Abstract

This study investigates the North Atlantic Oscillation (NAO) events with relatively long and short lifetimes based on an 8000-day perpetual-boreal-winter [December–February (DJF)] run result of the idealized Geophysical Fluid Dynamics Laboratory (GFDL) dynamical core atmospheric model. We identify the so-called long- and short-lived positive and negative NAO events from the 8000-day model output. The composite 300-hPa geopotential height anomalies show that the spatial patterns of the composite long-lived NAO events closely resemble the Northern Hemisphere annular mode (NAM) because the NAO dipole is accompanied with a statistically significant North Pacific meridional dipole (NPMD) at similar latitudes as that of the NAO dipole. The composite short-lived NAO events exhibit the locally confined canonical NAO. Twelve sets of modified initial-value experiments indicate that an absence (a presence) of the NPMD-type perturbations at the early stage of the long (short)-lived NAO events will decrease (increase) their intensities and naturally shorten (lengthen) their lifetimes. Thus, the preceding NPMD is an early factor that is conducive to the emergence of the long-lived NAO events in the model. We argue that through directly modulating the synoptic eddy forcing over the North Atlantic region, the preceding NPMD can gradually arouse the NAO-like circulation anomalies on the following days. That is the reason why the preceding NPMD can modulate the intensities and lifetimes of the NAO events.

1. Introduction

The North Atlantic Oscillation (NAO), the dominant low-frequency atmospheric mode over the North Atlantic (NA) sector, is characterized by a planetary-scale zonally localized meridional dipole mode, which corresponds to a meridional meander of the eddy-driven Atlantic jet and a large-scale redistribution of air mass between the Azores subtropical high and Iceland low pressure (Walker 1924; Wallace and Gutzler 1981). Although the NAO is considered as a localized phenomenon confined to the NA region, it has much influence on the atmosphere, ocean, and sea ice over the entire Northern Hemisphere (NH; Hurrell 1995; Hurrell et al. 2003). Some studies also treated the NAO as a regional expression of a hemispheric-scale atmospheric meridional dipolar mode: the Northern Hemisphere annular mode (NAM; Wallace 2000).1 Feldstein and Franzke (2006) argued that the behaviors of the NAO and the NAM are virtually indistinguishable.

The NAO contains a broad spectrum of variations from intraseasonal to interdecadal time scales but without any preferred time scales (Feldstein 2000). In the troposphere, the temporal variability of the NAO resembles a Markov process with an e-folding time scale of ~10 days (Feldstein 2000). This result implies that the NAO can be interpreted as a stochastic process in intraseasonal time scales. The characteristic time scale of a typical life cycle (growth and decay) of NAO events is estimated to be on the order of 10–15 days (Feldstein 2000, 2003). Therefore, the physical essence of the NAO is considered lying in intraseasonal time scales. However, in early studies, the NAO is normally studied by using monthly or seasonal mean data, which, obviously, suppresses the stochastic intraseasonal time-scale variability of the NAO greatly (e.g., van Loon and Rogers 1978; Wallace and Gutzler 1981; Barnston and Livezey 1987; Kushnir and Wallace 1989).

In recent years, many studies concerned about the NAO had drawn their attention to examine the fundamental mechanisms that determine the evolution of the NAO events by using daily reanalysis data or daily output of numerical simulations (Feldstein 2003; Benedict et al. 2004; Luo et al. 2007; Rivière and Orlanski 2007; Kunz et al. 2009; Barnes and Hartmann 2010; Jiang et al. 2013; Dai et al. 2016; Song 2016). Results of these studies indicated that the anomalous synoptic eddy forcing accompanied with the NAO over the NA region plays a key role in driving/maintaining the NAO. Thus, the variability of the NAO should be largely determined by local midlatitude tropospheric dynamics of the NA region. However, several studies pointed out that at least a part of the NAO’s variability is also influenced by upstream tropospheric circulation anomalies over the eastern North Pacific via modulating the seeding of downstream-propagating transient disturbances (Franzke et al. 2004; Rivière and Orlanski 2007; Strong and Magnusdottir 2008; Song et al. 2009; Li and Lau 2012a,b; Drouard et al. 2013, 2015; Rivière and Drouard 2015).

Moreover, evidence has accumulated that stratospheric variabilities, particularly those associated with the stratospheric polar vortex, can have a significant impact on the troposphere (Kidston et al. 2015; Waugh et al. 2017). In theNH, this dynamical coupling between the stratosphere and the troposphere is primarily manifested as a NAM-/NAO-like stratospheric anomalous circulation descending with time (Baldwin and Dunkerton 1999). Therefore, the stratosphere is another source that can modulate the variability of the NAO. In addition to the stratospheric variabilities, in the real atmosphere, many external factors such as tropical forcing (Cassou 2008; Lin et al. 2009, 2010; Li and Lau 2012a,b; Jiang et al. 2017; Zhang et al. 2019), SST variability at midlatitudes of North Atlantic (Czaja and Frankignoul 2002; Kushnir et al. 2002; Peng et al. 2003), volcanic aerosols (Stenchikov et al. 2002), anthropogenic forcing (Ulbrich and Christoph 1999; Woollings et al. 2010), and even variations in solar activity (Shindell et al. 2001) can influence the NAO’s phase, amplitude, and variability as well.

Although Feldstein (2003) reported that the typical life cycle of the NAO events is within about 2 weeks, durations of the observed NAO events exhibit a high variability from case to case. Some NAO events have a lifetime far longer than 2 weeks (e.g., see Fig. 3 of Rivière and Orlanski 2007), while some NAO events have a lifetime less than 1 week (e.g., see Fig. 1 of Benedict et al. 2004). Therefore, one might argue that there are long- and short-lived NAO events, respectively. According to the author’s knowledge, however, few attempts have been made on this subject yet.

In the present study, we will investigate the so-called long- and short-lived NAO events based upon a long-term run result of a simplified dry atmospheric model. The main purposes of this study are as follows: 1) explore the differences of tropospheric circulations between the long- and short-lived NAO events in that model and 2) disclose the tropospheric precursor that is conducive to the emergence of the long-lived NAO events in that model. The main reason that we focus on the NAO event in a simplified model rather than in observations is because this model excludes all of external factors and depicts tropospheric dynamical characteristics of the NAO well (the model is detailed in section 2). Therefore, the use of this simplified model enables us to avoid the unnecessary interferences of external factors and concentrate on the atmospheric internal dynamics itself.

The remainder of this paper is organized as follows. In section 2, the model, the data, and a vorticity budget equation used in this study are briefly described. Section 3 delineates definitions and features of the long- and short-lived NAO events. The tropospheric precursor that favors the emergence of the long-lived NAO events is unveiled and verified in section 4. A physical understanding about how the revealed tropospheric precursor favors the emergence of the long-lived NAO events is presented in section 5. Possible effects of the stratosphere on the long-lived NAO events are discussed in section 6. The last section contains conclusions and discussion of this study.

2. Methods

a. Model

The model’s data used to examine the long- and short-lived NAO events are generated from an 8000-day perpetual-boreal-winter [December–February (DJF)] run2 performed by the Geophysical Fluid Dynamics Laboratory (GFDL) dynamical core atmospheric model (Held and Suarez 1994, hereafter HS94). This experiment is carried out with a horizontal resolution of T42, using 20 evenly spaced sigma levels in the vertical. The original model is a dry, sigma-coordinate (σ = p/ps) primitive-equation spectral model on a sphere driven by Newtonian relaxation toward an ideal zonally symmetric equilibrium temperature profile Teq of HS94. Obviously, it is not capable of simulating the NAO since the resulting climatological mean circulations and storm tracks are highly ideal and zonally symmetric.

