A Practical Approach for Environmental Flow Calculation to Support Ecosystem Management in Wujiang River, China

Abstract

To promote ecosystem protection in the Wujiang River, this paper proposes a practical approach for calculating the environmental flow. The proposed approach combines the idea of the "guarantee rate" of the flow duration curve (FDC) method and the grading idea of the Tennant method. A daily flow series of the Wujiang River was compiled from 1956 to 2019 and used to compare the effect of the proposed approach versus the traditional approaches in four selected sections along the river. The results show that the environmental flow of the Wujiang River can be divided into five levels by the T-FDC method, with a level-by-level disparity, and all levels can capture the temporal and spatial variability of river flow. Additionally, the calculated basic environmental flow process ranges between the historical minimum and second minimum monthly average flow, and the threshold width of the optimal flow is more reasonable than the Tennant method. The T-FDC method can provide technical support for Wujiang River ecosystem management and sustainable development.

Full text

Citation: Ni, X.; Dong, Z.; Xie, W.;
Wu, S.; Chen, M.; Yao, H.; Jia, W. A
Practical Approach for
Environmental Flow Calculation to
Support Ecosystem Management in
Wujiang River, China. Int. J. Environ.
Res. Public Health 2022,19, 11615.
https://doi.org/10.3390/
ijerph191811615
Academic Editors: Yun Li,
Xiaogang Wang, Shimin Tian,
Jun Hou and Paul B. Tchounwou
Received: 31 July 2022
Accepted: 13 September 2022
Published: 15 September 2022
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International Journal of
Environmental Research
and Public Health
Article
A Practical Approach for Environmental Flow Calculation to
Support Ecosystem Management in Wujiang River, China
Xiaokuan Ni 1,2 , Zengchuan Dong 1, * , Wei Xie 3, Shujun Wu 1, Mufeng Chen 4, Hongyi Yao 5and Wenhao Jia 6
1College of Hydrology and Water Resources, Hohai University, Nanjing 210024, China
2Department of Water Resources and Ecosystems, UNESCO-IHE Institute for Water Education,
2611AX Delft, The Netherlands
3Department of Hydropower and Water Conservancy Engineering, POWERCHINA Huadong Engineering
Corporation Limited, Hangzhou 311122, China
4Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental
Research—UFZ, 39104 Magdeburg, Germany
5Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
6Pearl River Water Resources Research Institute, Guangzhou 510611, China
*Correspondence: zcdong@hhu.edu.cn
Abstract:
To promote ecosystem protection in the Wujiang River, this paper proposes a practical
approach for calculating the environmental flow. The proposed approach combines the idea of the
“guarantee rate” of the flow duration curve (FDC) method and the grading idea of the Tennant
method. A daily flow series of the Wujiang River was compiled from 1956 to 2019 and used to
compare the effect of the proposed approach versus the traditional approaches in four selected
sections along the river. The results show that the environmental flow of the Wujiang River can
be divided into five levels by the T-FDC method, with a level-by-level disparity, and all levels
can capture the temporal and spatial variability of river flow. Additionally, the calculated basic
environmental flow process ranges between the historical minimum and second minimum monthly
average flow, and the threshold width of the optimal flow is more reasonable than the Tennant
method. The T-FDC method can provide technical support for Wujiang River ecosystem management
and sustainable development.
Keywords:
environmental flow; hierarchical target; tennant method; flow duration curve; Wujiang
River Basin
1. Introduction
The impact of reservoir development on river ecosystems is of great concern in practice.
River hydrological processes have essential ecological effects on river channels and their
surrounding organisms [
1
,
2
]. While reservoirs regulate runoff for flood control, power
generation, and irrigation, they also change the ecological situation of the river to an extent,
causing some stress to the ecosystem [
3
,
4
]. How to mitigate or eliminate the negative
impacts of cascade reservoirs on river ecology is a complex systemic issue [5].
With the global emphasis on ecological protection, hydraulic projects are increas-
ingly required to address and account for river ecological functions in project design and
operation. Studies and practices show that one of the essential measures to reduce the
ecological impact of hydraulic projects, such as dams and reservoirs in rivers, is to take into
account the ecological needs of the river by optimizing the operation of those projects, or
the so-called “ecological operation” [
6
–
9
]. To formulate ecological operation schemes, a
prerequisite is identifying and characterizing the ecological requirement on the amount of
river flow, known as environmental flow, so that it can be incorporated in or accounted for
in the operation of hydraulic projects and maintain downstream health.
However, the cascade development of the Wujiang River Basin in southwest China
started long ago, mainly to generate electricity, and thus limited consideration of river
Int. J. Environ. Res. Public Health 2022,19, 11615. https://doi.org/10.3390/ijerph191811615 https://www.mdpi.com/journal/ijerph

Int. J. Environ. Res. Public Health 2022,19, 11615 2 of 18
ecology. Most reservoir projects have no targets for maintaining environmental flow when
beginning the design [
10
]. An easy-to-use and reasonable method for environmental
flow calculation is urgently needed to manage ecological operations. Determining rivers’
environmental flow requirement is also a research hotspot in ecology, hydrology, and water
resources [11–13].
Depending on their focus, available methods for calculating the environmental flow of
rivers can be divided into four main categories: (1) hydrological methods using historical
hydrological data, (2) hydraulic methods based on the hydraulic properties of river sections,
(3) habitat simulation methods built on habitat suitability analysis, and (4) holistic methods
comprehensively considering various factors [
14
,
15
]. The hydrological methods are most
widely used globally due to their many advantages, such as simple and easy operation, only
needing flow data, avoidance of expensive field observations, strong versatility, and quick
determination of value. According to some estimates, there are more than 200 calculation
methods for environmental flow, and hydrological methods account for about 30% [
16
,
17
].
The hydrological methods include the Tennant method [
18
], the Tessman method [
19
],
the indicators of hydrologic alteration/range of variability approach (IHA/RVA) method [
20
],
the flow duration curve (FDC) method [
21
] and so on, among which the two most com-
monly used are the Tennant method and the FDC method. The Tennant method, based on
the habits of aquatic organisms, divides a natural year into a fish spawning period and
a general water use period [
22
]. It relates river flow to fish habitat quality, links varying
ecological status to different flow levels of rivers, and then sets up the targets of ecological
river flow. The FDC is a statistical characteristic curve drawn based on the duration or
frequency of the flow equal to or exceeding a particular value during the observation time.
As the proportion of time when a specific flow exceeds all historical records, the FDC more
adequately reflects the runoff characteristics of the basin under various flow states from
low to high [23].
A common problem found for hydrological methods is that they ignore the temporal
and spatial variation in river flow and do not capture or reflect the hydrological variation
in natural river flow. In addition, the basis of ecological status grading is a fixed percentage,
which lacks physical connotation. The methods’ poor spatial transferability and vulnera-
bility to extreme flow events are also issues that need to be solved [
16
,
24
,
25
]. Given these
shortcomings of hydrological methods, many scholars proposed improvement strategies
from three aspects: characteristic flow, calculation period, and percentage coefficient. Ex-
amples include using the annual flow of a typical year or monthly average flow instead
of multi-year average flow [
26
], revising the division of periods based on the seasonal
characteristics of the river ecosystem and the activity cycle of the biological population [
27
],
calibrating the relationship between river flow and ecological health based on actual local
conditions [28], and so on.
Although factors affecting environmental flow are considered more and more carefully,
those improved hydrological methods [
29
] also make the calculation more complex and lose
the essential simplicity of hydrological methods. Furthermore, it is difficult to predict the
water regime at the beginning of the year in the actual operation and management of river
ecological protection [
30
]. This makes the improved methods for calculating environmental
flow challenging to operate in a practical way that considers the interannual variation in
water regimes and distinguishes the wet, normal, and dry years. The technique adopted
should not be too complicated from the perspective of practice.
In this paper, we propose and explore an alternative method for calculating the
environmental flow of the Wujiang River, called the “Tennant-FDC Method” (T-FDC), to
provide technical support for its healthy development. The development of the T-FDC
method explicitly considers the annual variation in the river hydrological process combined
with the advantage of the FDC method to truly reflect the runoff characteristics under each
flow state and the classification idea of the Tennant method. As such, the T-FDC method
captures the monthly variability of river flow and is spatially transferable.

