• Boer, G. J., 1989: Concerning the response of the atmosphere to a tropical sea surface temperature anomaly. J. Atmos. Sci.,46, 1898–1921.

  • Branstator, G., 1985: Analysis of general circulation model sea-surface temperature anomaly simulations using a linear model. Part I: Forced solutions. J. Atmos. Sci.,42, 2225–2241.

  • Farrara, J. D., C. R. Mechoso, and A. W. Robertson, 2000: Ensembles of AGCM two-tier predictions and simulations of the circulation anomalies during winter 1997–98. Mon. Wea. Rev.,128, 3589–3604.

  • Gill, A. E., 1980: Some simple solutions for heat induced tropical circulation. Quart. J. Roy. Meteor. Soc.,106, 447–462.

  • Haarsma, R. J., and J. D. Opsteegh, 1989: Nonlinear response to anomalous tropical forcing. J. Atmos. Sci.,46, 3240–3255.

  • Hall, N. M. J., 2000: A simple GCM based on dry dynamics and constant forcing. J. Atmos. Sci.,57, 1557–1572.

  • Held, I. M., and I.-S. Kang, 1987: Barotropic models of the extratropical response to El Niño. J. Atmos. Sci.,44, 3576–3586.

  • ——, S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci.,46, 163–174.

  • Hoerling, M. P., and M. Ting, 1994: Organization of extratropical transients during El Niño. J. Climate,7, 745–766.

  • ——, A. Kumar, and M. Zhong, 1997: El Niño, La Niña, and the nonlinearity of their teleconnections. J. Climate,10, 1769–1786.

  • Horel, J. D., and J. M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev.,109, 813–829.

  • Hoskins, B. J., and A. J. Simmons, 1975: A multi-layer spectral model and the semi-implicit method. Quart. J. Roy. Meteor. Soc.,101, 637–655.

  • ——, and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci.,38, 1179–1196.

  • Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci.,52, 307–319.

  • Klinker, E., and P. D. Sardeshmukh, 1992: The diagnosis of mechanical dissipation in the atmosphere from large-scale balance requirements. J. Atmos. Sci.,49, 608–627.

  • Kok, C. J., and J. D. Opsteegh, 1985: Possible causes of anomalies in seasonal mean circulation patterns during the 1982–83 El Niño event. J. Atmos. Sci.,42, 677–694.

  • Lin, H., and J. Derome, 1996: Changes in predictability associated with the PNA pattern. Tellus,48A, 553–571.

  • Marshall, J. M., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci.,50, 1792–1818.

  • Matsuno, T., 1966: Quasigeostrophic motions in the equatorial area. J. Meteor. Soc. Japan,44, 25–42.

  • Palmer, T. N., and D. A. Mansfield, 1986: A study of wintertime circulation anomalies during past El Niño events using a high-resolution general circulation model. I: Influence of model climatology. Quart. J. Roy. Meteor. Soc.,112, 613–638.

  • Roads, J. O., 1987: Predictability in the extended range. J. Atmos. Sci.,44, 3495–3527.

  • Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized tropical divergence. J. Atmos. Sci.,45, 1228–1251.

  • Sheng, J., J. Derome, and M. Klasa, 1998: The role of transient disturbances in the dynamics of the Pacific–North American pattern. J. Climate,11, 523–536.

  • Simmons, A. J., 1982: The forcing of stationary wave motion by tropical diabatic heating. Quart. J. Roy. Meteor. Soc.,108, 503–534.

  • ——, and D. M. Burridge, 1981: An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev.,109, 758–766.

  • Ting, M., and I. M. Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. J. Atmos. Sci.,47, 2546–2566.

  • ——, and P. D. Sardeshmukh, 1993: Factors determining the extratropical response to equatorial diabatic heating anomalies. J. Atmos. Sci.,50, 907–918.

  • Wallace, J. M., and D. S. Gutzler, 1981: Teleconnections in the geopotential field during the Northern Hemisphere winter. Mon. Wea. Rev.,109, 784–812.

  • View in gallery

    (a)–(d) Selected mean fields from the 9-yr DJF ECMWF climatology and (e)–(h) from a long integration of the SGCM. (a) and (e) 250-mb streamfunction with zonal mean removed. Contour intervals are 5 × 106 m2 s−1; zero contour dotted; negative contours dashed. (b) and (f) 550-mb geopotential height. Contour intervals 100 m. (c) and (g) 850-mb high-pass-filtered (cutoff <6 days) transient eddy northward temperature flux. Contour intervals 3 K m s−1; zero contour omitted; negative contours dashed. (d) and (h) 250-mb high-pass-filtered transient eddy momentum flux. Contour intervals 8 m2 s−2; zero contour omitted; negative contours dashed.

  • View in gallery

    Anomalous heating used as a tropical source in perturbation experiments. (a) At 350 mb; contour intervals are 0.025. (b) Zonal mean;contours 0.0025. Units are degrees per model time step. There are 64 timesteps per day. Maximum vertical average heating is 5°C day−1.

  • View in gallery

    Various indicators of long timescale (>15 days) variability in 550-mb geopotential height. (a) Change in state (drift) of SGCM after 15 days when initialized with observed mean DJF climatology. Contour intervals are 40 m; zero contour omitted; negative contours dashed. (b) As in (a) but initialized from SGCM’s own long-term mean climatology. (c) Standard deviation of an ensemble of initial conditions based on 54 observed 15-day means. Contours 20 m. (d) As in (a) but for ensemble-mean drift when the SGCM is initialized with this ensemble. (e) Difference between SGCM mean climatology and observed, i.e., Figs. 1f minus b. Contours 20 m.

  • View in gallery

    Time-dependent linear response to heating with observed climatological basic state up to 18 days. Streamfunction anomaly at 250 mb with zonal mean removed. Contour intervals are 2.5 × 106 m2 s−2; zero contour dotted; negative contours dashed.

