LU Yun-feng，TAN De-bao，LIANG Dong-ye（Yangtze River Scientific Research Institute，Wuhan 430010，China）

A Rapid and Accurate Computation Method of Three Gorges Reservoir Dynamic Storage

LU Yun-feng，TAN De-bao，LIANG Dong-ye
（Yangtze River Scientific Research Institute，Wuhan 430010，China）

The Three Gorges reservoir is the typical channel type reservoir in the Changjiang River，China.The dynamic storage can better reflect the true situation ofwater storage，so it’s one of the important parameters of the water balance’s calculation，runoff forecastand reservoir operation for a channel reservoir.Combining the GIS technology with the hydrody-namic method，this paper proposed a rapid and accurate computationmethod of the channel type reservoirs’dynamic stor-age.And themethod has been successfully applied to the Three Gorges Reservoir real-time operation.As the reservoir top-ographic DEM data is usually a great datamass and redundancy，the block-based processing，run-length encoding raster data compression method and multi-bands integration method were employed to manage the parameters.The efficiency of the spatial interpolation method’s computation has been evidently improved and the rapid computation of the dynamic stor-age has been realized.On the basis of the method，a software system of reservoir storage calculation was developed and used to calculate the dynamic storage of the Three Gorges Reservoir.The calculation speed is very quick and the calculated result errors are very small，which indicates that themethod is valid and feasible.

channel reservoir；dynamic storage；flood routingmodel；DEM

1 INTRODUCTION

The dynamic storage of a channel reservoir refers to the volume between reservoir real-time water surface and river bed from dam to reservoir backwater region terminal.It is composed of static storage and wedge storage.It is necessary to know the water storage in a channel network for calculations of water balance of a river basin and runoff forecast［1］.Furthermore，regard-ing the flood routing of channel reservoir，because there is biggish error between the water storage values calculated by the static storage capacitymethod and the true values，the former can not satisfy with the request of the channel reservoir real-time operation.The influ-ence of the dynamic storage on the flood routing should be considered［2］.The dynamic storage can perfectly reflect the situation of water storage for reservoir in-flow.In order to improve the accuracy of water bal-ance’s calculation，runoff forecast and real-time opera-tion for a channel reservoir，it’s necessary to research the rapid and accurate computationmethod of the chan-nel reservoir dynamic storage.

On the basis of statistical laws of channel network structures suggested by Horton，Strahler and Rzhan-itsyn，Gorbunov firstly divided the channel network in-to segments according to their similar morphological and hydrological characteristics，and then routine ob-serveational results of water stages were served as ini-tial data in the calculations ofwater storage.The errors in the calculations of total water storage are within 10 percent［1］.Themethod is confined by techniquemeas-ure in that time，so its calculated results aren’t accu-rate enough.According to the steady water flow equa-tion of the open channel，Tong etal.gave the relation-ship between the static flood control capacity and the dynamic flood control capacity.By analysis，he con-cluded that the dynamic flood control capacity has close relationswith watercourse’s topography，water level in front of dam，reservoir inflow，watercourse roughness coefficient，reservoir operation’smode and so on［3］.It denoted that the dynamic storage has close relation withwhichever of these factors.By assuming the water-course’s unsteady flow as steady flow，Xu et al.pro-posed the numerical-analytic method to calculate the dynamic storage and carried through the flood routing of the channel reservoir.Although this is reported that thismethod can give themost satisfactory results，stead flow simulations cann’t represent nature flood proceed-ing.In order to improve the accuracy of dynamic stor-age calculated results，unsteady flow simulationsmust be performed［4］.Because of absence of watercourse’s terrain data，Ai et al.simplified river geometry and calculated dynamic storage in combination with the one-dimensional（1D）unsteady flow hydrodynamic model［5］.The influence of the watercourse terrain on dynamic storage cann’tbe truely considered，so the re-sults aren’t accurate enough.

High resolution DEM can accurately simulate wa-tercourse terrain.By GIS technology，it’s easy toman-age and compute a greatmass of DEM data.And un-steady flow hydrodynamic model can be applied to sim-ulate the real-time motion state of nature flood.There aremany examples［6－9］representing the integration of the GIS technology with the hydrodynamicmethod，but most of them emphasize on the flood inundation and flood risk assessment.Few literatures discuss the rapid and accurate computation method of the channel reser-voir dynamic storage.Combining GIS technology with hydrodynamic method，this paper proposed a rapid and accurate computationmethod of the channel type reser-voirs’dynamic storage.From the method，a software system of reservoir storage calculation was developed and used to calculate and validate dynamic storage of the Three Gorges Reservoir.

