Analysis of Channel Leakage Law in Piedmont Plain of Haihe River

Basin

Jingsi Zhu

, Zhe Wang

, Tianyu Hou

* and Yu Li

Hydrology Bureau of Haihe River Water Conservancy Commission, MWR, Tianjin 300170, China

Tianjin Meteorological Bureau, TianJin 300000, China

Keywords:

Initial loss rate, Leakage loss, Leakage rate per unit river length

Abstract:

The channel leakage loss of piedmont plain in north China directly affects the flood evolution law and

ecological water diversion, especially in Haihe River Basin. The essay selected three typical river reaches of

the basin to analyze the leakage loss of the historical flood processes using statistical method, studying the

correlation between the leakage rate per unit river length and the upstream inflow, and the duration of flood

under different water storage conditions. Meanwhile, the initial leakage loss rate of flood with different

magnitude in each typical reach was estimated. The study results indicated: (1)The upstream inflow is

negatively correlated with the leakage rate per unit river length; the leakage rate per unit river length tends to

be stable when the upstream inflow increases to a certain value; (2)The duration of flood is negatively

correlated with the leakage rate per unit river length when there is bottom water; (3)The degree of dryness in

the early stage is one of the main factors affecting the seepage capacity; (4)The leakage rate per unit river

length is generally logarithmic or exponential related to the upstream inflow; (5)In Haihe River Basin, the

initial loss rate of medium and small water in typical reach is higher, more than 30%, and the initial loss rate

of large water is lower than that of medium and small water.

1 FOREWORD

The mutual conversion of surface water and

groundwater is a common natural phenomenon in

nature. The interaction between surface water and

groundwater has been regarded as one of the most

important and frontier research topics by the major

hydrology and water resources research institutions in

the world. Channel leakage is an important aspect of

surface water and groundwater exchange. The Haihe

River Basin (in north China) is semi - humid semi -

arid climate zone. There are many seasonal rivers in

the basin. The rivers are often dry up in the

discontinuous season. The basin has been in the

background of less rain since the "1996.08" flood, and

parts of the river have dried up for years. Therefore,

the flood leakage loss is large during the flood

routing, which changes the flood evolution process

and law under the natural state. Especially, the plain

channel leakage loss leads to prolonged flood

propagation time and significant increase of peak

clipping rate (Yu et al., 2017). Meanwhile, river

seepage is one of the important sources of

groundwater resources. Studying the law of channel

leakage loss in plain is of great significance for flood

evolution, ecological water diversion and

groundwater recharge. The research results provided

a basis for flood forecasting and management,

ecological water replenishment and other important

decisions.

At present, the research on channel leakage loss

estimation and simulation has achieved some

achievements. Boroughs & Abt (2003) evaluated

losses of river flows due to evaporation, seepage, and

transpiration, and empirical seasonal functions were

developed to relate flow loss to the flow rate in the

river. Grebenyukov (2002) choosed optimal

hydrogeological models for calculating seepage losses

from channels and rivers based on data of observations

performed in some parts of Kazakhstan. Yu, Ma, &

Fan (2017) summarized the research progress in the

simulation and calculation of channel leakage. Zhang,

Yan, & Cui (2002)

analyzed the correlation between

the upstream water, the recharge coefficient of river

infiltration and the loss rate of channel leakage in the

Hebei plain. Lu (2009) analyzed the channel seepage

characteristics using statistical method in piedmont

plain of Hebei province.

196

Zhu, J., Wang, Z., Hou, T. and Li, Y.

Analysis of Channel Leakage Law in Piedmont Plain of Haihe River Basin.

In Proceedings of the 7th International Conference on Water Resource and Environment (WRE 2021), pages 196-203

ISBN: 978-989-758-560-9; ISSN: 1755-1315

Currently, hydraulic models or statistical analysis

are mainly methods used in the research of channel

leakage. But the hydraulic model is often hard to meet

the dual requirements of time and accuracy in the

actual flood prediction, evaluation of river recharge

groundwater, etc. This paper emphasized on the deep

integration of scientific research and practice.

