Long-Lived Response of the Midlatitude Circulation and Storm Tracks to Pulses of Tropical Heating

Grant Branstator National Center for Atmospheric Research,* Boulder, Colorado

Search for other papers by Grant Branstator in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

The midlatitude response to localized equatorial heating events that last 2 days is examined through experimentation with an atmospheric general circulation model. Such responses are argued to be important because many tropical rainfall events only last a short time and because the responses to such pulses serve as building blocks with which to study the impacts of more general heating fluctuations.

The experiments indicate that short-lived heating produces responses in midlatitudes at locations far removed from the source and these responses persist much longer than the pulses themselves. Indeed pulse forcing, which is essentially white in time, produces upper-tropospheric responses that have an e-damping time of almost a week and that are detectable for more than two weeks in the experiments. Moreover the upper-tropospheric structure of the reaction to short pulses is remarkably similar to the reaction to steady tropical heating, including having a preference for occurring at special geographical locations and being composed of recurring patterns that resemble the leading patterns of responses to steady heating. This similarity is argued to be a consequence of the responses to pulses having little or no phase propagation in the extratropics. The impact of short-lived tropical heating also produces a persistent response in midlatitude surface fields and in the statistics of synoptic eddies.

The implications these results have for subseasonal variability are discussed. These include 1) the potential for improving subseasonal prediction through improved assimilation and short-range forecasts of tropical precipitation and 2) the difficulties involved in attributing subseasonal midlatitude events to tropical heating.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Grant Branstator, NCAR, P.O. Box 3000, Boulder, CO, 80307. E-mail: branst@ucar.edu

Abstract

The midlatitude response to localized equatorial heating events that last 2 days is examined through experimentation with an atmospheric general circulation model. Such responses are argued to be important because many tropical rainfall events only last a short time and because the responses to such pulses serve as building blocks with which to study the impacts of more general heating fluctuations.

The experiments indicate that short-lived heating produces responses in midlatitudes at locations far removed from the source and these responses persist much longer than the pulses themselves. Indeed pulse forcing, which is essentially white in time, produces upper-tropospheric responses that have an e-damping time of almost a week and that are detectable for more than two weeks in the experiments. Moreover the upper-tropospheric structure of the reaction to short pulses is remarkably similar to the reaction to steady tropical heating, including having a preference for occurring at special geographical locations and being composed of recurring patterns that resemble the leading patterns of responses to steady heating. This similarity is argued to be a consequence of the responses to pulses having little or no phase propagation in the extratropics. The impact of short-lived tropical heating also produces a persistent response in midlatitude surface fields and in the statistics of synoptic eddies.

The implications these results have for subseasonal variability are discussed. These include 1) the potential for improving subseasonal prediction through improved assimilation and short-range forecasts of tropical precipitation and 2) the difficulties involved in attributing subseasonal midlatitude events to tropical heating.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Grant Branstator, NCAR, P.O. Box 3000, Boulder, CO, 80307. E-mail: branst@ucar.edu

1. Introduction

It is well recognized that tropical heating anomalies can and do affect conditions in the midlatitudes. Inspired by the large interannual midlatitude signals generated by the quasi-steady heating anomalies produced by El Niño and La Niña events, much of the observational, modeling and theoretical research that has been directed at the influence of tropical heating fluctuations has concentrated on the response to steady, stationary sources. By contrast, here we report on a modeling study that characterizes the effects of short-lived pulses of tropical heating on the midlatitude circulation and synoptic eddies.

One reason we focus on short-lived rather than long-lived tropical heating events is that quasi-steady events actually make up a small fraction of tropical heating variability. This fact can be seen in Fig. 1, which displays for northern winter 1) the daily variance of outgoing longwave radiation (OLR, which serves as a surrogate for precipitation in the tropics) and 2) the ratio of the interannual variance of OLR to its daily variance. These are based on the National Oceanic and Atmospheric Administration (NOAA) interpolated OLR dataset (Liebmann and Smith 1996). Except in the vicinity of El Niño and La Niña events in the central tropical Pacific, long-lasting heating anomalies make up less than 20% of the total variance.

Fig. 1.
Fig. 1.

(a) Variance of daily values of OLR for the months of December, January, February, and March. The contour interval is 200 W2 m−4 with a maximum value of 1800 W2 m−4. (b) Ratio of variance of DJFM seasonal mean OLR to variance of daily values. The contour interval is 0.1 with a maximum value of 0.6. The plots use OLR departures from the climatological mean of each individual month.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

One possible approach for concentrating on heating that is not steady would be to decompose fluctuations into their harmonic components and consider the response to oscillations with a specific frequency of interest or more generally to study how the response depends on frequency. For example, observational (e.g., Knutson and Weickmann 1987; Cassou 2008; Roundy et al. 2010) and modeling papers (Matthews et al. 2004) have reported on the midlatitude anomalies that are driven by the oscillating heat sources associated with the narrow banded Madden–Julian oscillation (MJO), while Kiladis and Weickmann (1992, 1997) described extratropical features that are observed to be associated with tropical precipitation fluctuations in higher-frequency bands. And Yang and Hoskins (1996) analyzed the midlatitude response to sinusoidally varying tropical sources for a broad range of frequencies by employing a theoretical linear framework.

We have chosen an alternative approach for investigating the effect of tropical sources that are not steady. We have considered heat sources that switch on suddenly, last a short time, and then switch off, which is to say they are approximately delta functions. Silva Dias et al. (1983) studied the tropical response to similarly varying sources. Figure 2 demonstrates one reason this type of heating should be of interest. That figure shows the time series of OLR that was observed near the equator at 90°E during two northern winters. Figure 2a concerns December 1976 to March 1977 during which there were strong, short-lived spikes in convection on about the 25th, 60th, and 75th days of the winter. Examination of other winters reveals that such episodes are common. Even during winters when there are prominent oscillations like the MJO, which is apparent in the depiction in Fig. 2b of December 1985 to March 1986, superimposed on the regular oscillation are strong episodes of short duration.

Fig. 2.
Fig. 2.

Time series of daily OLR anomalies from the seasonal average during (a) December 1985–March 1986 and (b) December 1976–March 1977 averaged in a 22° lon × 9° lat box centered on the equator at 90°E. For the right-hand scale OLR has been converted to a column-average atmospheric heating rate based on the assumption that 1 W m−2 equals 0.09 mm day−1 of rainfall (Xie and Arkin 1998).

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

In addition to occurring frequently, the response to pulses of heating are of interest because any temporal variation can be decomposed into a sequence of pulses, much as one decomposes a function into a series of short constant segments in integral calculus. Provided the source is sufficiently weak, the response to a time-varying source at a particular time t will simply be the sum of the response to individual pulses that precede t with appropriate delays. For this reason, by learning about the response to short-lived pulses, one is learning about the building blocks that when combined give the response to any temporally varying source.

One might wonder whether the response to a pulse will in fact produce much of a reaction in midlatitudes. After all, the basic mechanism by which one expects energy to migrate from a tropical source to midlatitudes is via Rossby wave propagation, and one of the outcomes of linear analysis of such waves is that for high frequencies they are trapped in the tropics (Yang and Hoskins, 1996). But a pulse projects onto all frequencies; and in the limit of an infinitely short pulse all frequencies have equal amplitude. Hence, in the cases we examine, in which heating lasts for only 2 days, the response could be very different from the response to, say, an oscillating source with a period of 4 days, even though in both cases sources of one sign last for 2 days.

Motivated by these ideas we have carried out a series of numerical experiments to quantify and characterize the extratropical response to pulses of heating on the equator. Much has been learned about the steady response problem from linearized equations (e.g., Hoskins and Karoly 1981; Branstator 1983; Ting and Sardeshmukh 1993). Likewise, linear analysis has been fruitful for the related initial value problem (e.g., Jin and Hoskins 1995; Garcia and Salby 1987). But instead of considering linearized equations, we have used atmospheric general circulation model (AGCM) experiments for our study because linearized equations do not include potentially important processes. For example, it has been demonstrated that nonlinear interactions involving the midlatitude synoptic eddies make an important contribution to the steady response problem (Kok and Opsteegh 1985; Held et al. 1989). And various nonlinear resonances have been proposed as mechanisms that promote the intraseasonal midlatitude reaction of Rossby waves to tropical heating events (Raupp and Silva Dias 2009; Khouider et al. 2013). Furthermore, linearized equations that are complete enough to include what are known to be important processes for the response problem have some undesirable properties. These include the need to control linear resonances produced by interactions of forced perturbations with the climatological mean waves (Branstator 1990) and the necessity of restricting time-dependent experiments to short integrations so that baroclinically unstable modes do not dominate solutions (Hoskins and Jin 1991).

