The Extratropical Signal Generated by a Midlatitude SST Anomaly. Part II: Influence on Seasonal Forecasts

Nicholas M. J. Hall Department of Atmospheric and Oceanic Sciences and Centre for Climate and Global Change Research, McGill University, Montreal, Quebec, Canada

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Hai Lin Department of Atmospheric and Oceanic Sciences and Centre for Climate and Global Change Research, McGill University, Montreal, Quebec, Canada

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Jacques Derome 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 simple GCM based on a primitive equation model with empirically derived time-independent forcing is used to make forecasts in the extended to seasonal range. The results are analyzed in terms of the response to a midlatitude Pacific sea surface temperature anomaly (SSTA), represented here by a heating perturbation. A set of 90-day, 30-member ensemble forecasts is made with 54 widely differing initial conditions, both with and without the SSTA. The development of the response, defined as the difference between ensemble means, is split into three 30-day averages: month 1, month 2, and month 3.

During month 1, ensemble members separate, and the local response and remote teleconnections are established. The local response is not very sensitive to the initial condition.

In month 2, the extended range, the responses are relatively strong and vary greatly from one initial condition to another. However, a linear analysis reveals that large variations in the response do not correlate strongly with large variations in the initial condition. The initial perturbations required to generate the observed variations in the response are relatively small, and may be difficult to isolate in a real forecasting situation.

In month 3, the seasonal range, variations between responses are much smaller. The initial condition loses its influence and the responses all start to resemble the equilibrium response discussed in Part I.

Corresponding author address: Nicholas M. J. Hall, Laboratoire des Ecoulements Géophysiques et Industriels, BP53, 30841 Grenoble Cédex 9, France. Email: nick.hall@hmg.inpg.fr

Abstract

A simple GCM based on a primitive equation model with empirically derived time-independent forcing is used to make forecasts in the extended to seasonal range. The results are analyzed in terms of the response to a midlatitude Pacific sea surface temperature anomaly (SSTA), represented here by a heating perturbation. A set of 90-day, 30-member ensemble forecasts is made with 54 widely differing initial conditions, both with and without the SSTA. The development of the response, defined as the difference between ensemble means, is split into three 30-day averages: month 1, month 2, and month 3.

During month 1, ensemble members separate, and the local response and remote teleconnections are established. The local response is not very sensitive to the initial condition.

In month 2, the extended range, the responses are relatively strong and vary greatly from one initial condition to another. However, a linear analysis reveals that large variations in the response do not correlate strongly with large variations in the initial condition. The initial perturbations required to generate the observed variations in the response are relatively small, and may be difficult to isolate in a real forecasting situation.

In month 3, the seasonal range, variations between responses are much smaller. The initial condition loses its influence and the responses all start to resemble the equilibrium response discussed in Part I.

Corresponding author address: Nicholas M. J. Hall, Laboratoire des Ecoulements Géophysiques et Industriels, BP53, 30841 Grenoble Cédex 9, France. Email: nick.hall@hmg.inpg.fr

1. Introduction

The physical basis for extended range to seasonal forecasting lies in the fact that information contained in the lower boundary temperature decays more slowly than information contained in the initial condition. The chaotic nature of midlatitude atmospheric dynamics makes accurate weather forecasting practically impossible beyond a “predictability limit” of about 10–15 days. Within this period, small errors in the initial condition amplify unpredictably to the point where forecast skill is usually lost. Skillful forecasts beyond the predictability limit depend either on the initial condition being in a slowly evolving configuration, or on the continued influence of a long-lived feature of the lower boundary, for example, a sea surface temperature anomaly (SSTA). As the forecast lead time gets longer, the initial condition loses its influence and the lower boundary gains importance. We move from “extended range forecasting” reviewed by Royer (1993) to “seasonal forecasting” reviewed by Palmer and Anderson (1994). In this paper we study this transition, from the initial value problem to the boundary forcing problem, in terms of the influence of an SSTA in a large set of ensemble forecasts with a dynamical model.

Part of the variability on the extended and seasonal timescales is inherently unpredictable, so predictions on these timescales must be cast in a statistical form. They are therefore useful primarily to those whose interest spans a number of forecast periods. Because of the presence of the weather noise, in the midlatitudes at least, a forecast for a single period has relatively little worth. To overcome the effect of noise, a collection of forecasts encompassing several seasons must be considered. Statistical studies of climate variability based on data (Madden 1976; Rowell 1998 and references therein) and models (Harzallah and Sadourny 1995; Zwiers 1996) attempt to assess by statistical means the fraction of atmospheric variance that is attributable to the integrated effect of “weather noise,” and the fraction that is potentially predictable. They generally estimate that on seasonal timescales, less than half the signal variance is potentially predictable. Much of the predictability is associated with the effect of the El Niño–Southern Oscillation (ENSO) on the large-scale flow. The atmosphere is at its most predictable during extreme phases of ENSO (Yang et al. 1998; Derome et al. 2001).

There is some observational evidence, however, that SSTAs at midlatitudes can also contribute to seasonal predictability (Czaja and Frankignoul 1999). The prospect of improving on the signal given by ENSO has motivated a host of modeling studies, usually with GCMs, aimed at unraveling the influence of a midlatitude SSTA on the atmospheric circulation. These studies are listed in the companion paper, Hall et al. (2001, hereafter HDL) and reviewed by Robinson (2000). They are almost exclusively concerned with the equilibrium response to an imposed SSTA, that is to say, the long-term average perturbation to the flow associated with an SSTA, which is fixed for a very long integration. This is also the subject investigated by HDL.

A natural question to ask is “how relevant are such studies to the real problem of extended range forecasting?” Does the equilibrium response to an SSTA give a good guide to the way in which the same SSTA would affect a forecast? If so, at what lead time?

