The Effect of Using Cokriging against Ordinary Kriging When Estimating Phosphate Deposits at Elsebaiya Area, Egypt

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.

Evaluation of Different Topographic Parameters Extracted from the Digital Elevation Measurements with the Use of Geostatistical Interpolation Methods

Gradient slope, aspect slope, profiling and contourlines are important topographic parameters that can be derived from digital elevation data obtained from different sources with exploitation of different interpolation techniques. Geostatistical interpolation methods such as ordinary kriging models constitute reliable alternatives to deterministic approaches in creation of continuous surface models from discrete elevation data. This research aimed at extraction, analysis, and evaluation of different terrain parameters elevation measurements with the use of different ordinary kriging models including the linear model, the circular model, the spherical model, the exponential models, and the Gaussian model. Different ordinary kriging models under ESRI ArcView 3.3 package along with its 3D analyst and Spatial analysis extensions have been exploited in extraction of gradient slope maps, aspect slope maps, and hillshade maps in addition to contourline maps from a sample of elevation data. Visual analysis of the gradient slope maps shows great similarities between the slope maps from the linear, circular, spherical, and exponential OK models, however, that from OK Gaussian models look very different as different sizes and arrangements of the colour patches, referring to different tones and different textures where smooth tones and smooth textures dominate the gradient slope map from the OK Gaussian model. Thus, gradient slope degradation and smoothing are considerably high in the gradient slope map from Gaussian model compared to the slope maps from the other four OK models. Also, the mean slope in the Gaussian model records the lowest value with the lowest value of the standard deviation of slopes in the same map reflecting less structured and highly smoothed gradient slope map compared to the slope maps from the other OK models. Thus, similar sizes of the colour patches and similar tones and similar texture dominate the different aspect slope maps. This is not the case in Figure 2(e) which depicts the aspect slope map extracted with the use of the Gaussian OK model where the smooth colour patches, smooth tones and smooth textures can be observed. Also, the Aspect map, hillshade map and the contourline map from Gaussian OK model are visually and statistically different from their corresponding maps created with the other four OK models. Finally, analysis of extracted two groups of profiles shows that the profiles extracted with the use of linear, circular, spherical, and exponential OK models run close and show highly corrugated and varied terrain. This is different from the profiles with the use of the Gaussian model which are less corrugated and tend to smooth and approximate different parts of the terrains.

Spatial Interpolation of Daily Precipitation in China:1951-2005

Climate research relies heavily on good quality instrumental data; for modeling efforts gridded data are needed. So far, relatively little effort has been made to create gridded climate data for China. This is especially true for high-resolution daily data. This work, focuses on identifying an accurate method to produce gridded daily precipitation in China based on the observed data at 753 stations for the period 1951-2005. Five interpolation methods, including ordinary nearest neighbor, local polynomial, radial basis function, inverse distance weighting, and ordinary kriging, have been used and compared. Cross-validation shows that the ordinary kriging based on seasonal semi-variograms gives the best performance, closely followed by the inverse distance weighting with a power of 2. Finally the ordinary kriging is chosen to interpolate the station data to a 18 km× 18 km grid system covering the whole country. Precipitation for each 0.5°×0.5° latitude-longitude block is then obtained by averaging the values at the grid nodes within the block. Owing to the higher station density in the eastern part of the country, the interpolation errors are much smaller than those in the west （west of 100°E）. Excluding 145 stations in the western region, the daily, monthly, and annual relative mean absolute errors of the interpolation for the remaining 608 stations are 74%, 29%, and 16%, respectively. The interpolated daily precipitation has been made available on the internet for the scientific community.

Groundwater quality assessment using multivariate analysis,geostatistical modeling, and water quality index(WQI): a case of study in the Boumerzoug-El Khroub valley of Northeast Algeria

In this study,the analytical data set of 26 groundwater samples from the alluvial aquifer of Boumerzoug-E1 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 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.

