1. Introduction
One of the most important climate signals that has ever been observed is El Niño–Southern Oscillation (ENSO). It has a considerable impact on the atmospheric circulation not only in the Tropics, but also in the middle and high latitudes. ENSO is believed to be responsible for a dominant part of the skill in seasonal weather predictions (e.g., Kumar and Hoerling 1995; Shukla et al. 2000; Derome et al. 2001).
Studies aimed at understanding the atmospheric response to ENSO are numerous, and significant progress has been made, as reviewed by Trenberth et al. (1998). El Niño is associated with anomalous warm sea surface temperatures (SSTs) in the eastern equatorial Pacific, leading to enhanced deep convection and increased latent heating throughout the troposphere in the equatorial middle Pacific. An enhanced upward air motion is produced in response to this anomalous heating, which results in a strong divergent flow in the upper levels. In the tropical atmosphere, the local Hadley- and Walker-type circulations have been described by simple linear models (Matsuno 1966; Gill 1980). In the extratropics, more complicated processes are involved in the equivalent barotropic response. Observational studies show that the ENSO is associated with the Pacific–North American (PNA) pattern (Horel and Wallace 1981). The strong upper-tropical divergent flow and convergence in the subtropics act as a Rossby wave source (Sardeshmukh and Hoskins 1988). Linear wave propagation theory is able to predict the wave train emanating from the tropical heating (Egger 1977; Opsteegh and Van den Dool 1980; Hoskins and Karoly 1981). In the presence of a zonally asymmetric mean flow, the response to tropical heating takes the form of a preferred pattern that is similar to the PNA (Simmons et al. 1983). The effect of transients is another factor that contributes to the extratropical atmospheric response to the tropical forcing. It is shown in many studies that the transients help to enhance and organize the PNA pattern (e.g., Held et al. 1989; Klasa et al. 1992).
Most studies on the atmospheric response to ENSO are focused on the equilibrium response that is thus time independent. Observational studies are usually based on the seasonally averaged anomaly (e.g., Horel and Wallace 1981), while numerical modeling studies often look at the time-averaged response after the model reaches equilibrium (e.g., Palmer and Mansfield 1986; Lau and Nath 1994). Most linear studies are based on time-independent solutions to different equation sets, linearized about various climatological flows (e.g., Branstator 1985; Ting and Held 1990). It is not clear from these studies how the response develops before reaching an equilibrium state.
Jin and Hoskins (1995) and Hall and Derome (2000, hereafter HD) investigated the time-dependent atmospheric response to the tropical heating. In both studies, a time integration of a primitive-equation model was performed starting from a basic flow maintained by a constant forcing. They were able to provide a time scale of about 15 days for the extratropical atmosphere to establish a direct response. In this approach, a time-independent forcing is specified to maintain the basic flow, that is, the transport of momentum and heat by the basic flow is balanced by the forcing. After baroclinic transients develop, the basic state will no longer be the same, because now the sum of transports by both the basic flow and the transients is balanced by the same forcing. Therefore, this technique is valid only for a small-amplitude response before about 15 days, that is, before the baroclinic eddies develop to finite amplitudes. Also during the first 15 days, nonlinear interactions are only those associated with the interactions of the tropically forced wave with itself and the basic state, which are interactions that have only a small influence on the direct linear response, as shown in these studies. The contribution from the full nonlinear interactions to the response, including transients, is unclear. It also remains unexplained how the response evolves from the day-15 direct response to an equilibrium state.
Several recent studies have revealed nonlinear aspects of the atmospheric response to ENSO, that is, the responses to El Niño and La Niña are asymmetric. One feature in the North Pacific is that there is a phase shift of about 35° longitude in the upper-atmospheric response between the warm and cold events (Hoerling et al. 1997), which we will refer to as feature 1 hereafter. Another important feature (feature 2 hereafter) occurs in the North Atlantic and European regions. In both the El Niño and La Niña cases, the response takes the same polarity, resembling the positive phase of the North Atlantic Oscillation (NAO), and the response is more significant during La Niña than El Niño events (Pozo-Vazquez et al. 2001; Lin and Derome 2004; Wu and Hsieh 2004). The mechanisms responsible for the propagation of the tropical signal to the North Atlantic and for this nonlinearity are unclear. Hoerling et al. (1997) found that the maximum tropical rainfall anomalies are located east of the date line during El Niño events, but west of the date line during La Niña events, and attributed the 35° phase shift of the extratropical response in the PNA region to this difference in the tropical deep convection and diabatic heating. Lin and Derome (2004), however, showed that even without the displacement of the tropical heating, a similar nonlinearity exists in a simple general circulation model (SGCM). They attributed the nonlinearity in the North Atlantic region to the sensitivity of the response to the modified mean flow.
Whether or not the atmospheric response to El Niño and La Niña are asymmetric is not without controversy. For example, DeWeaver and Nigam (2002) demonstrated that despite the displacement of equatorial diabatic heating for La Niña compared to El Niño, the atmospheric response is almost antisymmetric over the Pacific, in contrast to Hoerling et al. (1997) who found a phase shift of about 35° longitude. They attributed this disagreement to the decadal variability that affects the choice of events that were used to do the analysis in Hoerling et al. (1997). Their argument that ENSO’s atmospheric response is mainly linear seems consistent with previous studies that address the insensitivity of the extratropical response to the location of tropical forcing (e.g., Geisler et al. 1985; Branstator 1985). Note, however, that they did notice a large nonlinear component over eastern North America, the Atlantic basin, and Europe, which is in agreement with feature 2 of the nonlinear response. Sardeshmukh et al. (2000) conducted a large ensemble of seasonal integrations with prescribed global SST fields for 1987 and 1989 winters, which represent El Niño and La Niña, respectively. They found that the GCM signal patterns for these 2 yr are much more antisymmetric than the observations, and thus questioned the significance of the observed asymmetry. Hoerling et al. (2001) also found less marked asymmetry in a GCM simulation.
In the present study, we use the same primitive-equation model (SGCM) as that in HD to investigate the atmospheric transient response to a tropical forcing. A time-independent forcing is used to maintain both the mean flow and transients. This allows for the full interactions between the response and the transients, as well as with the mean flow from the beginning of the integrations. Large ensembles (350 members) are produced from different initial conditions. Daily ensemble averages yield the signal coming from the heating/cooling source. In this study we try to bridge the gap between the first 15-day linear direct response and the equilibrium response to a tropical forcing. In addition, we examine the difference between the atmospheric response to a tropical heating and that to a cooling, and how this difference evolves with time. Hopefully, this will shed some light on the mechanisms behind the nonlinear response to ENSO.
