Tropical–extratropical interactions related to upper-level troughs at low latitudes

Dynamics of Atmospheres and Oceans 43 (2007) 36–62

Tropical–extratropical interactions related to upper-level troughs at low latitudes Peter Knippertz ∗ Institute of Atmospheric Physics, Johannes Gutenberg-University of Mainz, D-55099 Mainz, Germany Available online 20 November 2006

Abstract Momentum and kinetic energy fluxes associated with low-latitude transient disturbances at upper-levels play an important role in the general circulation of the atmosphere. They are related to eastward and equatorward propagating, positively tilted wave trains from the extratropics. Theoretical, modelling and observational studies show that this particular kind of tropical–extratropical interaction is most common in regions of mean upper-level westerlies at low latitudes, i.e. over the central and eastern Pacific and Atlantic Oceans during boreal winter and spring. The penetration of an upper-level trough into the Tropics is often associated with enhanced convection and the formation of an east- and poleward stretching elongated band of upper- and midlevel clouds, usually referred to as a ‘tropical plume’ (TP). The present study provides an overview of various aspects related to the penetration of upper-level disturbances to low latitudes, including a description of the involved meteorological phenomena, climatological aspects, interannual variability, linear Rossby-wave and critical line theory, results from barotropic and higher-complexity modelling studies, the vertical structure of the disturbances as well as sources for the wave energy. In addition, the dynamical relation of the upper-troughs to convection, moisture transports and precipitation in the subtropics will be discussed. The paper concludes with a number of research perspectives for future investigations. © 2006 Elsevier B.V. All rights reserved. Keywords: Planetary waves; Atmospheric convection; Climatology; Jet stream; Atmospheric precipitations; Moisture transfer

1. Introduction The existence of important interactions between the Tropics and extratropics has been perceived for a long time (e.g. Bjerknes, 1969). Early studies have mainly investigated the influence of ∗

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tropical heating anomalies on the extratropics on seasonal to interannual time-scales, for example in connection with the El Ni˜no/Southern Oscillation (ENSO; e.g. Horel and Wallace, 1981). More recently, there is growing interest in the impact of large-scale intraseasonal tropical heating anomalies associated with the Madden–Julian Oscillation (MJO; e.g. Madden and Julian, 1994; Zhang, 2005) on the extratropical circulation (Weickmann et al., 1985; Ferranti et al., 1990; Blad´e and Hartmann, 1995; Hendon et al., 2000; Jones et al., 2004). A prominent example of a tropical impact on midlatitudes on even smaller temporal and spatial scales is the transition of tropical cyclones into extratropical systems (e.g. Jones et al., 2003). There are, however, also situations when disturbances from the extratropics affect low latitudes. This kind of interaction is most important on synoptic to submonthly time-scales and is confined to certain parts of the Tropics, in particular during the boreal cool season. Specific examples include lower-tropospheric cold-surge events over East Asia, which are connected to an intensification of convection over Indonesia (e.g. Chang et al., 1979; Boyle and Chen, 1987), and incursions of transient upper-tropospheric troughs into the Tropics. The latter phenomenon will be the focus of this paper. It has been shown that low-latitude troughs are usually part of eastward and equatorward propagating coherent wave trains from the extratropics and that they can influence tropical convective activity (e.g. Liebmann and Hartmann, 1984; Kiladis and Weickmann, 1992b). Often elongated cloud bands form to the east of these troughs and then stretch from the Tropics into the subtropics or even midlatitudes. These bands are eye-catching signs of tropical–extratropical interactions in satellite imagery and have been termed ‘tropical plumes’ (TPs; McGuirk et al., 1988). In addition, studies of the general circulation of the atmosphere reveal that transient upper-level disturbances at low-latitudes accomplish a substantial part of the poleward transport of momentum and kinetic energy (e.g. Peixoto and Oort, 1992, their Figs. 11.7 and 13.8) making them an important element of the global and regional momentum balances (e.g. Kiladis and Feldstein, 1994). The present paper aims at providing a broad overview of observational results and placing these in a theoretical background. Sections 2 and 3 contain a summary of the climatology and structural characteristics of TPs and low-latitude upper-troughs, respectively. Section 4 deals with aspects of Rossby waves and their propagation into low latitudes: (1) theory, (2) barotropic and more complex modelling, (3) vertical structure of observed waves and (4) source regions of wave energy. This section is meant to elucidate the strength and limitations of a purely linear view of the problem. In Section 5 the physical mechanisms relating low-latitude upper-disturbances with convection will be discussed, followed by an analysis of the associated moisture transports and precipitation patterns in Section 6. Given the relatively broad spectrum of views on these issues in the existing literature, a synoptic model is presented that tries to incorporate key points from various studies. The final Section 7 provides conclusions and lists open questions for future research. 2. Observations of tropical plumes 2.1. Definition Comprehensive observations and a detailed description of elongated cloud bands connecting the Tropics and extratropics started with the advent of meteorological satellites in the 1960s and 1970s (Erickson and Winston, 1972; Gray and Clapp, 1978; Davis, 1981; Thepenier and Cruette, 1981). The infrared (IR) satellite image from 00 UTC 31 March 2002 shows a nice example of such a cloud band close to West Africa (Fig. 1). The range of names for this phenomenon includes