Spatial Information Research for Temperature and Precipitation Climate Data in Hengduan Mountains

[Objective] The aim was to study the spatial information of temperature and precipitation data in Hengduan mountains. [Method] Considering GIS spatial interpolation and numerical statistics theory, spatial prediction were carried out to the ten years average temperature and precipitation flux observation data in 109 sparse meteorological stations in Hengduan Mountains. Based on the spatial range of geographic position of Hengduan Mountains, and 1∶1 000 000 scale DEM as data sources, and using trend surface simulation and residual ordinary Kriging interpolation correction method, the spatial continuous surface for annual average temperature and precipitation were studied. [Result] It was scientific and reasonable to use certain unevenly distributed sparse climate observation station value, and by dint of trend simulation and residue interpolation method to get climate consecutive spatial result. This method can not only accurate the temperature and precipitation spatial distributions to grid point, but also can reflect macro and micro geography factors and topographic influence factor of variation. Furthermore, it can be predicted error term trend surface reasonable spatial distribution. Simulation results were basically in accordance with the objective law, and can be used for the region climate data spatial informatization simulation. [Conclusion] The study provided scientific spatial basic data for the further study of ecological and vegetation in Hengduan Mountains.

A comparative study of geometric and geostatistical methods for qualitative reserve estimation of limestone deposit

Mining projects especially relating to limestone deposits require an accurate knowledge of tonnage and grade,for both short and long-term planning.This is often difficult to establish as detailed exploration operations,which are required to get the accurate description of the deposit,are costly and time consuming.Geologists and mining engineers usually make use of geometric and geostatistical methods,for estimating the tonnage and grade of ore reserves.However,explicit assessments into the differences between these methods have not been reported in literature.To bridge this research gap,a comparative study is carried out to compare the qualitative reserve of Oyo-Iwa limestone deposit located in Nigeria,using geometric and geostatistical methods.The geometric method computes the reserve of the limestone deposit as 74,536,820 t(mean calcite,CaO grade=52.15)and 99,674,793 t(mean calcite,CaO grade=52.32),for the Northern and Southern zones of the deposit,respectively.On the other hand,the geostatistical method calculates the reserve as 81,626,729.65 t(mean calcite,CaO grade=53.36)and 100,098,697.46 t(mean calcite,CaO grade=52.96),for the two zones,respectively.The small relative difference in tonnage estimation between the two methods(i.e.,9.51%and 0.43%),proves that the geometric method is effective for tonnage estimation.In contrast,the relative difference in grade estimation between the two methods(i.e.,2.32%and 1.26%)is not negligible,and could be crucial in maintaining the profitability of the project.The geostatistical method is,therefore,more suitable,reliable and preferable for grade estimation,since it involves the use of spatial modelling and cross-validated interpolation.In addition,the geostatistical method is used to produce quality maps and three-dimensional(3-D)perspective view of the limestone deposit.The quality maps and 3-D view of the limestone deposit reveal the variability of the limestone grade within the deposit,and it is useful for operational management of the limestone raw materials.The qualitative mapping of the limestone deposit is key to effective production scheduling and accurate projection of raw materials for cement production.

A hybrid model for predicting spatial distribution of soil organic matter in a bamboo forest based on general regression neural network and interative algorithm

A general regression neural network model,combined with an interative algorithm(GRNNI)using sparsely distributed samples and auxiliary environmental variables was proposed to predict both spatial distribution and variability of soil organic matter(SOM)in a bamboo forest.The auxiliary environmental variables were:elevation,slope,mean annual temperature,mean annual precipitation,and normalized difference vegetation index.The prediction accuracy of this model was assessed via three accuracy indices,mean error(ME),mean absolute error(MAE),and root mean squared error(RMSE)for validation in sampling sites.Both the prediction accuracy and reliability of this model were compared to those of regression kriging(RK)and ordinary kriging(OK).The results show that the prediction accuracy of the GRNNI model was higher than that of both RK and OK.The three accuracy indices(ME,MAE,and RMSE)of the GRNNI model were lower than those of RK and OK.Relative improvements of RMSE of the GRNNI model compared with RK and OK were 13.6%and 17.5%,respectively.In addition,a more realistic spatial pattern of SOM was produced by the model because the GRNNI model was more suitable than multiple linear regression to capture the nonlinear relationship between SOM and the auxiliary environmental variables.Therefore,the GRNNI model can improve both prediction accuracy and reliability for determining spatial distribution and variability of SOM.

Spatially variable soils affecting geotechnical strip foundation design

Natural soil variability is a well-known issue in geotechnical design,although not frequently managed in practice.When subsoil must be characterized in terms of mechanical properties for infrastructure design,random finite element method(RFEM)can be effectively adopted for shallow foundation design to gain a twofold purpose:(1)understanding how much the bearing capacity is affected by the spatial variability structure of soils,and(2)optimisation of the foundation dimension(i.e.width B).The present study focuses on calculating the bearing capacity of shallow foundations by RFEM in terms of undrained and drained conditions.The spatial variability structure of soil is characterized by the autocorrelation function and the scale of fluctuation(δ).The latter has been derived by geostatistical tools such as the ordinary Kriging(OK)approach based on 182 cone penetration tests(CPTs)performed in the alluvial plain in Bologna Province,Italy.Results show that the increase of the B/δratio not only reduces the bearing capacity uncertainty but also increases its mean value under drained conditions.Conversely,under the undrained condition,the autocorrelation function strongly affects the mean values of bearing capacity.Therefore,the authors advise caution when selecting the autocorrelation function model for describing the soil spatial variability structure and point out that undrained conditions are more affected by soil variability compared to the drained ones.

