volume of the reservoir rock is calculated, and the accuracy of determining the porosity coefficient during the transition from laboratory studies to the average porosity coefficient in the field volume is estimated.

The upcoming technological breakthrough in the cropping system will offer a more detailed insight into soil-to-plant, man-to-soil, and man-to-plant impacts, thus improving the forecasting and ensuring more efficient in-field management. This study presents various on-the-go sensing procedures which were conducted in order to evaluate the quality of spatial estimations of soil physical properties such as soil compaction, soil moisture content, bulk density and texture. Standard statistical tools showed high positive correlations between soil specific resistance and soil compaction (R2 = .75), soil electromagnetic conductivity and moisture content (R2 = .72) and tractor wheel slip and soil compaction (R2 = .64). Variogram modeling of spatial autocorrelation gave the highest prediction error for tillage resistance (9.85%), followed by cone index (4.49%), moisture content (3.7%), bulk density (1.39%), clay + silt content (.98%), soil electromagnetic conductivity (.95%) and the least error was obtained for tractor wheel slip (.58%). The Central Composite Design (CCD) analysis confirmed significant contribution of soil compaction in the modeling of the specific soil resistance and tractor wheel slip, while soil moisture content and fine particle (clay + silt) content had a major impact on soil electromagnetic conductivity measurement. Soil bulk density had considerable importance in CCD modeling of tractor wheel slip.

Various liquefaction vulnerability indices (LVIs) have been proposed to quantify the severity of liquefaction, and used to create the liquefaction hazard map. In producing the liquefaction hazard map, the spatial variability of LVI is important because the number of available in-situ data is typically limited, and the values at the unmeasured locations are predicted using kriging operations that consider the spatial correlation of observed values. In addition, the liquefaction hazard map may vary significantly depending on how LVI was spatially interpolated. This study aims to evaluate the spatial variability of soil properties based on cone penetration test (CPT) data, and to investigate the changes in geostatistical properties of LVIs depending on shaking intensity. A simplified CPT-based procedure was used to calculate the factor of safety against liquefaction, and the geostatistical properties of LVI according to shaking intensity were evaluated using the parameters of semivariogram. In addition, the LVIs at unmeasured locations were predicted using two geostatistical modeling approaches, and their results were compared to investigate the accuracy of geostatistical approaches in predicting LVIs according to the peak ground acceleration (PGA).

Information about soil physico-chemical parameters plays an important role in precision farming. To examine the relationship among soil properties, pedometric mapping is essential and has been widely applied in agricultural activities. This paper is aimed at soil nutrient assessment by generating the geospatial distribution maps for Kestur, a village in Tumakuru district of Karnataka State, India. Using random sampling technique, a total of one hundred and sixty geo-coordinated surface (0–20 cm) soil samples were collected from different land cover regions including irrigated and dryland areas in Kestur village. The samples collected were analysed for pH, electrical conductivity (EC), organic carbon (OC), available nitrogen (N), phosphorus (P as P2O5), and potassium (K as K2O). Also, a structured questionnaire was used to collect data about demographic profile, farming practices, crops grown and fertilizers applied from each farmer under the study. The spatial distribution maps were generated for each soil property and were mapped using spatial variability by adopting Ordinary Kriging geostatistical method. Semivariogram models such as exponential for pH, spherical model for EC and OC and Gaussian for N, P2O5, and K2O were used based on the best-fit selection using least Mean Error (ME) and Root Mean Square Error (RMSE) values. The outcome of the study proved that the geostatistical methods can be utilized to develop the spatial distribution maps thereby resulting in a cost effective solution to soil fertility management.

In this study, a methodology was developed for AGR assessment, including site selection, non-stationary kriging, numerical modeling, and the long-term supply and demand sustainability. To achieve this, spatial variations maps of effective parameters were prepared using kriging techniques along with the Fuzzy logic method and GIS analytical functions for AGR site selection. To estimate how AGR is changing the water balance in the region, the Soil Water Assessment Tools (SWAT) hydrological model was coupled with an in house 2-D finite difference groundwater model. Based on the SWAT model results, by applying AGR, infiltration increased dramatically from 101 to 146 mm. In order to improve the model’s accuracy, transmissivity was regionalized through non-stationary kriging by splitting the region into sub-regions where the characteristics of each variogram are different. By using non-stationary kriging, the statistic R2 from single variogram to multiple variograms increased from 0.27 to 0.95, and the groundwater level was improved by 15%. Furthermore, for evaluating the sustainability of water resources, an index called Planning for Sustainable Index (PSUI) was utilized to measure AGR effects. PSUI, after applying AGR without changing in water withdrawal, was increased from 0.11 to 0.17 during 27-years time horizon. The case study is the aquifer in Qorveh Dehgolan sub-basin in Kordestan province, Iran. The results indicate that by applying AGR to the region, the rate of groundwater level reduction would decrease significantly for about 30%. However, for preventing the groundwater depletion, AGR should be accompanied by 50% reduction in withdrawals/pumping. The results show the significant value of utilizing a platform to assess the attributes and benefits of AGR. The proposed algorithm can be used for other geographical settings.

Sustainable soil management with appropriate understanding of soil characteristics is vital in maintaining and improving soil fertility. The objectives of thepresent study is to characterize the spatial variability across a soil for selected using GIS technique. A total of 120 geo-referenced representative soil samples (from 0 to 0.60 m depth) were collected from Sahl Al-Hussainiyah, Sharkia Governorate, Egypt. Analyses included pH,ECe, CaCO3, soil organic matter (OM), available N, P and K,cations exchange capacity (CEC) and bulk density (BD). Spatial distribution pattern varies from moderate to strong. The best fit semivariogram model of ECe, K and BD was stable model, whereas K-Bessel model was the best fit model of pH, OM and CEC.With the exponential model, the best fit was with CaCO3, N and P.According to the spatial distribution map, five zones were identified, where the study area was classified to 7.8 for pH, 11.5 dSm-1 for EC, 4.53% for CaCO3, 0.70% for OM, 62.6 mg kg-1 for N, 3.41 mg kg-1 for P. 132 mg kg-1 for K, 55.8 cmolc kg-1 for CEC and 1.52 Mg m-3 for BD. Thus, this methodology can be used succsseffly in Spatial Variability of some soil properties.

A functional analysis of the determination of the variogram value is very influential on the coal model formed (variography analysis). Variography is a series of activities ranging from data searching, modeling to analysis reports. Coal quality estimation is an activity to get a proper distribution of coal quality values, and the results can contribute as one of the control processes in coal mining activities. This research aims to estimate coal parameters (Ash Content, Calorific Value, Total Moisture, and Total Sulfur) using Ordinary Kriging. Comparison of Ordinary Kriging estimation variogram model with omnidirectional and omnidirectional-vertical model variogram results in the conclusion that the vertical variogram is quite capable of giving a positive effect on the Ordinary Kriging estimation results seen from the residual value of the results of cross-validation, although in general, the distribution of Ordinary Kriging results is not too much different.