When examining our AGCM experiments our goal is to address four general issues. First, we want to learn about the temporal and geographical extent of the response to a tropical heating pulse. Even though a pulse is of short duration, it can potentially produce a response that lasts much longer. After all, once the pulse has turned off, the features it produces will evolve just as any internally generated features would evolve and these are known to persist. And, just as a compact initial anomaly can evolve in such a way as to influence remote locations because of the dispersion of planetary waves (Hoskins et al. 1977), the features produced by the forcing can eventually have remote impacts. Second, we wish to quantify the temporal spectral characteristics of the fluctuations produced by a pulse. Just as a simple one-dimensional white noise–driven linear system with memory generates a red noise response (Hasselmann 1976; Griffies and Bryan 1997), the forcing of all frequencies more or less equally by a pulse may preferentially excite low-frequency responses. We wish to determine whether in fact pulses do produce responses that have more power at low frequencies than the pulses themselves. Third, we want to determine if the response to pulses is geographically organized and composed of special, prominent patterns even if there is no geographical organization to the pulses. We know the response to steady forcing has such organization (Gritsun and Branstator 2007; Shin et al. 2010). Fourth, we wish to identify midlatitude fields that are affected by pulse heating. Most of our analysis concerns the upper-tropospheric state, but we want to see whether the impact seen there carries over to fields at the surface and to the storm tracks, just as is well known to be true for steadily forced responses and quasi-stationary anomalies (Lau 1988; Held et al. 1989; Branstator 1995; Hurrell 1996; Hoerling and Kumar 2002).

2. Experiments

To investigate the effect of tropical heating pulses we have carried out two types of experiments with Community Atmospheric Model, version 3 (CAM3; Collins et al. 2006a), which is the atmospheric component of the Community Climate System Model, version 3 (CCSM3; Collins et al. 2006b). CAM3 has been used in numerous studies of the atmosphere by a large community of users. We have run it at a horizontal resolution of T42 and employed climatological mean sea surface temperatures that are a function of the day of the year but do not vary from year to year. Output from our experiments with this model is stored every 12 h on a standard 128 × 64 transform grid.

In one type of experiment we have addressed the problem of determining the steady response to a steady source. Often when considering the response to tropical sources models are forced by imposed anomalous sea surface temperatures, which lead to tropical heating anomalies. Instead, in order to more carefully control the anomalous heating felt by the atmosphere, we have directly forced the thermodynamic energy equation by adding a constant source term to its right-hand side. This term is of the form . Here c is a constant heating rate, s is a function of longitude and latitude that decreases linearly with distance from the central point until it vanishes at the distance r0 = 1.5 × 106 m, and , where is the model’s normalized pressure vertical coordinate. We sometimes refer to h as “disk heating.” Note that h is not intended to match any particular observed phenomenon but rather serves as a simple idealized prototype of localized heating that is concentrated in the middle troposphere. When we have repeated some of our experiments with r0 halved and c adjusted so that the area integral of h is unchanged, the responses are very similar to those presented below.

We have performed 24 heating experiments in which c has a value of 5°C day−1 and takes on the values 0, 15, … 335 degrees of longitude and . For each experiment we have done 100 integrations of length 62 days with each integration starting from a different realization of 1 December taken from a control integration of CAM3. We have then averaged fields during January from these 100 integrations to produce 3100-day means. We consider these averages to represent the equilibrated response of the model to the imposed heating. We have also done a second set of 24 experiments that are identical except c = −5°C day−1.

In the other type of experiment we have employed pulses of heating rather than heating that is constant. Again we have performed two sets of 24 experiments with heating that has the same structure and amplitude as that used in the steady heating experiments, but in these the heating is switched on during only the first 48 h of each realization. Two-day pulses are used as a compromise between needing sources that last long enough to produce a detectable signal and wanting sources of short enough duration that all but the most rapidly evolving forcing functions can be approximated by a combination of pulses. For these experiments each integration starts on a different 1 January taken from a control run and it proceeds for 20 days. Averages of 2000 such realizations are used to find the mean state associated with each stage of the model’s reaction to a pulse. The characteristics of these ensemble average responses constitute the main focus of our study.

Note that the ensembles we use for the pulse problem are qualitatively different from those used for weather prediction. In weather prediction an ensemble is centered on a particular observed state, while our ensembles start from a collection of states that approximately cover the attractor of CAM3. For this reason the ensemble mean responses we examine are the response of the model mean climate, albeit on much shorter time scales than is typically considered in climate response studies. One way we characterize the behavior of these mean responses is to compare them to the steady, equilibrated responses from the first type of experiment, which also constitute a change in the mean climate. When considering our results it is important to keep in mind that because we are examining averages across many initial conditions our results only reflect that component of the response that the different realizations have in common; among other consequences, this will tend to weaken the response, especially late in the experiments when the response for individual initial conditions can be very different from each other.

For both the pulse and steady experiments, in order to consider the anomalous response we could have subtracted appropriate mean values based on a control run of CAM3. Instead we have chosen to subtract the mean values of the negatively forced experiments from the corresponding positively forced experiments with the forcing in the same location. When we have examined ensemble mean departures from a control climate we have found that for most situations the anomalies for positive and negative heating at the same location are similar except for a change in sign. In some cases there are differences that may be interesting to quantify in a future study, but we have found that the similarities are so great that any loss in signal that results from combining positive and negative responses that are not exactly equal and opposite is more than made up for by the gain in signal to noise that results from doubling the sample size in the computation of anomalies. All results presented here are for ensemble mean differences between positively and negatively forced experiments divided by 2 so that they represent the response to heating with peak value 5°C day−1. (For variable x we denote such a mean difference by ). Given the structure of h this corresponds to volume-average heating of about 1°C day−1, which is comparable to rates that often occur in the region that Fig. 2 pertains to. Note that this rate is about the same as is associated with 4 mm day−1 rainfall (Lin 2009).

3. Response examples

We have chosen to use υ300, the meridional wind at 300 hPa, as the primary field for characterizing responses. Unlike geopotential height, its variability is not weak in the tropics, and for situations where energy propagation is prominent, it tends to have structure that is easier to interpret than streamfunction. On the other hand, it has the drawback that it does not capture all aspects of the solutions we study; perhaps most notably, the equatorial Kelvin wave component is missed.

The left column of Fig. 3 is an example of for an equatorial heating pulse. It shows the response 3, 6, and 9 days after a 2-day pulse at 135°E is first turned on. Similar plots for days 1 and 2 (not shown) consist of anomalies that are very close to the source. These local circulation features are a manifestation of the so-called Rossby wave source (Sardeshmukh and Hoskins 1988), which is produced as the upper-tropospheric divergence anomalies induced by the heat source interact with the background circulation to generate vorticity. By day 3 the response (Fig. 3a) is beginning to affect the midlatitudes. This is qualitatively similar to what has been found for simple linear wave propagation soon after the switch on of a steady tropical source (Jin and Hoskins 1995) or the insertion of an initial disturbance in the tropics (Hoskins and Jin 1991) and bears some resemblance to investigations of circulation features associated with intraseasonal OLR anomalies in this region (Kiladis and Weickmann 1997). Response energy propagates eastward, most strongly in the winter hemisphere, and extends about halfway around the globe by day 6. At that point the winter wave train begins to bend back toward the tropics. By day 9 the response has become more complex. There are strong features near the equator in the east Pacific and over South America, reminiscent of similar features seen in the linear barotropic response to steady forcing in the presence of a zonally varying basic state (Sardeshmukh and Hoskins 1988). Also a wave train arching across the North Atlantic has formed, so that about two-thirds of the globe has been affected. Note that the evolution after day 2, including the marked increase in the area impacted by the pulse and only moderate weakening of extratropical features that first formed by day 3, takes place without any ongoing forcing from the tropics.

Fig. 3.
Fig. 3.

Ensemble mean υ300 response in CAM3 to a 2-day pulse of heat at 0°N, 135°E (a) 3, (b) 6, and (c) 9 days after the pulse begins. (d)–(f) As in (a)–(c), but for a pulse at 0°N, 120°W.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

The right column of Fig. 3 shows for a second pulse, namely one at 120°W. In some ways this response is similar to the first case but shifted eastward by 105°, corresponding to the forcing being offset by that amount. To be sure, many details of the responses are not simple offsets. Even the phase of the local response relative to the heat pulse during days 1 and 2 (not shown) is not the same, presumably because the tropical and subtropical mean state (and hence the Rossby wave source) are quite different at 120°W compared to 135°E. But many characteristics of the midlatitude response are similar, including the speed at which the response moves poleward and eastward, the higher amplitudes in the winter hemisphere, and the preference for zonal waves 5 or 6 in midlatitudes. Another interesting characteristic that the two cases have in common is that many features in both responses are nearly stationary; except for the southern wave train in the 120°W case, there is little phase propagation. Also, despite the very different forcing positions, some response features occur in the same geographical location. These are most prominent at day 9 and include the wave train southeast of South America, the high-latitude North Pacific dipole, and the wave train that extends across the North Atlantic. Similarities in response structure for forcing at widely separated locations have also been noticed in numerous linear and GCM solutions with steady tropical heating (e.g., Simmons et al. 1983; Geisler et al. 1985; Branstator 1985; Grimm and Silva Dias 1995).

