(1)
Liu Yuelan and Li Shongheng
Institute of Hydraulic Research ,
Yellow River Conservation Commission, 450003,Zhengzhou, China, Tel.
(0371)6305443
Abstract: Flood disaster in the Lower Yellow River was the misery of China. Since the founding of the People’s Republic of China, the Lower Yellow River has not breached its embankment during flood season for 50 years consecutively. Besides the significant effect of enhancing flood control projects, flood forecasting and prediction have played an important role. This paper summarized the problems encountered when the hydrodynamic mathematical model is applied to the Yellow River, and the approaches taken for solving those problems. Special attentions are paid to the characteristics of the Yellow River when deal with the characterization of channel cross section, roughness of the channel and the flood plain, exchange of water between channel and the flood plain, and sediment deposition and scouring. Some updated research results are also adopted in this paper. A good agreement is found between the computed results and the field measurements.
Keywords: Lower Yellow River, hydrodynamic mathematical model, flood routing and flood stage prediction
1 INTRODUCTION
Based upon channel patterns and the characteristics of sediment deposition and scouring of the Lower Yellow River, a hydrodynamic mathematical model is established. This is a one-dimensional, non-equilibrium sediment transport, and non-steady flow model. Channel cross section is considered as compound sections. The model was calibrated on flood routing and flood stage prediction using the reach from HUAYANKOU to SHUNKOU.
Difficulties encountered in computing the
propagation of peak flow of flood in the Lower Yellow River lie in the compound
channel cross section (see Figure 1). The secondary flood plains (which have
less probability of being inundated) have large transverse bed slopes. Their
topographical conditions and the characteristics of roughness differ greatly
from the channel. Thus, the flood plains have significant impact on the
deformation of peak flow propagation. In establishing this model, the cross
section is divided into portions such as main channel, primary bars, secondary
flood plains, and the lips of the secondary flood plains (Figure 1). Special
treatments were given to the transverse exchanges of water and sediment between
the secondary flood plain and the main channel.
Prediction of flood stage in the Lower Yellow River is more difficult than it is in any other river. This is mainly due to the quick and large magnitude changes of deposition and erosion in the com-pound section during flood peak. During large flood, intensive scouring causes the main channel degraded rapidly. As a result, water stage at equivalent discharge reduces noticeably. During hyper-concentrated flood, flood plain rises quickly owing to massive deposition and the channel is narrowed. Extremely high water stage occurs often during middle size flood. To reflect the channel deformation more accurately, influences of sediment concentration and sediment composition on flow characters are considered besides using compound cross section. A sediment-carrying capacity formula which is suitable for the River is selected for the calculation of non-equilibrium sediment transport.
The four-point full implicit differential format was used to disperse the basic equations of flow and sediment. These equations were solved by non-coupling method.
The model was calibrated by several large floods occurred in recent years in the Lower Yellow River. Good agreements were observed between computed results and field measurements both for peak flow rates and flood stages along the river course.
2
CHANNEL CHARACTERISTICS AND THE CHARACTERIZATION OF CHANNEL CROSS SECTION
As described previously, the compound cross section includes the main channel, the primary bars and the secondary flood plain. Channel consists of the main channel and the primary bars. Since middle and small size floods are usually delivered by the channel, roughness of the primary bars and the main channel are very close. Topographical conditions of the secondary flood plain are complicated. Distinct lips have formed in the secondary flood plains after the implementation of river training works. The transverse slope is large. When water exceeds the lips of the flood plain, it flows towards the embankment of the river and then gathers at the low elevation areas near the embankment. Part of the gathered water is detained in pounds and the other part flows along the embankment. Since roughness and hydraulic factors in the flood plain and channel are different, the distribution of sediment deposition or erosion on the cross section differs. During large flood, deposition occurs in the flood plain and erosion occurs in the channel often.
Therefore, one-dimensional model is used. The early stage of flooding in the secondary flood plain is considered as the situation of water flowing over a broad-crested weir. When water stage in the flood plain exceeds the elevation of the lips of the flood plain, flow in the flood plain is routed together with the flow in the channel.
3 BASIC EQUATIONS
(1) Flow continuity equation
(1)
(2) Flow Momentum equation
(2)
(3) Sediment diffusion equation
(3)
(4) Bed deformation equation
(4)
(5) Sediment-carrying capacity equation
(5)
(5')
In
which,
is flow discharge, A is the area of flow cross section, B is the channel width,
is water stage,
is the lateral output discharge for unit length of channel, K is discharge
modules,
is the component of the lateral
velocity on the main stream direction,
is the area of deposition or
erosion over the cross section,
is the lateral sediment transport
rate, V, and h is the cross-sectional average velocity and water depth
respectively,
is the volumetric sediment
concentration of suspended load, S is the cross-sectional average sediment
concentration,
is the particle falling velocity
(in sediment-laden flow),
is KARMEN constant (for
sediment-laden flow),
is the specific gravity of
sediment,
is the specific gravity of the
sediment-laden flow,
is the mass density of sediment,
is the median diameter of bed
material,
is the coefficient of
recovery-saturation of suspended load, and
is the correction coefficient of the distributions of velocity, sediment
concentration, sediment-carrying capacity of the sub-section, respectively. They
are defined as follows:
(6)
(7)
(8)
(9)
Where j is the order of the sub-section (from 1 to n).
