Application Of Multivariate Statistical Methods And Stochastic Theory In The Study Of Groundwater In Yinchuan Plain

Groundwater resource is an important water sources for the survival and development of the arid irrigation plain. However, with the rapid growth of population and development of social economy, the demand of water resources is increased significantly, along with the irrational exploitation of groundwater resources and the development of agricultural irrigation, triggering a series of problems related to water resources and environmental pollution. In this context, this paper takes a typical arid area irrigation plain, the Yinchuan plain, as the research object, takes groundwater level and groundwater chemical information as a clue, integrated uses mathematical statistics, hydrogeology, hydrogeochemistry and several related theories, taking into account the hydrogeological background, the characteristics of groundwater recharge-runoff-discharge, the characteristics of chemical groundwater types, and space environment of groundwater in Yinchuan plain, using the semivariation function theory to analyze the spatial variability characteristics of the aquifer permeability coefficient in the study area, using the multivariate statistical method to determine the evolution characteristics and influencing factors of groundwater quality, using stochastic theory to predict the changing trend of groundwater level and water quality index, the use of PHREEQC software on the distribution of groundwater in the study area, the following results were obtained:（1） The permeability coefficient of phreatic aquifer of the study area exhibits a lognormal distribution, moderate variability. While the permeability coefficient of confined aquifer varied significantly less than the phreatic aquifer’s, showing positive skew normal distribution. The best fitting model of phreatic aquifer and confined aquifer were spherical model and exponential model, with spatial correlation of 0.582 and 0.518, respectively, showing aquifer permeability coefficient of the study area with moderate spatial correlation. Nugget value C0 of each fitting model for each aquifer are greater than 0, indicating that spatial continuity of these aquifers is poor, and phreatic aquifer is significantly worse than that of confined aquifer.（2） Factor analysis was applied to analysis samples of phreatic water, located in the west bank of the Yellow River. Based on principle of the eigenvalue greater than 1, 4 common factors were extracted, accounting for 82.7% of the total variance of original data. The first common factor represents the effect of evaporation; second factor represents stool pollution in life accumulation areas and human activities; While the third factor is mixing action of confined water and phreatic water; the fourth factor is decarbonation.For the east bank of the Yellow River, 3 principal components were extracted by principal component analysis, accounted 87.2% of the total variance of the original data. These 3 principal components can be summarized as evaporation, dissolution and precipitation of carbonate, potassium mineral and fluorite mineral, along with animal feces pollution and human activities.（3） For the samples of confined water, based on the eigenvalue greater than 1, 4 common factors were extracted using factor analysis method, accounting for 85.58% of the total variance of original data. The first common factors summarized as minerals dissolution such as halite, plagioclase, mirabilite and gypsum, the second common factor reflected the mixing effect of phreatic water and confined water, while the third and fourth common factors inferred as human exploitation activities and fluorite dissolution.（4） The application of cluster analysis on phreatic water in the left bank of the Yellow River, taking the distance of 9, the 127 samples can be divided into three categories: A, B and C. The samples of Class A were widely distributed in the left bank of the Yellow River of the study area. The main ions of theirs are Na⁺, Ca²⁺ and HCO₃^-, the water chemistry type are mainly HCO_3-Na、HCO_3-Mg、HCO_3-Ca and HCO_3-Mg·Na·Ca. The average concentrations of major ions and TDS are the lowest, showing good water quality. The 31 samples of Class B are mainly distributed in the alluvial fan at the west of Shizuishan City and the Yinchuan area. The main ions of class B were Mg²⁺, HCO₃^- and SO₄^2-, so the dominant water chemistry type is Cl^-Na. Major ions and TDS of class B is the middle. The 16 samples of Class C are mainly distributed in the lower reaches at Shizuishan region and scattered in the western human settlements of Yinchuan city. The major ions were Cl^- and Na⁺ and the water chemistry type is dominated by Cl^-Na, with the highest average concentrations of major ions and TDS, showing bad water quality.The 11 water samples of the right bank of the Yellow River, using cluster analysis, can be divided into three types: A, B and C, taking distance of 6. The samples of Class A were located close to bank of the Yellow River. The main ions were Na⁺, Cl^- and HCO₃^- and the water chemistry type is dominated by HCO_3-Na. Class B are located far away from the Yellow River and major ions and TDS is the minimum value of the three classes, displaying good water quality. The main ions were Na⁺, Cl^- and HCO₃^-, so the water chemical types are Cl^-Na、HCO_3-Na、HCO₃·Cl^-Na and HCO_3-Na·Mg, respectively. Major ions and TDS of Class C is the maximum value of the three classes, resulting poor water quality. Major ions are Na⁺ and Cl^-, so the chemical type is Cl^-Na.