Song (2016) modified this model by using a procedure developed by Chang (2006) and Chang and Zurita-Gotor (2007). The modification includes incorporating a full topography into the model and using the observed three-dimensional DJF time-mean temperature distribution with a reduced static stability (1.25 K km−1) plus an additional constant nonlinear diabatic heating field Q as Teq to drive the model. This Q is assumed to mimic the atmosphere releasing latent heating. It is obtained by iteratively running the model 35 times (in each integration, the model is run for 1200 days) starting from a first guess of Q0 = 0. After this modification, the model can realistically reproduce observed boreal-winter background circulations, storm tracks, and general dynamical properties of the NAO (see Figs. 1 and 2 of Song 2016).

The NAO pattern in the model are defined as the leading empirical orthogonal function mode (EOF1) of the 8000-day model’s sea level pressure (SLP) anomalies over the NA region (20°–85°N, 90°W–50°E). Its explained variance is 22.86%. The daily NAO index (NAOI) is defined as the corresponding normalized first principal component (PC1). The anomalies in the model are departures from the time mean of the entire 8000-day integration period since there is not the seasonal cycle in the model. Before performing the EOF analysis, the SLP anomalies were area weighted by the square root of the cosine of latitude to account for the decrease in grid area toward the pole. A similar analysis is also used to acquire the NAM pattern and the corresponding daily NAM index (NAMI) in the model. For the NAM, the EOF’s calculation domain is the NH (20°–90°N, 0°–360°). The explained variance of the NAM is 16.65%.

b. Data

Besides the model’s output, this study also uses two sets of reanalysis daily data including National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (NCEP-1; Kalnay et al. 1996) data and 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005) data. The horizontal resolution of these two sets of data is 2.5° × 2.5°. The time period that the data cover is 62 boreal winters (DJF) from 1948/49 to 2009/10 for NCEP-1 and 45 boreal winters from 1957/58 to 2001/02 for ERA-40. In both NCEP-1 and ERA-40, 29 February in each leap year has been removed. Therefore, that is 5580 days for NCEP-1 and 4050 days for ERA-40 in all. In this study, the term “anomaly” of NCEP-1 (ERA-40) is defined as the deviation from a seasonal cycle, which is the time mean of each calendar day in those 62 (45) boreal winters.

As the model, the same EOF analyses are used to acquire the NAO and NAM patterns in NCEP-1 and ERA-40 and their corresponding daily index. For NCEP-1 and ERA-40, the EOF’s calculation periods are the 62 (from 1948/49 to 2009/10) and 45 (from 1957/58 to 2001/02) boreal winters. The NAO’s explained variance is 19.38% for NCEP-1 and 19.11% for ERA-40. The explained variance of the NAM is 10.29% for NCEP-1 and 10.35% for ERA-40.

Figures 1 and 2 show, respectively, the patterns of the NAM and the NAO at the surface and upper troposphere by regressing the daily NAMI and NAOI onto the SLP and 300-hPa geopotential height anomalies for NCEP-1, ERA-40, and the model. It is clear that the NAM pattern is more zonally symmetric consisting of two zonally elongated meridional dipoles, one located in the North Pacific (NP) region (20°–85°N, 120°E–100°W), and the other located in the NA region, which obviously corresponds to the NAO. In Fig. 2, we see that the NAO’s localized quasi-barotropic meridional dipole over the NA region is well simulated in the model. However, for the model’s NAO, the meridional dipole over the NA region is simultaneously accompanied with a relatively weaker meridional dipole over the NP region. Thus, the spatial pattern of the NAO in the model bears some resemblance to that of the NAM (see Figs. 2e and 2f). That is the main differences of the NAO’s pattern between the model and the observations. Note that the model used in this study is a simplified dry atmospheric model, which only includes idealized physical parameterizations and excludes other external forcing. Therefore, the lifetimes of the NAO events in the model are entirely determined by the internal dynamics of atmosphere.

Fig. 1.

Daily NAM index–regressed anomalous (a) sea level pressure (SLP) and (b) 300-hPa geopotential height in NCEP-1 data. (c),(d) As in (a) and (b), but for ERA-40 data. (e),(f) As in (a) and (b), but for the long-term GFDL model simulation. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 2 hPa for (a), (c), and (e) and 20 gpm for (b), (d), and (f).

Fig. 1.

Daily NAM index–regressed anomalous (a) sea level pressure (SLP) and (b) 300-hPa geopotential height in NCEP-1 data. (c),(d) As in (a) and (b), but for ERA-40 data. (e),(f) As in (a) and (b), but for the long-term GFDL model simulation. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 2 hPa for (a), (c), and (e) and 20 gpm for (b), (d), and (f).

Fig. 2.

As in Fig. 1, but for the daily NAO index–regressed results.

Fig. 2.

As in Fig. 1, but for the daily NAO index–regressed results.

c. Vorticity budget equation

This study also utilizes a vorticity budget analysis to evaluate the relative importance of various dynamical processes in the formation of an anomalous circulation pattern. This vorticity budget analysis is based on a streamfunction tendency equation, which is

 
ψt=i=17ξi+residual,
(1)

where

 
ξ1=2(u¯ζx),ξ2=2(υ¯ζy),ξ3=2(uζ¯x),ξ4=2[υ(ζ¯y+β)],ξ5=2[ζ(u¯x+υ¯y)],ξ6=2[(ζ¯+f)(ux+υy)],ξ7=2[(Uζ)].
(2)

The residual is the residual component such as frictional dissipation and tilting term, ψ the streamfunction, U the horizontal wind vector, u and υ the zonal and meridional component of U, ζ the relative vorticity, f the Coriolis parameter, and β the planetary vorticity gradient. Overbar and prime symbol denote time mean and its departure, respectively. Briefly, ξ1 (ξ2) is the zonal (meridional) advection of anomalous vorticity by the background flows, ξ3 (ξ4) the zonal (meridional) advection of background vorticity by the anomalous flows, ξ5 and ξ6 the divergence term, and ξ7 the eddy vorticity forcing (EVF) term. It is noted that first six terms ξi, with i = (1, … ,6), represent linear processes, while ξ7 is the nonlinear term.

3. Long- and short-lived NAO events in the model

In this section, the different characteristics of the long- and short-lived NAO events in the model are compared and discussed.

Based on the model’s 8000-day NAOI dataset, the positive and negative NAO events are identified using a three-step procedure. 1) We search the maximum (minimum) of the daily NAOI dataset. If the maximum (minimum) found is greater (less) or equal to 1.0 (−1.0), then a positive (negative) NAO event is considered as have taken place. The day with the maximum (minimum) is defined as lag 0 day, that is, the peak or mature day of this positive (negative) NAO event. 2) The NAOI from lag −10 to 10 days of this NAO event are removed from the daily NAOI dataset. Here, lag −x days and lag +x days denotes x days before and after lag 0 day. 3) After that, the same search for the next maximum (minimum) is conducted in the rest of the daily NAOI dataset. This three-step procedure continues to cycle until the maximum (minimum) found is no longer ≥1.0 (≤−1.0). Through this procedure, 119 positive and 114 negative NAO events are identified from the 8000-day model output.

