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To exhange research ideas about the mathematics of climate both within and beyond the network, MCRN runs an online Colloquium series Mondays noon-1pm PDT. Speakers aim for 45 min talks, with the rest of the time devoted to discussion.
MCRN members receive Colloquium invitations by email. To join MCRN, please fill out this form. For inquiries about the Colloquium, please email Dr. Christian Sampson at csampson-at-ucar.edu.
Our 2024 schedule includes:
Aug. 12 Dynamics of glacial cycles
Hans Kaper, Georgetown U.
Abstract: The geological record shows great variability of Earth’s climate. During the Pleistocene Epoch (from approximately 2.6 Myr before present (BP) until approximately 11.7 Kyr BP), continental ice sheets expanded and contracted over significant areas, especially in the Northern Hemisphere. This happened in a more or less cyclical fashion, with periods of approximately 41 Kyr during the early Pleistocene and approximately 100 Kyr during the late Pleistocene. In this talk I will discuss a conceptual model first presented by Maasch and Saltzman (1990) to explain this persistence of glacial cycles as the result of the interaction of atmospheric carbon dioxide and the strength of the North Atlantic overturning circulation. The model consists of a system of three ordinary differential equations with a rich bifurcation structure.
Aug. 19 An overview of mathematical results regarding atmospheric convection
Roland Welter, U. Hamburg
Abstract: In the study of climate, general circulation models aim to accurately represent the motions of the atmosphere and ocean using equations from fluid dynamics. However, vertical accelerations are often set equal to zero in primitive equation models. This assumption is partially justified from a physical viewpoint, since the vertical accelerations should be small compared to more dominant forces (gravity, etc) which are in an approximate hydrostatic balance. Furthermore, this yields a significant mathematical benefit since the well-posedness theory for such equations is then much more satisfactory. On the other hand, such an assumption cannot be entirely physically accurate, and hence often in the climate community additional terms are included to account for the discrepancy. This procedure is known as parameterization, and there is not a consensus about a correct or optimal way to parameterize convection.
In this presentation, I will present recent results which develop a mathematically rigorous framework for studying vertical heat transport in turbulent convection. Starting from the paradigmatic Boussinesq-Oberbeck equations, heat transport is investigated via the HKC hierarchy of Galerkin truncated ODE models of increasing dimension. The dynamics of these models are studied, and particular attention is given to stable values of heat transport, as well as the convergence across models where the models accurately represent the PDE. Implications for energetically consistent parameterization of convection will then be discussed.
Aug. 26 Tipping and EWS in some nonautonomous scalar ODEs
Iacopo Longo, Imperial College London
Abstract: Unlike their autonomous counterparts, nonautonomous bifurcations are inherently complicated already in dimension one. Not only equilibria and periodic orbits become extremely rare, but also new phenomena appear which are not possible in the autonomous case. In this talk, we characterize the dynamical scenarios for nonautonomous scalar concave and d-concave differential equations and study the occurrence of nonautonomous saddle-node bifurcations of hyperbolic solutions. Concave and d-concave problems are largely used in theoretical ecology but also in theoretical climate science. Additionally, we investigate the use of finite-time Lyapunov Exponents as Early Warning signs of a critical transition and show how they can be successfully employed to avoid the collapse of a certain desirable state.
Sep. 9 The pending collapse of the Atlantic Overturning Circulation: a false alarm or an Early Warning Signal of a tipping point?
