Hua Zhang, Wes Dick
AMEC Earth & Environmental Limited
221-18th Street S.E., Calgary, Alberta, Canada T2E 6J5
Phone (403) 248-4331, Fax (403) 248-1590, E-mail: hua.zhang@amec.com,
E-mail: wes.dick@amec.com
Zhou Beida, Liu Dongrun, Zhang Zhenquan, Gu Qingfu
Hunan Hydro and Power Department,
418 Shaoshan Road N., Changsha, Hunan, China 41007
Phone
86-731-5531112-7223, Fax 86-731-5541642
Abstract:
A combined 1-D and 2-D hydrodynamic for the model was developed for Dongting
Lake, a hydraulically complex system of lakes, polders and rivers all located in
a wide alluvial plain. Some key
problems and solutions model are discussed.
A combination of 1-D channel and 2-D lake elements was selected to obtain
reasonable computation speed without sacrificing accuracy.
An adjustable rating curve was used
successfully to deal with a complete downstream boundary condition.
Simple models of polder dyke breaching were incorporated into the model
to allow lake managers to assess the effects of a breach.
The focus throughout the study was on practical, numerically robust
solutions.
Keywords: hydraulic forecast model, Yangtze River, Dongting Lake, flood forecast, flood control
Hydraulic modelling is a fairly mature science, with several well-developed and accepted models available. However, the application of existing models to real situations, particularly for operational real-time forecasting, is not always straightforward. This paper discusses some of the issues that had to be addressed in the development of a real-time forecasting two-dimensional hydrodynamic model for Dongting Lake in China, and describes the practical solutions that were developed.
The Dongting Lake area is a very complex hydraulic network of rivers, polders and lakes located south of the Yangtze River in China. Dongting Lake itself can be subdivided into three major lakes identified as the West Lake, the South Lake and the East Lake, with a total surface area of 2691 km2. Important river channels in the project area are the Yangtze River, a network of channels connecting the Yangtze River and the Lake (the Three Mouths), and four major tributaries which enter Dongting Lake from the south and west (the Four Rivers).
There is considerable development in polders around the lake, protected by dykes of various levels. Damaging floods occur frequently in the Dongting Lake area, either because of flood flows in the Yangtze River, or because of flood flows from the Four Rivers within Hunan or from a combination of these two sources. During flood events, some polder dykes may be overtopped or breached. A hydraulic forecast model is needed to predict lake levels in order to manage the lake and upstream reservoirs and to minimize flood damages and loss of life.
Beginning in 1990, China initiated a series of flood forecast studies of the Yangtze River under the supervision of the Ministry of Water Resources (MWR) and the Changjiang Water Resources Commission (CWRC). The hydraulics of Dongting Lake have been recognized as one of the most difficult components in the Yangtze River and Dongting Lake flood management, and thus have become the subject of many national research projects. The Nanjing Hydrological Research Institute (NHRI) [1] developed a combination one- and two-dimensional hydraulic model of Dongting Lake. The Danish Hydraulic Institute (DHI) in conjunction with CWRC [2], and Wuhan Hydroelectric University [3] developed 1-D models.
In 1997, the Hunan Hydro & Power Department
(HHPD) commissioned AMEC Earth & Environmental to carry out the Dongting
Lake Area Flood Management Study and to develop a Decision Support System (DSS)
for management of the lake. As part
of that study, AMEC and HHPD developed a two-dimensional hydrodynamic model of
Dongting Lake for operational real-time flood forecasting.
Some research results on the Dongting Lake hydraulic model were presented
by Zhang, et al [4] in 2000.
The hydraulic model simulates the movement of water through the network of channels and lakes that make up the Dongting Lake system. It includes the Three Mouths, reaches of the Yangtze River upstream of the lake to Yichang and downstream of the lake to Luoshan, and reaches of the Four Rivers upstream of the lake. Local inflows are applied to the model using 40 local inflow boundaries. The Dongting Lake model includes simulation of polder dyke breaching. The model was calibrated using the 1999 flood event as reported by Zhang et al [4].
In general, one-dimensional modelling is faster and less prone to numerical instability than two-dimensional modelling, and so would be preferred for real-time forecasting. However, the hydraulics of Dongting Lake are strongly two-dimensional at many locations. The solution adopted for this project was to select a model that allowed a combination of 1-D reaches and 2-D elements. The RMA2 hydrodynamic model as implemented in the Surface Water Modelling System (SMS) interface, was selected based on its ability to combine 1‑D and 2‑D hydraulics in a single model [6], [7]. The river channels were modeled using 1‑D elements, while the three interconnected lakes that make up Dongting Lake, and the complex connections between the lakes and the tributary channels, were modeled using a 2‑D finite element mesh. The average 2-D element size is about 3 km2.
