區塊運動波模式水理改進之研究

The study of hydrological improvement of Block Kinematic Wave Model

游翔麟(Hsiang-Lin Yu)

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(2013年)

https://doi.org/10.6342/NTU.2013.01278

摘要

本研究回顧《區塊運動波直接逕流模式之研發，2011》，其為一基於逕流歷線主要是受到集水區滯留體積驅動的概念所發展的物理化分布式區塊逕流模式。在半分布式區塊單元的劃分機制上，其是由DTM各流徑至集水區出口點的旅行時間分布劃分串聯型區塊計算單元。區塊內包含河川，擬穩態流假設未必成立；區塊空間上分散破碎，同區塊之降雨強度不同。於穩態條件下導出各區塊穩態蓄水體積─出流量函數時，匯流點上下游流徑水深為分段近似，未必連續；DTM流徑坡度因漥蓄填平機制而有過小的問題，其導致正常水深過深，均勻流假設下的穩態運動波模式求解方法未必成立；因流徑坡度過小，以地形指數線性參數式參數化流徑寬矩形斷面底寬與曼寧糙度值，上下游流徑變化劇烈而不理想。線上模擬時，是應用水庫演算法來計算各區塊之出流歷線，其無法反映不同的地貌對逕流傳遞與稽延的影響。
本研究針對前述的模式問題，在區塊劃分策略、穩態導出模式參數與線上模擬三個部分，提出水理改進的方法。本研究半分布式模型計算單元的劃分，是按照「逕流區塊─河川」與「流域集水區─子集水區─單元水文集水區─逕流區塊的層級」，利用DTM流徑關係、選定之河川線以及斷面樁位線，依照注入河川方向的不同(左岸、右岸與注入最上游)，將流至同一河川區段且注入方向相同之像元集合為逕流區塊，區塊內之像元具有空間連續之特性，符合台灣山區集水區降雨與逕流具高度空間變異性之特徵。穩態導出模式參數部分，以誤差函數的反函數來參數化流徑坡度門檻值，可修正因漥蓄填平演算所導致的坡度過小問題；以地形指數(Topographic Index，TI)為指標，分別以誤差函數的反函數與線性關係式，來參數化像元流徑梯形斷面的底寬與曼寧糙度值；以擴散波式的迴水方程式來計算各流徑間連續水剖面線，取代穩態運動波假設下分段近似的方法。非穩態線上模擬部分，則是以區塊尺度的非線性運動波差分式建立區塊運動波直接逕流模式，其具有水體以運動波波速於逕流區塊內通路(Flow Pathways)傳遞的稽延機制，與通路的空間分佈具有相當密切的關係。逕流區塊內，任一通路的運動波傳遞時間計算，是以迴水方程式來計算均勻穩態有效降雨強度下，通路上各流徑的連續迴水剖面線與對應的運動波波速及傳遞時間。將半分布式逕流區塊建立為區塊直接逕流模式計算單元的步驟，是選定一指標性穩態降雨強度，計算集水區各像元至河川為止的運動波旅行時間。再來，由小至大來排序區塊內像元的運動波旅行時間，以建立其通過比例分布函數並訂定分布函數上之切分點，將逕流區塊劃分為上游蓄水計算單元與下游運動波計算單元。最後，再以入流量與降雨強度為指標，建立運動波計算單元的流量傳遞之平均運動波旅行時間二維查詢表，以加快模擬演算速度。
在模式驗證與分析部分，第一部分為透過選定的降雨事件或降雨雨型，針對相同的計算單元，來比較使用穩態蓄水量─出流量函數關係之演算方法與使用流量傳遞之平均運動波旅行時間為指標之演算方法，在表現流量傳遞機制上的差異。第二部分則選取不同逕流區塊之下游運動波計算單元，以區塊內流徑之運動波旅行時間分布將其細分為若干子計算單元，以檢視運動波計算單元集合尺度對模擬結果之敏感度。最後，透過選定之颱風事件，來比較與驗證本研究之集水區逕流演算法架構，相較於前人所發展之區塊運動波直接逕流模式(Block Kinematic Wave Model，BKW)所做出之改善。