（5） Water samples of confined water of the study area, using cluster analysis and taking distance of 10, can be divided into two categories: A and B. The 59 water samples of Class A were widely distributed in the study area, showing not be contaminated, ion concentrations are low, displaying good water quality. The main ions were Na⁺, Mg²⁺ and HCO₃^-, so the dominant water chemistry types are HCO_3-Na、HCO_3-Mg and HCO_3-Na·Mg. Class B was located in the northern part of Shizuishan piedmont plain and Yinchuan region, respectively. Major ions and TDS of these samples were higher, shoeing poor water quality. The main anion is Na⁺ and the anions of three samples are not identical, therefore, the water chemical types were HCO_3-Na, Cl^-Na and SO₄^-Ca.（6） According to the dynamic monitoring data of groundwater level of phreatic water of Yinchuan area in 1991-2010, the application of Markov chain is calculated for groundwater level in 2011 and 2012, with basically consistent to the measured water level. The differences between them are-0.68-0.99 m for confined water sample C22 and-0.07-0.08 m for phreatic water sample S22, and the range of relative error of simulation are-0.06%-0.09% for C22 and-0.006%-0.007% for S22, respectively, showing the simulated water level and the actual monitoring value consistent. The results showed that the groundwater level of S22 remained relatively stable state in 2011 and 2012; while that of C22 in the relative volatility in 2011 and 2012, and has been in a state of high water level in recent years.According to the groundwater quality data of Yinchuan area of groundwater funnel area in 1991-2011, applying the Markov chain calculated each index in 2012, which were consistent with the actual state, individual indicators of individual feature points have relative difference, showing that the prediction state interval of groundwater quality index by using the Markov model is feasible, but the monitoring data series of short sequence need to be treated with caution.（7） Based on multivariate statistical analysis, hydrochemistry actions of water quality changes were researched for phreatic water and confined water, selecting the corresponding simulation path. The simulation results of water chemistry effect of phreatic water have different characteristics in the central and southern parts. The actions include gypsum and halite dissolution, and calcite mineral precipitation in Yinchuan area, making the water chemistry type from HCO_3-Mg to SO₄·HCO_3-Mg, showing the basic characteristics of water chemistry type change in runoff process: from simple to the complex.The southern part, Qingtongxia area, with irrigation water supply from the Yellow River, the groundwater mood of recharge, runoff and discharge will change. The actions include dissolution of gypsum, halite, albite, dolomite and potassium feldspar, and mineral precipitation of calcite, chalcedony and kaolinite. But the water chemical types did not change much, indicates the hydrochemical types changes small in runoff process and the types of main ions relatively less in downstream.The actions of confined water in the study area include dissolution of halite, gypsum, sodium feldspar and dolomite, and mineral precipitation of calcite, chalcedony and kaolinite. But their hydrochemical types are all HCO_3-Mg type.The research of this paper is combining the groundwater research and mathematical statistics such as multivariate statistical theory and the random mathematical statistics, as a try in this typical arid irrigation plain in China, the first time using semivariogram theory to analyze the characteristics of the spatial variation of permeability coefficient of each aquifers, applying Markov theory to analyze the groundwater level and water quality changes in a typical mining area, for the first time comprehensive application of multivariate statistical theory to analyze the influencing factors of the chemical composition of groundwater in the study area. It is a new field of groundwater science research in the current study, and as a new exploration, it has achieved satisfactory results and good effects, with a good reference for other similar irrigation plain.