Implementing geostatistical analysis to study spatio-temporal distribution patterns of swimming crabs(Portunus trituberculatus)

This study attempted to compare the performance of local polynomial interpolation,inverse distance weighted interpolation,and ordinary kriging in studying distribution patterns of swimming crabs.Cross-validation was used to select the optimum method to get distribution results,and kriging was used for making spatial variability analysis.Data were collected from 87 sampling stations in November of 2015(autumn)and February(winter),May(spring)and August(summer)of 2016.Results indicate that swimming crabs widely distributed in autumn and summer:in the summer,they were more spatially independent,and resources in each sampling station varied a lot;in the winter and spring,the abundance of crabs was much lower,but the individual crab size was bigger,and they showed the patchy and more concentrative distribution pattern,which means they were more spatially dependent.Distribution patterns were in accordance with ecological migration features of swimming crabs,which were affected by the changing marine environment.This study could infer that it is applicable to study crab fishery or even other crustacean species using geostatistical analysis.It not only helps practitioners have a better understanding of how swimming crabs migrate from season to season,but also assists researchers in carrying out a more comprehensive assessment of the fishery.Therefore,it may facilitate advancing the implementation in the pilot quota management program of swimming crabs in northern Zhejiang fishing grounds.

Performance evaluation of fixed-station sampling design for a fishery-independent survey with multiple objectives

Fixed-station sampling design was widely used in fishery-independent surveys because of its characteristics of convenient sampling station setting,but the non-probabilistic(fixed)nature made it more uncertainty of drawing inferences on population.The performance of fixed-station sampling design for multispecies survey has not been evaluated,and we are uncertain if the design could detect the temporal trends of different populations in multispecies fishery-independent survey.In this study,spatial distribution of abundance indices for three species with different spatial distribution patterns including small yellow croaker(Larimichthys polyactis),whitespotted conger(Conger myriaster)and Fang’s blenny(Enedrias fangi)were simulated using ordinary kriging interpolation as the“true”population distribution.The performance of fixed-station sampling design was compared with simple random sampling design by resampling the simulated“true”populations in this simulation study.The results showed that the fixed-station sampling design had the power to detect the seasonal trends of species abundance.The effectiveness of fixed-station sampling design were different in different species distribution patterns.When the species had even distribution,fixed-station sampling design could get high quality abundance data;when the distribution was uneven with heterogeneity or patchiness,fixed-station sampling design tended to underestimate or overestimate the abundance.Evidently,the estimates of abundance index based on the fixedstation sampling design must be calibrated cautiously while applying them for fisheries stock assessment and management.This study suggested that fixed-station sampling design could catch the temporal dynamics of population abundance,but the abundance estimates from the fixed-station sampling design could not be treated as the absolute estimates of populations.

Spatial variability of soil chemical properties of Moso bamboo forests of China

This study investigates the spatial variability of soil organic matter(SOM),soil organic carbon(SOC)and pH in the upper 20-cm layer and 20-40 cm layer in Moso bamboo(Phyllostachys pubescens Pradelle)forests using a geostatistics model.Interpolation maps of SOM,SOC,and pH were developed using ordinary kriging(OK)and inverse distance weighted(IDW)methods.The pH,SOC,and SOM of the two soil layers ranged from 4.6 to 4.7,from 1.5 to 2.7 g kg^(-1)and from 20.3 to 22.4 g kg^(-1),respectively.The coefficient of variation for SOM and SOC was 29.9-43.3%while a weak variability was found for pH.Gaussian and exponential models performed well in describing the spatial variability of SOC contents with R^(2)varying from 0.95 to 0.90.The nugget/sill values of pH are less than 25%,which indicates a strong spatial correlation,while the nugget/sill values of SOC and SOM fall under moderate spatial correlation.Interpolation using ordinary kriging and inverse distance weighted methods revealed that the spatial distribution of SOM,SOC,and pH was inconsistent due to external and internal factors across the plots.Regarding the cross-validation results,the ordinary kriging method performed better than inverse distance weighted method for selected soil properties.This study suggests that the spatial variability of soil chemical properties revealed by geostatistics modeling will help decision-makers improve the management of soil properties.

