GIS and Geostatistics. GIS applications in Groundwater studies

Case study 1: Determination of an optimal interpolation technique by using ordinary kriging to represent spatial distribution of Groundwater Quality Indices at YSR District, Andhra Pradesh, India

Abstract - This work emphasized on Geostatistical tools which relied on ordinary kriging technique to analyze and represent groundwater quality in Y.S.R district, Andhra Pradesh, India whilst maintaining prediction accuracy. The efficiency of the semivariograms of kriging interpolation technique was compared to best predict key groundwater quality indices such as pH,TH,SAR,Na⁺,Mg²⁺,Ca²⁺,Cl^-,HCO₃,TDS,EC and Groundwater levels in the study area. The exploratory data analysis along with cross-validation was performed. The best semivariogram model selection was made using ArcGIS 9.3. Prediction maps were prepared after systematic analysis based on Root Mean Square Error (RMSE) values.

Keywords - Geostatistical analysis, Nugget, Ordinary Kriging, Prediction maps, Sill, Spatial dependence.

1. Introduction

Groundwater is a commodity which is intended to be used judiciously whilst protecting its serenity and sanctity in terms of quality and quantity. Ubiquitous utilization in sectors such as industrial, municipal, commercial, agricultural and residential makes groundwater contaminated and converting it as a vulnerable entity. Population growth is in the forefront to create enhanced water demand due to everlasting shortage of surface water and overweening industrialization. Geographic Information Systems (GIS) initiated a beneficial symbiotic relationship with environmental concerns and natural resources in recent times. Vacuity in between GIS analysis and geostatistics is effectively bridged by ArcGIS Geostatistical analyst module. Several studies were attempted employing interpolation techniques devoid of Geostatistical tool and along with it. Hu et al (2005) conducted a study in which spatial variability existed in groundwater quality in Central North China was effectively determined using ordinary kriging. Zhu et al (1996) prepared a spatial distribution map of radon by employing GIS techniques and kriging in Belgium. D’Agostino et al (1998) compared ordinary kriging and co-kriging techniques whilst studying the spatial distribution of nitrate concentrations in an aquifer of central portion of Italy . Istok and Cooper (1998) showed that spherical model was the best fitted model for experimenting variograms of sulphate, Chloride and EC. The aims of this investigation are to provide an overview of current groundwater quality for key parameters such as pH, TH, Sodium Absorption Ratio (SAR), Na⁺, Mg²⁺,Ca²⁺,Cl^-, HCO₃,Total Dissolved Solids (TDS), Electrical Conductivity (EC), Groundwater level (GWL) and to represent the spatial distribution of key parameters of the study area using Geostatistical tools and GIS techniques.

2. Materials and Methods

The study area is one of the districts in Rayalaseema region extending from 780 to 790 longitudes to and 140 to 150 latitudes. The study is flourished with forest and water resources all over. The area is blessed with divine deities of Lord Venkateswara and Lord Rama who are popular in all parts of the world.