In this study we use the same “simple” GCM as HDL, with the same perturbation heating to represent an SSTA in the western North Pacific. Instead of running the model to statistical equilibrium, multiple 90-day ensemble integrations are carried out with and without the SSTA, sampling a wide range of initial conditions. Following the practice of some operational groups (e.g., Gagnon et al. 2000) the SSTA is held constant as the model is integrated forward, based on the observation that a typical decorrelation timescale for a midlatitude SSTA is 4–5 months (Frankignoul and Hasselmann 1977), so the signal persists for the 3-month timescale considered for most seasonal forecasts. In a similar idealized study with a coupled model, Miller and Roads (1990) found that evolving SSTAs did little or nothing to improve the forecast quality. The results of the 90-day integrations are analyzed to explore the transition from medium-range to seasonal forecasts in terms of the influence of a fixed SSTA on the evolving flow. We assess the point at which the equilibrium results referred to above become relevant, and quantify the ongoing influence of the initial conditions on the form and magnitude of the forecast perturbation.

In section 2, the model is described briefly and the experimental design is outlined. Results are shown concerning the unperturbed evolution of the model from climatological initial conditions, and the behavior of an ensemble of small initial perturbations. In section 3, a heating perturbation is added to represent the SSTA, and its influence on the ensemble-mean forecast is shown for three very different initial conditions. The results are generalized in section 4 to an extensive set of initial conditions and the findings are discussed in section 5.

2. Model drift and ensemble spread

The simple GCM used in this study is the same as that used by HDL. It is based on a global spectral primitive equation model with linear damping and diffusion, and an empirically derived time-independent forcing. The model and method are precisely as in HDL and the properties of this type of model, including parameter dependence are explored exhaustively by Hall (2000). The salient points are repeated here for completeness. The model integrates prognostic equations for vorticity, divergence, temperature, and log surface pressure at a horizontal resolution of T31 with 10 equally spaced sigma levels, using a split semi-implicit time step. Apart from the primitive equations, the only other terms are a linear damping and diffusion of momentum and temperature and a constant source term for all prognostic variables. The damping is strongest in the lowest two levels where the average coefficient corresponds to a timescale of one day for momentum and two days for temperature. At higher levels the damping timescales are 30 and 10 days, respectively. The diffusion takes the form of a ∇6 operator acting on vorticity, divergence, and temperature with a timescale of half a day on the smallest resolved scale. The time-independent forcing term is calculated from the average tendency given by the unforced model when it is initialized with a long sequence of observed atmospheric states and integrated for one time step. Assuming that the long-term trend in the observed record is small compared to its short-term fluctuations, the negative of the time-averaged model-generated tendency can be used as a source term to replace the average of observed tendencies arising from physical processes not captured by the damped primitive equations. We use observations from 9 yr (1980–81 to 1988–89) of half-daily operational analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) for the months December–February, to produce forcing terms for a perpetual northern winter simulation.

This approach ensures that the total fluxes due to the combined effect of mean flow and transient eddies are consistent between the model and observations. However, the partition of fluxes between mean and transients, and thus the individual realism of these measures of model climatology must be optimized through the choice of damping parameters. With the forcing and damping outlined above, the model can be integrated for a long time and it produces a realistic time-mean climate with reasonable transient eddy activity. The Northern Hemisphere jets and storm tracks are well simulated and are shown in HDL. Here we show in Fig. 1 just one diagnostic from the model's steady climatology: the systematic error (difference between model and observed climatology) in 550-mb geopotential height. It can be seen that the model slightly overestimates the strength of the Atlantic jet at this level and produces an east Pacific ridge that is too strong and slightly displaced. Other than this the model reproduces zonal mean and stationary wave features of the observed climatology quite faithfully.

If a single integration is made, starting with the model's own long-term mean climatology and lasting for 90 days, the model develops in a particular way, which includes synoptic development and low-frequency, large-scale development. The model state can be averaged into three consecutive 30-day means and the initial condition (in this case the model climatology) subtracted. We shall refer to the resulting fields as the “model drift” for “months” 1, 2, and 3 of the forecast. This is shown for the 550-mb height in Figs. 2a–c. In this case the model drift shows no sign of settling down into any consistent pattern, and this is to be expected since the model's own long-term mean climatology was used for an initial condition.

This example has been picked to illustrate the properties of the ensemble of small perturbations that we shall now apply to the initial condition. There are many ways of choosing perturbations for an ensemble forecast. Two methods currently being used operationally for short- and medium-range forecasts are the breeding method (Toth and Kalnay 1997), which optimizes growth preceding the start of the forecast, and the singular vector method (Buizza 1997), which optimizes growth for a fixed period afterward. The behavior of an ensemble in short- and medium-range forecasts may be sensitive to the choice of perturbations, but for extended to seasonal forecasts it has been found that there is little sensitivity, and the choice of perturbations does not greatly affect the development of their ensemble, especially if the ensemble is large (Anderson 1997). Boer (1993) and Derome et al. (2000) used time-lagged initial conditions to initialize the ensemble members. We take the simple approach of choosing 30 independent days of data from a very long control integration and scaling the deviations from the mean so that the maximum surface pressure perturbation is of the order of 0.05 mb. The choice of an ensemble size of 30 was based on the need for statistical significance in the response to an SST anomaly. Experiments with the equilibrium response shown by HDL revealed that at least 30 months of data were needed for the average monthly mean response to pass a two-sided t test with 99% confidence. Much of the work in seasonal forecasting up to now has used smaller ensembles, with numbers varying between 20 and 6 (Brankovic and Palmer 1997; Rowell 1998; Derome et al. 2000).