4. Response characteristics

When we have examined the ensemble mean response to pulses in all 24 locations we have noticed that several of the properties highlighted in the previous section are valid for many of these experiments. To quantify these characteristics, we first combine the 24 responses in various ways to focus on particular properties. Then, since such an analysis can obscure important distinctions among the different cases, we consider some ways in which the responses differ depending on the position of the pulse heating.

a. Duration and reach

Two properties of interest seen in the examples are the rate at which the response influences remote regions and the length of time the response is perceptible. To quantify the region that is influenced by a typical pulse a specified number of days after it was first turned on, we have longitudinally shifted the ensemble average response fields so that each pulse location is at the same longitude, and then calculated the RMS of these 24 maps at each grid point. Figure 4a shows the resulting quantity for disturbances 3 days after the pulse is first turned on, with the yellow dot indicating the position the heating has been shifted to. Just as in the Fig. 3 cases, on average the response to a pulse after 3 days is largely confined to the source region but is also beginning to influence midlatitudes. Figure 4b concerns the average response at day 6. It shows the expanding influence of the pulse, especially in the winter hemisphere, even though the forcing has not been present for 4 days. (The string of equatorial features east of the heating location is related to a strong response near the west coast of South America that occurs for many pulse positions; recall that the examples in Fig. 3 had this behavior.)

Fig. 4.
Fig. 4.

RMS response of ensemble mean υ300 to a 2-day pulse (a) 3 days and (b) 6 days after the pulse begins. These correspond to 24 cases in which the pulses are located at different equatorial locations separated by 15°. The response for each case is longitudinally translated to the longitude indicated by 0°, and then the RMS of these is plotted.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

To quantify the evolution of an average case in a more continuous fashion, we have concentrated on the latitudinal distribution of the quantity displayed in Fig. 4. Specifically we have calculated the RMS of values in such plots along latitude circles for days 0.5, 1.0, 1.5… and display them in Fig. 5a. During the first 2 days, while the heating is still present, the response near the pulse grows rapidly, especially 10° to 15° on either side where the directly forced Rossby waves have their strongest meridional winds. Once the source is turned off, however, the tropical response weakens while the midlatitude response strengths until about day 7 in both hemispheres. After this time the midlatitude response weakens gradually and becomes undetectable during the third week. Finite ensembles give only an approximation to the true mean response to a stimulus, even when the ensembles are very large, as in our study. As explained in the appendix, we accounted for the inflation in response amplitude that can result from finite sample errors by subtracting the variance of such errors in the Fig. 5 plots. When considering results like those in Fig. 5, one should recall that they represent averages of many realizations. As alluded to in section 2, cancellation among the realizations, each of which is affected by the pulse somewhat differently, weakens the response especially toward the end of the experiments.

Fig. 5.
Fig. 5.

RMS response of ensemble mean υ300 to 2-day pulses. (a) As a function of time after the pulses are initiated, fields analogous to those in Fig. 4 are calculated and then the RMS of these fields at each latitude is plotted. (b) As in (a), except the RMS of values between 30° and 60°N is plotted at each longitude.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

When we carry out a related calculation directed at longitudinal rather than latitudinal propagation of the impact of a typical pulse, we produce Fig. 5b. It portrays the RMS of values between 30° and 60°N1 in plots like those in Fig. 4. Using it we see that on average a pulse influences approximately a quarter of the Northern Hemisphere midlatitudes within 3 days of first being turned on and then the disturbance envelope expands primarily eastward at a speed of about 25 degrees of longitude per day. Within a little over a week virtually all longitudes have been affected. Consistent with the zonally averaged view of Fig. 5a, the impact persists for more than two weeks, with the influence becoming imperceptible more rapidly for longitudes far to the east of the source where the response is weakest. One other feature evident in Fig. 5b is the predominance of approximately zonal wavenumber 5 in the midlatitude response, a scale that other studies have found to be prominent in fluctuations of meridional wind near the subtropical jet of northern winter (Branstator 2002) and summer (e.g., Ding and Wang 2005; Schubert et al. 2011; Teng et al. 2013).

b. Stationarity

Another aspect of the Fig. 3 examples that we noticed above was a tendency for many response features to not propagate, a property we characterize by saying the response is stationary—not to be confused with the concept of statistical stationarity. When we examine all of the pulse experiments we find this property is apparent in many of them. To objectively measure this characteristic we have calculated the pattern correlation between at each stage of a pulse response experiment and 2 days later. In this calculation we only consider the state poleward of 30°. Averaging these pattern correlations for the 24 experiments leads to the dashed red line in Fig. 6. Also plotted, as a dotted black line, is the squared amplitude of as given by the area average of the 24 squared responses in the same range of latitudes. (One can arrive at this quantity by averaging squares of the results in the left panel of Fig. 5 poleward of 30°.) After about day 4 (i.e., once the midlatitude response has begun to have a large amplitude), the response becomes nearly stationary in most regions and most experiments as indicated by the average lag pattern correlation being about 0.80. This attribute lasts at least until about day 14–the day 12 and day 14 responses are still correlated with a value of about 0.70. It is possible that the responses continue to be nearly stationary even longer, but as the appendix shows, sampling errors are large after day 14, so it is difficult to draw conclusions about this aspect of the late stages of the experiments.

Fig. 6.
Fig. 6.

“Days” refers to the time after a 2-day equatorial pulse is initiated. Blue line: average, over 24 cases, of the pattern correlation between the ensemble mean υ300 response to a pulse and the steady response to a steady source at the same location. Red dashed line: average pattern correlation between ensemble mean υ300 at the indicated time and the response 2 days later. Black dotted line: average response amplitude to a pulse. As described in the appendix, the plotted quantity corresponds to the amount by which the average amplitude exceeds the amplitude expected from sampling errors. Pattern correlations and amplitudes in this figure are for locations poleward of 30°.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

An interesting consequence of the stationarity and high amplitudes that occur about 3 to 14 days after a pulse is switched on is that the response during this period must be structurally similar to the steady response to a steady heat source that has the same spatial structure as the pulse. This will be true even though in one case the system is forced by heating that lasts 2 days and in the other by heating that lasts indefinitely. That these responses should be similar can be seen if one recognizes that the response to a heat source with the same structure as the pulse and a sufficiently weak time-dependent amplitude can be approximated by
e1
where is the appropriately normalized mean response at to a 2-day pulse k days after it begins. For steady heating (1) implies that the steady response will be simply the sum of the pulse response at days 2, 4, …, 20. That is, the steady response to a steady disk forcing will be the sum of responses like those in one column of Fig. 3. Since the midlatitude response to a pulse has largest amplitudes between about days 4 and 14 and since the lack of phase propagation during this span means there is little destructive interference when they are combined, the steady response will be dominated by their contributions and will have about the same structure.

An example of the validity of (1) for our experiments is given in Fig. 7. Figure 7a is the steady January response of υ300 to a constant heat source at 0°N, 135°E, as produced by one of the steady heating cases described in section 2. Figure 7b is the approximate steady solution that results from using (1). Clearly (1) gives a good approximation to the steady response. Note the similarity in structure between both of these patterns and the response to a 0°N, 135°E pulse 6 and 9 days after initiation of the pulse (Figs. 3b,c), as anticipated by the above argument. Furthermore if we only employ contributions from k = 4, …, 14 in (1), which correspond to the ranges at which the response is quasi-stationary, then the estimate displayed in Fig. 7c is generated. Its similarity to Figs. 7a and 7b confirms that these are the primary contributions to the steady response.

Fig. 7.
Fig. 7.

(a) Ensemble mean, January mean, υ300 response to a steady heat source at 0°N, 135°E. (b) Ensemble mean υ300 response to a sequence of 2-day pulses that begin 2, 4, …, 20 days before the response time. (c) As in (b), but only pulses beginning 4, 6, …, 14 days before the response time are included.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

To more generally confirm the correspondence between the structure of the response to pulses and steady heating we have calculated the pattern correlation between of each of the 24 pulses and the corresponding response in our steady forcing experiments in the region poleward of 30°. The blue line in Fig. 6 shows the 24-case average of these pattern correlations at each range. As expected, similarities are largest in the midrange where the extratropical response to a pulse tends to be stationary and strong.

