Abstract

Flooding at small basins is characterized by weak predictability, sudden onset, and rapid disaster formation, especially in karst areas. Therefore, an accurate flood simulation will be helpful for flood control and disaster reduction. In this study, the reservoir unit is added into the original HEC-HMS model to improve the model and analyze the stagnation of the runoff process in karst basins. Then, the HEC-HMS model before and after improvement is used to simulate floods in the Xiajia basin, a typical karst area in southwest China. Before improvement, the calibration result shows that the accuracy of 31 flood simulations is poor, and the qualified rate is only 38.71%. After improvement, the qualified rate increases to 51.61% during calibration, and the simulation accuracy is increased by 12.90%. Moreover, the qualified rate reaches 61.11% during validation, and the simulation accuracy is increased by 22.40%. The improved HEC-HMS model can be applied to flood simulations in the study area and the study results can provide useful insights for flood warning and management in karst areas.

HIGHLIGHTS

  • The novelty of this study lies in adding karst reservoir units to the HEC-HMS model to quantify the effect of the karst system on the surface flow in the Xiajia watershed, a typical karst area in southwest China.

  • In this study, the results imply that the karst systems have an impact on the hydrology by effectively restraining the flood peak and increasing the underground runoff.

INTRODUCTION

The increasing magnitude and frequency of flood disasters result in an increasing number of’ human deaths and economic losses. Accurate flood simulation has been a hot topic in hydrological sciences as it is very helpful for flood warning, flood control, and flood disaster reduction. Commonly used hydrological models are often divided into two categories: the lumped hydrological model and the distributed hydrological model. The lumped hydrological model uses an approximate method to describe the runoff process without considering the physical mechanism of the hydrological phenomenon (Pan 2018). Therefore, distributed hydrological models with clear physical meaning parameters and accurate descriptions of the hydrological process have been developed and are widely used in hydrology (Gumindoga et al. 2017; Wang 2018a; Busico et al. 2020; Ferguson & Fenner 2020; Khaleghi et al. 2020). It is well known that karst fissures, sinkholes, and skylights are widely distributed in the karst basin, constituting a unique three-dimensional spatial system and making the hydrological process more complex. However, certain approaches for flood simulation in the karst basin remain limited. To improve the accuracy of flood simulation in the karst basin, researchers usually modify the original lumped or distributed hydrological model, as summarized in Table 1. As can be seen from Table 1, the improved hydrological models are only suitable for specific basins and have no universality. In addition, previous studies have shown that the HEC-HMS model has good accuracy for flood simulation in a small watershed (Kamali et al. 2013; Silva et al. 2014). In China, some studies have indicated that the HEC-HMS model is the optimum model for flood simulation in a small basin (Zhao et al. 2018; Zhang et al. 2019).

Table 1

A summary of the application of the hydrological models in the karst basin

ClassificationNameAuthorImprovementsAdvantages and disadvantages
Lumped hydrological model Xin'anjiang Song et al. (2015bAdded multiple series and parallel underground reservoirs for groundwater simulation Advantages: Less data demand and a simple structure. Disadvantages: the physical meaning of parameters is not clear and it ignores the spatial variability of the basin and cannot explain the physical mechanism of runoff yield and concentration well 
Tank Fleury et al. (2007)  Used three interconnected water tanks to simulate the flow in the soil and the underground runoff with different velocity 
Distributed hydrological model SWAT Palanisamy & Workman (2014)  Conceptualized the sinkholes located in the streambed of a karst watershed in Kentucky as orifices and flow through these orifices was modeled as a function of sinkhole diameter and added to the SWAT model to form a karst SWAT Advantages: easy acquisition of input data and high calculation efficiency. Disadvantages: difficult to be used for short-term flood process simulation 
Baffaut & Benson (2009)  The SWAT model simulates lost streams by specifying high soil conductivity in channels, simulates sinkholes as ponds with high hydraulic conductivity at the bottom, and calibrates the James river watershed in southwestern Missouri 
Nikolaidis et al. (2013)  The major modifications from the SWAT model are: (a) the input flow in the deep groundwater flow from SWAT and (b) a nitrate-N mass balance was included assuming that nitrate is conservative in the karst. 
TOPMODEL Suo et al. (2007)  Using the TOPMODEL model to calculate runoff yield in subwatershed Advantage: it requires fewer parameters and is easy to obtain. Disadvantage: the description of the groundwater hydrological process is too simple, and DEM cannot be used to generate sinks and underground rivers in karst watershed 
Pan (2014)  Regard karst depression as an independent hydrological unit, and use the TOPMODEL model to simulate hydrology, respectively 
SWMM Campbell & Sullivan (2002)  The SWMM is used to simulate the transport process of karst cave water flow Advantage: it can reflect the movement process of a flood wave in the pipeline more truthfully. Disadvantage: The SWMM is sensitive to the geometric characteristics of the pipeline and is only suitable for hydrological simulation of some pipeline systems with detailed survey data 
Zhang et al. (2007)  Taking the depression as a unit, the study area is generalized into six secondary catchment basins connected by pipeline 
 HEC-HMS Current study The reservoir unit method is used to reflect the stagnation of the runoff process in karst basins The HEC-HMS model has good accuracy and is widely used at small basin 
ClassificationNameAuthorImprovementsAdvantages and disadvantages
Lumped hydrological model Xin'anjiang Song et al. (2015bAdded multiple series and parallel underground reservoirs for groundwater simulation Advantages: Less data demand and a simple structure. Disadvantages: the physical meaning of parameters is not clear and it ignores the spatial variability of the basin and cannot explain the physical mechanism of runoff yield and concentration well 
Tank Fleury et al. (2007)  Used three interconnected water tanks to simulate the flow in the soil and the underground runoff with different velocity 
Distributed hydrological model SWAT Palanisamy & Workman (2014)  Conceptualized the sinkholes located in the streambed of a karst watershed in Kentucky as orifices and flow through these orifices was modeled as a function of sinkhole diameter and added to the SWAT model to form a karst SWAT Advantages: easy acquisition of input data and high calculation efficiency. Disadvantages: difficult to be used for short-term flood process simulation 
Baffaut & Benson (2009)  The SWAT model simulates lost streams by specifying high soil conductivity in channels, simulates sinkholes as ponds with high hydraulic conductivity at the bottom, and calibrates the James river watershed in southwestern Missouri 
Nikolaidis et al. (2013)  The major modifications from the SWAT model are: (a) the input flow in the deep groundwater flow from SWAT and (b) a nitrate-N mass balance was included assuming that nitrate is conservative in the karst. 
TOPMODEL Suo et al. (2007)  Using the TOPMODEL model to calculate runoff yield in subwatershed Advantage: it requires fewer parameters and is easy to obtain. Disadvantage: the description of the groundwater hydrological process is too simple, and DEM cannot be used to generate sinks and underground rivers in karst watershed 
Pan (2014)  Regard karst depression as an independent hydrological unit, and use the TOPMODEL model to simulate hydrology, respectively 
SWMM Campbell & Sullivan (2002)  The SWMM is used to simulate the transport process of karst cave water flow Advantage: it can reflect the movement process of a flood wave in the pipeline more truthfully. Disadvantage: The SWMM is sensitive to the geometric characteristics of the pipeline and is only suitable for hydrological simulation of some pipeline systems with detailed survey data 
Zhang et al. (2007)  Taking the depression as a unit, the study area is generalized into six secondary catchment basins connected by pipeline 
 HEC-HMS Current study The reservoir unit method is used to reflect the stagnation of the runoff process in karst basins The HEC-HMS model has good accuracy and is widely used at small basin 