  • View in gallery

    Height anomalies at 550 mb for linear perturbation model response to heating at day 15. (a) Observed climatological basic state. (b) Model climatology basic state. (c) Ensemble-mean response for 54 different basic states. Contour intervals are 20 m; zero contour dotted;negative contours dashed. (d) Standard deviation of ensemble day-15 results, which lead to mean shown in (c); contours 10 m.

  • View in gallery

    Height anomalies at 550 mb for SGCM tangent linear calculation (integration with anomalous heating minus unperturbed integration) at day 15. (a)–(c) Initial conditions the same as the basic states in Fig. 5. (d) Ensemble-mean result with 700-member ensemble consisting of daily data from SGCM long unperturbed integration. Contour intervals are 20 m; zero contour dotted; negative contours dashed.

  • View in gallery

    As in Fig. 5 but with full-amplitude heating, allowing nonlinearity to influence the solution.

  • View in gallery

    As in Fig. 6 but with full-amplitude heating, allowing nonlinearity to influence the solution.

  • View in gallery

    Anomaly in long-term mean climatology of 550-mb geopotential height for long integrations of the SGCM: perturbed minus unperturbed integration. (a) Tropical heating anomaly specified as in Fig. 2. (b) Heating anomaly at half amplitude. (c) Half-amplitude cooling anomaly. (d) Full-amplitude cooling anomaly. Contour intervals are 20 m; zero contour dotted; negative contours dashed. Shaded areas denote response is significant at the 99% confidence level according to a two-sided t test based on monthly means.

  • View in gallery

    (a) Time-mean transient eddy vorticity flux convergence anomaly from the SGCM integration (El Niño minus unperturbed). Field has been subjected to inverse Laplacian and multiplied by f/g to identify source of geopotential height. Contour intervals are 1 m day−1, zero contour omitted; negative contours dashed. (b) The 550-mb geopotential height anomaly from the linear perturbation model based on model climatology and forced with anomalous heating plus all transient flux convergence anomalies from the SGCM integrations, as in Eq. (9). Contours 20 m; zero contour dotted; negative contours dashed.

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Transience, Nonlinearity, and Eddy Feedback in the Remote Response to El Niño

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  • 1 Department of Atmospheric and Oceanic Sciences and Centre for Climate and Global Change Research, McGill University, Montreal, Quebec, Canada
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Abstract

A dry primitive equation model is used to investigate the remote response to a fixed tropical heat source. The basic forcing for the model takes the form of time-independent terms added to the prognostic equations in two configurations. One produces a perturbation model, in which anomalies grow on a fixed basic state. The other gives a simple GCM, which can be integrated for a long time and delivers a realistic climate simulation with realistic storm tracks. A series of experiments is performed, including 15-day perturbation runs, ensemble experiments, and long equilibrium runs, to isolate different dynamical influences on the fully developed Pacific–North American (PNA) type response to an equatorial heating anomaly centered on the date line.

The direct linear response is found to be very sensitive to changes in the basic state of the same order as the atmosphere’s natural variability, and to the natural progression of the basic state over the time period required to set up the response. However, interactions with synoptic-scale noise in the ambient flow are found to have very little systematic effect on the linear response. Nonlinear interactions with a fixed basic state lead to changes in the position, but not the amplitude, of the response. Feedback with finite-amplitude transient eddies leads to downstream amplification of the PNA pattern, both within the setup time for the response and in a fully adjusted equilibrium situation.

Nonlinearity of the midlatitude dynamics gives rise to considerable asymmetry between the response to tropical heating and the response to an equal and opposite cooling.

Corresponding author address: Dr. Nicholas M. J. Hall, Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), BP53, 38041 Grenoble Cedex 9, France.

Email: Nick.Hall@hmg.inpg.fr

Abstract

A dry primitive equation model is used to investigate the remote response to a fixed tropical heat source. The basic forcing for the model takes the form of time-independent terms added to the prognostic equations in two configurations. One produces a perturbation model, in which anomalies grow on a fixed basic state. The other gives a simple GCM, which can be integrated for a long time and delivers a realistic climate simulation with realistic storm tracks. A series of experiments is performed, including 15-day perturbation runs, ensemble experiments, and long equilibrium runs, to isolate different dynamical influences on the fully developed Pacific–North American (PNA) type response to an equatorial heating anomaly centered on the date line.

The direct linear response is found to be very sensitive to changes in the basic state of the same order as the atmosphere’s natural variability, and to the natural progression of the basic state over the time period required to set up the response. However, interactions with synoptic-scale noise in the ambient flow are found to have very little systematic effect on the linear response. Nonlinear interactions with a fixed basic state lead to changes in the position, but not the amplitude, of the response. Feedback with finite-amplitude transient eddies leads to downstream amplification of the PNA pattern, both within the setup time for the response and in a fully adjusted equilibrium situation.

Nonlinearity of the midlatitude dynamics gives rise to considerable asymmetry between the response to tropical heating and the response to an equal and opposite cooling.

Corresponding author address: Dr. Nicholas M. J. Hall, Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), BP53, 38041 Grenoble Cedex 9, France.

Email: Nick.Hall@hmg.inpg.fr

1. Introduction

El Niño is one of the strongest climate signals. The effect of an anomaly in the tropical Pacific sea surface temperature (SST) can be felt by the atmosphere on a global scale, and knowledge of the SST can potentially contribute to predictive skill on seasonal timescales in some extratropical locations. There has consequently been a large research effort devoted to understanding the links between the SST anomaly and the anomalous global circulation. The relationship is complicated, consisting of a sequence of physical and dynamical processes. The standard conceptual framework begins with enhanced deep convection in the equatorial mid-Pacific. This results in increased latent heating throughout the troposphere, leading to enhanced divergent flow at upper levels. Linear wave propagation theory then accounts for a baroclinic response in the Tropics (Matsuno 1966; Gill 1980) and an equivalent barotropic response in the extratropics (Hoskins and Karoly 1981; Simmons 1982), as Rossby waves emanate from a source region in the subtropics, where there is maximum convergence in the flux of vorticity by the divergent component of the wind (Sardeshmukh and Hoskins 1988).