Therefore, the statistical method was used to analyze

the leakage loss of typical river reaches in this paper.

This paper calculated the leakage loss per unit river

length, researched the correlation of the leakage rate

of unit river length and the upstream inflow, the

duration of flood under different water storage

conditions. Meanwhile, the initial leakage loss rate of

flood with different magnitude was estimated. The

research result was directly applied in the practical

work including flood prediction, evaluation of river

recharge groundwater. The flow chart is as follows

(Figure 1):

Figure 1: Flowchart.

2 CALCULATION METHOD AND

DATAUM

2.1 Calculation Method

During the evolution of a flood, the water loss

includes phreatic evaporation, vadose infiltration, and

leakage. Due to the small proportion of evaporation

and vadose infiltration in the process of flood

evolution, they are ignored in the analysis of water

loss. The channel leakage is expressed by the leakage

rate per unit river length. When the leakage rate per

unit river length is constant, the downstream section

flow is calculated using the upstream section inflow

and the leakage rate per unit river length (Eq. 1)

(Zhang et al., 2002).

(1 )





(1)

In the formula:

—the upstream inflow, Billion

cubic meters;

—the downstream inflow, Billion

cubic meters;



—the leakage rate of unit river

length, ‰; L——length of the river, km.

The calculation formula of leakage rate per unit

river length is (Eq. 2) :

1( )





(2)

2.2 Datum

The typical river reach should meet the following

requirements:

(1) Representation of reaches. The interval inflow

in typical river reach is negligible.

(2) Integrity of datum. The data series is long, and

there are several years of flood processes.

(3) Applicability of results. The typical reach of

different rivers was compared to analyze the common

law of leakage loss under different underlying surface

conditions.

Based on the above principles, this paper selected

three typical river reaches in the Haihe River Basin.

Yuecheng Reservoir~Caixiaozhuang located in

Zhanghe River, Huangbizhuang Reservoir~

Beizhongshan located in Hutuo River, Xinle ~

Beiguocun located in Sha River. The positions of the

three typical river reach in the Haihe River Basin are

shown in Figure 2.

The three river reaches are all located in areas

where human activities are concentrated. In recent

years, due to the influence of upstream water

diversion and impoundment projects, the inflow of

Analysis of Channel Leakage Law in Piedmont Plain of Haihe River Basin

197

the river reach has decreased sharply, leading to the

increased number of cut off days. All three reaches

are wide and shallow sandy beds. The basic

information and datum of the three reaches are shown

in Table 1.

Figure 2: Locations of typical river reaches.

Table 1: The basic information and datum of the reaches.

The serial number The name of reach

The length of

reach/km

Data time

Quantity of

data/

rou

Yuecheng Reservoir ~

Caixiaozhuang

76 1967-2016 21

Huangbizhuang Reservoir~

Beizhongshan

110 1963-2018 15

3 Xinle ~ Beiguocun 55 1965-2013 16

3 ANALYSIS OF LEAKAGE LAW

3.1 Law of Leakage Loss Per Unit

River Length

The main factors affecting the leakage rate of unit

river length are: the water storage conditions of the

channel before flood, the lithology of the riverbed, the

size of the inflow, the duration of the flood, and the

hydraulic conditions (Qin, 1989; Sun et al., 2010).

The water storage conditions of the channel before

flood includes bottom water and bottomless water.

The channel leakage loss with bottomless water

includes initial leakage loss and steady leakage loss.

The channel leakage loss with bottom water is steady

leakage loss. In this paper, the correlation analysis

between the upstream inflow, the duration of flood

and the leakage rate per unit river length is carried out

respectively under the condition of bottom water and

bottomless water. Figure 3 is correlation diagram of

upstream inflow and leakage rate per unit river length

in three typical river reaches. Figure 4 is correlation

diagram of the flood duration and leakage rate per

unit river length in three typical river reaches.