Soil contamination by heavy metals (HM) is a worldwide problem for human health. To reduce risk to human health from exposure to toxic chemicals associated with soil contamination, it is necessary to monitor and assess HM concentrations in the soil for places where the concentration exceeds the acceptable levels. Spatial patterning is a necessary tool for assessment of the exposure risk of HM contamination. Soil sampling (n = 65) was carried out in technogenically polluted soils located at Rostov oblast to study the content and spatial distribution of four HM (Cu, Zn, Pb, and Cr) in the surface layer (0–20 cm) of the impact zone of former Lake Atamanskoe (floodplain of the Seversky Donets River valley, Rostov region) with an area of 3.91 km2. Extremely high values of HM concentrations were found with the maximum values of 702 mg/kg, 72,886 mg/kg, 2300 mg/kg, 259 mg/kg for Cu, Zn, Pb, and Cr, respectively. Inverse distance-weighted (IDW) interpolation was used to prepare 3D monoelement images of HM. Lognormal kriging and indicator kriging techniques were applied to create elemental spatial distribution maps and HM probability maps. The results showed that the total content of Cu, Zn, Pb, and Cr was moderately spatially dependent (nugget-to-sill ratio ranged from 31 to 38%), whereas the contamination index Zc formed strong spatial dependence patterns (nugget-to-sill ratio ranged from 0 to 21.4%). The obtained results of this study could serve as a guide to the authorities in identifying those areas which need remediation. Moreover, this study provides a tool for assessing the hygienic situation in the vicinity of Kamensk-Shakhtinsky (Rostov region) for decision making that can help to minimize the environmental risk of technogenic soil contamination of HM.

The objective of this study was to generate information through the analysis of variability and given structure of spatial dependence as well as the linear correlation of physical and chemical attributes of the soil, in order to assist in the planning of agricultural activities in six cities in the province of El Oro, Ecuador. The soil sample collections were carried out every two kilometers in the form of a grid with smallchanges in the field with a Dutch-type auger and GPS for georeferencing, with a depth of 0-0.20 m, thus totaling 368 points in the sample grid. Chemical and physical attributes of six municipalities in the province of El Oro were evaluated: Huaquillas, Machala, Chilla, Atahualpa, Portovelo and Las Lajas. The sampling was carried out in each city, but notbetween them. Distances between cities were 20,000 km to 180,000 km. Each soil attribute was subjected to an initial descriptive analysis, geostatistics and simple linear correlation matrix. Only pH and sand showed a high variation coefficient (22.02% and 25.42%)andall other attributes showed very high variation. Most of the semivariograms were adjusted to the spherical model.The longest range was indicated by magnesium (41,500 m) and the shortest by copper (7,740 m). The Mg pair versus sum of bases was the highest linear correlation among all the analyzed attributes. The pH stood out with a greater linear correlation between the other chemical attributes of the soil and its specific management zones. In view of the great taxonomic variation of the soil, climatic types, cultures used and management adopted, a specific analysis in each city is recommended for betteragriculturalrecommendations.

Most soil management activities are implemented at farm scale, yet digital soil maps are commonly available at regional or national scale. Disaggregating these regional and/or national maps is applicable for farm-scale tasks, particularly in data-poor or limited situations. Although disaggregation is a frequently discussed topic in recent digital soil mapping literature, the uncertainty of the disaggregation process is not often discussed. Underestimation of inferential or predictive uncertainty in statistical modelling leads to inaccurate statistical summaries and overconfident decisions. The use of Bayesian inference allows for quantifying the uncertainty associated with the disaggregation process. In this study, a framework of Bayesian area-to-point regression kriging (ATPRK) is proposed for downscaling soil attributes, in particular, maps of soil organic carbon. An estimation of point support variograms from block-supported data was carried out using the Monte Carlo integration via the Metropolis–Hastings algorithm. A regional soil carbon map with a resolution of 100 m (block support) was disaggregated to 10 m (point support) information for a farm in northern New South Wales (NSW), Australia. The derived point support variogram has a higher partial sill and nugget, while the range and parameters do not deviate much from the block support data. The disaggregated fine-scale map (point support with a grid spacing of 10 m) using Bayesian ATPRK had an 87 % concordance correlation with the original coarse-scale map. The uncertainty estimates of the disaggregation process were given by a 95 % confidence interval (CI) limit. Narrow CI limits indicate that the disaggregation process gives a fair approximation of the mean soil organic carbon (SOC) content of the study site. The Bayesian ATPRK approach was compared with dissever, which is a regression-based disaggregation algorithm. The disaggregated maps generated by dissever had 96 % concordance correlation with the coarse-scale map. Dissever achieves this higher concordance correlation through an iteration process, while Bayesian ATPRK is a one-step process. The two disaggregated products were validated with 127 independent topsoil carbon observations. The validation concordance correlation coefficient for Bayesian ATPRK disaggregation was 23 %, while downscaled maps generated from dissever had 18 % concordance correlation coefficient (CCC). The advantages and limitations of both disaggregation algorithms are discussed.

It is commonly accepted that an estimated soil variogram can be transferred to another similar area for deriving the tolerable spacing of a sampling grid or, more generally, the sample size, given a requirement on the quality of the soil property map of the recipient area. The quality of the derived tolerable grid spacing depends on how similar the population variograms of the donor area and recipient area are. In practice we are uncertain about the variograms of both areas due to sampling errors. Ideally, the uncertainty about the variogram of the donor area is accounted for in deriving the tolerable grid spacing. To assess the transferability, we should also account for uncertainty in the estimated variogram of the recipient area. In this study the transferability of variograms of soil pH, P, Mg and K is analysed for three grassland fields in Ireland, which are similar in soil-forming factors. One field served as donor area, the other two as recipient area. For all three fields and for each soil property, 500 variograms were sampled from the posterior distribution of the variogram parameters. Results showed that the estimated variogram parameters of the recipient fields differed largely from those of the transferred variograms. The ranges of estimated mean kriging variance values for the various grid spacings, as obtained with the two sets of variograms (one set of the donor field, one set of the recipient field), did not overlap. Even after scaling the transferred variogram with an estimate of the variance of the recipient field, the transferred variogram was of no use for determining the tolerable grid spacing. The difference in the variograms can possibly be explained by the difference in historical land use. Highlights: Transferability of variograms to derive tolerable grid spacing for mapping grassland fields is assessed Transferability should be based on the uncertainty distributions of the tolerable grid spacings Due to difference in historical land use, local and transferred variograms differed largely Transferability of a variogram is very poor, even after scaling the transferred variogram.