In section 2 the model is briefly described and the experimental design is introduced. The response of the 550-hPa geopotential height to tropical forcing is presented in section 3. In section 4, the tropical response is analyzed in detail to see its connections with the extratropical flow. The modification in the synoptic-scale eddies and their feedback to the response is discussed in section 5. Section 6 gives a summary and discussion.
2. The model and experimental design
The model used in this study is a primitive-equation dry atmospheric model as described in detail in Hall (2000) and HD. It is a spectral model with a global domain. The resolution used in this study is triangular 31, with 10 equally spaced sigma (σ) levels. The model parameters used are described in HD. In addition to a scale-selective dissipation that takes the form of ∇6 with a time scale of 12 h at the smallest scale, the model also has a level-dependent linear damping that has shorter time scales for the lower levels. The model uses a time-averaged forcing calculated empirically from observed daily data. The forcing is obtained as a residual term for each time tendency equation by computing the dynamical terms of the model, together with the dissipation, with daily global analyses and averaging in time. This forcing thus includes all processes that are not resolved by the model’s dynamics, such as diabatic heating (including latent heat release related to the transient eddies) and the deviation of dissipative processes from linear damping. The model has no explicit orography, which is compensated for by the forcing that mimics the time mean orographic forcing. This approach to add forcing to the model was proposed by Roads (1987), and was used in a quasigeostrophic model by Marshall and Molteni (1993) and Lin and Derome (1996). As demonstrated in Hall (2000), this model reproduces the stationary planetary waves and the broad climatological characteristics of the transients remarkably well. This model was used to study the atmospheric response to anomalous forcings in the Tropics (HD; Lin and Derome 2004) and the extratropical regions (Hall et al. 2001a, b), and to study the interannual variability and trend of the NAO/Arctic Oscillation (AO) (Peterson et al. 2002; Greatbatch et al. 2003). It was also used to make seasonal predictions, and was found to be similar in skill to a more complex GCM (Derome et al. 2005).
The forcing fields used in this study are calculated based on the daily data of the National Centers for Environmental Predictions–National Center for Atmospheric Research (NCEP–NCAR) reanalyses (Kalnay et al. 1996). They cover 54 winters from 1948/49 to 2001/02, where the winter is defined as the 90-day period starting from 1 December. Forcing fields are calculated separately for each winter, and the time average of the 54 forcing fields is obtained as the time-independent climatological forcing.
The following three sets of experiments are conducted: 1) the control run, with climatological forcing; 2) the El Niño run, with climatological forcing plus a tropical heating anomaly; and 3) the La Niña run, with climatological forcing plus a tropical cooling anomaly. For each set of experiments, 350 integrations are performed from initial conditions that are taken from the winter observations. Each integration lasts 30 days. For the El Niño run, the tropical heating anomaly is added to the temperature equation, is switched on at t = 0, and persists during the integration. No forcing anomaly is applied for the vorticity, divergence, or mass equations. The heating perturbation represents a deep convection in the equatorial mid-Pacific. It is centered on the equator and the date line and takes an elliptical form in the horizontal, with semimajor and semiminor axes of 40° longitude and 12.5° latitude. The magnitude of the heating is proportional to the squared cosine of the distance from the center. The heating anomaly has a vertical profile of (1 − σ)sin[π(1 − σ)], which peaks at σ = 0.35, with a vertically averaged heating rate at the center of 5 K day−1. This rate is equivalent to a latent heating associated with a precipitation of 2 cm day−1. The only difference between the El Niño and La Niña runs is the sign of the heating anomaly, which is positive (heating) and negative (cooling) for El Niño and La Niña, respectively. The daily ensemble average for each set of experiments is calculated. The difference between a perturbation run and a control run represents a forced signal by the anomalous forcing field.
Integrations starting from observed states and the adjustment to model forcings can be expected to cause an initial model spinup. The difference between the model climate and the observed climate results in an initial drift, but, as pointed out in HD, the latter is insignificant. The control and perturbation runs start from the same initial conditions and have essentially the same drift. The spinup errors and drift are thus removed in the anomaly signal, that is, the difference between the ensemble mean of the perturbation run and that of the control run.
3. Extratropical response in 550-hPa geopotential height
The extratropical atmospheric response to a tropical heating anomaly is equivalent barotropic. Our analysis confirms this feature when looking at the response patterns at different levels (not shown). In this section, we only discuss the response at the 550-hPa level to focus on its time evolution and the difference in responses between the El Niño and La Niña runs.
Figure 1 gives the 550-hPa geopotential height anomaly for the El Niño run at 2-day intervals from days 3 to 13. The shaded regions are those where the response is significantly different from zero at the 0.01 level, according to a Student’s t test. A negative height anomaly in the North Pacific east of the date line starts to appear at day 3. It intensifies and its area expands afterward. Considering its extent and strength as well as the distance to the heating source, we will refer to this height anomaly as the major response center in the extratropics hereafter. A downstream wave train develops from day 5, with a positive anomaly center over northwestern North America. By day 7, the two centers that are parts of the PNA are well developed. These two anomaly centers stay in position and intensify afterward, while farther downstream anomalies develop in the North Atlantic region. Starting from day 7 (Fig. 1c), another positive height anomaly over the western Pacific develops. It reaches its maximum strength between days 9 and 11, and then weakens.
The development of the La Niña response is illustrated in Fig. 2. Up to day 7, the response pattern looks almost the same as that for the El Niño run, but with the sign reversed. After day 7, the positive center (major response) in the North Pacific begins to move westward, crosses the date line on day 11, and stays west of the date line afterward. By day 13, this positive center shows a westward phase shift of about 30° compared with the negative major response center in the El Niño run. The wave train is more zonal and extends farther to the east than its counterpart in the El Niño run. Also starting from day 7 (Fig. 2c), a negative height anomaly appears over the western Pacific. This anomaly remains weak and moves westward.
To assess the nonlinearity in the response, in Fig. 3 and Fig. 4 both the linear and nonlinear parts of the response are plotted. The linear part is represented as the difference between the El Niño and La Niña height anomalies, whereas the nonlinear part is estimated as their summation. The linear response is manifested by a wave train developed from the central Pacific, which is reminiscent of the PNA structure. Before day 7, no significant nonlinear response can be found, implying that the response is only a linear process in the extratropics during this period. Starting from day 7 (Fig. 4c), a significant east–west dipole structure is developed in the nonlinear response over the North Pacific, reflecting the phase shift in the major response centers for El Niño and La Niña, as well as the asymmetric response over the western Pacific. After about 4 days (Fig. 4e), the nonlinear response develops downstream over North America and the North Atlantic, taking the form of a zonally orientated wave train. Note that the contour interval in Fig. 4 is half of that in Fig. 3, indicating that the nonlinear component in the second week has an amplitude that is about half that of the linear component.