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198

(a) Yuecheng Reservoir ~ Caixiaozhuang located in

Zhanghe River

(b) Huangbizhuang Reservoir~ Beizhongshan

located in Hutuo River

Figure 3: Correlation diagram of upstream inflow and

leakage rate per unit river length.

(a) Yuecheng Reservoir ~ Caixiaozhuang located in

Zhanghe River

(b) Huangbizhuang Reservoir ~ Beizhongshan

located in Hutuo River

(c)

Xinle ~ Beiguocun located in Sha River

Figure 4: Correlation diagram of the flood duration and

leakage rate per unit river length.

From Figure 3 and Figure 4:

(1) The upstream inflow is negatively correlated

with the leakage rate per unit river length. The

leakage rate per unit river length tends to be stable

when the upstream inflow increases to a certain value.

Generally, the leakage loss is greater with the

increase of upstream inflow. But the relationship

between inflow and leakage rate is not the case(Lu,

S.Y.,2009). There is a significant negative correlation

between upstream inflow and leakage rate per unit

river length under the conditions of bottom water and

bottomless water. With the increase of upstream

inflow, the leakage rate per unit river length decreases

gradually. The leakage rate per unit river length tends

to be stable when the upstream inflow increases to a

certain value, which indicated that the channel

leakage rate is close to the leakage capacity.

Therefore, channel leakage has a greater impact on

the evolution of small-sized and medium-sized

floods, but less impact on the evolution of large

floods. The lower the inflow of upper section is, the

higher the leakage rate is, while the inflow decreases

along the river, so the leakage rate of the same reach

length increases along the river.

(2) The leakage rate per unit river length of

bottomless water is obviously higher than that of

bottom water.

Analysis of Channel Leakage Law in Piedmont Plain of Haihe River Basin

199

When there is bottomless water, the initial

seepage loss of the channel occurs before the steady

seepage loss. Under the present condition, the dry

period of most river channels is long in the Haihe

River basin. Even if the inflow is consistent with the

inflow of historical floods, the leakage is generally

higher than the historical situation.

(3) There is a negative correlation between flood

duration and leakage rate per unit river length when

there is bottom water.

The longer the flood duration is, the more

interaction between flood and channel is, but the

water-bearing strata tend to be saturated gradually.

When there is bottom water, the leakage rate per unit

length of three typical river reaches decreases with

the increase of flood duration. This indicates that,

under the condition of bottom water, the soil moisture

content tends to be saturated and the river infiltration

capacity decreases with the increase of time. When

there is bottomless water, the data points are

relatively scattered, without obvious correlation trend.

This is due to the previous dry channel. The thickness

of the underlying soil aeration zone was different,

leading to different water storage capacity and

different initial infiltration loss in the river basin.

Therefore, when there is bottomless water, there is no

obvious correlation between leakage rate per unit

river length and flood duration.

(4) The degree of river dryness is one of the main

factors affecting the seepage capacity.

The seepage capacity of the three typical reaches

is different due to the respectively underlying surface

conditions and early water storage conditions. Figure

5 shows the comparison of the leakage rate per unit

length of three typical river reaches when there is

bottomless water. Under the condition of bottomless

water, the leakage rate of unit river length in

Huangbizhuang~Beizhongshan and

Xinle~Beiguocun is obviously higher than that in

Yuecheng reservoir~Caixiaozhuang when the

upstream inflow is constant. This was mainly because

there were many floods in Yuecheng

Reservoir~Caixiaozhuang in recent 20 years, while

there were only one or two floods in the other two

typical river reaches. The dry period of the channel is

long, so the leakage capacity is large. It indicates that

the degree of river dryness is one of the main factors

affecting the seepage capacity.

Figure 5: The comparison of the leakage rate per unit length

with bottomless water.

