Water Quality Parameters of Tajan River Presenting a Proposed Method Based on Blind Kriging and Linear Regression

Introduction
The application of kriging in the field of environment is focused on four main sections: mapping of precipitation, quantitative and qualitative status of groundwater, quantitative and qualitative evaluation of surface water and spatial forecasting of air quality (Hanefi Bayraktar,2005; Nas, 2009; Chen et al., 2016; Sharma et al., 2017; Yang et al., 2018).
Different types of kriging have been developed, but the most popular of these is ordinary kriging (OK). The most important disadvantages of OK is that it assumes the mean of modelled variables to be constant and the prediction is only based on the spatial structure of the studied points. In addition, the effect of important parameters does not take into account the estimation result, and in some cases the predicted values by OK may be out of the studied range (Mukhopadhyay et al., 2017; Montero and Matthew, 2015). To overcome these problems, the universal kriging and blind kriging have been developed. Blind kriging (BK) is a more complete version of universal kriging and is based on Bayesian variable selection technique which is complicated and takes a lot of time to identify the unknown mean function.
In this research, due to the complexity of the Bayesian computation, we will combine the regression technique with blind kriging as the unknown mean function is defined by variable selection techniques that are used in linear regression analysis such as forward selection, backward elimination, and step-wise regression. The residuals at the known points are calculated from the difference of the observed values and the values of the selected function. Then the residual mean at the unknown point is solved by OK method.
Tajan River is one of the most important rivers in Mazandaran province. This permanent river is about 140 kilometers long and originates from the mountainous area on the northern slopes of Alborz Range. Tajan River runs to the plains carrying the water from various tributaries in the mountains and then drains into the Caspian Sea. Dodangeh, Lajim, Chahardangeh and Zarem rivers are the most important branches of it. The area of Tajan River watershed in the Aldehil region (before entering the Caspian Sea) is 4700 square kilometers. There are different land uses including agriculture, aquaculture, dam construction and industrial activities around the river. The necessity to perform a systematic study of the river water quality is, therefore, a need and of prime importance.
The objective of this study is to evaluate water quality parameters in different sites on Tajan River. This study also attempts to propose a modified kriging method, in which the unknown mean function is defined by using linear regression in order to simplify the computations of blind kriging. The proposed method and ordinary kriging were used to model the spatial variability of heavy metals and water quality index and their results were compared. This case study may be counted as an initial effort to study the spatial variability of water quality parameters, which may have many practical implications

Material and methods

The water sampling took place in spring of the year 2018. Sampling sites were selected based on natural conditions and accessibility to Tajan River by taking into account natural and human impacts, including river sub-branches, changes in the polluting sources such as agricultural lands, residential centers, existing industries, etc. Sampling sites were named 1 to 10 from downstream (near the Caspian Sea) to upstream (the Shahidrajae Dam). Water samples were collected by Nansen bottles and transferred into 1-liter bottles previously cleaned by nitric acid (0.1 N). The temperature, pH, electrical conductivity (EC), total dissolved solids (TDS), dissolved oxygen (DO), redox potential (Eh), and turbidity (Turb) of each water sample were directly measured at the sampling points. The biochemical oxygen demand (BOD5) was determined by the Winkler Azide method and chemical oxygen demand (COD) by the dichromate reflux method. Phosphate (PO4-P) and Nitrate nitrogen (NO3-N) were analyzed by spectrophotometric method, and fecal coliform (Fcoli) were measured by multiple tube method.
For measuring metals, each water sample was filtered through Whatman filter (0.45 μm) and about 5 mL of HNO3 (0.1 N) was added to the samples (until pH<2). Then, the samples were stored in the refrigerator at a temperature below 2 °C until being transferred to the laboratory. The measured elements included Arsenic (As), Barium (Ba), Calcium (Ca), Cobalt (Co), Chromium (Cr), Copper (Cu), Iron (Fe), Nickel (Ni), Lead (Pb) and Thorium (Th). Metal measurements were done by inductively coupled plasma optical emission spectrometry (ICP-OES). Analysis of the samples was done based on the instructions recommended by (APHA, 2005).
All mathematical and statistical computations were made using EXCEL 2016, SPSS 22 and ArcGIS 4.10.1.
The proposed method and ordinary kriging method were applied to interpole and predict IRWQI, Fe, Ni, Co, Th, Ba, As, Pb and Cr and their results were compared.

Results and discussions

IRWQI had low values in midstream (sites 5, 6 and 7) near Sari City and its value increases by moving away from the city to show an improvement in the water quality status. This is due to the effect of anthropogenic pollutants in Sari city which are negatively associated with the water quality index. The average range of pH was from 7.6 to 8.11. pH values of water samples indicated that it was slightly alkaline. The relatively higher pH in water are probably due to the presence of pollution and eutrophication status. The mean values for Eh ranged from 142 mV to 201 mV. The water of Tajan River (excepting in site 1 near the sea) is non-saline.
The mean function for each variable (IRWQI, Fe, Ni, Co, Th, Ba, As, Pb and Cr) was created by multiple linear regression. The coefficient of determination (R2) and adjusted R2 were used to check regression model adequacy. t-Test and residual analysis were used in testing the regression coefficients verifying of the applicability of the regression model. The coefficient of determination (R2) ,Coefficient of Variance (C.V.) and Root Mean Square Error (RMSE) were used to evaluate the results of the ordinary kriging and proposed method. The proposed method showed 8.8 percent improvement for Cr, 34 for Co, 56 for Pb, 62 for As, 44 for Ba and 169 for IRWQI. In addition, both methods for prediction of thorium and nickel were almost identical. While ordinary kriging performance was good in predicting iron and better than the proposed kriging, because for parameters whose correlation is strong with distance and spatial distribution, ordinary kriging method can work well in modeling them. the mean concentration of elements in the water followed the following pattern: Ca> Fe > Ba > Ni > As > Cr > Cu >Th> Co > pb. The mean concentration of elements (Co, Cr, Ni, Cu, pb and Th) demonstrate a similar pattern with a decreasing trend from the upstream to the downstream. This will strongly show a similar process and origin. while the mean concentration of Ba and As was increased at various sites from the upstream to the downstream.