4 CHARACTERISTICS OF ROUGHNESS AND THE PROCESSING METHOD
Roughness
condition is required when solve equation (1) and (2) in flow computation.
Observed roughness in the Lower Yellow River is very small (0.01 or even
smaller). This is related mainly to
the situations of fine bed material, wide channel and shallow water depth. When
flood inundates the secondary flood plain, flow section is characterized by
approach described previously. The slopes of all the sub-sections are assumed to
be the same. Using measured flow parameters, the roughness of the main channel,
the primary bars and the secondary flood plain is calculated then. As shown in
Figure 2 the roughness of the main channel increases with the decrease of
. When
is greater than 10, roughness (
) is smaller than 0.01. Roughness of the primary bars is equal or slightly
larger than the roughness of the main channel.
Figure 3 shows the variation of roughness in the secondary flood plain. Clearly: (1) Roughness decreases with the increase of the inundation water depth during a single flood. Such a phenomenon is mainly induced from the surface roughness of the flood plain; (2) For different floods of different years, the inundation water depths vary largely. Roughness is large for flood with deep inundation water, especially at the beginning of inundation when water is impounded. The corresponding water depth is large, thus the roughness is large (may be larger than 0.1). This is closely related to the effects of water detention and storage (caused by topographical conditions) in the flood plain. During the intermittent and late periods of flood, pounds are filled up. Even water depths vary with different flood events, the roughness variations are reduced (about 0.02 to 0.05).
For different forming mechanism of the flood plain roughness, different treatments are employed in the model. At the beginning of flooding, lateral diversion of flow is calculated using formula for broad-crested weir. That is to consider the lip of flood plain and the opening site of the productive dike as broad-crested weirs. Calculation of roughness in the flood plain is avoid. Intake flow rate of the flood plain is controlled by the storage capacity below the elevation of lip or the opening site of the productive dike. When this storage is used, flow above the elevation of lip or the opening site of the productive dike is routed simultaneously with the flow in the main channel. At this stage, the variation of roughness in the flood plain reduces. Value of 0.03 is used in computation. When Manning’s equation is applied to each sub-section, the discharge modules of each sub-section and the whole cross section are as follows:
(10)
(11)
Discharge of each sub-section equals:
(12)
Water
depth (
) and the area (
) of the sub-section is a function of water stage (
). Thus,
, discharge module K and
in equation (2) can be obtained
using numerical method.
5 CHARACTERISTICS OF SEDIMENT TRANSPORT AND PROCESSING APPROACH
5.1 Problems of wash load
During flood season, flow in the Lower Yellow River has high sediment concentration. Suspended load is relatively fine. Sediment transport has the character of “more sediments are delivered if more sediments are supplied.” The mechanism for forming such a character lies in: (1) the non-equilibrium transport of bed material load during the adjustment of deposition and erosion along the channel; and (2) massive amount of wash load supplied from the basin. Wash load is related to basin supply. Under same flow conditions, the character of “more sediments are delivered if more sediments are supplied” applies to wash load. Sediment concentration is the most convenient index in calculating the transport of wash load. Equation (5`) computes the sediment-carrying capacity of total suspended load which includes wash load. Sediment concentration is introduced through the sediment-carrying efficiency coefficient. In computation, sediment concentration at the entrance station is used for interested reach. In addition, when sediment concentration is low (less than 100 kg/m3) during a flood, the characteristics of flow are not affected largely by sediment concentration, neither does the dividing size between wash load and bed material. Wash load is deducted using a certain ratio, and only the carrying capacity of the bed material is calculated by using equation (5).
5.2 Influence of flow character on sediment transport
For flow with high sediment concentration, sediment-carrying capacity is related not only with the hydraulic factors but also with the character of sediment-laden flow. When using equation (5`) to calculate sediment-carrying capacity, or using equation (3) and (4) to calculate sediment concentration and channel deformation, flow characters such as viscosity and density shall be considered. The viscosity of the flow is affected not only by sediment concentration but also by the composition of suspended load. Changes of flow characters affect particle fall velocity and cause KARMEN constant and bed resistance to change. In turn, it affects the sediment-carrying capacity. To simplify the calculation, parameters of sediment-laden flow in equation (3) and (5) are computed as follows:
(13)
(14)
(15)
in
which
is the particle fall velocity in
clear water,
is median diameter of suspended
material,
=0.4,
is sediment concentration at the
entrance section of interested reach.