To see further developments in the response and its nonlinearity after 15 days of integration, when its modification in the transient activity becomes more important, in Figs. 5a,b the 550-hPa geopotential height anomaly is shown for the time average between days 16 and 30. It can be regarded as a transition from the direct response to the equilibrium response. Indeed, while the 16–30-day response shares features with the day-13 response (Fig. 1f and Fig. 2f), it also shares many features with the equilibrium response (as shown in Fig. 9 of HD). Comparing Figs. 5a,b, it is clear that over the North Pacific the major response in the La Niña run is stronger than (and about 30° to the west of) that in the El Niño run. This longitudinal phase shift is similar to feature 1 of the nonlinear response, as was found in the observational data (Hoerling et al. 1997; Lin and Derome 2004). It should be emphasized that in our experiments the heating and cooling forcing anomalies are at exactly the same location, so that clearly the atmospheric internal dynamics are the sole contributing factor to the nonlinear response to the tropical forcing. In the Atlantic and European region, the responses in both the El Niño and La Niña runs are largely in phase. The negative anomaly in the North Atlantic and the positive response centered over the Mediterranean constitute a pattern that would project to a positive phase of the NAO. This independence of phase of the NAO to the sign of the tropical Pacific forcing agrees with feature 2 of the nonlinear response as reported in previous observational studies (Pozo-Vazquez et al. 2001; Wu and Hsieh 2004; Lin and Derome 2004). The wave train response for La Niña takes a more zonal path, which extends farther downstream than the El Niño case.
Figures 5c,d depict the linear and nonlinear parts of the response for the 16–30-day period. Note that the contour levels are the same for Figs. 5c,d. As can be seen, the linear response has a stronger amplitude in the Pacific and North American region, while the nonlinear response is more important in the North Atlantic and Europe domain. In the North Pacific, the positive center in Fig. 5d reflects the westward shift of the positive center and the stronger amplitude in the La Niña case. The nonlinear response centers in the Atlantic and European regions result from the same polarity in both the El Niño and La Niña integrations.
4. Tropical response
In this section, we focus our attention on the tropical response in order to find its link with the middle and high latitudes.
a. Vertical motion and divergent flow
The height–longitude cross sections along the equator are plotted for the response in temperature (in thick contours) and vertical motion (omega in thin contours) fields. They are illustrated in Figs. 6 and 7 from days 1 to 6 for the El Niño and La Niña runs, respectively. In the El Niño run, a warm anomaly with upward motion is built up after 1 day of integration. With time the vertical motion anomaly stays at the same location with some enhancement. The temperature response amplifies in the upper troposphere over the heating anomaly, and the signal propagates eastward in the form of a Kelvin wave, nearly circling the equator in 6 days. The main structure of the La Niña response is similar, with cooling in the upper troposphere and downward motion. The strength of the descending motion, however, is notably stronger in the middle troposphere than that of its counterpart upward motion for the El Niño run. A comparison of the upper velocity potential response (not shown) also shows that the upper convergence is stronger in the La Niña response than the divergence in the El Niño run.
The asymmetry in the vertical motion and divergence field for El Niño and La Niña may explain the difference in the strength of the extratropical response when the heating and cooling have the same magnitude. It cannot, however, explain the asymmetry in the phase and spatial distribution, which is the most important aspect of the nonlinear response. Moreover, in nature, the SST anomaly and its associated diabatic heating anomaly for observed El Niños and La Niñas are different in strength. As will be discussed in section 6, an experiment with half the strength of the La Niña cooling shows a very similar distribution of the response to that of the full-strength La Niña, indicating that the response distribution is not determined by the forcing strength. Other mechanisms must be responsible for the asymmetric distribution of the response in El Niño and La Niña. We next look at the upper-tropical response and try to search for the answer.
b. Upper-tropospheric circulation response
Time evolutions of tropical horizontal wind, geopotential height, and streamfunction response are calculated at the level of 150 hPa, which is close to the maximum upper divergence response. Illustrated in Fig. 8 are horizontal wind and geopotential height responses from days 3 to 13 at a 2-day interval for both the El Niño and La Niña runs, and shown in Fig. 9 are the associated streamfunction responses. In the El Niño run, an upper divergent wind and positive height anomaly is built up over the heating source soon after the integration begins. From day 3 (Fig. 8a and Fig. 9a), to the west of the heating, a pair of anticyclones develop, which are associated with the equatorial Rossby wave response. At the same time, to the east is the Kelvin wave response with equatorial westerlies and a positive height anomaly that quickly propagates eastward along the equator. The equatorial response appears to be qualitatively consistent with the theoretical solution of Gill (1980). The equatorial westerlies of the Kelvin wave are disturbed when crossing the equatorial Central and South American continents, and continue to penetrate eastward. The front of the Kelvin wave accompanied with a positive geopotential tongue reaches about 150°E at day 9 (Fig. 8d), where it meets the outflow of the heating source. The response for La Niña is in general similar. A pair of cyclones are built up to the west of the cooling that correspond to the Rossby wave response. To the east, a Kelvin wave with equatorial easterlies and a negative height anomaly propagates eastward quickly.
Comparing El Niño with La Niña, several differences in the tropical response can be noted. First, there is a latitudinal shift of the equatorially trapped Rossby wave gyres. This is clear from the streamfunction response (Fig. 9). The anticyclonic response to the west of the forcing in El Niño is located at higher latitudes in both hemispheres than the cyclonic Rossby wave response in La Niña. Because La Niña has two Rossby wave gyres that are closer to the equator, the associated westerlies between them are notably stronger than the easterlies in the El Niño case (Fig. 8). The northern extension of the tropical Rossby wave response corresponds to the western Pacific positive (negative) height anomaly of the extratropical response for El Niño (La Niña) between days 7 and 11, as shown in Figs. 1c–e (Figs. 2c–e).
Second, the Kelvin wave flow has an asymmetric curvature over the west coast of the equatorial Central and South American continents. In the El Niño case, a westerly trough is formed over the equator near 90°W, whereas in La Niña, the corresponding easterly ridge is displaced to the west, near 120°W.