Rock quality index (RQD) is a parameter which reflects the degree of rock fragmentation and is an important index for evaluating the stability and properties of rock masses in the field. Taking Chang Shanhao open pit gold mine in Inner Mongolia as the research object, RQD data from geological exploration drill core from the southwest stope are analyzed using the indicator Kriging interpolation method, which are then used as the sample points for variogram fitting in order to simulate the spatial variability of rock mass quality. Based on the geostatistics simulation prediction, the rock quality of the stope is predicted via interpolation, and a three-dimensional model corresponding to the RQD percentage and the risk of the slope rock mass is established to predict the quality of the slope rock mass of the stope, and a three-dimensional rock mass quality prediction diagram is constructed. Results show that the potential landslide area in the three-dimensional rock mass quality prediction map is consistent with field data and is consistent with the landslide disaster area revealed by excavations.

Soil scientists are accustomed to geostatistical methods and tools such as semivariograms and kriging for analysis of observational data. Such methods assume and exploit that observations are spatially correlated. Conversely, analysis of variance (ANOVA) of designed experiments assumes that observations from different experimental units are independent, an assumption that is justified based on randomization. It may be beneficial, however, to perform an ANOVA assuming a geostatistical covariance model. Also, it is increasingly common to have multiple observations per experimental unit. Simple ANOVA assuming independence of observations is not appropriate for such data. Instead, a linear mixed model accounting for correlation among observations made on the same plot is required for proper analysis. The purpose of this paper is to demonstrate the benefits of integrating geostatistical covariance structures and ANOVA procedures into a linear mixed modelling framework. Two examples from designed experiments are considered in detail, making a link between terminologies and jargon used in geostatistical analysis on the one hand and linear mixed modelling on the other hand. We provide code in R and SAS for both examples in two supporting companion documents. HIGHLIGHTS: Analysis of variance and geostatistical analysis can be joined in a mixed model. Randomization justifies the independence assumption in analysis of variance. Geostatistical models imply a correlation of errors and can improve efficiency. Lacking randomization, spatial correlation can be accounted for in a mixed model.

Soil fertility and plant nutrition management have received much attention in order to increase efficiency, improve plant productivity and also reduce environmental hazards. Soil cation exchange ca...

Recreation is an important cultural ecosystem service and is able to significantly affect soil heterogeneity and vegetation functioning. This study investigated the role of the relief and tree stand density in the apparent soil electrical conductivity variation within an urban park. The most suitable variogram models were assessed to evaluate the autocorrelation of the regression models. The map of the spatial variability of apparent soil electrical conductivity was built on the basis of the most suitable variogram. The experimental polygon was located in the Botanical Garden of Oles Honchar Dnipro National University (Dnipro City, Ukraine). The experimental polygon was formed by a quasi-regular grid of measurement locations located about 30 m apart. The measurements of the apparent electrical conductivity of the soil in situ were made in May 2018 at 163 points. On average, the value of soil apparent electric conductivity within the investigated polygon was 0.55 dSm/m and varied within 0.17–1.10 dSm/m. Such environment predictors as tree stand density, relief altitude, topographic wetness index, and potential of relief to erosion were able to explain 48% of the observed variability of soil electrical conductivity. The relief altitude had the greatest influence on the variation of soil electrical conductivity, which was indicated with the highest values of beta regression coefficients. The most important trend of the electric conductivity variation was due to the influence of relief altitude and this dependence was nonlinear. The smallest values of the soil electrical conductivity were recorded in the highest and in lowest relief positions, and the largest values were detected in the relief slope. Recreational load can also be explained by the geomorphology predictors and tree stand density data. These predictors can explain 32% of the variation of recreational load. The variogram was built both for the soil apparent electrical conductivity dataset and for the residuals of the regression model. As a result of the procedure of the models’ selection on the basis of the AIC we obtained the best estimation of the variogram models parameters for the electrical conductivity and for the regression residuals of the electrical conductivity. The level of recreation was correlated statistically significantly with the apparent soil electrical conductivity. The residuals of regression models in which geomorphological indicators and tree stand density were used as predictors have a higher correlation level than the original variables. The soil electrical conductivity may be a sensitive indicator of the recreation load.

In this study, descriptive statistics, correlation matrix, multiple regression model, and geostatistical models were used to assess the contamination of groundwater with respect to trace elements in the Lower Tano river basin, Ghana, West Africa. A total number of 48 boreholes drilled across the basin with depths ranging from 18 to 60 m were used as data sources in this study. The results of the descriptive statistics showed that the average lead, iron, and aluminium concentrations exceeded the WHO permissible limits of 0.3 mg/L, 0.01 mg/L, and 0.2 mg/L respectively. Furthermore, copper, chromium, aluminium, zinc, manganese, nickel, iron, arsenic, electrical conductivity, and total dissolved solids were found to be extreme and highly positively skewed. Even though significant correlations exist among some variables, the statistical results showed that the quality of the boreholes drilled across the basin was mainly originating from geogenic and anthropogenic sources. In addition, each pair of correlated physical parameters and trace elements in the drilled boreholes were predicted using multiple regression models. Likewise, geostatistical modelling was used to assess the spatial analysis of each pair of correlated physical parameters and trace elements in the drilled boreholes. The cross-validation results revealed kriging model, as the most precise model for the spatial distribution maps for the correlated physical parameters, and correlated trace elements concentration in the boreholes drilled across the study region. The semivariogram models showed that most of the correlated physical parameters and correlated trace elements were weak moderately and strongly spatially dependent, suggesting fewer agronomic influences. The results of the spatial analysis were consistent with the multiple regression model and the Pearson correlation matrix.

One of the main objectives of utilizing intelligent compaction (IC) technology is to increase the uniformity and consistency of compaction operation. In this study, intelligent compaction measurement values (CMVs) in a reclaimed base project in Route 117, Vermont were used to perform a geo-statistical analysis. Semivariogram models were constructed to investigate the spatial structure and uniformity of compaction during the first and second reclaimed phases. The uniformity of the compaction operation was evaluated using the semivariogram model parameters (range, sill, and nugget). Furthermore, the semivariogram models of in-situ spot measurements were generated to verify the suitability of different types of measurements in capturing the geo-spatial trends in pavement layers. Then, the spatial statistics of each measurement were compared to the univariate statistics. It was found that the data variance might be closely related to each other, but there is no relation between these values and the spatial uniformity of the compacted area. The results indicated that the spatial structures of both compacted layers (i.e., first and second reclaimed layers) were successfully captured through all three types of measurements, where the second reclaimed phase revealed a higher degree of uniformity. In addition, geo-statistical analysis of both reclaimed layers revealed a higher degree of uniformity in dynamic cone penetration index (DCPI) data compared to other compaction measurements. On the other hand, a relatively high degree of inconsistency observed among the CMV measurements. It should be acknowledged that the conclusions of this study are based on data from only one project, specific to the characteristics/conditions of that project.

