arXiv subjects

Justin Finkel

Publications and source records attributed to Justin Finkel.

13 recordsLinked to original sources

arXiv2026

Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?

AI weather prediction (AIWP) models rival physics-based models, yet the sources of their unexpected forecast accuracy and the degree of their physical fidelity remain unclear. Here, across a hierarchy spanning observation-based reanalysis, a general circulation model, and the multi-scale Lorenz system, we show that AI models can be trained to skillfully predict the past (backcast), though backcasts are systematically less accurate than forecasts. However, skillful backcasting appears to violate the second law of thermodynamics, and all these forecasting and backcasting models miss the butterfly effect. We trace the surprising forecast accuracy, missing butterfly, and skillful backcasting to a single cause: inevitable coarse-graining of training data, which removes fast, small scales and/or some variables. From the Lorenz system to official Pangu-Weather models, reducing coarse-graining makes AI predictions more physics-like (arrow of time and butterfly-like effects emerge), but forecast accuracy declines. Results offer an explanation for AIWP models' forecast skill: unlike physics-based models, they implicitly learn how fast, small scales affect large scales without inheriting their rapid error growth. Broader implications are that AI models' proliferation calls for revisiting predictability theories and long-term climate emulation strategies, and backcasting offers a useful, new lens for such analyses.

physics.ao-ph↗

arXiv2026

Routes to rare events with optimally timed perturbations: a Tent Map is all you need

Extreme weather events are difficult to understand for the same reason that they are dangerous: they happen rarely, catching victims unprepared when they do occur and scientists unable to assess risks confidently, given such limited precedent to learn from in the real world and high computational expense to simulate more examples. Rare event sampling (RES) algorithms seek to reduce this expense by forcing simulations more directly towards the extremes and then compensating for that forcing in statistical analysis. But the performance of RES hinges on several hyperparameter choices which are ad hoc in practice, and must be better understood if RES is to be broadly useful. This paper addresses one particular parameter, the \emph{advance split time} (AST), which prescribes when to perturb a simulation to split off the most informative possible ensemble of alternative extreme event scenarios. We prescribe the optimal AST as the time it takes for an initial perturbation to amplify into the size (inverse rarity) of the extreme event being targeted. For the Logistic and Tent maps, two archetypal examples of one-dimensional chaos, we rigorously derive and express the rule as a simple log-ratio between perturbation size and event rarity. The pair of examples also illuminates where the rule breaks down, and subsequently, we generalize the rule into a maximum-entropy criterion that solidifies recent heuristic and empirical results. Despite the idealized setting, our results deliver theoretical clarity that can anchor future developments of principled RES methods applicable to real-world, high-impact weather and climate extremes.

physics.ao-ph↗

arXiv2025

Using a rare event sampling technique to quantify extreme El Ni\~no event statistics

Extreme El Ni\~no events, such as occurred in 1997--1998, can induce severe weather on a global scale, with significant socioeconomic impacts that motivate efforts to understand them better. However, extreme El Ni\~no events are rare, and even in a very long direct numerical simulation (DNS) occur too infrequently for robust statistical characterization. This study seeks to generate extreme El Ni\~no event model data at a lower cost, while preserving statistical fidelity, using a rare event sampling technique, which preferentially devotes computational resources toward extreme events by generating a large, branched ensemble of interrelated trajectories through successive targeted perturbations. We specifically use the ``trying-early adaptive multi-level splitting'' (TEAMS) algorithm, which is well-suited for El Ni\~no's relative timescales of predictability and event duration. We apply TEAMS to the Zebiak-Cane model, an intermediate-complexity ENSO model for which it is feasible to run a long DNS (500000 years) for validation. We compare extreme El Ni\~no event return time estimates from TEAMS to those from the long DNS to assess TEAMS' accuracy and efficiency. We find that TEAMS accurately reproduces the return time estimates of the DNS at about one fifth the computational cost. Therefore, TEAMS is an efficient approach to study rare ENSO events that can be plausibly applied to full-complexity climate models.

physics.ao-ph↗

arXiv2025

Rare event sampling for moving targets: extremes of temperature and daily precipitation in a general circulation model

Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few once-per-century events with straightforward model integration, but that cost can be much reduced with \emph{rare event sampling}, which nudges ensembles of simulations to convert moderate events to severe ones, e.g., by steering a cyclone directly through a region of interest. With proper statistical accounting, rare event algorithms can provide quantitative climate risk assessment at reduced cost. But this can only work if ensemble members diverge fast enough. Sudden, transient events characteristic of Earth's midlatitude storm track regions, such as heavy precipitation and heat extremes, pose a particular challenge because they come and go faster than an ensemble can explore the possibilities. Here we extend standard rare event algorithms to handle this challenging case in an idealized atmospheric general circulation model, achieving $\sim5-10$ times sped-up estimation of long return periods for extremes of surface temperature and daily precipitation (e.g., a return period of 150 years from 20 years of simulation). The algorithm, called TEAMS (``trying-early adaptive multilevel splitting''), was developed previously with a toy chaotic system, and relies on a key parameter -- the advance split time -- which may be estimated based on simple diagnostics of ensemble dispersion rates. The results are promising for accelerated risk assessment across a wide range of physical hazards using more realistic and complex models with acute computational constraints.