Int. J. Environ. Res. Public Health 2022,19, 11615 3 of 18
The rest of this paper is organized as follows: Section 2describes the regional situation
and requirements of the Wujiang River Basin in southwest China. Section 3describes the
steps of the T-FDC method to calculate multi-level environmental flow. Section 4shows
the results and compares them with other hydrological methods. Section 5concludes the
paper with some discussion.
2. Study Area and Datasets
The Wujiang River Basin is located at 104
◦
18
0
~109
◦
22
0
E and 26
◦
07
0
~30
◦
22
0
N, involv-
ing four provinces of Yunnan, Guizhou, Chongqing, and Hubei in China, with a total area
of 87,920 km
2
and mainstream length of 1037 km. It is the largest tributary on the south
bank of the upper Yangtze River and a representative river in southwest China. Its runoff
is mainly influenced by rainfall, with a clear distinction between wet and dry, with May to
September accounting for about 80% of the annual [31].
The Wujiang River Basin has a natural drop of 2124 m and an average channel gradient
of 0.205%, rich in hydropower resources. Since the 1970s, China carried out large-scale
hydropower development in the Wujiang River Basin and planned a 12-level development
scheme in the mainstream. Except for the Baima navigation and hydropower project at the
most downstream area, all the planned hydraulic engineering projects are completed, and
the impact on the ecological environment is gradually emerging. The geographical location
and water system distribution of the Wujiang River Basin are shown in Figure 1.
In this study, the daily runoff data of critical hydrological stations in the Wujiang River
Basin (Figure 1) from the past 64 years (1956~2019) were referenced from the Hydrological
Yearbook of the People’s Republic of China [32]. The environmental flow was calculated using
the collected data.
Considering the spatial variability of environmental flow, comprehensively evaluated
from the aspects of hydraulic connection, representativeness, monitoring degree and
adjustment degree, this study identified four critical cross sections located downstream of
the corresponding reservoir for ecological protection along the mainstream of the Wujiang
River, as shown in Table 1, the name of which is marked as red in Figure 1.
Table 1. Critical sections for ecological protection on the Wujiang River.
Cross Section Name Section Type
Hongjiadu (HJD) Upstream/midstream boundary section
Wujiangdu (WJD) Controlled hydraulic engineering section
Sinan (SN) Midstream/downstream boundary section
Wulong (WL) Basin outlet section

Int. J. Environ. Res. Public Health 2022,19, 11615 4 of 18
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 4 of 19
Figure 1. Map of the Wujiang River Basin.
In this study, the daily runoff data of critical hydrological stations in the Wujiang
River Basin (Figure 1) from the past 64 years (1956~2019) were referenced from the Hy-
drological Yearbook of the People’s Republic of China [32]. The environmental flow was cal-
culated using the collected data.
Considering the spatial variability of environmental flow, comprehensively evalu-
ated from the aspects of hydraulic connection, representativeness, monitoring degree and
adjustment degree, this study identified four critical cross sections located downstream
of the corresponding reservoir for ecological protection along the mainstream of the
Wujiang River, as shown in Table 1, the name of which is marked as red in Figure 1.
Table 1. Critical sections for ecological protection on the Wujiang River.
Cross Section Name Section Type
Hongjiadu (HJD) Upstream/midstream boundary section
Figure 1. Map of the Wujiang River Basin.
3. Methodology
The T-FDC method proposed in this paper is characterized by drawing on the classi-
fication idea of the Tennant method to obtain multi-level environmental flows. Figure 2
presents the design framework for the proposed T-FDC method.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 5 of 19
Wujiangdu (WJD) Controlled hydraulic engineering section
Sinan (SN) Midstream/downstream boundary section
Wulong (WL) Basin outlet section
3. Methodology
The T-FDC method proposed in this paper is characterized by drawing on the clas-
sification idea of the Tennant method to obtain multi-level environmental flows. Figure 2
presents the design framework for the proposed T-FDC method.
Figure 2. Technical route of the T-FDC method.
3.1. Monthly FDC
Generally, the T-FDC method prioritizes daily flow series and constructs FDCs
month by month based on the total period method, provided that data are available to
improve the time variability and accuracy of the method. Weekly and monthly flow se-
ries can also be used in case of poor data availability, making the method flexible.
To address the deficit of the calculated environmental flow, which is a single value
within or between years. The specific guarantee rate has greater empirical and regional
applicability from constructing curves on an annual scale [12]. This paper groups flow
data on a monthly basis (e.g., “all the Mays” within a range of years) and constructs the
FDC on a month-by-month basis [33] to enhance the representation of the temporal var-
iability of the flow regime.
Depending on the different processing of runoff data, major approaches to con-
structing FDC include the total period approach, the calendar year approach, and the
median annual approach [34]. The total period approach can comprehensively describe
the basin’s historical runoff changes. The calendar year approach and the median annual
approach have advantages in describing the interannual variation in runoff and reducing
the impact of extreme flow events. However, they significantly shorten the daily average
flow series length, resulting in increased uncertainty in the description of the monthly
variation characteristics of runoff by the FDC [35].
The time scale of flow points for constructing the FDC is self-defined according to
management requirements, which can be daily, weekly, or longer. However, the larger
the time scale is, the easier it is to blur the details of flow changes, especially in small flow
areas, such as sources and tributaries. The difference between FDCs constructed based on
daily flow versus monthly flow may be as high as 35% [36].
There are many methods for calculating curves. Some classical ones include the
technique based on the empirical frequency and the method based on information en-
tropy theory proposed by V. P. Singh [37], and so on. These methods have their statistical
basis, and the results are consistent. The FDC based on entropy theory can resist the in-
fluence of extreme values, but its estimation method is more complex. Therefore, con-
sidering the simplicity of the technique, this paper selects the empirical frequency to
construct a monthly FDC:
1
i
i
Pj
=+
(1)
Figure 2. Technical route of the T-FDC method.