In order to meet future food demands and ensure sustainability new technologies have been incorporated into agriculture. Some researchers believe that we are living in the fourth agricultural revolution or Agriculture 4.0. Among the many technologies involved in the Agriculture 4.0, it is necessary to highlight the importance of geostatistics in the implementation of those technologies. Geostatistics is a class of statistics used to analyze and predict the values associated with spatial or spatiotemporal phenomena, and it is very important to understand the spatial distribution of agricultural variables. Therefore, the objective of this review is to show the potential of geostatistics in Agriculture 4.0. The article presents an exhaustive literature review of geostatistics and its potential in agriculture, by showing a brief of geostatistical approaches, some practical use of geostatistics in agriculture, and a description of multivariate geostatistics for multi-source data fusion using some case studies. This review showed that geostatistics has been used for agricultural purposes and has been producing exciting results. In addition, more advanced analysis such as multivariate geostatistics in fuse heterogeneous data can be easily adapted to any experimental conditions and type of sensor data and/or sampling data to increase estimation accuracy. RESUMO Para atender as demandas futuras de alimentos e garantir sustentabilidade, novas tecnologias foram incorporadas à agricultura. Acredita-se que a quarta revolução agrícola ou Agricultura 4.0 esteja ocorrendo. Dentre as diversas tecnologias envolvidas na Agricultura 4.0, é necessário destacar a importância da geoestatística na implementação dessas tecnologias. A geoestatística é uma classe de estatística usada para analisar e predizer os valores associados à fenômenos espaciais ou espaço-temporais, e é muito importante para entender a distribuição espacial das variáveis agrícolas. Portanto, o objetivo desta revisão é mostrar o potencial da geoestatística na Agricultura 4.0. O artigo apresenta uma revisão exaustiva da literatura sobre geoestatística e seu potencial na agricultura, mostrando um resumo das abordagens geoestatísticas, alguns usos práticos da geoestatística na agricultura e uma descrição da geoestatística multivariada para fusão de dados de múltiplas fontes usando alguns estudos de caso. Esta revisão mostrou que a geoestatística tem sido usada para fins agrícolas e produzido resultados interessantes. Além disso, análises mais avançadas, como geoestatística multivariada na fusão de dados heterogêneos, podem ser facilmente adaptadas a quaisquer condições experimentais e tipo de dados de sensor e/ou dados de amostragem para aumentar a precisão da estimativa.

Understanding the spatial spreading patterns of plant-available sulphur (S) (AS) and plant-available micronutrients (available zinc (AZn), available iron (AFe), available copper (ACu), available manganese (AMn) and available boron (AB)) in soils, especially in coastal agricultural soils subjected to various natural and anthropogenic activities, is vital for sustainable crop production by adopting site-specific nutrient management (SSNM) strategies. We studied the spatial distribution patterns of AS, AZn, AFe, ACu, AMn, and AB in cultivated soils of coastal districts of India using geostatistical approaches. Altogether 39,097 soil samples from surface (0 to 15 cm depth) layers were gathered from farm lands of 68 coastal districts. The analysis of soil samples was carried out for soil pH, electrical conductivity (EC), soil organic carbon (SOC) and AS, AZn, AFe, ACu, AMn, and AB. Soil pH, EC and SOC varied from 3.70 to 9.90, 0.01 to 7.45 dS m-1 and 0.02 to 3.74%, respectively. The concentrations of AS, AZn, AFe, ACu, AMn, and AB varied widely in the study area with their corresponding mean values were 37.4±29.4, 1.50±1.53, 27.9±35.1, 2.14±1.74, 16.9±18.4 and 1.34±1.52 mg kg-1, respectively. The coefficient of variation values of analyzed soil parameters varied from 14.6 to 126%. The concentrations of AS, AZn, AFe, ACu, AMn, and AB were negatively and significantly correlated with soil pH and positively and significantly correlated with SOC. The geostatistical analysis indicated stable, Gaussian and exponential best-fit semivariogram models with moderate to strong spatial dependence for available nutrients. The generated spatial spreading maps revealed different distribution patterns for AS, AZn, AFe, ACu, AMn, and AB. There were variations in spatial spreading patterns of AS, AZn, AFe, ACu, AMn, and AB in east- and west-coastal area. About 62, 35, 12, 0.4, 23 and 45% of the study area had deficiency of AS, AZn, AFe, ACu, AMn, and AB, respectively. The spatial spreading maps will be highly useful for SSNM in the cultivated coastal soils of the country. This study could also be used as a base for assessing spatial spreading patterns of soil parameters in cultivated coastal areas of other parts of the world.

Application of geostatistical techniques when evaluating mineral deposits could reflect some geological characteristics which help through the stage of planning and production. In the present study, an attempt has been done on two phosphate deposits at Elsebaiya area on both sides of the River Nile namely: Um Tondoba mine at Elsebaiya East area and Western River Nile mine in Elsebaiya West area. Depending on the available data, statistical analysis illustrated differences in the distribution of P2O5 % and ore thickness within the studied areas. Geostatistics used to start with constructing variograms for P2O5 % and thickness for the two phosphate deposits to be used with ordinary kriging models, also constructing cross variograms between P2O5 % and thickness to be used with cokriging models where the difference in the variogram parameters reflected a specific variation for each deposit horizontally and vertically. The ordinary kriging models and cokriging models illustrated different distribution behavior through both the two kriging techniques.

Rare earth elements (REE) play a prominent role in the understanding of geochemical processes. Lanthanum (La) and neodymium (Nd) are considered as two representative examples of REE. The objectives of this study were to investigate their concentrations and spatial variability in coastal soils and to assess the effect of long-term reclamation. The coastal plain of Cixi City (China) has undergone reclamation for over 1000 years, providing an ideal place to perform such research. In total, 329 soils samples were collected by means of a nested sampling methodology, combined with grid and transect techniques. The total contents, as well as their diethylenetriamine penta-acetic acid (DTPA) extractable concentrations, were measured by an inductively coupled plasma-mass spectrometry (ICP-MS). Statistics and geostatistics tools were used to analyze their spatial variability. Combined variogram models were developed to quantitatively describe their spatial structure. Variance components were estimated to assess the proportion of their total variance captured by reclamation history and different sampling stages. Both the La and Nd concentrations showed great variability in space. Reclamation activity accounted for 42–84% of their total variance. There were significant differences in their contents between reclaimed zones (P < 0.05). They exhibited moderate spatial dependence, and the discontinuity in space generally occurred around sea dikes, as indicated by the spherical components of the La and Nd concentration variogram models. A gradually increasing tendency of elemental contents with reclamation time was observed, which was also reflected in the linear component of the variogram models. However, in the areas covered by the 3rd to the 10th zones, intensive application of phosphorus fertilizer, land consolidation, or household appliance factories led to large fluctuations of elemental contents being superimposed on the relatively homogeneous content distributions, thus causing the observed periodic features of their variogram models. Additionally, a 100-m sampling distance was found to be appropriate for future REE investigations. Geostatistical modeling showed a great potential to analyze quantitatively the spatial variability of La and Nd and to assess human forces on soil genesis. The investigation of the spatial distribution of REE identified the prominent role played by the geogenic component. By means of spatial analysis, a time-series of elemental contents on a millennium scale was also reconstructed. Accumulation of their concentrations with time, as well as pollution, occurred in the surface soils. Reclamation history was the most important factor controlling La and Nd spatiotemporal variability.