Figure 3 shows the time series of the daily NAOI from lag −10 to 10 days for each individual identified positive and negative NAO event (black thin lines). The typical temporal evolutions of the daily NAOI in the positive and negative NAO events are also depicted by showing the composite time series of the daily NAOI (red thick lines). Obviously, for both the positive and negative NAO events, the composite time series of the daily NAOI from lag −10 to 10 days exhibit a monotonous growth and decay. We define the lifetime of a positive (negative) NAO event as the number of days that the NAOI before and after the peak day are persistently ≥0.5 (≤−0.5). According to this lifetime definition, Fig. 3 shows that the lifetime of the composite positive (negative) NAO events is 14 (12) days, which is consistent well with the results of Feldstein (2003) that the typical life cycle of the NAO events is within about 2 weeks. Besides that, the peak amplitude of the NAOI for the composite positive (negative) NAO events is about 1.80 (−1.66). Thus, there is a minor asymmetry existing in the model’s positive and negative NAO events that the positive NAO events has a longer persistence and larger peak amplitude. However, it should point out that the asymmetry of the composite model’s NAO events is contrasted to its observational counterpart. Luo et al. (2018) reported that, in observations, on average, it is the negative NAO events, rather than the positive NAO events, that have a stronger peak amplitude and better persistence (see Fig. 3 of Luo et al. 2018).

Fig. 3.

Time series of the daily NAO index (black thin curves) for the individual (a) positive and (b) negative NAO events from lag −10 to 10 days. Red thick curves are their respective composite results. Pale green dashed line denotes the value of 0.5 in (a) and −0.5 in (b).

Fig. 3.

Time series of the daily NAO index (black thin curves) for the individual (a) positive and (b) negative NAO events from lag −10 to 10 days. Red thick curves are their respective composite results. Pale green dashed line denotes the value of 0.5 in (a) and −0.5 in (b).

Based on the length of the lifetime of each NAO event, now, the so-called long- and short-lived NAO events can be sorted out from the 119 positive and 114 negative NAO events. Before we conduct such analyses, it is helpful to evaluate the probability distributions of the length of the lifetimes of the NAO events first. The number of occurrence of the positive and negative NAO events with a lifetime of 3–21 days are calculated. It should be acknowledged that, here, the number of occurrences of the NAO events with a 21-day lifetime actually include those NAO events with a lifetime longer than 21 days, since individual identified NAO events only cover 21 days of data. Figure 4 shows their probability distributions in terms of the percentage of occurrence, which is equal to the number of occurrences of the positive (negative) NAO events with a certain lifetime divided by the total number of the positive (negative) NAO events and then multiplied by 100. Clearly, the NAO events with a lifetime of 13 days have the highest probability of occurrence for both the positive and negative NAO events. Around 12% of the NAO events have this lifetime. The NAO events with the second highest probability of occurrence are those with a lifetime no shorter than 21 days (around 11%). Generally speaking, the percentage of occurrence of the positive (negative) NAO events with a lifetime no longer than 8 days is about 27.7% (24.5%). This number is about 26.9% (28.0%) for those positive (negative) NAO events with a lifetime no shorter than 16 days. Thus, the occurrence of the NAO events with a relatively long or short lifetime is by no means rare.

Fig. 4.

The percentage of occurrence of the (a) positive and (b) negative NAO events with a lifetime of 3–21 days.

Fig. 4.

The percentage of occurrence of the (a) positive and (b) negative NAO events with a lifetime of 3–21 days.

We normalized the time series of the lifetime of the 119 positive NAO events. Then, taking 0.8 (−0.8) as a threshold,3 there are 28 (26) positive NAO events being identified as the long-lived (short-lived) positive NAO events. Similar analyses are also conducted but for the 114 negative NAO events, with the result that 25 (32) negative NAO events are selected as the long-lived (short-lived) negative NAO events. Hereafter, the long-lived positive and negative NAO events are respectively denoted as NAO+_LE and NAO−_LE for short. The short-lived positive and negative NAO events are denoted as NAO+_SE and NAO−_SE. Figure 5 shows the time series of the daily NAOI for each NAO+_LE, NAO−_LE, NAO+_SE, NAO−_SE, (black thin lines) and their respective composite results (red thick lines). The temporal evolutions of the composite daily NAOI in Fig. 5 show that the typical lifetime for the long-lived NAO events is much longer than 21 days, while the typical lifetime for the short-lived NAO events is within 6 days, approximately. In addition, the composite peak NAOI for NAO+_LE and NAO−_LE are about 2.34 and −2.02, respectively. These values are only about 1.36 and −1.33 for NAO+_SE and NAO−_SE. Thus, overall, the intensities of the long-lived NAO events are apparently stronger than that of the short-lived NAO events. Thus, one might argue that the intensities of the NAO events are the key factor that determines the durations of the NAO events. A stronger (weaker) NAO event naturally has a longer (shorter) lifetime. This viewpoint, however, is superficial because it is a postmortem interpretation. It does not provide any clues for predicting the lifetimes of the NAO events.

Fig. 5.

As in Fig. 3, but for (a) NAO+_LE, (b) NAO+_SE, (c) NAO−_LE, and (d) NAO−_SE.

Fig. 5.

As in Fig. 3, but for (a) NAO+_LE, (b) NAO+_SE, (c) NAO−_LE, and (d) NAO−_SE.

To demonstrate temporal evolution characteristics of the long- and short-lived NAO events and expose their differences, Figs. 6 and 7 show the lagged composite anomalies of the 300-hPa geopotential height in the NH for NAO+_LE, NAO+_SE, NAO−_LE, and NAO−_SE from lag −10 to lag 10 days, respectively. As expected, the persistence of the NAO-like meridional dipolar circulation anomalies over the NA region is much better in the long-lived NAO events. Another interesting characteristic that NAO+_LE and NAO−_LE share in common is that, from lag −10 to 10 days, there is an in-phase relationship of height anomalies between the NP and NA sectors. A “north negative–south positive” (north positive–south negative) NAO dipole of NAO+_LE (NAO−_LE) is accompanied with a similar meridional dipole but over the NP region at similar latitudes as that for the NAO dipole. Therefore, the spatial patterns of the composite long-lived NAO events closely resemble the NAM. Meanwhile, the composite short-lived NAO events exhibit the canonical locally confined NAO. It is noticed that there are some statistically significant circulation anomalies at the early stage of the short-lived NAO events over the NP region as well. However, these early signals are weak and unstable. For example, at the early stage of NAO+_SE (NAO−_SE), there is a “north positive–south negative” dipole over the NP region (anomalous wave train propagating across the NP to North America). But it decays and disappears very quickly right before the emergence of the NAO dipole (see Figs. 6l–n and Figs. 7l–n). Thus, it seems that the short-lived NAO events tend to develop in situ and barely have relationships with the circulation anomalies over the upstream of the NA region.

Fig. 6.

Composite anomalies of 300-hPa geopotential height for (a)–(k) NAO+_LE and (l)–(v) NAO+_SE from (top to bottom) lag −10 to 10 days. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 30 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 6.

Composite anomalies of 300-hPa geopotential height for (a)–(k) NAO+_LE and (l)–(v) NAO+_SE from (top to bottom) lag −10 to 10 days. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 30 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 7.

As in Fig. 6, but for (a)–(k) NAO−_LE and (l)–(v) NAO−_SE.

Fig. 7.

As in Fig. 6, but for (a)–(k) NAO−_LE and (l)–(v) NAO−_SE.

4. The North Pacific meridional dipole

As revealed in section 3, the composite long-lived NAO events’ patterns are highly similar to the NAM because the presence of the North Pacific meridional dipole (NPMD). Note that the signal of the NPMD is robust and stable and emerges at the very early stage of the composite long-lived NAO events. Meanwhile, it is completely absent for the composite short-lived NAO events. Therefore, it is argued that the preceding NPMD is an early factor that is conducive to the emergence of the long-lived NAO events that we identified. We hypothesize that an absence of the NPMD at the early stage of the long-lived NAO events might shorten their lifetimes, while a presence of the preceding NPMD might lengthen the lifetimes of the short-lived NAO events.

To verify this hypothesis, we set up and perform 12 sets of modified initial-value experiments of NAO+_LE, NAO−_LE, NAO+_SE, and NAO−_SE.