Ka-Kit Tung, University of Washington
Abstract: There has recently been intense publicity in news media about the pending collapse of AMOC, as early as 2025, with severe global climate consequences. AMOC is just one of many possible tipping points of the global climate system; there is urgent need to understand the possible Early Warning Signals (EWS) that tell us how close we are to any tipping point. We examine the mathematics and the data analyses of EWS. There does not appear to be any EWS in the deterministic system, but the behavior of noise in the stochastic system may yield some clues. Approaching a saddle-node bifurcation in a stochastic dynamical system, variance of the noise and its autocorrelations may increase and these are taken as classic examples of EWS, but they could also increase due to other external reasons. More sophisticated methods involve using results of Ornstein-Uhlenbeck process, and empirical generalized regression analyses. The need for deep mathematics has fostered close collaborations between climate scientists and mathematicians/statisticians, but going for ever deeper mathematics may not necessarily be the right approach. As EWS depends sensitively on the character of the “noise” in the time series, how data are collected, reanalyzed or assimilated also need to be carefully considered. Because of the large natural oscillations in AMOC, with a quasi-period of about 60-100 years, data lengths need to be at least 120 years. Our conclusion is that the existing prediction on tipping points are false alarms, and furthermore, the prospect of finding EWS may need to wait another hundred years.
Sep. 16 Transit times for nonautonomous compartmental systems and applications to ecology (Modified schedule: 8am PDT)
Martin Rasmussen, Imperial College London
Abstract: We develop a theory for transit times and mean ages for nonautonomous (linear) compartmental systems. We show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time. We apply these results two nonautonomous compartmental systems, modeling the terrestrial carbon cycle and breeder states of the Southern Fulmar seabird. Joint work with Alan Hastings, George Chappelle, Matthew Smith, Yiqi Luo, Folashade Agusto, Benito Chen-Charpentier, Forrest Hoffman, Jiang Jiang, Katherine Todd-Brown, Ying Wang, Ying-Ping Wang.
Sep. 23 The Maslov index in dynamical systems and PDEs: recent applications and connections to stability
Emmanuel Fleurantin, George Mason University and RENCI
Abstract: This talk introduces the Maslov index and its application to analyzing dynamical systems, particularly in the context of wave stability. The Maslov index, a topological invariant associated with classical oscillation theorems, has been generalized to detect instabilities in solutions of evolutionary partial differential equations. We will explore computational and analytical tools for stability analysis, presenting a method that represents solutions as angles fluctuating within the phase space of the eigenvalue problem. As a case study, we will examine the cubic nonlinear Schrödinger equation (NLSE) with a decaying potential. Although the NLSE is not widely used in large-scale climate modeling, it has applications in climate science and oceanography, providing an excellent model for our analysis. We will demonstrate how to count eigenstates in the gap on the imaginary axis beneath the essential spectrum, extending Sturm-Liouville theory via the Maslov index. This approach has broad implications across applied mathematics and physics, offering insights into complex phenomena in both natural and engineered systems.
Oct. 7 No need to reinvent the wheel: data assimilation in the age of AI
Ivo Pasmans, University of Reading
Abstract: In recent years, there has been a proliferation of studies which apply Artificial Intelligence (AI) to some scientific problem or another. However, in many cases, AI techniques—particularly those in machine learning— used in these studies function as a substitute for, or a variation of, traditional data assimilation methods which aim to combine limited observations with a prior estimate to retrieve the most likely value of the truth. This talk will explore the relationship between AI and data assimilation, focusing on key data assimilation techniques like Kalman filtering, variational methods, and ensemble-based approaches. We will examine the strengths and limitations of these methods and compare them with popular machine learning algorithms. Additionally, promising approaches that integrate machine learning with traditional data assimilation techniques will be discussed, offering new possibilities for enhancing predictive accuracy and computational efficiency in various scientific applications.
Oct. 14 Numerical Weather Prediction, JEDI , and a Hybrid Tangent Linear Model.
