在動態氣候下建構高時間解析度降雨極值模型

Modeling High-Resolution Rainfall Extremes in a Changing Climate

戴廷宇(Ting-Yu Dai)

指導教授 ： 汪立本

國立臺灣大學/工學院/土木工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101494

摘要

序率降雨模式近年來常用於產生長時間降雨時間序列，作為後續水文應用（例如城市排水系統設計）之輸入應用。這種模式的特性在於使用具有物理意義的參數，而不是單純使用其統計特徵來模擬降雨的物理過程。然而，在建立序率降雨模式的領域，還有兩大挑戰需要克服。包括： 一、 在亞小時時間尺度下有效模擬極端降雨特性；二、 如何將氣候變遷之效應導入序率降雨模擬。

近年來有數個研究研究試圖解決第一個挑戰，其中Onof and Wang(2020)重新推導、建構了以Bartlett-Lewis矩形脈衝 (BLRP)模型的序率降雨模式，並證明此模式可以有效地模擬、重現亞小時和小時時間尺度之極端降雨量。然而，第二個挑戰還待解決，其中Cross et al.(2020)提出了一個多變量線性回歸方法，以建立 BLRP參數與每月的平均溫度之線性關係，藉以捕捉潛在的動態氣候環境。然而此方法仍使用人為定義的「月」的概念，當作捕捉季節性的時間單位。這可能無法有效捕捉到年與年之間季節之自然變化、時間偏移與長度之差異。為了改善上述缺點，本研究導入「滑動視窗」(sliding window)的概念，搭配使用大氣參數，突破人為「月」的概念，增進識別不同年份之間最相似的氣候條件的準確性。

本論文進一步分別基於機器學習及深度學習理論，提出了兩種新方法，導入氣候變化之效應至序率降雨模式，來動態地模擬短時極端降雨之統計特性。第一種方法結合了最近鄰法(nearest neighbor method)以及動態時間規整演算法 (Dynamic Time Warping)，從過去資料尋找最相似的氣候環境，以估算該氣候環境下之降雨統計特性。第二種方法則是基於自我注意力機制(self-attention)建立一類神經網絡( neural network)，直接根據當下之氣候環境預測降雨統計特性。

本研究使用歐洲中期天氣預報中心（European Centre for Medium-Range Weather Forecasts, or ECMWF）第五代的再分析氣候數據(ECMWF fifth-generation reanalysis, or ERA5)以及一位於德國Nettebach之長期高解析度降雨站資料(49年、5分鐘降雨)，用於驗證本研究所提出的方法，模擬估計當前和未來氣候中的正常及極端降雨特性之變化。實驗結果證明，本研究提出之新方法，可以更好地描述季節性，並有效地將動態氣候之效應導入區域序率降雨降雨模式。此外，基於自我注意力機制建立之類神經網絡(self-attention network)能更好地預測出一些統計上的離群事件(outliers)，此結果也為深度學習之應用領域開啟新的一頁。

關鍵字

序率模擬 ； 極端降雨 ； 人工智慧 ； 機器學習 ； 深度學習 ； 氣候變遷

並列摘要

Stochastic modelling is an increasingly popular method to generate long rainfall time series as input for the subsequent hydrological applications, such as the design of urban drainage system. It aims to resemble the physical process of rainfall using parameters with physical meanings, instead of its statistical features. There are, however, two main challenges in stochastic rainfall modelling. These are 1) reproduction of rainfall extremes at sub-hourly timescales, and 2) incorporation of the impact of climate change. Some recent breakthroughs have been made to address the first challenge. Onof and Wang (2020) reformulated the equations of the randomised Bartlett-Lewis rectangular pulse (BLRP) models and showed that the improved models can well preserving rainfall extremes at sub-hourly (5- and 10-min) and hourly timescales. The second challenge is however yet to be overcome. Cross et al. (2020) recently presented a multivariate regression method that associates BLRP parameters to temperature estimates on a monthly basis, attempting to capture the dynamics of the underlying climate. However, the concept of ‘calendar month’ --an artificial period of time-- was still employed to represent natural seasonality. This may fail capturing the natural shift and length difference of seasons between years. To address the above drawback, it is critical to ‘relax’ the concept of calendar month, so that the most similar climate conditions between different years can be better identified. This thesis presents two new methods for estimating short duration rainfall extremes in a changing climate with mechanistic stochastic rainfall models to circumvent the above drawback. Through generated storm profiles, the physical realization of extreme rainfall estimation at sub-hourly scales could be improved by BLRP models to simulate the rainfall extremes. Methods using Dynamic Time Warping (DTW) and a self-attention network are developed in which selected atmospheric variables (e.g. geopotential, temperature and so on) from the ERA5 re-analysis datasets. The methods are applied to the test site in Germany and used to synthesize long rainfall time series for extreme statistics modelling. The results suggest that the proposed methods can effectively incorporate the (large-scale) climate dynamics into local (point) rainfall modelling. In particular, the method based upon self-attention network demonstrate the potential of using deep learning in the climate change related applications.

並列關鍵字

stochastic modeling ； extreme rainfall ； artificial intelligence ； machine learning ； deep learning ； climate change

參考文獻

M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat,G. Irving, M. Isard, et al. Tensorflow: A system for large­scale machine learning. In 12th {USENIX} symposium on operating systems design and implementation ({OSDI}16), pages 265–283, 201

N. K. Ahmed, A. F. Atiya, N. E. Gayar, and H. El­Shishiny. An empirical comparison of machine learning models for time series forecasting. Econometric Reviews, 29(5­6):594–621, 2010.

J. J. Beersma and T. A. Buishand. Multi­site simulation of daily precipitation and tem­perature conditional on the atmospheric circulation. Climate Research, 25(2):121–133,2003.

R. E. Benestad. Downscaling precipitation extremes. Theoretical and Applied Climatology, 100(1):1–21, 2010.

Y. Bengio, P. Simard, and P. Frasconi. Learning long­term dependencies with gradient descent is difficult. IEEE transactions on neural networks, 5(2):157–166, 1994.