First, we define the positive and negative NPMD-type circulation anomalies. The positive (negative) NPMD-type circulation anomalies are the composite three-dimensional circulation anomalies over a domain of the NP region (0°–90°N, 120°E–90°W) at lag −10 days of NAO+_LE (NAO−_LE), including vorticity, divergence, temperature, surface pressure, zonal and meridional wind velocity, and vertical velocity. Hence, the positive (negative) NPMD-type circulation anomalies in the upper troposphere are characterized by a “north negative–south positive” (north positive–south negative) meridional dipole over the NP region. Then we artificially introduce the half, the full, and the double of the positive (negative) NPMD-type circulation anomalies but with a reverse sign into the initial-value fields at lag −10 days of individual case of NAO+_LE (NAO−_LE). Through that way, we respectively acquire three sets of modified initial-value fields for NAO+_LE and NAO−_LE. It is argued that, in these modified initial-value fields, the signal of NPMD is weakened, removed, or even reversed. Then we rerun the 28 (25) NAO+_LE (NAO−_LE) cases using these three sets of modified initial-value fields. For NAO+_LE (NAO−_LE), these three sets of modified initial-value experiments are denoted as NAO+_LE_−0.5x, NAO+_LE_−1x, and NAO+_LE_−2x (NAO−_LE_−0.5x, NAO−_LE_−1x, and NAO−_LE_−2x), respectively. These experiments are integrated for 20 days, which covers the main lifetimes of the original long-lived NAO events. Clearly, the results of the rerun long-lived NAO events are useful to demonstrate the effects of the preceding NPMD on the lifetimes of the original long-lived NAO events.

To demonstrate the impacts of the modified initial-value fields on the following evolutions of the rerun long-lived NAO events, Fig. 8 shows the daily projected NAOI of the individual rerun long-lived NAO event4 from integration day 1 to day 20 (thin dashed lines). The corresponding daily projected NAOI of the original long-lived NAO event from lag −10 to 9 days (thin solid lines) are also shown in Fig. 8. Here, the daily projected NAOI are acquired by projecting the daily SLP anomalies associated with the rerun or original long-lived NAO events onto the NAO pattern (i.e., the EOF1 of the NA region). In Fig. 8 the composite time series of the projected NAOI of the rerun (blue thick lines) and the original (red thick lines) long-lived NAO events are also shown. Generally speaking, the rerun long-lived NAO events have weaker intensities and shorter lifetimes. It seems that the intensities and lifetimes of the rerun long-lived NAO events are dependent on the suppressing magnitude of the signal of NPMD in the initial-value fields: the more the signal of NPMD is suppressed, the weaker and shorter the intensities and lifetimes of the rerun long-lived NAO events become. Thus, the results of the rerun long-lived NAO events shown in Fig. 8 verify the first part of the hypothesis that an absence of the NPMD at the early stage of the long-lived NAO events will shorten their lifetimes.

Fig. 8.

The daily projected NAO index of each rerun long-lived NAO events (thin dashed lines) in (a) NAO+_LE_−0.5x, (b) NAO+_LE_−1x, (c) NAO+_LE_−2x, (d) NAO−_LE_−0.5x, (e) NAO−_LE_−1x, and (f) NAO−_LE_−2x from integration days 1 to 20. The projected NAO index of each original positive and negative long-lived NAO events (thin solid lines) from lag −10 to 9 days are also shown in (a)–(c) and (d)–(f), respectively. Blue (red) thick lines denote the composite time series of the projected NAO index of the rerun (original) long-lived NAO events.

Fig. 8.

The daily projected NAO index of each rerun long-lived NAO events (thin dashed lines) in (a) NAO+_LE_−0.5x, (b) NAO+_LE_−1x, (c) NAO+_LE_−2x, (d) NAO−_LE_−0.5x, (e) NAO−_LE_−1x, and (f) NAO−_LE_−2x from integration days 1 to 20. The projected NAO index of each original positive and negative long-lived NAO events (thin solid lines) from lag −10 to 9 days are also shown in (a)–(c) and (d)–(f), respectively. Blue (red) thick lines denote the composite time series of the projected NAO index of the rerun (original) long-lived NAO events.

To verify the second part of the hypothesis, another six sets of similar modified initial-value experiments but for the short-lived NAO events are conducted. Note that, for the short-lived NAO events, the absolute values of the composite NAOI are less than 0.5 before lag −2 days (see Figs. 5b and 5d). According to our definition of the lifetimes of the NAO events, on average, for the short-lived NAO events, those days before lag −2 days do not belong to the life cycles of the short-lived NAO events. Therefore, unlike the modified initial-value experiments for the long-lived NAO events, we chose to modify the initial-value fields at lag −2 days for the short-lived NAO events rather than at lag −10 days. Now, we artificially introduce the half, the full, and the double of the positive (negative) NPMD-type circulation anomalies into the initial-value fields at lag −2 days of each case of NAO+_SE (NAO−_SE). Thus, the newly acquired three sets of modified initial-values fields at lag −2 days of the short-lived NAO events contain the signal of the NPMD but with different magnitudes. Then the 26 (32) NAO+_SE (NAO−_SE) cases are rerun for 20 days using these three sets of modified initial-value fields. For NAO+_SE (NAO−_SE), these three sets of modified initial-value experiments are denoted as NAO+_SE_+0.5x, NAO+_SE_+1x, and NAO+_SE_+2x (NAO−_SE_+0.5x, NAO−_SE_+1x, and NAO−_SE_+2x), respectively.

Figure 9 is similar to Fig. 8 but illustrates the daily projected NAOI of each rerun short-lived NAO event from integration day 1 to day 20 (thin dashed lines), the corresponding daily projected NAOI of each original short-lived NAO event from lag −2 to 17 days (thin solid lines) as well as their respective composite results. Clearly, the additional signal of the NPMD introduced into the initial-value fields increases the peak intensities of the rerun short-lived NAO events and naturally lengthens their lifetimes, especially in NAO+_SE_+2x and NAO−_SE_+2x in which the additionally introduced signal of the NPMD is strong (see Figs. 9c and 9f). Thus, results of Fig. 9 are some pieces of strong evidence to support the second part of the hypothesis that a presence of the preceding NPMD will lengthen the lifetimes of the short-lived NAO events.

Fig. 9.

The daily projected NAO index of each rerun short-lived NAO events (thin dashed lines) in (a) NAO+_SE_+0.5x, (b) NAO+_SE_+1x, (c) NAO+_SE_+2x, (d) NAO-_SE_+0.5x, (e) NAO-_SE_+1x, and (f) NAO-_SE_+2x from integration days 1 to 20. The projected NAO index of each original positive and negative short-lived NAO events (thin solid lines) from lag −2 to 17 days are also shown in (a)–(c) and (d)–(f), respectively. Blue (red) thick lines denote the composite time series of the projected NAO index of the rerun (original) short-lived NAO events.

Fig. 9.

The daily projected NAO index of each rerun short-lived NAO events (thin dashed lines) in (a) NAO+_SE_+0.5x, (b) NAO+_SE_+1x, (c) NAO+_SE_+2x, (d) NAO-_SE_+0.5x, (e) NAO-_SE_+1x, and (f) NAO-_SE_+2x from integration days 1 to 20. The projected NAO index of each original positive and negative short-lived NAO events (thin solid lines) from lag −2 to 17 days are also shown in (a)–(c) and (d)–(f), respectively. Blue (red) thick lines denote the composite time series of the projected NAO index of the rerun (original) short-lived NAO events.

In summary, the results of the 12 sets of modified initial-value experiments indicate that the additionally introduced NPMD-type circulation anomalies in the initial-value fields can modulate the intensities and lifetimes of the original NAO events. An absence (a presence) of the positive/negative NPMD-type perturbations at the early stage of the positive/negative long (short)-lived NAO events will decrease (increase) their intensities and naturally shorten (lengthen) their lifetimes. These results support our viewpoint that the preceding NPMD is a precursor that favors the emergence of the long-lived NAO events in the model.