Christian Sampson, Joint Center for Satellite Data Assimilation
Abstract: Accurate weather prediction matters to everyone and has become even more important in our changing climate. We often refer to the combination of weather models and Data Assimilation as Numerical Weather Prediction (NWP), which aims to combine a model of the Earth's atmosphere with observations of it to produce as accurate a forecast as possible. This work is carried out in large operational centers across the globe which require massive compute power, many people, tons of code, and lots of science. Too often though, it can be difficult to incorporate new innovations into these systems, and when one innovation is proven, porting it to other agencies or groups requires a repetition of work slowing research to operations. The Joint Effort for Data assimilation Integration (JEDI) project aims to help alleviate this problem. JEDI is a generic Data Assimilation software suite developed for use by NOAA, NASA, The Navy, The Air Force and the UK Met Office at the Joint Center For Satellite Data Assimilation (JCSDA). This model agnostic system allows anyone with a model interface to JEDI to use its DA algorithms, observation operators, covariance matrices, and facilitate timely ingest of the newest observations. Further, when an innovation is added to JEDI it is available immediately for testing or deployment by multiple agencies and groups. In this talk I will briefly describe NWP, the JEDI project, and highlight one new innovation in the JEDI system, a hybrid tangent linear model for use in 4d-var schemes. I will also briefly describe how you can use JEDI or contribute to the project to accelerate your research to operations.
Oct. 21 Stability of floating objects
Dan Anderson, George Mason University
Abstract: We investigate with mathematical and computational techniques, along with simple table-top experiments, the stability of floating objects. Our focus is on long objects with uniform cross section. We explore both simple cross sectional shapes as well has highly complex shapes. We are motivated to explore this problem by observations of patterns on icebergs. While the iceberg problem involves complex shape evolution associated with processes such as melting and/or calving, we focus on simpler case of static floating objects. We apply Archimedes' Principle along with a potential energy formulation that nonetheless offers excellent insight into some of these observations. We compare our mathematical model predictions to measurements from simple table-top experiments. We also demonstrate an extension of our theory to objects that float at a two-fluid interface (e.g. oil-water). We have developed publicly-available code that, along with 3D printing technology, can be used to explore stability of floating shapes of the user's own design.
Oct. 28 Insights into how Earth accumulates heat: Manifestations of radiative forcing and feedback in the satellite record
Shiv Priyam Raghuraman, University of Illinois Urbana-Champaign
Abstract: How Earth gains and loses energy is key to its habitability because perturbations to the planetary radiation balance alters the entire climate system. We now not only have continuous satellite observations of Earth's radiation budget, but also climate models that represent the Earth system better than ever before. My talk will focus on understanding why Earth is accumulating heat rapidly by leveraging satellite observations and climate models. I will demonstrate how anthropogenic radiative forcing and feedbacks from greenhouse gases, aerosols, clouds, and sea-ice changes have caused an increase in Earth’s energy imbalance.
Nov. 18 Gradient Constrained Variational Problems: A Priori and A Posteriori Error Identities (Modified schedule: 8am PDT)
Rohit Khandelwal, George Mason University
Abstract: Nonsmooth variational problems are ubiquitous in science and engineering, for e.g., fracture modeling and contact mechanics. This talk presents a generic primal-dual framework to tackle these types of nonsmooth problems. Special attention is given to variational problems with gradient constraints. The key challenge here is how to project onto the constraint set both at the continuous and discrete levels. In fact, both a priori and a posteriori error analysis for such nonsmooth problems has remained open.
In this talk, on the basis of a (Fenchel) duality theory at the continuous level, an a posteriori error identity for arbitrary conforming approximations of primal-dual formulations is derived. In addition, on the basis of a (Fenchel) duality theory at the discrete level, an a priori error identity for primal (Crouzeix–Raviart) and dual (Raviart–Thomas) formulations is established. The talk concludes by deriving the optimal a priori error decay rates.
