양지팽
(Zhipeng Yang)
1
정 용
(Yong Jung)
2†
-
원광대학교 건설환경공학과 석사과정
(Wonkwang University․yangzhipeng325@gmail.com)
-
종신회원․교신저자․원광대학교 건설환경공학과 부교수, 공학박사
(Corresponding Author․Wonkwang University․yong_jung@wku.ac.kr)
Copyright © 2021 by the Korean Society of Civil Engineers
키워드
홍수자료공간확장, 미계측유역, 극한 유량 범위, 일반화
Key words
Stream propagation method (SPM), Ungauged watersheds, Extreme flood range, Generalization
1. Introduction
The streamflow data is the substantial requirement for flood control design in hydraulic
engineering. Flood disaster events have become the focus of more and more attention
of the international community, governments and scientific circles. Flood protection
infrastructure is built in small/medium-size watersheds, which require the largest
flood records in the region(Tran et al., 2018). However, there are fewer discharge observations in small/medium-size watersheds,
and most of the discharge data observations are obtained at hydrologically important
locations or downstream (Kim et al., 2019). A number of works have been done on flood research, mainly focusing on flood deduction
and forecast; flood management and detection; flood characteristic cause, risk and
disaster analysis and so on. In flood design studies, there are also empirical studies
using regional records of extreme floods to substantiate flood modeling and other
related analyses (e.g., Biondić et al., 2007: Extreme flooding in the Danube Basin, Croatia; Furey and Gupta, 2005; Furey and Gupta, 2007: Data from the Goodwin Creek experimental watershed; Kovacs, 1988: 30 sites in South Africa; Maréchal et al., 1997: European Survey of Extreme Floods; Kim et al., 2019: Regional flood study in Korea). In other studies, China’s Xin’anjiang lumped hydrological
model (Zhao and Liu, 1995) also used observational data for flood analysis.
Maximum flood records are limited for flood protection information in many developing
countries. Using the method of river space propagation can solve the problem of loss
of streamflow data in small/medium-size watersheds. Transfer streamflow data to an
ungauged watershed using flow data with similar characteristics near the watershed
(McDonnell and Beven, 2014; Merz and Blöschl, 2004; Oudin et al., 2008). For instance, the regression method finds relationships between streamflow data
and watershed characteristics and generates flow data for ungauged watersheds (Heřmanovský et al., 2017; Wagener et al., 2004). To address this conundrum, a robust method, namely the streamflow propagation method
(SPM, Kim et al., 2021), was proposed to generate ungauged streamflow data in small/medium-size watersheds
for use as an improved regionalization method.
The purpose of this study is the generalization of representing the ranges of extreme
floods for ungauged watersheds in Korea. This study generates ungauged flow data in
watersheds of various scales using the SPM and optimize it in a rainfall-runoff conceptual
model. At the same time, for the transmission of streamflow data in small/medium-size
watersheds with no streamflow data, we carried out simulation comparisons in three
different watersheds to observe the spatial distribution of streamflow in different
sizes of watersheds using specific floods on a regional scale. When analyzing specific
floods, we use three envelope curves to analyze spatial distribution of streamflow.
Based on the obtained spatial distributions we tried to obtain the maximum specific
flood extent within different watersheds to help manage small/medium-size watersheds.
In addition, this paper explores the factors affecting the spatial characteristics
of ungauged watersheds at different scales. The remainder of the paper is as follows:
Section 2 provides the methodology; Section 3 explains the study area for selected
storm events; Section 4 gives the generation of streamflow data with ranges of regional
specific floods and range generalization; and Section 5 summarizes the findings.
