Method for Characterizing Structure and Hydrological Response in Karst Water Systems: A Case Study in Y-M System in Three Gorges Area
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摘要: 岩溶水系统结构复杂难以刻画，介质结构对地下水文特征的控制机制不清.以三峡鱼迷岩溶水系统为研究对象，利用人工示踪试验和地下水动态监测技术，建立了对流-弥散模型和扩散模型，求取了标准衰减曲线，构建了电导率和流量的高斯混合分布模型.结果表明：该系统中存在“单源单汇”、“单源多汇”和“多源单汇”3种地下水循环模式；水文事件的响应阶段地下水运动以对流为主，管道流占优势，衰减阶段则以扩散为主，裂隙流和孔隙流占优势；鱼泉洞在丰、枯水期分别识别出5种和6种地下水径流组分，以电导率180 μS/cm和流量0.6 m3/s为界，低电导率和大流量组分为快速流，其平均时间贡献占比为3.5%，径流量占比为19%.岩溶水系统中，管道和溶洞是快速流的储蓄和运移空间，空间尺寸大、开放性强、易受降雨影响；裂隙和孔隙是慢速流的储蓄和运移空间，空间尺寸小、开放性弱、对降雨有一定调蓄作用.研究可为岩溶水系统结构识别和水文机制研究提供参考，为岩溶流域水文地质调查提供理论依据.Abstract: In order to describe the structure and hydrological response mechanism of the karst water systems, the dispersion model, the diffusion model, the standard attenuation curve, and the Gaussian mixture models are presented for identifying the structure and explaining hydrological response. Successful application of these methods in the Y-M karst water system in the Three Gorges area shows that "single recharge-single discharge", "single recharge-multiple discharges" and "multiple recharge-single discharge" flow path patterns occurred in the area. After rainfalls, groundwater was dominated by convection in the response stage, while diffusion in the attenuation stage. The groundwater runoff components were divided into 5 and 6 grades for the rainy season and dry season, respectively. The conductivity and discharge thresholds dividing fast and slow flow were determined to be approximately 180 μS/cm and 0.6 m3/s, respectively, with fast flow exhibiting lower conductivity and larger discharge. On an quarterly basis, fast flow occurred 3.5% of the time and accounted for 19% of total water volume. The fast flow moved in the conduits, leading to the sharply variation of discharge and electrical conductivity, while the slow flow moved in the fissures and pores, which resulted in weak response. This study provides novel alternative methods for quantitative evaluation of structure and hydrological response of karst water systems.
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图 3 某岩溶水系统电导率和流量频率分布
镶图为电导率和流量的时间序列
Fig. 3. The frequency distribution of conductance and discharge
图 4 示踪试验浓度历时曲线及模拟结果
Fig. 4. Breakthrough curves for tacers, Eq.1 was used in dispersion model (blue), Eq.2 was used in diffusion model (black)
图 6 鱼泉洞、迷宫泉中快、慢速流组分占比与降雨量的关系
Fig. 6. Relationships between runoff components and precipitation for YQD spring and MGQ spring
图 7 鱼泉洞电导率和流量高斯混合模型模拟结果
虚线为电导率和流量频率实际分布形态；实线为高斯混合分布拟合结果.图中左上角镶图为电导率或流量的时间序列, 横坐标为时间（年－月）
Fig. 7. Frequency distributions of conductivity and discharge for YQD spring (dashed lines) and fitting normally distributed populations (solid lines). Time series of conductivity and discharge were shown as insets
图 8 鱼泉洞快速流、慢速流的平均电导率时间占比(a)和平均流量时间占比(b)
Fig. 8. The average conductivity and time proportion of fast flow and slow flow (a) and the average discharge and time proportion of fast flow and slow flow (b)
图 9 鱼泉洞径流量计算结果
Fig. 9. Calculated runoff of YQD spring based on Gaussian mixture models
表 1 基于示踪试验求得的部分水力参数及径流通道参数
Table 1. Calculated hydraulic parameter and flow channel parameters based on tracer tests
项目 猪粪池-鱼泉洞 猪粪池-迷宫泉 汪家大淌-迷宫泉 庙坪-鱼泉洞 投放时间 06-04 06-04 06-04 08-08 示踪剂 罗丹明 罗丹明 荧光增白剂 荧光增白剂 最大流速(m/h) 372 608 850 287 平均流速(m/h) 158 242 203 40.680 管道储水量(m3) 199 880 61 305 139 550 62 616 管道横截面积(m2) 62.242 17.541 22.635 11.132 管道平均直径(m) 4.451 2.363 2.684 1.882 佩克莱数 13.397 20.299 9.216 42.223 雷诺数 340 710 278 490 265 360 37 317 注：最大流速=水平距离/初次检测时间，平均流速=平面距离/示踪剂平均滞留时间; 投放时间均为2017年. 
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表 2 电导率和流量高斯混合模型模拟结果及鱼泉洞平均流量
Table 2. Gaussian mixture models and the mean annual discharge of YQD Spring
组分 P1 P2 P3 P4 P慢 P5 P6 P快 Qm(m3/s) 电导率高斯混合模型 时间贡献εe(%) 2017雨季 20.78 26.44 31.14 16.69 95.06 3.36 1.58 4.94 0.40 2017枯季 23.15 27.92 34.40 13.25 98.72 1.28 / 1.28 0.23 2018雨季 19.62 26.38 32.23 17.36 95.59 3.23 1.19 4.41 0.38 数学期望μq(m3/s) 2017雨季 287.61 259.30 232.14 195.98 245.47 148.49 116.96 138.39 0.40 2017枯季 351.65 299.57 261.37 222.32 287.33 151.07 / 151.07 0.23 2018雨季 289.68 259.95 223.50 194.72 241.92 116.07 70.76 103.88 0.38 流量高斯混合分布模型 时间贡献εe(%) 2017雨季 24.96 30.07 31.02 11.33 97.38 0.70 1.92 2.62 0.40 2017枯季 17.85 36.28 39.44 5.66 99.23 0.77 / 0.77 0.23 2018雨季 24.79 31.09 36.06 6.34 98.28 0.79 0.93 1.72 0.38 数学期望μq(m3/s) 2017雨季 0.16 0.28 0.38 0.60 0.36 2.22 3.12 2.67 0.40 2017枯季 0.15 0.20 0.29 0.49 0.28 2.04 / 2.04 0.23 2018雨季 0.17 0.23 0.39 0.53 0.33 1.98 2.75 2.37 0.38 注：各研究期识别出的径流组分数量有所差异，“/”表示未出现该级次的径流组分.
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