Third, the eastward penetration of the westerly wind front of the Kelvin wave pulse in El Niño reaches farther than the corresponding easterly wind front in La Niña. This is clear after day 7, as can be seen in Figs. 8d–f. The front of the positive height anomaly along the equator associated with the Kelvin wave reaches about 150°E from day 9 in the El Niño run (Figs. 8d–f), whereas in the La Niña run the tongue of the negative height anomaly stays to the west of 120°E (Figs. 8j–l). As a result, in the El Niño run, strong equatorial westerlies of the Kelvin wave pulse can get almost as far as the center of the heating source, while in the La Niña case the equatorial easterlies of the Kelvin wave pulse only reach about 120°E. The strong eastward penetration of the Kelvin wave westerlies in El Niño interferes and reduces the Rossby wave gyre response near the date line. As can be seen from Figs. 9d–f, the anticyclonic Rossby wave gyres become less and less clear for El Niño. In the La Niña case, however, the cyclonic Rossby wave gyres near the date line remains almost intact (Figs. 9j–l). It is worth noting that the flow structures seen in Figs. 9f,l for El Niño and La Niña at day 13 are nearly identical to the equilibrium responses (not shown).
The linear and nonlinear components of the upper-tropical response are shown in Fig. 10 for the 150-hPa horizontal wind and geopotential height, which represent the difference between and the sum of the El Niño and La Niña responses, respectively. The linear response (Figs. 10a–f) describes a typical tropical response to an equatorial heating, that is, a pair of anticyclonic Rossby wave gyres are developed to the west of the heating, and to the east there is a Kelvin wave with equatorial westerlies and a positive height anomaly that propagates eastward quickly.
Significant nonlinearity develops for the tropical response after about 5 days from the beginning of the integration (Figs. 10g–l). Starting from day 5 (Fig. 10h), a pair of negative height anomalies can be seen straddling the equator near 150°E, associated with equatorial westerlies. Positive height anomaly centers are developed in the western subtropical Pacific in both hemispheres, accompanied by anticyclonic wind flows. This reflects the latitudinal shift of the Rossby wave response between El Niño and La Niña. La Niña has a Rossby wave response that is closer to the equator than that in El Niño, which is stronger in the subtropics. Recall the asymmetric response in the extratropical Pacific for El Niño and La Niña (Fig. 1 and Fig. 2). In the La Niña case, the Pacific wave train seems to be shifted westward and equatorward compared to that in El Niño. This may be related to the difference in the tropical Rossby wave gyre response.
Another nonlinear feature developed from day 5 is the pair of negative height anomalies on both sides of the equator near the west coast of the equatorial Central and South American continents, associated with a pair of cyclonic circulations with westerlies at the equator. This corresponds to the 30° longitudinal shift in phase of an equatorial wave in this region, which is seen in Fig. 8.
Starting from day 9 (Figs. 10j–l), a band of positive height anomaly along the equator emerges with a maximum near 120°E, associated with equatorial westerlies. This reflects the stronger Kelvin wave penetration in El Niño than that in La Niña. The nonlinear response in the Tropics is connected with that in the higher latitudes in a form of wave train. Thus, the asymmetry in the Kelvin wave penetration also contributes to the nonlinearity in the extratropics.
c. Discussion
As described above, significant asymmetry in the upper-tropical response between El Niño and La Niña develops after about 5 days from the beginning of the integration. What causes this asymmetry is of great interest.
In a nonlinear integration of a GCM, like the one in the current study, the tropical wave response interacts with the mean flow. In the case of El Niño (La Niña), upper divergent (convergent) flow over the heating (cooling) source produces a pair of anticyclonic (cyclonic) Rossby wave gyres to the west, with a easterly (westerly) wind anomaly at the equator and a westerly (easterly) anomaly in the subtropics. This zonal wind response simultaneously modifies the mean flow, which may influence the further development of the Rossby wave. The fact that the development of the Rossby wave gyre occurs near the equator in La Niña but at higher latitudes in El Niño indicates that a westerly mean flow is more favorable for the Rossby wave development.
The different extents in the eastward penetration of the Kelvin wave pulse between El Niño and La Niña may also be determined by the modified mean flow at the equator to the west of the forcing. In La Niña, a strong westerly anomaly is associated with upper convergence and cyclonic Rossby wave gyres straddling the equator, whereas in El Niño upper divergence and anticyclonic Rossby wave gyres produce an easterly anomaly. When the eastward-traveling Kelvin wave pulse reaches the equatorial western Pacific at about day 7, it encounters the already changed zonal mean flow. The farther-reaching Kelvin wave pulse penetration in El Niño than in La Niña implies that the Kelvin wave pulse can propagate more easily in an easterly mean flow.
Using a linear model, Zhang and Webster (1992) studied the equatorial waves forced by a middle-latitude forcing. They found that the amplitude of the tropical wave response is dependent on the mean zonal wind. The Rossby wave mode is stronger in mean westerlies than in mean easterlies, while the Kelvin wave response exhibits a larger amplitude in mean easterlies than in mean westerlies. Our results are therefore similar to their findings, despite the fact that their forcing is of a much shorter time scale (∼1 day).
In the case of a stationary forcing, ωf = 0; A is then calculated for the equatorial Kelvin wave and Rossby wave for u = +10 m s−1 and u = −10 m s−1. The parameters used are as follows: β = 2.2 × 10−11 m−1 s−1, H = 200 m. The results are show in Fig. 11. As can be seen, the Kelvin wave response is stronger in an easterly zonal flow than that in a westerly flow (Fig. 11a). The difference is the largest for the forcing with wavenumbers 2–6. For the Rossby wave response, it is clear that the amplitude is stronger when the zonal wind is westerly.
Under the assumption that changes in the local basic state have a large scale and will influence further development of waves, the different extents in the eastward penetration of the Kelvin wave pulse between El Niño and La Niña may be determined by the modified local mean flow at the equator to the west of the forcing. When the eastward-traveling Kelvin wave pulse reaches the equatorial western Pacific, it encounters the already changed local zonal mean flow, which is an easterly anomaly in the El Niño case. Figure 11a indicates that the Kelvin wave pulse could more easily penetrate through the easterly wind anomaly in El Niño. In the case of La Niña, to the west of the cooling, upper convergence produces an equatorial local westerly mean flow. Figure 11b implies that the equatorial Rossby wave response is stronger that in La Niña. The North Pacific nonlinearity is linked to a phase shift of the Rossby wave train. The tropical response to the west of the forcing is at the starting point of the Rossby wave train. The nonlinearity in this tropical area has important influences on the wave train and the response in the extratropics.