Once established, the linear Rossby wave response in the extratropics projects strongly onto the positive Pacific–North American (PNA) pattern defined by Wallace and Gutzler (1981) and closely resembles observational regression analyses such as that of Horel and Wallace (1981). This pattern has come to be known as the “direct response.” It has been studied as a time-independent solution to various equation sets, linearized about various climatologies. Barotropic models forced with a subtropical vorticity source (Branstator 1985; Held and Kang 1987; Held et al. 1989) can capture the essential upper-level extratropical flow. Baroclinic models forced directly with equatorial heating (Ting and Held 1990; Ting and Sardeshmukh 1993) can give information about the vertical structure and the tropical response. A time-dependent study by Jin and Hoskins (1995, hereafter JH) provides a timescale to establish the direct response: about 1 week for the Tropics and 2 weeks for the extratropics.

Beyond the direct response, a number of other factors need to be considered. These can be gouped into linear effects and nonlinear effects.Possible linear effects are

  • dependence on sampling a variety of basic states (low-frequency variability of the background flow),
  • interaction with existing synoptic-scale eddies (high-frequency variability of the background flow), and
  • temporal and spatial variations in the forcing.
Possible nonlinear effects are
  • wave–wave interaction in the direct response,
  • transient eddy feedback (forcing due to anomalous transient eddy fluxes), and
  • further feedbacks due to altered physical processes.

Some of these issues have been addressed by some of the authors cited above. Ting and Sardeshmukh (1993) find that small variations in the basic state, of the same order as systematic errors commonly found in GCMs, can make important differences to the direct response. They also find, as do JH, that the nature of the response depends on the longitude of the heating. In this study we do not alter the details of the heating perturbation but concentrate instead on the interaction of the response with the ambient flow. Held and Kang (1987) and Haarsma and Opsteegh (1989) studied the steady nonlinear barotropic problem and found that in realistic regimes the results are similar to the linear solution. Jin and Hoskins (1995) make the same claim for their baroclinic solutions. Nonlinear interactions with transient eddies, on the other hand, are usually found to reinforce the direct response. Kok and Opsteegh (1985), Held et al. (1989), Ting and Held (1990), and Hoerling and Ting (1994) augment their linear modeling with the anomalous midlatitude transient eddy forcing taken from observations and from GCM output. An amplification of the direct response is obtained in all cases. This effect has been invoked to account for the amplitudes attained in GCM simulations such as those of Palmer and Mansfield (1986) and Hoerling et al. (1997).

In this paper, we attempt to work forward from the direct response, extending the results of JH to examine transience in the basic state and transient eddy feedback in a selection of short “perturbation” integrations and in a long equilibrium run of a “simple GCM” (SGCM). Both types of experiment are based on a spectral primitive equation model (essentially the same as that used by JH) driven by empirically derived, time-independent forcing functions. First, a perturbation model is used that has a forcing that maintains a fixed basic state. Then the SGCM is used, both for perturbation experiments with a time-dependent basic state and for long integrations that achieve statistical equilibrium. The SGCM is forced in such a way as to give a realistic time-mean climate with realistic transient eddies. Apart from the forcing, the two models are identical and are used together to study the response to tropical heating in a purely dynamical setting. Experiments will be performed of increasing complexity, designed to isolate some of the dynamical considerations listed above, and to bridge the gap between idealized studies of the direct response and full GCM studies.

In section 2 the model is described and the method of calculating the forcing is outlined. Results are shown comparing the model’s climatology with observations, and the experimental design of some perturbation experiments is discussed. Section 3 contains results based on linear perturbation studies, and section 4 contains nonlinear results, both perturbation studies, and the equilibrium SGCM response. The nonlinearity with respect to the sign of the forcing, El Niño versus La Niña, is also investigated. Conclusions are given in section 5.

2. The modeling hierarchy

a. A simple GCM

The starting point for all the numerical experiments described below is the dry spectral primitive equation model developed by Hoskins and Simmons (1975), and used by numerous authors since then, including JH. The version used here differs from the original in some details. It has a split time scheme, so that physical processes such as diffusion and diabatic forcing are not passed through the semi-implicit timestep. It also has an angular momentum conserving vertical scheme due to Simmons and Burridge (1981). Both these points are common with the version used by JH. The resolution used here is triangular 31, with 10 equally spaced sigma (σ) levels. Dissipation is in the form of a scale-selective ∇6 hyperdiffusion with a timescale of 12 h at the smallest scale, applied to vorticity, divergence, and temperature. A level-dependent linear damping is also imposed on temperature and momentum. For upper levels, the timescale of this damping is 30 days for momentum and 10 days for temperature. Below 800 mb, in the model’s two lowest layers, this damping is increased so that for momentum the timescales are 2 days (σ = 0.85) and 0.67 days (σ = 0.95); and for temperature the damping is half as strong—that is, the timescales are double these values.

The only other diabatic term is an empirically derived time-independent forcing, applied to all model variables at all levels. A detailed account of the specification of this forcing is given by Hall (2000). For the SGCM it is based on correcting the systematic errors arising from a sequence of single time step integrations of the primitive equations when initialized with observational analyses, following a method first proposed by Roads (1987), and also used in a quasigeostrophic setting by Marshall and Molteni (1993) and Lin and Derome (1996). In the current implementation, the method is equivalent to calculating the budget residual of a given variable in the manner of Klinker and Sardeshmukh (1992), and then adding it to the predictive equation, as further described below.

Consider an observed atmospheric state, represented by a vector of coefficients Φ in some basis. The time evolution of Φ is given by
i1520-0469-57-24-3992-e1
where N is a nonlinear operator, in our case the primitive equations with some linear damping; and f represents all the processes not captured by N, including the effect of external (boundary) forcing and internal processes such as condensation heating. We approximate Eq. (1) for a model state vector Ψ, by assuming that f(t) can be replaced by the constant vector g:
i1520-0469-57-24-3992-e2
The physical interpretation of the model described by Eq. (2) depends on the specification of g. Suppose we set g = −N(Φ), where overbar denotes the mean over many observations Φ, which may come from a long time series. Provided there is no significant trend in this time series, this is equivalent to setting g = f since the left-hand side of (1) has a time mean of zero. We caclulate g by integrating the primitive equation model (including the damping terms) for one time step from a sequence of observed states, and then averaging. The data are taken from 9 yr (1980/81–1988/89) of half-daily observational analyses for the winter season (DJF) from the European Centre for Medium-Range Weather Forecasts (ECMWF) (the seasonal trend is a negligible part of the mean tendency).