The ensemble perturbations are smaller than normally used to initialize a weather forecast, and are not intended to represent errors in the analysis. They are introduced so that the model can generate its own disparate trajectories, using much of “month 1” to spin up the ensemble. The terminology month 1, month 2, etc., should therefore not be taken at face value. It is the behavior of the ensemble that tells us where we are with respect to the predictability limit. This is shown in Figs. 2d–f, which gives the ensemble mean model drift for the same initial condition as before, and Figs. 2g–i, which gives the ensemble spread (standard deviation). We see that during month 1 the ensemble members essentially track together. The ensemble mean is nearly identical to the unperturbed result and the maximum ensemble spread is less than 10 m (and does not appear on the plot). In month 2 the ensemble mean drift bears some resemblance to the unperturbed result but is obviously weaker. The ensemble mean could be said to have produced a skillful forecast of the “truth” in this month, although the ensemble spread is now considerable. In month 3 the ensemble mean drift is virtually zero, and the spread has grown to the point where it is comparable to the time variability seen in a long integration. Apparently the ensemble is now sampling the full range of the model's variability, so its mean now looks like the model climatology, giving zero drift. At this point the initial condition has very little influence on the ensemble-mean state.

Figure 2 represents the basis of the forecasting experiments to be shown in the next section. Months 1, 2, and 3 can be loosely identified with deterministic development with quasi-linear perturbations; nonlinear chaotic development that is still possibly influenced by the initial conditions; and nonlinear chaotic development, where the only hope for forecast skill is through long-lived boundary anomalies.

3. The effect of a midlatitude SST anomaly

a. The heating perturbation

After El Niño, the second largest observed mode of Pacific SST variability is centred in the northwest Pacific Ocean (Deser and Blackmon 1995) and it is here that many GCM studies site their idealized SSTA. Here, as in HDL, we place an SSTA at 40°N, 160°E with an elliptical squared cosine distribution spanning 40° of latitude and 80° of longitude. The effect of the SSTA is represented by a constant heat source with a fixed shallow vertical profile, proportional to σ4. As explained in HDL, this is equivalent to a vertical flux parameterization that depends linearly on the difference between the atmospheric temperature anomaly and a fixed SSTA. This is true because the damping in the model is linear. Nonlinear effects on the flux due to variable surface winds are not accounted for and are not the focus of this study. An evaluation of the sensitivity of the response to this effect is given in HDL. The imposed heating anomaly has a vertical average magnitude of 2.5°C day−1, which would correspond to a precipitation anomaly of 10 mm day−1 if all the heating came from condensation. Following experience from GCMs, and allowing for the associated damping effect due to the creation of a warm anomaly in the atmosphere (see HDL), this heating rate is roughly consistent with a maximum SSTA of about 3°C. This is quite a large anomaly, so the influence it has on the flow described in the following sections could be regarded as a best case for extended range forecasting.

b. The response

The aim of this work is to determine the effect of the heating perturbation on an extended forecast for a variety of initial conditions. The discussion will henceforth be centered on the response to heating, defined as the difference between the ensemble means of two sets of 90-day integrations, one with a heating perturbation and one without. In each case the ensemble has 30 members, with the same set of small perturbations about the initial condition. In this section we consider three very different initial conditions, chosen subjectively from observational analyses to try and capture the range of the observed Pacific westerlies. These three initial conditions are shown in Fig. 3 in terms of the 250-mb zonal wind. The first is the 9-yr December–January–February (DJF) climatology. The second is a 15-day average taken from the second half of January 1983 when the jet was particularly strong. The third comes from the first half of December 1985 when the jet was very weak. Also shown in Fig. 3 is the position of the simulated SSTA. The shaded area is where the vertical average heating perturbation exceeds 2.0°C day−1.

Note that when the model is initialized with these observed states, the ensemble mean drift will no longer be zero after a long time, as it was in the last section where the model climatology was used as an initial condition. For example, the ensemble mean drift of month 3 with the observed climatological initial condition (not shown) closely resembles the model's systematic error (Fig. 1), as expected. The fact that the model's state is drifting on average can affect the mean response to heating, as discussed by Hall and Derome (2000) in the context of El Niño. However, since all GCMs have systematic errors, it was considered more realistic to base this set of experiments on observed initial conditions rather than model-generated ones.

The response for months 1, 2, and 3 is shown in Fig. 4 in terms of the 550-mb height for the three initial conditions shown in Fig. 3. A measure of the ensemble spread can be gleaned from the shading on the figures, which denotes the area where the response passes a two-sided t test based on variations between ensemble members at the 99% confidence level. As the spread increases from month 1 to 3, the significant area gets smaller, approaching the equilibrium limit that was considered when choosing the size of the ensemble.1 The response itself shows marked variation from one month to the next. With observed climatological initial conditions (Figs. 4a–c) the initial response is a downstream ridge at 550 mb, which becomes a trough at lower levels (not shown). More remote features of the response are equivalent barotropic and have the appearance of a wave train, but by month 2 they have transformed to a deep low over the pole with a succession of ridges at midlatitudes. In month 3 the response is different again and now resembles more closely the equilibrium response discussed by HDL (see their Fig. 3a). The downstream ridge is baroclinic near the anomaly heat source but becomes equivalent barotropic farther east and the dipole over Europe is equivalent barotropic. To assess the effect of model drift on the response we did the same experiment with the model climatology as the initial condition (not shown). This yields somewhat different results, even though the model climatology is close to the observed. The basic structure of the local response is similar but the deep low seen over the pole in month 2 is no longer present, and the month 3 response resembles the equilibrium solution even more closely.

