波浪與水位為造成海岸溢淹之重要因子，海堤為台灣目前最主要的海岸防禦措施。海堤高度的決定對海堤設計成敗關係甚鉅，通常以設計波高、天文潮位、暴潮位等海況參數的線性累加數值作為設計值，亦即將最大波浪與最高水位視為同時候發生。本研究利用聯合機率分析方法，探討波高與水位的發生機率，與傳統分析結果比較。
本文於台灣東部、南部、西部和北部各選擇一處同時有波浪和水位紀錄的測站，由於颱風是造成海堤破壞主要的原因，本文以颱風期間同時發生之有義波高與水位為分析對象，四個測站合計有111個颱風事件，資料共有7440筆。分析結果顯示，颱風期間的有義波高屬於韋伯分佈，水位變化符合極端值一型分佈，透過頻率分析，可以獲得各重現期年的有義波高與水位。本文以機率分析方法繪製各復現期之波高週期聯合機率分佈圖。波高水位聯合機率分析結果與傳統頻率分析方法結果比較顯示，傳統頻率分析結果有較保守的趨勢，在相同發生機率條件下，聯合機率分析所得之設計總水位結果高於傳統頻率分析所得。
本研究透過蒙地卡羅模擬大量且多次的數據來從事波高水位聯合機率分佈的不確定性分析，以變異係數為不確定的度量指標，分析結果顯示，相近的資料筆數條件下，由模擬資料計算所得的不確定性低於現場觀測數據計算所得，顯示透過大量資料繁衍分析可以獲得穩定且較可靠的設計波高或水位，而大量現場資料的蒐集可以確保模擬結果的準確性，定量上的分析結果顯示，當模擬資料筆數超過1000筆時，由波高水位聯合機率分析求得的波高或水位之變異係數低於10%。此結果可作為日後蒐集現場資料數量上的參考。

Waves and water levels are the important factors of inundation in coastal area. Currently, Sea dike is the most important sea defenses in coastal area of Taiwan. The deterministic height of a dike will be much concerned to the success or failure for designed dike. Generally, the deterministic value of a dike height will be a linear accumulation value to the oceanic parameters of designed wave height, astronomical tide level and storm surge, i.e., the maximum wave height and the maximum water level will be considered to happen in a same time. This paper is a study to utilize the analytic approach of joint probability to probe into the recurrent probability of waves and water levels. Meanwhile, it will also make a comparison with the result of traditional analytic approaches. Survey stations which contain the wave height and the water tide level records in a same time will be selected one each from the eastern, southern, western and the northern of Taiwan respectively in this paper. Taking into account the mainly reason of dike’s damage due to typhoon in Taiwan, the analytic objective will be restrictedly focused on the maximum wave and the maximum water levels during the typhoon attacked period. In order to getting the adequate data from the field, it will assume that the observed data of each station and typhoon would be independent each other respectively. All the data will be combined into one group of wave height and water level versus the time series. So 111 typhoons data are obtained and there are 7,440 groups of data totally. The analytic result shows that the maximum wave height is a Weibull Distribution during the typhoon period and the maximum water level fits the Extreme Type I Distribution. The wave height and water levels in each recurrence period’s year will be derived via the frequency analysis. After Comparing with the result of Joint probability - wave heights and water levels, the total designed water level of traditional frequency analysis is towards conservative. Under the same condition, the analytic result of Joint probability is higher than the result of traditional frequency analysis.
Besides, method for the uncertainty analysis of Joint probability of waves and water levels is the Mote Carlo Simulation which is utilized to simulate numerous and repeated data in the paper. The coefficient of variation is an index of measure for the uncertainty analysis. The analysis result shows, under the condition of similar data quantities, the uncertainty index counting up from the simulation data is lower than the one counting up from the observation data of field. It means that a stable and reliable wave height or water level will be deterministic via the simulation of numerous data. Simultaneously, accuracy for the result of simulation will be confirmed via a collection of numerous data of field. In accordance with the result of quantity analysis, the coefficient of variation of waves or water levels which is derived from the joint probability of waves and water levels will be less than 10 % when the quantities of simulating data are exceeded in 1,000. So this result can be a reference for the collecting data of field hereafter.

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