The forcing strategy described above is an objective empirical method that can be applied to any model. Provided the damping contained within N is linear and diagonal, this method is mathematically equivalent to the “restoration” forcing employed by numerous authors for more idealized studies (the associated restoration state is just the forcing divided by the damping). However, the specification for g now includes source terms for all the model’s prognostic equations: temperature, momentum, and mass. Each of these source terms is strongly dependent on the form of the damping employed. For example, much of the derived temperature forcing exists only to balance the temperature damping (in fact the magnitude of this balance is arbitrary, as it depends on an arbitrary reference temperature). The resulting diabatic heating and cooling can be rationalized as a representation of real physical processes. Sources and sinks of momentum are harder to rationalize. For the current model specification, the dominant balance at upper levels is between transient eddy flux convergence and the mean meridional circulation. An excess of westerly force by the former is removed by the small upper-level damping, and the residual is corrected by small sources and sinks contained within g. At the lowest levels the term that balances surface drag (damping) depends strongly on latitude. At 45°N it is the meridional circulation, but at 40°N an artificial eastward force is necessary within g. The latter is unphysical and is presumably due to shortcomings in our representation of physical momentum sinks. It is to be expected that more realistic schemes, such as a nondiagonal diffusive approach or a nonlinear drag law, would improve matters, given enough tuning of the parameters. The lack of orography in the model is similarly compensated for by empirically derived sources of vorticity. Further details of the source terms, and attempts to diminish nonphysical forcing, are given in Hall (2000). In terms of the time-mean flow, these source terms compensate perfectly for inadequacies in drag laws and boundary conditions. In terms of flow variability, however, the model may misrepresent certain processes, such as the interaction of transients with orography. For our purposes, we accept these imperfections as the price of a simple, yet realistic, simulation system, and continue.

The long runs of the SGCM presented below are based on 1000-day integrations, starting from the 9-yr mean observed DJF climatology. Results are shown using the mean of the last 700 days, discarding the first 300. The results do not differ significantly from those obtained by starting from a resting isothermal state. Figure 1 shows selected fields from the control integration compared to the ECMWF analyses. The SGCM clearly has an adequate climatology in both time-mean fields and transient eddies to justify its use in the current investigation.

b. A perturbation model

An alternative specification of g allows us to consider the growth of anomalies on a time-independent basic state. Imagine we are interested in deviations from some fixed climatology Λ. We denote these deviations x = ΨΛ. N can be expanded about Λ to give
NΨNΛLΛxEΛx
where L is a linear operator that depends on Λ, and E is nonlinear to the same degree as N and contains no linear terms. Here E only depends on Λ if N has cubic or higher-order nonlinearity. If we set g = −N(Λ) and initialize (2) with Ψ = Λ, with an additional perturbation forcing fp, the integration will then satisfy
i1520-0469-57-24-3992-e4
with x = 0 at t = 0. The model is thereby converted into a time-dependent perturbation model about the climatology Λ, due to perturbation forcing fp. This is the approach followed by JH. If x remains small, we have a linear perturbation model. This is easy to arrange for a limited time by making fp small.

c. Experiments with anomalous forcing

The forcing perturbation represents a deep convective heat source in the equatorial mid-Pacific, and is shown in Fig. 2. It is centered on the equator and the date line and is elliptical, with semi-major and semi-minor axes of 40° longitude and 12.5° latitude. The magnitude of the heating depends on the squared cosine of the distance from the center, and the vertical profile is proportional to (1 − σ) sinπσ, following Ting and Held (1990). The central peak vertical-mean value used is 5°C day−1, corresponding to a precipitation anomaly of 2 cm day−1. This is the same as the value used by Ting and Sardeshmukh (1993) and double the value used by JH. It corresponds to the heat source associated with a strong El Niño. For linear experiments, the heating rate is divided by 104 and the solutions scaled back up for presentation.

In addition to some straightforward integrations of the perturbation model about the observed climatology Φ, some further experiments will be shown using alternative basic states and addressing the problem of time-dependent interactions. In the introduction, time dependence in the background flow was split into two categories: low and high frequencies. For our purposes, low frequency refers to timescales longer than the timescale to establish the direct response. We can get an idea of the importance of this component of the variability by looking at the way the SGCM evolves in 15 days when initialized with the observed climatology, or indeed with its own long-term time-mean climatology. This evolution, which we shall refer to as the “drift,” is shown in Figs. 3a,b. The magnitude is similar to that of the signal we are looking for. This amount of development in the background state is therefore likely to have an effect on that signal. Another measure of the importance of slow variability is the variation within an ensemble of basic states, based on 15-day means. The 9-yr DJF dataset yields 54 such basic states. The standard deviation of this ensemble is shown in Fig. 3c for the 550-mb geopotential height. The ensemble mean of the 15-day drift of the SGCM when initialized with each of these states is shown in Fig. 3d. In all cases the variation is greater than the SGCM’s time-mean systematic error, shown in Fig. 3e. This serves to demonstrate further that the SGCM’s climatology is adequate for investigating the importance of these effects.