For an additional perspective on the long-lasting, quasi-stationary characteristic of anomalies produced by equatorial pulses, we have carried out one additional calculation in which we have estimated the response to a time evolving equatorial heating function consisting of random 2-day pulses. The heating function at the initial time is determined by assigning random amplitudes drawn from a Gaussian distribution to disk heating at each of our 24 pulse locations. Every two days new random amplitudes are assigned until 10 000 days of heating fields are generated. Then (1) is used to find the ensemble average response of υ300 to this time-dependent forcing under the assumption that the response to forcing at each pulse location is independent. When we calculate power spectra for the heating and response by calculating a spectrum at each grid point on the globe and averaging these together with area weighting, the curves in Fig. 8 are produced. Since, aside from being constant during 2-day intervals, the forcing is uncorrelated in time it is not surprising that the heating spectrum is essentially white for periods longer than about 5 days. On the other hand, the response is very red. A consequence of this stark contrast is that the lag 2-day autocorrelation for the heating fields is 0 while it is 0.73 for the response (corresponding to an e-damping time of 6.4 days).

Fig. 8.
Fig. 8.

Red line: average spectrum of heating consisting of a long sequence of collections of 24 pulses, each lasting 2 days and each having a random amplitude. Blue line: average spectrum of the ensemble mean υ300 response to heating consisting of equatorial pulses like those used to calculate the red line. These spectra have been evaluated at frequencies i (100 days)−1, i = 1, …, 100, and the “fraction of variance” is with respect to the total variance in these 100 frequencies.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

c. Spatial structure

The next characteristic we consider is the geographical organization of responses, including the occurrence of recurring structures. One indication that there is such organization is in Fig. 9a, which, like Fig. 5b, shows the RMS of the ensemble mean response between 30° and 60°N for our 24 pulses as a function of time since the pulse was initiated. For this calculation, however, the responses are not longitudinally translated to place the heating at a common position. One other difference with Fig. 5b is that here the response is represented by 300-hPa streamfunction; for this calculation υ300 gives a much noisier diagram. The figure indicates that even when we are considering a collection of experiments for which there is no preferred heating longitude, within about 4 days of pulse initiation the response tends to be especially strong in three preferred midlatitude regions. Furthermore, these locations are the same regions that are preferentially excited by steady equatorial heating. This fact is seen when Fig. 9a is compared to Fig. 9b, which displays the same quantity but for our 24 steady solutions. Note these same three regions of strong variance exist for fluctuations in nature (Blackmon et al. 1984) as well as for intrinsic variability of monthly and longer variations in CAM3 (not shown).

Fig. 9.
Fig. 9.

(a) RMS of the 300-hPa streamfunction response between 30° and 60°N to pulses at 24 equatorial longitudes. (b) As in (a), but for the steady response to steady heating at the same 24 locations.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

To construct Fig. 9a we have again taken the conservative approach of only plotting the amount by which the RMS response exceeds the average contribution expected from sampling errors. Taking this into consideration it is noteworthy that the response near the date line maintains its high amplitude longer than the other preferred regions do and appears to be substantially greater than zero perhaps for 20 days after the pulses are first turned on.

A second indication of organization is the large amount of variance explained by just a few patterns when we do an empirical orthogonal function analysis (EOF) of the 24 Northern Hemisphere ensemble mean responses to pulses (with no longitudinal translation) a specified number of days after the heating occurs. Again we use 300-hPa streamfunction since it gives patterns that are similar to those of geopotential, which is the variable often used for such an analysis. Also we remove its zonal mean. The leading EOFs for the first few days of the experiments are confined to the tropics. An example of this behavior is EOF1 of the day 3 responses (Fig. 10a). It explains about 21% of the variance and is concentrated near the Greenwich meridian. Other day 3 leading EOFs also consist of one or two large-scale features but in other parts of the tropics. Later in the experiments the leading EOFs continue to have large-scale tropical features but they are associated with arching midlatitude wave patterns. EOF1 for day 6, which explains 23% of the variance, is an example (Fig. 10b). The relative importance of the midlatitude features grows with time so that by day 9 they become at least as strong as the tropical features, as seen for example in EOF1 (Fig. 10c). Also by day 9 the preference for a few patterns becomes more distinct as the leading three EOFs explain about 61% of the variability whereas for day 3 they explained only 49%. Interestingly the midlatitude features in EOF1 for both day 6 and day 9 (as well as for all other days beyond day 6) bear some resemblance to the well-known pattern associated with El Niño and La Niña events. Furthermore, when we plot EOF1 for our 24 steady forcing cases (Fig. 10d) and compare it to Figs. 10b and 10c, we again see a strong correspondence between the structure of steadily forced circulations and patterns that occur in response to pulses.

Fig. 10.
Fig. 10.

Leading EOF of the responses of 300-hPa streamfunction, with its zonal mean removed, to 2-day pulses at 24 equatorial locations (a) 3 days, (b) 6 days, and (c) 9 days after the pulses begin. (d) As in (a)–(c), but for the steady response to heating at the same 24 locations.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

A consequence of the geographical organization seen in this section is that, in contrast to the simplifying assumption we made in some of our earlier analyses, the response to pulses located at different longitudes must not be the same to within a longitudinal translation. Recall that Fig. 3 showed an example of the difference in structure in the response to two pulses. Comprehensively characterizing the dependence of the response to the longitude of an equatorial pulse is beyond the scope of this study, but to give an idea of how strong this dependence is we show a new set of diagrams. These diagrams depict averaged between 30° and 60°N a given number of days after the pulse is initiated for each of our experiments individually.

Figure 11a shows such a diagram for the response at day 5. The abscissa represents the longitude of the response and the ordinate corresponds to the longitude of the pulse. Pulse position is also shown by the thick line along the diagonal. Consistent with Fig. 5b, by day 5 the midlatitude response extends well east of the longitude of the pulse that drives it. For each location the structure of the response is rather similar except for simple offsets, but the strength and eastward reach of the responses depend substantially on the location of the heating. Pulses located in the eastern Indian Ocean, the western Pacific, and the eastern Pacific appear to be especially effective at stimulating a response well downstream in CAM3. Nine days after a pulse begins (Fig. 11b) the character of the response has undergone a qualitative change. Now the responses to some of the pulses are no longer even approximately related to each other by an offset, especially for pulses in the Indian Ocean and western Pacific. Instead the responses to pulses in those locations all have a maximum just east of the date line, the same location identified in Fig. 9 as being easily excited. By day 13 (Fig. 11c) the preference for this location is so strong that there is a strong response there for almost every pulse, although its sign depends on pulse position. Also, as we might expect from many of our earlier results, the 13-day response is structurally very similar to the response in our steady heating experiments (Fig. 11d).

Fig. 11.
Fig. 11.

The 30°–60°N latitudinal average ensemble mean υ300 response to a 2-day pulse located at each of 24 longitudes, which are indicated by the y axis. Plotted are the response (a) 5 days, (b) 9 days, and (c) 13 days after the pulse heating begins. (d) As in (a)–(c), for the steady response to steady heating. The plotted fields have been smoothed to emphasize the large-scale features.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

d. Impacts at the surface and to the synoptic eddies

Given the persistent character of upper-tropospheric disturbances produced by our equatorial pulses, and the association found in other studies between quasi-stationary upper-tropospheric disturbances and anomalies at the surface and in the storm tracks, one would expect that equatorial pulses can also impact these quantities. When we have considered the evolution of disturbances produced by typical pulses in the sea level pressure and 2-m temperature fields, we have found that their behavior is very much like that of υ300. Figure 12a gives an example of this, namely the evolution of RMS ensemble mean surface pressure where, as in Fig. 5a, the RMS is taken over the 24 pulse cases and over longitude. In most ways it is very similar to Fig. 5a although midlatitude features appear slightly later and perhaps last somewhat longer. The corresponding plot for 2-m temperature (not shown) portrays a midlatitude response that is at higher latitudes and is delayed even further. Indeed, its maximum does not occur until about day 10, and it retains half this amplitude until about day 17.

Fig. 12.
Fig. 12.

(a) As in Fig. 5a, but for sea level pressure. (b) As in (a), but for the variance of departures from running 4.5-day mean 300-hPa streamfunction.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

From a dynamical standpoint perhaps more interesting is that the heating pulses also have a long-lasting effect on the midlatitude synoptic eddies. To quantify this effect we have calculated departures from running 4.5-day-mean 300-hPa streamfunction for each member of our pulse ensemble integrations and then calculated the ensemble average of the squares of these departures. This gives the distribution of synoptic eddies, including the storm tracks. When we consider the difference between experiments with positive and negative pulses and process them in the same way we have processed υ300 (Fig. 5a) and sea level pressure (Fig. 12a), we see (Fig. 12b) how indeed there is a response of the storm tracks to pulse heating that occurs in concert with the response of the mean circulation and lasts nearly two weeks.