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Fig. 1. Meteosat infrared image of a tropical plume over northwest Africa at 00 UTC 31 March 2002. Superimposed are streamlines and isotachs on the 345-K isentropic level (dashed contours at 40, 50, 60, and 70 m s−1 ) from the ECMWF TOGA analysis. The 345-K level is close to 200 hPa in the Tropics (slightly modified from Knippertz, 2005).

‘tropical intrusions’, ‘cloud surges’, ‘cirrus surges’, ‘moisture bursts’ or ‘tropical plumes’ (TPs), the latter of which will be used for the remainder of this paper. McGuirk et al. (1987) were the first to give an objective definition of TPs. It is based on visual inspection of IR satellite imagery and defines a TP as a continuous band of upper and middle clouds that is at least 2000 km in length and crosses 15◦ N (only in the Northern Hemisphere, NH hereafter). Similar definitions were given by Kuhnel (1989) and Iskenderian (1995), but with 20◦ latitude distance to the equator. In addition Kuhnel’s (1989) definition requests a length of at least 25◦ longitude, a maximal width of at least 5◦ latitude, a diagonal alignment crossing at least 10◦ latitude and a homogenous texture (see the example in Fig. 1). McGuirk et al. (1987) and Iskenderian (1995) define the ‘beginning time’ of a TP as the first evidence of a poleward progression of clouds, which later satisfy the TP definition. Additionally McGuirk et al. (1987) include the rather rare cases of an equatorward crossing of 15◦ N by a sufficiently long and continuous cold frontal cloud band from the extratropics, despite the potentially different dynamical processes involved. The ‘ending’ of a TP is the time when the cloud band ceases to cross the latitude circle used in the TP definition. This is usually related to a poleward migration of the clouds. All the definitions referenced above entirely rely on the geometry of cloud features in IR satellite imagery. They do not directly imply information on vertical depth of the clouds, on precipitation, on moisture transports, on a particular dynamical mechanism or on the role of convection. Therefore ‘TP’ should primarily be regarded as a generic term for a variety of cloud features connecting the Tropics and extratropics. It will be shown in the following, however, that the majority of TPs do in fact have common characteristics beyond their appearance in IR imagery (see Section 2.3).