Dec. 2 Pathways to spatial instability in a model of fire propagation
Olivia Chandrasekhar, Los Alamos National Laboratory and University of North Carolina at Chapel Hill
Abstract: An equilibrium solution to a time-dependent system is considered stable if small disturbances decay in time and the solution eventually returns to its original form, perhaps up to a translation. Instability, on the other hand, is characterized by disturbances that grow exponentially and cause the solution to transition to a new, qualitatively different form. Often, the onset of instability leads to the formation of spatially patterned states. This type of spatial patterning is characteristic of a number of emergent phenomena in the field of wildland fire science. In this talk, we introduce several such phenomena and investigate pathways to instability in a model that captures key features of the underlying physical system. Specifically, we investigate a reaction-diffusion model of temperature and fuel concentration with a spatially dependent wind term. Our findings demonstrate that the existence of a spatially dependent, first-order forcing term capturing the dynamics of the local wind velocity leads to the emergence of patterned front solutions.
Dec. 9 From Traits to Temperatures: Predicting the Risk of Mosquito-Borne Disease Outbreaks
Kyle Dahlin, Virginia Tech
Abstract: Mosquito-borne diseases, such as malaria, dengue, and Zika, are pressing global health concerns, with rising burdens exacerbated by climate change. Warming temperatures will likely expand mosquito habitats and accelerate their life cycle, necessitating the development of better tools for outbreak prediction. I will present a mathematical framework for mosquito-borne pathogen transmission that incorporates host ecological characteristics and thermal performance curves describing temperature-dependent mosquito traits. Our results show that host availability and biting tolerance shift transmission thermal optima and niches, while host life history traits modulate transmission potential. These nonlinear interactions between temperature, host traits, and mosquito traits highlight the importance of including host behavior and ecological traits in outbreak prediction models. These insights increase our understanding of the mechanisms driving disease risk and emphasize the critical role of mathematics in guiding public health strategies under changing climatic conditions.
Dec. 16 An investigation of tipping mechanisms in a carbon cycle model
Katherine Slyman, Boston College
Abstract: Abstract: 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. We investigate 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 is straightforward, N-tipping poses challenges due to a periodic orbit forming the basin boundary for the attracting fixed point of the underlying deterministic system. Furthermore, in the case of N-tipping, we are interested in the case where noise is away from the small noise limit, as it is more appropriate for the application. We compute the most probable escape path (MPEP) for our system, resulting in a firm grasp on the least action path in an asymmetric system of higher scale. Our analysis shows that the carbon cycle model is susceptible to both tipping mechanisms.
Our 2025 schedule includes:
Jan. 27 Computing Lyapunov exponents efficiently
Evelyn Sander, George Mason University
Abstract: The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics, with the size of the exponent indicating the strength of the chaos, or in the case of a negative exponent, a measure of the how far an orbit is from being chaotic. However, the standard orthogonalization-based method for computing Lyapunov exponents converges slowly---if at all. Many alternatively techniques have been developed to distinguish between regular and chaotic orbits, though most do not compute the exponents. In this talk, I will discuss how to compute the Lyapunov spectrum in three ways, comparing and contrast these three methods: the standard method, the weighted Birkhoff average (WBA), and the ``mean exponential growth rate for nearby orbits'' (MEGNO).
Feb. 10 New insights into CO2 radiative forcing
Nadir Jeevanjee, National Oceanic and Atmospheric Administration
Abstract: CO2 radiative forcing has been well studied for decades, and detailed benchmark models simulate it in idealized cases with great accuracy. At the same time, coarse-resolution global climate models (GCMs) differ in their estimates of global CO2 forcing, and questions linger regarding its spatial variations as well as its logarithmic scaling with CO2 concentration. In this talk we present a recently developed analytical model for CO2 forcing which answers these questions and also illuminates a previously unidentified, major source of spread in GCM estimates of CO2 forcing.
Feb. 24 Robustness of pushed and pulled invasion fronts in singularly perturbed reaction-diffusion systems
Matt Holzer, George Mason University
Abstract: When studying invasion fronts in systems of reaction-diffusion equations one often considers asymptotic limits where a system parameter is taken to be asymptotically large or small. In this limit, it is sometimes possible to obtain a reduced equation which is more amenable to analysis. This talk will focus on mathematical techniques to justify this reduction. Using a combination of geometric singular perturbation theory and persistence results under regular perturbations, we show that the pushed and pulled fronts obtained in the reduced system persist for the full system. The primary example to be considered is a logistic Keller-Segel equation with chemorepulsion. This is joint work with Montie Avery and Arnd Scheel.