For southwest China, floods are the main disaster during the flood season. However, most of the basins are karst basins, with complex topography and geological conditions (Pu 2009). Karst peak clusters, sinkholes, and skylights are widely distributed, forming a unique three-dimensional spatial system. Thus, the mechanism of flood formation is more complex, and the simulations of the flooding are more difficult than those in non-karst basins. Therefore, the objective of this study is to add a karst reservoir unit to the HEC-HMS model to form a flood simulation tool for a small karst basin, the Xiajia basin in southwest China. Furthermore, this study tries to determine whether the added karst reservoir unit has a certain effect on the HEC-HMS model performance. The findings of this study can provide a useful insight for flood warning and management in karst areas.

STUDY AREA

The Xiajia basin is located in Lingyun County, Baise city, Guangxi, China, with a total catchment area of 799.20 km2 and an average annual rainfall of 1,708.3 mm. Information for each station is shown in Table 2, and the location of the Xiajia basin is shown in Figure 1. There is a natural karst cave – water source cave – located on the southeast side of Lingyun County, and most of the runoff in the upper reaches of the cave is the underground undercurrent. The middle part of the Xiajia basin is hilly landform, while the northeast side has a karst peak-cluster depression topography. The basin is a typical karst basin in southwest China (Huang 1995).

Table 2

Discharge station information

CodeNameLongitudeLatitude
20000900 Chaoli 106°30′14.736″E 24°14′21.567″N 
20001300 Donghe 106°43′25.983″E 24°21′37.121″N 
20000800 Lingyun 106°34′26.216″E 24°20′42.088″N 
20001000 Xiajia 106°38′51.175″E 24°17′18.718″N 
CodeNameLongitudeLatitude
20000900 Chaoli 106°30′14.736″E 24°14′21.567″N 
20001300 Donghe 106°43′25.983″E 24°21′37.121″N 
20000800 Lingyun 106°34′26.216″E 24°20′42.088″N 
20001000 Xiajia 106°38′51.175″E 24°17′18.718″N 
Figure 1

The location of the Xiajia basin.

Figure 1

The location of the Xiajia basin.

HEC-HMS MODEL

Model construction

First, the DEM data with a resolution of 30 m was downloaded from www.gscloud.cn/. Then, HEC-GeoHMS was applied to obtain the sub-basins and river channel of the Xiajia basin, as shown in Figure 2 and Table 3. W01–W12 represent 12 sub-basin units, and R01–R05 represent four river channel units. In addition, soil data and land cover data with resolutions of 1 × 1 km were downloaded from the HWSD and IGBP_LUCC database, respectively, and the land cover and soil type of the Xiajia basin were obtained (Figure 3). The common methods for runoff calculation are the SCS curve method (Fang et al. 2007) and the initial losses-lateral losses method (Zhang et al. 2017). In this study, it was found that the SCS curve method had better results in the sub-basins W02–W04 and W06–W12, while the initial losses-lateral losses method had better results only in the sub-basins W01, W03 and W05. Therefore, the SCS curve method was adopted. As suggested by Ge (2016) and Wang (2018b), the Snyder unit line method was used for direct runoff confluence calculation, and the exponential attenuation method was applied to the base-flow separation. Finally, the Muskingum method was employed to calculate the river confluence due to its better applicability, fewer parameters, and easy calibration (Li 2020). The principle flow of the model is shown in Figure 4 (Li & He 2015).

Table 3

Basic information for sub-basins

Sub-basinsArea (km2)Average slope (%)Channel length (km)
W01 174.85 20.5 34.47 
W02 34.94 32.5 8.06 
W03 82.89 20.2 12.05 
W04 38.90 24.1 5.47 
W05 62.61 22.0 4.56 
W06 5.60 25.1 2.79 
W07 186.39 22.4 24.90 
W08 14.92 25.9 5.41 
W09 53.12 18.7 6.17 
W10 11.25 24.2 6.84 
W11 92.41 23.7 13.08 
W12 41.34 21.3 3.24 
Sub-basinsArea (km2)Average slope (%)Channel length (km)
W01 174.85 20.5 34.47 
W02 34.94 32.5 8.06 
W03 82.89 20.2 12.05 
W04 38.90 24.1 5.47 
W05 62.61 22.0 4.56 
W06 5.60 25.1 2.79 
W07 186.39 22.4 24.90 
W08 14.92 25.9 5.41 
W09 53.12 18.7 6.17 
W10 11.25 24.2 6.84 
W11 92.41 23.7 13.08 
W12 41.34 21.3 3.24 
Figure 2

Results of sub-basin division.

