灰色理论在新乡百泉泉水流量动态分析中的应用

新乡百泉具有供水、农灌、人文、旅游及生态等多种功能，研究其泉水流量动态，建立泉水流量动态预测模型，对泉域水资源评价和泉水资源保护具有重要意义。为了进一步研究新乡百泉天然状态下泉水流量动态特征、评价泉域岩溶水资源，基于1964—1978年泉水年均实测流量和泉域年均降水量资料，通过逐步回归分析，确定泉水流量的主要影响因素为前1年降水量，并建立了逐步回归模型，其回归效果显著；在逐步回归分析的基础上建立了泉水流量动态预测的GM(1,2)模型、NSGM(1, 2)模型和GM(0, 2)模型。结果表明：1964—1978年百泉泉水流量动态主要受泉域降水控制，且泉水流量滞后降水1年，反映了天然状态下泉水动态特征。3种灰色模型的精度等级均为最高级（优）。1964—1978年百泉泉水实测流量为2.347～6.448 m3/s，平均为3.904 m3/s；逐步回归模型预测值为1.882～6.383 m3/s，平均为3.904 m3/s;GM(1,2)模型预测值为2.327～6.448 m3/s，平均为3.939 m3/s;NSGM(1,2)模型预测值为2.133～6.448 m3/s，平均为3.927 m...

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

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.