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2.2. Climatology and interannual variability Table 1 summarizes the database, approach and some key results of four TP climatologies, part of which are based on the definitions explained in Section 2.1. Thepenier and Cruette (1981) subjectively identified 145 cloud bands with origins between 100◦ W and 160◦ W and end points over the North Atlantic from 3 years of GOES-1 IR imagery. This corresponds to an average of four events per month. The bands have typical lengths of 4000–16,000 km, widths between 400 and 1200 km and lifetimes of 3–9 days. The most active time of the year is November–April with a clear occurrence maximum in December. Usually, the cloud bands originate between 5◦ N and 25◦ N, which qualifies most of them as TPs according to the definitions in Section 2.1. In 70% of the cases Thepenier and Cruette (1981) find that the cloud ‘embryo’ is part of the intertropical convergence zone (ITCZ). The climatology by McGuirk et al. (1987) focuses on the NH Pacific (160◦ E–90◦ W) using data from the GOES-West satellite for three cool seasons (November–April, see Table 1). In total they identify 183 TPs, which corresponds to 10.2 per month. Most active months are November and April with a relative minimum in February/March. Lifetimes range between 0.5 and 9.5 days with an average of 2.6 days. 71% of the days have at least one TP somewhere over the area. In the most active region, 160◦ E–120◦ W, about 6.6 events per cool season per 10◦ longitude strip are identified. The most comprehensive climatology by Iskenderian (1995) is based on NOAA polar-orbiting satellites, and covers the entire NH and 10 extended cool seasons (October–May, 1974–1984; Table 1). A total of 1062 TPs is identified corresponding to 13.3 per month for the entire hemisphere. Very few TPs in this dataset originate within a few degrees of the equator. Frequency maxima are found over the eastern Pacific (∼145W) and over the Atlantic (∼35W). Most TPs are observed in October and May and least during February/March. The majority of TPs exist for only 1–3 days, but several are identified for as long as nine days, resulting in an average lifetime of 2.7 days in close agreement with McGuirk et al. (1987). The only global climatology is the one by Kuhnel (1989) based on TIROS-N/NOAA IR satellite imagery during the period January 1979–December 1983. In contrast to the three other studies summarized in Table 1, Kuhnel (1989) does not identify single TP systems with beginning and ending times, but determines days with TP occurrences in seven northern and seven southern hemispheric regions. His dataset is strongly dominated by the quasi-permanent, quasi-stationary cloud and precipitation bands of the South Pacific/Atlantic convergence zones (SPCZ/SACZ) in the southern hemisphere (SH; e.g. Kodama, 1992, 1993; Vincent, 1994) that sometimes continuously satisfy the TP definition for weeks. This leads to a very pronounced austral summer maximum in the SH, when both the SPCZ and the SACZ are usually most active. The same is partly true for the quasi-stationary cloud band over the northwestern Pacific in the NH during boreal summer (Kodama, 1992, 1993). Following a comment of McGuirk et al. (1987, p. 789) these quasi-stationary cloud and precipitation bands should be considered a different meteorological phenomenon than the short-lived transient TPs of the cold season and this paper will concentrate on the latter. Nevertheless also Kuhnel (1989) finds pronounced cool season TP activity over the NH eastern Pacific and Atlantic Oceans with occurrence maxima in October/November in agreement with Iskenderian (1995) and McGuirk et al. (1987). He also confirms the clear activity minimum during June–September evident in Thepenier and Cruette’s study (1981). The analysis periods listed in Table 1 are rather short for a thorough investigation of the interannual variability of TP occurrence. Nevertheless both Iskenderian (1995) and McGuirk et al. (1987) find a marked decrease in TP occurrence over the central and eastern Pacific during the strong El Ni˜no of 1982/1983 with a slight increase farther east. Iskenderian notes a general

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Author

Data

Period

Area

#TPs

Maximum frequency

Most active regions

Life-time

Comment

Thepenier and Cruette (1981) McGuirk et al. (1987)

GOES-1, at least daily GOES-West, 6-hourly

NH 160◦ W–100◦ W NH 160◦ E–90◦ W

145

December

N/A

3–9 days

183

November and April

160◦ E–120◦ W

0.5–9.5 days, mean 2.6 days

No clear objective definition Objective definition for systems

Kuhnel (1989)

TIROS-N/NOAA, once daily

Whole year 1976–1978 November–April 1975/1976, 1977/1978, 1981/1982 Whole year 1979–1983

Global

N/A

NH: 90◦ E–150◦ E, SH: 170◦ E–140◦ W

N/A

Objective definition for TP days

Iskenderian (1995)

NOAA polar-orbiting satellites, twice daily

October–May 1974–1984

NH

1062

NH: October/November and April, SH: December/January October and May

145W, 35W

Mean 2.7 days

Objective definition for systems

Provided information include the employed data, period and area of study, number of identified TPs as well as comments on the identification method. Columns 6–8 contain months with highest TP occurrence, most active geographical regions and TP lifetimes.