5. Extratropical wave activities
a. Changes in extratropical transient eddies
A tropical forcing influences the extratropical atmospheric flow by changing the circulation pattern as a direct response. This changed circulation pattern then modifies the path and strength of the storm track and synoptic-scale transients. The modified transient activity, in turn, feeds back onto the response pattern. In this section, we look at the alteration of the transients and storm track associated with the El Niño and La Niña forcings. Specifically, we are interested in its time evolution, and the time required for the change in transient activity to become important. Another important aspect we are looking at is the role played by transients in the nonlinear response to the El Niño and La Niña forcings.
It should be kept in mind that the transients in our nonlinear experiments are different from those in the 30-day integrations of Jin and Hoskins (1995) and HD. In these two referenced studies, there are no transients at the beginning of the integrations. The transients develop because of baroclinic instability and become significant after about 15 days. In our experiments, however, the transients are present from the beginning of the experiments, and evolve and interact with flows of different scales during the integrations. The storm track and transients are altered with the development of the extratropical response to the tropical forcing. It is then possible in our case that the eddy activity is modified and feeds back onto the response in the first 15 days.
To estimate the transient activity and its evolution during the 30-day integrations, we calculate the root-mean-square (rms) of the 550-hPa height field separately for every 5 days of nonoverlapping periods. The 5-day time average for each period was removed before the rms calculation. This method was used by Palmer and Sun (1985) when studying the modification of the storm track by an SST anomaly in the North Atlantic. The rms is calculated for each member of the ensemble, and then the average is computed for the ensemble of integrations. The anomaly of the transient activity for a perturbation run is defined as the difference between its rms and that of the control run.
Figure 12 shows the transient activity anomalies of days 6–10, 11–15, and 16–30 for the El Niño and La Niña runs. The rms for the 16–30-day period is the average of the rms that are calculated separately over three periods (16–20, 21–25, and 26–30). The shaded areas represent anomalies with a significance level better than 0.01 according to a Student’s t test. Even at the early stage of days 6–10 (Figs. 12a,b), significant transient activity anomalies can be seen for both the El Niño and La Niña runs. The main feature is an enhanced (reduced) storm activity in the Pacific jet exit region in El Niño (La Niña). As was discussed in section 4, an upper-tropospheric direct response to El Niño (La Niña) increases (decreases) the strength of the westerly jet in the subtropical Pacific, leading to changes in transient activity. During the period of days 11–15, bands of the rms anomaly are observed to the north and south sides of the climatological North Pacific storm-track position (around 40°N). For the El Niño run (Fig. 12c), there is a southward displacement of the storm track, while for the La Niña run (Fig. 12d) the transient activity shifts to the north. This arises from the flow response in the North Pacific and is in agreement with the association between the baroclinic waves and ENSO as reported in previous studies (e.g., Lin and Derome 1997). The change of the transient activity is asymmetric for El Niño and La Niña; El Niño has a stronger transient activity anomaly east of the date line, while the La Niña produces a clear northward displacement of storm track just west of the date line, reflecting the phase shift of the major response center, as observed in Fig. 1 and Fig. 2. For the period of days 16–30, significant transient activity anomalies appear over many regions in the Northern Hemisphere, in addition to the features in the North Pacific that are seen for the early periods. Near the west coast of Canada, reduced (enhanced) transient activity is associated with the positive (negative) height anomaly response in the El Niño (La Niña) run. The North Atlantic storm track is shifted to the southeast in both the El Niño and La Niña runs, with reduced transient activity near the east coast of Canada and increased activity in the central Atlantic. Another region of decreased transient activity is observed near the North African region.
In Fig. 13 we present the height tendency anomaly of days 6–10, 11–15, and 16–30 for the El Niño and La Niña runs. The tendency anomaly for the period of days 16–30 is that averaged over three 5-day periods. Significant feedbacks of the transients on the response can be seen even for the early period of days 6–10. The feedback is, however, asymmetric between the El Niño and La Niña runs in both strength and location in the North Pacific. For the El Niño case (Fig. 13a), a large area of positive height tendency appears in the western Pacific, with one center over the subtropical date line and another northeast of Japan. Compared with the height response (Fig. 1c–e), this height tendency represents an enhancement of the positive height response center in the western Pacific. The corresponding negative height tendency for the La Niña case, however, is weaker and located farther west (Fig. 13b). In the major height response region over the central Pacific, El Niño has a very weak negative tendency centered near 160°W, whereas a much stronger positive tendency is found in La Niña, which is about 30° to the west of its El Niño counterpart. This indicates that the transient feedback contributes to reinforce and maintain the asymmetric height response pattern in this period. Another feature in the tendency field is the positive (negative) anomaly over the west coast of North America in El Niño (La Niña), which again helps to maintain the height anomaly in this place. On the east coast of North America and for the North Atlantic regions, a quite symmetric structure of the tendency field is observed during this early stage of integration, that is, there is a negative (positive) tendency over Greenland and a belt of positive (negative) tendency along the east coast of North America and in the mid-latitude Atlantic for El Niño (La Niña).
At later stages, the transient feedback structure in the North Pacific remains to reinforce the height response. The eddy feedback becomes more important in the North Atlantic region, and the asymmetry becomes more obvious. During the period of days 16–30 (Figs. 13e,f), the spatial pattern for the El Niño run is similar to that of the La Niña run. Negative height tendencies in the North Atlantic near Greenland and positive tendencies near Portugal are observed. The height tendency anomaly is approximately in phase with the height anomaly itself in the North Atlantic and adjacent areas (Figs. 5a,b), indicating that the transients feed back to reinforce the response, which has the same polarity in El Niño and La Niña.
b. Rossby wave propagation
The atmospheric response signal to a tropical forcing propagates into the middle and high latitudes in the form of a Rossby wave. As discussed in Hoskins and Ambrizzi (1993), the path and amplitude of the extratropical wave activity are likely associated with a strong waveguide in the Asian jet and a weaker waveguide in the North Atlantic jet. Over the tropical eastern Pacific and Atlantic, there are upper mean westerlies in winter, where Rossby waves are allowed to propagate into the deep Tropics and even to cross the equator (Webster and Holton 1982). The waveguide analysis can also likely explain the wave propagation into the equatorial Pacific and Atlantic Oceans, and even across these regions. The degree of wave propagation into the Tropics is largely determined by the time mean zonal flow. The large-scale waves approaching the equator encounter a decreasing background westerly zonal flow. A critical line is reached when the wave phase speed matches the zonal wind speed, which, for stationary waves, is where the westerly zonal wind changes to easterlies. The tropical upper easterlies over the Eastern Hemisphere thus act as a barrier for the equatorward Rossby wave propagation.
