A STUDY OF THE FLOOD FORECASTING MODEL FOR THE WEST RIVER OF THE PEARL RIVER BASIN

Huang Guoru¹,  Wang  Linli²,   Hu Heping¹

¹ Department of Hydraulic Engineering, Tsinghua University, Beijing 100084,

China (86)-(010)-(62772158),  E-mail: huangguoru@263.net

² Water Resources Information Center, MWR, Beijing,100761, China

Abstract: This paper mainly presents a flood forecasting model of the West River of the Pearl River Basin. The model is made up of two parts based on the principles of flood forecasting for river-basin system. One is the rainfall-runoff model, and the other is the channel flood routing model. The rainfall-runoff is simulated using the NAM model, and it may be used for any type basin of the producing runoff. The channel flood routing is modeled by the diffusive wave difference method. The method has itself some forecast period based on the concept of the numerical dispersion of the difference solution to the linear kinematic wave equation simulating the physical dispersion of the diffusive wave in certain condition. Years of observed data are used to calibrate the model parameters, and other observed data is used for the model verification. Good results have been obtained in calibration and verification of the model. The model has been applied to the operational flood forecasting at the Wuzhou station.

 Keywords: river-basin system, rainfall-runoff, NAM model, channel flood routing, diffusive wave, kinematic wave

1    INTRODUCTION

In the practical flood forecasting, there are generally three types of flood forecasting problem. The first is the rainfall-runoff forecasting, the hydrograph at the basin outlet is forecasted based on rainfall distributed at the basin by using the theory of the runoff producing and flow consentration. The second is the channel flood routing, the hydrograph at the downstream boundary is modeled using the hydrograph at the upstream boundary at a channel by using the principle of the flood wave movement. The third is the river-basin flood forecasting. A basin may generally be subdivided into several subbasins without nesting each other according to the natural watershed, and the subbasins are connected with rivers. Firstly, rainfall- runoff for each subbasin is solved, then contributions made by each subbasin to the basin outlet hydrograph can be obtained using the channel flood routing and are summed to become the flood hydrograph at the basin outlet. The two aspects above mentioned constitute the thought of river-basin flood forecasting, and the method is based on the rainfall-runoff theory and the flood wave movement principle.

2    THE FLOOD FORECASTING MODEL

2.1    Rainfall-Runoff model

The rainfall-runoff theory and its calculation are always main research field in the hydrology, and the research object is mainly the hydrologic cycle among water, soil and plant and the basin runoff cycle. From 1960s, many basin hydrologic models have been applied at the practical flood forecasting(Zhao Renjun 1984). The NAM model, which was put forward in 1973 by the Denmark University of Science and technology, have been widely applied to many basins in Denmark.

The NAM model is a conceptual hydrologic model, and it simulates the rainfall-runoff producing process of the natural basin. In the model, the soil status in the hydrologic cycle is described as a series of simplification quantity using mathematics formula. The producing runoff and flow consentration are simulated using four layers storage locations, which are separately snow storage, surface storage, lower zone storage and groundwater storage.

The snow storage in the model is selective. While the air temperature reaches certain temperature that may make snow slushy, the snow runoff directly enters the surface storage. After precipitation including rainfall and slushy snow enters the surface storage, it is firstly used for the plant evaporation and the surface storage water. When the surface storage exceeds the surface storage capacity, the surplus water is assigned two parts, which one part produces the overland flow and another part is infiltration. The infiltration is again subdivided into two parts entering separately the lower zone storage and the groundwater storage. The interflow runoff is produced in the surface storage and it is calculated with two layers evapotranspiration model. The groundwater storage exchanges water with the lower zone storage by capillarity except producing the baseflow runoff.

The NAM model has several distinct characteristics. The model structure is relatively simple, main parameters have definite physical meaning and they are easy to calibrate. The every runoff component is computed using the simple linear relation. The parting of water source in the model is isochronous with the calculation of the runoff field, therefore, that accords with the natural principle of rainfall-runoff. 

