具有稳定噪声的风暴潮随机动力学
Stochastic dynamics of storm surge with stable noise
摘要：
先进的环流（ADCIRC）和模拟近岸波（SWAN）耦合模式进行了修改，包括随机项的浅水方程，表示随机外力从碎片携带的浪涌和短期的本地规模的大气波动。我们在耦合模式的强迫项中加入了$α$ -稳定的噪声，在空间和时间上不相关。模型的输入是来自地形和水深、土地覆盖分类、潮汐势成分和大气强迫的非结构化计算网格。该模型模拟了塔克洛班市中心附近以每秒4米的速度冲过的约5米的浪涌高度。预计低估的模拟涌浪高度与裸地球模型和流体源的控制方程的情况下，而高估的模拟峰值高度也会发生由于存在混凝土障碍物，减少涌浪高度和淹没程度。在低潮和相对较高的流体速度时，随机模型对随机外力敏感。低潮发生在流速最大、水位最低的时候，而流速较高则是由风暴潮等外力带来的。然而，从确定性的解决方案的随机解的差异平均为零，并没有显着改善风暴潮模型在一般情况下，当涉及到加性噪声。这是预期的结果，因为所使用的噪声具有零均值。随着$α$趋于零，更大的跳跃发生得更频繁，因此为了仿真稳定性，$σ$需要与$10^{-8}$一样小。
英文摘要：
The Advanced Circulation (ADCIRC) and Simulating Nearshore Waves (SWAN) coupled model is modified to include a stochastic term in the shallow water equations that represents random external forces from debris carried by surge and short-term local scale atmospheric fluctuations. We added $α$-stable noise, uncorrelated in space and time, in the forcing terms of the coupled model. Inputs to the model are unstructured computational mesh derived from topography and bathymetry, land cover classification, tidal potential constituents and atmospheric forcing. The model simulated surge height of around five meters rushing at four meters per second near Tacloban City downtown. Underestimation of simulated surge height is expected with use of bare earth model and absence of fluid sources on the governing equations, while overestimation of simulated peak height also occurs due to presence of concrete barriers that reduced surge height and inundation extent. The stochastic model is sensitive to random external forces during low tide and relatively higher fluid speed. Low tide happens when the fluid speed is maximum and water elevation is lowest, while higher fluid speed is brought by external forces like storm surge. However, the difference of stochastic solutions from the deterministic solution averages to zero and there is no significant improvement of the storm surge model in general when it comes to additive noise. This is an expected result since the noise used has zero mean. As $α$ goes to zero larger jumps occur more frequently so $σ$ needs to be as small as $10^{-8}$ for simulation stability.
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