Now if the SGCM is initialized with Φ, the equation for the drift, Δ = ΨΨ(t = 0) = ΨΦ, is
i1520-0469-57-24-3992-e5
If a forcing perturbation fp is then added, the resulting anomaly in Δ is given by
i1520-0469-57-24-3992-e6
Equation (6) describes a tangent model, expressing the development of the direct response x on the time-dependent model-generated flow starting from initial condition Φ. Similar equations can be written for other initial conditions. Note that if g is such that Δ = 0, then we recover the basic time-dependent response about an unchanging basic state given by (4). Provided the nonlinearity contained within N is quadratic, (6) can be rewritten as
i1520-0469-57-24-3992-e7
where Q is a linear operator defined by E(Ψ) = Ψ († denotes transpose). Note that Q is independent of the initial condition and the form of L depends linearly on it. If fp is small, the anomaly x will be small and the fourth term in (7) will be negligible, reducing the model to tangent-linear form. Equation (7) can be integrated from a variety of initial conditions with mean Φ, using appropriate versions of L. If x remains small, the ensemble-mean response [x] then evolves according to
i1520-0469-57-24-3992-e8
where * denotes a deviation from the ensemble mean [ ]. Note that (8) is linear in x and contains no effects from anomalous transient eddy forcing arising from transient wave–wave interaction. The first term in curly brackets is the linear effect of ensemble-mean drift on the ensemble-mean response. The second is the linear effect of interactions between deviations from the ensemble mean and is independent of the ensemble-mean drift. We identify the first term with the a slow adjustment of the basic state associated with processes acting on timescales beyond 15 days. We identify the second term with all other linear processes, including any systematic rectifying effects due to shorter timescale synoptic development. In interpreting the significance of this term, we are assuming that a considerable amount of synoptic-scale “noise” has been smoothed out by the ensemble averaging. Perturbation experiments designed to isolate the effect of these two terms will be used to try and gauge the importance of the first and second linear effects listed in the introduction.

The importance of the first nonlinear effect listed in the introduction, namely, wave–wave interaction with a fixed basic state, is easily measured by allowing fp to have realistic amplitude and thereby seeing how much difference the second term in (4) makes to the solution. Ensemble experiments can also be repeated with finite-amplitude fp to see the effect of nonlinearity on the ensemble mean and ensemble variance of solutions to (4) and (6) and thereby asses the validity of the linear approximation in (8) after 15 days.

Finally, the role of transient eddy feedback, the generation of perturbation forcing by anomalous transient eddy fluxes, can be further investigated through a long integration of the SGCM. The time-mean budget for two long integrations, a control run Ψc, and a perturbation run Ψp with additional forcing fp yields
i1520-0469-57-24-3992-e9
The second term on the right-hand side is the anomalous eddy forcing. In the SGCM this can be diagnosed purely from knowledge of the two time-mean climates, because all the “physics” in the model is linear. Furthermore, the right-hand side of (9) can be scaled down and put back into (4) to asses the direct linear response to the perturbation eddy forcing.

3. Linear results

An integration of Eq. (4) using the observed climatology Φ as shown in Figs. 1a,b as a fixed basic state and with an infinitesimal perturbation as in Fig. 2 yields the direct linear response. This is given in Fig. 4 for 3-day intervals up to 18 days. The stationary wave component of the 250-mb streamfunction shows an initial Gill (1980) type baroclinic quadrupole in the Tropics with a Kelvin wave traveling rapidly eastward. As shown by JH, the solution fills the tropical band within 10 days and a stationary Rossby wave shows group propagation over North America, establishing a PNA type response by day 15. If the integration continues much beyond 20 days the solution gives way to an unstable baroclinic normal mode in the midlatitude Pacific that is quite independent of the structure of the forcing.

The day-15 550-mb geopotential height from this solution is shown in Fig. 5a. The zonal-mean response at this level is relatively small, so the full field is plotted and the wave train over North America can be seen, with the Pacific low by far the strongest center. A similar perturbation experiment is shown in Fig. 5b, where the forcing g and initial conditions are chosen to give a linear solution using the SGCM’s own climatology, shown in Figs. 1e,f as a fixed basic state (the difference between the two basic states is shown in Fig. 3e). Figure 5c then shows the mean of an ensemble of 54 linear perturbation experiments that have 15-day means as basic states. The similarities between these three pictures are more striking than the differences. The systematic error of the SGCM has had some effect on the direct response, deepening the Pacific low, but the pattern is very similar. The ensemble-mean response hardly differs from the response based on the mean climatology. This is a reflection of the fact that the nonlinearity of N is essentially quadratic, so the mean of L for all basic states in the ensemble is close to LΦ (note that the mean climatology Φ is is the mean of the ensemble, by construction). However, the variation from one ensemble member to another is much larger. This is evident from the standard deviation of the ensemble response shown in Fig. 5d, which is of the same order as the actual response. So the low-frequency (monthly timescale) variability of the background state can make a significant difference to the direct response, even if it has no significant rectifying effect on the average direct response.

We now turn to linear perturbation runs in which the basic state is time-dependent, and for this we use the SGCM in tangent mode as expressed by Eqs. (6)–(8). Figure 6a shows the day-15 perturbation when the SGCM is initialized with the observed climatology Φ. (On day 15 the background flow differs from Φ by the amount shown in Fig. 3a.) The perturbation response has clearly undergone some modification due to the change in the background state. There is more small-scale noise in the picture, but it can be seen that the downstream high and low of the PNA response have gained amplitude. The same thing happens when the model is initialized with its own long-term mean climatology, which evolves over 15 days as in Fig. 3b. This response is shown in Fig. 6b. The noise is cleaned up by using the ensemble of initial conditions based on 54 15-day means from the observational dataset. There is still a drift in the ensemble mean, because the SGCM’s climatology is not identical to the observed climatology. The ensemble-mean response [Eq. (8)] retains the enhanced downstream PNA pattern, but is much smoother, as shown in Fig. 6c. Which term in Eq. (8) is responsible for the downstream enhancement? Is it the ensemble-mean drift term or the term due to variations within the ensemble? To answer this question another ensemble was used in which 700 flow realizations, taken from the last 700 days of the control SGCM integration, were used to initialize the tangent experiments. The drift in this ensemble-mean is virtually zero, as expected, since it is merely equivalent to shifting the 700-day averaging period by 15 days. The day-15 ensemble-mean response is shown in Fig. 6d. It is almost identical to the direct response about the model climatology shown in Fig. 5b. So it is the drift term that makes the difference. For an ensemble with no ensemble-mean drift, the synoptic-scale noise has a negligible systematic effect on the ensemble-mean solution. However, if the ensemble-mean state changes during the 15-day integration, this can affect the solution substantially. Supplementary perturbation experiments (not shown) linearized about the day-15 drifted climatology confirm that the direct response is indeed sensitive enough to this change to account for the differences seen.