2.2    Channel flood routing modle

We know that the diffusive wave may better simulate the flood wave movement in channel, therefore, many scientists always pay attention to the diffusive wave, and they achieve many famous routing methods including the analytical solution and the difference solution.

In 1969, Cunge firstly found that the numerical dispersion of the difference solution to the linear kinematic wave equation may simulate the physical dispersion of the diffusive wave in certain condition and achieved the known Muskingum-Cunge flood routing method (Cunge 1969). Based on the concept above mentioned, a new flood routing method is developed in this paper. The method not only may simulate the physical dispersion of the diffusive wave, but also it itself has some forecast period.

2.3    Foundation of the flood routing equation

The diffusive wave equation can be written as follow (Cunge 1969):

                           (1)

where  is discharge; , are separately the celerity and attenuation coefficient of the diffusive  wave;  is longitudinal coordinate;  is time. If the right diffusive term in Eq.(1) is omitted, Eq.(1) presents the kinematic wave equation:

                           (2)

In Eq.(2), the spatial derivative  is evaluated between the upstream and downstream section at time , and a new approach has been taken for the discretization of the time derivative , therefore, a difference equation may be obtained(Hoos 1989):

            (3)

where , is separately the spatial and time discretization index;  is weighting factor. The resulting explicit finite difference equation is given by:

                                 (4)

where ， ， ，are  the coefficients of the difference equation,  is the Courant number, .

It is apparent that making channel flood routing by the Eq.(4) has oneself one time step forecast period. Whereas Eq. (4) is the difference solution to the kinematic wave equation Eq.(2), and the present problem is whether it can be used for the flood routing for diffusive wave.  

2.4    The condition of the numerical dispersion simulating the physical dispersion

Replacement of Eq.(2) with Eq.(3) must result in the truncation error, using a Taylor-series expansion leads to truncation error :

           (4)

where  is second-order precision truncation error. Eq.(4) may be written simply as:

                        (5)

and  in Eq.(5) is first-order precision truncation error, and it can be obtained by Eq.(6)

                (6)

Eq.(5) is compared with the diffusive wave equation Eq.(1), the value in the parenthesis in Eq.(6) is considered as the numerical dispersion coefficient. Therefore, the physical dispersion of diffusive wave may be simulated by the numerical dispersion, namely:

                    (7)

then Eq.(5) may be rewritten as follow:

                  (8)

In Eq.(8), although Eq.(3) is a first-order approximation of the kinematic wave equation Eq.(2), it is shown that the Eq.(3) becomes a second-order approximation of the diffusive wave equation Eq.(1) subject to Eq.(7). In other words, the difference scheme not only may simulate the physical diffusion, but also can improve the solution precision to second-order. 

In Eq.(7), grouping terms containing  and simplifying as the condition of numerical dispersion simulating the physical diffusion:

                                   (9)

where  is the grid Peclet number, . To ensure that wave amplification does not occur (i.e.. that error or disturbances are damped or “diffused”), we set  in Eq.(7), yielding the stability condition(Rui Xiaofang 2000):

  ,  ,                        (10)

3    APPLICATION OF THE FLOOD FORECASTING MODEL

3.1    Case study area

The flood forecasting model developed in this paper was applied at a case study area from Jiangkou station to Wuzhou station of the Lower West River, a tributary of the Pearl River in the south of china. (Fig. 1). There are three tributaries in the area, Beiliu River, Meng River, and Gui River, treated as the lumped lateral inflow on the two banks of the channel. In addition, some uniformly distributed lateral inflow runs along the main channel and is not controlled by the hydrologic station.

The research is aimed at making discharge forecasting project at the Wuzhou station. The flood at the Wuzhou station come mainly from the upstream main channel inflow, three tributaries inflow and later inflow without controlled by hydrologic station. The main channel and three tributaries are all lumped inflow, and the lateral inflow is distributed inflow. Therefore, the flood forecasting model at the Wuzhou station is a flow calculation system made up of several lumped inflow and distributed inflow, including rainfall-runoff model and channel flood routing.