Int. J. Environ. Res. Public Health 2022,19, 11615 5 of 18
3.1. Monthly FDC
Generally, the T-FDC method prioritizes daily flow series and constructs FDCs month
by month based on the total period method, provided that data are available to improve
the time variability and accuracy of the method. Weekly and monthly flow series can also
be used in case of poor data availability, making the method flexible.
To address the deficit of the calculated environmental flow, which is a single value
within or between years. The specific guarantee rate has greater empirical and regional
applicability from constructing curves on an annual scale [
12
]. This paper groups flow data
on a monthly basis (e.g., “all the Mays” within a range of years) and constructs the FDC on
a month-by-month basis [
33
] to enhance the representation of the temporal variability of
the flow regime.
Depending on the different processing of runoff data, major approaches to constructing
FDC include the total period approach, the calendar year approach, and the median
annual approach [
34
]. The total period approach can comprehensively describe the basin’s
historical runoff changes. The calendar year approach and the median annual approach
have advantages in describing the interannual variation in runoff and reducing the impact
of extreme flow events. However, they significantly shorten the daily average flow series
length, resulting in increased uncertainty in the description of the monthly variation
characteristics of runoff by the FDC [35].
The time scale of flow points for constructing the FDC is self-defined according to
management requirements, which can be daily, weekly, or longer. However, the larger the
time scale is, the easier it is to blur the details of flow changes, especially in small flow
areas, such as sources and tributaries. The difference between FDCs constructed based on
daily flow versus monthly flow may be as high as 35% [36].
There are many methods for calculating curves. Some classical ones include the
technique based on the empirical frequency and the method based on information entropy
theory proposed by V. P. Singh [
37
], and so on. These methods have their statistical basis,
and the results are consistent. The FDC based on entropy theory can resist the influence
of extreme values, but its estimation method is more complex. Therefore, considering
the simplicity of the technique, this paper selects the empirical frequency to construct a
monthly FDC:
Pi=i
j+1(1)
where P
i
is the empirical frequency of a measured daily flow in a specific month, iis the
descending number of all daily flows of the month in all years, and jis the sample size (i.e.,
the number of days of the month in all years).
For the FDC of each month, different distributions, such as polynomial function, ra-
tional function, power function [
38
,
39
] and others, are used to fit the data and estimate
corresponding parameters. The reliability and practicability of the fitting results are evalu-
ated by the coefficient of determination (R2) to get the best estimates of the parameters.
3.2. Basic Environmental Flow
The basic environmental flow refers to the minimum value of discharge that needs to
be maintained in a river to ensure basic conditions for existing ecosystems [
40
], according
to appropriate criteria based on hydrological and environmental conditions.
The flow Q
90
or Q
95
at 90% or 95% of the period of record is often selected as the
basic environmental flow in the FDC method [
41
,
42
]. However, the specific positioning
of Q
90
and Q
95
in terms of river ecosystem function is ambiguous in existing studies, and
their adaptability varies across rivers. Therefore, to improve the transferability of the basic
environmental flow index, the T-FDC method selects the mean value of Q
90
and Q
95
as the
basic environmental flow. For a specific month, the basic environmental flow is:
Emin =Q90 +Q95
2(2)

Int. J. Environ. Res. Public Health 2022,19, 11615 6 of 18
where E
min
is the basic environmental flow, Q
90
and Q
95
are the flow at the 90% and 95%
period of the record on the FDC of the corresponding month, respectively.
3.3. Optimal Environmental Flow
The optimal environmental flow refers to the runoff process of maintaining a sound
ecological condition of the water body, which is the control index for developing and
utilizing water resources.
Using predetermined percentages of average annual flow as environmental flow
criteria (Table 2), the Tennant method divides the ecological status into ten levels based on
arithmetic progression. It takes the 6th~10th level as the optimal ecological state. This idea
of grading is a bright spot in all environmental flow calculation methods.
Table 2. The ecological status grading system of the Tennant method [18].
Narrative Description
of Flows
Recommended Base Flow Regimens of the Average Flow (%)
General Water Use Period Fish Spawning Period
Optimum range (60, 100] (60–100]
Outstanding [40, 60] 60
Excellent [30, 40) [50, 60)
Good [20, 30) [40, 50)
Fair or degrading (10, 20) [30, 40)
Poor or minimum 10 [10, 30)
Severe degradation (0, 10) (0, 10)
For the deficiency that the specific guarantee rate has a greater degree of empirical
and regional applicability to the traditional FDC method, the grading idea of the Tennant
method is borrowed and combined with the concept of guarantee rate of the FDC method.
Taking the flow at 50% of the period of record on the FDC as the upper limit of the optimal
environmental flow [
16
,
43
] divides the range from the basic environmental flow to the
upper limit into ten levels, and 6th~10th levels are taken as the optimal ecological range, of
which the 6th level is the lower limit, that is:
Eopt =hEopt.lower,Eo pt.u pperi
(Eopt.up per =Q50
Eopt.lower =Eopt.u pp er−Emin
9×5+Emin =5
9Q50 +4
9Emin
(3)
where E
opt
is the optimal environmental flow range, E
opt.lower
and E
opt.upper
are the lower
and upper limits of the range, respectively, Q
50
is the flow at the 50% period of the record
on the FDC of the corresponding month, and E
min
is the basic environmental flow defined
by Equation (2).
3.4. Multi-Level Environmental Flow
As shown in Table 2, the arithmetic progression of the Tennant method is based on
the percentage of the river flow in the natural multi-year average. To avoid the impact of
extreme wet or dry events, modify the difference value between the basic environmental
flow and the lower limit of optimal environmental flow to 10% of the monthly Q
50
. Then,
the number of levels from basic environmental flow to the lower bound of the optimal
range in a specific month of any particular section is:
n=Eopt.lower −Emin
0.1Q50 +1=5
9×Q50 −Emin
0.1Q50 +1 (4)
where nis the number of levels, h i represents the rounding operation.
To facilitate the actual engineering operation, the number of environmental flow levels
in each month of the same section should preferably be a fixed value. For taking one from