4. Nonlinear results

a. 15-day perturbation studies

The experiments described in section 3 are repeated in this section with finite-amplitude perturbation forcing fp. Figure 7 thus shows the nonlinear versions of the time-dependent perturbation experiments about an unchanging basic state, to be compared with the linear experiments shown in Fig. 5. The difference is due to the second term in (4), which represents wave–wave interaction in the direct response, and is now nonzero. As noted by JH, this effect appears to be slight. There is an eastward shift of the Pacific low that seems to be robust since it occurs for both observed and model climatologies (Figs. 7a,b) and also in the ensemble-mean response (Fig. 7c). There is also a hint of some intensification of the downstream PNA response, but this latter effect is clearly basic-state dependent and does not show up in the ensemble mean. The variation between ensemble members is shown in Fig. 7d, and looks much like the linear case except that the spurious bull’s-eyes arising from normal-mode growth off the east coast of Asia have now saturated.

The nonlinear versions of the tangent perturbation runs, based on the SGCM-generated time-dependent basic state, are shown in Fig. 8, which should be compared with the linear versions in Fig. 6. The single tangent runs, initialized with observed and SGCM climatologies (Figs. 8a,b), are too noisy to draw any conclusions about the systematic effects of nonlinearity, but the 54- and 700-member ensemble-mean results shown in Figs. 8c,d give a clear signal. They both display the eastward shift of the Pacific low already noted for the fixed basic state, and in addition there is a downstream amplification of the PNA pattern at day-15 compared to the linear runs. The conclusion is that the synoptic-scale noise, as represented by the variations among ensemble members, can lead to a systematic change in the day-15 response, but only if we allow finite-amplitude wave–wave interaction to occur. The fourth term in (7), xQx, is therefore important in providing an extra source term, which acts to enhance the direct response, particularly in the second and third centers of action of the PNA pattern.

b. 1000-day SGCM integrations

Since the SGCM is capable of maintaining a realistic equilibrium climate, it is worthwhile examining the effect of the tropical heating perturbation on a long integration. The resulting time-mean anomaly will have features in common with the direct response and features that are driven by transient eddy flux convergence, as shown in (9). In fact four integrations were carried out, with finite-amplitude perturbations: fp; fp/2; −fp/2; and −fp. The resulting 550-mb geopotential height anomalies are shown in Fig. 9.

The strong-heating run shown in Fig. 9a displays a very strong enhancement of the high center over Canada compared to the day-15 perturbation results seen so far. The low centers, on the other hand, are not greatly altered. Equally strong anomaly centers appear farther afield, the high over western Europe in particular. Interestingly, the prominence of the PNA high is reduced for the weak-heating case (Fig. 9b), although the whole pattern is still enhanced compared to direct response (which would be half the magnitude seen in previous figures) and the strong European feature persists. The latter is obviously an eddy-driven feature that is probably quite model dependent. Extended ensemble integrations (not shown) indicate that this feature grows as a zonal extension of the PNA response after about a month, and a further month is required to establish the north–south dipole characteristic seen for the full heating. It should therefore be considered part of this model’s response to El Niño, but it is, of course, unrealistic compared to observed El Niño responses. It projects strongly onto the model’s natural low-frequency variability, and the fact that it has been excited by the tropical heating may imply that this mode is too sensitive in this model, possibly because of the simplified damping prescription discussed in section 2. It may also reflect errors in the specification of the heat source compared to the anomalies typically associated with a real El Niño, discussed further in the conclusions.

The other two panels in Fig. 9 correspond to a weak and strong La Niña. As we progress in this direction, the second center of the PNA, now a low, decreases its prominence even more compared to the other two centers. The strong cooling case is clearly not just the opposite of the strong heating case, even though the tropical forcing perturbation is equal and opposite. The same effect is also seen in 15-day nonlinear ensemble tangent perturbation runs with tropical cooling (not shown). In reality, a phenomenon such as this could be further augmented by a difference in the location of the source between El Niño and La Niña, as discussed by Hoerling et al. (1997)

To illustrate better the role of the second term on the right-hand side of (9), it has been evaluated for the 550-mb transient eddy vorticity flux convergence. This is displayed in Fig. 10a after first taking the inverse Laplacian and multiplying by f/g to emulate the the geostrophic “source” of a geopotential height anomaly. There is much small-scale structure in the field and it is difficult to attribute a response to any single local feature. A high source can be identified over western Canada potentially reinforcing the PNA high. The transient eddy temperature flux convergence (not shown) leads to a sink in the same location. Sheng et al. (1998) have shown that for either phase of the observed PNA, transient thermal fluxes are dissipative whereas momentum fluxes reinforce the pattern. To give some indication of the role of these eddy terms in the response, a 15-day integration of Eq. (4) was carried out, based on the SGCM control climatology, and forced with the entire right-hand side of (9). This anomalous forcing was scaled down to give the linear direct response to the tropical heating plus associated anomalous transient eddy forcing in all model variables. The result at day 15 is shown in Fig. 10b. It looks like an exaggerated version of the SGCM equilibrium response. The exaggeration probably stems from the linear nature of the experiment. Now that the perturbation forcing contains sources of vorticity outside the tropical zone, the use of a 15-day timescale as a proxy for an equilibrium response becomes questionable. However, the qualitative agreement between Figs. 10b and 9a confirms our expectations from Eq. (9).

5. Conclusions

A primitive equation model has been used in two modes, as a perturbation model and as a simple GCM, to deconstruct the midlatitude response to a tropical heat source. The simulations are quite realistic, both in terms of the SGCM’s time mean and transient eddy climatology and the response to an El Niño type forcing. In the introduction a list of dynamical considerations was given, and experiments have been performed with the idea of isolating each one, to gauge its relative importance. The results lead to the following broad conclusions.