3.2    Calibration of the model parameters

The rainfall-runoff model for the case study area is developed based on the NAM model using  the Jinji basin and Taiping basin. The model may be displaced to other place without field data by hydrologic analogy method.  

The Jinji basin is located at the upper part of the Jinji station of the Beiliu River, the Taiping basin is located at the upper part of the Taiping station of the Meng River, and they have respectively nine and five precipitation stations uniformly distributed. There are ten flood events for each basin to calibrate the parameters, and the good results are all obtained.

The channel system is simplified in Fig. 2. The lateral inflow without controlled by hydrologic station is also main flood component in the Wuzhou station, consequently, the lateral inflow is calculated based on the NAM model using the hydrologic analogy method. The lateral inflow is simplified as the lumped inflow, its center of figure is placed at some position of the main channel(example 1/2 or 1/3 channel length), and the position is regarded as input point of the lumped inflow. Consequently, the hydrographs at Jiangkou, Jinji, Taiping, Shaoping station and the later inflow are all known regarding as the input of the channel routing model. They are separately routed to the basin outlet by the diffusive wave model, then are summed to become the hydrograph at the basin outlet.

The parameters in the model mainly include celerity and attenuation coefficient , and they may be obtained by the formula with the field hydrograph(Rui Xiaofang 1994). There are five flood events with less lateral inflow to calibrate the routing parameters, and the calibration precision is very high.

3.3    Verification forecasting

The verification process is separated into two parts. Firstly, the hydrographs at Jinji and Taiping station are computed with NAM model, and the hydrographs at the Shaoping station and the lateral inflow are calculated using the NAM model with the hydrologic analogy. Secondly, they are all regarded as the lumped inflow of the Wuzhou station, and the hydrographs are separately routed to the basin outlet, then are linearly summed to become to the hydrograph at the Wuzhou station.

The four flood events with more large lateral inflow are selected to verify the forecasting process, and the results are referenced at Tab. 1 and Fig. 3. It is obvious that the simulated precision of each flood event is very high. From another point of view, it proves that the NAM model is suitable to the case study area, the parameters in the NAM model can be displaced to other basin without hydrologic data, and the flood wave movement at the Lower West River satisfied the diffusive wave principle.

4    CONCLUSION

A new flood forecasting method of the West River of the Pearl River Basin was conducted based on the case study area situation and river characteristics. The forecasting system includes the rainfall-runoff model and channel flood routing model. The rainfall-runoff is simulated by the NAM model resulting good result. Therefore, the model is suitable and reliable for flood forecasting. The diffusive wave method with some forecast period is successfully applied to the flood routing at the Wuzhou station. It is proved that the flood forecasting project is successful by means of the simulation of many flood events.

References

[1]  Cunge J A(1969). On the subject of a flood propagation computation method(Muskingum  method), Journal of Hydraulic Research, 7(2).

[2]  Hoos, A B, Koussis, A D(1989). A channel dynamics model for real-time flood forecasting, Water Resources Research, 25(4).

[3]  Rui Xiaofang(1994). the theory of the runoff producing and flow consentration, Water  Resources and Electric Power Press, Beijing, China(in chinese).

[4]  Rui Xiaofang(2000). A study of flood routing method with forecast perriod, Advance of Water Science, 11(3)(in chinese).

[5]  Zhao Renjun(1984). The basin hydrologic modeling, Xinanjiang model and Shenbei model. Water Resources and Electric Power Press, Beijing, China(in chinese).

 Table 1   The verification forecasting at the Wuzhou station

 Fig.1    The water system for the case study area

Fig.2  The skatch of catchment, channel length and average travel time for each channel

Fig.3    Comparision between observed and simulated hydrographs