Abstracts (of past and future lecture)
Seminar 1 - February 14, 10:30 am : "Chaos and Forecasting:
Fact and Fiction"
This is the first of a series of seminars on the dynamics of nonlinear systems and their applications to forecast weather and model climate. This talk provides something of an overview including
Seminars 2 and 3 - February 28 and March 14 : "Model Error in Operational Weather Forecasting"
Operational weather forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. These two lectures will focus on the second of these effects and how the two might be distinguished in large simulation models, ideally using only current operational diagnostic outputs. The concept of local model drift is introduced and deployed in the case of the ECMWF operational forecasts and a simple relation is developed to estimate shadowing times from estimates of drift. Current results indicate error growth with is not exponential in time (nor is it exponential-on-average) but rather grows as the square root of time, suggesting that state-dependent model error plays a significant role in limiting the utility of these forecasts. Options for incorporating this information into forecasts and into model development programs is discussed.
Seminar 4 - March 24, 4:00 pm : "Dynamics of Uncertainty"
An initial uncertainty in the state of a chaotic system is expected to grow even under a perfect model; the dynamics of this uncertainty during the early stages of its evolution are investigated. A variety of ``error growth" statistics are contrasted, illustrating their relative strengths when applied to chaotic systems, all within a perfect model scenario. We show how to establish the existence of regions of a strange attractor within which all infinitesimal uncertainties decrease with time and prove that such regions exist in the Lorenz 63 attractor; similar regions of decreasing uncertainty exist in the Ikeda attractor. No such regions exist in either the Rossler system or the Moore-Spiegel system. Numerically, strange attractors in each of these systems are observed to sample regions of state space where the Jacobians have eigenvalues with negative real parts, yet when the Jacobians are not normal matrices this does not guarantee that uncertainties will decrease. Discussions of predictability often focus on the evolution of infinitesimal uncertainties; clearly, as long as an uncertainty remains infinitesimal it cannot pose a limit to predictability. To reflect realistic boundaries, any proposed ``limit of predictability" must be defined with respect to the nonlinear behaviour of perfect ensembles. Such limits may vary significantly with the initial state of the system, the accuracy of the observations, and the aim of the forecaster. Perfect model analogues of operational weather forecasting ensemble schemes with finite initial uncertainties are contrasted with both perfect ensembles and uncertainty statistics based upon the dynamics infinitesimal uncertainties.
Related Reading:
Adaptive observation strategies in numerical weather prediction aim to improve forecasts by exploiting additional observations at locations that are themselves optimized with respect to the current state of the atmosphere (and our knowledge of it). The aim here is to take the observation that is most likely to yield maximum information relative to some forecast goal. We will see that the assimilation scheme, or more precisely, the magnitude of the analysis error, is crucial in limiting the applicability of dynamically based strategies. We will contrast two approaches, one based upon our believes regarding potential (counter-factual) observations, the second based upon distinguishing between the ensemble members we have in hand In short, strategies based on linearized dynamics require that analysis error is sufficiently small so that the model linearization about the analysis is relevant to linearized dynamics of the full system about the true system state. Inasmuch as the analysis error depends on the assimilation scheme, the level of observational error, the spatial distribution of observations, and model imperfection, so too will the preferred adaptive observation strategy. For analysis errors of sufficiently small magnitude (and models of sufficiently high adequacy), dynamically based selection schemes will outperform those based only upon uncertainty estimates, while their performance relative ensemble discrimination methods is less clear.
Seminar 6 - April 4, 10:30 am : "Measures of Forecast Utility: BBs, MSTs and full PDFs"
Operational weather prediction has played a leading role in moving beyond single point forecasts and providing ensemble forecasts for complex physical systems in real time. Moving away from point forecasts, however, requires moving away from skill scores like the root-mean-square error, if the additional information available in an ensemble is even to be quantified, much less exploited. This lecture will present three approaches to evaluating ensemble forecasts: (1) the Bounding Box, (2) the Minimum Spanning Tree, and (3) interpretation of the ensemble as a probability density function. The first two approaches directly interpret the ensemble as a collection of points in a high dimensional space, while the third requires first reinterpreting the ensemble as a function (for example by kernel dressing, or by conditioning on the joint distribution). In the Perfect Model Scenario, each method contributes toward identifying the quality of an ensemble relative to a perfect ensemble. In practice (that is, outside PMS), value of each method depends on the interest of the forecast user.
Seminar 7 - April 11, 10:30 am : "Ensemble Seasonal Forecasts: DEMETER, Her Offspring and Applications"
Given the frequent inaccuracies in next week's weather forecast, our ability to make useful seasonal forecasts may come as something of a surprise. After noting the physical origins of potential skill on seasonal time scales, and carefully noting seasonal forecaster's definition of "skill", operational and pseudo-operational multi-model multi-initial-condition ensemble methods are examined. Only recently has the physical simulation approach become a serious rival to purely statistical methods on seasonal time scales; several foundational questions regarding how the simulations can be best interpreted are noted. A number of these open questions hinge on rather basic statistical issues, ranging from questions of bias correction to the detection of utility beyond linear skill of the ensemble mean.
Seminar 8 - April 18, 10:30 am : "Designing climateprediction.net: A Vicious Circle of Priors in Simulation Modeling"
This talk is an introduction to climate modelling as a statistical problem. We will consider two distinct points of view, contrasting that of a statistically naive physicist with that of a physically naive statistician; both of our players will be computationally sophisticated. Historically, climate research has been dominated by the naive physicist's view, climateprediction.net and other ensemble climate experiments represent the emergence of the naive statistician's view as a force to be reckoned with. This talk traces the attempt for a less naive approach to experiment design in Earths System Science in general, and climate modelling in particular. The attempt fails, but in doing so reveals a number of fairly basic statistical issues which, at present, limit the utility of simulation modelling for policy makers, decision support consultants, and risk managers.
Please contact Sujit Ghosh or Leonard A. Smith for details.