Figure 2

Results of sub-basin division.

Figure 3

Land cover and soil type.

Figure 3

Land cover and soil type.

Figure 4

Principle of the HEC-HMS model.

Figure 4

Principle of the HEC-HMS model.

SCS curve method

The calculation formulas of the SCS curve method are as follows (Bosznay 1989):
formula
(1)
formula
(2)
formula
(3)
where is the empirical coefficient and can be determined depending on the land cover type and the soil hydrology group information, as shown in Table 4 (US Army Corps of Engineers 1994; Li & He 2015); Ia is the initial loss value of rainfall, mm; F is the total rainfall loss in the later period, mm; is the maximum retention in the basin, mm; Q is the flow, m3/s; and P is the total precipitation, mm.
Table 4

Summary of the land cover type and soil hydrology group

Land cover typeHydrologic conditionSoil hydrology group
ABCD
Cultivated land Poor 76 85 90 93 
Good 74 83 88 90 
Orchard grove Poor 57 73 82 86 
Average 43 65 76 82 
Good 32 58 72 79 
Woodland Poor 48 68 77 83 
Average 35 56 70 77 
Good 30 48 65 73 
Grasslands 30 58 71 78 
Urban land 98 98 98 98 
Land cover typeHydrologic conditionSoil hydrology group
ABCD
Cultivated land Poor 76 85 90 93 
Good 74 83 88 90 
Orchard grove Poor 57 73 82 86 
Average 43 65 76 82 
Good 32 58 72 79 
Woodland Poor 48 68 77 83 
Average 35 56 70 77 
Good 30 48 65 73 
Grasslands 30 58 71 78 
Urban land 98 98 98 98 

Snyder unit line method

When using the Snyder unit line method, the time lag parameter tp needs to be determined and can be calculated by the following empirical formula (Feng 2016):
formula
(4)
where L is the main river length; Y is the basin slope, %; and CN is the empirical coefficient of the SCS curve.

Exponential attenuation method

The exponential attenuation method is as follows (Cheng 2019):
formula
(5)
where Q0 is the initial base-flow, m3/s; k is the attenuation coefficient that needs to be calibrated; and t is the time, h.

Muskingum method

The calculation formula of the Muskingum method is given as follows (Wang et al. 2018):
formula
(6)
formula
(7)
formula
(8)
formula
(9)
where and are the upstream inflow and downstream inflow at the beginning of the period, respectively; and represent the upstream outflow and downstream outflow at the end of the period, respectively; C0, C1 and C2 are functions of K and x, respectively; ; K is the propagation time of steady flow in the reach, h; and x is the flow specific gravity coefficient.

Improved HEC-HMS model

A sub-basin is divided into karst areas and non-karst areas, and for karst areas, the karst features (natural karst cave, etc.) are considered as karst reservoirs, and the structure is shown in Figure 5. Suppose there is a sub-basin Wa, the sub-basin adjacent to Wa is Wb, and the direction of water flow is from Wa to Wb. Then, the flow yield in the karst area of Wa can be estimated by the karst reservoir (VB1), and the water flowing from Wa to Wb is calculated by using a linear reservoir (VB2) and the unit line method. The principle of the improved HEC-HMS model (Cheng 1988) is shown in Figure 6, and the constructions for karst reservoirs and linear reservoirs are as follows.

Figure 5

Karst water storage structure.

Figure 5

Karst water storage structure.

Figure 6

Principle of the improved HEC-HMS model.

Figure 6

Principle of the improved HEC-HMS model.

Construction of karst reservoir (VB1)

Surface runoff calculation
The surface runoff in the karst area of Wa is denoted as RBS and can be calculated as:
formula
(10)
formula
(11)
formula
(12)
where SB is the storage of the karst reservoir; P is the precipitation; EM is the evapotranspiration capacity; K is the evaporation coefficient; BM is the maximum storage capacity of the karst reservoir; RBS is the surface runoff in the karst area of Wa.
Therefore, the total surface runoff in Wa can be calculated as:
formula
(13)
where RS is the total surface runoff in Wa and RAS is the surface runoff in the non-karst areas of Wa.
Karst conduit flow. The karst conduit flow in the karst area of Wa is denoted as RB and can be calculated as:
formula
(14)
where RB is the karst conduit flow; HB is the threshold value; and KB is the outflow coefficient of karst conduit flow.
Underground runoff
The underground runoff in the karst area of Wa is denoted as RBG and can be calculated as:
formula
(15)
where RBG is the underground runoff in the karst area of Wa and KBG is the linear outflow coefficient.
Therefore, the total underground runoff in Wa can be calculated as:
formula
(16)
where RG is the total underground runoff of Wa and RAG is the underground runoff in the non-karst areas of Wa.

Construction of linear reservoirs (VB2)

Interflow
The interflow (QI) flowing from the non-karst areas of Wa to Wb can be calculated as:
formula
(17)
where CI is the regression coefficient of the soil mid-stream reservoir; RI is the interflow; and is the unit conversion coefficient.
Karst conduit flow
The karst conduit flow flowing from the karst areas of Wa to Wb can be denoted as QB and calculated as:
formula
(18)
where CB is the regression coefficient of the karst water and u is the unit conversion coefficient.
Underground runoff
The underground runoff flowing from Wa to Wb is denoted as QG and can be calculated as:
formula
(19)
where CG is the regression coefficient of the groundwater reservoir and u is the unit conversion coefficient.