3.2 Channel Leakage Equation

Through the optimal curve fitting, the calculation

formulas of leakage rate per unit length of three river

reaches are:

1.Yuecheng Reservoir ~ Caixiaozhuang

3.21ln( ) 0.742



 

bottomless water (3)

1.13ln( ) 0.195



 

bottom water (4)

2. Huangbizhuang Reservoir~ Beizhongshan

0.114

27.29







bottomless water (5)

0.51n( ) 0.198



 

bottom water (6)

3.Xinle ~ Beiguocun

31n( ) 1.561



 

bottomless water (7)

1.91n( ) 0.689



 

bottom water (8)

and



has the same meaning as Formula

(1).

From the above formulas, it can be seen that the

leakage rate per unit river length is generally

logarithmic or exponential related to the upstream

inflow. Bigger R

is regarded as the criteria of optimal

curve fitting when selecting logarithmic or

exponential equations. When the upstream inflow is

known, the leakage rate per unit river length in the

case of either bottom water or bottomless water can

be calculated by using formulas (3) ~ (8), and then the

downstream inflow can be further estimated by using

formula (1).

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200

4 ESTIMATION OF INITIAL

LOSS RATE

The dry period of most rivers is long in Haihe River

Basin, so it is difficult to estimate the initial leakage

loss of the first flood in each year. Therefore, this

paper analyzed the characteristics of the initial loss

rate with different magnitude floods, to provide

reference for flood prediction and groundwater

recharge evaluation. When there is bottomless water,

the channel leakage loss includes initial seepage loss

and steady seepage loss. When there is bottom water,

the channel leakage loss is steady seepage loss. The

estimation method is as follows:

(1) Calculate the steady seepage loss rate. The

ratio of the loss of bottom water process to the

duration of flood was used as the average steady

permeability rate.

(2) Calculate the steady seepage loss. The steady

seepage loss in bottomless water process is obtained

by multiplying the average steady seepage rate by the

steady seepage duration. In recent years, local

rainstorms are frequent in Haihe River Basin, and the

runoff generation mode is mostly mixed runoff.

Therefore, the steady seepage time of bottomless

water process is approximated by the total flood

duration.

(3) Calculate the initial loss. The initial loss is

obtained by deducting the steady seepage loss from

the total loss of the bottomless water process.

(4) Calculate the initial loss rate. The initial loss

rate is the ratio of initial loss to upstream inflow.

The steady infiltration rate of Yuecheng

Reservoir~Caixiaozhuang was calculated by five

floods with bottom water since 1982, which was

0.011 million m

/d. The Huangbizhuang

Reservoir~Beizhongshan adopted three floods with

bottom water since 1964, and the steady infiltration

rate was 0.012 million m

/d. The Xinle~Beiguocun

used ten floods with bottom water since 1970, and the

steady infiltration rate was 0.007 million m

/d. The

calculation results of initial loss rate were shown in

Table 2~Table 4.

The initial loss rate of medium and small water

(upstream inflow less than 150 million m

) in the

Yuecheng Reservoir~Caixiaozhuang is 30%~50%,

which concentrated in 30%~40%. The initial loss rate

of large water is 10%~25%.

The initial loss rate of medium and small water

(upstream inflow less than 100 million m

) in

Huangbizhuang Reservoir~Beizhongshan ranges

from 50% to 80%, which concentrated in 60% to 80%.

The initial loss rate of large water is 20%~30%.

Table 2: The calculation results of initial loss rate in Yuecheng Reservoir~Caixiaozhuang.

Unit: The amount of water-billion cubic meters; Duration—day.

Number

Time

Flood

duration

Upstream

inflow

Downstream

flow

The initial

loss

The initial

loss rate/%

Yea

Month and Date

1 1969 6.15-7.10 26 1.54 1.11 0.15 9

2 1970 6.18-6.25 9 1.88 1.49 0.29 16

3 1988 8.11-8.17 7 1.79 1.28 0.43 24

4 1996 8.3-8.21 17 7.92 6.72 1.01 13

5 2001 7.3-7.8 6 0.33 0.16 0.10 32

6 2006 4.9-4.15 7 0.82 0.43 0.31 38

7 2008 6.2-6.20 19 1.25 0.66 0.38 30

8 2012 8.2-8.9 8 0.60 0.23 0.28 47

9 2013 7.17-8.1 16 2.31 1.70 0.43 19

10 2016 7.23-8.10 19 2.47 1.68 0.58 24

Table 3: The calculation results of initial loss rate in Huangbizhuang Reservoir~ Beizhongshan.