When the initial condition is changed, the response changes too. In month 1 the strong jet and weak jet cases show some similarity in the local response but the remote response is set up differently. In month 2 the responses are very strong and bear no relation whatsoever to one another, even though individually they are statistically significant (separate calculations confirm that the differences between them are also highly significant). In month 3 the responses converge again as they all start to look like equilibrium response of HDL. The differences between them are no longer statistically significant.

The three months can again be characterized as in section 2. In month 1 the response is similar for each ensemble member, but the development of the flow and the growth of the response still shows some departure from linearity. Separate experiments with the same model but with a very small heating perturbation (not shown) reveal that the “tangent-linear” month 1 response differs from the responses shown, in that it has a regular remote wave train that has largely saturated in the nonlinear case. The differences between the month 1 responses for different initial conditions probably reflect to some extent the differences in the linear waveguide presented by the basic state for the establishment of teleconnections. By month 2, on the other hand, the tangent linear response bears no resemblance to the nonlinear response at all and we are clearly in a nonlinear chaotic regime. However, there is still some link to the initial conditions, as evidenced by the dramatic differences between Figs. 4b,e,h. By month 3 we start to converge to a state where the boundary anomaly influences the solution in a similar way for all initial conditions. The initial condition has effectively been forgotten, the ensemble perturbations now sample a wide variety of model states, and the response resembles the equilibrium solution.

4. Superensemble experiments

The three initial conditions considered in section 3 were chosen subjectively for the sole purpose of illustrating the sensitivity of the response. There is no guarantee that they will give a reliable indication of any systematic link that may exist between the initial condition and the response to an SSTA. In this section we therefore try to generalize the results to a large selection of initial conditions that fully represents the possible range of observed variability. Since we are dealing with long-range forecasts, it is desirable that we span the observed low-frequency variability of the atmosphere smoothly with a limited number of initial conditions, avoiding contamination from large amplitude transient events. Therefore, 15-day averages were used to filter out the high frequencies and still provide a reasonably large dataset. The nine winters used to determine the model forcing yield 54 of these 15-day averages (including the “strong jet” and “weak jet” cases from the last section). The standard deviation of this set of initial conditions is shown in Fig. 5. Maximum variability is located downstream of the Pacific storm track, as expected.

Ensemble forecasts of 30 members were made from each of the 54 initial conditions, with and without a heating perturbation (SSTA). The 54 ensemble mean responses have been averaged together and displayed in Fig. 6, along with their standard deviation. This “superensemble” average response displays an orderly growth from month 1 to month 3. The local response appears first and the teleconnections are established in months 2 and 3, which now look quite similar. The intensification of both local response and teleconnections with time echoes the intensification of the equilibrium response due to transient-eddy feedback compared to the “time-independent linear solution,” discussed in HDL (to summarize their findings: the weakened Pacific jet is weakened further by reduced transient eddy momentum flux convergence). The range of different ensemble mean responses, as depicted by the standard deviation, shows an interesting development. There is little variation in month 1. The local response is fairly consistent from one initial condition to another and the teleconnections, although disparate, are relatively weak. In month 2 there is a lot of variation in the responses from one initial condition to another. The standard deviation has the same magnitude as the response itself. In month 3, however, the standard deviation has reduced again, reflecting the fact that although the response is strong it is fairly consistent everywhere and is becoming independent of the initial condition. The month 3 superensemble response again resembles the equilibrium result of HDL, although there are some differences, indicating that the initial condition has not been forgotten completely, and on average the drift from observed to model climatology has had some influence, as discussed above.

It is month 2 that is in some ways the most interesting. In this month the amount of variance suggests that the initial condition still has some influence. The interesting question is whether this influence is systematic, and whether it can be characterized in terms of identifiable features of the initial condition and the response. Characteristic modes of variation can be identified by means of empirical orthogonal function (EOF) analysis. In Fig. 7 the first four EOF patterns are shown for variations among the 54 initial conditions drawn from 15-day averages of the ECMWF data (decomposing the variance map shown in Fig. 5). Between them these EOFs account for more than half the total variance. The first EOF describes height variations in the eastern Pacific with teleconnections to Europe. The second connects the west Pacific with the Atlantic. The third connects the North Pacific and polar regions with North America and the Atlantic and the fourth has its strongest variation over Siberia. None of the patterns are local; they are all large scale, but large projections onto these patterns will occur in the initial conditions, so they constitute a reasonably strong potential signal to be identified by the forecaster.

To find out if the major modes of variation in the initial condition have a discernible impact on the response, a linear regression was performed. The month 2 ensemble-mean response was regressed onto the principal component of each EOF in the corresponding initial condition. This provides information about the kind of response that might be expected if the initial condition projects strongly onto a given EOF. The four regressed responses associated with positive projections onto the four EOFs are shown in Fig. 8. The superensemble mean response shown in Fig. 6b has not been subtracted, so fields shown in Fig. 8 can be interpreted as the effect of the SSTA, not the anomaly in the effect of the SSTA. The immediate impression from these four pictures is that they all look quite similar, that is, they all resemble Fig. 6b. The differences between them certainly do not account for the large variations seen in the month 2 responses. Positive projections of the initial condition onto the first EOF tend to lead to a weakened European teleconnection in the response. The second EOF has relatively little impact on the response (Fig. 8b is most like Fig. 6b). The third leads to a weakening of the ridge over North America and the fourth to a weaker local response and a stronger ridge over North America. These variations in the response are minor compared to other variations that are apparently not related to the first four EOFs of the initial conditions.

