序率淹水模擬與疏散規劃分析

Stochastic Analysis of Inundation Simulations and Evacuation Planning

石宜軒(Yi-Hsuan Shih)

指導教授 ： 胡明哲

共同指導教授 ： 張倉榮(Tsang-Jung Chang)

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.10678

摘要

洪災為台灣最常見的天然災害之一，防災、減災為政府決策的重要課題。而淹水模擬提供決策者決策依據。在以往淹水模擬，都是使用定率方式，以單一最佳參數進行模擬，並未考慮環境與模式之不確定性，造成結果偏差。序率方法能夠改善不確定性所造成之誤差，而在疏散規畫中，也需將不確定性納入考量，作為決策依序。
序率方式雖能夠將不確定性納入考量，但也因此增加模擬次數，耗時耗力。研究透過4種取樣方法﹝蒙地卡羅法、拉丁高次法、小中取大法、最小相關性法﹞，3個不確定性來源進行河川水位模擬。不確定性來源包含5組上游邊界流量、5組下游邊界水位、17組曼寧糙度係數，共425組參數組合進行模擬。使用425組參數結果平均為參考值。比較不同取樣方法優劣，進而找出建議取樣數量。研究顯示拉丁高次法取樣遠優於蒙地卡羅法，能夠有效降低模式誤差。而小中取大法與最小相關性法雖能夠增加取樣間差異。對於模式結果的改善並不顯著。研究建議取樣數量為參數總組和之35%，可將誤差降低至模式最大誤差之2%。若增加取樣至50%，誤差可再降至1.5%。
本研究亦發展一多目標序率規畫疏散模式。模式分為兩階段：第一階段早期決策，在洪災發生前，決定各避難所容量擴充量；第二階段為洪災反應，在淹水發生後，決定疏散路徑。模式目標為最小擴充成本與平均每人疏散時間。本研究以景美溪與木柵區域為例，透過河川模擬結果所劃定之溢流警戒區域。以需疏散區域作為不確定性來源，使用3種不同情境，做最佳化決策分析。透過多目標規劃能夠表現出疏散路網與避難所間互償關係。研究發現，當疏散成本增加到一定值，疏散路徑不再改變。此時即發生最大疏散量與最小避難所擴充量。研究從水文模式至疏散規畫，都將不確定性納入考量，以作為未來減災規畫設計之依據。

關鍵字

不確定性 ； 拉丁高次取樣法 ； 淹水模擬 ； 多目標序率規畫 ； 疏散規畫

並列摘要

Flood inundation is one of the most usual hazards in Taiwan. To mitigate the impact of flood, inundation mapping plays a significant role. In general, a deterministic approach using optimal parameter sets is applied to analyze the inundation. However, without taking the impact of uncertainties into consideration, it may cause over or underestimate of the model. The stochastic process will improve the weakness of deterministic model. Also, it provides a better basis for decision makers, for example, evacuation planning.
Although stochastic approach considers the influence of uncertainties, it is often a time consuming process. In the study, four sampling strategies (Monte Carlo Simulation, Latin Hypercube Sampling, Maximin Distance, Minimum Correlation), three uncertainty factors are applied to a one dimensional hydraulic model. The uncertainty factors include five water flows as upper boundary condition, five water stages as lower boundary condition, and seventeen manning roughness coefficients. The mean water stage of 425 combination of parameter sets are taken as a reference in comparison of each sampling strategy. Result represents that Latin Hypercube sampling performs almost ten times better than Monte Carlo simulation. And though other sampling strategies can enhance sampling discrepancy, the improvement of the result is not significant. The sample size chosen may depend on the tradeoff between acceptance accuracy of model and computational time. The suggested sample sizes are 35% and 50% of total simulation area.
The study also proposes a multiobjective stochastic programming analysis for uncertain inundation evacuation. A two stage stochastic programming model under inundation uncertainty is built. Expansion of shelter capacity is decided in the first stage before flood. The second stage determines the evacuation plan providing the optimal route to shelters for all evacuees. A case study of MuZha, Taipei is conducted. Based on the result of hydraulic model, three different regions of warning zone for overflow are taken to be the uncertainty resource. The model with multiobjective shows the tradeoff between shelter expansion and transportation time. The result shows that as the unit cost of shelter expansion exceed to a certain level, the total evacuation time and amount of shelter expansion will remain the same. It represents the minimum shelter expansion and maximum evacuation time. From the hydraulic model to optimal programming, the study focuses on how uncertainty affects the models, provides a decision making system for flood inundation.

並列關鍵字

Uncertainty ； Latin Hypercube Sampling ； Flood simulation ； multiobjective stochastic programming ； evacuation planning

參考文獻

Chen, Y. C. & J. H. Chen (2006) A discussion of uncertainty in ecological risk assessment. Journal of Science and Engineering Technology, 2, 49-60.

Kongsomsaksakul, S., C. Yang & A. CHen (2005) Shelter location-allocation model for flood evacuation planning. Journal of the Eastern Asia Society for Transportation Studies, 6.

Apel, H., A. H. Thieken, B. Merz & G. Bloschl (2004) Flood risk assessment and associated uncertainty. Natural Hazards and Earth System Sciences, 4, 295-308.

Aronica, G. T., F. Franza, P. D. Bates & J. C. Neal (2012) Probabilistic evaluation of flood hazard in urban areas using Monte Carlo simulation. Hydrological Process, 26, 3962-3972.

Domeneghetti, A., S. Vorogushyn, A. Castellarin, B. Merz & A. Brath (2013) Probabilistic flood hazard mapping: effects of uncertain boundary conditions. Hydrology and Earth System Sciences, 17, 3127-3140.