In RMA2, 1-D channels must be input as trapezoidal sections. The real cross sections were simplified to trapezoids that duplicated the channel top width, cross-sectional area and side slope as closely as possible at flood stage. This simplification resulted in bed elevations that could be significantly different from the real bed elevations, and as a result the model does not simulate low flows precisely. In general, however, the simplified cross-sections provided very good results for flood conditions, which are the focus of the model. An example of a river calibration result using a 1-D cross-section simplification is illustrated in Figure 1.
In the RMA-2 model, a downstream boundary condition can be specified as a time series of water levels or discharge, or as a stage-discharge relationship. When the model is simulating historical conditions, recorded water levels are used as the downstream boundary condition. However, in forecast mode, the model expects a single-valued stage-discharge rating curve, that is
Q = f (H) (1)
Specifically, RMA2 expects an equation in the form:
Q = A + C ´ ( H – B ) D (2)
where: Q = discharge;
H = stage; and
A, B, C and D are constants.
Fig.1 Effect of 1D cross-section simplication on yuanshui river calibration
However, on the Yangtze River in its middle and lower reaches there is a significant hysteresis in the stage-discharge rating curve. The hysteresis occurs because the river gradient is flat relative to the slope of the flood wave. In this case, there is not a unique relationship between water level and discharge. For a given discharge, the stage may vary within a wide range of values, depending on whether the discharge is rising or falling. Historically observed stage-discharge data for the Yangtze River at Luoshan, the downstream boundary of the Dongting Lake model, are shown on Figure 2. For a given discharge the water level difference can be as much as four meters. The variability is particularly evident at high flows, which are the focus of the model. Evidently, the single-valued rating curve approach cannot be applied to the Dongting Lake hydraulic model downstream boundary.
A pragmatic solution to this problem was
developed. The historical
stage-discharge data was used to develop a family of rating curves, with each
curve representing a different rate of change of water level.
The three-day forecast period is divided into three one-day simulations,
and a new rating curve is developed for each simulation based on the family of
curves, the rate of water level change during the previous day and the current
(observed or forecast) stage and discharge.
The parameters in equation (2) were fit to the family of rating curves. The fitted values of C and D are constants, while A and B are functions of the rate of water level change. When the rate of change of water level is zero, the equation is:
Q = 3367 + 138 ´ ( H – 10.76 ) 2 (3)
with H in metres and Q in m3/s.
At any given time, the actual stage and discharge may not fall exactly on the rating curve, even if the rate of change of water level is considered. It is desirable to use a rating curve in the next day simulation that includes the stage and discharge at the end of the current day, for two reasons: 1) The relationship is automatically adjusted for any error in the family of curves, and 2) No numerical shocks are introduced by the transition from one day’s simulation to another.
Fig. 2 Stage-discharge relationship: yangtze river at luoshan
Of the two parameters, B affects the shape and slope of the rating curve, while A affects only the position of the curve. It is expected that when the actual stage and discharge are not on the theoretical curve, the slope of the rating curve can still be described reasonably well by the rating curve equations. Therefore B is calculated from the water level rate of change, and A is selected so that the resulting curve passes through the most recent (observed or modeled) stage-discharge point. These values are calculated and supplied to the hydraulic model automatically by the DSS.
The results of using the adjustable rating curve
are illustrated on Figure 3 for Chenglinji, which is an important hydrometric
station at the outlet of Dongting Lake, upstream of Luoshan. The water levels
modeled using the rating curve are very close to the levels modeled using the
observed levels at Luoshan for forecasting lead times of one, two and three
days.
Fig.3 Effect of luoshan downstream boundary conditions on chenglinji water levels
Polder dykes around Dongting Lake may be breached by piping or overtopping failure (unplanned breaching) or may be breached or opened as a deliberate flood control measure (planned breaching). Breaching dykes around Dongting Lake can reduce the peak discharge and peak water levels in the Yangtze River. Therefore, dyke breaching can play an important role in protecting the Jinjiang Bank upstream of the Three Mouths, Wuhan City, 250 km downstream of Chenglinji and other major Dongting polders.