5. Understanding

How can the additionally introduced NPMD-type circulation anomalies in the initial-value fields modulate the intensities and lifetimes of the original NAO events? To answer this question, we show the composite differences of 300-hPa geopotential height between the rerun long-lived NAO events of NAO+_LE_−1x (NAO−_LE_−1x) and the original long-lived positive (negative) NAO events from integration day 1 to day 19 in Fig. 10. Likewise, Fig. 11 shows the composite differences of 300-hPa geopotential height between the rerun short-lived NAO events of NAO+_SE_+1x (NAO−_SE_+1x) and the original short-lived positive (negative) NAO events from integration day 1 to day 19. The evolution of the composite differences of 300-hPa geopotential height shown in both the Figs. 10 and 11 indicate that the preceding positive (negative) NPMD-type circulation anomalies are followed by the positive (negative) NAO-like circulation anomalies at around integration days 9–13 over the NA region. Thus, we argue that that there is a lagged linkage between the NPMD and the NAO. The preceding positive (negative) NPMD-type circulation anomalies tend to gradually arouse the positive (negative) NAO-like circulation anomalies on the following days. Thus, depending on the phase signs of the original NAO events, the additionally introduced NPMD-type circulation anomalies will increase or decrease the intensities and lengthen or shorten the lifetimes of the original NAO events through reinforcing or neutralizing the meridional dipole circulation anomalies of the original NAO events.5

Fig. 10.

(a)–(j) Composite differences of 300-hPa geopotential height between the rerun long-lived NAO events of NAO+_LE_−1x and the original long-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun long-lived NAO events of NAO−_LE_−1x and the original long-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 20 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 10.

(a)–(j) Composite differences of 300-hPa geopotential height between the rerun long-lived NAO events of NAO+_LE_−1x and the original long-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun long-lived NAO events of NAO−_LE_−1x and the original long-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 20 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 11.

(a)–(j) Composite differences of 300-hPa geopotential height between the rerun short-lived NAO events of NAO+_SE_+1x and the original short-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun short-lived NAO events of NAO−_SE_+1x and the original short-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 20 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 11.

(a)–(j) Composite differences of 300-hPa geopotential height between the rerun short-lived NAO events of NAO+_SE_+1x and the original short-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun short-lived NAO events of NAO−_SE_+1x and the original short-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 20 gpm and composite results significant at the 95% confidence level are stippled.

Another question will be addressed in the following paragraphs is, Through what physical processes will the NPMD-type circulation anomalies gradually arouse the NAO-like circulation anomalies on the following days? Feldstein (2003) reported that the nonlinear synoptic eddy fluxes are the fundamental physical process that drives the formation of the NAO. To investigate whether the NAO-like circulation anomalies aroused by the additionally introduced NPMD-type circulation anomalies are also primarily driven by the synoptic eddy fluxes, Fig. 12 shows the composite differences of 300-hPa synoptic-scale eddy vorticity forcing (SCEVF)6 in terms of streamfunction tendency between the rerun long-lived NAO events of NAO+_LE_−1x (NAO−_LE_−1x) and the original long-lived positive (negative) NAO events from integration day 1 to day 19. At the first beginning, as we expect, there are notable SCEVF differences over the NP region due to the additionally introduced NPMD-type circulation anomalies. The SCEVF differences over the NA region are barely found (see Figs. 12a and 12k). After that, a somewhat noisy “north positive–south negative” (north negative–south positive) meridional dipole of the SCEVF differences gradually emergences over the NA region and peaks at around integration day 11 (day 9) for NAO+_LE_−1x (NAO−_LE_−1x). Clearly, this meridional dipole of SCEVF differences match well with the NAO-like geopotential height differences shown in Fig. 10, suggesting the NAO-like circulation anomalies aroused by the additionally introduced NPMD-type circulation anomalies are closely related to the SCEVF.

Fig. 12.

As in Fig. 10, but for the composite difference of 300-hPa SCEVF. The contour interval is 7 m2 s−2.

Fig. 12.

As in Fig. 10, but for the composite difference of 300-hPa SCEVF. The contour interval is 7 m2 s−2.

We also perform a vorticity budget analysis similar to Feldstein (2003) using the streamfunction tendency equation introduced in section 2c. As in Feldstein (2003), we diagnose the roles of linear processes and nonlinear EVF playing in the temporal evolutions of the composite differences of 300-hPa streamfunction between the rerun long-lived NAO events of NAO+_LE_−1x (NAO−_LE_−1x) and the original long-lived positive (negative) NAO events from integration day 1 to day 19 by projecting the composite difference of each term of Eq. (2) on the NAO pattern. For clarity’s sake, only the projection results of ψ/t, the EVF term, and its synoptic component (i.e., SCEVF) for NAO+_LE_−1x and NAO−_LE_−1x are illustrated in Fig. 13. Consistent with Feldstein (2003), the projection results indicate that the growths of the NAO-like circulation anomalies aroused by the additionally introduced NPMD-type circulation anomalies in NAO+_LE_−1x and NAO−_LE_−1x are indeed primarily driven by the nonlinear EVF term, especially its synoptic component.

Fig. 13.

Projections of ψ/t (tendency; black lines), the ξ7 term (EVF, red lines) and its synoptic component (SCEVF; blue lines) in the streamfunction tendency equation onto the NAO pattern for (a) NAO+_LE_−1x and (b) NAO−_LE_−1x.

Fig. 13.

Projections of ψ/t (tendency; black lines), the ξ7 term (EVF, red lines) and its synoptic component (SCEVF; blue lines) in the streamfunction tendency equation onto the NAO pattern for (a) NAO+_LE_−1x and (b) NAO−_LE_−1x.

Therefore, it is argued that, through modulating the SCEVF, the additionally introduced NPMD-type circulation anomalies gradually arouse the NAO-like circulation anomalies at the following days. Naturally, the next question that should be answered is, How can the NPMD-type circulation anomalies that locate over the NP region impact the SCEVF over the NA region? Here, a very straightforward mechanism is provided by using an anomalous SCEVF decomposition procedure of Song (2016). According to this procedure, the composite differences of SCEVF between the rerun and the original long-lived NAO events (denoted as SCEVFDIF) shown in Fig. 12 can be decomposed as follows:

 
SCEVFDIF[(UOζD)]EVF1+[(UDζO)]EVF2+[(UDζD)]EVF3,
(3)

where the angle brackets denotes an ensemble calculation, UD=ζRUO and ζD=ζRζO, and UR(UO) and ζR(ζO) denote the anomalous wind and vorticity fields associated with the synoptic eddy in each case of the rerun (original) long-lived NAO events, respectively. Details of the derivation of Eq. (3) are given in section 2b of Song (2016). We use ψR and ψO to represent the synoptic eddy of the rerun and original long-lived NAO events, and define ψD=ψRψO to denote the difference between ψR and ψO. Clearly, in Eq. (3), EVF3 is the ψD self-interaction term representing the anomalous EVF directly produced by the differences of the synoptic eddy. EVF1 and EVF2 also involve ψD, as well as its interaction with ψO.