Mar. 3 Rate-Induced Tipping in a Moving Habitat
Blake Barker, Brigham Young University
Abstract: We consider a scalar reaction-diffusion equation with a non-autonomous reaction term representing a spatially localized, single-species, favorable habitat zone moving from one location to another. We identify a critical displacement value above which tipping occurs, and we demonstrate in this scenario the existence of a critical rate at which the system undergoes rate-induced tipping. That is, we identify a critical rate above which an initially thriving habitat population becomes extinct due to the habitat changing too rapidly.
Mar. 10 Metastability of the Altantic ocean circulation in an intermediate-complexity earth system model
Reyk Börner, Utrecht University
Abstract: There is growing concern that the Atlantic Meridional Overturning Circulation (AMOC), a vital Earth system component, could weaken or even collapse under climate change. Despite the severe potential impacts associated with such a transition, it remains extremely challenging to reliably estimate the proximity to a critical threshold and to predict the AMOC's fate under future anthropogenic forcing. We argue that a global stability view on the dynamics beyond the detection of early-warning signals is needed for a robust risk assessment. Here we explore the phase space of an intermediate-complexity earth system model, PlaSim-LSG, featuring a multistable AMOC. For two different atmospheric carbon dioxide (CO2) levels, we explicitly compute the Melancholia (M) state that separates the strong and weak AMOC attractors found in the model. The M state is a chaotic saddle, an edge state embedded in the basin boundary between the competing states. We show that, while being unstable, the M state can govern the transient climate for centuries. The M state exhibits strong AMOC oscillations on centennial timescales driven by sea ice and oceanic convection in the North Atlantic. Combining these insights with simulations under future CO2 forcing scenarios (SSPs), we demonstrate that in our model the AMOC undergoes a boundary crisis at CO2 levels projected to be reached in the next decade. Near the crisis, the AMOC behavior becomes highly unpredictable. Founded in dynamical systems theory, our results offer an interpretation of diverging ensemble simulations recently observed in state-of-the-art earth system models under nonautonomous forcing.
Mar. 31 The importance of being discrete: flow-kick models of environmental disturbance
Kate Meyer, Carleton College
Abstract: Climate change is shifting disturbance patterns in ecosystems, including fires, hurricanes, and droughts. To incorporate ongoing disturbances into a differential equation (DE) model of ecological processes, one might embed the disturbance continuously in the DE or resolve the disturbance discretely. In this talk we’ll explore the flow-kick approach to modeling repeated, discrete disturbances and examine the dynamic implications of this modeling choice. We’ll position continuous disturbances as limits of repeated, discrete ones and share recent results on how flow-kick systems both mimic and depart from their continuous analogs.
Apr. 14 Dimension Reduction for Data Assimilation
Erik Van Vleck, University of Kansas
Abstract: Data assimilation (DA) techniques combine models and data to make improved predictions often in a Bayesian context. Important challenges including addressing nonlinearity in models and data, detecting intermittent non-Gaussian behavior, and high dimensional models and data. The focus of the talk is on the adaptation of techniques to DA that have proven to be highly successful in the numerical solution of PDEs, adaptive spatial meshing (ASM) and reduced order modeling (ROM), and their potential for integration within DA techniques. After some motivation and discussion of challenges, current research results will be presented, followed by an outlook toward the future.