2 RESEARCH REGION

The drainage area of the Three Gorges Reservoir is about1 084 km2and its length is about660 km and its watercourse averagewidth is about1.1 km.It is a typ-ical channel type reservoir.We choose the Three Gor-ges Reservoir’s 156 m water storage process within the period from September to October in 2006 as a case study.The reservoir backwater region terminal is loca-ted at Cuntan，so research region includes all themain stream and branches from Cuntan to the Three Gorges Dam.Watercourse terrain DEM data and hydrologic data are given by the China Three Gorges Project Cor-poration.The DEM data cover the regions in which el-evation is less than 200m in themain stream reach and branches reach from Cuntan to the dam（Fig.1）.The grid size of DEM is 2.5 m×2.5 m.

3 METHODOLOGY

The calculation method of the channel type reser-voirs’dynamic storage is as follows.Firstly，a flood routingmodel based on the unsteady flow hydrodynamic modelwas developed to simulate reservoir inflow’s rou-ting and used to calculate real-time water surface pro-file.Secondly，using GIS component secondary devel-opment technology，water surface’s DEM of reservoir watercourse could be created by spatial interpolation method based on water surface profile data and reser-voir watercourse’s DEM data.Finally，using water-course terrain DEM and water surface’s DEM of reser-voir watercourse，the dynamic storage was calculated by integralmethod，as formula（1）.

Fig.1 The watercourse terrain DEM data of the Three Gorges Reservoir from the Cuntan to the dam

where：Vtis the value of the dynamic storage at t，（x，y）denotes the random point in the regions of the reser-voir’s water storage，x denotes the cross section’s di-rection and y denotes the direction along watercourse，Zsm（x，y，t）represents the water level at point（x，y）at t，Zhd（x，y，t）expresses the riverbed’s elevation at point（x，y）at t，l（y）and r（y）are two solutions of the equation：Zsm（x，y，t）＝Zhd（x，y，t）｜y，t（as-suming that l（y）＜r（y）），i.e.the x value is located at the waterside of random section’s（y）in the leftbank and right bank.

3.1 Watercourse flood routing model

Hydraulic model is usually applied to simulate the motion state ofwatercourse flood.Although two-dimen-sional（2D）hydraulic model can directly get the wa-tercourse water surface’s elevation，there are some drawbacks thatmake this approach less applicable.For example，it can’t satisfy with the requirement of rapid-ly calculating the water surface profile.Another disad-vantage is that application of a 2Dmodel requires com-prehensive and consistent data of the area which may not be readily obtained under the feasibility study stage，and also that due to computational demands the reaches studied are often limited in their area1 exten-sion［10］.

An alternative is to determine stages in the river using a 1D flow model and then interpolate these data to get the watercourse water surface’s elevation based on GIS techniques.By increasing the number of cross sections along the river and decreasing the cross-sec-tional spacing，the accuracy of spatial interpolation can be improved.One dimensional（1D）Saint-Venant’s equations including continuity equation（2）and mo-mentum equation（3）are used for river network flow simulation.

where：t is time step length，S denotes the distance a-long the channel between two adjacent cross-sections，B expresses the channelwidth，Z represents the water-course surface level，A is the wetted cross-sectional ar-ea，Q shows the discharge through A，q indicates the lateral inflow，g is the gravity acceleration constant，C is the Chezy’s coefficient，R is the hydraulic radius.These equations are discretized using the finite-differ-ence method and solved using a four-point implicit（box）method.