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Table 1 Summary of four climatological studies on tropical plumes (TPs)

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tendency for anomalous seasons over the eastern Pacific to be balanced by opposite anomalies over the Atlantic. McGuirk et al. (1987) hypothesize that there exist two different states of the Hadley cell over the eastern Pacific: one zonally symmetric, strong-ITCZ mode typical of the summer months or El Ni˜no conditions and a transient eddy mode with more synoptic-scale variability during the cool season. This idea is supported by the upper-level water vapour distribution in two composites for quiescent and active TP periods presented by McGuirk and Ulsh (1990). 2.3. Structure A number of typical structural characteristics of TPs have been observed that are not contained in the definitions given in Section 2.1. The most common is a poleward and eastward orientation of the TP with an anticyclonic curvature in the subtropics (McGuirk et al., 1987; Fig. 1). On occasion, however, almost meridional TPs have been observed, too (e.g. Knippertz and Martin, 2005, their Fig. 4). As stated above, most TPs are rooted in an active segment of the ITCZ and this convective ‘source’ typically migrates poleward and eastward over time (McGuirk et al., 1987). TPs can also be related to cirrus clouds produced by tropical cyclones; other TPs have no obvious convective origins at all (Iskenderian, 1995). There are observations that the intensification of tropical convection in the TP source region is at times related to waves in the tropical low-level easterlies (McGuirk et al., 1988). The most prominent dynamical feature that is practically always present poleward and westward of a TP is a mobile synoptic-scale upper-level trough penetrating into the Tropics (e.g. McGuirk et al., 1988), often with a strong positive tilt (i.e. SW–NE-orientation in the NH; Iskenderian, 1995, his Fig. 4). Such a feature is clearly evident in the streamlines in Fig. 1. The large poleward momentum fluxes associated with this trough orientation lead to an increase in the subtropical westerlies farther downstream (McGuirk et al., 1987). Consequently, TPs are usually accompanied by a pronounced subtropical jet (STJ) streak of sometimes more than 80 m s−1 (e.g. McGuirk et al., 1988; Kuhnel, 1990; Ziv, 2001; Knippertz, 2005; see isotachs in Fig. 1). McGuirk et al. (1988) observe that a typical ending of a TP occurs when the eastward moving extratropical portion of the trough “outruns” the almost stationary tropical portion. Along this extratropical portion TPs can have frontal characteristics (McGuirk et al., 1988) and interact with midlatitude synoptic systems (Thepenier and Cruette, 1981). Another typical feature is a very dry (dark) area in water vapour (WV) satellite imagery to the northwest of the TP (McGuirk and Ulsh, 1990; Blackwell and McGuirk, 1996; Blackwell, 2000; Knippertz, 2005). TP composites over the NH Pacific by McGuirk and Ulsh (1990) reveal that a large gradient in upper- and midlevel water vapour exists between the moist TP and this nearby dry region. In accordance, McGuirk et al. (1988) and Blackwell (2000) find moderate to strong subsidence at midlevels in this area. It is interesting to note that the dry air from the subsidence region of a low-latitude trough and TP can intrude into the deep Tropics and influence conditions for convection as shown by a case study for the western Pacific by Yoneyama and Parsons (1999) (their Fig. 12). 3. Low-latitude upper-level troughs and their relation to convection and TPs 3.1. Climatology of upper-level troughs at low latitudes Due to the weak gradients in geopotential height at low latitudes, most investigations of upperlevel troughs in the Tropics or subtropics are based on either streamfunction on pressure levels

