Colloqium
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: TBD
Feb. 10 TBD
Nadir Jeevanjee, National Oceanic and Atmospheric Administration
Abstract: TBD
Feb. 24 TBD
Laura Silvinski, National Oceanic and Atmospheric Administration
Abstract: TBD
Mar. 3 Rate induced tipping in a habitat PDE model
Blake Barker, Brigham Young University
Abstract: TBD
Mar. 10 Metastability of the Altantic ocean circulation in an intermediate-complexity earth system model
Reyk Börner, University of Reading
Abstract: TBD
Mar. 17 TBD
John Gemmer, Wake Forest University
Abstract: TBD
Mar. 31 TBD
Kate Meyer, Carleton College
Abstract: TBD
Apr. 7 TBD (Modified schedule: 2pm EDT)
Jason Mireles-James, Florida Atlantic University
Abstract: TBD
Apr. 14 TBD
Erik Van Vleck, University of Kansas
Abstract: TBD
May 5 TBD
Michael Robert, Virginia Tech
Abstract: TBD
May 19 Data-driven dynamics of phytoplankton blooms in a reaction-diffusion NPZ model
Seth Cowall, University of Georgia
Abstract: TBD