Minisymposium: Dynamical Systems And Climate
Meeting: SIAM Conference of Nonlinear Waves and Coherent Structures
Organizers: Graham Cox (UNC) and Thomas Bellsky (ASU)
Dates: August 11-14, 2014
Abstract: Over the past few decades it has become apparent that the Earth's climate is a rich source of applied mathematical problems, particularly in the fields of dynamical systems and data assimilation. The rigorous study of conceptual models has provided new insight into climate dynamics, along the way necessitating the development of exciting new mathematical tools. These TWO minisymposia focus on the application of dynamical methods to problems in such diverse areas as data assimilation, desertification, and ocean circulation, with an emphasis on the unique mathematical challenges arising in such studies.
MS82 - Dynamical Systems and Climate - Part I of II
Thursday, August 14, 2:00 PM - 4:00 PM
Room: Fellows Dining Room - Concourse (1st Floor)
2:00-2:25 A Search for Chaotic Behaviour in Stratospheric Variability
Gualtiero Badin, University of Hamburg, Germany
Abstract. Stratospheric extratropical variability in both the Southern and Northern Hemisphere is investigated with respect to chaotic behaviour. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan–Yorke dimension are estimated. A finite value of the dimensions can be computed for different variables, however a large variability between the values of the dimensions suggests that the values might be associated not a strange attractor but to the projection of the trajectories into a smaller embedded space. The consequences of the results for the formulation of a stochastic model, rather than a low dimensional deterministic model, are discussed.
2:30-2:55 Semi-Strong Desertification Dynamics with a Slowly Changing Parameter
Eric Siero and Arjen Doelman, Leiden University, Netherlands; Thomas Bellsky, Arizona State University, USA
Abstract. We introduce a slowly changing parameter in the framework of semi-strong interaction of pulses in reaction diffusion systems, which appear as models for vegetation in (semi-)arid regions. Geometric singular perturbation theory yields laws of motion for the pulses and spectral (in)stability of the configuration. Crucial is understanding the interplay between the inherent slow dynamics of the pulse interactions and the rate of change of the changing parameter: will ecosystem response be fast enough to postpone destabilization by a changing parameter?
3:00-3:25 Tipping and Warning Signs for Patterns and Propagation Failure in SPDEs
Karna V. Gowda, Northwestern University, USA; Christian Kuehn, Vienna University of Technology, Austria
Abstract. In this talk, I shall report on recent results on early- warning signs for pattern formation in stochastic partial differential equations. In particular, it will be shown that classical scaling laws from stochastic ordinary differential equations can be carried over to the SPDE case. This is illustrated in the context of the Swift- Hohenberg equation, analytically and numerically. Furthermore, I shall discuss numerical results for warning signs for the stochastic Fisher- KPP equation in the case of noisy invasion front travelling waves near positive absorption probability events leading to propagation failure.
3:30-3:55 Joint State and Parameter Estimation by Two-stage Filtering Method
Naratip Santitissadeekorn, University of Surrey, United Kingdom
Abstract. This work presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The stage augmentation technique, in which the state vector is augmented by the model parameters, has been investigated in many previous studies and some success with this technique has been reported in the case where model parameters are additive. However, many geophysical or climate models contains non-additive parameters such as those arising from physical parametrization of sub-grid scale processes, in which case the state augmentation technique may not be effective since its inference about parameters from partially observed states based on the cross covariance between states and parameters is inadequate if states and parameters are not linearly correlated. Therefore, we propose a two-stage filtering technique that runs Particle Filtering (PF) to estimate parameters while updating the state estimate using the Ensemble Kalman Filter (EnKF); these two "sub-filters" interact.
MS90 - Dynamical Systems and Climate - Part II of II
Thursday, August 14, 4:30 PM - 6:30 PM
Room: Fellows Dining Room - Concourse (1st Floor)
4:30-4:55 Estimation of CO2 Flux from Targeted Satellite Observations: A Bayesian Approach
Graham Cox, University of North Carolina, Chapel Hill, USA
Abstract. We consider the estimation of carbon dioxide flux at the ocean–atmosphere interface, given weighted averages of the mixing ratio in a vertical atmospheric column. In particular we examine the dependence of the posterior covariance on the weighting function used in taking observations, motivated by the fact that this function is instrument-dependent, hence one needs the ability to compare different weights. The estimation problem is considered using a variational data assimilation method, which is shown to admit an equivalent infinite-dimensional Bayesian formulation. The main tool in our investigation is an explicit formula for the posterior covariance in terms of the prior covariance and observation operator. Using this formula, we compare weighting functions concentrated near the surface of the earth with those concentrated near the top of the atmosphere, in terms of the resulting covariance operators. We also consider the problem of observational targeting, and ask if it is possible to reduce the covariance in a prescribed direction through an appropriate choice of weighting function. We find that this is not the case—there exist directions in which one can never gain information, regardless of the choice of weight.
5:00-5:25 Generalized Hopf Bifurcation in a Nonsmooth Ocean Circulation Model
Julie Leifeld, University of Minnesota, USA
Abstract. In this talk we discuss a generalized Hopf bifurcation described by Filippov, as applied to a well known ocean convection model formulated by Welander. Oscillations in the model are directly caused by the inclusion of a nonsmooth variable. We also discuss persistance of oscillations between the smooth and nonsmooth versions of this model.
5:30-5:55 Existence and Stability of Relative Equilibria in N-Vortex Problems
Anna M. Barry, University of Minnesota, USA
Abstract. Over the last millennium there have been many analytical studies of equilibria in the classical N-vortex problem that is derived from the Euler equations. Considerably less work has focused on other geophysically-motivated point vortex models- e.g. quasigeostrophic and surface quasigeostrophic. With this in mind, we analyze existence and stability of a number of relative equilibria in a family of point vortex models, including the two mentioned above. We compare our findings to analogous results in the classical problem, and use them to comment on examples of vortex equilibria observed in nature. This is joint work with Gualtiero Badin (U. Hamburg).
1. Stablility of Localized Structure for a Semi-Arid Climate Model, Thomas Bellsky
2. Semi-Strong Desertification Dynamics with a Slowly Changing Parameter, Eric Siero
3. Pattern Formation and Tipping Points in Semiarid Ecosystems, Karna Gowda
4. Model Reduction and Response for Two-Timescale Systems Using Fluctuation-Dissipation, Marc Kjerland
5. Mixed Mode Oscillations in Conceptual Climate Models: A General Perspective, Esther Widiasih
6. Mixed mode oscillations in conceptual climate models: An in-depth discussion, Andrew Roberts
7. Data Assimilation for Quadratic Dissipative Dynamical Systems, Kody Law
8. Automatic Recognition and Tagging of Topologically Different Regimes in Dynamical Systems, Jesse Berwald
|When:||Monday 11 August, 2014 12:00 pm EDT - Thursday 14 August, 2014 9:00 pm EDT|