Jacques Derome
McGill University, Montreal, Canada

A dry primitive equation model is used to investigate the response to sea surface temperature (SST) anomalies. Both tropical and mid-latitude SST anomalies are considered. The model is formulated in such a way that it is possible to obtain: (1) the nonlinear response to finite-amplitude anomalies, (2) the linear response about a time-independent basic state, and (3) the linear response about a time-evolving basic state.

We first describe the model and show that in spite of having time-independent empirical forcing terms, it has a good climatology in terms of both the time-mean variables and the transient eddy statistics. We then present the response to a tropical heat source and compare the nonlinear and linear responses. The role of the eddy feedback mechanism is illustrated.

We then describe the response to a mid-Pacific heat source, and again compare the linear and nonlinear solutions, highlighting the eddy feedback mechanism. The effect of moving the heat source with respect to the jet position is examined.

This work is the result of a collaboration with Drs. N.M.J. Hall and H. Lin of McGill University.

John Fyfe (1), Adam Monahan (2) and Greg Flato (1)
(1) Canadian Centre for Climate Modelling and Analysis Meteorological Service of Canada, Victoria, BC , Canada
(2) Institut fuer Mathematik, Humboldt-Universitaet zu Berlin, Germany

The leading mode of wintertime variability in Northern Hemisphere sea level pressure (SLP) is the Arctic Oscillation. It is usually obtained using linear principal component analysis, which produces the optimal, although somewhat restrictive, linear approximation to the SLP data. Here we describe the use a recently introduced nonlinear principal component analysis to find the optimal nonlinear approximation to SLP data produced by a 1001 year integration of the CCCma coupled general circulation model. This approximation's associated time series is strongly bimodal and partitions the data into two distinct regimes. The first and more persistent regime describes a standing oscillation whose signature in the mid-troposphere is alternating amplification and attenuation of the climatological ridge over Northern Europe, with associated decreasing and increasing daily variance over Northern Eurasia. The second and more episodic regime describes a split-flow south of Greenland with much enhanced daily variance in the Arctic. In a 500 year integration with atmospheric CO2 stabilized at concentrations projected for year 2100, the occupation statistics of these preferred modes of variability change, such that the episodic split-flow regime occurs less frequently while the standing oscillation regime occurs more frequently.

Michael Ghil
University of California, Los Angeles

The large-scale flow of the mid-latitude oceans is dominated by the presence of a larger, anticyclonic and a smaller, cyclonic gyre. The two gyres share the eastward extension of western boundary currents, such as the Gulf Stream or Kuroshio, and are induced by the shear in the winds that cross the respective ocean basins. The boundary currents and eastward jets carry substantial amounts of heat and momentum; the jets also contribute to mixing in the oceans by their "whiplashing" oscillations and the detachment of eddies from them.

The low-frequency variability of this double-gyre circulation, for time-constant and purely periodic wind stress, is studied by the methods of nonlinear dynamics, analytically and numerically. Symmetry-breaking bifurcations occur, from steady to periodic and aperiodic flows. Two types of oscillatory instabilities arise, with periods of a few months and a few years, respectively. The results are compared with decade-long in situ and more recent, satellite observations of three ocean basins, the North and South Atlantic, and the North Pacific. The possible impact of these double-gyre oscillations on climate variability is discussed.

This talk reflects collaborative work with K.-I. Chang (KORDI), H. Dijkstra (Utrecht), Y. Feliks (IIBR, Israel), K. Ide (UCLA), S. Jiang (MIT), F.-f. Jin (U. Hawaii), C. A. Lai (LANL), G. Loeper (ENS, Paris), E. Simonnet (LMD, Paris, & INLN, Nice), S. Speich (UBO/Ifremer, Brest), L. U. Sushama (UCLA), R. Témam (Indiana U. & Paris-Sud/Orsay), & S. Wang (Indiana U.).

Eigil Kaas
Danish Meteorological Institute, Lyngbyvej 100, DK2100 Copenhagen

This paper discusses the importance of non-linear processes on the development of systematic errors in atmospheric model simulations. The paper is to a large extend based on results from the recently finalised EU project, POTENTIALS, which had estimation of initial tendency errors in models of different complexity as its main objective. The forcing errors estimated this way were used 1) as a guideline to improve the physical parameterisation in the models and 2) to set up 3D flux corrected models, i.e. models which are modified via an additional empirical term in their prognostic differential equations. In both cases some interesting results concerning the importance of non-linear processes have been obtained.

One of the physical parameterisations which were investigated was the parameterisation of unresolved scale interactions. The tendency errors clearly showed that direct interactions take place between large horizontal scales with total wave numbers around 4-10 and much smaller scales (wave number 30 and higher). The parameterisation of unresolved scale interactions is sometimes referred to as horizontal diffusion and in practise the tuning constants (basically damping coefficients of different spectral wave numbers) of this parameterisation were optimised using information from the initial tendency errors. Implementation of the modified tuning constants in the model revealed [as in many previous studies] that horizontal diffusion impacts the large scale behaviour and thus to systematic model errors.