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or potential vorticity (PV) fields, usually on an isentropic surface in the vicinity of the subtropical tropopause. Case studies have shown that these upper-troughs often take the form of elongated stratospheric PV streamers or cut-offs (e.g. Kiladis and Weickmann, 1992b, their Fig. 6b; Knippertz and Martin, 2006). An example from a study by Tomas and Webster (1994) using PV on the 345 K isentropic level is reproduced as Fig. 2. It shows a strongly tilted streamer of high PV over the NH central Pacific with values larger than 1 PVU (cross-hatched area in Fig. 2) extending into the deep Tropics near 140◦ W. Along its eastern flank, a tongue of negative PV reaches across the equator from the SH, followed by a weaker NH PV streamer over the eastern Pacific. Another positively-tilted, low-latitude PV streamer can be seen in the SH near 170◦ W. Wernli and Sprenger (in press) generated 15-year climatologies of NH stratospheric PV cut-offs and streamers on different isentropic levels using European Centre for Medium-Range Weather Forecast (ECMWF) re-analysis data. For winter (December–February) they find distinct frequency maxima near 25◦ N, 22◦ W and 29◦ N, 130◦ W on 330 K (their Figs. 5d and 6d) that correspond with the most active TP regions (see Section 2.2). During summer (June–August) these activity maxima shift northwestward and to higher isentropic levels in accordance with the seasonal cycle in temperature. Waugh and Polvani (2000) calculated a 20-year climatology of low-latitude PV streamers (that they call ‘intrusions’) by detecting occurrences of |PV| > 2 PVU at 350 K within 10◦ latitude of the equator. Events related to small isolated regions of high PV are subjectively removed from the dataset. The example shown in Fig. 2 does clearly fulfil this criterion for the 345-K level near 130◦ W. PV intrusions according to this definition occur predominantly during the cool season (November–April) with highest frequencies in January and show geographical maxima over the central Pacific (180◦ W–100◦ W) and eastern Atlantic (50◦ W–0◦ ) in both hemispheres in agreement with TP climatologies (see Section 2.2). Again there is large interannual variability and a conspicuous drop in activity during the strong El Ni˜no events 1982/1983 and 1997/1998 over the Pacific. Waugh and Polvani (2000) find a close relationship between intrusion frequency and the strength of the upper-level westerly winds with respect to seasonality, longitudinal and interannual distribution. This point will be further discussed in Section 4.

Fig. 2. Example of a low-latitude potential vorticity streamer on the 345-K isentropic surface on 03 February 1984 based on ECMWF analysis. The contour interval is 1 × 10−6 K m2 kg−1 s−1 (=1 PVU) with the ±0.5 PVU contours added; the interval between 1 and 2 PVU is cross-hatched. (From Tomas and Webster, 1994. Reprinted with permission from the American Meteorological Society.)

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PV streamers are often the result of the equatorward transport of extratropical stratospheric air during the breaking of a Rossby wave in the extratropics. Rossby wave-breaking (RWB) is manifested in the large and rapid irreversible overturning of PV contours as evident over the NH Pacific between 180◦ W and 130◦ W in Fig. 2. A 10-year RWB climatology by Postel and Hitchman (1999) for the 350-K isentropic surface shows a clear occurrence maximum during summer in both hemispheres. In the NH highest RWB frequencies are observed over the subtropical central Pacific and western to central Atlantic in agreement with the PV streamer climatology by Wernli and Sprenger (in press). These results, together with the intrusion climatology by Waugh and Polvani (2000), suggest that RWB, even though more frequent during summer, tend not to produce strong low-latitude PV anomalies. 3.2. The relation between upper-level troughs and convection A number of studies have investigated the relationship between low-latitude PV, geopotential height or streamfunction anomalies on one hand and convection, upper-level relative humidity or TP occurrence on the other hand. Waugh and Funatsu (2003), for instance, investigated the intrusion events over the North Pacific (180◦ W–100◦ W) from the climatology by Waugh and Polvani (2000) (see Section 3.1). They found that the majority of these events are accompanied by low values of outgoing longwave radiation (OLR) along the eastern edge of the regions of high PV, which indicates the existence of cold cloud tops and most likely deep convection. Fig. 3 shows composite fields of 350-K PV and OLR that have been constructed by averaging over all intrusion events after a shift to the reference longitude of 140◦ W. It reveals a distinct OLR signal that crosses 20◦ N and has a length of almost 2000 km, suggesting a relationship to TPs. The composite PV streamer has a weak positive tilt in the subtropics, but is almost north–south

