基于迟滞排泄水箱模型模拟岩溶断流泉水文过程

岑鑫雨; 钟金先; 邓国仕; 许模

doi:10.11932/karst20230407

基于迟滞排泄水箱模型模拟岩溶断流泉水文过程

doi: 10.11932/karst20230407

1.
中国地质调查局成都地质调查中心, 四川成都 610218
2.
成都理工大学地质灾害防治与地质环境保护国家重点实验室, 四川成都 610059

基金项目: 中国地质调查局地质调查项目（DD20211381）

详细信息

作者简介:
岑鑫雨（1994－），女，博士，工程师，主要从事水文水资源研究。E-mail：cenxinyukl2@163.com

通讯作者:
钟金先（1984－），男，硕士，高级工程师，主要从事水工环方向研究。E-mail：110674929@qq.com

中图分类号: P641.2
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出版历程
- 收稿日期: 2023-01-20
- 网络出版日期: 2023-11-28
- 刊出日期: 2023-11-28

Modelling the hydrological process of the dried-up karst spring based on a reservoir model for hysteretic discharge

1.
Chengdu Center of China Geological Survey, Chengdu, Sichuan 610218, China
2.
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, Sichuan 610059, China

摘要

摘要: 传统的连续排泄水箱难以模拟岩溶泉断流现象，通过将表层岩溶带调蓄水箱对管道水箱的补给设置为迟滞排泄模式，模拟岩溶断流泉水文过程，并应用于丽江市黑龙潭岩溶泉域。研究结果表明，该模型较好地模拟了泉群流量动态及断流现象；当降雨量明显增大时，通过表层岩溶带调蓄水箱进入裂隙水箱的水量变幅不明显，而管道水箱的分配水量迅速增加，反映了集中补给的大气降水在岩溶系统中形成快速流的过程；黑龙潭泉群水量的绝大部分（82%~95%）来自于管道水箱，岩溶水流在时间和空间上分配的不均匀性易导致泉群断流。该研究提供了将水箱模型应用于岩溶断流泉模拟的参考，有助于理解该类型岩溶水系统的水文过程。
- 岩溶泉 /
- 水箱模型 /
- 迟滞排泄 /
- 水文过程 /
- 黑龙潭
Abstract: Karst is highly developed and widely distributed in Southwest China which is endowed with rich karst water resources but in different temporal and spatial distribution. As the main water source for the ecology and landscape of Lijiang Ancient City, Heilongtan springs have frequently dried up in recent years, which has seriously affected the production activities, daily life, and tourism quality of Lijiang Ancient City. The principle of reservoir model is to divide the karst aquifer system into different parts according to its structure or hydrological process. Based on the above division, each part has been generalized into a corresponding reservoir connected by a certain way in order to simulate the discharge of karst springs. The conventional reservoir model of continuous discharge has been widely used for reproducing the discharge of perennial springs. However, this continuous discharge model performs poorly in simulating the dry-up of karst springs. By setting the discharge law from epikarst reservoir to conduit reservoir as a hysteretic transfer function, this study reasonably reproduced the hydrological process of the dried-up springs. Several conclusions have been drawn as below. Firstly, Heilongtan spring area can be generalized as a reservoir model composed of epikarst regulation reservoir (E), matrix reservoir (M), and conduit reservoir (C). Discharge of Heilongtan springs has been successfully reproduced by the above model. Secondly, the rainy season and the normal season models can effectively simulate the spring dynamics based on the continuously discharge law. By setting the hysteretic discharge of the epikarst reservoir, the dry-up of the springs can be reproduced. To further characterize the multi-year regulation and storage characteristics of karst aquifers, additional reservoirs are needed. Thirdly, the simulation results show that the recharge from Reservoir E to Reservoir M is not sensitive to the rainfall, while the discharge from Reservoir E to Reservoir C is very sensitive to the rainfall, which indicates that the karst conduit in the Heilongtan spring area is developed and well connected, leading to the concentrated recharge and rapid increase of discharge at springs. Finally, the vast majority (82-95%) of Heilongtan spring water is recharged from Reservoir C. The threshold of rainfall required to trigger the rapid replenishment from Reservoir E to Reservoir C is relatively high. Moreover, the discharge from Reservoir C is characterized by sharp increase and decrease. The above characteristics cause uneven temporal and spatial distribution of karst groundwater, which can lead to the dry-up of springs. The research findings provide a reference for applying the hysteretic reservoir model to the simulation of karstic dried-up springs and help to understand the hydrological process of this type of karst system.
- karst spring /
- reservoir model /
- hysteretic discharge /
- hydrological process /
- Heilongtan

HTML

图 1 黑龙潭泉域水文地质简图

Figure 1. Hydrogeological sketch map of Heilongtan spring area

下载: 全尺寸图片幻灯片

图 2 水箱模型结构概化图

Figure 2. Structure of hysteretic reservoir model

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图 3 黑龙潭泉群流量模拟结果. a.模型I；b.模型II；c.模型III；d.模型IV