The empirically flux corrected models used in POTENTIALS showed considerable reduction in their systematic errors, both regarding the long term mean behaviour and the variability. It is interesting that the bulk of the systematic error reduction was obtained using a flux correction that was fixed in time. This indicates that imperfect simulation of temporarily varying non-linear processes in atmospheric models is of relative less importance than the simple linear response to long term average forcing errors. In a relatively simple model (QG 3 level model), however, a substantial further reduction of systematic errors was obtained by a non-linear parameterisation of the forcing errors. This was done via an analogue technique where observed weather situations [similar to the actual model state] were identified. The initial tendency errors from these historical data were then used as a dynamic (temporarily varying) flux correction. It has even been shown in POTENTIALS that highly simplified models behaving surprisingly well in terms of long term mean and variability characteristics can be constructed when a dynamical flux correction is used.

It should be noted that even a fixed empirical flux correction will reflect the accumulated effect of wrongly modelled linear as well as non-linear processes. Hence one cannot conclude directly from the results in POTENTIALS that non-linear processes are modelled fairly well in present day climate models.

John Marshall
Massachusetts Institute of Technology, Cambridge, Mass.

We begin by reviewing simple stochastic climate models of middle-latitude air-sea interaction and show how, when the effects of ocean circulation are taken in to account, they can take on delayed oscillator form.

The framework provided by the elaborated model guides an observational study of air-sea interaction in the Atlantic Sector. An index of sea surface temperature (SST) variability - delta T - is introduced that measures the difference in SST across the separated Gulf Stream. By analyzing a long observational record of SST and sea level pressure (SLP), we show that delta T exhibits damped oscillations of decadal period and covaries with the strength of the Greenland-Iceland Low. Analysis in the frequency domain shows a broad 'peak' in the 10-20 year frequency band in both delta T and SLP data and a striking decrease in power at lower frequency.

The observations are interpreted in the framework of the delayed-oscillator model in which ocean dynamics provides the delay and delta T modulates the strength of the Greenland-Iceland low on decadal timescales.

F. Molteni (1) and S. Corti (2)
(1) International Centre for Theoretical Physics, Trieste, Italy
(2) CINECA - Interuniversity Computing Centre, Bologna, Italy

In nonlinear chaotic systems with multiple flow regimes, relatively small changes in the forcing parameters may induce significant variations in the regime properties, such as position in phase space and frequency of occurrence. If the system is close to a bifurcation point, forcing variations may even modify the number of regimes. The interpretation of the atmospheric response to an anomalous forcing based on changes in the frequency of flow regimes was proposed in the early 1990's to explain non-linear aspects of tropical-extratropical interactions during ENSO events. It has been subsequently applied to other climatic phenomena, such as the interactions between intraseasonal and interannual variability of the Asian summer monsoon, and the multi-decadal variations in the northern extratropical circulation (possibly arising from anthropogenic effects).

Observational evidence on the existence of regimes in the northern extratropical circulation will be reviewed, based on results obtained from the 50-year record of the NCAR/NCEP reanalysis, with separate analyses for the Pacific-North American and the Euro-Atlantic sectors. Theoretical and modelling results supporting the existence of multiple regimes will be discussed. It will be shown that the interpretation of interdecadal variability based only on changes in regime frequencies is clearly applicable to the Euro-Atlantic sector, whereas in the Pacific region the forcing due to ENSO variability is sufficiently strong to alter the number of regimes. Specifically, warm ENSO events appear to force the Pacific circulation into a unimodal state on monthly time-scale.

The existence of regimes in the Asian summer monsoon circulation and its relationship to ENSO will be addressed using a set of 10-member ensemble simulations with the ECMWF GCM, covering 9 years in the 1980's and early 1990's with different ENSO characteristics. The model does possess a bimodal distribution of monsoon rainfall (as deduced from 5-day-mean fields in the the South Asia/Indian Ocean region), but the relation between the regimes distribution and ENSO is more complex than that accounted for by the simple regime-frequency paradigm. As for the extratropical Pacific, the effect of ENSO on regimes properties is substantial, with bimodality being evident mainly during cold (La Nina) ENSO events. (This part of the talk presents collaborative work with L. Ferranti (ECMWF) and J. Slingo (UGAMP - Univ. of Reading))

T.N. Palmer
ECMWF, Shinfield Park, Reading RG2 9AX, UK

Conventional parametrisation schemes in weather and climate prediction models describe the effects of sub­grid scale processes by deterministic bulk formulae which depend on local resolved­scale variables and a number of adjustable parameters. Despite the unquestionable success of such models for weather and climate prediction, it is impossible to justify the use of such formulae from first principles. Using low­order dynamical­systems models, and elementary results from dynamical­systems and turbulence theory, it is shown that even if unresolved scales only describe a small fraction of the total variance of the system, neglecting their variability can, in some circumstances, lead to gross errors in the climatology of the dominant scales. It is suggested that some of the remaining errors in weather and climate prediction models may have their origin in the neglect of sub­grid scale variability, and that such variability should be parametrised by nonlocal dynamically­based stochastic parametrisation schemes. Results from existing schemes are described, and meteorologically­ based mechanisms which might account for the impact of random parametrisation error on planetary­scale motions are discussed. Proposals for the development of stochastic­dynamic parametrisation schemes are outlined, based on potential vorticity diagnosis, singular vector analysis and a simple stochastic cellular automaton model.