Int. J. Environ. Res. Public Health 2022,19, 11615 7 of 18
different values, there can be options for taking the minimum, the maximum, the average,
and the mode. In practical engineering, a smaller number of grades is more convenient
for operation, so the maximum value is unsuitable. Whereas the minimum does not cater
for the rest of the months in statistical significance, and the mode is a better indicator of
the most demand, rather than the average. Therefore, take the mode of each month’s level
number as the final environmental flow level number of the corresponding section. If the
mode is not unique, then take the smallest integer greater than or equal to the average of
these modes, that is:
N=lMo{n}m(5)
where Nis the final level number from the basic to lower bound of a specific section; {n} is
the set of level numbers for each month of the section; and Mo and
d e
represent the mode
and ceiling operations, respectively.
Ultimately, based on the grading idea of the Tennant method, the environmental flow
at all levels from basic to lower bound in a particular month is:
Em=Emin +5
9×m−1
N−1×(Q50 −Emin)(m=1, 2, · · · ,N)(6)
where E
m
is the m-th level environmental flow. E
1
is the basic environmental flow, E
N
is
the lower limit of the optimal environmental flow range, and Q
50
is the upper limit of
the range.
4. Results and Discussion
4.1. Calculation Results of Multi-Level Environmental Flow
Based on the historical daily runoff data, the monthly FDCs of each critical section were
fitted, respectively, (regarding Appendices A–Dfor details). Then the environmental flow
with different levels at separate sections was calculated and compared. More specifically,
in terms of the calculated multi-level environmental flow, there are five environmental
flow levels at each section (HJD, WJD, SN, and WL, four sections in total), respectively,
E
1
~E
5
, of which are recorded in Table 3, and vividly shown in Figure 3. Where E
1
is the
basic environmental flow, E
2
and E
3
are the second and third levels of environmental flow
representing, respectively, fair and good ecological status, and E
4
and E
5
are the lower and
upper limit of the optimal environmental flow, respectively.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 8 of 19
cifically, in terms of the calculated multi-level environmental flow, there are five envi-
ronmental flow levels at each section (HJD, WJD, SN, and WL, four sections in total),
respectively, E1~E5, of which are recorded in Table 3, and vividly shown in Figure 3.
Where E1 is the basic environmental flow, E2 and E3 are the second and third levels of
environmental flow representing, respectively, fair and good ecological status, and E4
and E5 are the lower and upper limit of the optimal environmental flow, respectively.
Table 3. Environmental flows of Wujiang River calculated by the T-FDC method.
January February March April May June July August September October November December
Hongjiadu
E1 40.82 35.68 29.03 26.85 44.92 122.15 145.02 89.53 90.78 73.68 61.88 45.56
E2 42.49 37.61 31.20 32.57 63.36 153.59 167.63 115.73 116.59 87.10 66.84 48.42
E3 44.16 39.54 33.38 38.30 81.79 185.02 190.24 141.94 142.40 100.51 71.81 51.27
E4 45.83 41.47 35.55 44.02 100.23 216.46 212.85 168.15 168.21 113.93 76.77 54.13
E5 49.84 46.11 40.77 57.76 144.48 291.91 267.12 231.05 230.15 146.13 88.69 60.99
Wujiangdu
E1 109.79 111.56 103.30 111.31 244.82 522.44 439.91 284.56 293.53 247.58 149.98 104.22
E2 120.52 119.90 110.51 132.04 301.56 630.82 539.70 370.23 357.28 298.74 180.73 123.18
E3 131.25 128.25 117.73 152.77 358.31 739.21 639.49 455.90 421.04 349.89 211.49 142.15
E4 141.98 136.60 124.94 173.50 415.05 847.59 739.28 541.57 484.79 401.05 242.24 161.11
E5 167.74 156.63 142.26 223.25 551.24 1107.71 978.78 747.18 637.81 523.82 316.05 206.63
Sinan
E1 183.74 184.69 171.06 234.04 594.67 1010.28 721.70 381.39 468.37 400.17 269.10 153.63
E2 200.93 198.97 189.69 300.52 705.70 1213.71 894.73 526.61 562.10 478.82 334.40 187.87
E3 218.11 213.26 208.33 367.00 816.73 1417.14 1067.77 671.83 655.83 557.48 399.70 222.12
E4 235.30 227.55 226.97 433.48 927.76 1620.57 1240.81 817.05 749.56 636.14 464.99 256.36
E5 276.55 261.85 271.70 593.03 1194.24 2108.80 1656.11 1165.57 974.51 824.92 621.71 338.55
Wulong
E1 277.43 304.44 327.20 588.73 1340.95 2190.71 1201.19 689.37 673.46 805.17 456.66 285.55
E2 302.84 323.65 357.60 724.55 1559.16 2488.50 1543.55 852.14 942.09 936.91 573.25 329.41
E3 328.26 342.86 388.00 860.37 1777.36 2786.30 1885.92 1014.91 1210.73 1068.64 689.83 373.26
E4 353.67 362.08 418.41 996.20 1995.57 3084.09 2228.29 1177.68 1479.36 1200.38 806.42 417.12
E5 414.67 408.19 491.38 1322.17 2519.26 3798.80 3049.97 1568.34 2124.09 1516.55 1086.22 522.38
Figure 3. Multi-level environmental flow processes of Wujiang River.
It turns out that the results of the multi-level environmental flow calculated through
the T-FDC method proposed in this paper present pronounced monthly variability and
level-by-level disparity. The variation shows a reasonable correlation with the wet and
dry seasons of the Wujiang River Basin, which is abundant from May to September, and
preliminarily proves the feasibility of the calculation method.
In addition, concerning the multi-level environmental flow of the Wujiang River
calculated through the T-FDC method, there are five levels for each section, while there
Figure 3. Multi-level environmental flow processes of Wujiang River.