5. Discussion and conclusions

The results of our GCM experiments give support to the notion that when considering the influence of tropical rainfall anomalies on extratropical conditions, attention should be paid not only to interannual variations but also to intraseasonal fluctuations. Interannual variations in precipitation comprise a small fraction of total variability in the tropics, and our experiments demonstrate that heating events that last as little as 2 days can impact distance midlatitude regions and can have an effect well beyond the lifetime of the heating itself. Indeed, we found that for a typical pulse its effect on midlatitudes is strongest roughly one week after the heating occurs and is nearly circumglobal within a little more than a week. When the pulse has an amplitude similar to the amplitude of commonly observed equatorial rainfall anomalies, on average its effect persists for at least two weeks and even longer in certain regions. (If we had considered the response to individual initial states rather than averages for many initial conditions, the duration would have been even longer.) Moreover, the same should also be true for heating episodes that are even shorter than 2 days although the amplitude of their effects will be proportionately less. Note that the impact of short-lived pulses is qualitatively different from the response to sources oscillating at high frequency, which are tropically trapped, at least in a linear setting.

One interesting characteristic of extratropical reactions to short-lived tropical heating is their similarity to the more commonly investigated reactions to steady heating. The structure of the responses tends to be stationary in space just like a steady response. Also, the responses tend to be strongest in certain preferred midlatitude locations, and these locations match the regions where the response to steady forcing is strongest. Similarly the responses to pulses and steady forcing tend to be composed of similar recurring patterns. Our results indicate that these similarities in structure occur because the response to steady forcing is essentially the sum of the response to a sequence of pulses. Since the pulse responses have weak phase propagation, when they combine to give the steady response its structure will be similar to that of the pulses. The long-lived, stationary character of the response to short-lived tropical heating may potentially play a significant role in the production of subseasonal extratropical events, thus providing a link between weather and climate time scale fluctuations. These characteristics also mean that attribution of such events is perhaps more complicated than one might imagine since it is not sufficient to only consider heating events that persist on subseasonal time scales when searching for sources of subseasonal circulation events.

Our investigation focused on the impact that tropical heating events can have on the upper troposphere, but we also found they can influence weather-related fields including sea level pressure, surface temperature, and storm tracks. To further make this point we show a specific example that gives a synoptic view of a pulse affecting these fields. Figure 13 depicts these fields reacting to a pulse located at 0°N, 135°E, the same situation for which the upper-tropospheric response was shown in Figs. 3a–c. Just as for υ300 the reaction is largely confined to the region of the heating during the first days, but by day 6 surface conditions on the west coast of North America are being affected as well as the storm track just off the coast. And by day 9 the entire continent is impacted.

Fig. 13.
Fig. 13.

Ensemble mean response of (top) sea level pressure, (middle) 2-m temperature, and (bottom) variance of synoptic eddies to a 2-day pulse at 0°N, 135°E (left) 3 days, (middle) 6 days, and (right) 9 days after the pulse begins. Contour intervals are 0.1 hPa, 0.05°C, and 4 × 1011 m2 s−1, respectively.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

One encouraging consequence of this remote, delayed impact of transient tropical heating events is that there may be more opportunity for tropical heating to lead to enhanced predictability of midlatitude upper-tropospheric and surface conditions than is generally recognized. The MJO has been demonstrated to be a predictable phenomenon at subseasonal ranges, and as its prediction in the tropics has improved, there is evidence of a corresponding improvement in the skill of elements of the extratropical circulation that it influences (Vitart 2014). But the results of our experiments indicate that it is not necessary to successfully predict tropical heating for a week or longer in order to benefit extratropical predictions at ranges longer than a week. If one accurately predicts heating for a day or two, that will affect the midlatitude prediction for perhaps two weeks. Extending this idea even further, an additional implication of the delayed impact of tropical heating is that if one took observed tropical precipitation into account during data assimilation, the assimilation products would be better. Hence initial conditions for forecasts and the predictions themselves would improve. These improvements would be realized even if one had no predictive capabilities for tropical precipitation. An alternative perspective on heating events and weather prediction is that errors in predictions of tropical precipitation, even at short range, will detrimentally affect extratropical predictions at the extended range. The increase in the spread of European Centre for Medium-Range Weather Forecasts Ensemble Prediction System predictions that is found to occur during episodes of transient Rossby wave trains developing downstream of tropical cyclones as they transition to the extratropics (Waliser et al. 2012) could be evidence of this effect.

One facet of the response to pulses that we have not paid much attention to is the amplitude of the response. Through use of very large ensembles and an analysis of sampling errors we have been careful to show results that are not statistical artifacts. But from a practical standpoint whether the responses are strong enough to be discernable in the presence of natural fluctuations is also important. At first glance they may in fact appear to be weak. For example, note that the maximum sea level pressure response in the Fig. 13 example is only about 1 hPa and the maximum 2-m temperature response is about 0.5°C. On the other hand, the responses we have examined are reactions to pulses that occur at one location of the tropics and last for only 2 days. The combined effect of pulses that occur at many locations and over an extended time is potentially much larger. That they can combine in a constructive manner is made especially likely considering that the reactions last for a couple of weeks and tend to be spatially organized. Perhaps more importantly, by considering responses averaged over 2000 initial conditions, our results necessarily weaken the response that would occur for any single start date.

Another topic we have considered in only a cursory fashion is the physical mechanisms that contribute to the response behavior we have documented. Beyond interpreting some of the responses in terms of energy propagation, our investigation has not concerned the dynamics of the responses it analyzed. Given the similarities that we have pointed out must and do exist between the response to steady and pulse heating, one would expect that many of the mechanisms familiar from the steady problem are also at play for the pulse problem. Investigations of the steady problem have found many attributes, including the three-dimensional structure and amplitude of the forcing, diabatic feedbacks, and the mean climate state, can all affect the response, so until such factors and mechanisms are considered elsewhere it is best to only focus on the qualitative attributes of the solutions we have reported. One thing that is clear is that it was prudent to do our study using solutions from a GCM. Related studies that utilize linearized equations provide extremely valuable insight, but some of the concerns we mentioned in the introduction about relying solely on such an approach proved valid. The fact that we found that the responses we analyzed last as much as 20 days suggests that using linearized equations that are unrealistic after about two weeks excludes potentially interesting behavior. Furthermore, our results indicate that the synoptic eddies react to pulse heating, leaving open the possibility that feedbacks from these disturbances play an important part in the midlatitude response. Ongoing research supports this possibility.

Finally we wish to reiterate the potential value that pulse experiments have for studying more than the response to short-lived forcing events, for they provide building blocks with which to study the response to virtually any time-dependent forcing.

Acknowledgments

We have benefited greatly from discussions with H. Teng, J. Tribbia, R. Buizza, G. Kiladis, and M. Moncrief, as well as from reviews by George Kiladis, Pedro Silva Dias, and an anonymous reviewer of an earlier version of this paper. The GCM experiments were run and processed by A. Mai, who also coded the generation of the figures. Support for this work was provided by NOAA Contract NA09OAR4310187 and NASA NEWS via NASA Award NNX13AH92G.

APPENDIX

Sampling Errors

Consider the two 2000-member ensembles produced by our experiments for variable x (say υ300 at a grid point) k days after positive and negative pulse heating is initiated at location j. If is half the difference between the ith member of each ensemble, then our estimate of the response at day k is
eq1
A standard result is that if one assumes the are members of a Gaussian distribution then the variance in that results from estimating it from a finite ensemble is
ea1
The correspond to sampling errors in the estimate of .

One way to summarize these error variances is shown in Fig. A1. For this figure we have calculated for υ300 at each grid point at a particular latitude and averaged them over j = 1, …, 24 and longitude. Then taking the square root gives the values designated in the figure as occurring between day 0 and 20. The increasing values in this plot indicate the differences between pairs starting from the same initial condition increase with integration time. The divergence resulting from one member of a pair feeling a positive pulse and the other a negative pulse does not contribute to the increasing values in the figure, because is based on departures from ensemble means (A1). Instead it is because the modeled system is chaotic that the pairs spread more and more. Eventually this spread will be as large as for averages of states randomly drawn from the undisturbed system. For reference the RMS of differences in this limiting case has been approximated by calculating averages of 2000 random draws from a control run and then finding the RMS of many pairs of such mean fields. The result of this calculation is plotted in Fig. A1 in the interval between 20 days and infinity (inf). Apparently, ensembles at the end of the 20-day experiments are not quite composed of random states.

Fig. A1.
Fig. A1.