What are the characteristic variations of the month 2 response and how are they related to the initial condition? To answer this question we perform the same analysis the other way round. Figure 9 shows the first four EOFs of the response at month 2. Together they account for 73% of the variance seen in Fig. 6e. The first EOF describes variations in the strength of the European teleconnection. The second EOF describes variations in the strength of the local and upstream response, with some connection to the Atlantic ridge. The third EOF describes variations in the strength of the downstream equivalent barotropic ridge and its extension over North America, and the fourth EOF links the downstream ridge with the Atlantic ridge. It is worth noting that the first three EOFs of the month 2 response are almost identical to the first three EOFs of monthly mean model variability deduced from a long integration with no SST perturbation, presented by HDL (see their Fig. 10). Most of the variability in the response can therefore be interpreted as an indirect effect due to the perturbation exciting the model's internal modes of variability. If there are any clues in the initial condition as to which of these EOFs the anomaly in the response is most likely to project onto, they may be revealed by performing a linear regression of the initial conditions onto the principal component associated with each EOF in the corresponding response. The results are shown in Fig. 10. These are the signals that the forecaster should seek out in the initial condition for guidance on the type of variation to expect in the month 2 response. The first thing to note when looking at these signals is that although they indicate large variations in the response, they are relatively weak. Naturally, they do not resemble the EOFs shown in Fig. 7 (which were strong signals, but were not associated with large variations in the response), and they would probably be difficult to isolate in noisy data. The maxima are typically about a third of the maximum variability shown in Fig. 5.

If the linear connection assumed by the regression analysis holds, then the following associations can be made: a weakened Greenland trough might give a stronger European teleconnection and/or a weaker local response (EOFs 1 and 2); a weakened Aleutian or North Pacific ridge might give a stronger downstream ridge response (EOFs 3 and 4). Since the analysis is linear, the opposite associations apply equally. However, since the system is nonlinear, it is questionable that any of these associations will be reliable as a forecasting tool. A simple test of their reliability is to take the regression maps shown in Fig. 10 and use them as perturbations to the climatological initial condition in four more pairs of ensemble forecast experiments, with and without the perturbation heating as before. If the resulting ensemble-mean responses look like the typical patterns of variation shown in Fig. 9, then the regression analysis contains useful information.

The results for month 2 are shown in Fig. 11. This time the superensemble mean response (Fig. 6b) has been subtracted so that the patterns can be compared qualitatively with those of Fig. 9. We see that they are not well correlated. For the first EOF, there is a very similar pattern but the sign is opposite. For the second EOF there is an anomaly center of the right sign in the right place. For the other two EOFs the patterns appear unrelated. At best we can conclude that the regressed initial condition anomaly patterns in Fig. 10 may give some guidance about which mode of variability will be present in the response, but not about the sign. Even this is difficult, as the pattern in Fig. 10a would be hard to separate with confidence from the pattern in Fig. 10b.

The fact that the linear regression does not provide much useful forecast information for month 2 should not be too much of a surprise. After all, we have already seen that a single ensemble forecast from the climatological initial condition is somewhat different from the average month 2 response (cf. Figs. 4b and 6b). A more fruitful comparison might be made using ensemble forecasts with more widely varying initial perturbations, possibly subsets of the superensemble.

5. Discussion

The problem of extended range and seasonal forecasting stretches computer resources to its limits. The issue is one of identifying statistical relationships in a dynamical system and there are a great many potentially interesting sensitivities to be explored in the hope of further narrowing the uncertainties in a forecast product that is ultimately probabilistic. In this study we have examined the sensitivity to a midlatitude SSTA at a single location for a range of initial conditions. As the forecast progresses and the influence of the initial condition steadily decays, the response to the heating anomaly steadily becomes more uniform in its spatial structure from one ensemble forecast to another. The three forecast months considered here can be characterized in terms of the spread of the forecast ensemble and the behavior of the response to heating.

In month 1 the ensemble members stay close together and the response to the heating anomaly grows and radiates to distant regions, establishing teleconnections in preferred locations. The solution is not strictly linear, but since the initial perturbations that make up the ensemble were small, they have not yet separated by large amplitudes. The first month is therefore a spinup period for the experiment. The start date of a real forecast would occur sometime during this month with an established SSTA, a flow that has to some degree adjusted to the SSTA, and an initial ensemble that is separated by a small but measurable amount.

In month 2 we are into the extended range and the spread of each ensemble approaches the natural variability of the model. The average response to heating has now matured and has an amplitude of about 60 m at 550 mb. This is of the order of two-thirds the amplitude of the natural (unpredictable) variability. Individual responses are highly significant across each ensemble, but the variation from one initial condition to another is large, having a similar magnitude to the response itself. The initial condition therefore still has some influence, but the effect is difficult to predict. Linear correlation analysis reveals that the dominant modes of variability in the initial condition do not provide much information on variations in the response, and the initial perturbations required for a big impact on the month 2 response are smaller, and may be difficult to pick out of noisy data. The linear analysis precludes robust detailed conclusions on the type of response to be expected from a given perturbation in the initial condition in a nonlinear system. It mainly serves to demonstrate that although the response is highly variable, and entirely determined by the initial condition, the link between the two is nevertheless elusive. The possibility remains that some nonlinear method of analysis might give a better indication of the link between initial condition and month 2 response. Composites based on cluster analysis may identify more robust relationships, although considerably more that 54 experiments would be needed. Ultimately it should be remembered that the model itself may have some skill in this matter. Just because the variation from one initial condition to another is large in month 2, it does not mean the skill is lower than for later times. A peak in variance among ensemble means does not necessarily mean a gap in predictive skill. Individual ensemble experiments still show much more statistical significance than they do for month 3, where the ensemble spread approaches the model's monthly internal variability.

In month 3 we are essentially looking at an analogue for a seasonal forecast. The initial condition is almost forgotten and the response looks similar to the equilibrium response discussed by HDL. To this extent it is safe to say that the equilibrium problem studied by so many GCM modelers has some relevance for a practical forecasting problem. The fact that the month 3 response is not identical to HDL's result implies that the influence of the initial condition is not completely absent and the average solution has been affected by model drift, to which no GCM is immune. Care should therefore be taken in interpreting equilibrium results in a forecasting context, although other factors such as the development of the SSTA and the seasonal cycle are probably more important.