Int. J. Environ. Res. Public Health 2022,19, 11615 8 of 18
Table 3. Environmental flows of Wujiang River calculated by the T-FDC method.
January February March April May June July August September October November December
Hongjiadu
E
140.82 35.68 29.03 26.85 44.92 122.15 145.02 89.53 90.78 73.68 61.88 45.56
E
242.49 37.61 31.20 32.57 63.36 153.59 167.63 115.73 116.59 87.10 66.84 48.42
E
344.16 39.54 33.38 38.30 81.79 185.02 190.24 141.94 142.40 100.51 71.81 51.27
E
445.83 41.47 35.55 44.02
100.23
216.46 212.85 168.15 168.21 113.93 76.77 54.13
E
549.84 46.11 40.77 57.76
144.48
291.91 267.12 231.05 230.15 146.13 88.69 60.99
Wujiangdu
E
1109.79 111.56 103.30 111.31
244.82
522.44 439.91 284.56 293.53 247.58 149.98 104.22
E
2120.52 119.90 110.51 132.04
301.56
630.82 539.70 370.23 357.28 298.74 180.73 123.18
E
3131.25 128.25 117.73 152.77
358.31
739.21 639.49 455.90 421.04 349.89 211.49 142.15
E
4141.98 136.60 124.94 173.50
415.05
847.59 739.28 541.57 484.79 401.05 242.24 161.11
E
5167.74 156.63 142.26 223.25
551.24
1107.71
978.78 747.18 637.81 523.82 316.05 206.63
Sinan
E
1183.74 184.69 171.06 234.04
594.67
1010.28
721.70 381.39 468.37 400.17 269.10 153.63
E
2200.93 198.97 189.69 300.52
705.70
1213.71
894.73 526.61 562.10 478.82 334.40 187.87
E
3218.11 213.26 208.33 367.00
816.73
1417.14 1067.77
671.83 655.83 557.48 399.70 222.12
E
4235.30 227.55 226.97 433.48
927.76
1620.57 1240.81
817.05 749.56 636.14 464.99 256.36
E
5276.55 261.85 271.70 593.03
1194.24
2108.80 1656.11 1165.57
974.51 824.92 621.71 338.55
Wulong
E
1277.43 304.44 327.20 588.73
1340.95
2190.71 1201.19
689.37 673.46 805.17 456.66 285.55
E
2302.84 323.65 357.60 724.55
1559.16
2488.50 1543.55
852.14 942.09 936.91 573.25 329.41
E
3328.26 342.86 388.00 860.37
1777.36
2786.30 1885.92 1014.91
1210.73 1068.64 689.83 373.26
E
4353.67 362.08 418.41 996.20
1995.57
3084.09 2228.29 1177.68
1479.36 1200.38 806.42 417.12
E
5414.67 408.19 491.38
1322.17
2519.26
3798.80 3049.97 1568.34
2124.09 1516.55 1086.22 522.38
It turns out that the results of the multi-level environmental flow calculated through
the T-FDC method proposed in this paper present pronounced monthly variability and
level-by-level disparity. The variation shows a reasonable correlation with the wet and
dry seasons of the Wujiang River Basin, which is abundant from May to September, and
preliminarily proves the feasibility of the calculation method.
In addition, concerning the multi-level environmental flow of the Wujiang River
calculated through the T-FDC method, there are five levels for each section, while there
are seven levels for each region with the Tennant method applied. As a matter of fact,
during actual management operation, the more environmental flow levels are taken into
consideration, the more difficult it becomes for the actual reservoir operation and water
resource allocation. Therefore, the T-FDC method gained an edge over the other in this case.
Figure 4shows the values of basic environmental flow and the upper and lower limits
of optimal environmental flow at different sections. In addition to the apparent monthly
variability shown in the figure, the values of environmental flow calculated by the T-FDC
method from upstream to downstream of the Wujiang River vary considerably, which
exhibits good spatial variability. Furthermore, the similar pattern (enclosing shape) of the
environmental flow radar plots for different levels at each section obtained through the
T-FDC method reflects its stability.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 9 of 19
are seven levels for each region with the Tennant method applied. As a matter of fact,
during actual management operation, the more environmental flow levels are taken into
consideration, the more difficult it becomes for the actual reservoir operation and water
resource allocation. Therefore, the T-FDC method gained an edge over the other in this
case.
Figure 4 shows the values of basic environmental flow and the upper and lower
limits of optimal environmental flow at different sections. In addition to the apparent
monthly variability shown in the figure, the values of environmental flow calculated by
the T-FDC method from upstream to downstream of the Wujiang River vary considera-
bly, which exhibits good spatial variability. Furthermore, the similar pattern (enclosing
shape) of the environmental flow radar plots for different levels at each section obtained
through the T-FDC method reflects its stability.
Figure 4. Environmental flow processes of each section.
4.2. Comparison in Terms of Basic Environmental Flow
To further assess the validity of the T-FDC method in the Wujiang River Basin, some
typical hydrological methods were selected for comparison. Among the existing meth-
ods, only the environmental flow obtained through the Tennant method has multiple
levels, while the rest merely focus on the basic environmental flow. In addition, with the
common methods implemented, including the traditional Tennant method, basic envi-
ronmental flows of constant value within the year are obtained, lacking monthly varia-
tion. Therefore, for the basic environmental flow calculation, the improved monthly
Tennant method [25] and the dynamic calculation method (DC) [44], which is widely
used in China and recommended by the Chinese National Standard (SL/T 712-2021),
were chosen for comparison with the T-FDC proposed in this paper. The improved
monthly Tennant method was selected for comparison for the optimal environmental
flow calculation.
Together with the historical minimum and second minimum monthly average flow
process (MMAF and MMAF-II) in the measured runoff of the Wujiang River, the ob-
tained results of the basic environmental flow calculation with the T-FDC method, the
monthly Tennant method, and the DC method, respectively, applied were plotted as in
Figure 5.
Figure 4. Environmental flow processes of each section.

Int. J. Environ. Res. Public Health 2022,19, 11615 9 of 18
4.2. Comparison in Terms of Basic Environmental Flow
To further assess the validity of the T-FDC method in the Wujiang River Basin, some
typical hydrological methods were selected for comparison. Among the existing methods,
only the environmental flow obtained through the Tennant method has multiple levels,
while the rest merely focus on the basic environmental flow. In addition, with the common
methods implemented, including the traditional Tennant method, basic environmental
flows of constant value within the year are obtained, lacking monthly variation. Therefore,
for the basic environmental flow calculation, the improved monthly Tennant method [
25
]
and the dynamic calculation method (DC) [
44
], which is widely used in China and recom-
mended by the Chinese National Standard (SL/T 712-2021), were chosen for comparison
with the T-FDC proposed in this paper. The improved monthly Tennant method was
selected for comparison for the optimal environmental flow calculation.
Together with the historical minimum and second minimum monthly average flow
process (MMAF and MMAF-II) in the measured runoff of the Wujiang River, the obtained
results of the basic environmental flow calculation with the T-FDC method, the monthly
Tennant method, and the DC method, respectively, applied were plotted as in Figure 5.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 10 of 19
Figure 5. Basic environmental flow calculated by various methods and measured small flow.
The basic environmental flow process by the T-FDC method is relatively stable,
ranging between the historical MMAF and MMAF-II. In contrast, the basic environmen-
tal flow by the Tennant method turns out to be much lower than the natural MMAF,
which is very unfavourable to the maintenance of river ecological health. This variability
from low natural flows is due to the vulnerability of the Tennant method to the extremes
of the natural hydrological situation, showing its poor spatial portability, which is not
suitable for the Wu River.
Compared with the Tennant method, the environmental flow process calculated by
the DC method shows better monthly variability, with values closer to the natural small
flow process. Notwithstanding, compared with the T-FDC method, the values obtained
by the DC method are generally smaller. Additionally, the values through such methods
are significantly lower than the natural MMAF during the dry months of the year and
higher than those by the T-FDC method and the natural MMAF-II at the end of the flood
season. For the actual reservoir operation management, this is not conducive to ecologi-
cal protection during the dry season and the realization of power generation benefits at
the end of the flood season. Therefore, in comparison, the basic environmental flow
process by the T-FDC method is more feasible and reasonable.
4.3. Comparison in Terms of Optimal Environmental Flow
The optimal environmental flow results by the T-FDC method and the improved
Tennant method are shown in Figure 6.
Figure 5. Basic environmental flow calculated by various methods and measured small flow.
The basic environmental flow process by the T-FDC method is relatively stable, ranging
between the historical MMAF and MMAF-II. In contrast, the basic environmental flow
by the Tennant method turns out to be much lower than the natural MMAF, which is
very unfavourable to the maintenance of river ecological health. This variability from
low natural flows is due to the vulnerability of the Tennant method to the extremes of the
natural hydrological situation, showing its poor spatial portability, which is not suitable for
the Wu River.
Compared with the Tennant method, the environmental flow process calculated by
the DC method shows better monthly variability, with values closer to the natural small
flow process. Notwithstanding, compared with the T-FDC method, the values obtained
by the DC method are generally smaller. Additionally, the values through such methods
are significantly lower than the natural MMAF during the dry months of the year and
higher than those by the T-FDC method and the natural MMAF-II at the end of the flood
season. For the actual reservoir operation management, this is not conducive to ecological
protection during the dry season and the realization of power generation benefits at the
end of the flood season. Therefore, in comparison, the basic environmental flow process by
the T-FDC method is more feasible and reasonable.

