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T. N. Palmer

Meteorology is a wonderfully interdisciplinary subject. But can nonlinear thinking about predictability of weather and climate contribute usefully to issues in fundamental physics? Although this might seem extremely unlikely at first sight, an attempt is made to answer the question positively. The long-standing conceptual problems of quantum theory are outlined, focusing on indeterminacy and nonlocal causality, problems that led Einstein to reject quantum mechanics as a fundamental theory of physics (a glossary of some of the key terms used in this paper is given in the sidebar). These conceptual problems are considered in the light of both low-order chaos and the more radical (and less well known) paradigm of the finite-time predictability horizon associated with the self-similar upscale cascade of uncertainty in a turbulent fluid. The analysis of these dynamical systems calls into doubt one of the key pieces of logic used in quantum nonlocality theorems: that of counterfactual reasoning. By considering an idealization of the upscale cascade (which provides a novel representation of complex numbers and quaternions), a case is made for reinterpreting the quantum wave function as a set of intricately encoded binary sequences. In this reinterpretation, it is argued that the quantum world has no need for dice-playing deities, undead cats, multiple universes, or “spooky action at a distance.”

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T. N. Palmer

The physical basis for extended-range prediction is explored using the famous three-component Lorenz convection model, taken as a conceptual representation of the chaotic extratropical circulation, and extended by coupling to a linear oscillator to represent large-scale tropical–extratropical interactions. The model is used to analyze the roles of time averaging and ensemble forecasting, and, in extended form, the impact of both anomalous tropical sea surface temperature and anomalous extratropical sea surface temperature. The conceptual paradigms and analytic calculations presented are used to interpret results from numerical weather prediction and general circulation model experiments. Some remarks on the relevance of predictability studies for the climate change problem are given.

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T. N. Palmer

Abstract

A nonlinear dynamical perspective on climate prediction is outlined, based on a treatment of climate as the attractor of a nonlinear dynamical system D with distinct quasi-stationary regimes. The main application is toward anthropogenic climate change, considered as the response of D to a small-amplitude imposed forcing f.

The primary features of this perspective can be summarized as follows. First, the response to f will be manifest primarily in terms of changes to the residence frequency associated with the quasi-stationary regimes. Second, the geographical structures of these regimes will be relatively insensitive to f. Third, the large-scale signal will be most strongly influenced by f in rather localized regions of space and time. In this perspective, the signal arising from f will be strongly dependent of D’s natural variability.

A theoretical framework for the perspective is developed based on a singular vector decomposition of D’s tangent propagator. Evidence for the dyamical perspective is drawn from a number of observational and modeling studies of intraseasonal, interannual, and interdecadal variability, and from climate change integrations. It is claimed that the dynamical perspective might resolve the apparent discrepancy in global warming trends deduced from surface and free troposphere temperature measurements.

A number of specific recommendations for the evaluation of climate models are put forward, based on the ideas developed in this paper.

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T. N. Palmer

Abstract

Properties of the quasi-geostrophic Eliassen-Palm (EP) flux for planetary scale motions are discussed, in order to clarify how these properties generalize from their beta-plane counterparts when no restriction on the variation of the Coriolis parameter is imposed. These properties include the relationships between the divergence of the EP flux and the meridional flux of potential vorticity, and between the EP flux, group velocity and refractive index.

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T. N. Palmer

Abstract

The intense wavenumber-2 stratospheric warming of February 1979 is analyzed in a transformed Eulerian-mean formalism, and compared with diagnostics generated by the model warming of Dunkerton et al. (1981). Significant differences in the evolution of the zonal mean flow are found. The corresponding differences in wave, mean-flow interaction are examined by studying planetary wave activity in the troposphere and stratosphere, as measured by the Eliassen-Palm flux and its divergence. It is found that in the stratosphere, the direction of this flux changes several times during the warming. Zonal flow deceleration is most intense when the midlatitude stratospheric flux has positive poleward and upward components. Conversely, deceleration is smallest when the flux is directed equatorward. Some mechanisms that may account for this switching are discussed. However, unlike the model, the high-latitude zonal flow reversal does not arise from nonlinear critical layer interaction with the waves.

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T. N. Palmer

Carl-Gustaf Rossby's work leading to the dispersion equation for his eponymous atmospheric wave form was motivated by his quest to understand interrelationships between fluctuations in the zonal mean wind and the quasi-stationary waves. Rossby believed that climate variability on almost all timescales could be understood in terms of changes in the frequency of occurrence of states of high and low zonal index. Using modern-day terminology and ideas, Rossby's perception of climate variability can be viewed in terms of low-frequency changes to the probability distribution of the nonlinear weather regimes that characterize our chaotic climate attractor.

A perspective on possible future climate change is outlined, based on these ideas. One of the most basic notions to emerge is that even if such change is predominantly anthropogenically induced, its manifestation may be predominantly onto the natural “modes” of variability of the climate system.