  • Natural variations in the extratropical flow on timescales longer than the time needed to set up the direct linear response can lead to very large modifications to the response. Indeed, the changes in the response that arise from this factor are typically as large as the response itself. It is also likely that the slow evolution of the basic state over the 15-day period considered here, and referred to as the “drift,” will influence the response to some degree. This effect varies from one basic state or initial condition to another and has no systematic signature.
  • The net linear effect, on the direct linear response, of shorter-timescale synoptic eddies (as represented by variations between ensemble members) is much less important. Any systematic rectifying effect that the storm track might have should appear in the third term in (8), and is found to be small compared to the changes in the linear response due to the slow evolution of an ensemble-mean basic state.
  • Nonlinear wave–wave interactions in the direct response on a fixed basic state do not affect the amplitude very much. They do, however, produce a consistent eastward shift of the Pacific low.
  • Nonlinear interactions in the direct response, in the presence of synoptic-scale noise, have a large impact on the solution, even within the 15-day period in which the response is being established. These interactions arise from including the wave–wave term xQx in (7). This term is clearly important in allowing the anomalous transient eddy fluxes that constitute the extra source term shown in (9). Since the response is altered, however, the other terms in (7) that concern the interaction of the finite-amplitude response with the time-dependent flow may now also be altered, and subsequently contribute to the solution. The principal effect is an amplification of the PNA high over western Canada.
  • There is an asymmetry between the response to heating and cooling, even though the forcing perturbation is equal and opposite, which must be ascribed to nonlinear midlatitude dynamics. In the model used here, the asymmetry takes the form of a dramatic change in the prominence of the second center of the PNA pattern.

Some of these results confirm the findings of previous workers. Others complement them, and quantify their relative importance. The use of just one model with exactly the same parameters in several different modes of operation leads to a particularly clean set of experiments. The interpretation of the results is further simplified by the absence of any detailed representation of physical processes. The role of feedbacks due to altered physical processes cannot be addressed by this model, but the range of behavior observed with dry dynamics alone is still very rich.

There is further potential to explore the sensitivity of the system to changes in the distribution of the heating in time and space. We have only looked at two extremes in terms of timescale: the setup time and the equilibrium solution. The same range of models could be used to simulate the response to a realistic evolution of heating. We have also only looked at one spatial distribution, concentrating exclusively on the tropical heat source associated with an idealized El Niño. We have neglected the effect of the cooling anomaly to the east typically associated with El Niño, and this may have affected our solutions, particularly in the long equilibrium integration where the zonal-mean tropical heating acts to accelerate the midlatitude westerlies. A budget study by Boer (1989) indicates that observed local cooling anomalies have a significant impact on sources of vorticity. Furthermore it is well known that not all El Niños are the same, as illustrated by the work of Hoerling and Ting (1994). Recent GCM integrations by Farrara et al. (2000) show that changes in the heating as far afield as the Indian Ocean can also make an important contribution to the midlatitude response over the Pacific. Factors such as these may account for the differences between simple model results and observations. In addition to this, the observed asymmetry between El Niño and La Niña may arise in part from a shift in the forcing anomaly (Hoerling et al. 1997), although the results shown above imply that this is not the only factor at play.

In the final analysis, the predictive facility of models is based on their ability to simulate the processes considered above. At best, knowledge of tropical SSTs is likely to improve this facility only in a statistical sense, and studies such as this one, which add successive layers onto the simple linear solution, can help us understand the statistics of general circulation models.

Acknowledgments

N. Hall gratefully acknowledges many conversations with Prashant Sardeshmukh that helped form the initial impetus for this work. We thank Brian Hoskins and the team at Reading University for making the model available, and the three reviewers for comments that led to improvements in the manuscript. Thanks also to Hai Lin for providing the shading on Fig. 9. This work was funded by the Atmospheric Environment Service of Canada through the Canadian Institute for Climate Studies, and by the Fonds pour la Formation de Chercheurs et l’Aide à la Recherche through the Centre for Climate and Global Change Research.

REFERENCES

  • Boer, G. J., 1989: Concerning the response of the atmosphere to a tropical sea surface temperature anomaly. J. Atmos. Sci.,46, 1898–1921.

  • Branstator, G., 1985: Analysis of general circulation model sea-surface temperature anomaly simulations using a linear model. Part I: Forced solutions. J. Atmos. Sci.,42, 2225–2241.

  • Farrara, J. D., C. R. Mechoso, and A. W. Robertson, 2000: Ensembles of AGCM two-tier predictions and simulations of the circulation anomalies during winter 1997–98. Mon. Wea. Rev.,128, 3589–3604.

  • Gill, A. E., 1980: Some simple solutions for heat induced tropical circulation. Quart. J. Roy. Meteor. Soc.,106, 447–462.

  • Haarsma, R. J., and J. D. Opsteegh, 1989: Nonlinear response to anomalous tropical forcing. J. Atmos. Sci.,46, 3240–3255.

  • Hall, N. M. J., 2000: A simple GCM based on dry dynamics and constant forcing. J. Atmos. Sci.,57, 1557–1572.

  • Held, I. M., and I.-S. Kang, 1987: Barotropic models of the extratropical response to El Niño. J. Atmos. Sci.,44, 3576–3586.

  • ——, S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci.,46, 163–174.

  • Hoerling, M. P., and M. Ting, 1994: Organization of extratropical transients during El Niño. J. Climate,7, 745–766.

  • ——, A. Kumar, and M. Zhong, 1997: El Niño, La Niña, and the nonlinearity of their teleconnections. J. Climate,10, 1769–1786.

  • Horel, J. D., and J. M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev.,109, 813–829.

  • Hoskins, B. J., and A. J. Simmons, 1975: A multi-layer spectral model and the semi-implicit method. Quart. J. Roy. Meteor. Soc.,101, 637–655.

  • ——, and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci.,38, 1179–1196.

  • Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci.,52, 307–319.

  • Klinker, E., and P. D. Sardeshmukh, 1992: The diagnosis of mechanical dissipation in the atmosphere from large-scale balance requirements. J. Atmos. Sci.,49, 608–627.

  • Kok, C. J., and J. D. Opsteegh, 1985: Possible causes of anomalies in seasonal mean circulation patterns during the 1982–83 El Niño event. J. Atmos. Sci.,42, 677–694.