Values for days 0 to 20 are the RMS of errors in estimates of half the difference between the ensemble mean υ300 response to two pulses caused by using 2000-member ensembles to estimate the ensemble means. The values between 20 and inf are the RMS of half the difference between two υ300 fields, each of which is found by averaging 2000 random draws from a control integration.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

Figure A1 shows how large our estimates of would be had we employed pulses that were vanishingly small in our experiments. So it is only the amount by which estimates of are larger than these values that we should consider to be caused by the effect of forcing with a finite-amplitude pulse. It is for this reason that in Fig. 5a we plot RMS values of minus Fig. A1’s estimate of the RMS of sampling errors. As an example of how large an effect this has, we show as the blue line in Fig. A2 the estimated RMS of in the regions poleward of 30°, while the dashed red line indicates the RMS due to sampling errors; that is, the red line is the RMS of values poleward of 30° in Fig. A1. The black dashed line is the difference of these two lines, which is also the RMS of values in Fig. 5a poleward of 30°. Clearly we would have substantially overestimated the response to the pulses for days beyond about 10 if we had not adjusted for the contribution from sampling errors.

Fig. A2.
Fig. A2.

Blue line: RMS amplitude of half the difference in the ensemble mean υ300 response between positive and negative pulses when evaluated poleward of 30°. Red dashed line: RMS amplitude of the sampling error for such estimates made from ensembles of size 2000. Black dotted line: the amount by which the blue line exceeds the red line, which corresponds to that part of the response estimate that is not caused by sampling errors.

Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00312.1

In a similar fashion estimates of the contribution from sampling errors are also removed from the quantities plotted in Figs. 5b, 9, 12a, and 12b.

REFERENCES

  • Blackmon, M. L., Y.-H. Lee, and J. M. Wallace, 1984: Horizontal structure of 500-mb height fluctuations with long, intermediate and short time scales. J. Atmos. Sci., 41, 961980, doi:10.1175/1520-0469(1984)041<0961:HSOMHF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1983: Horizontal energy propagation in a barotropic atmosphere with meridional and zonal structure. J. Atmos. Sci., 40, 16891708, doi:10.1175/1520-0469(1983)040<1689:HEPIAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, 22252241, doi:10.1175/1520-0469(1985)042<2225:AOGCMS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1990: Low-frequency patterns induced by stationary waves. J. Atmos. Sci., 47, 629649, doi:10.1175/1520-0469(1990)047<0629:LFPIBS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1995: Organization of storm track anomalies by recurring low-frequency circulation anomalies. J. Atmos. Sci., 52, 207226, doi:10.1175/1520-0469(1995)052<0207:OOSTAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 2002: Circumglobal teleconnections, the jet stream waveguide, and the North Atlantic Oscillation. J. Climate, 15, 18931910, doi:10.1175/1520-0442(2002)015<1893:CTTJSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cassou, C., 2008: Intraseasonal interaction between the Madden–Julian oscillation and the North Atlantic Oscillation. Nature, 455, 523527, doi:10.1038/nature07286.

    • Search Google Scholar
    • Export Citation
  • Collins, W. D., and Coauthors, 2006a: The formulation and atmospheric simulation of the Community Atmospheric Model version 3 (CAM3). J. Climate, 19, 21442161, doi:10.1175/JCLI3760.1.

    • Search Google Scholar
    • Export Citation
  • Collins, W. D., and Coauthors, 2006b: The Community Climate System Model version 3 (CCSM3). J. Climate, 19, 21222143, doi:10.1175/JCLI3761.1.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and B. Wang, 2005: Circumglobal teleconnections in the Northern Hemisphere summer. J. Climate, 18, 34833505, doi:10.1175/JCLI3473.1.

    • Search Google Scholar
    • Export Citation
  • Garcia, R., and M. Salby, 1987: Transient response to localized episodic heating in the tropics: Part II: Far-field response. J. Atmos. Sci., 44, 499532, doi:10.1175/1520-0469(1987)044<0499:TRTLEH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, doi:10.1175/1520-0469(1985)042<1037:SOJCRT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., and K. Bryan, 1997: A predictability study of simulated North Atlantic multidecadal variability. Climate Dyn., 13, 459488, doi:10.1007/s003820050177.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., and P. L. Silva Dias, 1995: Analysis of tropical–extratropical interactions with influence functions of a barotropic model. J. Atmos. Sci., 52, 35383555, doi:10.1175/1520-0469(1995)052<3538:AOTIWI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gritsun, A., and G. Branstator, 2007: Climate response using a three-dimensional operator based on the fluctuation–dissipation theorem. J. Atmos. Sci., 64, 25582575, doi:10.1175/JAS3943.1.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1976: Stochastic climate models. Part I: Theory. Tellus,28, 473–485, doi:10.1111/j.2153-3490.1976.tb00696.x.

  • Held, I. M., S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci., 46, 163174, doi:10.1175/1520-0469(1989)046<0163:TATERT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoerling, M. P., and A. Kumar, 2002: Atmospheric response patterns associated with tropical forcing. J. Climate, 15, 21842203, doi:10.1175/1520-0442(2002)015<2184:ARPAWT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and D. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38, 11791196, doi:10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and F.-F. Jin, 1991: The initial value problem for tropical perturbations to a baroclinic atmosphere. Quart. J. Roy. Meteor. Soc., 117, 299317, doi:10.1002/qj.49711749803.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., A. J. Simmons, and D. G. Andrews, 1977: Energy dispersion in a barotropic atmosphere. Quart. J. Roy. Meteor. Soc., 103, 553567, doi:10.1002/qj.49710343802.

    • Search Google Scholar
    • Export Citation
  • Hurrell, J., 1996: Influence of variations in extratropical wintertime teleconnections on Northern Hemisphere temperature. Geophys. Res. Lett., 23, 665668, doi:10.1029/96GL00459.

    • Search Google Scholar
    • Export Citation
  • Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci., 52, 307319, doi:10.1175/1520-0469(1995)052<0307:TDRTTH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., A. J. Majda, and S. N. Stechmann, 2013: Climate science in the tropics: Waves, vortices and PDEs. Nonlinearity, 26, R1R68, doi:10.1088/0951-7715/26/1/R1.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., and K. M. Weickmann, 1992: Circulation anomalies associated with tropical convection during northern winter. Mon. Wea. Rev., 120, 19001923, doi:10.1175/1520-0493(1992)120<1900:CAAWTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., and K. M. Weickmann, 1997: Horizontal structure and seasonality of large-scale circulations associated with submonthly tropical convection. Mon. Wea. Rev., 125, 19972013, doi:10.1175/1520-0493(1997)125<1997:HSASOL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Knutson, T., and K. Weickmann, 1987: 30–60 day atmospheric oscillation: Composite life cycles of convection and circulation anomalies. Mon. Wea. Rev., 115, 14071436, doi:10.1175/1520-0493(1987)115<1407:DAOCLC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kok, C., and J. Opsteegh, 1985: Possible causes of anomalies in seasonal mean circulation patterns during the 1982–83 El Niño event. J. Atmos. Sci., 42, 677694, doi:10.1175/1520-0469(1985)042<0677:PCOAIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, 27182743, doi:10.1175/1520-0469(1988)045<2718:VOTOMS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc., 77, 12751277.

    • Search Google Scholar
    • Export Citation
  • Lin, H., 2009: Global extratropical response to diabatic heating variability of the Asian summer monsoon. J. Atmos. Sci., 66, 26972713, doi:10.1175/2009JAS3008.1.

    • Search Google Scholar
    • Export Citation
  • Matthews, A. J., B. J. Hoskins, and M. Masutani, 2004: The global response to tropical heating in the Madden–Julian oscillation during the northern winter. Quart. J. Roy. Meteor. Soc., 130, 19912011, doi:10.1256/qj.02.123.

    • Search Google Scholar
    • Export Citation
  • Raupp, C. F. M., and P. L. Silva Dias, 2009: Resonant wave interactions in the presence of a diurnally varying heat source. J. Atmos. Sci., 66, 31653183, doi:10.1175/2009JAS2899.1.

    • Search Google Scholar
    • Export Citation
  • Roundy, P., K. MacRitchie, J. Asuma, and T. Melino, 2010: Modulation of the global atmospheric circulation by combined activity in the Madden–Julian oscillation and the El Niño–Southern Oscillation during boreal winter. J. Climate, 23, 40464059, doi:10.1175/2010JCLI3446.1.

    • Search Google Scholar
    • Export Citation
  • Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized tropical divergence. J. Atmos. Sci., 45, 12281251, doi:10.1175/1520-0469(1988)045<1228:TGOGRF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., H. Wang, and M. Suarez, 2011: Warm season subseasonal variability and climate extremes in the Northern Hemisphere: The role of stationary Rossby waves. J. Climate, 24, 47734792, doi:10.1175/JCLI-D-10-05035.1.