In vertisols, accounting for the spatial variability of micronutrients is important for sustainable agriculture. In this study, the assessment of spatial variability maps is carried out by the geostatistical technique in SpaceStat 4.0®. A total of 68 random soil samples were collected from small-scale agricultural lands from Kalaburagi, Karnataka, India. The chemical analysis for iron (Fe), manganese (Mn), copper (Cu), and zinc (Zn) was carried out in microwave plasma-atomic emission spectroscopy. The coefficient of variation (CV) showed different micronutrients variability (CV > 35%). The significant correlation is among Cu with Fe and Mn (r = 0.753 and 0.258, respectively). The Box–Cox transformation converted the raw data to normal distribution efficiently. Spherical semivariogram model defined the spatial structure for all micronutrients. The nugget/sill ratio specifies that the Zn showed strong spatial dependence and rest micronutrients moderate. Ordinary kriging is applied for generating maps. The spatial variability maps exhibited different distribution pattern; maps generated are utilized as initial guidance for site-specific management practices and the amount of fertilizer application rate planned in the vertisols. The obtained range and spatial distribution maps act as the baseline in this region for administration planners.

Three-dimensional models of petrophysical properties were constructed using stochastic methods to reduce ambiguities associated with estimates for which data is limited to well locations alone. The aim of this study is to define accurate and efficient petrophysical property models that best characterize reservoirs in the Niger Delta Basin at well locations and predicting their spatial continuities elsewhere within the field. Seismic data and well log data were employed in this study. Petrophysical properties estimated for both reservoirs range between 0.15 and 0.35 for porosity, 0.27 and 0.30 for water saturation, and 0.10 and 0.25 for shale volume. Variogram modelling and calculations were performed to guide the distribution of petrophysical properties outside wells, hence, extending their spatial variability in all directions. Transformation of pillar grids of reservoir properties using sequential Gaussian simulation with collocated cokriging algorithm yielded equiprobable petrophysical models. Uncertainties in petrophysical property predictions were performed and visualized based on three realizations generated for each property. The results obtained show reliable approximations of the geological continuity of petrophysical property estimates over the entire geospace.

Lithofacies are very influential in the transmission of fluids within the reservoir. The objective of this study is to use geostatistical techniques of sequential indicator simulation (SISIM) a variogram-based algorithm (VBA), single normal equation simulation (SNESIM) and filter-based simulation (FILTERSIM) of multiple-point geostatistics (MPG) in developing realistic facies model. A reservoir sand package “Reservoir-E” was correlated across five wells in the field. Synthetic seismogram of well HT-1 was generated, and Horizon E picked on seismic section to produce time and depth surfaces of the reservoir. The conditional if statement to generate lithofacies was applied on the extracted volume of shale data within “Reservoir-E,” and the data were inputted in Stanford Geostatistics Modeling Software for facies modeling. The first realization from SISIM was converted to a training image used for MPG. Visually, the MPG algorithm of SNESIM and FILTERSIM produced realization that is substantially better and more realistic than the VBA of SISIM. The magnitude of correlation coefficients of algorithms was carried out using the mean and variance of realizations, the results revealed mean and variance magnitude of correlation coefficients between SISIM and SNESIM with 0.8933 and 0.9637, SISIM and FILTERSIM with 0.8639 and 0.5097 and SNESIM and FILTERSIM with 0.9717 and 0.8603. The results revealed a very good mean and variance magnitude of correlation coefficients between SISIM and SNESIM; good between SISIM and FILTERSIM; and very good mean and variance correlation coefficient between SNESIM and FILTERSIM. The qualitative interpretation of the model built with SNESIM and FILTERSIM clearly detects lithofacies in the field which makes them a better algorithm in facies modeling.

Characterizing the spatial variability of soil thermal properties and quantifying their relationships with commonly measured soil physical properties is important for successful implementation of precision agriculture practices. However, such information at field scale is scarce. This study aimed to characterize the spatial variability of soil thermal properties and to quantify their spatial relationships with soil physical properties at a field scale. Measurements of soil water content (SWC) and thermal properties were carried out at 80 locations using a time domain reflectometry (TDR) probe and a heat pulse probe (Decagon KD2 Pro), respectively in a cultivated cornfield in southwestern QC, Canada. Soil texture and total organic carbon (TOC) at those locations were also determined in the laboratory. Both coefficient of variation (CV%) and variogram range showed a weak to moderate variability and spatial dependency for the soil properties which was attributed to the homogeneity of the soil, crop, and land management practices. Results of principle component analysis (PCA) indicated that the soil thermal properties and soil water content (SWC) had strong correlations with principle component 2 (PC2). The variogram ranges indicated that the soil thermal properties varied on a similar spatial scale as the SWC in the field. Cross variograms indicated strong spatial correlations between SWC and thermal properties, particularly thermal conductivity (k) and thermal diffusivity (D). Overall, results of this study showed that the SWC had a stronger influence on the spatial variability of soil thermal properties than the other properties such as TOC and soil texture at the field scale. Therefore, the results of this study could be useful for accurate modeling of the soil thermal regimes and mass-energy exchange processes at the field scale as well as developing successful agricultural management strategies such as precision irrigation. Future studies should explore the relationships between the thermal properties and other soil properties such as bulk density under various cropping systems.

The continuous and indiscriminate use of NPK fertilizers for boosting productivity in the farming sector longer periods resulted in the imbalance of soil nutrients in the long run. This nutrient disparity in soil gradually throw back in crops, animals and human beings, leading to various degenerative and deficiency related diseases now more than ever. This constrained site specific nutrient management for crops, which essentially rely upon evaluation of variability spatially and temporarily. In this study we scrutinized the spatial variation of soil fertility in exhaustive plough lands of Thrissur district, Kerala, India. A total of 600 geo referred soil samples were collected from different agroecological units of the district and examined for selected micronutrients such as Fe, Cu, Mn, Zn and B. Geo-statistical mapping tool (Arc GIS10.2.2) was used to quantify the degree of spatial variability in various soil fertility parameters. The spatial variation of nutrients in the study area was assessed by using semivariogram method in kriging interpolation and spatial dependence was calculated. The best fit model was applied to the kriging interpolation according to the determination coefficient, which is the correlation of measured and predicted values on space and spatial distribution maps of all the micronutrients. Among the variables analyzed, B revealed strong spatial dependence (24%), Zn with weak spatial dependence (78%) with model gaussian and others with moderate spatial dependence. The results from the present study call to develop a strategy for site-specific management for the parameters showing moderate spatial dependence and weak spatial dependence. But for B, showing strong spatial dependence, only uniform management is needed because it was greatly affected by the structural factors such as climate, topography and parent material. Spatial variability of soil properties is essential for precision agriculture because soil parameters with little or no spatial dependence will not be conducive to site-specific management, and will be managed on the average level only.