2. Methodology
2.1 Streamflow Generation for Ungauged Watersheds
The lumped conceptual model (i.e. Storage Function Model, Kimura, 1961) is used to generate streamflow values in ungauged small/medium-size watersheds using
the Streamflow Propagation Method (Kim et al., 2019) for this study. The two independent sets of parameters are distinguished such as
physics-based parameters and time-varying (i.e. event-based) initial conditions. Physical
parameters highly related to watershed characteristics are fixed for all separated
smaller watersheds, while initial conditions are optimized to fit streamflow data
at a selected downstream. The essential difference between this method and conventional
regionalization methods is the separation of parameters and the concentration time
of the simulation (i.e., not for prediction, but for past data generation). In the
process of spatial propagation of streamflow data, the fixed parameters related to
physical properties minimize the simulated streamflow data variances compared with
the measured data. With these given conditions the error rates for each watershed
will be minimally controlled for all separated smaller watersheds. For small to medium
ungauged watersheds located upstream, streamflow data can be generated while we tried
to match measured streamflow data at a selected downstream using optimizations of
an event-based parameter with fixed physical parameters. For the SPM, as event-based
initial conditions (Rsa: cumulative saturated rainfall, mm/h) was optimized based
the generalized other parameters (K and P: constant parameters; and Tl: lag time,
h). During the propagation process, we used the observed inflow value of CJD, SJD,
and ADD as a criterion for optimization. The criterion of optimization is the Nash
– Sutcliffe Efficiency (NSE, Nash and Sutcliffe, 1970).
where Yi is the observed and simulated values and Yobs mean is the mean value of the
observations.
2.2 Ranges of maximum streamflow
After streamflow data is generated for ungauged small/ medium-size watersheds, the
flow distribution of river watersheds of different sizes is observed through the specific
flood distribution analysis. The specific flood distribution analysis typically analyzes
the streamflow of each rainfall event. In this study, we applied this method to show
the possible maximum streamflow ranges of watersheds of different sizes. The range
of possible maximum streamflow distribution are expressed by envelope curve equations
such as: the Creager envelope (2) (Creager et al., 1945), the Francou-Rodier envelope (3) (Biondić et al., 2007), the Kovacs regional maximum flood (4) (Kovacs, 1988), and the Korean regional maximum flood (KRMF) (5) (Kim et al., 2019) equations. These equations are displayed in Eqs. (2)~(5).
where q is the specific flood (m³/s·km²); C is the Creager coefficient; A is Area
(km²); and a and b are constant variables.
where Q is maximum discharge (m³ s-1); A is catchment area (km²); K is the Francou-Rodier
coefficient; Q0= 106 m³ s-1; and A0 = 108 km²
where Q is the streamflow (m³/sec); A is the area (km²); and K is the coefficient
representing the characteristics of watersheds.
In the formula, q is the specific flood (m³/s·km²), and A is the area (km²).
2.3 Spatial Characteristics and Generalization
According to the specific flood distribution analysis, the Creager envelope equation,
the Francou-Rodier envelope, the Kovacs regional maximum flood equation and the KRMF
equation analysis compare time-flood plots with area-watershed plots for the CJD,
SJD, and ADD watersheds. After individual watershed analysis, CJD, SJD, and ADD information
were added together for generalization. For generalization, an analysis of variance
(ANOVA) test was used to verify its results to prove our conjecture about possible
generalization with all information together. We use the RMSE (Root Mean Square Error)
to calculate the RMSE-maximum and RMSE-minimum values for a trend line of maximum
and minimum of specific flood using three envelop curves. The RMSE equation looks
like this:
where a is actual target, p is predicted target, n is select the amount of data.
3. Study Area
The topography of watersheds varies and consists of different terrain types. South
Korea is a country with numerous mountains and with planes. For this study we selected
three different watersheds as shown in Fig. 1 (i.e., Chungju Dam, Seomjin Dam, and Andong Dam watersheds). The Chungju Dam (CJD)
watershed located at the upper reaches of the Southern Han River. The CJD watershed
covers an area of about 6648 km² and percent of mountain is about 41.43 %. The slope
of 55.1 % of CJD watershed is 40 %, and 8.3 % of the watershed has a slope of more
than 80 %. The CJD watershed is divided into 35 small watersheds. To determine the
spatial characteristics of flood in a large watershed, we need spatially distributed
streamflow data. The observations from 12 streamflow stations are not enough to reflect
the spatial characteristics of flood in the area. We used three different water level
gauges (i.e., Youngwol (YW), Youngwol 1 (YW1), Youngchun (YC)) as verification points.
For the propagation process, the CJD inflow is the main criteria for the propagation
process.
The size of Seomjin Dam (SJD) watershed is 4,896.5 km² including 38.65 % mountainous
areas. The SJD watershed is divided into 34 small watersheds. We used four different
water level gauges (i.e., H_ Jwapo Bridge (JP), S_ Im Woon-gyo (IW), Y- Seongsu (SS))
as verification points. The SJD inflow is the main information we want to match as
the CJD watershed.
