以希伯特黃轉換及其不確定性分析探討氣候變遷下河川流量和泥砂運動之變化

Abstract

本研究可分為河川流量分析和泥砂運動之模擬兩大方向，目的為探討流量及其泥砂顆粒在氣候變遷影響下流量和極端事件的變化情形。第一部份將Huang Transform (HHT)應用於台灣北部長時間的河川日流量資料，HHT為一種適用於非線性和非穩態時間序列的資料分析方法且可分為兩個部分：第一步為經驗模態分解法(Empirical Mode Decomposition)可將資料分成數個本質模態函數(Intrinsic Mode Function)；第二步為希伯特轉換，將各個IMF轉換成時間-頻率-能量的頻譜，可同時分析單一事件在時間軸和頻率域的改變情形。 本研究採用能量權重公式計算隱含於IMF中的各個時間尺度和長時間的變化趨勢，接著由特定的幾個時間尺度做為韋伯公式的門檻值搭配HHT做頻率分析，以進一步了解極端事件發生次數改變之情形。 此外亦考量到原始資料中可能因測量上的誤差或各種因素導致資料帶有不確定性，由點估計(PEM)和蒙地卡羅法(MC)的不確定性分析方法搭配HHT，此舉不僅能得到原本定率的IMF也可得到每個IMF的信心區間增加IMF結果的可信度，也可比較出各個不確定性方法之間的差異性。 泥砂運動模擬則是採用隨機跳躍擴散粒子追蹤模型(Stochastic jump diffusion-particle tracking model)，此模型包含三個基本元素:平均漂移項、紊流項和跳躍項，可用來模擬顆粒再不同流況中的運動情形，此外，考量到顆粒沉降到底床後再度懸浮的可能，本研究加入了pickup probability的機制模擬顆粒被帶起的情形，並由兩種不同顆粒的實驗數據做測試，發現粒徑較大也較重的顆粒並無法有效呈現出顆粒的軌跡。現地的模擬化簡了一些無法取得的參數，並由實際的流量資料搭配曼寧公式推得流速，長時間的模擬包含了隨時間變化速度項和頻率變化的探討，其中頻率變化的參數是由HHT的趨勢所推得，短時間則是比較隨機跳躍擴散模型(SJD)和隨機擴散模型(SD)在一颱風事件中顆粒由上游釋放之運動情形，並進一步推估實際可能到達水庫所需之時間。

The Hilbert-Huang transform (HHT), a data analysis method for dynamic and nonlinear timeseries, is applied to our analysis of flow rates and temperatures of rivers in northern Taiwan. HHT consists of two independent analytical methods: empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). EMD will decompose the time series data into several independent intrinsic mode functions (IMFs) and then derive the trend from the whole data span. As the EMD suffers from the problem of mode mixing, a new developed noise-assisted method called ensemble empirical mode decomposition (EEMD) will be adopted. Next, Hilbert transform turns the derived IMFs into time-frequency-energy functions, designated as Hilbert spectrum. An energy weighted measurement equation is adopted to calculate the hidden scales in the IMFs. The resulting time scales can range from a few months to decades and a long term trend. Furthermore, we combine the Weibull formula and HHT to estimate the occurrences number of extreme flow events per year. Results of frequency analysis can provide the change in extreme flow event occurrences under climate change. Meanwhile, uncertainty embedded in the flow rate data is also concerned. By using two kinds of Pont Estimate Methods and Monte Carlo simulation, one can obtain not only the derived IMFs and trend, but also uncertainty bands of the model predictions. The result of PEM show a little difference in the last few IMFs but give similar results as the Monte Carlo simulation. On the other hand, we simulate the particle movement in this area with the stochastic jump diffusion particle tracking model (SJD-PTM). Mechanism of resuspension is considered by the model of pickup probability. Two kinds of experimental data are tested here. It found that only the smaller and finer particles present a clear view of particle trajectories. Particles with larger diameter cannot be resuspended until the arrival of extreme events. Applications to the field data can be divided into long term simulation and an event based simulation (short period). Both include temporal velocity variation in the mean drift and frequency change in the Poisson process. Simulations with SJD-PTM will come out the ensemble means and variances of the particle trajectory. This result can be used to estimate the possible time for particles to reach the reservoir.