To avoid an unnecessary reiteration, only the decomposition results of SCEVFDIF in terms of streamfunction tendency from integration day 1 to day 19 for NAO+_LE_−1x are shown in Fig. 14. Unlike the somewhat noisy spatial structures of the composite anomalous SCEVF shown in Fig. 12, the spatial patterns of ensemble EVF1 and EVF2 are neat and clear. With a “north positive–south negative” dipolar structure in the meridional direction, EVF1 emerges over the NP region at integration day 1 [see Fig. 14a(1)]. Then this “north positive–south negative” meridional dipole of EVF1 gradually strengthens and extends downstream to the NA region reaching its maximum at around integration day 9–11 [see Figs. 14a(5) and 14a(6)] and then followed by a gradual decline. Clearly, EVF1 is largely offset by EVF2 since the spatial structure of EVF2 approximately mirrors that of EVF1 but with a reversed sign. Unlike EVF1 and EVF2, EVF3 is very weak at the early stage of NAO+_LE_−1x [see Figs. 14c(1)–(3)] and is undetectable until integration day 7 [see Fig. 14c(4)]. In the last stage of the integration period, EVF3 develops with a spatial pattern similar to the climatological mean SCEVF [see Figs. 14c(8)–(10)].

Fig. 14.

[a(1)]–[a(10)] Ensemble EVF1 in terms of streamfunction tendency at 300 hPa for NAO+_LE_−1x from integration days 1 to 19. [b(1)]–[b(10)] As in [a(1)]–[a(10)], but for EVF2. [c(1)]–[c(10)] As in [a(1)]–[a(10)], but for EVF3. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 40 m2 s–2.

Fig. 14.

[a(1)]–[a(10)] Ensemble EVF1 in terms of streamfunction tendency at 300 hPa for NAO+_LE_−1x from integration days 1 to 19. [b(1)]–[b(10)] As in [a(1)]–[a(10)], but for EVF2. [c(1)]–[c(10)] As in [a(1)]–[a(10)], but for EVF3. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 40 m2 s–2.

Obviously, EVF1 is the backbone of SCEVFDIF over the NA region for NAO+_LE_−1x shown in Fig. 12, since the other two terms cannot provide a “north positive–south negative” EVF meridional dipole pattern. Thus, at the lowest-order approximation, we might use EVF1 to represent SCEVFDIF. Thus, the physical processes that lead to the emergence of EVF1 over the NA region might be also used to interpret the emergence of SCEVFDIF. Clearly, EVF1 over the NA region is caused by the interaction between ψD and ψO. To understand their interaction, the typical spatial structures of ψO and ψD, and their typical relative spatial relationships are revealed by using a “base-point-shifted fields” composite method. Here, we use 300-hPa zonal wave-5–12 streamfunction anomalies fields in each original (rerun) long-lived NAO event to represent ψO(ψR). The ψD could be easily acquired by subtracting ψO from the corresponding ψR. The base-point-shifted fields composite calculation is carried out as follows. For each day of each original NAO+_LE, the point with a minimum value of ψO over a specific domain of the midlatitudes is found. This point is defined as the base point of ψO for this NAO+_LE on this day over that domain. This gives 28 base points of ψO for each day, one for each NAO+_LE. Then the fields of ψO of the 28 NAO+_LE are shifted in longitude and latitude so that the 28 base points coincide at a pseudolocation (0°, 0°). The 28 shifted fields of ψO can then be composited to give the typical ψO around the base points for each day of the 28 NAO+_LE over that domain. Likewise, using the same base points of ψO to shift the fields of ψR and ψD in the 27 rerun positive long-lived NAO events of NAO+LE_−1x, the composite results of the shifted fields of ψR and ψD are calculated, which represent the typical ψR and ψD around the base points of ψO, respectively.

Figure 15 shows the composite ψO (color shading), ψR (thick contours), and ψD (thin contours) for NAO+_LE_−1x from integration day 1 to day 19 over the NP domain (20°–60°N, 180°–90°W) and the NA domain (20°–60°N, 90°W–0°,). Because the “north positive–south negative” meridional dipole associated with additionally introduced NPMD-type circulation anomalies in NAO+_LE_−1x (see Fig. 12a) corresponds to negative westerly anomalies over the midlatitude of the NP region, the total westerly jet over the NP region in NAO+LE_–1x is weaker than that in the original NAO+_LE. According to the equations for the phase speed of Rossby waves, ψR will have a slower eastward phase speed than ψO. Thus, from the beginning, the composite ψR are located slightly upstream of the composite ψO over the NP region, leading to a small phase difference between the composite ψR and ψO. This minor phase difference is notable since integration day 3 (see Figs. 15b–f). Resulting from this phase difference, a cyclone (an anticyclone) of the composite ψO is embraced by a cyclone (an anticyclone) and an anticyclone (a cyclone) of the composite ψD on its upstream and downstream sides simultaneously, forming a sandwich-like structure (e.g., see Fig. 15b). The sandwich structure of ψO and ψD indicate that a strong interaction between ψO and ψD is inevitable. Song (2018) had shown that, with this sandwich-like structure, the interaction between ψO and ψD will naturally produce a “north positive–south negative” meridional dipolar pattern of EVF1. Note that, over the NA region, this kind of sandwich-like structure of ψO and ψD is not evident until integration day 5 (see Fig. 15m). The emergence of this sandwich-like structure of ψO and ψD over the NA region well corresponds to the downstream extension of EVF1 from the NP region to the NA region [see Fig. 14a(3)].

Fig. 15.

Composite ψO, ψR, and ψD in terms of the 300-hPa anomalous synoptic-scale (zonal wave-5–12) streamfunction for the original long-lived positive NAO events and the rerun long-lived positive NAO events in NAO+_LE_−1x from integration days 1 to 19 over domains of (a)–(j) 20°–60°N, 180°–90°W and (k)–(t) 20°–60°N, 90°–0°. ψO is denoted by color shading, and ψR(ψD) is denoted by thick (thin) contours. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The interval of the thick (thin) contours is 4 × 106 m2 s−1 (2 × 106 m2 s−1).

Fig. 15.

Composite ψO, ψR, and ψD in terms of the 300-hPa anomalous synoptic-scale (zonal wave-5–12) streamfunction for the original long-lived positive NAO events and the rerun long-lived positive NAO events in NAO+_LE_−1x from integration days 1 to 19 over domains of (a)–(j) 20°–60°N, 180°–90°W and (k)–(t) 20°–60°N, 90°–0°. ψO is denoted by color shading, and ψR(ψD) is denoted by thick (thin) contours. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The interval of the thick (thin) contours is 4 × 106 m2 s−1 (2 × 106 m2 s−1).

Similarly, the emergence of sandwich-like structure of ψO and ψD over the NA region should be directly attributed to the weakening of the total westerly jet over there. We notice that, at the first beginning of NAO+_LE_−1x, the “north positive” lobe of the “north positive–south negative” meridional dipole of EVF1 extents to the high latitudes of the NA region [see Fig. 14a(1)]. This positive streamfunction tendency tends to arouse anticyclonic circulation anomalies and thus slows down the midlatitude westerly jet over the NA region. Thus, the physical processes responsible for the impact of the additionally introduced NPMD-type circulation anomalies on the SCEVF over the NA region in NAO+_LE_−1x can be understood as follows:

  1. The additionally introduced negative NPMD-type circulation anomalies weaken the background midlatitude westerly jet over the NP region, resulting in phase differences between ψR and ψO and forming a sandwich-like structure of ψD and ψO.

  2. The sandwich-like structure of ψD and ψO leads to the interactions between ψD and ψO generating a “north positive–south negative” meridional dipole of EVF1 over the NP region. The “north positive” lobe of the “north positive–south negative” meridional dipole of EVF1 extents to the high latitudes of the NA region and slows down the midlatitude westerly jet over there.

  3. Likewise, because of a weaker background midlatitude westerly jet, ψR has a slower eastward phase speed than ψO over the NA region forming a similar sandwich-like structure of ψD and ψO as in the NP region.

  4. The interactions between ψD and ψO with this kind of sandwich-like structure over the NA region produce a similar “north positive–south negative” meridional dipole of EVF1 over there.