Qualitative and Comparative Study of Different Methods of Interpolation for the Mapping of Groundwater Salinity: Case Study of Thermal Waters Used for Irrigation in Northeastern Algeria

Faced with the scarcity of surface water accentuated by climate change, particularly in many arid and semi-arid countries, the quality of groundwater used for irrigation is a concern to agronomists and hydrogeologists. When these waters are of deep origin, they may have high mineralization and chemical compositions unsuitable for irrigation;in particular, they may alter soils and crops. It is therefore important to optimize the spatial estimation of the salinity of these waters and contribute to better knowledge of their quality, through an adapted and robust statistical and geostatistical approach. In the case of north-eastern Algeria, the objective of this study is to characterize the quality of deep waters and to test two interpolation methods (Inverse distance weight and ordinary Kriging) of their electrical conductivity (EC) as an indicator of their salinity and of the risk of damaging irrigated soils. 51 groundwater samples were taken in this region where there are many thermal springs, the water of which is used for irrigation and often is highly mineralized (EC between 0.6 and 26.6 dS/m). The geology is composed of karstic rocks crossed by large faults that allow deep water to rise. Based on major elements contents, analysis of the hydrochemical facies of these waters shows that the main facies are hyperchlorinated sodium (38%) and sulfated calcium (32%). The RSC (Residual Sodium Carbonate) and SAR (Irrigation water salt) indexes were used to assess the water quality. The results indicate that the majority of the sampled groundwater present a risk for soils irrigated with these waters (almost 1/3 presents a strong risk). The risk for the soils seems to be explained by the positive value of the residual alkalinity, and the high risks of sodization and alkalinization. The geostatistical analysis reveals strong heterogeneity in electrical conductivity (salinity). The maps based on this analysis allow the identification of risk areas. The comparison of Inverse distance weight and ordinary Kriging methods indicates similar results being obtained through both methods. However, ordinary kriging appears to be more accurate, less biased, and seemingly better represents the organization of the groundwater resources, as NE-SW alignments are visible. With the proposed approach, it is possible to calculate the surface areas of the different salinity thresholds and then optimize the use of deep groundwater for irrigation.

Mapping of Precipitation, Temperature and Evaporation Distributions in the Porsuk Basin Using Distant Forecasting Methods

Geographical data are of great importance in meteorology and climate science. These data can create the areal distribution models analyzed by spatial interpolation methods. The values of the areas without measurement data are estimated with these distribution models. In this study, distribution of meteorological parameters such as precipitation, temperature and evaporation in Porsuk basin, which is determined as research area, was investigated by Inverse Distance Weighting (IDW) and Ordinary Kriging methods. Actual meteorological data analyzed of the basin do not show a normal distribution statistically. Therefore, the data were firstly subjected to normalization and then analyzed according to the IDW and Ordinary Kriging methods to create distribution maps of precipitation, temperature and evaporation data. Quadratic mean error values were compared to investigate the reliability of analyzes. In this study, the analysis results of precipitation, temperature and evaporation data have been calculated by two different methods. Ordinary Kriging method has been determined as the method making the most accurate estimation.

DESIGN OF GROUNDWATER LEVEL MONITORING NETWORK WITH ORDINARY KRIGING

The primary network of groundwater level observation wells aims at realizing a regional groundwater management policy. It may give a regional picture of groundwater level with emphasis on the natural situation. Observation data from the primary network can be used to estimate the actual state of groundwater system. Since the cost of the installation and maintenance of a groundwater monitoring network is extremely high, the assessment of effectiveness of the network becomes very necessary. Groundwater level monitoring networks are the examples of discontinuous sampling on variables presenting spatial continuity and highly skewed frequency distributions. Anywhere in the aquifer, ordinary kriging provides estimates of the variable sampled and a standard error of the estimate. In this article, the average Kriging standard deviation was used as a criterion for the determination of network density,and the GIS-based approach was analysized. A case study of groundwater level network simulation in the Chaiwopu Basin, Xinjiang Uygur Autonomous Region, China, was presented. In the case study, the initial phreatic water observation wells were 18, a comparison of the three variogram parameters of the three defferent variogram models shows that the Gaussian model is the best. Finally, a network with 55 wells was constructed.