It could be argued that using the full range of observed atmospheric states to define the set of initial conditions is unrealistic. In reality the atmosphere–ocean system is coupled and at midlatitudes the atmosphere usually leads the ocean. The idea of using midlatitude SSTAs for extended forecasts is based on the notion that once established by atmospheric forcing, an SSTA will persist long enough to influence the subsequent development of the atmosphere. A subset of initial conditions that are consistent with the establishment of an SSTA by atmospheric forcing may yield different results for the subsequent development. Conclusions as to the exact nature of the response may therefore be altered by subsampling the set of initial conditions used here with reference to SST data, especially if there is a strong correlation between the existence of midlatitude SSTAs and the atmospheric conditions that generate them. The fact that SSTAs are more persistent than atmospheric states must logically limit the strength of this correlation, and to this extent vindicates the inclusion of other atmospheric states as initial conditions. Even if this experimental setup is not a faithfull analogue of true forecasting experience, it is adequate to test the dynamical sensitivity of the midlatitude atmosphere to perturbations in the boundary forcing, which is the focus of this work.

Operational centers that run seasonal forecasts do not use their full resolution weather prediction models to do it. The resources are put instead into ensemble integrations at lower resolution. Here we carry this philosophy a stage further by using a stripped down dynamical model. The essential nonlinear dynamics are still well represented but the model's efficiency allows the use of large ensembles. The computational advantage of this approach makes it well suited for further investigations into how much potential forecast skill lies in a midlatitude boundary anomaly, and how it compares with the signal emanating from the Tropics. There may even be potential for operational forecasts with this type of model.

Acknowledgments

We thank the two reviewers for comments that led to improvements in the manuscript. This work was funded by the Meteorological 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.

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  • Boer, G. J., 1993: Systematic and random errors in an extended-range forecasting experiment. Mon. Wea. Rev., 121 , 173188.

  • Brankovic, C., and T. N. Palmer, 1997: Atmospheric seasonal predictability and estimates of ensemble size. Mon. Wea. Rev., 125 , 859874.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1997: Potential forecasts skill of ensemble prediction and spread and skill distribution of the ECMWF ensemble prediction system. Mon. Wea. Rev., 125 , 99119.

    • Search Google Scholar
    • Export Citation
  • Czaja, A., and C. Frankignoul, 1999: Influence of the North Atlantic SST on the atmospheric circulation. Geophys. Res. Lett., 26 , 29692972.

    • Search Google Scholar
    • Export Citation
  • Derome, J., and Coauthors, 2001: Seasonal predictions based on two dynamical models. Atmos.–Ocean, in press.

  • Deser, C., and M. L. Blackmon, 1995: On the relationship between tropical and North Pacific sea surface temperature variations. J. Climate, 8 , 16771680.

    • Search Google Scholar
    • Export Citation
  • Frankignoul, C., and K. Hasselmann, 1977: Stochastic climate models II: Application to sea surface temperature variability and thermocline variability. Tellus, 29 , 284305.

    • Search Google Scholar
    • Export Citation
  • Gagnon, N., R. Verret, A. Plante, L. Lefaivre, and G. Richard, 2000: Long-range forecast verification. Preprints, 15th Conf. on Probability and Statistics in the Atmospheric Sciences, Asheville, NC, Amer. Meteor. Soc., 65–68.

    • Search Google Scholar
    • Export Citation
  • Hall, N. M. J., 2000: A simple GCM based on dry dynamics and constant forcing. J. Atmos. Sci., 57 , 15571572.

  • ——, and Derome, J., 2000: Transience, nonlinearity and eddy feedback in the remote response to El Niño. J. Atmos. Sci., 57 , 39924007.

    • Search Google Scholar
    • Export Citation
  • ——, ——, and Lin, H., 2001: The extratropical signal generated by a midlatitude SST anomaly. Part I: Sensitivity at equilibrium. J. Climate, 14 , 20352053.

    • Search Google Scholar
    • Export Citation
  • Harzallah, A., and R. Sadourny, 1995: Internal versus SST-forced atmospheric variability as simulated by an atmospheric general circulation model. J. Climate, 8 , 474495.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., 1976: Estimates of natural variability of time-averaged sea level pressure. Mon. Wea. Rev., 104 , 942952.

  • Miller, A. J., and J. O. Roads, 1990: A simplified coupled model of extended-range predictability. J. Climate, 3 , 523542.

  • Palmer, T. N., and D. L. T. Anderson, 1994: The prospects for seasonal forecasting—A review paper. Quart. J. Roy. Meteor. Soc., 120 , 755793.

    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 2000: Review of WETS—The workshop on extratropical SST anomalies. Bull. Amer. Meteor. Soc., 81 , 657577.

  • Rowell, D. P., 1998: Assessing potential seasonal predictability with an ensemble of multidecadal GCM simulations. J. Climate, 11 , 109120.

    • Search Google Scholar
    • Export Citation
  • Royer, J-F., 1993: Review of recent advances in dynamical extended-range forecasting for the extratropics. Proceedings of NATO workshop ‘Prediction of interannual climate variations.’ Global Environmental Change, J. Shukla, Ed., NATO ASI Series, Vol. 16, Springer-Verlag, 49–69.

    • Search Google Scholar
    • Export Citation
  • Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125 , 32973313.

  • Yang, X-Q., J. L. Anderson, and W. F. Stern, 1998: Reproducible forced modes in AGCM ensemble integrations and potential predictability of atmospheric seasonal variations in the extratropics. J. Climate, 11 , 29422959.