physics.ao-ph↗

arXiv2025

Boosting Ensembles for Statistics of Tails at Conditionally Optimal Advance Split Times

Climate science needs more efficient ways to study high-impact, low-probability extreme events. Ensemble boosting, a form of rare event sampling, offers a novel strategy to extract more information from those occasional simulated events, by perturbing them slightly to probe alternative scenarios immediately instead of waiting many simulation-years for the next event. But statistical accuracy and efficiency depend on the perturbation details. In particular for sudden and transient events like precipitation, performance of boosting depends sensitively on the \emph{advance split time} (AST), which must be long enough before the event to let the ensemble diversify, but not so much as to destroy the event. In pursuit of principled guidelines, we study the effect of AST for sampling tracer fluctuations in a quasigeostrophic flow, an idealized but informative model of midlatitude storm track dynamics. We formulate AST selection as an optimization problem for statistical fidelity with a ground truth. Since ground truth is not known in practice, we propose a proxy objective function of \emph{thresholded entropy}, which rewards ensembles with both a high mean and a large spread. We show that ensemble boosting, when given a well-chosen AST and equipped with methods to estimate probabilities, can accurately sample extremes at long return periods. We furthermore find evidence that thresholded entropy successfully identifies an optimal AST, which is roughly 1-3 eddy turnover timescales in the quasigeostrophic system. Moreover, this proxy captures the \emph{variation} of AST with the target location of the tracer within the flow field, suggesting generalizability to climate models. Large-scale deployment of our method will require further development in adaptive optimization strategies, but our work here is an essential first step for establishing what must be optimized.

physics.ao-ph↗

arXiv2024

Using Explainable AI and Transfer Learning to understand and predict the maintenance of Atlantic blocking with limited observational data

Blocking events are an important cause of extreme weather, especially long-lasting blocking events that trap weather systems in place. The duration of blocking events is, however, underestimated in climate models. Explainable Artificial Intelligence are a class of data analysis methods that can help identify physical causes of prolonged blocking events and diagnose model deficiencies. We demonstrate this approach on an idealized quasigeostrophic model developed by Marshall and Molteni (1993). We train a convolutional neural network (CNN), and subsequently, build a sparse predictive model for the persistence of Atlantic blocking, conditioned on an initial high-pressure anomaly. Shapley Additive ExPlanation (SHAP) analysis reveals that high-pressure anomalies in the American Southeast and North Atlantic, separated by a trough over Atlantic Canada, contribute significantly to prediction of sustained blocking events in the Atlantic region. This agrees with previous work that identified precursors in the same regions via wave train analysis. When we apply the same CNN to blockings in the ERA5 atmospheric reanalysis, there is insufficient data to accurately predict persistent blocks. We partially overcome this limitation by pre-training the CNN on the plentiful data of the Marshall-Molteni model, and then using Transfer Learning to achieve better predictions than direct training. SHAP analysis before and after transfer learning allows a comparison between the predictive features in the reanalysis and the quasigeostrophic model, quantifying dynamical biases in the idealized model. This work demonstrates the potential for machine learning methods to extract meaningful precursors of extreme weather events and achieve better prediction using limited observational data.

physics.ao-ph↗

arXiv2024

Bringing statistics to storylines: rare event sampling for sudden, transient extreme events

A leading goal for climate science and weather risk management is to accurately model both the physics and statistics of extreme events. These two goals are fundamentally at odds: the higher a computational model's resolution, the more expensive are the ensembles needed to capture accurate statistics in the tail of the distribution. Here, we focus on events that are localized in space and time, such as heavy precipitation events, which can start suddenly and decay rapidly. We advance a method for sampling such events more efficiently than straightforward climate model simulation. Our method combines elements of two recent approaches: adaptive multilevel splitting (AMS), a rare event algorithm that generates rigorous statistics at reduced cost, but that does not work well for sudden, transient extreme events; and "ensemble boosting" which generates physically plausible storylines of these events but not their statistics. We modify AMS by splitting trajectories well in advance of the event's onset following the approach of ensemble boosting, and this is shown to be critical for amplifying and diversifying simulated events in tests with the Lorenz-96 model. Early splitting requires a rejection step that reduces efficiency, but nevertheless we demonstrate improved sampling of extreme local events by a factor of order 10 relative to direct sampling in Lorenz-96. Our work makes progress on the challenge posed by fast dynamical timescales for rare event sampling, and it draws connections with existing methods in reliability engineering which, we believe, can be further exploited for weather risk assessment.