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T. N. Palmer and S. Tibaldi

Abstract

Using 10-day forecast 500 mb height data from the last 7 yr, the potential to predict the skill of numerical weather forecasts is discussed. Four possible predictor sets are described. The first, giving the consistency between adjacent forecasts, is apparently more skillful if the anomaly correlation coefficient, rather than RMS difference, is used as measure of forecast spread and forecast skill. It is concluded that much of this enhanced skill results from the dependence of the anomaly correlation coefficient on the magnitude of the forecast anomaly. It is noted that the spread between “today's” and “yesterday's” forecast is a more reliable estimate of the skill of yesterday's forecast than today's, and the implications of this on lagged-average ensemble forecasts are discussed. The impact of temporal filtering of the data in spread/skill correlations are also described.

The second predictor set is derived from a regression analysis between RMS error skill scores and EOF coefficients of the forecast and/or initial 500 mb heights. The predictors themselves are large-scale anomaly patterns, some of which, towards the end of the forecast period, resemble low-frequency teleconnection patterns of the atmosphere. It is shown that forecast EOF coefficients are more skilful predictors than EOF coefficients of the initial conditions, and that when both sets of coefficients are used in the regression there is a danger of overfitting. The dependence of these patterns on the truncation of the EOF expansion and of temporal filtering is discussed. In particular, it is shown that when a severe EOF truncation is made, some of the forecast flow anomaly patterns become less geographically localized, indicating poorer predictive skill.

The third predictor is defined as the RMS skill of the day-1 forecast. Both upstream and local correlations are studied. It is shown that with day-1 forecast error leading day-3 RMS error by up to 3 days, there appears to be a propagating signal, in addition to a quasi-stationary one. In general, the latter appears to be dominant. The fourth predictor is defined as the RMS difference between the forecast 500 mb height, and the initial 500 mb height. Use of this latter predictor was motivated by diagnostic studies showing relationships between interannual variability of forecast scores and interannual variability of persistence errors. These studies are partly described here. It is shown that the use of forecast persistence as a predictor gives partial skill, at least towards the end of the forecast period.

The skill of the predictors are tested, and the regression coefficients derived, on data from six winters, for both regional and hemispheric skill scores. As an independent test, the predictors are also applied separately to the seventh winter period 1986/87. It is concluded that some aspects of the low-frequency component of forecast skill variability can be satisfactorily predicted, though significant high frequency variability remains unpredicted.

In discussing the physical mechanisms that underlie the use of these predictors, three important components of forecast skill variability are discussed: the quality of the initial analysis, the intrinsic instability of the flow, and the role of model systematic errors.

It is shown that results from the EOF predictor for the European region towards the end of the forecast period are strongly influenced by model systematic error. On the other hand, over the Pacific/North American region, growth of errors on flows with varying barotropic stability characteristics are an important component of medium-range forecast variability. This is discussed using a barotropic model with basic states defined from the results of the regression analyses for various regions. At shorter range it is suggested that growth of errors by baroclinic processes is probably dominant.

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A. Busalacchi and T. N. Palmer
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Jouni Räisänen and T. N. Palmer

Abstract

Because of the inherent uncertainties in the computational representation of climate and because of unforced chaotic climate variability, it is argued that climate change projections should be expressed in probabilistic form. In this paper, 17 Coupled Model Intercomparison Project second-phase experiments sharing the same gradual increase in atmospheric CO2 are treated as a probabilistic multimodel ensemble projection of future climate. Tools commonly used for evaluation of probabilistic weather and seasonal forecasts are applied to this climate change ensemble. The probabilities of some temperature- and precipitation-related events defined for 20-yr seasonal means of climate are first studied. A cross-verification exercise is then used to obtain an upper estimate of the quality of these probability forecasts in terms of Brier skill scores, reliability diagrams, and potential economic value. Skill and value estimates are consistently higher for temperature-related events (e.g., will the 20-yr period around the doubling of CO2 be at least 1°C warmer than the present?) than for precipitation-related events (e.g., will the mean precipitation decrease by 10% or more?). For large enough CO2 forcing, however, probabilistic projections of precipitation-related events also exhibit substantial potential economic value for a range of cost–loss ratios. The treatment of climate change information in a probabilistic rather than deterministic manner (e.g., using the ensemble consensus forecast) can greatly enhance its potential value.

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R. Buizza and T. N. Palmer

Abstract

The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic.

The relation between ensemble spread and control error is studied using L 2, L 8, and L norms to measure distances between ensemble members and the control forecast or the verification. It is argued that the supremum norm is a more suitable measure of distance, given the strategy for constructing ensemble perturbations from rapidly growing singular vectors. Results indicate that, for the supremum norm, any increase of ensemble size within the range considered in this paper is strongly beneficial. With the smaller ensemble sizes, ensemble spread does not provide a reliable bound on control error in many cases. By contrast, with 32 members, spread provides a bound on control error in nearly all cases. It could be anticipated that further improvement could be achieved with higher ensemble size still. On the other hand, spread–skill relationship was not consistently improved with higher ensemble size using the L 2 norm.

The overall conclusion is that the extent to which an increase of ensemble size (particularly from 8 to 16, and 16 to 32 members) improves EPS performance, is strongly dependent on the measure used to assess performance. In addition to the spread–skill relationship, the measures most sensitive to ensemble size are shown to be the skill of the best ensemble member (particularly when evaluated on a point-wise basis) and the outlier statistic.

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