High-severity wildfires have a major impact on soil properties. Moreover, recently burned areas are highly sensitive to intense rainfall events. However, little is known about the impact of extreme rainfall on the relationship between soil properties and their spatial distribution. The objective of this study is to examine the effects of an intense rainfall event on soil properties and their spatial distribution in a small area using principal component analysis (PCA). The variables studied were aggregate stability (AS), total nitrogen (TN), soil organic matter (SOM), inorganic carbon (IC), C/N ratio, calcium carbonates (CaCO3), pH, electrical conductivity (EC), available phosphorus (P), extractable calcium (Ca), extractable magnesium (Mg), extractable sodium (Na) and extractable potassium (K). Each PCA (before and after intense rainfall event) allowed us to extract five factors. Factor 1 in the pre-intense rainfall event PCA explained the variance of EC, available P, extractable Mg and K; factor 2 accounted for TN, SOM (high loadings), IC and CaCO3 (low loadings); factor 3 explained AS, extractable Ca and Na; and, factors 4 and 5 accounted for C/N and pH, respectively. Factor 1 in the after intense rainfall event PCA explained the variance of TN, SOM, EC, available P, extractable Mg and K (high loadings) and pH (low loading); factor 2 accounted for IC and CaCO3; factor 3 explained extractable Ca and Na; factor 4 accounted for AS; and, factor 5 for C/N. The results showed that the intense rainfall event changed the relationship between the variables, strengthening the correlation between them, especially in the case of TN, SOM, EC, available P, extractable Mg and extractable Ca with AS. In the case of the pre-intense rainfall event PCA, the best- fit variogram models were: factors 1 and 2 – the linear model; factors 3 and 4 – the pure nugget effect; and, factor 5 – the spherical model. In the case of the factors after intense rainfall event PCA, with the exception of factor 5 (spherical model), the best fit model was the linear model. The PCA score maps illustrated a marked change in the spatial distribution of the variables before and after the intense rainfall event. Important differences were detected in AS, pH, C/N IC, CaCO3, extractable Ca and Na.

Thick sediment (over 2,500 m), fractured basement and high thermal gradient (up to 19.10 C/100 m) of Central Sumatra Basin are suitable factors to have the Enhanced Geothermal System (EGS) potential. A number of 130 wells data were used to evaluate the EGS of the basin. The assessment is divided into the number of estimation within the grid cell (1x1 km) of sediment thickness, heat flow, thermal conductivity and technical potential calculated starting from basement-sediment layer interface. The distribution of heat flow and gradient thermal values correspond to the sediment layer. The autocorrelation test indicates the data is stationary. The variance of data gets bigger after a depth over 5.5 km. According to the Beardsmore protocol, the technical potential value ranged from 0.5 MW up to 4.7 MW at a depth of 3.5 km. In addition, the lowest technical potential is 0.66 MW and the highest is 5.76 MW at a depth of 4.5 km. The ordinary kriging, using the number of lags 10 in variogram modeling, estimated the technical potential distribution is higher to the southwest.

Three levels of uncertainty and their impact on reservoir estimation and forecasting are examined: (1) definition of reservoir facies geometry derived from uncertain geologic and geophysical information; (2) non-uniqueness of identifying the permeability distribution through inverse parameter estimation using injection and production data; and (3) unknown, fine-scale spatial variation in the heterogeneous rock properties. Inverse parameter estimation with pilot points and kriging is used to create accurate estimates of the permeability field. Efficient sampling of the uncertainty space surrounding these estimates through both probability-field (p-field) simulation and sequential Gaussian simulation (sGs) is demonstrated using a test case reservoir with permeability dominated by a sand-shale, facies distribution. A geologic conceptual model, measured permeabilities at the wells and 2100 days of injection and production data are used to estimate the permeability distribution and create empirical prediction intervals for future production. Diversity of the estimated and sampled fields across all three levels of uncertainty is examined through multi-dimensional scaling. Sampled permeability fields provide precise and accurate parameter estimation from injection and production data. The sGs fields create a wider prediction interval and underestimate the true production rates relative to the p-field samples. For a given estimated variogram model, the p-field samples result in shorter ranges and lower nugget values relative to the sGs fields. Conditional sampling through p-field and sGs simulation provides greater diversity in the solution space than the parameter estimation alone for a fraction of the computational expense.

A localized rainfall kinetic energy (E) equation and an erosivity map were developed, and the suitability of the universal soil loss equation (USLE) for assessing the soil erosion of a non‐US region was investigated. After accurately measuring and gathering data regarding raindrop size using disdrometers in four northern Taiwan locations, this study investigated the drop size distribution under different conditions by categorizing the rainfall patterns to develop regression equations for estimating the unit volume‐specific kinetic energy (KEₘₘ) and the unit time‐specific kinetic energy (KEₜᵢₘₑ) of northern Taiwan. Climate zoning, which is not considered in currently used designs, was then implemented along with two‐stage cluster analysis to construct a rainfall erosivity (R) distribution map using the kriging model. The binary polynomial regression function of KEₜᵢₘₑ, which had the highest correlation (R² = 0.98), was suggested to estimate E in northern Taiwan. It was found that the pattern and intensity (I) of rainfall will slightly affect E. The climatic influence on the root mean square of the semivariogram was significant, which suggests that climate zoning can help estimate the rainfall erosivity (R). The outcomes were extended to estimate R in areas without rainfall stations.

Soil physical attributes are affected by several events. The ability to identify the variation of those attributes can be used to decide the best crop management. Although it is known that smaller grids are more representative, predicting the least number of points while maintaining accuracy is a tool that might reflect a gain in yield and time. The aims of this study were to evaluate the spatial physical variability and to define the minimum sampling density in a tropical Typic Haplustults soil using a scaled semivariogram in a central pivot area with pinto bean (Phaseolus vulgaris L.) after the eighth bean harvest in Cristalina, Goias State. Soil samples were collected at a regular grid of 10-m intervals, totaling 180 points, and at depths of 0.00–0.10 m, 0.10–0.20 m, and 0.20–0.30 m to determine total sand content (TS), silt (SIL), clay (CL), water-dispersed clay (WDC), mean weight diameter of soil aggregates (MWD), soil penetration resistance (PR), soil macroporosity (Ma), soil microporosity (Mi), and soil bulk density (BD). The results demonstrated that management promoted superficial soil compaction with increasing BD and Mi and decreasing Ma and TP. The scaled semivariogram demonstrated similarity between attributes in the three studied soil layers, evidencing strong spatial dependency. The sample density showed a strong influence of WDC in the irrigated soil properties. Adoption of a scaled semivariogram is a strategy that can be used to determine a minimum number of points that represents the spatial variability of soil physical attributes and to assist the best management in irrigated soils.