Fig. 3. Relationship between low-latitude potential vorticity (PV) intrusions over the North Pacific and outgoing longwave radiation (OLR). PV intrusions are defined as occurrences of PV > 2 PVU at the 350-K isentropic level at 10◦ N (horizontal dashed line). The figure shows a composite over all intrusions between 180◦ E and 100◦ E based on the NCAR-NCEP re-analyses 1980–1999. Displayed are 350-K PV (thick isopleths every 1 PVU with a thicker 2-PVU contour) and OLR south of 30◦ N (thin isopleths every 20 W m−2 and shading for values less than 240 W m−2 ). Before averaging the single events have been shifted to the reference longitude 140◦ W (vertical dashed line). (Slightly modified from Waugh and Funatsu, 2003. Reprinted with permission from the American Meteorological Society.)

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oriented between 10◦ N and 15◦ N in contrast to the case example of Fig. 2 and most TP case studies (cf. Fig. 1 and Section 2). In the author’s view this discrepancy in tilt is unexpected and requires further study. In a more recent work Waugh (2005) used a similar approach to reveal the large contrast in upper-level (200–250 hPa) relative humidity between the region of low OLR to the east and the western side of the intrusions. This result is again in agreement with satellite studies on TPs (e.g. McGuirk and Ulsh, 1990). Other authors base their analyses on the convective signal at low latitudes, usually expressed through time-averaged, composited or filtered anomalies in OLR. Liebmann and Hartmann (1984) found that wintertime 5- and 10-day mean anomalies in tropical cloudiness (10◦ N–15◦ N) over the central Atlantic and North Pacific east of the date line tend to be preceded by wave trains in the extratropical 500 hPa geopotential height field. The time averaging produces zonally elongated features with little tilt. Kiladis and Weickmann (1992b) chose a similar approach, but with an OLR base region at 5◦ N–15◦ N and wintertime 6–14-days filtered 200 hPa streamfunction and wind anomalies. Fig. 4 shows their results for the longitudinal range 140◦ W–130◦ W. The streamfunction anomalies indicate a southeastward oriented, positively tilted wave train from East Asia across the North Pacific. Similar patterns are obtained for other base regions between 170◦ W and 110◦ W and somewhat weaker signals for the Atlantic (base regions 0◦ N–10◦ N, 50◦ W–0◦ ). Lead-lag correlations reveal a southeastward propagation of the wave trains (Kiladis and Weickmann, 1992b, their Fig. 2; Kiladis, 1998, his Fig. 1). A positively tilted trough upstream of the convection is evident in the composite 350-K PV field in the study by Kiladis (1998). Kiladis and Weickmann (1997) extended this approach to a longer dataset, 6–30-day filtered data and other seasons. For spring, they found a similar relation between tropical convection over the North Pacific and Atlantic Oceans and wave trains from the extratropics, with a slight shift of the active region to the west in the latter basin. Summer and fall, however, show significantly different patterns that indicate little tropical–extratropical interactions. This is inconsistent with the observed high TP frequencies in October and November (Section 2.2). Both winter and spring reveal cross-equatorial wave dispersion in the active regions in the considered frequency band (see also Kiladis, 1998, his Fig. 1). During boreal winter there are indications for TP formation

Fig. 4. Relationship between outgoing longwave radiation (OLR) anomalies over the tropical eastern Pacific and wave trains from the extratropics. Displayed are 6–14-day anomalies in OLR, 200 hPa streamfunction and locally significant wind vectors for a –1 standard deviation in OLR at 5◦ N–15◦ N, 140◦ W–130◦ W (shown by open box). The contour interval is 10 × 105 m2 s−1 , with the zero contour omitted. The largest wind vectors are about 5 m s−1 . Shading outlines regions of OLR anomaly less than −6 W m−2 . Data basis are the NMC analyses December–February 1983/1984–1987/1988. (From Kiladis and Weickmann, 1992a. Reprinted with permission from the American Meteorological Society.)