Clearly, the above physical processes are different to those previous studies that suggest that the upstream circulation anomalies over the eastern North Pacific impact the anomalous synoptic eddies forcing over the NA region via modulating the seeding of downstream-propagating transient disturbances (Franzke et al. 2004; Rivière and Orlanski 2007; Strong and Magnusdottir 2008; Song et al. 2009; Li and Lau 2012a,b; Drouard et al. 2013, 2015; Rivière and Drouard 2015).

6. Effects of the stratosphere

Obviously, the investigation about the long-lived NAO events and their precursor in sections 4 and 5 are restricted in the troposphere. This is mainly because the NAO itself is primarily determined by the tropospheric dynamical processes. However, previous works had already pointed out that a dynamic active stratosphere is capable of lengthening the time scale of the tropospheric annular mode during winter (Gerber and Polvani 2009; Simpson et al. 2011; Kim and Reichler 2016). Therefore, the state of stratosphere associated with the long-lived NAO events is also a possible candidate served as a precursor or favorable condition for giving rise to the long-lived NAO events. Besides that, we argue that the NPMD served as a precursor that favors the formation of the long-lived NAO events directly going through tropospheric dynamical processes. However, we cannot preclude the possibility that the NPMD’s influences on the NAO events taking effect is by virtue of its interaction with the stratospheric circulations.

To clarify these confusions, first, we show the lagged composite anomalies of the geopotential height at 20 hPa in the NH for NAO+_LE and NAO+_SE from lag −10 to lag 10 days in Fig. 16. Clearly, the horizontal patterns of the composite stratospheric geopotential height anomalies associated with NAO+_LE have a zonal wave-1 structure with positive anomalies over North America/North Atlantic and negative anomalies over Eurasia, representing a displacement of the polar vortex. Generally speaking, the composite stratospheric geopotential height anomalies of NAO+_SE are negative right above the Arctic, which obviously corresponds to a deeper or stronger NH polar vortex. Likewise, Fig. 17 shows the lagged composite anomalies of the 20-hPa geopotential height in the NH but for NAO−_LE and NAO−_SE from lag −10 to lag 10 days. For NAO−_LE, the patterns of the composite results are also a zonal wave-1 structure resembling that of the NAO+_LE but with reverse signs. A common feature of the composite results of NAO−_SE is difficult to summarize because they are highly variable and less systematical.

Fig. 16.

Composite anomalies of 20-hPa geopotential height for (a)–(k) NAO+_LE and (l)–(v) NAO+_SE from lag −10 to 10 days. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 40 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 16.

Composite anomalies of 20-hPa geopotential height for (a)–(k) NAO+_LE and (l)–(v) NAO+_SE from lag −10 to 10 days. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 40 gpm and composite results significant at the 95% confidence level are stippled.

Fig. 17.

As in Fig. 16, but for (a)–(k) NAO−_LE and (l) –(v) NAO−_SE.

Fig. 17.

As in Fig. 16, but for (a)–(k) NAO−_LE and (l) –(v) NAO−_SE.

Recently, mounting evidence suggests that the downward reflection of planetary waves, particularly, the vertical refection of zonal wave 1, plays a role in dynamical troposphere–stratosphere coupling (Perlwitz and Harnik 2003; Shaw et al. 2010; Shaw and Perlwitz 2013; Shaw et al. 2014). It is interesting to notice that the zonal wave-1 patterns of the composite results for NAO+_LE and NAO−_LE are reminiscent of the spatial patterns of the vertical reflective stratospheric wave 1 (see Fig. 3 of Perlwitz and Harnik 2003, Fig. 2 of Shaw et al. 2014, or Fig. 2 of Lubis et al. 2016), implying that the stratospheric circulation anomalies might play a role in the formation of the long-lived NAO event via the downward reflection of the stratospheric wave 1. Shaw and Perlwitz (2013) pointed out that the downward reflection of a wave from the stratosphere to the troposphere is associated with a clear eastward phase tilt with increasing altitude in vertical structures of wave-1 geopotential height at high-latitude regions (e.g., see Fig. 4 of Shaw and Perlwitz 2013). However, this feature is not found during the whole life cycle of the long-lived NAO events (not shown), indicating there is no prominent downward reflection of wave occurring. Thus, we argue that the formation of the long-lived NAO events identified in this study is not necessarily related to the downward reflection of the planetary wave.

Certainly, the composite stratospheric anomalous circulations associated with the long-lived NAO events might still favor the existence of the long-lived NAO events via other mechanisms including directly influencing the tropospheric circulations through geostrophic and hydrostatic adjustment of the atmospheric column due to the localized stratospheric potential vorticity (PV) anomalies (Hartley et al. 1998; Black 2002; Ambaum and Hoskins 2002), directly and indirectly impacting the synoptic waves in the troposphere by altering tropopause height (Williams 2006), stratospheric shear (Wittman et al. 2007), residual-mean meridional circulation (Haynes et al. 1991), the propagation characteristics of tropospheric planetary waves (Smith and Scott 2016). However, no matter through what mechanism, numerous observational and modeling studies have pointed out that, in a zonal-mean framework, a strengthening (weakening) of the Arctic stratospheric vortex associated with positive (negative) stratospheric PV anomalies tends to favor the emergence of the positive (negative) NAM-/NAO-like tropospheric circulation anomalies on the following days (e.g., Charlton-Perez et al. 2018; Scaife et al. 2016; Hitchcock and Simpson 2014; Kunz and Greatbatch 2013; Limpasuvan et al. 2005; Polvani and Kushner 2002). Obviously, it is not suitable to generalize this result to a local situation immediately. However, this result stimulates us to hypothesize that, to be conducive to the formation of NAO+_LE (NAO−_LE), the local stratospheric PV over the NA region should be positive (negative) anomalies. Note that, generally speaking, the composite life cycle of NAO+_LE (NAO−_LE) is associated with positive (negative) stratospheric geopotential height anomalies, that is, local negative (positive) stratospheric PV anomalies, over the NA region, which are not a favorable condition for the maintenance of the positive (negative) NAO events. Therefore, we argue that, for the formation of the long-lived NAO events identified in this study, the state of the stratosphere is not helpful to lengthen their durations.7

Next, to answer the question of whether the stratosphere is another pathway to communicate the NPMD and the following NAO-like circulation anomalies, we show the 1000–10-hPa vertical distributions of composite differences of geopotential height and zonal wind averaged from 90°W to 0° between the NAO+_LE_−1x (NAO−_LE_−1x) and the original long-lived positive (negative) NAO events from integration day 1 to day 19 in Fig. 18. Note that, at the integration day 1, the artificially removed positive (negative) NPMD-type circulation anomalies in the initial-value fields of NAO+_LE_−1x (NAO−_LE_−1x) give rise to negative (positive) stratospheric geopotential height anomalies over the mid–high latitudes of the NA region accompanying a stronger (weaker) polar night jet. At integration day 9–13 of NAO+_LE_−1x (NAO−_LE_−1x), there is a midlatitude “north negative–south positive” (north positive–south negative) quasi-barotropic meridional dipole of tropospheric zonal wind anomalies, which obviously denotes the lagged linkage between the NPMD and the NAO shown in Fig. 10. Besides that, another conspicuous feature in Fig. 18 is a gradual downward extension of the mid- to high-latitude positive (negative) stratospheric zonal wind anomalies at around integration days 11–19 of NAO+_LE_−1x (NAO−_LE_−1x), which, in confirmation of previous works, represents the influences of the stratospheric circulation anomalies on the troposphere. Clearly, the results shown in Fig. 18 indicate that the lagged NPDM’s effect on the NAO and the influences of the stratospheric circulation anomalies on the troposphere are independent to each other, since the times, locations, and spatial patterns of their occurrence are totally different. Therefore, the key dynamics of the NPMD’s effect on the NAO is tropospheric and does not rely on the stratospheric variability.