    • Search Google Scholar
    • Export Citation
  • Shin, S.-I., P. D. Sardeshmukh, and R. S. Webb, 2010: Optimal tropical sea surface temperature forcing of North American drought. J. Climate, 23, 39073917, doi:10.1175/2010JCLI3360.1.

    • Search Google Scholar
    • Export Citation
  • Silva Dias, P., W. Schubert, and M. DeMaria, 1983: Large-scale response of the tropical atmosphere to transient convection. J. Atmos. Sci., 40, 26892707, doi:10.1175/1520-0469(1983)040<2689:LSROTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., J. M. Wallace, and G. W. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci., 40, 13631392, doi:10.1175/1520-0469(1983)040<1363:BWPAIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Teng, H., G. Branstator, H. Wang, G. A. Meehl, and W. M. Washington, 2013: Probability of U.S. heat waves affected by a subseasonal planetary wave pattern. Nat. Geosci., 6, 10561061, doi:10.1038/ngeo1988.

    • Search Google Scholar
    • Export Citation
  • Ting, M., and P. D. Sardeshmukh, 1993: Factors determining the extratropical response to equatorial diabatic heating anomalies. J. Atmos. Sci., 50, 907918, doi:10.1175/1520-0469(1993)050<0907:FDTERT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vitart, F., 2014: Evolution of ECMWF sub-seasonal forecast skill score. Quart. J. Roy. Meteor. Soc., 140, 18891899, doi:10.1002/qj.2256.

    • Search Google Scholar
    • Export Citation
  • Waliser, D., and Coauthors, 2012: The “year” of tropical convection (May 2008–April 2012): Climate variability and weather highlights. Bull. Amer. Meteor. Soc., 93, 11891218, doi:10.1175/2011BAMS3095.1.

    • Search Google Scholar
    • Export Citation
  • Xie, P., and P. A. Arkin, 1998: Global monthly precipitation estimates from satellite-observed outgoing longwave radiation. J. Climate, 11, 137164, doi:10.1175/1520-0442(1998)011<0137:GMPEFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., and B. Hoskins, 1996: Propagation of Rossby waves of nonzero frequency. J. Atmos. Sci., 53, 23652377, doi:10.1175/1520-0469(1996)053<2365:PORWON>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
1

Here and elsewhere where it is appropriate area weighting has been employed.

Save
  • Blackmon, M. L., Y.-H. Lee, and J. M. Wallace, 1984: Horizontal structure of 500-mb height fluctuations with long, intermediate and short time scales. J. Atmos. Sci., 41, 961980, doi:10.1175/1520-0469(1984)041<0961:HSOMHF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1983: Horizontal energy propagation in a barotropic atmosphere with meridional and zonal structure. J. Atmos. Sci., 40, 16891708, doi:10.1175/1520-0469(1983)040<1689:HEPIAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, 22252241, doi:10.1175/1520-0469(1985)042<2225:AOGCMS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1990: Low-frequency patterns induced by stationary waves. J. Atmos. Sci., 47, 629649, doi:10.1175/1520-0469(1990)047<0629:LFPIBS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 1995: Organization of storm track anomalies by recurring low-frequency circulation anomalies. J. Atmos. Sci., 52, 207226, doi:10.1175/1520-0469(1995)052<0207:OOSTAB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Branstator, G., 2002: Circumglobal teleconnections, the jet stream waveguide, and the North Atlantic Oscillation. J. Climate, 15, 18931910, doi:10.1175/1520-0442(2002)015<1893:CTTJSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cassou, C., 2008: Intraseasonal interaction between the Madden–Julian oscillation and the North Atlantic Oscillation. Nature, 455, 523527, doi:10.1038/nature07286.

    • Search Google Scholar
    • Export Citation
  • Collins, W. D., and Coauthors, 2006a: The formulation and atmospheric simulation of the Community Atmospheric Model version 3 (CAM3). J. Climate, 19, 21442161, doi:10.1175/JCLI3760.1.

    • Search Google Scholar
    • Export Citation
  • Collins, W. D., and Coauthors, 2006b: The Community Climate System Model version 3 (CCSM3). J. Climate, 19, 21222143, doi:10.1175/JCLI3761.1.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and B. Wang, 2005: Circumglobal teleconnections in the Northern Hemisphere summer. J. Climate, 18, 34833505, doi:10.1175/JCLI3473.1.

    • Search Google Scholar
    • Export Citation
  • Garcia, R., and M. Salby, 1987: Transient response to localized episodic heating in the tropics: Part II: Far-field response. J. Atmos. Sci., 44, 499532, doi:10.1175/1520-0469(1987)044<0499:TRTLEH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, doi:10.1175/1520-0469(1985)042<1037:SOJCRT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., and K. Bryan, 1997: A predictability study of simulated North Atlantic multidecadal variability. Climate Dyn., 13, 459488, doi:10.1007/s003820050177.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., and P. L. Silva Dias, 1995: Analysis of tropical–extratropical interactions with influence functions of a barotropic model. J. Atmos. Sci., 52, 35383555, doi:10.1175/1520-0469(1995)052<3538:AOTIWI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gritsun, A., and G. Branstator, 2007: Climate response using a three-dimensional operator based on the fluctuation–dissipation theorem. J. Atmos. Sci., 64, 25582575, doi:10.1175/JAS3943.1.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1976: Stochastic climate models. Part I: Theory. Tellus,28, 473–485, doi:10.1111/j.2153-3490.1976.tb00696.x.

  • Held, I. M., S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci., 46, 163174, doi:10.1175/1520-0469(1989)046<0163:TATERT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoerling, M. P., and A. Kumar, 2002: Atmospheric response patterns associated with tropical forcing. J. Climate, 15, 21842203, doi:10.1175/1520-0442(2002)015<2184:ARPAWT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and D. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38, 11791196, doi:10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., and F.-F. Jin, 1991: The initial value problem for tropical perturbations to a baroclinic atmosphere. Quart. J. Roy. Meteor. Soc., 117, 299317, doi:10.1002/qj.49711749803.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., A. J. Simmons, and D. G. Andrews, 1977: Energy dispersion in a barotropic atmosphere. Quart. J. Roy. Meteor. Soc., 103, 553567, doi:10.1002/qj.49710343802.

    • Search Google Scholar
    • Export Citation
  • Hurrell, J., 1996: Influence of variations in extratropical wintertime teleconnections on Northern Hemisphere temperature. Geophys. Res. Lett., 23, 665668, doi:10.1029/96GL00459.

    • Search Google Scholar
    • Export Citation
  • Jin, F., and B. J. Hoskins, 1995: The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci., 52, 307319, doi:10.1175/1520-0469(1995)052<0307:TDRTTH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., A. J. Majda, and S. N. Stechmann, 2013: Climate science in the tropics: Waves, vortices and PDEs. Nonlinearity, 26, R1R68, doi:10.1088/0951-7715/26/1/R1.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., and K. M. Weickmann, 1992: Circulation anomalies associated with tropical convection during northern winter. Mon. Wea. Rev., 120, 19001923, doi:10.1175/1520-0493(1992)120<1900:CAAWTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., and K. M. Weickmann, 1997: Horizontal structure and seasonality of large-scale circulations associated with submonthly tropical convection. Mon. Wea. Rev., 125, 19972013, doi:10.1175/1520-0493(1997)125<1997:HSASOL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Knutson, T., and K. Weickmann, 1987: 30–60 day atmospheric oscillation: Composite life cycles of convection and circulation anomalies. Mon. Wea. Rev., 115, 14071436, doi:10.1175/1520-0493(1987)115<1407:DAOCLC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kok, C., and J. Opsteegh, 1985: Possible causes of anomalies in seasonal mean circulation patterns during the 1982–83 El Niño event. J. Atmos. Sci., 42, 677694, doi:10.1175/1520-0469(1985)042<0677:PCOAIS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, 27182743, doi:10.1175/1520-0469(1988)045<2718:VOTOMS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liebmann, B., and C. A. Smith, 1996: Description of a complete (interpolated) outgoing longwave radiation dataset. Bull. Amer. Meteor. Soc., 77, 12751277.

    • Search Google Scholar
    • Export Citation
  • Lin, H., 2009: Global extratropical response to diabatic heating variability of the Asian summer monsoon. J. Atmos. Sci., 66, 26972713, doi:10.1175/2009JAS3008.1.

    • Search Google Scholar
    • Export Citation
  • Matthews, A. J., B. J. Hoskins, and M. Masutani, 2004: The global response to tropical heating in the Madden–Julian oscillation during the northern winter. Quart. J. Roy. Meteor. Soc., 130, 19912011, doi:10.1256/qj.02.123.

