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Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping (N-tipping) occurs when there are random transitions between two attractors of the underlying deterministic system. This work investigates R-tipping and N-tipping events in a carbonate system in the upper ocean, in which the key objective is understanding how the system undergoes tipping away from a stable fixed point in a bistable regime. While R-tipping away from the fixed point fits the framework of an established scenario, N-tipping poses challenges due to a periodic orbit forming the basin boundary for the attracting fixed point of the underlying deterministic system. Furthermore, for N-tipping, we are interested in the situation where noise is away from the small noise limit as it is more appropriate for the application. We postulate that two key points on the basin boundary are critical to understanding the noisy behavior: the exit point of what we find to be the most probable escape path (MPEP), which is determined by the Onsager–Machlup functional, and the pivot point, a point identified through the Maslov index, which appears as an obstacle to the movement of the escape region of noisy trajectories through the periodic orbit as noise increases. 

We investigate ocean circulation changes through the lens of data assimilation using a reduced-order model. Our primary interest lies in the Stommel box model, which reveals itself to be one of the most practicable models that has the ability of reproducing the meridional overturning circulation. The Stommel box model has at most two regimes: TH (temperature driven circulation with sinking near the north pole) and SA (salinity driven with sinking near the equator). Currently, the meridional overturning is in the TH regime. Using box-averaged Met Office EN4 ocean temperature and salinity data, our goal is to provide a probability that a future regime change occurs and establish how this probability depends on the uncertainties in initial conditions, parameters, and forcings. We will achieve this using data assimilation tools and DAPPER within the Stommel box model with fast oscillatory regimes. 

Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth’s atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ, forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ(t), the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics. 

The disparity in the impact of COVID-19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number (\begin{document}$$ R_t $$\end{document}), can be hard to calculate from this data especially for individual populations. Furthermore, disparities in the availability of testing, record keeping infrastructure, or government funding in disadvantaged populations can produce incomplete data sets. In this work, we apply ensemble data assimilation techniques which optimally combine model and data to produce a more complete data set providing better estimates of the critical metrics used by public health officials and epidemiologists. We employ a multi-population SEIR (Susceptible, Exposed, Infected and Recovered) model with a time dependent reproductive number and age stratified contact rate matrix for each population. We assimilate the daily death data for populations separated by ethnic/racial groupings using a technique called Ensemble Smoothing with Multiple Data Assimilation (ESMDA) to estimate model parameters and produce an \begin{document}$$R_t(n)$$\end{document} for the \begin{document}$$n^{th}$$\end{document} population. We do this with three distinct approaches, (1) using the same contact matrices and prior \begin{document}$$R_t(n)$$\end{document} for each population, (2) assigning contact matrices with increased contact rates for working age and older adults to populations experiencing disparity and (3) as in (2) but with a time-continuous update to \begin{document}$$R_t(n)$$\end{document}. We make a study of 9 U.S. states and the District of Columbia providing a complete time series of the pandemic in each and, in some cases, identifying disparities not otherwise evident in the aggregate statistics.