The semivariogram, which measures the spatial variability between experimental data, is generally used as a structural input in all two-point geostatistical procedures. However, in most geoscience applications, experimental semivariograms are usually computed from a limited number of sparsely spaced measurements, which results in uncertainty associated with the semivariance values estimated for a specified number of lags. More importantly, considering a spatial variable modelled by a nonstationary random field, uncertainty is not only in the experimental semivariogram of the residuals, but also in the coefficients of the drift model estimated from the available experimental data. Therefore, when assessing the reliability of an experimental semivariogram (or estimated semivariances) in the nonstationary case, both aforementioned uncertainties should be taken into account. The aim of this paper is to extend the “Generalised Bootstrap” procedure to the nonstationary model by propagating the uncertainty associated with the estimated drift coefficients into the uncertainty in the experimental semivariogram of the residuals. The proposed methodology is demonstrated in a case study using abundant geophysical measurements characterised by a nonstationary random function. Two scenarios are evaluated in the case study: (1) it is assumed that the drift coefficients can be estimated without any uncertainty, and (2) uncertainty of the drift coefficients is taken into account. We have explained the methodology that allows to assess the uncertainty of the semivariogram lag estimates in the presence of the drift in the mean. Considering the second scenario, uncertainty is obviously larger than the case where uncertainty of the drift in the mean is ignored. This evaluation should be considered in applications where the data is often rather limited, such as subsurface hydrology (i.e. porosity, transmissivity), soil science (i.e. heavy metal content, soil moisture) and mining (i.e. scoping or pre-feasibility stage of the project). In fact, modern geostatistics should provide not only the semivariogram estimates but also estimation of its uncertainty.

Delineation of mineralization-related geochemical anomalies of stream sediment data is an essential stage in regional geochemical exploration. In this study, principal component analysis (PCA) was applied to 12 selected elements to acquire a multi-element geochemical signature associated with Cu-Au mineralization in Feizabad district, NE Iran. The spatial distribution of enhanced multi-element geochemical signature of the second component (PC2) was modeled by different geostatistical procedures including variogram calculation, ordinary kriging (OK) and inverse distance weighting (IDW) interpolation techniques. Concentration-area (C-A) fractal and U-spatial statistics models were then applied to the continuous-value interpolated models for delineation of geochemical anomalies. Quantitative comparison of results based on the known mineral occurrences in the study area was carried out using normalized density index and success-rate curves. All generated models represent a high positive relation with known Cu (±Au) deposits in the study area, although, comparison of the results revealed that the OK-based U-spatial statistics model was superior to the rest of models. Besides, the low, moderate and high-intensity anomalies are spatially associated with geological-structural features in the study area.

This paper presents the results of the design and implementation of a new geological tool, named as HUMGEOSTAT, for advanced geostatistical analysis of mineral deposit, a case study at the Sin Quyen, one of the important mines for the Vietnam mining industry in Vietnam. The tool is developed based on the Stanford Geostatistical Modeling Software (SgeMS) platform, which is an open-source computer package for solving problems involving spatially related variables. The tool is capable of supporting users in reducing uncertainty and improving the quality of mining exploration tasks. The tool has all the functions needed to solve a complete geostatistical issues i.e. Variogram models (such as Spherical, Exponential, Gausian, Linear and Pure nugget effect); and four commonly used Kriging methods (Ordinary Kriging, Simple Kriging, Indicator Kriging, Co-Kriging). The tool was applied to test various types of input data and particularly for complex copper ore bodies of Sin Quyen mine. The results of analysis of orebody spatial structure has found that Cu content has non-uniform change, regional anisotropy in north-south (0±22.50) direction, and anisotropic index is around 1.3. The mineral reserves are estimated according to sub-blocks and points in the orebody-space. The results indicate that the Ordinary Kriging (OK) has reliable results, variance estimation is small; the predicted result gained from OK have strong correlation (K=0.905) with ore samples. HUMGEOSTAT was applied at the Sin Quyen mine and various coal mines, the results were adapted with reality of mines.

Introduction:Building a large number of static models to analyze reservoir performance is vital in reservoir development planning. For the purpose of maximizing oil recovery, reservoir behavior must be modelled properly to predict its performance. This requires the study of the variation of the reservoir petrophysical properties as a function of spatial location.Methods:In recent times, the method used to analyze reservoir behavior is the use of reservoir simulation. Hence, this study seeks to analyze the spatial distribution pattern of reservoir petrophysical properties such as porosity, permeability, thickness, saturation and ascertain its effect on cumulative oil production. Geostatistical techniques were used to distribute the petrophysical properties in building a 2D static model of the reservoir and construction of dynamic model to analyze reservoir performance. Vertical to horizontal permeability anisotropy ratio affects horizontal wells drilled in the 2D static reservoir. The performance of the horizontal wells appeared to be increasing steadily as kv/kh increases. At kv/kh value of 0.55, a higher cumulative oil production was observed compared to a kv/kh ratio of 0.4, 0.2, and 0.1. In addition, horizontal well length significantly affects cumulative oil production of the petroleum reservoir studied.Results:At kv/kh of 0.55, the results of the analysis showed a rapid decrement in cumulative oil production as the horizontal well length decreases. Considering horizontal well length of 3000 ft, 2000 ft, and 1500 ft, a minimum cumulative oil production was obtained from a horizontal well length of 1500 ft.Conclusion:The geostatistical and reservoir simulation methods employed in this study will serve as an insight in analyzing horizontal well performance.

Soil particle size distribution (PSD) is a fundamental physical property affecting other soil properties. Characterizing spatial variability of soil texture is very important in environmental research. The objectives of this work were: 1) to partition PSD of 75 soil samples, collected from a flat field in the University of Guilan, Iran, into two scaling domains using a piecewise fractal model to evaluate the relationships between fractal dimensions of scaling domains and soil clay, silt, and sand fractions and 2) to assess the potential of fractal parameters as an index used in a geostatistical approach reflecting the spatial variability of soil texture. Features of PSD of soil samples were studied using fractal geometry, and geostatistical techniques were used to characterize the spatial variability of fractal and soil textural parameters. There were two scaling domains for the PSD of soil samples. The fractal dimensions of these two scaling domains (D1 and D2) were then used to characterize different ranges of soil particle sizes and their relationships to the soil textural parameters. There was a positive correlation between D1 and clay content (R2 = 0.924), a negative correlation between D1 and silt content (R2 = 0.801), and a negative correlation between D2 and sand content (R2 = 0.913). The geometric mean diameter of soil particles had a negative correlation with D1 (R2 = 0.569) and D2 (R2 = 0.682). Semivariograms of fractal dimensions and soil textural parameters were calculated and the maps of spatial variation of D1 and D2 and soil PSD parameters were provided using ordinary kriging. The results showed that there were also spatial correlations between D1 and D2 and particle size fractions. According to the semivariogram models and validation parameters, the fractal parameters had powerful spatial structure and could better describe the spatial variability of soil texture.