Int. J. Environ. Res. Public Health 2022,19, 11615 10 of 18
4.3. Comparison in Terms of Optimal Environmental Flow
The optimal environmental flow results by the T-FDC method and the improved
Tennant method are shown in Figure 6.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 11 of 19
Figure 6. Optimal environmental flow calculated by two methods.
Overall, in the Wujiang River Basin, the T-FDC method’s optimal flow range covers
that of the Tennant method. In addition, the ranges of optimal flow by the two methods
are similar in the dry season, but the lower limit by the Tennant method is much lower
than that by the T-FDC method in flood season. This is because the water volume
changes drastically in flood season, which is prone to inducing extreme flow events,
causing the mean value to deviate from the overall distribution and thus leading to a
wide range of variations in the optimal environmental flow through applying the Ten-
nant method. Thus, the T-FDC method proves more scientific and reasonable than the
Tennant method for the ecosystem management in the Wujiang River.
5. Conclusions
This paper studied the development of environmental flow management objectives
in the Wujiang River, with the most fundamental problems of the traditional hydrologi-
cal methods pertinent to the subject analyzed. In an effort to address the problems
thereof, a T-FDC method was proposed by combining the FDC method’s guarantee rate
idea with the Tennant method’s grading idea. The results show its effectiveness and fea-
sibility:
1. The T-FDC method is well applicable in the Wujiang River, showing monthly vari-
ability and spatial transferability, excluding the influence of extreme wet or dry
events. Furthermore, the basic environmental flow process obtained through this
method is stable, ranging between the historical minimum and the second minimum
monthly average flow. In contrast, the threshold width of the optimal environmental
flow is more reasonable than the Tennant method.
2. Only the measured runoff data, which can be on any time scale, is needed as the
input required for the T-FDC method, which helps the handling of shortage for daily
runoff processes and eliminates errors caused by interpolation, effectively improv-
ing the method’s adaptability.
3. Regarding practical engineering management, the proposed T-FDC method im-
proved operability by reducing the number of environmental flow levels taken into
consideration.
Several improvements can be incorporated into our proposed method. First, alt-
hough the T-FDC method achieved successful application in the Wujiang River Basin, it
is still necessary to further explore the applicability to rivers with different hydraulic
conditions other than the Wujiang River and to evaluate the robustness, reproducibility,
Figure 6. Optimal environmental flow calculated by two methods.
Overall, in the Wujiang River Basin, the T-FDC method’s optimal flow range covers
that of the Tennant method. In addition, the ranges of optimal flow by the two methods
are similar in the dry season, but the lower limit by the Tennant method is much lower
than that by the T-FDC method in flood season. This is because the water volume changes
drastically in flood season, which is prone to inducing extreme flow events, causing the
mean value to deviate from the overall distribution and thus leading to a wide range of
variations in the optimal environmental flow through applying the Tennant method. Thus,
the T-FDC method proves more scientific and reasonable than the Tennant method for the
ecosystem management in the Wujiang River.
5. Conclusions
This paper studied the development of environmental flow management objectives
in the Wujiang River, with the most fundamental problems of the traditional hydrological
methods pertinent to the subject analyzed. In an effort to address the problems thereof, a
T-FDC method was proposed by combining the FDC method’s guarantee rate idea with
the Tennant method’s grading idea. The results show its effectiveness and feasibility:
1.
The T-FDC method is well applicable in the Wujiang River, showing monthly variabil-
ity and spatial transferability, excluding the influence of extreme wet or dry events.
Furthermore, the basic environmental flow process obtained through this method is
stable, ranging between the historical minimum and the second minimum monthly
average flow. In contrast, the threshold width of the optimal environmental flow is
more reasonable than the Tennant method.
2.
Only the measured runoff data, which can be on any time scale, is needed as the input
required for the T-FDC method, which helps the handling of shortage for daily runoff
processes and eliminates errors caused by interpolation, effectively improving the
method’s adaptability.
3.
Regarding practical engineering management, the proposed T-FDC method im-
proved operability by reducing the number of environmental flow levels taken
into consideration.

Int. J. Environ. Res. Public Health 2022,19, 11615 11 of 18
Several improvements can be incorporated into our proposed method. First, although
the T-FDC method achieved successful application in the Wujiang River Basin, it is still
necessary to further explore the applicability to rivers with different hydraulic conditions
other than the Wujiang River and to evaluate the robustness, reproducibility, and spatial
portability of the method. In addition, the T-FDC method proposes not to distinguish the
interannual variation in wet and dry from the point of view of the operational simplicity of
practical management. It can potentially result in too high a standard in dry years, which is
challenging to operate in actuality and can moderately enhance the method’s adaptability
to synchronous wet/dry events.
Author Contributions:
Conceptualization, Z.D.; methodology, X.N.; validation, M.C.; formal anal-
ysis, W.J.; resources, Z.D.; data curation, H.Y.; writing—original draft preparation, X.N.; writing—
review and editing, W.X.; visualization, X.N. and S.W.; project administration, Z.D.; funding acquisi-
tion, Z.D. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the National Key Research & Development Project of China,
grant number 2016YFC0402209, and the China Scholarship Council.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data that support the findings of this study are available from the
corresponding author upon reasonable request.
Acknowledgments:
We would like to thank Zhuolin He of Water Resources Bureau of Qiannan
Prefecture, Guizhou Province, China for his assistance in providing some runoff data, and thank
Yong Jiang of UNESCO-IHE Institute for Water Education, Delft, The Netherlands for his comments
of this paper.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. Fitted FDC of Hongjiadu
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 12 of 19
and spatial portability of the method. In addition, the T-FDC method proposes not to
distinguish the interannual variation in wet and dry from the point of view of the opera-
tional simplicity of practical management. It can potentially result in too high a standard
in dry years, which is challenging to operate in actuality and can moderately enhance the
method’s adaptability to synchronous wet/dry events.
Author Contributions: Conceptualization, Z.D.; methodology, X.N.; validation, M.C.; formal
analysis, W.J.; resources, Z.D.; data curation, H.Y.; writing—original draft preparation, X.N.; writ-
ing—review and editing, W.X.; visualization, X.N. and S.W.; project administration, Z.D.; funding
acquisition, Z.D. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Key Research & Development Project of China,
grant number 2016YFC0402209, and the China Scholarship Council.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data that support the findings of this study are available from
the corresponding author upon reasonable request.
Acknowledgments: We would like to thank Zhuolin He of Water Resources Bureau of Qiannan
Prefecture, Guizhou Province, China for his assistance in providing some runoff data, and thank
Yong Jiang of UNESCO-IHE Institute for Water Education, Delft, The Netherlands for his com-
ments of this paper.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. Fitted FDC of Hongjiadu
Figure A1. Cont.

