Applied Geostatistics Project On Groundwater Quality Mapping Using Geo-Statistics In Northern Somalia

Introduction

Somalia is situated in the Horn of Africa and covers an area of 637, 657 km2 with population approximately 11million (theodora. com). Groundwater is the main source of water for the majority of the people in Somalia. Except for the population residing along the Juba and Shabelle rivers, which also use surface water to meet their water needs, groundwater from dug wells, boreholes and springs are the primary sources of water for the population in the most of the country. Groundwater is utilized by the rural and urban population to meet domestic and livestock water needs as well as for small scale irrigation. Recently year’s country face water crisis. So a main issue is become to find optimum locations for high quality groundwater for both domestic and livestock water demands. Geostatistics is technique to handle spatially distributed data. The techniques are based on a set of theoretical concepts known as the “Theory of Regionalized Variable” and involve a study of the spatial relationships between sample values, thickness, or any geological phenomena showing intrinsic dispersion. There is no study that was conducted to map the quality water in Northern Somalia. Therefore, this study is conducted at Northern Somalia to check drinking water quality and to suggest appropriate water treated mechanism.

Material and Methods

Study area

Northern region in Somalia consist 8 regions with total area 294, 756 km². The population is approximately 7 million according 2015 census. The annual precipitation is range from 50mm to 300 and the climate is semi-arid. Groundwater is the main source of drinking and irrigation water.

Data

Groundwater samples were collected and analyzed by Somalia Water and land Information Management (SWALIM) in 2008. And data were obtained from SWALIM.

Geostatistical analysis and modeling

Kriging method was used in this study to Specifying spatial distribution of groundwater quality Kriging method has three steps.

Exploratory Data Analysis (statistics)

Our data consist PH values from 155 wells distributed throughout the northern region, which is approximately 622km in east-west extent and 551km north-south. Statistical data analysis was carried out to explore data and to check normality of data and also to remove outlier. The reason is because the Geostatistical method give best estimation when data are normally distributed and stationary. Firstly, since our median, mode and mean are same value it indicates that the data are normally distributed Coefficient of variation, CV = = = 0. 067 < 0. 33 second indicator to assume the normal assumption. Finally since the probability plot and histrogram follow our previous assupmtion we can conclude that our data is normal distributed.

In summary, our best guest unbiased estimate for true standard deviation is 0. 51 and we are 95% confident that true value lies between 0. 458 and 0. 573.

Variogram modeling

A variogram is a characterization of spatial correlation of the data. The experimental variogram is a discrete function calculated using a measure of variability between pairs of points at various distances. The exact measure used depends on the variogram type selected.

To calculate experimental semi-variogram JEOSTAT has been used first required parameters has been inserted such direction angle and their tolerance 0- 90which is one of the predefined direction, lag spacing, number of lag and lag incremental. To find the best fit semi-variogram different lag incremental has been tried and lastly 20, 000m has been found to be the best incremental. After all parameters inserted the program compute the semi- variogram by utilizing the following equation. Euclidean distance, d = (1)Semi-variogram, = (2)Exponential model = + C {1- exp ()} when h > 0 (3)

After calculation of experimental semi-variogram, variogram modeling is mandatory because in order to estimate the kriging the variogram model parameter are required. In this study, we tested 7 semivariogram models (Linear, Generalized Linear, Spherical, Exponential, Gaussian, Hole Effect and Paddington Mix) Exponential model shows the best fit. There is nugget effect which is equal 0. 1, a range of influence of 237, 494 meter and a sill of 0. 348.

Cross validation can be used to assess the variogram model, in terms of prediction accuracy. To verify the selected model and its predictive performance the cross-validation was used. The values of mean error (ME), mean square error (MSE), root mean error (RMSE), average standard error (ASE) and root mean square standardized error (RMMSE) were estimated to test and validate the selected model. RMSE is used to investigate the best model by comparing its value, and the smallest value of RMSE indicates the most suitable model to the data. The ME, MSE values were close to zero and RMMSE values were close to one which means a good prediction model. In other hand the exponential shows the smallest value of RMSE and we can conclude the most suitable model for this data is exponential.

Kriging

Kriging is a family of estimators used to interpolate spatial data. This family includes ordinary kriging, universal kriging, indicator kriging, and co-kriging. The most commonly used method is ordinary kriging, which was selected for this study. The linear estimator of is expressed as = (3)Where We first estimate the ordinary kriging weights by:B’ = (4)And ordinary kriging estimator can expressed as= Bg (5)The ordinary-kriging estimation variance is:-(T, T) (6)The standard error of the kriging estimate is= (7)The spatial distribution of groundwater quality parameter PH were carried out using geostatistical techniques in ArcGIS 10. 1. The distribution map shows several values of PH in the study are with maximum value 8. 7 which is more than WHO standard and 6 which is pretty less, its maybe because of areas geological formations. On the standard error map we can see that the area which collected samples are close each other the error value is quite lower compare the area where the distance between our samples are too far. The error can be reduced if the control points are closer to location where the estimate is to be made and this agree the First Law of Geography, according to Waldo Tobler, "everything is related to everything else, but near things are more related than distant things. "

Conclusion

The main objective of this study was to map Spatial disturbution of groundwater quality (PH). In this study, ordinary kriging has been applied to predict and estimate groundwater qaulity PH. Before estimating the kriging various variogram model were tested and exponentail model showed best fitted. Cross-validation was carried out to verify model predictive performance which shows good prediction model. It has also been highlighted on pratical application of estimation variance to assess the uncertianty, and residual analaysis to evaluate the error distribution. Furthermore, error map of kriging method has been prepred. Overall according to WHO criteria the water quality in study area can classified good. Further studies considering large water quality parameters will be necessary to evaluate the concentrations of different ions present in the water.