Apr. 22 (Tue) Emulation and Calibration of an Arctic Sea Ice Model with Spatial Outputs (Modified schedule: Tuesday 2pm EDT)
Yawen Guan, Colorado State University
Abstract: Arctic sea ice plays a critical role in the global climate system. Physical models of sea ice simulate key characteristics such as thickness, concentration, and motion, offering valuable insights into its behavior and future projections. However, these models often exhibit large parametric uncertainties due to poorly constrained input parameters. Statistical calibration provides a formal framework for estimating these parameters using observational data while also quantifying the uncertainty in model projections. Calibrating sea ice models poses unique challenges, as both model output and observational data are high-dimensional multivariate spatial fields. In this talk, I present a hierarchical latent variable model that leverages principal component analysis to capture spatial dependence and radial basis functions to model discrepancies between simulations and observations. This method is demonstrated through the calibration of MPAS-Seaice, the sea ice component of the E3SM, using satellite observations of Arctic sea ice.
Apr. 28 Exponential Dichotomies and Their Application in Higher-Dimensional Spatial Dynamics for Elliptic PDEs
Alanna Haslam-Hyde, Boston University
Abstract: Exponential dichotomies, when they exist, provide powerful information about the structure of bounded solutions even in the case of an ill-posed evolutionary equation. The method of spatial dynamics, in which one views a spatial variable as a time-like evolutionary variable, allows for the use of classical dynamical systems techniques, such as exponential dichotomies, in broader contexts. This has been utilized to study stationary solutions of PDEs on spatial domains with a distinguished unbounded direction (e.g. the real line or a channel of the form ℝ⨉Ω). Recent work has shown how to extend the spatial dynamics framework to elliptic PDEs posed on general multi-dimensional spatial domains. In this talk we show that, in the same context, exponential dichotomies do exist, thus allowing for their use in future analyses of coherent structures, such as spatial patterns in reaction-diffusion equations on more general domains.
May 5 Mathematical models of climatic drivers of mosquito-borne disease emergence: the case of dengue in Central Argentina
Michael Robert, Virginia Tech
Abstract: Mosquito-borne diseases endemic to areas with tropical climates have been spreading in temperate regions of the world with greater frequency in recent years. Numerous factors contribute to this spread, including urbanization, increases in global travel, and changes in temperature, precipitation, and humidity patterns leading to anomalies from historical averages. Mathematical modeling is a useful tool to examine how these different influences impact transmission and spread of pathogens and for projecting how potential future changes in these factors could affect pathogen dynamics. Models have been employed for years to study disease dynamics, but diseases emerging in new regions present particular challenges. To that end, we have developed mathematical, statistical, and computational models to study the introduction, emergence, and spread of dengue fever in Central Argentina. Dengue, caused by a virus transmitted by Aedes aegypti mosquitoes, first emerged in temperate Argentinian cities in 2009, and multiple outbreaks of increasing incidence have occurred since. With particular focus on the role of meteorological influences on dengue emergence, I present mathematical models designed to study seasonal Aedes aegypti and dengue dynamics in temperate Argentinian cities. I will show how different seasonal patterns influence the risk of outbreaks and how projected increases in average temperatures may influence future transmission risk. I will also discuss the implications of our work for dengue and mosquito mitigation strategies, and address some of the issues and areas for improvement in modeling emerging pathogens transmitted by mosquitoes.
May 19 Data-driven dynamics of phytoplankton blooms in a reaction-diffusion NPZ model
Seth Cowall, University of Georgia
Abstract: Phytoplankton are the base of the marine food web. They are also responsible for much of the oxygen we breathe, and they remove carbon dioxide from the atmosphere. The mechanisms that govern the timing of seasonal phytoplankton blooms is a highly debated topic in oceanography. Here, we present a macroscale plankton ecology model consisting of coupled, nonlinear reaction-diffusion equations with spatially and temporally changing coefficients to offer insight into the causes of phytoplankton blooms. This model simulates biological interactions between nutrients, phytoplankton and zooplankton. It also incorporates seasonally varying solar radiation, diffusion and depth of the ocean’s upper mixed layer because of their impact on phytoplankton growth. The model’s predictions are dependent on the dynamical behavior of the model. The model is analyzed using seasonal oceanic data with the goals of understanding the model’s dependence on its parameters and of understanding seasonal changes in plankton biomass. A study of varying parameter values and the resulting effects on the solutions, the stability of the steady-states, and the timing of phytoplankton blooms is carried out. The model’s simulated blooms result from a temporary attraction to one of the model’s steady-states.