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The water samples were collected from bore wells all over the district during January 2010 and January 2011.The toposheets of YSR district was obtained at 1:50000 scales and were digitized with UTM coordinate system through on-screen digitization. The software’s used for the entire study were ArcGIS Geostatistical analyst and ArcGIS along with kriging methods for interpolation. Kriging technique is the optimal linear prediction of processes which are spatially linked. This technique is used in environmental monitoring, hydrology, geology and allied branches for interpolation of spatial data. The statistical and mathematical properties of the sample points are taken into consideration by Geostatistical techniques for interpolation such as kriging. The spatial configuration and autocorrelation of the measured points around the location can be quantified using Geostatistical techniques. As stated by Nas B (2009), it’s been an interesting assumption that in kriging the data is from a stochastic stationary process while other methods involve normally distributed data. The kriging interpolation technique was performed in two systematic tasks starting with quantification of spatial structure followed by production of prediction maps. This technique utilizes fitted models derived from variography to predict unknown values of a specified sample location. Several variants such as ordinary kriging, simple kriging, universal kriging, co-kriging, block kriging and disjunctive kriging are in general use for various studies. Among all the variants, it was felt that the most reliable method is ordinary kriging after a systematic statistical comparative analysis. The semivariogram plot was obtained and the values were fitted into the models such as Circular (C), Spherical (S), Tetraspherical (T), Pentaspherical (P), Exponential (E), Gaussian (G), Rationale quartile (R), Hole effect (H), K-Bessel (K), J-Bessel (J) and Stable (S). Due to prediction accuracy and simplicity when compared with other kriging methods, ordinary kriging method was used. In the current study, semivariogram models are tested against each data set parameter. The model which provided best predictions was done by performing cross validation. Spatial dependence among the groundwater quality indices were also tested by calculating nugget and sill percentages for each model along with the parameter dataset. According to Taghizadeh et al (2008), If (Nugget/Sill) % is <25% then can be inferred that the variable has a strong spatial dependence, if the value ranges between 25-75% then it can be inferred that moderate spatial dependence exists. If the calculated value is greater than 75% then the variable has weak spatial dependence.

3. Results and Discussion

The samples were collected from 36 wells in the study area. The summary statistics can be viewed in Table 1. It was observed that pH, TH, SAR, Na, Mg, Ca, Cl, HCO₃ ,TDS, Electrical conductivity and groundwater level never showed normal distribution. Since the data for each parameter is asymmetrical, log transformation was applied in order to make distribution to normal. Semivariogram models were tested for each dataset. The prediction accuracies for each model was analyzed through cross validation and can be viewed from Table 2 through Table 11. The maximum and minimum values of pH was 7 and 8.35 respectively and the best fit is the circular model with a Standardized Mean Error (SME) of 0.01234 and it is close to zero with a Root Mean Square standardized of 0.7942. If the Root mean square standardized error value is close to the average estimated prediction standard error, then it is said to be appropriate. For pH and TDS it is observed that Circular model is the best fit. Likewise all the parameters were tested which yielded the best fitted models. It was observed that for TH, SAR, Na, Mg, Ca, HCO3, GWL J-Bessel model was the best fit. For Chloride and Electrical conductivity, the best fitted model was the Hole effect. Spatial dependence was also calculated and tabulated in Table 12. After calculating the best model for each parameter dataset, prediction maps were prepared which can be seen from figure 1 through figure 11.

4. Conclusions

Groundwater is quintessential entity in the study area which comprises urban and peri-urban localities. Since the standard of living is low most of the population depends on groundwater wells since two to three decades. The objective of the present study is evaluating the groundwater quality of Y.S.R district, Andhra Pradesh, India and produce prediction maps. The spatial distribution of the key parameters such as pH, total hardness, SAR, sodium, Magnesium, Calcium, Chloride, Bicarbonates, Total dissolved solids, Electrical conductivity and groundwater level were successfully done via Geostatistical and GIS techniques. After checking the data for normal distribution with the help of histograms and QQ plots, it was decided that ordinary kriging is the appropriate method along with semivariograms will be the best to prepare prediction maps. Cross validation was performed to analyze the accuracy. It is sensed that there is an immediate need to monitor and mitigate groundwater quality by the local authorities. It is also advised to take into consideration the prediction maps before drilling new wells and any other establishments where groundwater is linked.

5. Illustrations

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Table 1. Summary Statistics

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Table 2. Selection of best fit for pH through cross validation.

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Table 3. Selection of best fit for TH through cross validation

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Table 4. Selection of best fit for SAR through cross validation

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Table 5. Selection of best fit for Na through cross validation

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Table 6. Selection of best fit for Mg through cross validation

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Table 7. Selection of best fit for Ca through cross validation

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Table 8. Selection of best fit for Cl through cross validation

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Table 9. Selection of best fit for bicarbonate through cross validation

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