RESULTS

Calibration result for the initial HEC-HMS model

The discharge and precipitation data (2002–2018) used in this study were recorded by Chaoli, Donghe, Lingyun and Xiajia stations and provided by the Chengbi River Reservoir Management Bureau. Wang et al. (2019) showed that the determination of hydrological model parameters is closely related to the flood peak and the flood volume of the flood used during the calibration. A calibration using variable size flood samples is helpful to obtain more stable and representative model parameters. Therefore, 31 different size flood samples were applied to calibrate the model in this study. Among the flood samples, the maximum flood peak was 358 m3/s (number 20100628), the minimum flood peak was 101 m3/s (number 20050614), the average value was 179 m3/s, and the standard deviation was 69 m3/s. Take the maximum measured flood peak (358 m3/s) as the reference and take one-third (119 m3/s) and two-thirds (239 m3/s) as the bases for flood classification. Finally, the samples can be divided into three categories: category (i) (Qm < 119 m3/s), category (ii) (119 m3/s < Qm < 239 m3/s), and category (iii) (Qm > 239 m3/s). The flood and their corresponding rainfall samples are shown in the appendix (Supplementary material, Table A1). In addition, to study the influence of the rainfall data with different centers on the model simulation results, the watershed was divided into four different rainfall centers and the division results are shown in Figure 7 (Sun et al. 2014).

Figure 7

Indication of precipitation gravity center zoning.

Figure 7

Indication of precipitation gravity center zoning.

The relative error (Re) of the flood peak, the of the flood volume, the deviation of the peak time , and the Nash efficiency coefficient (NSE) (Moriasi et al. 2007) were selected as the evaluation indices of the model simulation accuracy. A simulation with Re ≤ 20%, , and NSE ≥ 0.5 can be considered as a qualified simulation. Additionally, the square of R (R2) and the mean absolute error (MAE) were applied to give a better understanding of the overall goodness-of-fitness. The optimization parameters obtained by the Nelder–Mead method (Zettel & Hitzmann 2017) were substituted into the initial HEC-HMS model to simulate 31 floods in the calibration period, and the parameters are shown in the appendix (Supplementary material, Table A3). Finally, it is shown that the simulation result was poor, and the qualified rate (, n is the number of qualified simulations, N is the number of total simulations) was only 38.71%. Due to space limitations, only the simulations with three different size flood samples numbered 20080926 (category i), 20050620 (category ii), and 20100628 (category iii) were analysed, and the results are shown in Table 5 and Figure 8. For the simulation with flood sample numbered 20080926, the simulated curve and measured curve were close, and the peak time was the same, but the simulated flood peak and flood volume were slightly larger than the measured values. After the flood peak, a small amount of precipitation also caused obvious fluctuation in the simulated flow. The values of the flood peak and flood volume were 23.53 and 40.65%; the was 0; and the NSE, R2, and MAE were 0.38, 0.96 and 18.9, respectively. For the simulation with the flood sample numbered 20050620, the simulated flood peak was obviously larger than the measured value, and the simulated flood volume was slightly larger than the measured value. After the flood peak, there was also a fluctuation in the large flow caused by small precipitation. The values of the flood peak and flood volume were 76.09 and 10.14%, the was –11, and the NSE, R2, and MAE were –1.5, 0.82 and 26.3. For the simulation with the flood sample numbered 20100628, the simulated flood peak and flood volume were far beyond the measured values. The values of the flood peak and flood volumes were 149.44 and 182.17%, the was 4, and the NSE, R2, and MAE were –15.6, 0.69 and 284.2, respectively.

Table 5

Calibration results for the initial HEC-HMS model

Flood numberFlood peak (m3/s)
Deviation of peak time (h)
Flood volume (mm)
NSER2MAE
MeaSimRe (%)MeaSimMeaSimRe (%)
20080926 119 147 23.53 14:00 14:00 21.4 30.1 40.65 0.38 0.96 18.9 
20050620 138 242.6 76.09 21:00 8:00 –11 66.1 72.8 10.14 –1.5 0.82 26.3 
20100628 358 892.5 149.44 6:00 10:00 57.2 161.4 182.17 –15.6 0.69 284.2 
Flood numberFlood peak (m3/s)
Deviation of peak time (h)
Flood volume (mm)
NSER2MAE
MeaSimRe (%)MeaSimMeaSimRe (%)
20080926 119 147 23.53 14:00 14:00 21.4 30.1 40.65 0.38 0.96 18.9 
20050620 138 242.6 76.09 21:00 8:00 –11 66.1 72.8 10.14 –1.5 0.82 26.3 
20100628 358 892.5 149.44 6:00 10:00 57.2 161.4 182.17 –15.6 0.69 284.2 

Mea is measurement; Sim is simulation.

Figure 8

Calibration results for the initial HEC-HMS model.

Figure 8

Calibration results for the initial HEC-HMS model.