In our tropical forcing experiments, the zonal wind response in the tropical and extratropical regions interacts and modifies the mean flow, which in turn influences the wave propagation. Illustrated in Figs. 14a,b are the stationary wavenumber Ks, calculated for the 250-hPa zonal wind averaged for days 11–15 for El Niño and La Niña, respectively. As can be seen, in the El Niño case, the Asian–Pacific jet over the Pacific extends farther eastward than that in La Niña, such that it is connected to both the North American waveguide and the high-Ks-value region in the equatorial eastern Pacific. The stronger Pacific jet in the El Niño simulation is related to the upper divergent flow from the heating source and the northern branch of the Rossby wave response to the west. With this strong Pacific jet, the waveguide is split into two parts—one continuing over North America, and the other moving southward into the equatorial eastern Pacific. Such a split of wave train in the exit of the Pacific jet was also seen in observations (e.g., Kiladis and Weickmann 1992). In the La Niña experiment, however, the Pacific jet waveguide is disconnected from the tropical and North American waveguides. Another important difference between El Niño and La Niña is the area of imaginary values of Ks in the Tropics, where the propagation of Rossby waves is forbidden. In the El Niño case, imaginary Ks values are limited only to the tropical Eastern Hemisphere. Large positive Ks exists over the other part of the Tropics, especially over the eastern Pacific and Atlantic, allowing Rossby waves to propagate into or through these regions. In the La Niña experiment, however, almost all of the global Tropics are covered with imaginary Ks, indicating that Rossby waves are confined to the extratropical regions. As observed in Figs. 5a,b, in the later stage of integrations, the extratropical response in the La Niña experiment is stronger and has a more zonal wave propagation than that in El Niño, which may be explained by the above difference in stationary wavenumber. However, what happens at the critical line is unclear. In the vicinity of the critical line nonlinear effects become important (e.g., Warn and Warn 1978; Brunet and Haynes 1996; Abatzoglou and Magnusdottir 2006) and the above discussion in terms of a refractive index, based on linear theory, is clearly inadequate.
6. Summary and discussion
A primitive-equation dry atmospheric model was used to study the atmospheric response to a tropical thermal forcing. With an anomalous heat source introduced right at the beginning of integrations and kept constant, 350 runs were conducted from different initial conditions that were taken from daily states of the atmosphere. The daily response was obtained from the ensemble average. Two aspects were given special attention—one is the transient process from the emergence of the tropical signal to the establishment of the extratropical response; another aspect is the nonlinearity of the response as a function of the amplitude of tropical forcing. Feature 1 of the nonlinearity is in the North Pacific where the major response in a La Niña is located about 30° west of that of an El Niño, and feature 2 of the nonlinearity occurs in the North Atlantic and Europe regions where both an El Niño and La Niña forcing tend to produce response patterns that have the same polarity. The possible mechanism of this nonlinearity was discussed.
The response in the Pacific–North American region is well developed even within 1 week after the anomalous thermal forcing is introduced in the equatorial middle Pacific. The response pattern resembles the PNA. The signal in the North Atlantic area is established by the end of the second week. Together with the anomalous flow response, the storm track and transient eddy activity are modified in the process. The transients feed back onto the flow anomaly, reinforcing the response in the extratropics.
The nonlinearity in the response to the tropical forcing shows up as early as 5 days after turning on the anomalous forcing when the positive height anomaly in the western Pacific in El Niño is notably stronger than the negative height anomaly in La Niña. Then, the major response shows a longitudinal phase shift. The nonlinearity increases with time. After about 2 weeks, both of the observed features are present; for example, there is an about 30° phase difference in the longitude of the North Pacific response center between the El Niño and La Niña cases, the response over the North Atlantic region is stronger in La Niña than that in El Niño, and the North Atlantic response projects positively to a NAO pattern for both El Niño and La Niña.
The above results are based on two sets of experiments with tropical forcings of opposite signs but the same magnitude. In reality, the tropical heating response to a La Niña is weaker than that to an El Niño. Whether the above nonlinear behavior over the Pacific, and especially downstream over the Atlantic, is associated with modifications to the mean flow by the larger magnitude of the La Niña divergent flow or is related to just the opposite sign is of great interest. To address this, another set of experiments is conducted, which is also composed of 350 member integrations. It has the same setup of the La Niña run, except that the cooling has a magnitude that is reduced by half. Figure 15 shows the 550-hPa geopotential height anomaly for this run at 2-day intervals from days 3 to 13. Compared with the full-strength La Niña run (Fig. 2), it can be seen that the response has almost the same distribution, except a reduced (by about half) amplitude, indicating that the response distribution is not determined by the forcing strength. The sign of the forcing is really responsible for the nonlinearity of the response.
The factors that contribute to the nonlinearity of the response can be summarized as follows:
With the same forcing strength, both stronger downward motion and upper-level convergence over the La Niña forcing than the upward motion and upper-level divergence over the El Niño forcing are produced. This is caused by the changed static stability of the air column resulting from the temperature response in the upper troposphere.
The major contributors that lead to the asymmetric response distribution and phase difference lie in the Tropics. First, there is a latitudinal displacement between El Niño and La Niña for the Rossby wave gyre response to the west of the forcing, which is likely responsible for the 30° phase difference in the North Pacific major response. Second, there is a difference in the eastward penetration of the Kelvin wave that leads to a different interference of the Kelvin wave after circling the equator with the response over the forcing. The different behavior of the tropical wave response is possibly associated with the modified upper mean zonal flow to the west of the forcing, where the equatorial westerlies in La Niña are favorable for further Rossby wave development near the equator, but prevent a later intrusion of Kelvin wave from the west; in El Niño the situation is the opposite.
The tropical and extratropical response interact with and modify the mean zonal flow, which in turn changes the property of Rossby wave propagations. In La Niña, equatorial easterlies prevent extratropical waves from propagating into the Tropics, leading to a stronger and more zonally propagating wave train.
The feedback from the synoptic-scale eddies through the transient vorticity flux convergence makes a positive contribution for the response in the extratropics. This process also helps to generate and maintain the nonlinear response.