The Andong Dam (ADD) watershed is located in the upstream of Nakdong river with a
drainage area (23,384 km²). The mountain coverage is about 67.84 % which is larger
than others in this study. In this study, the ADD watershed was divided into 55 small
watersheds without streamflow information. Three water level gauges were selected
for the validation purpose (i.e.: S_Yangsam Bridge (YS), H_ Docheongyo Bridge (DC),
H_ Punghori (PH)). Based on the data availability and the streamflow representativeness,
the SPM verification points were chosen. The separated smaller watersheds are based
on the DEM analysis at COSFIM simulator provide by K-water. This study selected the
19 largest precipitation events from 2001 to 2019.
Fig. 1. Chungju Dam, Seomjin Dam, and Andong Dam watersheds. Diagrams of the Relationship between Selected Water Gauges and Dams (Schematics of Watersheds from the Korean Research File:Water Environment Information System, 2022)
4. Results and discussion
4.1 Generation of Streamflow Data
Fig. 2(a) is a comprehensive graph of the comparison between observed and simulated values
using the streamflow propagation method (SPM) for the CJD，SJD and ADD watersheds.
We obtained the observed and simulated values of heavy streamflow events from 2001
to 2019 from the observation stations identified in the three major watersheds (described
in Chapter 2). Fig. 2(b) is a graph of the peak streamflow data collected by various observation stations
in the CJD, SJD, and ADD watersheds. Fig. 2(c) is box plots of the optimized and verified NSE values of observation stations after
SPM process in the three major watersheds. In Fig. 2(c), four box plots are a group according to the order of the CJD, SJD, and the ADD watershed.
The first box plots, (i.e., Dark color) in each group are the optimization points,
and the remaining points are data propagated points.
In Fig. 2(a), the data for all watersheds generally show an upward trend in both simulated and
observed values along a linear trend. The streamflow data of the CJD (blue), ADD (green),
and SJD (red) watersheds are distributed in the range of CJD<14000 m³/s, SJD<6000
m³/s and ADD <3000 m³/s, respectively. These various distributions are based on the
different size and weather coalitions may produce these differences.
Fig. 2(b) is a graph of the peak streamflow data collected by each observation station in the
CJD, SJD and ADD watersheds. Through the distribution of each peak point in the figure,
the distribution range of the peak flow data of each watershed can be known. The distribution
ranges of the CJD station optimization point and the other three verification points
are less than 10000 m³/s. The distribution range of peak data in the SJD watershed
is <2500 m³/s. The distribution range of peak data in the ADD watershed is <6000 m³/s.
At the same time, the distribution of the peak data of the verification points in
each watershed is roughly consistent with the peak data distribution of the optimization
points. Fig. 2(c) shows that in different areas within different watersheds, the data of the optimization
points can reflect the general situation of the data of the verification points. By
comparing the peak data of each watershed, we found that the size and distribution
of the peak data in each watershed also have an impact on the size of the NSE value
of the optimization and verification points in each watershed. The finalized mean
NSE values of the CJD, SJD, and ADD watersheds were 0.85,0.83, and 0.84, respectively.
By the comparison of the box plots of the verification points, the SJD watershed is
the most stable compared with other watersheds based on the variances size. Due to
the different geographical locations and area sizes of the three watersheds, the NSE
values at the verification points for the SPM in each watershed were fluctuated.
Fig. 2. (a) A Composite Plot of the Observed-Simulated Values for the CJD, SJD and ADD Watersheds; (b) A Graph of the Maximum Peak Data of Streamflow Data Collected by Various Observation Stations in the CJD, SJD, and ADD Watersheds from 2001 to 2019; (c) NSEs of Each Observation Station
4.2 Ranges of Regional Specific Floods
The envelope curve method is used to establish the regional relationship between the
ranges of maximum streamflow data and the size of watersheds for ungauged watersheds.
We assume that the hydrological climate of the study area is stable, and the size
of the watershed area is the main control feature for the scale of the streamflow
data. Figs. 3~5 shows the maximum regional streamflow in the CJD, SJD, and ADD watersheds. The maximum
streamflow data generated by the SPM is ranged by various regional maximum flood equations.