(IF N/A [2018]; Q3); International audience; In this study, the analytical data set of 26 groundwater samples from the alluvial aquifer of Boumerzoug-El khroub valley has been processed simultaneously with Multivariate analysis, geostatistical modeling, WQI, and geochemical modeling. Cluster analysis identified three main water types based on the major ion contents, where mineralization increased from group 1 to group 3. These groups were confirmed by FA/PCA, which demonstrated that groundwater quality is influenced by geochemical processes (water–rock interaction) and human practice (irrigation). The exponential semivariogram model fitted best for all hydrochemical parameters values and WQI. Groundwater chemistry has a strong spatial structure for Mg, Na, Cl, and NO3, and a moderate spatial structure for EC, Ca, K, HCO3, and SO4. Water quality maps generated using ordinary Kriging are consistent with the HCA and PCA results. All water groups are supersaturated with respect to carbonate minerals, and dissolution of kaolinite and Ca-smectite is one of the processes responsible for hydrochemical evolution in the area.

Excessive extraction from groundwater supplies in recent years has caused substantial land subsidence over large area. Therefore, the groundwater exploration from aquifer needs information about maximum subsidence of basin. The aim of this study is to use the ability of both numerical model and data driven algorithms for robust and fast prediction of land subsidence. In this way, the subsidence package in framework of MODFLOW is used to determine effect of groundwater fluctuant on subsidence rate through the Tehran basin. To evaluate the permeability (T) effect on uncertainty simulation model, four realization of T generated using different variogram based on borehole information. Regarding to the high run time for simulation of each realization and evaluate uncertainty of parameters, two type of model tree algorithm was trained with information of deformation rates. The non-dimensional geological and hydrogeological parameters of the aquifer were used to train the model tree. Result of numerical model show that deformation rate generated by spherical variogram show the high correlation (0.96) with low SD value (13.04) between simulated and observed data. Also, pruned M5′ tree model with depth of 7 shows the high value of correlation coefficient (0.965) between simulated and predicted subsidence values.

Resource estimation of mineral deposits requires spatial modelling of orebody boundaries based on a set of exploration borehole data. Given lateritic bauxite deposits, the spacing between the boreholes is often determined based on the grade continuity. As a result, the selected drill spacing might not capture the underlying (true) lateral variability apparent in the orebody boundaries. The purpose of this study is to investigate and address the limitations imposed by such problems in lateritic metal deposits through multiple-point statistics (MPS) framework. Rather than relying on a semivariogram model, we obtain the required structural information from the footwall topographies exposed after previous mining operations. The investigation utilising the MPS was carried out using the Direct Sampling (DS) MPS algorithm. Two historical mine areas along with their mined-out surfaces and ground penetrating radar surveys were incorporated as a bivariate training image to perform the MPS simulations. In addition, geostatistical simulations using the Turning Bands method were also performed to make the comparison against the MPS results. The performances were assessed using several statistical indicators including higher-order spatial cumulants. The results have shown that the DS can satisfactorily simulate the orebody boundaries by using prior information from the previously mined-out areas.

Although nation-wide assessments on the grassland soil carbon storage have been conducted in Japan, the uncertainty of the estimation accuracy remains with its local variability. In the present study, using geostatistical approach, we assessed the spatial variability and distribution pattern of organic carbon (OC) and estimated its total stock in the surface soils (0–5 cm) over Mt. Wakakusa grassland (30.2 ha) of Central Japan. The exploratory statistics indicated that the surface soils had 1.88 ± 0.28 kg C m−2 of soil OC density on average (n = 147) with a moderate variability (CV = 18.8%), while the geostatistical analysis unveiled that its semivariogram was well fitted by a spherical model (R2 = 0.93, RSS = 1.15E−05) and had a strong spatial dependency (nugget–sill ratio = 0.31). Based on these results, we constructed an interpolated map and estimated total OC stock to 552 Mg C in the surface soil of Mt. Wakakusa grassland.

Monitoring the evolution of the CO2 plume during geologic storage is essential for conformance, verification, and risk assessment and mitigation. Monitoring data also play a critical role in characterizing the storage formation and improving the reliability of predictive models. We investigate the feasibility of using the ensemble Kalman filter (EnKF) data assimilation framework to estimate the hydraulic properties of storage formations and to predict the migration of CO2 plume from monitoring measurements, including transient pressure and saturation data at scattered wells and time-lapse seismic data (modeled as vertically-averaged saturation differences in time). To properly account for the uncertainty in the knowledge about saline aquifer properties, the initial ensemble of formation properties is generated based on uncertain statistical model (variogram) parameters. While integration of data from scattered wells provides limited improvement in reducing the uncertainty in the initial ensemble, assimilation of time-lapse seismic measurements (represented by vertically-averaged saturation differences in time) with the EnKF leads to more noticeable uncertainty reduction and reasonable estimates of the general connectivity trends in aquifer hydraulic properties. The estimation and sensitivity analysis results suggest important differences in filter performance during and after CO2 injection. This difference is attributed to the change in flow behavior and the dominant forces before and after injection (pressure versus gravitational forces, respectively). Additionally, when prior model realizations miss essential flow-related elements (e.g., fractures) in an aquifer, the filter provides out-of-range updates, which could be interpreted as a systematic problem in the filter design, in this case possible inconsistency in the prior models.

Heavy metal pollution is a major environmental problem facing humankind. Locating the source and distribution of heavy metal pollutants around mines can provide a scientific basis for environmental control. The structure effect and random effect of a semivariogram can be used to determine the reason for spatial differences in the heavy metal content in surface soil, and the coefficient of variation and regression analysis can be used to confirm that the verification accuracy meets the geostatistical requirements. According to the maximum difference method, the content of heavy metals in the surface soil of the mining area is higher than that of the surroundings, and Cu and Zn levels are higher than the background values for Inner Mongolia. In the present case, Zn, Mn, Pb, Cr, Ni, and Cu levels exceeded the background values for the surroundings of the study area by 65.10%, 53.72%, 52.17%, 46.24%, 33.08%, and 29.49%, respectively. The results show that human activities play a decisive role in the spatial distribution of heavy metals, leading to their spatial distribution in the form of “core periphery”. This distribution pattern was significantly affected by the slope, NDVI value, and the distance from the mining area, but the spatial distribution of Pb was significantly related to high-grade roads. The research methods and conclusions have reference significance for the sources and spatial distribution characteristics of heavy metal pollution in similar mining areas and provide a target for the prevention and control of environmental pollution in the study area.