Flood simulation by using the improved HEC-HMS model

Calibration results

The precipitation and flood samples used in the calibration for the improved HEC-HMS model are the same as for the initial HEC-HMS model. The simulation results are summarized in Table 6. Overall, 16 of the 31 simulations are qualified, and the qualified rate is 51.61%. Among the unqualified simulations, six simulations are unqualified for the of the flood peak, seven simulations are unqualified for the , eight simulations are unqualified for the of the flood volume, and seven simulations are unqualified for the Nash efficiency coefficient. In addition, the spatial variation of the evaluation indices is shown in Figure 9. Six precipitation centers fall in zone I, and the corresponding qualified rate of the flood simulation is 66.67%, the NSE value is 0.93, and R2 is 0.94. Five precipitation centers fall in zone II, and the corresponding qualified rate of the flood simulation is 40.00%, the NSE value is 0.44, and R2 is 0.91. Ten precipitation centers fall in zone III, and the corresponding qualified rate of the flood simulation is 70.00%, the NSE value is 0.88, and the R2 value is 0.90. Ten precipitation centers fall in zone IV, and the corresponding qualified rate of the flood simulation is 60.00%, the NSE value is 0.83, and R2 is 0.88. Thus, the correlation between the flood simulation effectiveness and precipitation center is not significant, and the difference in the precipitation center has little effect on the flood simulation result. Additionally, according to precipitation forcing of the People's Republic of China (GB/T 28592–2012), 24-hour rainfall can be divided into six grades: light rain, moderate rain, heavy rain, rainstorms, heavy rainstorms, and extraordinary rainstorms. It was found that among the precipitation samples, one sample was heavy rain, and the corresponding flood simulation result was unqualified. Eight samples were rainstorms, and the maximum precipitation was 96.74 mm, the minimum precipitation was 54.18 mm, the average was 76.03 mm, the standard deviation was 12.62, and the corresponding flood simulation qualified rate was 87.5%. Twenty samples were heavy rainstorms, and the maximum and minimum precipitation were 239.46 and 102.71 mm, respectively. The average was 160.17 mm, the standard deviation was 41.38, and the corresponding flood simulation qualified rate was 55.0%. Two samples were extraordinary rainstorms, and the maximum precipitation was 263.63 mm, the minimum precipitation was 253.18 mm, the average was 258.41 mm, the standard deviation was 7.39, and the corresponding flood simulation qualified rate was 50.0%. For flood peak type, 19 floods were single-peak, with concentrated corresponding precipitation processes and large flood peak values, and the qualified rate was 73.68%. Twelve floods were multi-peak, with relatively scattered corresponding precipitation processes, and the qualified rate was 41.67%. The flood simulation effectiveness was related to the flood peak type, and the flood simulation effectiveness of the single-peak floods was better than that of the multi-peak floods.

Table 6

Simulation results for the improved HEC-HMS model during calibration

Flood numberPeak (m3/s)
Peak time (h)
Flood volume (mm)
NSEQualified
MeaSimRe (%)MeaSimMeaSimRe (%)
20020602 125 119 4.80 7:00 6:00 38.0 36.6 3.68 0.95 Yes 
20020616 126 150 19.05 8:00 5:00 41.4 38.3 7.49 0.48 No 
20020630 138 114 17.39 10:00 11:00 –1 30.0 26.9 10.33 0.88 Yes 
20020721 115 176 53.04 11:00 16:00 19 35.0 37.2 6.29 0.39 No 
20030528 130 149 14.62 12:00 12:00 28.1 26.5 5.69 0.51 Yes 
20030610 127 161 26.77 6:00 0:00 48.6 48.2 0.82 0.90 No 
20030622 327 338 3.36 2:00 2:00 60.8 73.8 21.38 0.67 No 
20030720 139 137 1.44 12:00 12:00 19.3 23.0 19.17 0.63 Yes 
20030726 157 113 28.03 10:00 20:00 –12 64.8 46.2 28.70 0.42 No 
20040626 102 55 46.08 9:00 20:00 –11 29.8 17.6 40.94 –2.57 No 
20040710 251 238 5.18 21:00 22:00 –1 50.6 56.6 11.86 0.90 Yes 
20040721 160 203 26.88 5:00 0:00 70.3 66.4 5.55 0.77 No 
20050606 138 120 13.04 6:00 6:00 39.5 35.5 10.13 0.81 Yes 
20050614 101 116 14.85 7:00 6:00 16.3 18.3 12.27 –0.22 No 
20050620 138 161 16.67 21:00 6:00 –9 66.1 58.6 11.35 0.53 No 
20060708 195 195 0.00 6:00 6:00 46.1 48.4 4.99 0.98 Yes 
20060718 158 169 6.96 14:00 12:00 63.8 49.7 22.10 0.32 No 
20060806 211 232 9.95 9:00 6:00 78.1 69.6 10.88 0.92 Yes 
20070628 187 120 35.83 4:00 4:00 29.3 32.2 9.90 0.73 No 
20070903 149 145 2.68 14:00 13:00 24.8 26.8 8.06 0.86 Yes 
20070909 200 181 9.50 8:00 9:00 –1 49.1 48.2 1.83 0.98 Yes 
20080530 139 149 7.19 8:00 9:00 –1 23.0 30.7 33.48 0.82 No 
20080609 167 152 8.98 12:00 9:00 44.5 43.0 3.37 0.92 Yes 
20080612 325 319 1.85 11:00 10:00 50.1 58.5 16.77 0.77 Yes 
20080813 137 128 6.57 13:00 11:00 27.3 25.7 5.86 0.88 Yes 
20080926 119 136 14.29 14:00 11:00 21.4 24.9 16.36 0.88 Yes 
20081103 103 114 10.68 20:00 23:00 21 49.4 35.8 27.53 0.50 No 
20100628 358 337 5.87 6:00 7:00 –1 57.2 69.1 20.80 0.69 No 
20100721 222 263 18.47 10:00 10:00 86.1 94.5 9.76 0.73 Yes 
20120521 273 322 17.95 6:00 6:00 46.9 67.2 43.28 –0.12 No 
20120608 244 263 7.79 12:00 12:00 112.2 120.8 7.66 0.63 Yes 
Flood numberPeak (m3/s)
Peak time (h)
Flood volume (mm)
NSEQualified
MeaSimRe (%)MeaSimMeaSimRe (%)
20020602 125 119 4.80 7:00 6:00 38.0 36.6 3.68 0.95 Yes 
20020616 126 150 19.05 8:00 5:00 41.4 38.3 7.49 0.48 No 
20020630 138 114 17.39 10:00 11:00 –1 30.0 26.9 10.33 0.88 Yes 
20020721 115 176 53.04 11:00 16:00 19 35.0 37.2 6.29 0.39 No 
20030528 130 149 14.62 12:00 12:00 28.1 26.5 5.69 0.51 Yes 
20030610 127 161 26.77 6:00 0:00 48.6 48.2 0.82 0.90 No 
20030622 327 338 3.36 2:00 2:00 60.8 73.8 21.38 0.67 No 
20030720 139 137 1.44 12:00 12:00 19.3 23.0 19.17 0.63 Yes 
20030726 157 113 28.03 10:00 20:00 –12 64.8 46.2 28.70 0.42 No 
20040626 102 55 46.08 9:00 20:00 –11 29.8 17.6 40.94 –2.57 No 
20040710 251 238 5.18 21:00 22:00 –1 50.6 56.6 11.86 0.90 Yes 
20040721 160 203 26.88 5:00 0:00 70.3 66.4 5.55 0.77 No 
20050606 138 120 13.04 6:00 6:00 39.5 35.5 10.13 0.81 Yes 
20050614 101 116 14.85 7:00 6:00 16.3 18.3 12.27 –0.22 No 
20050620 138 161 16.67 21:00 6:00 –9 66.1 58.6 11.35 0.53 No 
20060708 195 195 0.00 6:00 6:00 46.1 48.4 4.99 0.98 Yes 
20060718 158 169 6.96 14:00 12:00 63.8 49.7 22.10 0.32 No 
20060806 211 232 9.95 9:00 6:00 78.1 69.6 10.88 0.92 Yes 
20070628 187 120 35.83 4:00 4:00 29.3 32.2 9.90 0.73 No 
20070903 149 145 2.68 14:00 13:00 24.8 26.8 8.06 0.86 Yes 
20070909 200 181 9.50 8:00 9:00 –1 49.1 48.2 1.83 0.98 Yes 
20080530 139 149 7.19 8:00 9:00 –1 23.0 30.7 33.48 0.82 No 
20080609 167 152 8.98 12:00 9:00 44.5 43.0 3.37 0.92 Yes 
20080612 325 319 1.85 11:00 10:00 50.1 58.5 16.77 0.77 Yes 
20080813 137 128 6.57 13:00 11:00 27.3 25.7 5.86 0.88 Yes 
20080926 119 136 14.29 14:00 11:00 21.4 24.9 16.36 0.88 Yes 
20081103 103 114 10.68 20:00 23:00 21 49.4 35.8 27.53 0.50 No 
20100628 358 337 5.87 6:00 7:00 –1 57.2 69.1 20.80 0.69 No 
20100721 222 263 18.47 10:00 10:00 86.1 94.5 9.76 0.73 Yes 
20120521 273 322 17.95 6:00 6:00 46.9 67.2 43.28 –0.12 No 
20120608 244 263 7.79 12:00 12:00 112.2 120.8 7.66 0.63 Yes 