3.2 The calculation method of dynam ic storage based on the watercourse DEM and water surface profile

Each cross-section’s water level can be got by u- sing the hydraulic model calculations.In order to cal-culate the dynamic storage using equation（1），each grid’s elevation of the watercourse water surface must be computed by subsequently spatial interpolation based on GIS technology.Water level of each grid be-tween two adjacent cross-section lines is in direct pro-portion to distance from the upstream cross-section line and in inverse proportion to distance from the down-stream cross-section line.Furthermore，the water-course shape between two adjacent cross-section lines is comparatively straight when cross-section lines are sliced.In compliance with 1D hydraulic model calcu-lations，water levels are assumed to be constant along each cross section line.So each grid’swater level can be got by linear interpolation in relation to the dis-tances between grid and two adjacent cross-section lines.Equation（4）is the linear interpolation formula.

where Z（x，y）is the water level of the point（x，y）to be interpolated，d1and d2are respectively the distances from the point（x，y）to the adjacent upstream cross-section line and to the adjacent downstream cross-sec-tion line，Z1and Z2denote respectively water levels of the upstream and downsteam cross section lines adja-cent to the point（x，y）.

The interpolation method has two merits.One is thatwater levels of the points locating at cross-section line are equal to water level of the cross-section line.Another is that the less the spacing between two adja-cent cross-section lines，the less the difference ofwater levels between them，so the interpolation results have adequate accuracy.

Furthermore，there are some slim branches in the channel network，because of absence of the routine ob-servational data ofwater stages，theirwatercoursewater surface profile can’t be calculated by hydraulicmodel.But their water storages can’t be ignored.In order to calculate their water storages，they are firstly separated from the channel network.Because they are usually short，water level of the center point at confluence of channel’smain stream and each branch can be approx-imately regarded as the branch’s water level.Water level of the center point can be gotby spatial interpola-ting using equation（4）.

Using the scan line seed filling algorithm，water surface’s DEM of the reservoir channel can be created by subsequently spatial interpolation based on the wa-tercourse terrain DEM.In combination the watercourse terrain DEM with water surface’s DEM，reservoir dy-namic storages can be calculated using formula（1）.

3.3 Approaches to im prove the efficiency of cal-culating dynam ic storages

（1）In the spatial interpolating process，the pa-rameters such as the number of the cross-section lines adjacent to the interpolated point，d1and d2in formula（4）are all constant，so they can be calculated in ad-vance.Imitating the storage method of the multispec-tral remote image，the watercourse terrain DEM and the parameters can be integrated into a four-band’s ras-ter data.By introducing thismethod，it can evidently decrease the consuming time to search the data in the spatial interpolating process.The efficiency of the spa-tial interpolation calculation can be evidently im-proved.

（2）As the integrated four-band’s raster data are usually a greatmass and redundancy，the block-based processing and the run-length encoding raster data compression method are adopted tomanage these data.By introducing themethods，on the one hand the stor-age space can be saved.On the other hand multi-blocks data can be synchronously calculated by using themultiprocessing programmingmode.

Using the above approaches，dynamic storage of the great type channel reservoir can be rapidly calculat-ed.

4 A CASE：COMPUTATION OF DYNAM IC STORAGES IN THE THREE GORGES RESER-VOIR’S 156M WATER STOR-AGE PROCESS

4.1 Calculating and validating water surface pro-file of the Three Gorges Reservoir

The reaches from Cuntan to the Three Gorges Dam are selected as the regions of hydraulic model calcula-tion.376 cross-sections have been arranged along the main stream，and 44 cross-sections have been arranged along themain branch Wujiang.Fig.2 shows themain hydrological stations and their cross-sectional numbers.The cross-sectional spacing in themajority of reaches is 2－4 km.In order to represent the natural geometry of a river，the cross-sectional spacing in the straight rea-ches is biggish，and that in the wandering reaches is lesser.The terrain data of cross-sections can be direct-ly got from the watercourse terrain DEM.

Fig.2 Themain hydrological stations and their cross-sectional numbers in the Three Gorges Reservoir

Using a 1D unsteady hydraulic model simulated the water surface profiles of the Three Gorges reser-voir’s 156 m water storage process within the period from September-October in 2006.A high flow event of May-September in 2004 was selected for the calibration of themanning’s roughness coefficients by adjusting the simulated peak discharge.The time step length equals 180 s.Fig.3 shows the comparison of simulated and observed hydrographs at Cuntan，Qingxichang，Zhongxian and Fengjie hydrological stations after cali-bration of the parameters.As can be seen from the graph，the difference between the simulated and ob-served water levels is very small.The absolute values of average level errors are about0.1 m.

