Simulation of Rare Events in Stochastic Systems

The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.

Predicting Monsoon Intraseasonal Precipitation using a Low-Order Nonlinear Stochastic Model

The authors assess the predictability of large-scale monsoon intraseasonal oscillations (MISOs) as measured by precipitation. An advanced nonlinear data analysis technique, nonlinear Laplacian spectral analysis (NLSA), is applied to the daily precipitation data, resulting in two spatial modes associated with the MISO. The large-scale MISO patterns are predicted in two steps. First, a physics-constrained low-order nonlinear stochastic model is developed to predict the highly intermittent time series of these two MISO modes. The model involves two observed MISO variables and two hidden variables that characterize the strong intermittency and random oscillations in the MISO time series. It is shown that the precipitation MISO indices can be skillfully predicted from 20 to 50 days in advance. Second, an effective and practical spatiotemporal reconstruction algorithm is designed, which overcomes the fundamental difficulty in most data decomposition techniques with lagged embedding that requires extra information in the future beyond the predicted range of the time series. The predicted spatiotemporal patterns often have comparable skill to the MISO indices. One of the main advantages of the proposed model is that a short (3 year) training period is sufficient to describe the essential characteristics of the MISO and retain skillful predictions. In addition, both model statistics and prediction skill indicate that outgoing longwave radiation is an accurate proxy for precipitation in describing the MISO. Notably, the length of the lagged embedding window used in NLSA is crucial in capturing the main features and assessing the predictability of MISOs.

Data-Driven Localization Mappings in Filtering the Monsoon–Hadley Multicloud Convective Flows

This paper demonstrates the efficacy of data-driven localization mappings for assimilating satellite-like observations in a dynamical system of intermediate complexity. In particular, a sparse network of synthetic brightness temperature measurements is simulated using an idealized radiative transfer model and assimilated to the monsoon–Hadley multicloud model, a nonlinear stochastic model containing several thousands of model coordinates. A serial ensemble Kalman filter is implemented in which the empirical correlation statistics are improved using localization maps obtained from a supervised learning algorithm. The impact of the localization mappings is assessed in perfect-model observing system simulation experiments (OSSEs) as well as in the presence of model errors resulting from the misspecification of key convective closure parameters. In perfect-model OSSEs, the localization mappings that use adjacent correlations to improve the correlation estimated from small ensemble sizes produce robust accurate analysis estimates. In the presence of model error, the filter skills of the localization maps trained on perfect- and imperfect-model data are comparable.

Nonlinear Stochastic Analysis for Lateral Vibration of Footbridge under Pedestrian Narrowband Excitation

During the lateral vibration of footbridge, the pedestrian lateral load shows two distinct features: one is the vibration-dependency; another is the narrowband randomness caused by the variability between two subsequent walking steps. In this case, the lateral vibration of footbridge is actually a complicated, nonlinear stochastic system. In this paper, a novel nonlinear stochastic model for lateral vibration of footbridge is proposed, in which a velocity-dependent load model developed from Nakamura model is adopted to represent the pedestrian-bridge interaction and the narrowband stochastic characteristic is considered. The amplitude and phase involved Itô equations are established using the multiscale method. Based on the maximal Lyapunov exponent derived from these equations, the critical condition for triggering a large lateral vibration can be obtained by solving the stability problem. The validity of the proposed method is confirmed, based on performing the case studies of two bridges. Meanwhile, through parameter analysis, the influences of several crucial parameters on the stability of vibration are discussed.