Int. J. Environ. Res. Public Health 2022,19, 11615 12 of 18
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 12 of 19
and spatial portability of the method. In addition, the T-FDC method proposes not to
distinguish the interannual variation in wet and dry from the point of view of the opera-
tional simplicity of practical management. It can potentially result in too high a standard
in dry years, which is challenging to operate in actuality and can moderately enhance the
method’s adaptability to synchronous wet/dry events.
Author Contributions: Conceptualization, Z.D.; methodology, X.N.; validation, M.C.; formal
analysis, W.J.; resources, Z.D.; data curation, H.Y.; writing—original draft preparation, X.N.; writ-
ing—review and editing, W.X.; visualization, X.N. and S.W.; project administration, Z.D.; funding
acquisition, Z.D. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Key Research & Development Project of China,
grant number 2016YFC0402209, and the China Scholarship Council.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data that support the findings of this study are available from
the corresponding author upon reasonable request.
Acknowledgments: We would like to thank Zhuolin He of Water Resources Bureau of Qiannan
Prefecture, Guizhou Province, China for his assistance in providing some runoff data, and thank
Yong Jiang of UNESCO-IHE Institute for Water Education, Delft, The Netherlands for his com-
ments of this paper.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A. Fitted FDC of Hongjiadu
Figure A1. Monthly fitted FDC of Hongjiadu section.
Table A1. Fit type and equation form of Hongjiadu section.
Month Fit Type Degree Equation Form
Numerator Denominator
January Polynomial 3f(x) = a1x3+a2x2+a3x+a4
February Power - f(x) = a1xa2+a3
March Power - f(x) = a1xa2+a3
April Rational 1 3 f(x) = a1x+a2
x3+a3x2+a4x+a5
May Polynomial 5f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
June Rational 3 3 f(x) = a1x3+a2x2+a3x+a4
x3+a5x2+a6x+a7
July Rational 4 2 f(x) = a1x4+a2x3+a3x2+a4x+a5
x2+a6x+a7
August Rational 0 3 f(x) = a1
x3+a2x2+a3x+a4
September Polynomial 4f(x) = a1x4+a2x3+a3x2+a4x+a5
October Polynomial 4f(x) = a1x4+a2x3+a3x2+a4x+a5
November Polynomial 3f(x) = a1x3+a2x2+a3x+a4
December Polynomial 5f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
Table A2. Specific parameters of Hongjiadu section.
Month a1a2a3a4a5a6a7R2
January −66.96 134 −107.1 78.25 - - - 0.981
February 82.21 −0.1915 −47.76 - - - - 0.988
March −43.62 0.5355 70.87 - - - - 0.991
April 19.39 9.285 −0.2621 0.42 0.05906 0.982
May −4990 11,720 −9801 3562 −811.8 308.4 - 0.993
June −83.85 269 −154.4 30.21 −0.4225 −0.05657 0.04252 0.995
July 112.7 −488.5 599 −137.6 13.11 −0.2484 0.02413 0.992
August 39.36 −1.019 0.5199 0.04017 - - - 0.974
September 3608 −9135 7943 −3007 664.3 - - 0.973
October −360.1 575.9 −219.9 −192.2 247.7 - - 0.993
November −285.8 453.8 −261.1 141.5 - - - 0.976
December −1.284 1.546 −2.555 −0.1121 −2.637 61 - 0.980

Int. J. Environ. Res. Public Health 2022,19, 11615 13 of 18
Appendix B. Fitted FDC of Wujiangdu
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 14 of 19
Appendix B. Fitted FDC of Wujiangdu
Figure A2. Monthly fitted FDC of Wujiangdu section.
Table A3. Fit type and equation form of Wujiangdu section.
Month Fit Type Degree Equation Form
Numerator Denominator
January Polynomial 4
()
432
12345
f x ax ax ax ax a=++++
February Rational 1 5
()
1
5432
2345
6
ax
fx xaxaxaxaxa
=+++++
March Power - -
()
2
13
a
fx ax a=+
April Polynomial 6
()
6
65432
12345
f
xaxaxaxaxaxax
a
=++++++
May Polynomial 4
()
432
12345
f x ax ax ax ax a=++++
June Polynomial 5
()
6
5432
1234 5
f
xaxaxaxaxaxa=+++++
July Polynomial 4
()
432
12345
f x ax ax ax ax a=++++
August Polynomial 5
()
6
5432
1234 5
f
xaxaxaxaxaxa=+ ++ ++
September Polynomial 4
()
432
12345
f
xaxaxaxaxa=++++
October Polynomial 5
()
6
5432
1234 5
f
xaxaxaxaxaxa=+++++
November Polynomial 4
()
432
12345
f x ax ax ax ax a=++++
December Polynomial 4
()
432
12345
f
xaxaxaxaxa=++++
Figure A2. Monthly fitted FDC of Wujiangdu section.
Table A3. Fit type and equation form of Wujiangdu section.
Month Fit Type Degree Equation Form
Numerator Denominator
January Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
February Rational 1 5 f(x) = a1x
x5+a2x4+a3x3+a4x2+a5x+a6
March Power - - f(x) = a1xa2+a3
April Polynomial 6 f(x) = a1x6+a2x5+a3x4+a4x3+a5x2+a6x+a7
May Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
June Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
July Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
August Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
September Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
October Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
November Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
December Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5

Int. J. Environ. Res. Public Health 2022,19, 11615 14 of 18
Table A4. Specific parameters of Wujiangdu section.
Month a1a2a3a4a5a6a7R2
January −667.7 1212 −679.2 −16.14 235.8 - - 0.996
February −4.157 5.794 −2.738 2.771 −1.279 0.2573 0.00839 0.997
March 678.8 −0.09016 −580.3 - - - - 0.985
April 35,450 −126,600 175,600 −118,600 40,140 −6766 820.6 0.997
May 4667 −11,000 8890 −3498 1161 - - 0.984
June −58,890 158,000 −152,900 64,400 −12,720 2448 - 0.983
July −1131 2057 −865.1 −1479 1748 - - 0.991
August −22,210 71,200 −84,760 46,120 −12,310 2209 - 0.986
September 203.2 −4012 6658 −4322 1623 - - 0.950
October −3179 10,900 −12,690 6022 −1683 863.9 - 0.990
November 1796 −4439 3435 −1155 477.3 - - 0.987
December 986.5 −3174 3176 −1342 418.7 - - 0.978
Appendix C. Fitted FDC of Sinan
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 15 of 19
Table A4. Specific parameters of Wujiangdu section.
Month a1 a2 a3 a4 a5 a6 a7 R
2
January −667.7 1212 −679.2 −16.14 235.8 - - 0.996
February −4.157 5.794 −2.738 2.771 −1.279 0.2573 0.00839 0.997
March 678.8 −0.09016 −580.3 - - - - 0.985
April 35,450 −126,600 175,600 −118,600 40,140 −6766 820.6 0.997
May 4667 −11,000 8890 −3498 1161 - - 0.984
June −58,890 158,000 −152,900 64,400 −12,720 2448 - 0.983
July −1131 2057 −865.1 −1479 1748 - - 0.991
August −22,210 71,200 −84,760 46,120 −12,310 2209 - 0.986
September 203.2 −4012 6658 −4322 1623 - - 0.950
October −3179 10,900 −12,690 6022 −1683 863.9 - 0.990
November 1796 −4439 3435 −1155 477.3 - - 0.987
December 986.5 −3174 3176 −1342 418.7 - - 0.978
Appendix C. Fitted FDC of Sinan
Figure A3. Monthly fitted FDC of Sinan section.
Figure A3. Monthly fitted FDC of Sinan section.