June 2 Modeling Online-to-Offline Spillovers: Epidemic and Reaction-Diffusion Approaches
Nancy Rodriguez, University of Colorado Boulder
Abstract: With about two-thirds of the global population using social media, online interactions often influence offline events such as protests and violence. This talk presents two mathematical frameworks to model these online-to-offline spillovers. The first framework uses an epidemic-type model on networks, exploring mean field approximations to the stochastic processes and deriving reproductive numbers for these models. We also examine how network structure impacts the accuracy of these approximations. The second framework applies a reaction-diffusion model on networks to analyze the spreading speeds of traveling wave solutions. We identify parameter regimes for approximating these speeds on k-ary trees and characterize scenarios involving pushed, pulled, and pinned waves. These models provide insights into how information spreads across networks and triggers offline behaviors.
June 9 A mathematical mechanism of reservoir computing for dynamical systems (Modified schedule: 6pm EDT)
Masato Hara, Kyoto University
Abstract: Reservoir computing is a kind of machine learning technique that uses recurrent neural networks. It is known that a reservoir can learn a time-series generated by a dynamical system, such as the logistic map or the Lorenz system. In this talk, to explain the mechanism of reservoir computing, I will introduce a theorem that guarantees a reservoir after training become (weakly semi-)conjugate to the learnt dynamical system under some assumptions. I will also describe the sketch of its proof, which includes some ideas of classical theory of dynamical systems. This talk is based on the joint work with Professor Hiroshi Kokubu (Kyoto U.).
June 23 Disentangling climate polarization
Ekaterina Landgren, University of Colorado Boulder
Abstract: Despite climate change being a polarizing issue in the United States, many climate mitigation policies enjoy support from large public majorities. Yet most Americans underestimate this support—often by 20 percentage points or more. Such widespread misperception can suppress individual advocacy and influence legislative outcomes. In this work, we combine theory and empirics to investigate two potential drivers of this gap: homophily, or the tendency of like-minded individuals to selectively associate; and false balance in media, where critical viewpoints are overrepresented relative to actual public opinion. Using an agent-based model of social networks and opinion perception, we estimate the severity of homophily and false balance required to produce the observed misperception. We then analyze 2,072 U.S. TV news transcripts to assess how climate policy is framed. The model suggests that homophily alone is insufficient, but that its combination with false balance could explain the misperception. However, our empirical analysis finds no systematic evidence of false balance. Instead, climate policy is often omitted from climate coverage, and when it is mentioned, it is discussed in polarized ways across outlets. To extend our analysis beyond traditional media, we examine climate discourse on Reddit. By mapping how topics like renewable energy, sustainable diets, and public transit are discussed across politically distinct communities, we reveal which policy issues become entangled in partisan identity. These findings point to the limitations of common explanations and suggest alternative hypotheses for future research on perceived public opinion.
June 30 A Topological Perspective on Weather Regimes (Modified schedule: 1pm EDT)
Kristian Strommen, University of Oxford
Abstract: It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as ‘weather regimes’, loosely categorised as regions of phase space with above-average density and/or extended persistence. Their existence and behaviour has been extensively studied in climate science, due to their potential for drastically simplifying the complex and chaotic mid-latitude dynamics. Several well-known, simple non-linear dynamical systems have been used as toy-models of the atmosphere in order to understand and exemplify such regime behaviour. Nevertheless, no agreed-upon and clear-cut definition of a ‘regime’ exists in the literature, and unambiguously detecting their existence in the atmospheric circulation is stymied by the high dimensionality of the system. We argue here for an approach which equates the existence of regimes in a dynamical system with the existence of non-trivial topological structure of the system’s attractor. We show using persistent homology, an algorithmic tool in topological data analysis, that this approach is computationally tractable, practically informative, and identifies the relevant regime structure across a range of examples.