  • Lin, H., and J. Derome, 1996: Changes in predictability associated with the PNA pattern. Tellus,48A, 553–571.

  • Marshall, J. M., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci.,50, 1792–1818.

  • Matsuno, T., 1966: Quasigeostrophic motions in the equatorial area. J. Meteor. Soc. Japan,44, 25–42.

  • Palmer, T. N., and D. A. Mansfield, 1986: A study of wintertime circulation anomalies during past El Niño events using a high-resolution general circulation model. I: Influence of model climatology. Quart. J. Roy. Meteor. Soc.,112, 613–638.

  • Roads, J. O., 1987: Predictability in the extended range. J. Atmos. Sci.,44, 3495–3527.

  • Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized tropical divergence. J. Atmos. Sci.,45, 1228–1251.

  • Sheng, J., J. Derome, and M. Klasa, 1998: The role of transient disturbances in the dynamics of the Pacific–North American pattern. J. Climate,11, 523–536.

  • Simmons, A. J., 1982: The forcing of stationary wave motion by tropical diabatic heating. Quart. J. Roy. Meteor. Soc.,108, 503–534.

  • ——, and D. M. Burridge, 1981: An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev.,109, 758–766.

  • Ting, M., and I. M. Held, 1990: The stationary wave response to a tropical SST anomaly in an idealized GCM. J. Atmos. Sci.,47, 2546–2566.

  • ——, and P. D. Sardeshmukh, 1993: Factors determining the extratropical response to equatorial diabatic heating anomalies. J. Atmos. Sci.,50, 907–918.

  • Wallace, J. M., and D. S. Gutzler, 1981: Teleconnections in the geopotential field during the Northern Hemisphere winter. Mon. Wea. Rev.,109, 784–812.

Fig. 1.
Fig. 1.

(a)–(d) Selected mean fields from the 9-yr DJF ECMWF climatology and (e)–(h) from a long integration of the SGCM. (a) and (e) 250-mb streamfunction with zonal mean removed. Contour intervals are 5 × 106 m2 s−1; zero contour dotted; negative contours dashed. (b) and (f) 550-mb geopotential height. Contour intervals 100 m. (c) and (g) 850-mb high-pass-filtered (cutoff <6 days) transient eddy northward temperature flux. Contour intervals 3 K m s−1; zero contour omitted; negative contours dashed. (d) and (h) 250-mb high-pass-filtered transient eddy momentum flux. Contour intervals 8 m2 s−2; zero contour omitted; negative contours dashed.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 2.
Fig. 2.

Anomalous heating used as a tropical source in perturbation experiments. (a) At 350 mb; contour intervals are 0.025. (b) Zonal mean;contours 0.0025. Units are degrees per model time step. There are 64 timesteps per day. Maximum vertical average heating is 5°C day−1.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 3.
Fig. 3.

Various indicators of long timescale (>15 days) variability in 550-mb geopotential height. (a) Change in state (drift) of SGCM after 15 days when initialized with observed mean DJF climatology. Contour intervals are 40 m; zero contour omitted; negative contours dashed. (b) As in (a) but initialized from SGCM’s own long-term mean climatology. (c) Standard deviation of an ensemble of initial conditions based on 54 observed 15-day means. Contours 20 m. (d) As in (a) but for ensemble-mean drift when the SGCM is initialized with this ensemble. (e) Difference between SGCM mean climatology and observed, i.e., Figs. 1f minus b. Contours 20 m.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 4.
Fig. 4.

Time-dependent linear response to heating with observed climatological basic state up to 18 days. Streamfunction anomaly at 250 mb with zonal mean removed. Contour intervals are 2.5 × 106 m2 s−2; zero contour dotted; negative contours dashed.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 5.
Fig. 5.

Height anomalies at 550 mb for linear perturbation model response to heating at day 15. (a) Observed climatological basic state. (b) Model climatology basic state. (c) Ensemble-mean response for 54 different basic states. Contour intervals are 20 m; zero contour dotted;negative contours dashed. (d) Standard deviation of ensemble day-15 results, which lead to mean shown in (c); contours 10 m.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 6.
Fig. 6.

Height anomalies at 550 mb for SGCM tangent linear calculation (integration with anomalous heating minus unperturbed integration) at day 15. (a)–(c) Initial conditions the same as the basic states in Fig. 5. (d) Ensemble-mean result with 700-member ensemble consisting of daily data from SGCM long unperturbed integration. Contour intervals are 20 m; zero contour dotted; negative contours dashed.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 7.
Fig. 7.

As in Fig. 5 but with full-amplitude heating, allowing nonlinearity to influence the solution.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 8.
Fig. 8.

As in Fig. 6 but with full-amplitude heating, allowing nonlinearity to influence the solution.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 9.
Fig. 9.

Anomaly in long-term mean climatology of 550-mb geopotential height for long integrations of the SGCM: perturbed minus unperturbed integration. (a) Tropical heating anomaly specified as in Fig. 2. (b) Heating anomaly at half amplitude. (c) Half-amplitude cooling anomaly. (d) Full-amplitude cooling anomaly. Contour intervals are 20 m; zero contour dotted; negative contours dashed. Shaded areas denote response is significant at the 99% confidence level according to a two-sided t test based on monthly means.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

Fig. 10.
Fig. 10.

(a) Time-mean transient eddy vorticity flux convergence anomaly from the SGCM integration (El Niño minus unperturbed). Field has been subjected to inverse Laplacian and multiplied by f/g to identify source of geopotential height. Contour intervals are 1 m day−1, zero contour omitted; negative contours dashed. (b) The 550-mb geopotential height anomaly from the linear perturbation model based on model climatology and forced with anomalous heating plus all transient flux convergence anomalies from the SGCM integrations, as in Eq. (9). Contours 20 m; zero contour dotted; negative contours dashed.

Citation: Journal of the Atmospheric Sciences 57, 24; 10.1175/1520-0469(2001)058<3992:TNAEFI>2.0.CO;2

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