    • Search Google Scholar
    • Export Citation
  • Raupp, C. F. M., and P. L. Silva Dias, 2009: Resonant wave interactions in the presence of a diurnally varying heat source. J. Atmos. Sci., 66, 31653183, doi:10.1175/2009JAS2899.1.

    • Search Google Scholar
    • Export Citation
  • Roundy, P., K. MacRitchie, J. Asuma, and T. Melino, 2010: Modulation of the global atmospheric circulation by combined activity in the Madden–Julian oscillation and the El Niño–Southern Oscillation during boreal winter. J. Climate, 23, 40464059, doi:10.1175/2010JCLI3446.1.

    • Search Google Scholar
    • Export Citation
  • Sardeshmukh, P. D., and B. J. Hoskins, 1988: The generation of global rotational flow by steady idealized tropical divergence. J. Atmos. Sci., 45, 12281251, doi:10.1175/1520-0469(1988)045<1228:TGOGRF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., H. Wang, and M. Suarez, 2011: Warm season subseasonal variability and climate extremes in the Northern Hemisphere: The role of stationary Rossby waves. J. Climate, 24, 47734792, doi:10.1175/JCLI-D-10-05035.1.

    • Search Google Scholar
    • Export Citation
  • Shin, S.-I., P. D. Sardeshmukh, and R. S. Webb, 2010: Optimal tropical sea surface temperature forcing of North American drought. J. Climate, 23, 39073917, doi:10.1175/2010JCLI3360.1.

    • Search Google Scholar
    • Export Citation
  • Silva Dias, P., W. Schubert, and M. DeMaria, 1983: Large-scale response of the tropical atmosphere to transient convection. J. Atmos. Sci., 40, 26892707, doi:10.1175/1520-0469(1983)040<2689:LSROTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., J. M. Wallace, and G. W. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci., 40, 13631392, doi:10.1175/1520-0469(1983)040<1363:BWPAIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Teng, H., G. Branstator, H. Wang, G. A. Meehl, and W. M. Washington, 2013: Probability of U.S. heat waves affected by a subseasonal planetary wave pattern. Nat. Geosci., 6, 10561061, doi:10.1038/ngeo1988.

    • Search Google Scholar
    • Export Citation
  • Ting, M., and P. D. Sardeshmukh, 1993: Factors determining the extratropical response to equatorial diabatic heating anomalies. J. Atmos. Sci., 50, 907918, doi:10.1175/1520-0469(1993)050<0907:FDTERT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vitart, F., 2014: Evolution of ECMWF sub-seasonal forecast skill score. Quart. J. Roy. Meteor. Soc., 140, 18891899, doi:10.1002/qj.2256.

    • Search Google Scholar
    • Export Citation
  • Waliser, D., and Coauthors, 2012: The “year” of tropical convection (May 2008–April 2012): Climate variability and weather highlights. Bull. Amer. Meteor. Soc., 93, 11891218, doi:10.1175/2011BAMS3095.1.

    • Search Google Scholar
    • Export Citation
  • Xie, P., and P. A. Arkin, 1998: Global monthly precipitation estimates from satellite-observed outgoing longwave radiation. J. Climate, 11, 137164, doi:10.1175/1520-0442(1998)011<0137:GMPEFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yang, G.-Y., and B. Hoskins, 1996: Propagation of Rossby waves of nonzero frequency. J. Atmos. Sci., 53, 23652377, doi:10.1175/1520-0469(1996)053<2365:PORWON>2.0.CO;2.

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

    (a) Variance of daily values of OLR for the months of December, January, February, and March. The contour interval is 200 W2 m−4 with a maximum value of 1800 W2 m−4. (b) Ratio of variance of DJFM seasonal mean OLR to variance of daily values. The contour interval is 0.1 with a maximum value of 0.6. The plots use OLR departures from the climatological mean of each individual month.

  • Fig. 2.

    Time series of daily OLR anomalies from the seasonal average during (a) December 1985–March 1986 and (b) December 1976–March 1977 averaged in a 22° lon × 9° lat box centered on the equator at 90°E. For the right-hand scale OLR has been converted to a column-average atmospheric heating rate based on the assumption that 1 W m−2 equals 0.09 mm day−1 of rainfall (Xie and Arkin 1998).

  • Fig. 3.

    Ensemble mean υ300 response in CAM3 to a 2-day pulse of heat at 0°N, 135°E (a) 3, (b) 6, and (c) 9 days after the pulse begins. (d)–(f) As in (a)–(c), but for a pulse at 0°N, 120°W.

  • Fig. 4.

    RMS response of ensemble mean υ300 to a 2-day pulse (a) 3 days and (b) 6 days after the pulse begins. These correspond to 24 cases in which the pulses are located at different equatorial locations separated by 15°. The response for each case is longitudinally translated to the longitude indicated by 0°, and then the RMS of these is plotted.

  • Fig. 5.

    RMS response of ensemble mean υ300 to 2-day pulses. (a) As a function of time after the pulses are initiated, fields analogous to those in Fig. 4 are calculated and then the RMS of these fields at each latitude is plotted. (b) As in (a), except the RMS of values between 30° and 60°N is plotted at each longitude.

  • Fig. 6.

    “Days” refers to the time after a 2-day equatorial pulse is initiated. Blue line: average, over 24 cases, of the pattern correlation between the ensemble mean υ300 response to a pulse and the steady response to a steady source at the same location. Red dashed line: average pattern correlation between ensemble mean υ300 at the indicated time and the response 2 days later. Black dotted line: average response amplitude to a pulse. As described in the appendix, the plotted quantity corresponds to the amount by which the average amplitude exceeds the amplitude expected from sampling errors. Pattern correlations and amplitudes in this figure are for locations poleward of 30°.

  • Fig. 7.

    (a) Ensemble mean, January mean, υ300 response to a steady heat source at 0°N, 135°E. (b) Ensemble mean υ300 response to a sequence of 2-day pulses that begin 2, 4, …, 20 days before the response time. (c) As in (b), but only pulses beginning 4, 6, …, 14 days before the response time are included.

  • Fig. 8.

    Red line: average spectrum of heating consisting of a long sequence of collections of 24 pulses, each lasting 2 days and each having a random amplitude. Blue line: average spectrum of the ensemble mean υ300 response to heating consisting of equatorial pulses like those used to calculate the red line. These spectra have been evaluated at frequencies i (100 days)−1, i = 1, …, 100, and the “fraction of variance” is with respect to the total variance in these 100 frequencies.

  • Fig. 9.

    (a) RMS of the 300-hPa streamfunction response between 30° and 60°N to pulses at 24 equatorial longitudes. (b) As in (a), but for the steady response to steady heating at the same 24 locations.

  • Fig. 10.

    Leading EOF of the responses of 300-hPa streamfunction, with its zonal mean removed, to 2-day pulses at 24 equatorial locations (a) 3 days, (b) 6 days, and (c) 9 days after the pulses begin. (d) As in (a)–(c), but for the steady response to heating at the same 24 locations.

  • Fig. 11.

    The 30°–60°N latitudinal average ensemble mean υ300 response to a 2-day pulse located at each of 24 longitudes, which are indicated by the y axis. Plotted are the response (a) 5 days, (b) 9 days, and (c) 13 days after the pulse heating begins. (d) As in (a)–(c), for the steady response to steady heating. The plotted fields have been smoothed to emphasize the large-scale features.

  • Fig. 12.

    (a) As in Fig. 5a, but for sea level pressure. (b) As in (a), but for the variance of departures from running 4.5-day mean 300-hPa streamfunction.

  • Fig. 13.

    Ensemble mean response of (top) sea level pressure, (middle) 2-m temperature, and (bottom) variance of synoptic eddies to a 2-day pulse at 0°N, 135°E (left) 3 days, (middle) 6 days, and (right) 9 days after the pulse begins. Contour intervals are 0.1 hPa, 0.05°C, and 4 × 1011 m2 s−1, respectively.

  • Fig. A1.

    Values for days 0 to 20 are the RMS of errors in estimates of half the difference between the ensemble mean υ300 response to two pulses caused by using 2000-member ensembles to estimate the ensemble means. The values between 20 and inf are the RMS of half the difference between two υ300 fields, each of which is found by averaging 2000 random draws from a control integration.

  • Fig. A2.

    Blue line: RMS amplitude of half the difference in the ensemble mean υ300 response between positive and negative pulses when evaluated poleward of 30°. Red dashed line: RMS amplitude of the sampling error for such estimates made from ensembles of size 2000. Black dotted line: the amount by which the blue line exceeds the red line, which corresponds to that part of the response estimate that is not caused by sampling errors.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 807 132 2
PDF Downloads 418 109 7