Mea is measurement; Sim is simulation.

Figure 9

The spatial variation of the evaluation indices in the calibration. (a) NSE; (b) R2; and (c) Qualified rate.

Figure 9

The spatial variation of the evaluation indices in the calibration. (a) NSE; (b) R2; and (c) Qualified rate.

Based on the comprehensive analysis of the precipitation level, precipitation center and flood peak type, it can be concluded that the HEC-HMS model constructed in this study has better simulation results under the conditions of heavy rainfall and concentrated precipitation processes.

Validation results

The precipitation and flood samples used in the validation for the improved HEC-HMS model included 18 different size flood samples and their corresponding precipitations, and the simulation results are summarized in Table 7. Overall, 11 simulations were qualified, and the qualified rate was 61.11%. Three floods were selected as the representative, and the variation of flood hydrograph and karst storage is shown in Figure 10. It can be seen from Figure 10 that the karst storage was variable, which shows that the karst reservoir unit can simulate the stagnation of the runoff process in the karst area well. In addition, the spatial variation of the evaluation indices is shown in Figure 11. One precipitation center falls in zone I, and the corresponding qualified rate of the flood simulation was 100% with the NSE and R2 values of 1.00. Two precipitation centers fall in zone II, and the corresponding qualified rate of the flood simulation was 100.00% with the NSE and R2 values of 1.00. Seven precipitation centers fall in zone III, and the corresponding qualified rate of the flood simulation was 71.43% with the NSE value of 0.94 and R2 of 0.96. Eight precipitation centers fall in zone IV, and the corresponding qualified rate of the flood simulation was 37.50% with the NSE value of 0.55, and R2 of 0.85. For precipitation level, three precipitation samples were rainstorms, the maximum precipitation was 95.49 mm, the minimum precipitation was 76.63 mm, the average was 84.90 mm, the standard deviation was 10.00, and the simulation qualified rate was 66.67%. Thirteen precipitation samples were heavy rainstorms with the maximum and minimum values of 203.06 and 109.58 mm. The average was 141.45 mm, the standard deviation was 23.83, and the simulation qualified rate was 61.54%. Two precipitation samples were extraordinary rainstorms with maximum and minimum values of 301.38 and 273.51 mm, respectively. The standard deviation was 19.71, and the simulation qualified rate was 50.00%. For flood peak type, nine flood samples were single-peak with concentrated corresponding precipitation processes and large flood peak values, and the qualified rate was 77.78%. Nine flood samples were multi-peak with relatively scattered corresponding precipitation processes, and the qualified rate was 44.44%. The flood simulation effectiveness is related to the flood peak type, and the flood simulation effectiveness of the single-peak floods is better than that of the multi-peak floods.

