Application of Empirical Path Model based on kernel density estimation in the construction of synthetic typhoon in Northwest Pacific Ocean
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摘要: 合理评估台风对沿海区域的影响程度与风险对于科学抵御台风灾害而言十分重要，而我国具有详细的台风观测记录至今也仅有60多年的历史，这使得在推算具有一定重现期的极值风速及相应的极值波高和潮位等特征参数时存在局限性，同时台风观测样本量的不足也限制了如深度学习等数据驱动型模型在台风灾害预报中的应用。因此，有必要基于实际台风行进规律构建虚拟台风以克服历史数据量不足的问题。故本文采用基于核密度估计的经验路径模型，在西北太平洋海域构建了18 671场虚拟台风，将虚拟台风的起始与终止位置、发生频数、行进速度和行进方向等参数与实际发生的台风进行统计意义上的对比分析。结果表明，基于本文方法构建的虚拟台风总体上符合西北太平洋历史台风的行进规律。通过这些虚拟台风的构建，可为中国沿海极值波浪和风暴增水研究提供数据量足够且性能可靠的虚拟台风样本数据库。Abstract: Reliable assessment of the impact and risk of typhoons on coastal areas is very important for scientific resistance to typhoon disasters. China has a detailed typhoon observation record with a history of only 60 years, which makes it limited in estimating extreme wind speed with a long recurrence period and corresponding extreme wave height and tide level. The insufficient records also limits the application of data-driven models in typhoon disaster prediction. Therefore, it is necessary to construct synthetic typhoons based on the actual typhoon travel law to overcome the problem of insufficient historical observations. In this paper, 18 671 synthetic typhoons were constructed in the Northwest Pacific Ocean by using the Empirical Path Model based on kernel density estimation, and the parameters such as the start and end position, frequency of occurrence, travel speed and direction of the synthetic typhoons were statistically compared and analyzed with historical typhoons. The results show that the synthetic typhoon constructed based on the proposed method is generally consistent with the traveling characteristics of historical typhoons in the Northwest Pacific Ocean. Through the construction of these synthetic typhoons, a synthetic typhoon database with sufficient data and reliable performance can be provided for the study of extreme wave and storm surge along the coast of China.
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图 2 西北太平洋1959−2020年间历史台风路径
Fig. 2 Historical typhoon tracks from 1959 to 2020 in Northwest Pacific Ocean
图 3 台风起始参数累积分布密度拟合
a. 台风年发生频数；b. 台风初始移速；c. 台风初始移向
Fig. 3 Typhoon initial parameter cumulative distribution density fitting
a. Annual frequency of typhoon occurrence; b. initial moving speed of typhoon; c. initial moving direction of typhoon
图 4 历史台风路径（a）与随机抽取的1 520场虚拟台风路径（b）
Fig. 4 Historical typhoon tracks (a) and randomly selected 1 520 sysnthtic typhoon tracks (b)
图 5 历史台风与随机抽取的1 520场虚拟台风起始点对比（a）与终止点对比（b）
Fig. 5 Comparison between historical typhoons and 1 520 randomly selected synthetic typhoons generating points (a) and disappearing points (b)
图 7 影响各站点的历史台风与虚拟台风的年发生频数对比（a）和台风中心最大风速平均值和标准差对比（b）
Fig. 7 Comparison of annual frequency of historical typhoons and synthetic typhoons affecting each station (a) and comparison of mean and standard deviation of maximum wind speed at the center (b)
图 8 影响M25（a）、M30（b）和M35（c）的历史台风与虚拟台风的各强度等级占比
Fig. 8 The proportion of historical typhoons and virtual typhoons affecting M25 (a), M30 (b), and M35 (c) at different intensity levels
图 9 12个特征点处的历史台风及虚拟台风移速的累计概率分布曲线对比
Fig. 9 Comparison of cumulative probability distribution curves of historical and virtual typhoon movement speeds at 12 characteristic stations
图 10 12个特征点处的历史台风及虚拟台风移向的概率密度曲线对比
Fig. 10 Comparison of probability density curves of historical and virtual typhoon movement directions at 12 characteristic stations
表 1 热带气旋分类标准
Tab. 1 Standard for classification of tropical cyclones
热带气旋类型 底层中心附近最大平均风速（10 min平均风速）/（m·s−1） 超强台风 ≥ 51 强台风 41.5～50.9 台风 32.7～41.4 强热带风暴 24.5～32.6 热带风暴 17.2～24.4 热带低压 10.8～17.1 
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表 2 各分布的5%显著水平下的KS检验
Tab. 2 KS test at 5% significance level for each distribution
分布类型 $ {D}_{n} $ 样本量 $ {D}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t},\; 0.05} $ 泊松分布
（台风年发生频数）0.066 62 0.173 伽马分布
（台风初始移速）0.026 1520 0.035 双峰分布
（台风初始移向）0.015 1520 0.035
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