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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

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

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

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
and
J. A. Owen

Abstract

From observations and a variety of general circulation modeling evidence, it is suggested that the exceptionally cold weather experienced over much of the United States during some recent winter months (e.g., January 1985, December 1976–February 1977) was associated with enhanced latent heat release over the tropical West Pacific. The mechanism associated with such enhancement may not be unique.

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Čedo Branković
and
T. N. Palmer

Abstract

Results from a set of nine-member ensemble seasonal integrations with a T63L19 version of the European Centre for Medium-Range Weather Forecasts (ECMWF) model are presented. The integrations are made using observed specified sea surface temperature (SST) from the 5-year period 1986–90, which included both warm and cold El Niño–Southern Oscillation (ENSO) events. The distributions of ensemble skill scores and internal ensemble consistency are studied. For years in which ENSO was strong, the model generally exhibits a relative high skill and high consistency in the Tropics. In the northern extratropics, the highest skill and consistency are found for the northern Pacific–North American region in winter, whereas for the northern Atlantic–European region the spring season appears to be both skillful and consistent. For years in which ENSO was weak, the distributions of ensemble skill and consistency are relatively broad and no clear distinction between Tropics and extratropics can be made.

Applying a t test to interannual fluctuations over various tropical and extratropical regions, estimates of a minimum useful ensemble size are made. Explicit calculations are done with ensemble size varying between three and nine members; estimates for larger sizes are made by extrapolating the t values. Based on an analysis of 2-m temperature and precipitation, the use of relatively large (approximately 20 members) ensembles for extratropical predictions is likely to be required; in the Tropics, smaller-sized ensembles may be adequate during years in which ENSO is strong, particularly for regions such as the Sahel.

The role of the SST forcing in a seasonal timescale ensemble is to bias the probability distribution function (PDF) of atmospheric states. Such PDFs can, in addition, be a convenient way of condensing a vast amount of data usually obtained from ensemble predictions. Interannual variability in PDFs of monsoon rainfall and regional geopotential height probabilities is discussed.

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J. A. Owen
and
T. N. Palmer

Abstract

Two ensembles of 90-day forecasts for 1982–83 have been made with the UK Meteorological Office 11-layer atmospheric general circulation model. Each ensemble comprised three integrations initialized one day apart, using analyses from December 1982. The first ensemble used observed SSTs and the second used climatological SSTs. Our objectives were to compare the skill of the two ensembles and to compare the results with a longer climate sensitivity experiment.

The skill of the forecasts for 10-, 30- and 90-day means was assessed using root-mean-square wind errors at 200 mb. In the tropics, the skill was improved with observed SSTs on all time scales. In the extratropics, the skill was improved on the 30-day time scale except at the initial stages of the forecasts, and the skill was also improved for 90-day means. On the 10-day time scale, however, the improvement was not consistent, and there were periods in which the errors were larger with observed SSTs. The response of the model to the observed SSTs was found to be similar to that of a 540-day perpetual January integration with the winter mean SST anomaly for 1982–83.

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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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