Fig. 18.

(a)–(j) Composite differences of zonal average over 90°W–0° of geopotential height (colors) and zonal wind (contours) between the rerun long-lived NAO events of NAO+_LE_−1x and the original long-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun long-lived NAO events of NAO−_LE_−1x and the original long-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 60 gpm for geopotential height and 2 m s−1 for zonal wind.

Fig. 18.

(a)–(j) Composite differences of zonal average over 90°W–0° of geopotential height (colors) and zonal wind (contours) between the rerun long-lived NAO events of NAO+_LE_−1x and the original long-lived positive NAO events from integration days 1 to 19. (k)–(t) As in (a)–(j), but for the composite differences between the rerun long-lived NAO events of NAO−_LE_−1x and the original long-lived negative NAO events. Solid (dashed) contours represent positive (negative) values; zero contours are omitted. The contour interval is 60 gpm for geopotential height and 2 m s−1 for zonal wind.

7. Conclusions and discussion

a. Conclusions

In this study, we investigate the long- and short-lived NAO events based upon an 8000-day perpetual-boreal-winter run of the GFDL dynamical core atmospheric model. The main conclusions of this study are summarized as follows:

  1. The occurrence of the NAO events in this model with a relatively long or short lifetime is by no means rare. More than one-quarter of the NAO events’ lifetimes are no shorter than 16 days or no longer than 8 days.

  2. The spatial pattern of the composite long-lived NAO events in this model closely resembles that of the NAM because the NAO dipole is always accompanied with a statistically significant NPMD at similar latitudes. The composite short-lived NAO events exhibit the canonical locally confined NAO.

  3. The preceding NPMD is an early factor that favors the emergence of the long-lived NAO events in this model because 12 sets modified initial-value experiments prove that an absence (a presence) of the NPMD-type perturbations at the early stage of the long-lived (short-lived) NAO events will decrease (increase) their intensities and naturally shorten (lengthen) their lifetimes.

  4. There is a lagged linkage between the preceding NPMD and the NAO. Through directly modulating the synoptic eddy forcing over the NA region, the preceding NPMD can gradually arouse the NAO-like circulation anomalies on the following days. That is the reason why the preceding NPMD can modulate the intensities and lifetimes of the NAO events.

  5. In the modified initial-value experiments, the occurring times, locations, and spatial patterns of the influences of the stratospheric circulation anomalies associated with NPMD on the troposphere are different with NPMD’s effect on the NAO. Thus, the dynamical processes responsible for the NPMD’s effect on the NAO should be tropospheric.

b. Discussion

Although the main conclusions of this study are drawn based on a long-term run result of a simplified dry atmospheric model, we find the lagged linkage between the preceding NPMD and the NAO found in the model also exists in observations. Note that the spatial pattern of the NPMD is strongly similar to that of the Pacific center of action of the NAM (denoted as NAM_P). Thus, in observations, we use the NAM_P to represent the NPMD and define the daily NAM_P index by projecting the anomalous SLP in NCEP-1 and ERA-40 onto their corresponding NAM_P pattern. Here, the NAM_P pattern is defined as the regional pattern of the NAM over the NP region.

To investigate the lagged linkage between preceding NAM_P and the NAO in observations, we calculate the lagged correlation coefficients between the daily NAM_P index and the NAOI from lag 0 to 20 days for NCEP-1 and ERA-40 and show them in Fig. 19. Lag x day denotes the daily NAOI lagging the daily NAM_P index by x days. Clearly, the correlation between the NAM_P index and the NAOI is highest at lag 0 days. Then their correlation declines sharply. It is interesting to notice that the lagged correlations have a rebound from about lag 6 to 15 days. This rebound peaks at lag 12 (13) days for NCEP-1 (ERA-40). The results shown in Fig. 19 indicate that, in observations, the preceding NAM_P, as in the model, can also reinforce the NAO-like circulation anomalies on the following days. It is interesting to notice that, in the model, the amplitudes of the NAO-like circulation anomalies aroused by the preceding NPMD peak at about integration day 11 (see Figs. 10f and 10p), which is very close to the lagged correlation rebound peak day shown in Fig. 19.

Fig. 19.

Lagged correlation between the daily NAM_P index and the NAOI from lag 0 to 20 days for (a) NCEP-1 and (b) ERA-40.

Fig. 19.

Lagged correlation between the daily NAM_P index and the NAOI from lag 0 to 20 days for (a) NCEP-1 and (b) ERA-40.

Next, we discuss the implications of the results of this study for the physical essence of the NAM briefly. Since the concept of the NAM was proposed, there is a debate on its physical meaning. Some studies claimed that the NAM is not even a robust physical mode because the Atlantic and Pacific centers of action for the NAM are not significantly correlated with each other (Deser 2000; Ambaum et al. 2001). In this study, we find that the composite short-lived NAO events exhibits the canonical NAO, while the spatial pattern of the composite long-lived NAO events closely resembles the NAM because of the presence of the NPMD. Thus, we argue that, at least in the model used in this study, the NAM might reflect the existence of the long-lived NAO events. In other words, the NAM is the long-lived NAO in a certain sense. We calculate the autocorrelations of the NAMI and NAOI from lag −30 to 30 days for NCEP-1, ERA-40, and this model. These results are shown in Fig. 20. It is clear that the persistence of the NAMI is better than that of the NAOI. Thus, generally speaking, the NAM events have a longer lifetime than the NAO events. Obviously, these results support our thinking about the physical meaning of the NAM.

Fig. 20.

Autocorrelations of the NAMI and NAOI from lag −30 to 30 days for (a) NCEP-1, (b) ERA-40, and (c) the model.

Fig. 20.

Autocorrelations of the NAMI and NAOI from lag −30 to 30 days for (a) NCEP-1, (b) ERA-40, and (c) the model.

Acknowledgments

The author would like to thank Dr. Sandro Lubis and an anonymous reviewer whose comments and suggestions have significantly improved the paper. This work was supported by the 973 Program (Grant 2015CB453202) and the National Natural Science Foundation of China (Grants 41790473, 41490642, and 41430533).

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Footnotes

© 2019 American Meteorological Society.

1

The NAM is also known as the Arctic Oscillation (AO; Thompson and Wallace 1998, 2000).

2

In fact, the entire integration time is 8200 days. The outputs of the first 200 days are discarded as spinup.

3

The following composite results of the long- and short-lived NAO events are not sensitive to the choice of threshold.

4

It should be pointed out that one rerun long-lived NAO event in NAO+_LE_−1x does not complete the 20 days integration because of the integration instability. In NAO+_LE_−2x, the number of the uncompleted cases is 11. In other experiments, all of the rerun long- or short-lived NAO events accomplish the 20-day integration.

5

Note that in the modified initial-value experiments for the long-lived NAO events, a suppression of the positive (negative) NPMD circulation anomalies in the original positive (negative) long-lived NAO events is equivalent to introducing negative (positive) NPMD-type circulation anomalies.

6

Normally, we use high-frequency-filtered component of the transient eddy to represent the synoptic eddy. However, the integration time of the modified initial-value experiments is only 20 days. It is impossible to filter out the high-frequency components of the transient eddy in such a short integration. Therefore, here, Fourier decomposition is used as a spatial filter to isolate the synoptic-scale (zonal wavenumbers 5–12) eddy to represent the synoptic eddy.

7

This does not mean that the anomalous circulation of the stratosphere cannot impact the duration of the NAO events. In fact, we have conducted several experiments. These experiments prove that the local positive (negative) stratospheric PV anomalies over the NA region will increase the lifetime of the positive (negative) NAO events. These results will be reported in another paper.