The use of a simple model allowed us to do a large ensemble of integrations, and the choice of an idealized forcing and the absence of any detailed representation of physical processes allowed for a simpler interpretation of the results than would have been possible with a more complete GCM. For example, one can easily rule out the hypothesis that the observed phase shift of the North Pacific response between La Niña and El Niño requires a phase difference in the tropical forcing. On the other hand, the contribution from physical processes, such as precipitation, and their interactions with the response cannot be addressed by this model.
With a large ensemble size, a robust result is obtained in the present study that the atmospheric responses to El Niño and La Niña are asymmetric. This may contribute to clarification of the controversy on this issue, as discussed in the introduction. There are, however, still some aspects in the nonlinearity that are not completely clear. The argument of the difference between the tropical Rossby wave and Kelvin wave response is speculated from its dependence on the changed mean zonal flow, which is based on a linear theory. How a local change of the mean zonal flow influences the shape of the Rossby wave and propagation of an existing Kelvin wave is not clear. Another issue that requires further study is the dynamics of the equatorial cyclonic troughs near the west coast of Central and South America when both equatorial westerlies and easterlies flow over the continent. The current SGCM does not explicitly include the topography; instead, its time mean effect is represented in the climatological forcing field and by different specifications of damping for the land and sea. A complete understanding of these issues requires theoretical studies and numerical simulations using a more complex full GCM.
Acknowledgments
This research was made possible by funds provided to the Canadian CLIVAR Research Network by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Foundation for Climate and Atmospheric Sciences (CF-CAS). We thank two anonymous reviewers for their insightful and constructive comments and suggestions.
REFERENCES
Abatzoglou, J. T., and G. Magnusdottir, 2006: Planetary wave breaking and nonlinear reflection: Seasonal cycle and interannual variability. J. Climate, 19 , 6139–6152.
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.
Brunet, G., and P. H. Haynes, 1996: Low-latitude reflection of Rossby wave trains. J. Atmos. Sci., 53 , 482–496.
Derome, J., and Coauthors, 2001: Seasonal predictions based on two dynamical models. Atmos.–Ocean, 39 , 485–501.
Derome, J., H. Lin, and G. Brunet, 2005: Seasonal forecasting with a simple general circulation model. J. Climate, 18 , 597–609.
DeWeaver, E., and S. Nigam, 2002: Linearity in ENSO’s atmospheric response. J. Climate, 15 , 2446–2461.
Egger, J., 1977: On the linear theory of the atmospheric response to sea surface temperature anomalies. J. Atmos. Sci., 34 , 603–614.
Geisler, J. E., M. L. Blackmon, G. T. Bates, and S. Munoz, 1985: Sensitivity of January climate response to the magnitude and position of equatorial Pacific sea surface temperature anomalies. J. Atmos. Sci., 42 , 1037–1049.
Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulations. Quart. J. Roy. Meteor. Soc., 106 , 447–462.
Greatbatch, R. J., H. Lin, J. Lu, K. A. Peterson, and J. Derome, 2003: Tropical/extratropical forcing of the AO/NAO: A corrigendum. Geophys. Res. Lett., 30 .1738, doi:10.1029/2003GL017406.
Hall, N. M. J., 2000: A simple GCM based on dry dynamics and constant forcing. J. Atmos. Sci., 57 , 1557–1572.
Hall, N. M. J., and J. Derome, 2000: Transients, nonlinearity, and eddy feedback in the remote response to El Niño. J. Atmos. Sci., 57 , 3992–4007.
Hall, N. M. J., J. Derome, and H. Lin, 2001a: The extratropical signal generated by a midlatitude SST anomaly. Part I: Sensitivity at equilibrium. J. Climate, 14 , 2035–2053.
Hall, N. M. J., H. Lin, and J. Derome, 2001b: The extratropical signal generated by a midlatitude SST anomaly. Part II: Influence on seasonal forecasts. J. Climate, 14 , 2696–2709.
Held, I. M., S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci., 46 , 163–174.
Hoerling, M., A. Kumar, and M. Zhong, 1997: El Niño, La Niña, and the nonlinearity of their teleconnections. J. Climate, 10 , 1769–1786.
Hoerling, M., A. Kumar, and T. Xu, 2001: Robustness of the nonlinear climate response to ENSO’s extreme phases. J. Climate, 14 , 1277–1293.
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 D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38 , 1179–1196.
Hoskins, B. J., and T. Ambrizzi, 1993: Rossby wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci., 50 , 1661–1671.
Hoskins, B. J., and G. Yang, 2000: The equatorial response to high-latitude forcing. J. Atmos. Sci., 57 , 1197–1213.
Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci., 52 , 307–319.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437–471.
Kiladis, G. N., and K. M. Weickmann, 1992: Extratropical forcing of tropical Pacific convection during Northern winter. Mon. Wea. Rev., 120 , 1924–1938.
Klasa, M., J. Derome, and J. Sheng, 1992: On the interaction between the synoptic-scale eddies and the PNA teleconnection pattern. Beitr. Phys. Atmos., 65 , 211–222.
Kumar, A., and M. P. Hoerling, 1995: Prospects and limitations of atmospheric GCM climate predictions. Bull. Amer. Meteor. Soc., 76 , 335–345.
Lau, N-C., 1988: Variability of the observed midlatitude storm tracks in relation to low-frequency changes in the circulation pattern. J. Atmos. Sci., 45 , 2718–2743.
Lau, N-C., and M. J. Nath, 1994: A modeling study of the relative roles of tropical and extratropical SST anomalies in the variability of the global atmosphere–ocean system. J. Climate, 7 , 1184–1207.
Lin, H., and J. Derome, 1996: Changes in predictability associated with the PNA pattern. Tellus, 48A , 553–571.
Lin, H., and J. Derome, 1997: On the modification of the high and low-frequency eddies associated with PNA anomaly: An observational study. Tellus, 49A , 87–99.
Lin, H., and J. Derome, 2004: Nonlinearity of extratropical response to tropical forcing. J. Climate, 17 , 2597–2608.
Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci., 50 , 1792–1818.
Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial area. J. Meteor. Soc. Japan, 44 , 25–43.
Opsteegh, J. D., and H. M. Van den Dool, 1980: Seasonal differences in the stationary response of a linearized primitive equation model: Prospects for long range weather forecasting? J. Atmos. Sci., 37 , 2169–2185.
Palmer, T. N., and Z. Sun, 1985: A modelling and observational study of the relationship between sea surface temperature in the northwest Atlantic and atmospheric general circulation. Quart. J. Roy. Meteor. Soc., 111 , 947–975.
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. Part I: Influence of model climatology. Quart. J. Roy. Meteor. Soc., 112 , 613–638.