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over West Africa in connection with wave trains over the North Atlantic (Kiladis and Weickmann, 1997, their Figs. 6b and c) and for an interaction between wave trains over the SH Indian Ocean and the Australian summer monsoon (their Fig. 2d). The latter indicates a modification of the quasi-permanent SPCZ by transient disturbances (Kodama, 1993; Vincent, 1994). Iskenderian (1995) composited unfiltered 200 hPa streamfunction and OLR for 41 TPs over the eastern Pacific (mainly during the cool season) and also identified southeastward propagating wave trains with pronounced positive tilts similar to Fig. 4 (his Fig. 5). Large OLR anomalies, however, are confined to south of 20◦ N in his composite. The results summarized here all underline the close relation between wave trains, tropical convection and TP formation. 4. Rossby-wave considerations Results presented in Sections 2 and 3 show that tropical–extratropical interactions connected to low-latitude upper-troughs and TPs are mainly confined to the NH central and eastern Pacific, and Atlantic during the cool season. Analysis of 200 hPa climatological conditions show that these times and locations are characterised by mean westerly flow (e.g. Kiladis and Weickmann, 1997, their Fig. 1). This relationship has motivated many studies to seek explanation for their observations in linear Rossby-wave theory as explained in following Section 4.1. Testing these theoretical considerations with the help of barotropic and more complex numerical models will be detailed in Section 4.2. Section 4.3 contains a discussion of the vertical structure of the waves, both in theory and observations. The aspect of a forcing of the waves through baroclinic and diabatic processes upstream of the low-latitude troughs will be addressed in Section 4.4. 4.1. The theory of linear Rossby wave propagation 4.1.1. Stationary waves Despite the transient nature of the wave trains in observations the overview of the theoretical background shall begin with the simplest case of a stationary Rossby wave, closely following Section 2 in Hoskins and Ambrizzi (1993). Starting with a constant westerly basic state the dispersion relation for barotropic Rossby plane-wave perturbations of the form exp[i(kx + ly − ωt)] ¯ − (βk/K2 ), where U¯ is the basic state zonal wind, β the meridional gradient of the is ω = Uk Coriolis parameter and K = (k2 + l2 )1/2 is the total wavenumber. For stationary waves, ω is zero ¯ 1/2 . Thus, stationary waves are possible only, if the flow is westerly and we get K = Ks = (β/U) ¯ ¯ (U positive). If U varies with latitude, we have to replace β in the dispersion relation with the 2 ). The zonal wavenumber, k, is still ¯ meridional gradient of absolute vorticity, β∗ = β − (∂2 U/∂y constant, but the meridional wavenumber, l, will vary such that the local dispersion relation is satisfied. Stationarity requires positive U¯ and β* , with the latter condition being equivalent to barotropic stability. Hoskins and Ambrizzi (1993) calculate the dependence of the refraction of a stationary Rossby ray path on Ks . With α being the angle the vector group velocity, cg = (∂ω/∂k), (∂ω/∂l), makes with the eastward direction, tan α = l/k and the temporal change of α moving with the group velocity can be determined: dg α/dt = (2k/Ks2 )cg (dKs /dy), where cg is the magnitude of the group velocity. To derive this formula one has to assume that the basic flow varies slowly with latitude compared with the scale of the waves (known as the Wentzel–Kramer–Brillouin–Jeffreys (WKBJ) theory, see p. 1191 in Hoskins and Karoly, 1981). The above relation implies that Rossby rays are always refracted toward latitudes with larger Ks . If a perturbation has an initial group