July 8 The Simplex Ensemble Transport (SEnT) filter, with application to sea ice data assimilation
Ian Grooms, University of Colorado Boulder
Abstract: The Ensemble Kalman Filter (EnKF) is a powerful tool to integrate observations into dynamical models for an improved estimate of the state. However, the Gaussian assumptions underlying EnKFs limit their applicability for problems with non-Gaussian behavior. Modeled sea ice distributions are highly non-Gaussian due to constraints on the state; many models divide sea ice within a grid cell into thickness categories with a fractional area coverage and mean thickness for each category. The total fractional area, including open water, must sum to 1, which means that the fractional areas lie on a simplex. Each thickness category's mean thickness must remain within the bounds that define the category. Gaussian distributions do not respect these constraints, and standard EnKFs produce analysis ensemble members with physically-inconsistent states. There are ways to assimilate sea ice observations using EnKF approaches by post-processing or nonlinear transformations, but many of these are ad hoc and do not address the geometry of the problem directly. This work aims to improve the assimilation of sea ice observations into models by developing an approach that is fully non-Gaussian, within the two-step framework first put forward by Anderson (2003). Given an observation of sea ice concentration, the two-step framework first applies a scalar Quantile Conserving Ensemble Filter (QCEF) update to the open water fraction. Then, the second step uses an approach based on a mixed-Dirichlet distribution to update the remaining variables in the state vector, i.e the fractional area of ice, and mean thicknesses in the other categories. We will present details on the method and results from OSSE experiments that compare EnKF performance with our two-step method in the context of the Icepack model, which is a single-column version of CICE. Though developed here in the context of the sea ice thickness distribution, the approach is directly applicable to any dynamical system with a state vector on the simplex, including epidemic models whose categories (e.g. susceptible, infected, removed) are non-negative and sum to the total population.
July 14 Introduction to the parameterization method for invariant manifolds
Jason Mireles-James, Florida Atlantic University
Abstract: The parameterization method is a functional analytic toolkit for studying invariant manifolds and their attached local stable/unstable manifolds in all kinds of dynamical systems (maps, ODEs, DDEs, PDEs, etcetera). As such, it can be helpful for establishing abstract existence results and developing computational techniques for studying these objects. I'll review some of the basic ideas, with an eye toward numerical examples.
July 28 Computational Inference of a Continuum Model for Sea Ice From Data
Gonzalo Gonzalez de Diego, Courant Institute New York University
Abstract: Sea ice plays a vital role in Earth's climate system, covering about 10% of the ocean's surface at its maximum extent. It significantly affects the planet’s energy balance due to its high albedo and is involved in key oceanographic processes. There are two main approaches to modeling sea ice: discrete element methods (DEMs) and continuum models. DEMs simulate individual ice floes and their interactions with high accuracy, but at a high computational cost. In contrast, continuum models are much more computationally efficient, solving partial differential equations (PDEs) to approximate sea ice behavior. However, a major challenge with continuum models is their dependence on unverifiable, ad-hoc parameterizations. Our research addresses this challenge using a novel, data-driven approach. Instead of relying on speculative first principles, we represent the continuum model’s rheology—the relationship between stress and strain that needs to be parameterized—using a neural network. To ensure physical realism, we constrain the network’s structure accordingly. We then generate velocity data using SubZero, an advanced DEM for sea ice, and use PDE-constrained optimization to train the neural network. This process allows the continuum model’s velocity field to closely match that of SubZero. As a result, we develop a continuum model that not only replicates SubZero’s simulations with high accuracy but also yields a rheological law that offers new insights into sea ice behavior under varying conditions.
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