灰色理论在新乡百泉泉水流量动态分析中的应用

李志超, 姜宝良, 潘登, 卢金阁, 王秀明. 灰色理论在新乡百泉泉水流量动态分析中的应用[J]. 水文地质工程地质, 2023, 50(2): 34-43. doi: 10.16030/j.cnki.issn.1000-3665.202205047
引用本文: 李志超, 姜宝良, 潘登, 卢金阁, 王秀明. 灰色理论在新乡百泉泉水流量动态分析中的应用[J]. 水文地质工程地质, 2023, 50(2): 34-43. doi: 10.16030/j.cnki.issn.1000-3665.202205047
LI Zhichao, JIANG Baoliang, PAN Deng, LU Jinge, WANG Xiuming. Application of the grey theory to dynamic analyses of the Baiquan Spring flow rate in Xinxiang[J]. Hydrogeology & Engineering Geology, 2023, 50(2): 34-43. doi: 10.16030/j.cnki.issn.1000-3665.202205047
Citation: LI Zhichao, JIANG Baoliang, PAN Deng, LU Jinge, WANG Xiuming. Application of the grey theory to dynamic analyses of the Baiquan Spring flow rate in Xinxiang[J]. Hydrogeology & Engineering Geology, 2023, 50(2): 34-43. doi: 10.16030/j.cnki.issn.1000-3665.202205047

灰色理论在新乡百泉泉水流量动态分析中的应用

  • 基金项目: 中国地质调查局地质调查项目(WT2019188B)
详细信息
    作者简介: 李志超(1998-),男,硕士研究生,主要从事水文地质、工程地质、环境地质等方面的研究。E-mail:lzc15537345765@163.com
    通讯作者: 姜宝良(1962-),男,学士,教授级高工,硕士生导师,主要从事水文地质、工程地质、环境地质等方面的研究。E-mail:13703849008@163.com
  • 中图分类号: P641.8

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

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  • 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 m3/s;GM(0,2)模型预测值为1.787~6.448 m3/s,平均为3.907 m3/s。逐步回归模型和前述3种灰色模型的平均相对误差分别为7.794%、7.292%、7.122%、7.797%,均<10%,可用于泉水流量动态预测;其中NSGM(1,2)模型精度更高、对曲线“拐点”的拟合更好。根据4种模型预测的1964—2030年泉水流量,从保泉角度评价百泉泉域岩溶水的开采资源量不得超过1.69 m3/s。研究成果可为泉水流量动态预测和泉域水资源评价提供科学依据,也可为类似地区地下水动态研究提供参考。

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  • 图 1  新乡百泉泉域裂隙岩溶水水文地质示意图

    Figure 1. 

    图 2  1964—1978年百泉年均流量与降水量动态图

    Figure 2. 

    图 3  4种模型泉水流量预测值与实测值对比图

    Figure 3. 

    图 4  1979—2030年百泉泉水流量实测值及预测结果图

    Figure 4. 

    图 5  泉水流量与P-Ⅲ型曲线拟合图

    Figure 5. 

    表 1  1979—2021年百泉泉水复流情况

    Table 1.  Statistics of re-flow of the Baiquan Spring from 1979 to 2021

    复流年份复流情况
    19828月15日复流至次年5月断流,最大出水量为6.65 m3/s
    19888月中旬复流,次年断流(断流日期不详),最大出水量约为5 m3/s
    19968月3日复流,次年4月17日断流,最大出水量为3.10 m3/s
    19989月2日复流,次年1月8日断流,最大出水量为1.91 m3/s
    20009月21复流,10月26日断流,最高湖水位仅为40 cm
    200310月26复流,次年3月28日断流,最大出水量为2.35 m3/s
    20048月28日复流,次年1月31断流,最大出水量为1.40 m3/s
    2021百泉泉域遭遇有气象记录以来的特大降雨,7月23日复流,最大出水量为10 m3/s。2022年7月,仍有近4 m3/s
    下载: 导出CSV

    表 2  灰色模型精度等级评价

    Table 2.  Evaluation of the accuracy grade of the grey model

    精度等级PC
    0.95<P≤1.000.00<C≤0.350.90<≤1.00
    0.80<P≤0.950.35<C≤0.500.80<≤0.90
    0.70<P≤0.800.50<C≤ 0.650.70<≤0.80
    0.00<P≤0.700.65<C≤1.000.00<≤0.70
    下载: 导出CSV

    表 3  1964—1978年泉水流量预测值与实测值对比结果

    Table 3.  Comparison results between the predicted and measured values of the spring flow rate from 1964 to 1978

    年份年均降水量
    /mm
    实测值
    /(m³·s−1
    逐步回归模型GM(1, 2)模型NSGM(1, 2)模型GM(0. 2)模型
    预测值/ (m³·s−1相对误差/%预测值/ (m³·s−1相对误差/%预测值/(m³·s−1相对误差/%预测值/(m³·s−1相对误差/%
    1963 1240.0
    1964886.06.4486.3831.0166.4480.0006.4480.0006.4480.000
    1965340.04.5754.6120.8174.1569.1584.6782.2514.6561.770
    1966470.02.3701.88220.5832.3271.8142.13310.0001.78724.599
    1967540.02.3472.5327.8922.58510.1412.5207.3712.4705.241
    1968590.02.5042.88215.0162.87614.8562.87014.6172.83813.339
    1969755.03.5373.13211.4433.12611.6203.12611.6203.10112.327
    1970807.03.9763.9570.4693.9960.5033.8991.9373.9680.201
    1971935.04.3494.2173.0274.2711.7944.1983.4724.2412.483
    1972660.04.7114.8573.1084.9485.0314.8062.0174.9144.309
    1973560.03.7333.4826.7163.4936.4293.6023.5093.4687.099
    1974666.02.8332.9825.2692.9644.6243.0497.6242.9433.883
    19751030.03.2153.5129.2473.5259.6423.4878.4603.5008.865
    1976950.05.2325.3321.9205.4514.1865.1810.9755.4133.459
    1977735.05.5094.93210.4665.0288.7314.95410.0744.9939.366
    1978548.03.2193.85719.8303.89020.8453.95622.8953.86320.006
    最大值1240.06.4486.38319.8306.44820.8456.44822.8956.44820.006
    最小值340.02.3471.8820.4692.3270.0002.1330.0001.7870.000
    平均值732.03.9043.9047.7943.9397.2923.9277.1223.9077.797
    下载: 导出CSV

    表 4  灰色模型检验指标计算结果

    Table 4.  Calculation results of the grey model test index

    模型PC
    GM(1, 2)1.00000.26530.9974
    NSGM(1, 2)1.00000.20040.9997
    GM(0, 2)1.00000.27470.9963
    下载: 导出CSV

    表 5  不同保证率泉水流量

    Table 5.  Spring flow rate with different guarantee rates

    保证率/%泉水流量/ (m³·s−1
    逐步回归GM(1, 2)NSGM(1, 2)GM(0, 2)平均
    104.914.944.944.944.93
    204.354.384.374.374.37
    503.423.443.433.413.43
    752.802.812.812.772.80
    952.082.092.112.022.08
    991.691.691.741.621.69
    下载: 导出CSV
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收稿日期:  2022-05-18
修回日期:  2022-07-15
刊出日期:  2023-03-15

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