Table 7

Simulation results for the improved HEC-HMS model during validation

Flood numberFlood peak (m3/s)
Peak time (h)
Flood volume (mm)
NSEQualified
MeaSimRe (%)MeaSimMeaSimRe (%)
20141004 163 155.4 4.66 10:00 10:00 36.6 36.4 0.55 0.94 Yes 
20150523 161 200.2 24.35 5:00 3:00 71.5 87.0 21.68 0.60 No 
20150621 159 186.5 17.30 16:00 14:00 49.2 49.2 0.00 0.77 Yes 
20150704 160 190.3 18.94 8:00 7:00 69.9 70.5 0.86 0.87 Yes 
20150819 205 252.3 23.07 12:00 11:00 50.8 61.3 20.67 0.61 No 
20150829 110 141.9 29.00 14:00 12:00 58.1 54.5 6.20 0.57 No 
20170616 115 121.5 5.65 8:00 5:00 51.7 45.2 12.57 0.66 Yes 
20170628 106 132.5 25.00 7:00 6:00 56.1 48.2 14.08 0.51 No 
20170712 195 199 2.05 7:00 8:00 –1 61.5 49.0 20.33 0.83 No 
20170809 144 155 7.64 8:00 6:00 47.9 39.9 16.70 0.56 Yes 
20170814 222 262 18.02 7:00 17:00 –10 54.6 58.6 7.33 0.50 No 
20170825 126 134 6.35 7:00 19:00 12 38.1 37.2 2.36 0.84 No 
20170906 111 97 12.61 13:00 11:00 45.7 39.9 12.69 0.56 Yes 
20180604 106 116 9.43 16:00 13:00 28.7 28.0 2.44 0.77 Yes 
20180624 148 153 3.38 6:00 4:00 49.7 40.6 18.31 0.78 Yes 
20180709 217 214 1.38 5:00 3:00 55.2 50.9 7.79 0.90 Yes 
20180808 321 323 0.62 6:00 6:00 118.6 110.1 7.17 0.70 Yes 
20180902 216 203 6.02 2:00 3:00 –1 27.3 31.0 13.55 0.90 Yes 
Flood numberFlood peak (m3/s)
Peak time (h)
Flood volume (mm)
NSEQualified
MeaSimRe (%)MeaSimMeaSimRe (%)
20141004 163 155.4 4.66 10:00 10:00 36.6 36.4 0.55 0.94 Yes 
20150523 161 200.2 24.35 5:00 3:00 71.5 87.0 21.68 0.60 No 
20150621 159 186.5 17.30 16:00 14:00 49.2 49.2 0.00 0.77 Yes 
20150704 160 190.3 18.94 8:00 7:00 69.9 70.5 0.86 0.87 Yes 
20150819 205 252.3 23.07 12:00 11:00 50.8 61.3 20.67 0.61 No 
20150829 110 141.9 29.00 14:00 12:00 58.1 54.5 6.20 0.57 No 
20170616 115 121.5 5.65 8:00 5:00 51.7 45.2 12.57 0.66 Yes 
20170628 106 132.5 25.00 7:00 6:00 56.1 48.2 14.08 0.51 No 
20170712 195 199 2.05 7:00 8:00 –1 61.5 49.0 20.33 0.83 No 
20170809 144 155 7.64 8:00 6:00 47.9 39.9 16.70 0.56 Yes 
20170814 222 262 18.02 7:00 17:00 –10 54.6 58.6 7.33 0.50 No 
20170825 126 134 6.35 7:00 19:00 12 38.1 37.2 2.36 0.84 No 
20170906 111 97 12.61 13:00 11:00 45.7 39.9 12.69 0.56 Yes 
20180604 106 116 9.43 16:00 13:00 28.7 28.0 2.44 0.77 Yes 
20180624 148 153 3.38 6:00 4:00 49.7 40.6 18.31 0.78 Yes 
20180709 217 214 1.38 5:00 3:00 55.2 50.9 7.79 0.90 Yes 
20180808 321 323 0.62 6:00 6:00 118.6 110.1 7.17 0.70 Yes 
20180902 216 203 6.02 2:00 3:00 –1 27.3 31.0 13.55 0.90 Yes 

Mea is measurement; Sim is simulation.

Figure 10

Changes in flood hydrograph and karst storage. (a) 20170814, (b) 20170906, (c) 20180604.

Figure 10

Changes in flood hydrograph and karst storage. (a) 20170814, (b) 20170906, (c) 20180604.

Figure 11

The spatial variation of the evaluation indices in the validation. (a) NSE; (b) R2; and (c) Qualified rate.

Figure 11

The spatial variation of the evaluation indices in the validation. (a) NSE; (b) R2; and (c) Qualified rate.

DISCUSSION

The calibration results of the original HEC-HMS model are generally poor, and the simulated values overestimate the measured values. To determine the reasons why the simulation results are poor, three hypotheses are proposed: (1) there are incorrect parameter values; (2) the studied basin is not a closed basin due to the influence of karst landforms, leading to a large number of flows flowing down to other basins through karst pipelines (Xu et al. 2017); and (3) the karst cave, called a water source cave, has a detention effect on floods (Chen 2018).

For assumption (1), the Morse method (Song et al. 2015a) is applied to analyze the sensitivity of the parameters, and the results are shown in Table 8 and Figure 12. Taking the floods numbered 20080926, 20050620, and 20100628 as examples, for flood peak, CN is the most sensitive parameter (e ranges from 5.818 to 13.451), followed by Cp, tp and Ia. For peak time, the sensitivity of each parameter is low, among which, Cp is the most sensitive parameter (e ranges from 0.050 to 0.100), followed by K and tp. For flood volume, CN is the most sensitive parameter (e ranges from 1.596 to 2.438), followed by Cp, tp, k and r. The above sensitivity analysis results imply that adjusting the sensitive parameters can change the simulation output and therefore improve the simulation accuracy of the model to a certain extent. However, an over-adjustment of the model parameters may make it lose its actual physical meaning. For example, when the CN value in this study drops to approximately one-third of its initial value, the simulated flood peak value of the large flood is equivalent to the measured value, but the CN value will be far from that of the land condition represented by the original land cover and soil hydrological group. Chen et al. (2016) and Liao (2017) also proved that it is unreasonable to significantly reduce the CN value. Therefore, it is believed that the values of the parameters in this study are reasonable and that they are not the main cause of the low accuracy simulation.