physics.ao-ph↗

arXiv2022

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. We illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

physics.comp-ph↗

arXiv2022

Revealing the statistics of extreme events hidden in short weather forecast data

Extreme weather events have significant consequences, dominating the impact of climate on society. While high-resolution weather models can forecast many types of extreme events on synoptic timescales, long-term climatological risk assessment is an altogether different problem. A once-in-a-century event takes, on average, 100 years of simulation time to appear just once, far beyond the typical integration length of a weather forecast model. Therefore, this task is left to cheaper, but less accurate, low-resolution or statistical models. But there is untapped potential in weather model output: despite being short in duration, weather forecast ensembles are produced multiple times a week. Integrations are launched with independent perturbations, causing them to spread apart over time and broadly sample phase space. Collectively, these integrations add up to thousands of years of data. We establish methods to extract climatological information from these short weather simulations. Using ensemble hindcasts by the European Center for Medium-range Weather Forecasting (ECMWF) archived in the subseasonal-to-seasonal (S2S) database, we characterize sudden stratospheric warming (SSW) events with multi-centennial return times. Consistent results are found between alternative methods, including basic counting strategies and Markov state modeling. By carefully combining trajectories together, we obtain estimates of SSW frequencies and their seasonal distributions that are consistent with reanalysis-derived estimates for moderately rare events, but with much tighter uncertainty bounds, and which can be extended to events of unprecedented severity that have not yet been observed historically. These methods hold potential for assessing extreme events throughout the climate system, beyond this example of stratospheric extremes.

physics.ao-ph↗

arXiv2022

Snow topography on undeformed Arctic sea ice captured by an idealized "snow dune" model

Our ability to predict the future of Arctic sea ice is limited by ice's sensitivity to detailed surface conditions such as the distribution of snow and melt ponds. Snow on top of the ice decreases ice's thermal conductivity, increases its reflectivity (albedo), and provides a source of meltwater for melt ponds during summer that decrease the ice's albedo. In this paper, we develop a simple model of pre-melt snow topography that accurately describes snow cover of flat, undeformed Arctic sea ice on several study sites for which data was available. The model considers a surface that is a sum of randomly sized and placed "snow dunes" represented as Gaussian mounds. This model generalizes the "void model" of Popovi\'c et al. (2018) and, as such, accurately describes the statistics of melt pond geometry. We test this model against detailed LiDAR measurements of the pre-melt snow topography. We show that the model snow-depth distribution is statistically indistinguishable from the measurements on flat ice, while small disagreement exists if the ice is deformed. We then use this model to determine analytic expressions for the conductive heat flux through the ice and for melt pond coverage evolution during an early stage of pond formation. We also formulate a criterion for ice to remain pond-free throughout the summer. Results from our model could be directly included in large-scale models, thereby improving our understanding of energy balance on sea ice and allowing for more reliable predictions of Arctic sea ice in a future climate.

nlin.PS↗

arXiv2021

Data-driven transition path analysis yields a statistical understanding of sudden stratospheric warming events in an idealized model

Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting), and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective "average event." We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT's capacities on a wave-mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass (1976), which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article (Finkel et al. 2021) studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also \emph{backward in time} to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the \emph{reactive current}. The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.

physics.ao-ph↗

arXiv2021

Learning forecasts of rare stratospheric transitions from short simulations

Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, Sudden Stratospheric Warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These \emph{optimal forecasts} concretely measure the event's progress. Direct numerical simulation can estimate them in principle, but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are \emph{short} compared to the timescale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass (1976) and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in timescales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

physics.ao-ph↗

arXiv2020

Path properties of atmospheric transitions: illustration with a low-order sudden stratospheric warming model

Many rare weather events, including hurricanes, droughts, and floods, dramatically impact human life. To accurately forecast these events and characterize their climatology requires specialized mathematical techniques to fully leverage the limited data that are available. Here we describe \emph{transition path theory} (TPT), a framework originally developed for molecular simulation, and argue that it is a useful paradigm for developing mechanistic understanding of rare climate events. TPT provides a method to calculate statistical properties of the paths into the event. As an initial demonstration of the utility of TPT, we analyze a low-order model of sudden stratospheric warming (SSW), a dramatic disturbance to the polar vortex which can induce extreme cold spells at the surface in the midlatitudes. SSW events pose a major challenge for seasonal weather prediction because of their rapid, complex onset and development. Climate models struggle to capture the long-term statistics of SSW, owing to their diversity and intermittent nature. We use a stochastically forced Holton-Mass-type model with two stable states, corresponding to radiative equilibrium and a vacillating SSW-like regime. In this stochastic bistable setting, from certain probabilistic forecasts TPT facilitates estimation of dominant transition pathways and return times of transitions. These "dynamical statistics" are obtained by solving partial differential equations in the model's phase space. With future application to more complex models, TPT and its constituent quantities promise to improve the predictability of extreme weather events, through both generation and principled evaluation of forecasts.

physics.ao-ph↗