Int. J. Environ. Res. Public Health 2022,19, 11615 15 of 18
Table A5. Fit type and equation form of Sinan section.
Month Fit Type Degree Equation Form
Numerator Denominator
January Rational 2 5 f(x) = a1x2+a2x+a3
x5+a4x4+a5x3+a6x2+a7x+a8
February Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
March Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
April Rational 0 3 f(x) = a1
x3+a2x2+a3x+a4
May Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
June Polynomial 6 f(x) = a1x6+a2x5+a3x4+a4x3+a5x2+a6x+a7
July Polynomial 3 f(x) = a1x3+a2x2+a3x+a4
August Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
September Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
October Polynomial 3 f(x) = a1x3+a2x2+a3x+a4
November Power - f(x) = a1xa2+a3
December Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
Table A6. Specific parameters of Sinan section.
Month a1a2a3a4a5a6a7a8R2
January −0.2816 8.041 1.938 −2.172 1.72 −0.5942 0.1184 0.00016 0.997
February 424.3 −1850 2446 −1434 572.1 - - - 0.964
March −16,530 45,480 −46,880 22,300 −5048 752.7 - - 0.973
April 82.98 −1.086 0.4871 0.04298 - - - - 0.992
May −40,600 95,210 −79,690 28,900 −5878 2189 - - 0.992
June 82,660 −337,800 535,300 −411,700 157,400 −29,970 5020 0.988
July 2342 −3297 −1178 2777 - - - - 0.986
August −27,420 70,330 −65,500 26,930 −6627 2396 - - 0.982
September
−49,260 122,600 −115,100 52,050 −13,160 2802 - - 0.994
October −1890 3371 −2837 1637 - - - - 0.987
November
−673.4 1.43 871.6 - - - - - 0.996
December −13,120 32,160 −30,790 14,670 −3779 808.4 - - 0.989
Appendix D. Fitted FDC of Wulong
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 17 of 19
Appendix D. Fitted FDC of Wulong
Figure A4. Monthly fitted FDC of Wulong section.
Table A7. Fit type and equation form of Wulong section.
Month
Fit Type
Degree
Equation Form
Numerator
Denominator
January
Rational
0
3
( )
1
32
2 3 4
a
fx x a x a x a
=+ + +
February
Polynomial
3
( )
32
1 2 3 4
f x a x a x a x a= + + +
March
Polynomial
4
( )
4 3 2
1 2 3 4 5
f x a x a x a x a x a= + + + +
April
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
May
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
June
Rational
2
3
( )
2
1 2 3
32
4 5 6 7
a x a x a
fx a x a x a x a
++
=+ + +
July
Power
-
( )
2
13
a
f x a x a=+
August
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
September
Polynomial
6
( )
6
6 5 4 3 2
1 2 3 4 5 7
f x a x a x a x a x a x a x a= + + + + + +
October
Power
-
( )
2
13
a
f x a x a=+
November
Rational
0
3
( )
1
32
2 3 4
a
fx x a x a x a
=+ + +
Figure A4. Cont.

Int. J. Environ. Res. Public Health 2022,19, 11615 16 of 18
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW 17 of 19
Appendix D. Fitted FDC of Wulong
Figure A4. Monthly fitted FDC of Wulong section.
Table A7. Fit type and equation form of Wulong section.
Month
Fit Type
Degree
Equation Form
Numerator
Denominator
January
Rational
0
3
( )
1
32
2 3 4
a
fx x a x a x a
=+ + +
February
Polynomial
3
( )
32
1 2 3 4
f x a x a x a x a= + + +
March
Polynomial
4
( )
4 3 2
1 2 3 4 5
f x a x a x a x a x a= + + + +
April
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
May
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
June
Rational
2
3
( )
2
1 2 3
32
4 5 6 7
a x a x a
fx a x a x a x a
++
=+ + +
July
Power
-
( )
2
13
a
f x a x a=+
August
Polynomial
5
( )
6
5 4 3 2
1 2 3 4 5
f x a x a x a x a x a x a= + + + + +
September
Polynomial
6
( )
6
6 5 4 3 2
1 2 3 4 5 7
f x a x a x a x a x a x a x a= + + + + + +
October
Power
-
( )
2
13
a
f x a x a=+
November
Rational
0
3
( )
1
32
2 3 4
a
fx x a x a x a
=+ + +
Figure A4. Monthly fitted FDC of Wulong section.
Table A7. Fit type and equation form of Wulong section.
Month Fit Type Degree Equation Form
Numerator Denominator
January Rational 0 3 f(x) = a1
x3+a2x2+a3x+a4
February Polynomial 3 f(x) = a1x3+a2x2+a3x+a4
March Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
April Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
May Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
June Rational 2 3 f(x) = a1x2+a2x+a3
a4x3+a5x2+a6x+a7
July Power - f(x) = a1xa2+a3
August Polynomial 5 f(x) = a1x5+a2x4+a3x3+a4x2+a5x+a6
September Polynomial 6 f(x) = a1x6+a2x5+a3x4+a4x3+a5x2+a6x+a7
October Power - f(x) = a1xa2+a3
November Rational 0 3 f(x) = a1
x3+a2x2+a3x+a4
December Polynomial 4 f(x) = a1x4+a2x3+a3x2+a4x+a5
Table A8. Specific parameters of Wulong section.
Month a1a2a3a4a5a6a7R2
January 142.2 −1.399 0.8248 0.1555 - - - 0.978
February −1413 2721 −1904 856.6 - - - 0.987
March 5427 −14,370 13,500 −5629 1390 - - 0.984
April −118,500 317,500 −320,100 150,100 −33,660 4504 - 0.992
May −24,740 44,050 −25,890 7044 −3954 3992 - 0.997
June 3239 −3426 960.5 −0.5323 −0.2408 0.1435 - 0.995
July −5084 0.7955 5980 - - - - 0.993
August −107,600 274,200 −262,600 121,300 −31,520 6044 - 0.988
September −198,300 547,900 −541,700 214,700 −16,700 −10,460 4526 0.997
October −2962 0.4657 3661 - - - - 0.986
November 312.7 −0.6969 0.3614 0.1564 - - - 0.993
December 2364 −7650 8070 −3784 1206 - - 0.976
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