The RMA-2 hydraulic model does not explicitly include a dambreak function. It would have been possible to model each polder breach using a separate dambreak model and then input the resulting hydrograph as a boundary condition in the hydraulic model, but that approach was considered to be too complex for a real-time forecast model. Therefore two other approaches were developed to simulate planned and unplanned polder breaching in ways that are numerically robust, conceptually simple and computationally fast.
Eight planned flood control polders have been identified by HHPD. These flood control polders and designed breach locations (fuse plug dykes) are simulated in the hydraulic model as 1-D elements separated from the lake or river by gates. This approach allows the model to simulate the flow into the polder as well as the return flow back to the lake system after the polder has filled and the lake level begins to drop. The 1-D element dimensions were selected to replicate the storage capacity curve and the bottom elevation of the physical polder. The dyke breaching is simulated using control structures at the planned locations. Gate opening sequences can be assigned based on observed inflow hydrographs during historical events. The polder breaching process is simulated using gate control structure elements in the model. The breach discharge is dependent on the gate opening width and on the water level difference between the lake and the polder. When a polder dyke is breached, a designated gate opens at appropriate time and location to simulate polder breaching flow. The gate is opened over several time steps to reduce the numerical shock to the RMA2 model.
Most historical polder dyke breaches in the Dongting lake area have been unplanned. These breaches may occur at various locations around the lake or along the rivers. One well-documented example of polder dyke breaching occurred in 1999 at Mingzu Polder. The breach hydrograph for other unplanned breaches is estimated by prorating the Mingzu breach hydrograph. The observed hydrograph is adjusted to other situations by estimating that the peak flow is proportional to the head across the breach raised to the 1.5 power as in standard weir equations, and that the inflow hydrograph volume is equal to the storage volume of the polder. Using this method, the breach hydrograph can be estimated quickly and applied at any local inflow boundary node or polder gate in the hydraulic model. The model includes 40 existing node boundaries where inflows occur and 26 polder inflow points, so the user can simply select the nearest appropriate boundary node(s) or gate and apply the breach hydrograph there. This approach does not provide for return flows when the lake level begins to fall, but it allows greater flexibility in selecting the breach locations than the method used for the planned breaches.
Both methods of simulating polder breaches are illustrated on Figure 4 for the case of the 1999 Mingzu polder breach. The breach was modeled twice, once with the planned breaching simulation and once with the unplanned breaching simulation. The resulting simulated water levels at Yiyang, upstream of the polder, are compared to the observed levels on Figure 4. The planned breaching simulation overestimated the effect of the breach on observed levels at Yiyang. Some of the overestimate is presumably due to the fact that the simulated breach was closer to Yiyang than the actual breach. The unplanned process modeled the Yiyang water levels more accurately.
Fig. 4 Effect of mingzu polder dyke breach on water level at yiyang
The RMA2 hydrodynamic model was applied to the
complex 1-D and 2‑D hydraulics of the Dongting Lake system.
Some of the issues encountered in developing a real-time forecast model,
and their practical solutions have been discussed.
The result is a valuable tool for planning and optimizing flood
management measures, and assessing the benefits of flood control strategies.
Acknowledgements
This project was commissioned by the Hunan Hydro and Power Department, and was financed by the World Bank.
References
[1] Nanjing Hydrological Research Institute, 1995. Yangtze Protection System Modeling (Report)
[2] Changjiang Water Resources Commission, 1994, Numerical Modeling of Yangtze Midstream Flood Forecast and Operation (Report).
[3] Wuhan Hydroelectric University (WHU), 1997. Numerical Modeling of Dongting Lake Flood Polder Operation (Report).
[4]
Zhang Hua, Wes Dick, Yujuin Yang, Ray S. Pentland, Beida Zhou, Qingfu Gu,
Dongrun Liu, Zhengquan Zhang, 2000. Two-dimensional
Hydrodynamic Modeling of Dongting Lake. In Stochastic Hydraulics 2000, Wang
& Hu (eds), pp 861-867.
[5] Ministry of Water Resources and Electrical Power of People抯 Republic of China, 1985. Guidelines for Hydrological Information Forecasting. SD-138-85.
[6]
Brigham Young University (BYU), 1997. SMS
Surface-Water Modeling System - Reference Manual, Version 5.0. March, 1997.
Engineering Computer Graphics Laboratory, BYU.
[7]
WES, 1996. Users Guide to RMA2 -
Version 4.3, February, 1996, US Army Corps of Engineers, Waterway Experiment
Station - Hydraulic laboratory.