G. Philander
Princeton University

Stability analyses of tropical ocean-atmosphere interactions usually focus on the properties of different modes in terms of non-dimensional numbers, but are there simple criteria for instability? (corresponding to a critical vertical shear for baroclinic instability say). Under what conditions is El Nino a severely damped mode? or alternatively a highly unstable mode? This lecture re-examines the stability analyses and shows that, in principle, there are two very different families of modes. For instability, both require the zonal winds to exceed a certain intensity; a shallow equatorial thermocline favors one mode which plays a role in the annual cycle and has a short period of a year or two, while a deep thermocline favors the other (delayed oscillator) type mode which has a period of several years. El Nino as observed over the past few decades is a hybrid mode, with some properties of each family. The presence of random perturbations, especially sporadic bursts of westerly winds near the dateline, can either amplify or diminish the amplitude of El Nino, depending on the timing of the burst relative to the phase of the Southern Oscillation. These bursts cause each El Nino to be distinct and limit its predictability.

J. Shukla
George Mason University - Center for Ocean-Land-Atmosphere Studies (COLA)

This paper describes the results of two case studies: One for the Indian monsoon rainfall, and the other for the height anomalies over the Pacific-North American region. The primary motivation was to understand the relationship between the intraseasonal variability and the interannual variability, and in particular, to examine whether the large interannual variability of seasonal means is a manifestation of changes in the externally forced response that is distinctly different from the day-to-day (intraseasonal) variability that could occur even in the absence of external forcing.

The daily monsoon rainfall data over India was analyzed for 70 years (1901-1970). It was found that the nature of intraseasonal variability is not different during the strong monsoon (flood) years and the weak monsoon (drought) years. This suggests that flood and drought years can be explained by a simple conceptual model in which seasonal mean rainfall should be considered to consist of a linear combination of a large-scale, persistent seasonal mean component and a statistical average of intraseasonal variations.

A brief review of current research to investigate the predictability of seasonal mean atmospheric anomalies shows that the winter mean circulation over the Pacific-North American region is highly predictable in the presence of large SST anomalies in the equatorial Pacific. However, it is shown that, contrary to the conventional wisdom that the ENSO forces PNA, the ENSO-forced signal over the Pacific-North American region is different from PNA.

Julia Slingo
Centre for Global Atmospheric Modelling Department of Meteorology, University of Reading

This talk will explore ways in which non-linearities in the tropical climate system influence the potential predictability of the tropics on seasonal to interannual timescales. The discussion will commence with the most obvious non-linearity - the Clausius-Clapeyron equation and its implications for the relationship between sea surface temperature and convection. The talk will also explore the interaction between the tropics and extratropics, and between intraseasonal and interannual timescales, as possible sources of non-linearity. Finally the apparent potential predictability of the tropical climate, as suggested by statistical methods, has yet to be realised in dynamical models. The possible role of model systematic errors in limiting our ability to predict on seasonal to interannual timescales will be discussed.

Alfonso Sutera
Department of Physics University of Rome La Sapienza, Rome, Italy

An unsettled question in climate behavior is the physical processes that determine the equator to pole temperature gradient. In the present work we study some of these processes by means of simple two level quasi-geostrophic and primitive equation models. In both cases we find that a barotropic governor mechanism is a dominant component of the adjustment process. It is interesting to notice that a similar conclusion holds regardless the nature of the stationary symmetric solution supported by the models. We also notice that in the presence of baroclinic eddies a Hadley cell is formed without an internal dissipation mechanism.

The present work is a collaborative effort with R. Caballero Augi , Danish Center for Earth System Science, University of Copenhagen, Denmark

Eli Tziperman
Weizmann Institute of Science, Rehovot, Israel

We conduct a local predictability analysis of ENSO by analyzing the evolution of small disturbances to an unstable 4.3-year ENSO cycle (unstable periodic orbit) in a Cane-Zebiak model forced by perpetual July conditions. Both eigenmode and singular-vector disturbance growth analyses suggest that there is a predictability barrier associated with the growth phase of El-Nino conditions. This implies a reduced predictability skill during the development of a warm El Nino event... This barrier arises because the growth mechanism for disturbances to the cycle is nearly the same as the growth mechanism for the El Nino conditions themselves. The local amplification of disturbances during the growth phase is several times greater than the eigenmode amplification associated with time-dependent (Floquet) normal-mode instability of the cycle. We suggest that the existence of an ENSO predictability barrier tied to the growth phase of El Nino conditions is likely a robust result, independent of the particular model we use.

Robert Vautard
Laboratoire de Meteorologie Dynamique - Ecole Polytechnique, Paris

The problem of weather predictability is discussed in the general framework of dynamical systems with many scales. A discussion about the dimensionality of synoptic weather with examples is given. Then some theoretical considerations about ensemble predictions are given. Finally, the issue of predictability using assimilation is addressed.