Unit: The amount of water-billion cubic meters; Duration-day.

Number

Time

Flood

duration

Upstream

inflow

Downstream

flow

The initial

loss

The initial

loss rate/%

Yea

Month and Date

1 1970 4.20-6.2 44 5.53 1.2 3.80 69

2 1971 3.15-5.30 77 7.34 1.85 4.57 62

3 1977 5.30-10.1 125 14.64 10.18 2.96 20

4 1978 9.23-10.21 29 1.65 0.18 1.12 68

5 1979 7.7-10.14 100 6.98 2.06 3.72 53

6 1991 6.29-7.24 26 4.12 0.54 3.27 79

Analysis of Channel Leakage Law in Piedmont Plain of Haihe River Basin

201

7 1996 8.3-9.2 31 22.31 16.18 5.76 26

8 1996 9.4-10.20 47 9.84 4.09 5.19 53

9 1997 4.22-5.16 25 2.76 0.13 2.33 84

10 2016 7.20-8.10 21 4.70 0.67 3.78 80

Table 4: The calculation results of initial loss rate in Xinle ~ Beiguocun.

Unit: The amount of water-billion cubic meters; Duration-day.

Number

Time

Flood

duration

Upstream

inflow

Downstream

flow

The initial

loss

The initial

loss rate/%

Yea

Month and Date

1 1965 7.26-8.7 13 0.17 0.07 0.08 46

2 1968 7.18-8.13 44 0.41 0.18 0.15 36

3 1978 5.25-6.16 23 15.49 9.44 6.00 38

4 1979 10.3-10.21 19 8.31 5.43 2.84 33

5 1988 8.3-9.8 33 8.29 4.94 3.29 38

6 1990 7.29-8.10 13 0.59 0.25 0.32 43

7 2013 7.11-7.19 9 0.24 0.05 0.17 53

The initial loss rate of medium and small water

(upstream inflow less than 100 million m

) in

Xinle~Beiguocun is 35%~55%, which concentrated

in 40%~50%. The initial loss rate of large water is

30%~40%.

The initial loss rate of medium and small water in

each reach is higher, more than 30%, and the initial

loss rate of large water is lower than that of medium

and small water. In Yuecheng~Caixiaozhuang

section, the initial loss rate of all-range water is lower

than that of the other two typical sections. The initial

loss rate of medium and small water in

Huangbizhuang reservoir~Beizhongshan is higher

than that in Xinle~Beiguocun, while that of large

water is lower than that in Xinle~Beiguocun.

5 CONCLUSIONS

In North China (Haihe River Basin as an example):

(1) The upstream inflow is negatively correlated

with the leakage rate per unit river length, and when

the upstream inflow increases to a certain value, the

leakage rate per unit river length tends to be stable; he

leakage loss rate increases along the river course.

There is a negative correlation between water

duration and leakage rate per unit river length when

there is bottom water.

(2) The dryness degree of river channel is one of

the main factors affecting the seepage capacity.

(3) The leakage rate per unit river length is

generally logarithmic or exponential related to the

upstream inflow. Through the optimal curve fitting,

the formula for calculating the leakage rate per unit

length of each typical reach is obtained by given

upstream inflow.

(4) The initial loss rate of medium and small water

in each typical reach is higher, more than 30%, and

the initial loss rate of large water is lower than that of

medium and small water.

This study has innovatively put forward the law of

channel leakage in North China (Haihe River Basin

as an example). The research results have strong

practicability and could really guide the practical

work including flood prediction, evaluation of river

recharge groundwater, etc.

ACKNOWLEDGEMENT

This work was supported by the National Key R&D

Program of China (Grant No., 2018YFE0106500).

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