Table 8

Calculations of the sensitivity of the parameters

ParameterFlood peak
Peak time
Flood volume
200809262005062020100628200809262005062020100628200809262005062020100628
CN 7.367 5.818 13.451 0.022 0.067 0.044 2.152 1.596 2.438 
Ia 0.929 0.982 1.636 0.000 0.044 0.000 0.223 0.280 0.292 
tp 1.744 1.171 3.573 0.000 0.067 0.044 0.306 0.171 0.510 
Cp 2.460 1.113 6.148 0.050 0.075 0.100 0.296 0.274 0.626 
0.549 0.711 0.220 0.000 0.000 0.000 0.324 1.238 0.849 
0.000 0.036 0.000 0.000 0.000 0.000 0.310 0.544 0.709 
0.013 0.080 0.076 0.000 0.089 0.000 0.003 0.000 0.008 
0.000 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 
ParameterFlood peak
Peak time
Flood volume
200809262005062020100628200809262005062020100628200809262005062020100628
CN 7.367 5.818 13.451 0.022 0.067 0.044 2.152 1.596 2.438 
Ia 0.929 0.982 1.636 0.000 0.044 0.000 0.223 0.280 0.292 
tp 1.744 1.171 3.573 0.000 0.067 0.044 0.306 0.171 0.510 
Cp 2.460 1.113 6.148 0.050 0.075 0.100 0.296 0.274 0.626 
0.549 0.711 0.220 0.000 0.000 0.000 0.324 1.238 0.849 
0.000 0.036 0.000 0.000 0.000 0.000 0.310 0.544 0.709 
0.013 0.080 0.076 0.000 0.089 0.000 0.003 0.000 0.008 
0.000 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 
Figure 12

Sensitivity comparison of each parameter: (a) flood peak; (b) peak time; and (c) flood volume.

Figure 12

Sensitivity comparison of each parameter: (a) flood peak; (b) peak time; and (c) flood volume.

For assumption (2), an analysis of water balance is applied to find out whether the studied basin is a closed basin or not, and the results are shown in Table 9. In terms of multi-year averages, the water of the studied basin is unbalanced, which implies that the studied basin is not a closed basin. However, the value of implies that some water from the adjacent basin may flow into the studied basin through karst pipes. Thus, assumption (2) is not true.

Table 9

Calculations of water balance for different watersheds

Annual average precipitation (P)/mmAnnual average evaporation (E)/mmAnnual average runoff (R)/mm
1,569.2 1,332.7 631 2.668 
Annual average precipitation (P)/mmAnnual average evaporation (E)/mmAnnual average runoff (R)/mm
1,569.2 1,332.7 631 2.668 

For assumption (3), as stated above, a natural karst cave, called a water source cave, is located in sub-basin W06. The calibration results show that the simulated values with the flood samples that belong to category i are similar to the measured values, while the simulated values with the flood samples that belong to category iii are far beyond the measured values. This phenomenon can be explained from the perspective of detention storage, that is, when the incoming flow is small, it is the free outflow of the open channel, and as the discharge increases, it gradually changes to pressure orifice outflow, and therefore, some water cannot be discharged and stagnate in the karst area during the flooding time, and finally this water will gradually discharge after the flood recedes. This suggests that the drainage basin in the karst area above the water source cave has a stagnant effect on water flow. Thus, assumption (3) is reasonable.

Additionally, it should be noted that although the simulation result has been improved after adding a reservoir unit to the original HEC-HEM model, the simulation accuracy of this study is still low compared to that in non-karst basins (Feng 2016). The reason may be that the hydrological processes in karst basins are extremely complex, and not all the karst features and their effects can be considered in the model improvement, resulting in some errors. In addition, it is found that the model will have better simulation results when the rainfall is heavy and the precipitation process is concentrated. The reason may lie in that when the rainfall runoff is heavy, the rapid flow increases. Meanwhile, the evaporation and the karst underground pipe network consumption are relatively small. Therefore, the simulation accuracy is relatively high.

CONCLUSIONS

An accurate flood simulation is crucial for flood warning, flood control, and flood disaster reduction, especially in karst areas with more complex flood features. Therefore, the objective of this study was to add a karst reservoir unit to the HEC-HMS model to analyze the impact of karst system occurrence on flood peaks and form a more accurate model for flood simulation. Some major findings were as follows: The HEC-HMS model with a karst reservoir unit outperformed the original model. After adding the karst reservoir unit, the qualified rate was increased by 22.40 and 22.58% during calibration and validation, respectively. Furthermore, for flood peaks and flood volumes, the parameter CN was the most sensitive parameter, followed by Cp and tp. Also, a comprehensive analysis of the flood sample data (Tables A1 and A2 in the Supplementary material) and simulation results (Tables 6 and 7) showed that the results were better for the simulation with a rainstorm and a single-peak type flood than that with a non-rainstorm and a multi-peak type flood. Additionally, the simulation results were better when the gravity center of precipitation fell in zone III, zone I, and zone IV.

The novelty of this study lay in adding a karst reservoir unit to the HEC-HMS model to quantify the effect of the karst system on the surface flow in a karst basin. Finally, the results implied that karst systems had an impact on hydrology by effectively restraining flood peaks and increasing underground runoff, which agreed with the findings of Bailly-Comte et al. (2008), Palanisamy & Workman (2014), and Zhao et al. (2019). However, some shortcomings remain to be addressed. Only one hydrological station is located in the studied basin, meaning the model has to be calibrated and validated by the data from one hydrological station. Further hydrological research is required to study the application of a reservoir unit in flood modelling at karst basins. Additionally, the differences in runoff parameters between karst areas and non-karst areas, the alternation of open flow and buried flow, and the mutual conversion between surface water and groundwater need to be further studied, and some useful advice can be found in Sun (2015). Besides, only one basin in Guangxi Province was considered in this study, and it is not realistic to extrapolate the findings of this study to larger spatial scales. Thus, more universal results need to be studied.

ACKNOWLEDGEMENTS

The authors are grateful for the support of the Natural Science Foundation of China (51969004 and 51579059), the National Key Research and Development Program of China (2017YFC1502405 and 2016YFC0401303), the Guangxi Natural Science Foundation of China (2017GXNSFAA198361), and the Innovation Project of Guangxi Graduate Education (YCBZ2019022).

DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

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Supplementary data