Figure 3. Simulation results of the Heilongtan springs. Subplots a-d are corresponding to models from I to IV

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图 4 模型质量评价参数散点图

Figure 4. Scatter plot of quality evaluation parameters for the reservoir model

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图 5 由表层岩溶带分别进入裂隙系统和管道系统的年均水量分配柱状图

Figure 5. Histogram of annual groundwater distribution from epikarst reservoir (E) into matrix reservoir (M) and conduit reservoir (C)

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图 6 $ {Q}_{EM} $与$ {Q}_{hyEC} $随时间变化曲线图

Figure 6. Dynamic plot of $ {Q}_{EM} $ and $ {Q}_{hyEC} $

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图 7 水箱E迟滞补给上、下水位阈值散点图

Figure 7. Scatter plot of the upper and lower threshold levels of Reservoir E

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图 8 黑龙潭泉群年均水量来源成分图

Figure 8. Composition histogram of annual water source of the Heilongtan springs

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表 1 水箱模型模拟时段划分表

Table 1. Division of simulation time for reservoir model

模型编号	模拟时段	降雨量特征	预热期	校正期	验证期
I	1993.1—1997.12	平水年	1993.1—1993.12	1994.1—1994.12	1995.1—1997.12
II	1998.1—2004.12	丰水年	1998.1—1998.5	1998.6—1999.7	1999.8—2004.12
III	2005.1—2010.12	平水年	2005.1—2005.12	2006.1—2006.12	2007.1—2010.12
IV	2011.1—2017.12	枯水年	2009.1—2009.9	2009.10—2010.11	2010.12—2017.12

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表 2 水箱模型校正参数释义及初始值设置表

Table 2. Interpretation of calibration parameters and initial value settings for the reservoir model

参数符号	单位	参数释义	是否为校正参数	取值或校正区间
$ {E}_{0} $	mm	$ E $水箱初始水位	×	模型I和III：15 模型II：30 模型IV：5
$ {E}_{min} $	mm	$ E $水箱排泄至$ M $水箱阈值	√	(30,100)
$ {C}_{0} $	mm	$ C $水箱初始水位	×	模型I~III：0 模型IV：10
$ {M}_{0} $	mm	$ M $水箱初始水位	×	0
$ {k}_{em} $	mm·d⁻¹	$ E $水箱至$ M $水箱连续排泄系数	√	(e⁻⁴,e⁻²)
$ {k}_{hy} $	mm·d⁻¹	$ E $水箱迟滞排泄系数	√	(0.01,1)
$ {E}_{hy} $	mm	$ E $水箱迟滞排泄上产流阈值	√	(0,200)
$ {DE}_{hy} $	mm	$ E $水箱迟滞排泄下产流阈值	√	(0,50)
$ {\alpha }_{hy} $	−	迟滞排泄指数	√	(1,4)
$ {k}_{cs} $	mm·d⁻¹	$ C $水箱至泉连续排泄系数	√	(0.1,20)
$ {k}_{ms} $	mm·d⁻¹	$ M $水箱至泉连续排泄系数	√	(e⁻⁴,e⁻²)
$ {\alpha }_{cs} $	−	$ C $水箱至泉连续排泄指数	√	(0.2,4)
$ S $	km²	降雨入渗和蒸散发面积	×	168

下载: 导出CSV

表 3 水箱模型参数校正值

Table 3. Calibrated values for the reservoir model

参数符号	单位	校正结果
参数符号	单位	模型编号I	模型编号II	模型编号III	模型编号IV
$ {E}_{min} $	mm	10.2	21.3	11.8	1.9
$ {k}_{em} $	mm·d⁻¹	0.002 8	0.003 3	0.003	0.003 1
$ {k}_{hy} $	mm·d⁻¹	0.065 6	0.084 5	0.059 8	0.034 2
$ {E}_{hy} $	mm	147	92	138	172
$ {DE}_{hy} $	mm	42	18	32	85
$ {\alpha }_{hy} $	−	1.32	1.41	1.19	1.27
$ {k}_{cs} $	mm·d⁻¹	0.102	0.093	0.098	0.113
$ {k}_{ms} $	mm·d⁻¹	0.001 2	0.002 2	0.002 4	0.001 9
$ {\alpha }_{cs} $	−	0.509	0.329	0.447	0.58

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表 4 模型质量评价参数表

Table 4. Quality evaluation parameters for the reservoir model

模型编号	评价指标	评价时期
模型编号	评价指标	校正期	验证期
I	$ NSE $	0.85	0.33
	$ BE $	0.92	0.96
	$ {W}_{obj} $	0.87	0.52
II	$ NSE $	0.63	0.55
	$ BE $	0.98	0.95
	$ {W}_{obj} $	0.96	0.67
III	$ NSE $	0.44	0.46
	$ BE $	0.97	0.96
	$ {W}_{obj} $	0.6	0.61
IV	$ NSE $	0.33	−0.21
	$ BE $	0.92	0.19
	$ {W}_{obj} $	0.51	−0.09

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