Application of the grey theory to dynamic analyses of the Baiquan Spring flow rate in Xinxiang

Abstract

The Baiquan Spring in Xinxiang has many functions, such as water supply, agricultural irrigation, humanities, tourism and ecology. It is of great significance to study the dynamics of the spring flow rate and establish a dynamic prediction model for the spring water resources evaluation and protection. In order to further study the dynamic characteristics of the Baiquan Spring flow rate in Xinxiang and evaluate karst water resources in the spring area, based on the data of annually measured spring flow rate and annual average precipitation in the spring area from 1964 to 1978, the main influencing factors of the spring flow rate are determined by using the stepwise regression analysis, and a stepwise regression model is established, with remarkable regression effect. On the basis of the stepwise regression analysis, this paper establishes the GM(1, 2) model, NSGM(1, 2) model and GM(0, 2) model for the dynamic prediction of the spring flow rate. The results show that (1) from 1964 to 1978, the Baiquan spring flow rate was mainly controlled by the precipitation in the spring area, and the spring flow rate lagged behind the precipitation for one year, reflecting the dynamic characteristics of the spring water in the natural state. (2) The accuracy levels of the three grey models are the highest (excellent). (3) From 1964 to 1978, the measured discharge of the Baiquan spring ranged from 2.347 to 6.448 m3/s, with an average of 3.904 m3/s. The predicted values of the stepwise regression model range from 1.882 to 6.383 m3/s, with an average of 3.904 m3/s. The predicted value of the GM(1, 2) model varies between 2.327 and 6.448 m3/s, with an average of 3.939 m3/s. The predicted values of the NSGM(1, 2) model range from 2.133 to 6.448 m3/s, with an average of 3.927 m3/s. The predicted values of the GM(0, 2) model range from 1.787 to 6.448 m3/s, with an average of 3.907 m3/s. (4) The average relative errors of the stepwise regression model and the three grey models mentioned above are 7.794%, 7.292%, 7.122% and 7.797% respectively, all of which are less than 10%, indicating that they can be used for dynamic prediction of the spring water. Among them, the NSGM(1, 2) model has a higher accuracy and better fitting to the inflection point of the curve. (5) According to the spring flow rate from 1964 to 2030 predicted by the four models, the exploitation resources of the karst water in the Baiquan spring area should not exceed 1.69 m3/s from the angle of spring protection. The research results can not only provide scientific basis for spring flow dynamic prediction and spring area water resources evaluation, but also provide reference for the study of groundwater dynamics in similar areas.

Keywords

• baiquan spring in xinxiang
• stepwise regression analysis
• gm(1, n) model
• nsgm(1, n) model
• gm(0, n) model
• p-ⅲ curve