    • Search Google Scholar
    • Export Citation
  • Zwiers, F. W., 1996: Interannual variability and predictability in an ensemble of AMIP climate simulations conducted with the CCC GCM2. Climate Dyn., 12 , 825848.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Systematic error (difference between means) of the time-mean 550-mb geopotential height generated by a long (1400 day) integration of the model, compared to the mean over nine winters (DJF) of ECMWF analyses. Contours 20 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 2.
Fig. 2.

Time development of 550-mb height of monthly mean model state for 90-day integrations with model-climatology initial condition. (a), (b), and (c): Single (unperturbed) integration for months 1, 2, and 3 (initial condition subtracted). (d), (e), and (f): Same as (a)–(c) but for the mean of an ensemble based on small perturbations to the initial condition. (g), (h), and (i): Standard deviation among ensemble members. Contours 20 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 3.
Fig. 3.

Zonal wind at 250 mb over the Pacific for the three initial conditions considered in the text: (a) observed DJF climatology, (b) strong jet case, (c) weak jet case (see text for details). Contours 8 m s−1, zero dotted, negative dashed. Shaded region shows where the anomaly heating from the SSTA is above 80% of its peak value

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 4.
Fig. 4.

Time development of the monthly mean 550-mb ensemble-mean height response to the imposed SSTA, that is, difference between integration with SSTA and without (position of SSTA center shown by a star). (a), (b), and (c): Months 1, 2, and 3 for a 90-day integration with the observed DJF climatology as the initial condition. (d), (e), and (f): Strong jet initial condition. (g), (h), and (i): Weak jet initial condition. Contours 20 m, zero dotted, negative dashed. Areas where the response is significant at 99% confidence level are shaded

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 5.
Fig. 5.

Standard deviation of 550-mb height for the 54 observed 15-day averages used as initial conditions in the superensemble experiments. Contours 20 m

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 6.
Fig. 6.

(a), (b) and (c) Same as in Fig. 4 (a), (b), and (c), but for the average response from all 54 ensemble experiments with different initial conditions. The standard deviations of the 54 ensemble-mean responses are given in (d), (e), and (f). Contours 20 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 7.
Fig. 7.

EOF patterns of the 550-mb height for the 54 observed 15-day averages used as initial conditions. Percentage of variance explained is noted on the figure. Zero contour dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 8.
Fig. 8.

Results of a linear regression of the month 2 response onto the principal components of the four EOFs of the corresponding initial condition shown in Fig. 7. The superensemble mean response (Fig. 6b) has not been subtracted. Deviations from the mean in the four figures correspond to a single standard deviation variation in the associated principal component. Contours 20 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 9.
Fig. 9.

EOF patterns of the 550-mb height response for the 54 experiments. Percentage of variance explained is noted on the figure. Zero contour dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 10.
Fig. 10.

Results of a linear regression of the initial conditions (climatology subtracted) onto the principal components of the four EOFs of the corresponding response shown in Fig. 9. Magnitudes correspond to a single standard deviation variation in the principal component. Note: Contours 5 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

Fig. 11.
Fig. 11.

Month 2 550-mb height ensemble-mean response (SSTA − control) for experiments initialized with observed climatology plus the perturbations shown in Fig. 10. The superensemble mean response (Fig. 6b) has been subtracted to give response anomalies, to be compared qualitatively with the typical response variations shown in Fig. 9. Contours 20 m, zero dotted, negative dashed

Citation: Journal of Climate 14, 12; 10.1175/1520-0442(2001)014<2696:TESGBA>2.0.CO;2

1

Note that in month 1, since the ensemble perturbations are small enough to behave linearly for part of the time they are not truly independent, and t-test results should not be interpreted as indicating any measure of “skill” in this spinup period.

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  • Anderson, J. L., 1997: The impact of dynamical constraints on the selection of initial conditions for ensemble predictions: Low-order perfect model results. Mon. Wea. Rev., 125 , 29692983.

    • Search Google Scholar
    • Export Citation
  • Boer, G. J., 1993: Systematic and random errors in an extended-range forecasting experiment. Mon. Wea. Rev., 121 , 173188.

  • Brankovic, C., and T. N. Palmer, 1997: Atmospheric seasonal predictability and estimates of ensemble size. Mon. Wea. Rev., 125 , 859874.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1997: Potential forecasts skill of ensemble prediction and spread and skill distribution of the ECMWF ensemble prediction system. Mon. Wea. Rev., 125 , 99119.

    • Search Google Scholar
    • Export Citation
  • Czaja, A., and C. Frankignoul, 1999: Influence of the North Atlantic SST on the atmospheric circulation. Geophys. Res. Lett., 26 , 29692972.

    • Search Google Scholar
    • Export Citation
  • Derome, J., and Coauthors, 2001: Seasonal predictions based on two dynamical models. Atmos.–Ocean, in press.

  • Deser, C., and M. L. Blackmon, 1995: On the relationship between tropical and North Pacific sea surface temperature variations. J. Climate, 8 , 16771680.

    • Search Google Scholar
    • Export Citation
  • Frankignoul, C., and K. Hasselmann, 1977: Stochastic climate models II: Application to sea surface temperature variability and thermocline variability. Tellus, 29 , 284305.

    • Search Google Scholar
    • Export Citation
  • Gagnon, N., R. Verret, A. Plante, L. Lefaivre, and G. Richard, 2000: Long-range forecast verification. Preprints, 15th Conf. on Probability and Statistics in the Atmospheric Sciences, Asheville, NC, Amer. Meteor. Soc., 65–68.

    • Search Google Scholar
    • Export Citation
  • Hall, N. M. J., 2000: A simple GCM based on dry dynamics and constant forcing. J. Atmos. Sci., 57 , 15571572.