Peterson, K. A., R. J. Greatbatch, J. Lu, H. Lin, and J. Derome, 2002: Hindcasting the NAO using diabatic forcing of a simple AGCM. Geophys. Res. Lett., 29 .1336, doi:10.1029/2001GL014502.
Pozo-Vazquez, D., M. J. Esteban-Parra, F. S. Rodrigo, and Y. Castro-Diez, 2001: The association between ENSO and winter atmospheric circulation and temperature in the North Atlantic region. J. Climate, 14 , 3408–3420.
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.
Sardeshmukh, P. D., G. P. Compo, and C. Penland, 2000: Changes of probability associated with El Niño. J. Climate, 13 , 4268–4286.
Shukla, J. S., and Coauthors, 2000: Dynamical seasonal prediction. Bull. Amer. Meteor. Soc., 81 , 2593–2606.
Simmons, A. J., J. M. Wallace, and G. W. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci., 40 , 1363–1392.
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.
Trenberth, K. E., G. W. Branstator, D. Karoly, A. Kumar, N. Lau, and C. Ropelewski, 1998: Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperature. J. Geophys. Res., 103 , 14291–14324.
Warn, T., and H. Warn, 1978: The evolution of a nonlinear critical level. Stud. Appl. Math., 59 , 37–71.
Webster, P. J., and J. R. Holton, 1982: Cross-equatorial response to middle latitude forcing in zonally varying basic state. J. Atmos. Sci., 39 , 722–733.
Wu, A., and W. W. Hsieh, 2004: The nonlinear Northern Hemisphere atmospheric response to ENSO. Geophys. Res. Lett., 31 .L02203, doi:10.1029/2003GL018885.
Zhang, C., 1993: Laterally forced equatorial perturbations in a linear model. Part II: Mobile forcing. J. Atmos. Sci., 50 , 807–821.
Zhang, C., and P. J. Webster, 1992: Laterally forced equatorial perturbations in a linear model. Part I: Stationary transient forcing. J. Atmos. Sci., 49 , 585–607.
The 550-hPa geopotential height response to El Niño forcing from days 3 to 13 at a 2-day interval. The contour interval is 10 m. Contours with negative values are dashed. Zero line is not plotted. The shaded areas represent values different from zero with a significant level of 0.01 according to a Student’s t test.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Same as Fig. 1, but for La Niña forcing.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Linear component of the 550-hPa geopotential height response, which is defined as the difference between the El Niño and La Niña responses, from days 3 to 13 at a 2-day interval. The contour interval is 20 m. Contours with negative values are dashed. Zero line is not plotted. The shaded areas represent values different from zero with a significant level of 0.01 according to a Student’s t test.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Nonlinear component of the 550-hPa geopotential height response, which is defined as the sum of the El Niño and La Niña responses, from days 3 to 13 at a 2-day interval. The contour interval is 10 m. Contours with negative values are dashed. Zero line is not plotted. The shaded areas represent values different from zero with a significant level of 0.01 according to a Student’s t test.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The 550-hPa geopotential height response averaged between days 16 and 30 for (a) El Niño and (b) La Niña forcings; (c) linear component of the 550-hPa geopotential height anomalies as estimated by the difference between (a) and (b); and (d) nonlinear component of the 550-hPa geopotential height anomalies as estimated by the sum of (a) plus (b). The contour interval is 10 m for (a) and (b), 20 m for (c) and (d). Contours with negative values are dashed. Zero line is not plotted. The shaded areas represent values different from zero with a significant level of 0.01 according to a Student’s t test.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Time-dependent longitude–height profile on the equator of temperature (thick contours) and omega (thin contours) response up to day 6 for the El Niño run. Contour interval for omega is 2 hPa h−1, and that for temperature is 0.5°. Contours with negative values are dashed. Zero line is not plotted.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Same as Fig. 6, but for the La Niña run.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The 150-hPa geopotential height (in contour) and horizontal wind (in vector) responses to (a)–(f) El Niño forcing and (g)–(l) La Niña forcing from days 3 to 13 at a 2-day interval. The contour interval is 15 m. Contours with positive and negative values are solid and dashed, respectively. Zero line is not plotted. Scaling for arrows is given below the lowest panels (m s−1).
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The 150-hPa streamfunction response to (a)–(f) El Niño forcing and (g)–(l) La Niña forcing from days 3 to 13 at a 2-day interval. The contour interval is 2.5 × 106 m2 s−1. Contours with negative values are dashed. Zero line is not plotted.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
(a)–(f) Linear and (g)–(l) nonlinear components of 150-hPa geopotential height (in contour) and horizontal wind (in vector) response, from days 3 to 13 at a 2-day interval. The contour interval is 30 m for the linear component and 10 m for the nonlinear component. Contours with positive and negative values are red and blue, respectively. The shaded areas in the nonlinear component represent geopotential values different from zero with a significant level of 0.01. Zero line is not plotted.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The amplification factor A of response to a stationary forcing for (a) Kelvin wave and (b) equatorial Rossby waves (n = 1 and 2). The solid curves are for the mean zonal flow u = 10 m s−1, and the dashed curves for u = −10 m s−1.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Rms anomaly of 550-hPa geopotential height for (a) days 6–10 of the El Niño run, (b) days 6–10 of the La Niña run, (c) days 11–15 of the El Niño run, (d) days 11–15 of the La Niña run, (e) days 16–30 of the El Niño run, and (f) days 16–30 of the La Niña run. Contour interval is 2 m. Zero line is not shown. Shaded areas are those with significance level better than 0.01.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The 550-hPa geopotential height tendency anomaly caused by transient vorticity flux convergence for (a) days 6–10 of the El Niño run, (b) days 6–10 of the La Niña run, (c) days 11–15 of the El Niño run, (d) days 11–15 of the La Niña run, (e) days 16–30 of the El Niño run, and (f) days 16–30 of the La Niña run. Contour interval is 0.4 × 10−5 m s−1. Zero line is omitted. Shaded areas are those with significance level better than 0.01.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
The 250-hPa stationary wavenumber Ks calculated with zonal wind averaged for days 11–15 for the (a) El Niño and (b) La Niña runs. Plotted as contours are stationary wavenumber 0, 4, 5, 6, 7, 8, 10, and 15. Regions with a Ks greater than 6 are lightly shaded, and that with imaginary values are heavily shaded.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
Same as Fig. 2, but for forcing of half amplitude and contour interval is 5 m.
Citation: Journal of Climate 20, 22; 10.1175/2007JCLI1383.1