5.3 Distribution of sediment concentration over compound cross section
To calculate the deformation of each sub-section, sediment concentration and sediment-carrying capacity of each sub-section has to be known. Analysis of field measurements indicates that sediment concentration of each sub-section in the main channel is related to the flow intensity of that sub-section. That is
(16)
where
is an index less than unity. Flow
intensity is expressed by the sediment-carrying capacity equation (that is,
equation 5) as follows:
(17)
By the
definition of sectional sediment concentration,
(18)
Solve equation (16) and (18), one get
(19)
Equation (19) gives the distribution of sediment concentration on each sub-section in the main channel, the sediment concentration of intake flow of the flood plain equal the sediment concentration of the flood plain lips.
By substituting equation (18) and (19) into equation (7), (8) and (9), we have a2, a3, a4.
6 CALIBRATION BY OBSERVED FLOOD
Several large floods occurred in recent years are used for calibration.
6.1 Flood of August 1982
Flow discharge increased rapidly at HUAYANKOU
station for this flood. The peak flow rate was measured at 15300 m3/s
at this station which was the largest peak flow rate had observed since 1958.
Due to low inflow from the upper and middle reaches of the Yellow River during
70s and the effect of flood peak retaining by SANMENXIA reservoir, the flood
plains had less chance being inundated. In addition, productive dikes blocked
the passages for water entering into the flood plain. Thus, when channel and the
flood plain lips were elevated due to deposition, the flood plain enclosed by
the embankment
and the
productive dike was
low in
elevation (See Figure 1). With the
rising of water stage in the channel during large flood, productive dikes
are broken up for diverting flow. Since the flood plain has a large capacity in
detaining water, the effect of reducing flow rate is significant. During flood
falling period, the remaining productive dikes block the water from returning to
the channel. In turn, it slows down the flood propagation toward the downstream.
Once the productive dikes breach again, water remained in the flood plain will
gather and return to the main channel thus to form a late flood peak. The flood
hydrograph calculated by the model and the
measured values are illustrated
in Figure 4. As shown in Figure 4 the calculated
flow hydrograph for JIAHETAN station agrees with the measurements
basically. In GAOCHUN and SHUNKOU station the flood peak time calculated was
earlier than that measured significantly.
6.2 Flood of August 1992
This was a hyper-concentrated flood with medium discharge values. The peak flow rate at HUAYANKOU was 6350 m3/s and the maximum sediment concentration was 488 kg/m3. Water stages observed at some sections both at upper stream and downstream of HUAYANKOU were the highest ever in records even through the discharges were medium. Flood propagation time from HUAYANKOU to JIAHETAN increased from 14 hours as for ordinary flood to 30 hours for this particular flood event. To test the applicability of this model to hyper-concentrated flood, calibration calculations were performed for the river reach from HUAYANKOU to JIAHETAN. The results were given in Figure 5. Computed peak time for JIAHETAN station was earlier than it was observed and the peak flow rate was slightly larger than the value measured. This was mainly induced from the non-coupling method used in this model. That was to solve the flow variables first, and then to solve the sediment distribution and the bed deformation. As a result, the effects of massive sediment deposition both on water balance and flow rate reduction along the river were ignored. Figure 6 shows that the water stage-discharge curves calculated agree well with the stages measured at HUAYANKOU section. The highest water stages in history were observed during this flood. This model can simulate the stages well means that the calculation of bed deformation for hyper-concentrated flood is fairly reasonable.
References
[1] Wei, Zhilin, et al., “Hydrodynamic Mathematical Model for Flood Forecasting of the Lower Yellow River,” March, 1990.
[2] Zhang, Hongwu, and Zhang, Qing, “Sediment-carrying Capacity Formula of the Yellow River,” The People’s Yellow River, Nov. 1992.
[3] Liu, Yuelan, Han, Shaoga, and Wu, Zhi, “Computation Method for Aggredation and Degredation of the Lower Yellow River,” Sediment Research, Vol. 3, 1987.
[4] Liu, Yuelan, et al., “Treatment and Calculation of Several Key Problems in the Hydrodynamic Mathematical Model for Flood Forecasting of the Lower Yellow River,” August, 1994.
[5] Mahmood, K, and Yevevich, V, Unsteady Flow in Open Channels, Translated by Dr. Lin, Bingnan, Hydraulic and Electrical Press, 1987.
[6] Long, Yuqian, et al., “Verification of the Sediment-carrying Capacity Formula,” Technical Report, Institute of Hydraulic Research, the Yellow River Conservancy Commission, 1994.
Fig.3 Variation of roughness in the flood plain
Fig.4 Flood hydrograph (1982.8.1-7)
Fig.5 The flood hydrograph at JIAHETA
[1] The research in supported by National Natural Science Fund and Ministry of Water Resources in Program No.59890200