4.2 The calculated result and discussion

On the basis of the abovemethod，a software sys-tem of channel reservoir’s dynamic storage calculation was developed and used to calculate the dynamic stora-ges of the Three Gorges Reservoir’s 156 m water stor-age process.The calculation time（as performed on a standard 2 GHz PC with 2 GB memory and Windows XP professional sp3）is about 10 minutes.Fig.4 shows the calculation results.According to the results，the accumulativewater storagewithin two time-intervals was calculated and used to validate the calculation re-sults’accuracy by comparing them with the promulgated contemporaneous results by the China Three Gorges Project Corporation.Table Ishows the comparison.Ascan be seen from table 1，the errors are very small，which indicates that themethod is valid and feasible.

Although themethod presented gives a satisfactory result，the factors of arousing the errors are still de-served to be discussed.The errors from the water sur-faces profile of hydraulicmodel simulations are the im-portantone of the factors.As hydraulicmodels are sen- sitive to the geometric description（the number of cross sections，spacing between cross sections，and bottom slope）and model parameters（Manning’s n）of the channel，uncertainty of the parameters is introduced in dynamic storage calculations through hydraulic model-ing［11］.In order to improve the efficiency of hydraulic model simulations，on one hand，the natural geometry of channelmust be accurately represented based on the high accurate terrain DEM（2.5 m）of the Three Gor-ges Reservoir’s watercourse.On the other hand，the manning’s roughness coefficients must be calibrated well by using the real-time hydrological observations.

Another factor of the errors arises from the inter-polation method.Although decreasing the cross-sec-tional spacing，the accuracy of spatial interpolating can be improved，the efficiency of dynamic storage calcula-tionswill fall.A balance between the accuracy and ef-ficiency of dynamic storage calculations should be ex-amined by experiments.

Furthermore，the errors obtained from the calcula-tions of those slim branches’water storage one of the factors either.But absence of the routine hydrological observations，their water storages have to be calculated by using the approximatemethod.As theirwater stora-ges are generally very small，the influence on the re-sults is finite.

Fig.3 The com parison of simulated and observed hydrographs at themain hydrological stations in the Three Gorges Reservoir

Fig.4 The dynam ic storages of the Three Gorges Reservoir’s 156 m water storage p rocess

Table 1 The comparsion of accumulative water storage in the Three Gorges Reservoir’s 156 m water storage process

5 CONCLUSIONS

Dynamic storage of the channel reservoir has close relationswith the factors such as watercourse’s topogra-phy，water level in front of dam，reservoir inflow，wa-tercourse roughness coefficient，reservoir operation’s mode and so on.In order to calculate the dynamic stor-ages of the Three Gorges Reservoir，a software system of channel reservoir’s dynamic storage calculation has been developed in combination GIS technology with the hy-drodynamic method.The factors have been considered.By computing dynamic storages of the Three Gorges Reservoir’s 156 m water storage process，the method presented has been proved to be very applicable.And the calculation speed is very quick and the calculation accuracy is very high.At present，themethod has been applied to the Three Gorges Reservoir real-time opera-tion.Themethod is also applicable to the other channel reservoirs possessing the watercourse terrain DEM data.

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（Edited by LIU Yun-fei，YIXin-hua）

一种三峡水库动态库容快速准确计算方法

芦云峰，谭德宝，梁东业
（长江科学院空间信息技术应用研究所，武汉 430010）

三峡水库是典型的河道型水库。动态库容较好地反映了洪水进入河道型水库后蓄水量的实际情况，是水库水量平衡计算、径流预报和水库实时调度的重要参数之一。结合GIS技术和水力学方法，本文提出一种河道型水库动态库容快速而准确的计算方法，并成功应用于三峡水库实时调度。由于三峡水库河道地形DEM数据量较大且存在较多冗余，通过采用分块、游程编码压缩和多波段集成方法存储管理空间插值方法中用到的相关参数，有效地提高了空间插值计算效率，实现了动库容的实时计算。通过运用该方法开发通用的动态库容计算软件对三峡水库动库容进行了计算，计算速度较快，计算结果误差较小，表明该方法准确有效。

河道型水库；动库容；洪水演进模型；DEM

Document code：A

1001－5485（2010）01－0080－06

date：2009-08-16；Revised date：2009-11-10

LU Yun-feng（1974-），male，Engineer，Ph.D.，Hismain interests are involved in research of resource and environment，wetlands ecosystems and application of GIS technology.（Tel.）027-82826550（E-mail）06fengyun＠163.com