關鍵字

半分布式模型 ； 逕流區塊 ； 非線性運動波方程式 ； 迴水方程式 ； 流量傳遞之平均運動波旅行時間

並列摘要

This paper revisit the “Developing Block Kinematic Wave Model for Direct Runoff Hydrograph Estimate”(2011), which propose a physically-based distributed block direct runoff model that is based on the idea that runoff is derived by retention volume in watershed. The delineation of its semi-distributed blocks, is based on the travel time distribution of DTM pixels on watershed outlet , which produce connected blocks. Its runoff block contains river , pseudo-steady assumption may not be correct ; runoff block is spatially scattered broken , rainfall intensity in a runoff block may not be the same. When deriving each runoff block’s “steady storage – outflow” function under steady condition , confluence point’s upstream links’ and downstream links’ water depth are piece-wise approximation , may not be continuous; DTM link’s slope may be too small due to fill sinks mechanism, causing links’ normal depth abnormally large, means the solving method for links water depth the use steady-kinematic-wave model may not be correct; using Topographic Index(TI) to parameterize DTM link’s wide rectangular channel cross section’s bottom width and Manning Roughness Coefficient , because of too small link’s slope , will cause dramatic changes to bottom width and Manning Roughness Coefficient of along two connected links. Unsteady simulation uses Level Pool Routing to calculating each runoff block’s outflow hydrograph , which can not reflect different geomorphic influences to runoff propagation.
For the foregoing model problems, this paper proposes a hydrological improvement on “runoff block delineation method” , “deriving model parameters under steady condition” and “Unsteady simulation method”.This paper’s delineation of semi-distributed model’s calculated unit follows “Runoff-Block-River” and also four lumping scale levels as “Watershed - Subwatershed – Hydrologic Unit Catchment – Runoff Block”, using “DTM pixel’s linkage relationship” , “selected river lines” and “cross section piles’ lines”, according to pouring angle to river lines(Left Riverside Flows in , Right Riverside flows in and Most Upstream Stream Pixel Flow in) , lumping pixels that flow to same river segment as Runoff Block which has spatially continuity characteristics which is in sccordance with the fact that runoff and rainfall in Taiwan’s mountains watershed have large spatially variability. For “deriving model parameters under steady condtion” part , using inverse error function to parameterize link’s slope threshold( floor) to fix too minor slope problems due to fill sinks mechanism; using TI as index , then using inverse error function to parameterize link’s trapezoidal channel bottom width and linear function to parameterize link’s Manning Roughness Coefficient; using diffusive-wave type backwater equation to calculate continuous water depth along links , replacing piecewise approximation method. For “Unsteady simulation method” part , using block-scale nonlinear kinematic wave direct runoff routing model to establish this paper’s block kinematic wave direct runoff routing model , which has a time-delaying mechanism for a water body travelling over a Runoff Block with kinematic wave celerity on flow pathways that has a close relationship to spatial distribution of flow pathways in a Runoff Block. Each flow path’s transported kinematic wave travel time in a Runoff Block is calculated by using backwater equation to calculate continuous water profile and corresponding kinematic wave celerity and transported time under steady uniform rainfall intensity over a Runoff Block.The procedure to establish kinematic wave calculated units from semi-distributed Runoff Blocks : first of all , selecting an indicative steady uniform excess rainfall intensity to calculating each DTM pixel’s time to travel to watershed outlet; then, sorting block’s pixels’ kinematic wave travel time from little to large and then establish accumulated travel time distribution curves ; then , setting cutting points on these curves to split large enough Runoff Blocks into upstream storage calculated units and downstream kinematic wave calculated units. Finally , establishing a two dimensioned averaged kinematic wave travel time referenced table for downstream kinematic wave calculated units by taking inflow and rainfall intensity as the referenced index , in order to speed up calculation time.
For model’s verification and behavior analysis, the first part will use selected rainfall event as well as rainfall pattern , a comparsion are done for specified calculated units that use different routing method such as “storage-outflow relationship” or “averaged kinematic wave travel time” by checking its runoff transporting behaviors. The second part will select different Runoff Blocks’ downstream kinematic wave calculated units , delineating sub-calculated units based on Runoff Block’s pixels’ travel time distribution, to examine sensitivity to simulation results of different lumping scale for “kinematic wave calculated units”. Finally , using selected Typhoon Event to verify the improvement of the proposed model in comparison with previous Block Kinematic Wave Model(BKW).

並列關鍵字

Semi-Distributed Model ； Runoff Block ； nonlinear kinematic wave eqution ； backwater equation ； averaged kinematic wave travel time

參考文獻

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