Figs. 3~5(a) show the applications of the Creager envelope curve. The two Creager curves show
the range of a maximum streamflow in each watershed. We selected optimal envelope
curves based on RMSE between propagated values and envelope curves. As an example,
the parameters of upper and lower Creager curve equations for CJD are C = 12, a =
0.936, and b = -0.025; and C =1, a = 1.18, and b = −0. 007. As shown in Figs. 3~5(a), there are larger specific variances in smaller watersheds, because the smaller watersheds
response sensitively on rainfall amount and terrain conditions. Figs. 3~5(b) show the applications of Kovacs area-specific flood equation. The given maximum specific
floods of CJD, SJD, and ADD watersheds are in the Kovacs coefficient between K = 5.4
and K = 2.4. The maximum range of the specific flood can be represented in K=5.4 –
5.2 for three dams and the minimum ranges are 2.4 – 3.7. Figs. 3~5(c) show the applications of the Francou-Rodier envelope curve. The Francou-Rodier curve
also show the maximum/minimum formula for specific floods in each watershed. In Figs. 3~5(c), it can also be proved that there is a larger specific variance in smaller watersheds.
Figs. 3~5(d) are drawn for the Korean regional maximum flood (KRMF) equation. The maximum of specific
floods based on KRMF do not represent the real maximum specific flood values produced
by SPM. Therefore, the equation needs to be modified to represent the maximum of specific
floods in Korea (Kim et al., 2021).
The RMSE-max (i.e. optimization result of upper envelop curve) and RMSE-min (i.e.
optimization result of lower envelop curve) in the three watersheds are shown in Table 1. From Table 1, the optimal RMSEs of the RMSE-max from the Creager curve equations for SJD and ADD
were 2.07 and1.87. The RMSE-max for CJD using Creager envelop curve has slightly higher
value. The RMSE values of the RMSE-max obtained by the Kovacs curve equations for
CJD, SJD, and ADD have 1.65, 2.22, and 2.21, respectively. The envelop curves of Francou-Rodier
have higher RMSE vales for all watersheds. The optimization results of the RMSE show
that the Creager curve equation in the three watersheds fit the given envelope curves
well based on the averaged RMSE-max and -min. Larger RMSE-max were obtained at the
Francou-Rodier envelope equations (1.61, 2.37 and 2.33). In the case of the RMSE-max
obtained from the Kovacs and Francou-Rodier envelope curves, the SJD and ADD watersheds
have relatively larger RMSE compared to the CJD because the SJD and ADD watersheds
have more mountainous areas. It also shows that the three envelope curves we selected
also represent the RMSE-min well.
Fig. 3. The Specific Flood with the Maximum Flood Equations for CJD Watershed
Fig. 4. The Specific Flood with the Maximum Flood Equations for SJD Watershed
Fig. 5. The Specific Flood with the Maximum Flood Equations for ADD Watershed
Table 1. The Maximum and Minimum RMSE Values Calculated by the Three Methods for the CJD, SJD, and ADD Watersheds
|
Unit: ㎥/s·㎢
|
CJD
|
SJD
|
ADD
|
|
Creager
|
Kovacs
|
Francou-Rodier
|
Creager
|
Kovacs
|
Francou-Rodier
|
Creager
|
Kovacs
|
Francou-Rodier
|
|
RMSE-max
|
1.82
|
1.65
|
1.61
|
2.07
|
2.22
|
2.37
|
1.87
|
2.21
|
2.33
|
|
RMSE-min
|
0.3
|
0.84
|
0.93
|
0.87
|
0.83
|
1.03
|
0.98
|
0.97
|
0.88
|
|
Average
|
1.28
|
1.29
|
1.31
|
1.57
|
1.65
|
1.81
|
1.51
|
1.74
|
1.79
|
4.3 Generalization
The dimensions of the CJD, SJD, and ADD watersheds are different as 6648 km², 786
km², and 1576 km², respectively. Based on the distribution of specific floods shown
in Fig. 6, the distribution of specific flood data in the range of 100-1000 km² is relatively
concentrated with the largest specific flood data. In the range of 1000-10000 km²,
the specific flood data shows a decreasing state with the increase of the watershed
size. Considering the characteristics of watersheds, which refers to area, shape,
slope, longitudinal section and topography have a possible impact on the size of specific
flood. The higher and more stepped terrain has the faster water flow which increased
flood size (Gitau and Indrajeet, 2010). The mountain percentages in the CJD, SJD, and ADD watersheds were 41.43 %, 38.65
%, and 67.84 %, respectively. The ADD watershed with the highest proportion of mountains
(73.4 %) has the higher specific flood in the rage of 400-1000 km². Greater streamflow,
which makes specific floods larger, exacerbating flooding. Therefore, the characteristics
of topographical conditions produces different scales of specific floods.