  • ——, and Derome, J., 2000: Transience, nonlinearity and eddy feedback in the remote response to El Niño. J. Atmos. Sci., 57 , 39924007.

    • Search Google Scholar
    • Export Citation
  • ——, ——, and Lin, H., 2001: The extratropical signal generated by a midlatitude SST anomaly. Part I: Sensitivity at equilibrium. J. Climate, 14 , 20352053.

    • Search Google Scholar
    • Export Citation
  • Harzallah, A., and R. Sadourny, 1995: Internal versus SST-forced atmospheric variability as simulated by an atmospheric general circulation model. J. Climate, 8 , 474495.

    • Search Google Scholar
    • Export Citation
  • Madden, R. A., 1976: Estimates of natural variability of time-averaged sea level pressure. Mon. Wea. Rev., 104 , 942952.

  • Miller, A. J., and J. O. Roads, 1990: A simplified coupled model of extended-range predictability. J. Climate, 3 , 523542.

  • Palmer, T. N., and D. L. T. Anderson, 1994: The prospects for seasonal forecasting—A review paper. Quart. J. Roy. Meteor. Soc., 120 , 755793.

    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 2000: Review of WETS—The workshop on extratropical SST anomalies. Bull. Amer. Meteor. Soc., 81 , 657577.

  • Rowell, D. P., 1998: Assessing potential seasonal predictability with an ensemble of multidecadal GCM simulations. J. Climate, 11 , 109120.

    • Search Google Scholar
    • Export Citation
  • Royer, J-F., 1993: Review of recent advances in dynamical extended-range forecasting for the extratropics. Proceedings of NATO workshop ‘Prediction of interannual climate variations.’ Global Environmental Change, J. Shukla, Ed., NATO ASI Series, Vol. 16, Springer-Verlag, 49–69.

    • Search Google Scholar
    • Export Citation
  • Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125 , 32973313.

  • Yang, X-Q., J. L. Anderson, and W. F. Stern, 1998: Reproducible forced modes in AGCM ensemble integrations and potential predictability of atmospheric seasonal variations in the extratropics. J. Climate, 11 , 29422959.

    • Search Google Scholar
    • Export Citation
  • Zwiers, F. W., 1996: Interannual variability and predictability in an ensemble of AMIP climate simulations conducted with the CCC GCM2. Climate Dyn., 12 , 825848.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Systematic error (difference between means) of the time-mean 550-mb geopotential height generated by a long (1400 day) integration of the model, compared to the mean over nine winters (DJF) of ECMWF analyses. Contours 20 m, zero dotted, negative dashed

  • Fig. 2.

    Time development of 550-mb height of monthly mean model state for 90-day integrations with model-climatology initial condition. (a), (b), and (c): Single (unperturbed) integration for months 1, 2, and 3 (initial condition subtracted). (d), (e), and (f): Same as (a)–(c) but for the mean of an ensemble based on small perturbations to the initial condition. (g), (h), and (i): Standard deviation among ensemble members. Contours 20 m, zero dotted, negative dashed

  • Fig. 3.

    Zonal wind at 250 mb over the Pacific for the three initial conditions considered in the text: (a) observed DJF climatology, (b) strong jet case, (c) weak jet case (see text for details). Contours 8 m s−1, zero dotted, negative dashed. Shaded region shows where the anomaly heating from the SSTA is above 80% of its peak value

  • Fig. 4.

    Time development of the monthly mean 550-mb ensemble-mean height response to the imposed SSTA, that is, difference between integration with SSTA and without (position of SSTA center shown by a star). (a), (b), and (c): Months 1, 2, and 3 for a 90-day integration with the observed DJF climatology as the initial condition. (d), (e), and (f): Strong jet initial condition. (g), (h), and (i): Weak jet initial condition. Contours 20 m, zero dotted, negative dashed. Areas where the response is significant at 99% confidence level are shaded

  • Fig. 5.

    Standard deviation of 550-mb height for the 54 observed 15-day averages used as initial conditions in the superensemble experiments. Contours 20 m

  • Fig. 6.

    (a), (b) and (c) Same as in Fig. 4 (a), (b), and (c), but for the average response from all 54 ensemble experiments with different initial conditions. The standard deviations of the 54 ensemble-mean responses are given in (d), (e), and (f). Contours 20 m, zero dotted, negative dashed

  • Fig. 7.

    EOF patterns of the 550-mb height for the 54 observed 15-day averages used as initial conditions. Percentage of variance explained is noted on the figure. Zero contour dotted, negative dashed

  • Fig. 8.

    Results of a linear regression of the month 2 response onto the principal components of the four EOFs of the corresponding initial condition shown in Fig. 7. The superensemble mean response (Fig. 6b) has not been subtracted. Deviations from the mean in the four figures correspond to a single standard deviation variation in the associated principal component. Contours 20 m, zero dotted, negative dashed

  • Fig. 9.

    EOF patterns of the 550-mb height response for the 54 experiments. Percentage of variance explained is noted on the figure. Zero contour dotted, negative dashed

  • Fig. 10.

    Results of a linear regression of the initial conditions (climatology subtracted) onto the principal components of the four EOFs of the corresponding response shown in Fig. 9. Magnitudes correspond to a single standard deviation variation in the principal component. Note: Contours 5 m, zero dotted, negative dashed

  • Fig. 11.

    Month 2 550-mb height ensemble-mean response (SSTA − control) for experiments initialized with observed climatology plus the perturbations shown in Fig. 10. The superensemble mean response (Fig. 6b) has been subtracted to give response anomalies, to be compared qualitatively with the typical response variations shown in Fig. 9. Contours 20 m, zero dotted, negative dashed

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