區塊運動波直接逕流模式之研發

Developing Block Kinematic Wave Model for Direct Runoff Hydrograph Estimate

胡修華(Shiou-Hua Hu)

指導教授 ： 李天浩

國立臺灣大學/工學院/土木工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.02167

摘要

單位歷線法等傳統黑盒有效降雨－直接逕流模式，皆應用出流量和降雨強度呈正比的線性假設。但從運動波模式可知，決定河段出流量的主要因素是接近出口的當時水位，並不是降雨強度。若是集水區集流時間長度（亦為降雨強度的函數）內降雨強度變化大，或是建立和應用單位歷線事件的有效降雨強度差異大，則會出現相對顯著的推估誤差。近年利用集水區40公尺解析度DEM建立逕流流徑，配合Kinematic Wave法計算每個流徑水深和流量，不需要作線性假設，但是必須儲存每個流徑的狀態變數。這類地貌型直接逕流模式，因為計算單元多而通常相當耗時；另外，應用均勻、穩態假設的運動波模式，計算集水區上游蓄水量少、流量變化大的山溝流徑的非穩態水位、流量時，極容易發生數值問題。
本論文提出能解決上述集水區逕流水理和數值問題的Block Kinematic Wave (BKW) rainfall-runoff model。模式的算式為：首先，利用ArcInfo地理資訊系統和外掛軟體，由40*40m DEM建構集水區範圍內連接各像元(pixel)的流徑和河川網路；其次，計算每個每個流徑的（地形指數）Topographic Index, or TI；第三，利用TI參數化不同流徑的斷面形狀和曼寧糙度係數；第四，應用運動波模式計算不同穩態強度降雨條件下每個像元流到出口的旅行時間；第五，利用旅行時間將集水區分為若干個區塊（blocks），將不同降雨強度下會出現在不同區塊的像元作適當處理；第六，在某有效降雨強度下，計算每個流徑的蓄水量和流量，按照區塊加總蓄水量和所有自區塊流出的逕流量，建立不同有效降雨強度下，各區塊的蓄水量和出流量關係曲線；第七，由每個區塊的有效降雨強度－出流量關係曲線、降雨強度、上游區塊流入流量，和連續方程式，採用水庫演算法，計算各區塊的出流量。BKW降雨逕流模式，因為：(1)絕大部分的計算都是在建模時離線執行，即時只須按順序執行幾個水庫演算法，計算效率高；(2)計算出每個區塊的蓄水量－出流量關係曲線，符合由蓄水量決定出流量的物理理解，也不須作線性假設；(3)以穩態降雨強度的方式應用運動波模式，並將區塊內相當數量的流徑蓄水量累加為區塊蓄水量，當蓄水量小、流量變化大時，應用較小的時間間距和隱式法計算便不會出現數值問題。基於以上三個特性，BKW模式特別適合應用於台灣的洪水預報模式中計算直接逕流歷線。
本論文採用觀測系統實驗(Observing Systerm Experiment)的方式檢驗BKW模式的差異。方法是使用地貌型Muskingum-Cunge演算法的GRUNOFF model，建立降雨事件之「真實」有效降雨－直接逕流歷線；利用輸入GRUNOFF模式的有效降雨歷線，檢定BKW模式模式，檢驗BKW模式模式推估的差異性；同時評估BKW模式和GRUNOFF model在計算時間上的差異。

關鍵字

區塊運動波 ； 運動波 ； 地貌型 ； 單位歷線 ； 直接逕流 ； 地形指數

並列摘要

Open channel hydraulics show that the main factor determining discharge of a long channel is the water depth (or storage) near the channel exit, not the rainfall intensity on the river, not the upstream inflow. The later two factors affect discharge by increasing or decreasing storage. However, unit hydrograph (UH) and other traditional black-box rainfall-runoff models assume direct runoff respond linearly to excess rainfall intensity. The effect of storage within the watershed is not considered in UH, and the linear assumption does not really valid in a watershed. Estimation error maybe large if rainfall intensity varies significantly within a catchment’s time of concentration (which is a function of rainfall intensity too), or when the average rainfall intensity used to create UH is very different from that using UH to estimate runoff hydrograph.
In recent years, Digital Elevation Model and GIS make possible to construct a watershed’s runoff flow path network. Apply Kinematic Wave (KW) model to compute the flow speed on the flow paths, runoff hydrograph can be calculated without using linear assumption. The KW model computation is time-consuming. When KW is applied to flood forecast, the state variables of each link must be saved at the end of one forecast and retrieved at the beginning of next. Numerical problems may occur applying the essentially steady-state KW model to rapidly varying hyetograph. The numerical problem is more serious at the upstream flow paths where the channel storages are less.
We propose a rainfall-runoff model called Block Kinematic Wave (BKW). It does not apply the linear assumption, and it does not have the numerical problem of KW. It’s algorithm follows. First, apply the ArcInfo geographic information system and HEC GeoHMS tool module to construct the 40-meter resolution flow paths and river network. Then, compute the Topographic Index (TI) of each flow path. Thirdly, utilize TI to parameterize the cross-section and Manning’s n of each flow path. Fourth, assume different excess rainfall intensity and compute the travel time (TT) of all pixels to watershed exit for all intensities. Fifth, divide the catchment into several equal area blocks, handle the pixels go across block boundaries at different rainfall intensities. Sixth, calculate the storage on each flow path and total the flow path storage, S, of a block given an effective rainfall intensity. Also, compute the total discharge at all block boundaries, Q. Construct the storage – discharge relationship for each block using all different steady-state excess rainfall intensity results. Seventh, compute the direct runoff from each block using reservoir routing. That is using continuity equation and S-Q relationship. By doing so, the discharge from a block is mainly determined by its storage. Here, excess rainfall intensity is only one of the inputs to the block storage.
The BKW model uses steady state rainfall intensities to construct the S-Q relationship for each block. No linear assumption is involved. The BKW model does not suffer the numerical problem of KW given non-constant hyetograph because it uses KW for steady-state computation only. The BKW model for direct runoff is computationally very efficient, because most of the calculations are pr-processed and carried out offline. There are only a few reservoir routing computations to be executed online. With these three nice properties, BKW model is especially suitable to calculate direct runoff hydrograph within Taiwan's flash flood forecast system.
Observing Systerm Experiments are designed to compare the performances of BKW. A Muskingum-Cunge based flow-path computation model is assumed to produce the “true direct runoff hydrograph” from a watershed. BKW model is then validated with some other “the true direct runoff hydrographs”. Computation time of BKW and the “True” model are also compared.

並列關鍵字

Block-Kinematic-Wave ； kinematic wave ； Geo-morphology ； unit hydrograph ； direct runoff ； topographic index

參考文獻

3. Beven, K. J., Kirkby, M. J., A dynamic TOPMODEL. Hydrol. Process., Vol. 15, 2001.

7. Cunge, J. A., On the subject of a flood propagation computation method (Muskingum Method).Journal of Hydraulic Research, Vol. 7, No. 2, pp. 205-230, 1969.

8. Laurenson, E. M., A catchment storage model for runoff routing. Journal of Hydrology, Vol. 2, pp. 141-163, 1964.

9. Lee, K. T., Yen, B. C., Geomorphology and kinematic-wave based bydrograph deviation. J. Hydr. Engrg., ASCE, Vol. 123, No. 1, pp. 73-80, 1997.

10. Lyon, S. W., Walter, M. T., Pierre G′erard-Marchant, Steenhuis T. S., Using a topographic index to distribute variable source area runoff predicted with the SCS curve-number equatiom. Hydrol. Process., Vol. 18, pp. 2757-2771, 2004.