Fig. 6. Applications of Envelop Curves for Integrated Streamflow Data from CJD, SJD, and ADD Watersheds
To generalize the ranges of maximum of specific flood, we sum all data for the three
watersheds and try to obtain an envelope curve. Before adding all data, ANOVA test
was performed the one-way balanced to evaluate different specific flood data (SF)
across the three watersheds as variables. The differences in specific floods between
different watersheds may result from errors. With a total of 3 subjects in our study,
the obtained F ratio was 8.9031 with a p-value of 0.0003. According to the ANOVA test
result, the combined specific flood generated by SPM was not significantly different.
Although the scales of the SJD and ADD watersheds were small, the specific flood data
in their watersheds did not fluctuate significantly.
Figs. 6(a), (b) and (c) are the aggregation of specific flood with application of various envelop curves
for the CJD, SJD and ADD watersheds. Fig. 6(d) is to analyze the variance specific floods for divided sizes of regions. The upper
and lower Creager curve equations are optimized at a = 141.78, b =−0.403, C = 70 and
a = 5.019, b =−0.397, C = 2. The larger watersheds have little impacts on rainfall
sizes, compared to smaller watersheds because within a smaller watershed the response
of maximum streamflow is lager with a faster peak time. The Kovacs coefficients were
ranged between 2.4 and 5.4 which is same to the previously analyzed as separated regions
at the section of 4.2. The Francou-Rodier envelop curve has a larger averaged RMSE
(2.22) of RMSE-max and -min compared to other methods to represent the degree of agreement.
The generalized equations for the maximum specific flood extent are as follows:
where x is the size of the watershed.
The Creager and Kovacs envelop curves have averaged RMSEs at 1.45 and 1.51, respectively.
Beside of these formulas, the comprehensive generalized formula has lower RMSE (1.03
<1.45), which is smaller than the value calculated by the Creager and Kovacs. This
shows that the proposed comprehensive generalized formula can accurately generate
specific flood ranges for various scales of ungauged watersheds. Table 2 and Fig. 7 show the results of the generalized formula for range representation.
Fig. 7. Generalized Equations for the Maximum Specific Flood Extent
Table 2. The Maximum and Minimum RMSE Values Calculated by the Three Methods for the Specific Flood for Three Watersheds
|
Unit: ㎥/s·㎢
|
Creager
|
Kovacs
|
Francou-Rodier
|
Generalization
|
|
RMSE-max
|
1.92
|
1.96
|
2.58
|
1.04
|
|
RMSE-min
|
0.75
|
0.87
|
1.81
|
1.01
|
|
Average
|
1.45
|
1.51
|
2.22
|
1.03
|
5. Conclusion
Streamflow information is an important part of managing water resources and flood
control. Different scales of watersheds have different effects on the streamflow data
simulations. However, due to the lack of streamflow data, it is difficult to provide
sufficient information on spatial distribution of streamflow. The streamflow propagation
method (SPM) can provide spatially distributed streamflow data for ungauged watersheds.
In the process of analyzing the relationship between specific floods and watershed
sizes, the topography of watersheds potentially has an influence on the distribution
pattern of specific floods. If the terrain in a watershed has higher slopes, the streamflow
data in the middle and lower reaches of a watershed is relatively large. For this
study, watersheds with mountain area over 58 % (i.e., ADD) has more fluctuated specific
flood distributions.
The three integrated dam watersheds (i.e., CJD, SJD and ADD) also use the Creager,
Kovacs, and the Francou-Rodier envelope curve formula to get the representative equation
for maximum specific flood for various sizes of watersheds. Based on the RMSE comparison,
the generalized formula is recommended to represent the range of specific floods for
various sizes of watersheds.
Acknowledgement
This work was supported by the National Research Foundation of Korea (NRF) grant
funded by the Korea government (MSIT) (NRF-2022R1A2C1092215). Specially thanks to
the K-water for the model support (COSFIM).
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