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velocity toward lower Ks , it will at some point reach a turning latitude, where Ks = k and l = 0. In general, all rays must turn before a latitude where β* = Ks = 0, if there exists one. If U¯ goes to zero, Ks becomes infinite and rays are refracted normally into such a ‘critical latitude’ but with their meridional scale, l−1 , and the group velocity, cg , tending to zero. Linear theory is not valid close to such a critical line and depending on the amplitude of the wave non-linear effects can lead to absorption or reflection of wave energy (e.g. Abatzoglou and Magnusdottir, 2004). The important implication for tropical–extratropical interactions is that stationary wave trains from the extratropics cannot propagate into latitudes with mean easterly flow. Hoskins and Karoly (1981) present a ray theory for stationary Rossby waves which accounts for the spherical geometry of the earth (their Section 5b). In an atmosphere with constant angular velocity the ray paths follow great circle routes, implying the possibility that Rossby wave trains from the Tropics reach a turning latitude at midlatitudes and then return into the Tropics, thus being related to tropical–extratropical interactions in both directions. From observed upper-level wave trains Kiladis (1998) estimated phase and group velocities along a great circle path and found in fact satisfactory agreement with the theoretically predicted values despite non-stationarity, and zonal and meridional gradients in the flow. An important next step toward a more realistic basic state is to include a non-zero mean meridional velocity, V¯ , and to allow longitudinal variations. Hoskins and Ambrizzi (1993) argue that as long as there is a dominance of U¯ over V¯ and of latitudinal over longitudinal gradients in the absolute vorticity of the basic flow, Ks as defined above can be used locally (Ks (x,y)) and provides at least qualitatively useful results. Examples for Ks calculations for upper-tropospheric winter mean conditions can be found in Hoskins and Ambrizzi (1993) and are reproduced here as Fig. 5a (see also Kiladis, 1998, his Fig. 10a). The large, but bounded values of Ks over the equatorial east Pacific and Atlantic Oceans in Fig. 5a reveal the possibility for equatorward or even cross-equatorial wave propagation. In an earlier study Webster and Holton (1982) termed these regions ‘westerly ducts’, since they allow the exchange of wave energy between the two hemispheres. Kiladis and Weickmann (1992b) do in fact observe cross-equatorial wave dispersion in these regions (their Figs. 2 and 7). Kiladis (1998) demonstrates that the changes in upper-level zonal wind associated with El Ni˜no effectively close the duct for stationary Rossby waves in agreement with the interannual variability of TPs and upper-troughs reported in Sections 2 and 3 (see also Matthews and Kiladis, 1999a). Tomas and Webster (1994) discuss the problem of ray theory and longitudinal variations of the basic state and argue that as long as the waves under consideration are of a smaller zonal scale than the westerly duct itself, they can pass through to the other hemisphere. One-point correlation results support such a relation between duct width and wave dimensions. 4.1.2. Transient waves As reported above, various studies (e.g. Kiladis and Weickmann, 1992b) found southeastward propagating rather than stationary Rossby waves being related to convection over the tropical eastern Pacific. Therefore we will now present a modification to the theory explained in Section 4.1.1 that incorporates transients. Yang and Hoskins (1996) discuss the effects of non-zero ω on Rossby ray paths. For positive frequencies, i.e. eastward propagation, the group velocity vector, cg , is smaller and less meridionally oriented than for the stationary case (their Fig. 1a). This indicates a smaller tendency for transient wave energy to disperse towards the equator. Critical lines exist for regions with U¯ > 0, in particular, for high frequencies, ω, and small zonal wavenumbers, k (i.e. long waves; see Yang and Hoskins, 1996, their Fig. 2a), which effectively narrows the westerly ducts for this kind of waves. Fig. 5b exemplarily shows total wavenumber, K, and critical lines

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Fig. 5. Wavenumber calculations based on climatological December–February flow at 300 hPa from ECMWF analysis data. (a) Stationary wavenumber, Ks , as defined in Section 4.1.1 (from Hoskins and Ambrizzi, 1993) and (b) total wavenumber K for zonal wavenumber k = 4 and a wave period of +14 days (from Yang and Hoskins, 1996). Contours are drawn at zonal wavenumbers 0 (dotted) and 4, 5, 6, 7, 8, 10 and 15 (solid) in (a) and for every integer wavenumber from 4 to 10 in (b). Thickened contours indicate critical lines (i.e. singular values of Ks and K, respectively). Lines with K = k = 4 in (b) are reflection lines. (Both figures reproduced with permission from the American Meteorological Society.)

for k = 4 and wave periods of 14 days. A comparison to Fig. 5a indicates that the westerly ducts do indeed close over the Pacific and Atlantic, even though there is still a possibility for wave propagation into near-equatorial regions from the NH. Over the Atlantic similar results are found for k between 2 and 10 (Yang and Hoskins, 1996, their Fig. 11a). An alternative way to analyze and visualize transient eddies is to employ E-vector diagnostics  = (v 2 − u 2 , −u v ), where the bar signifies a (Hoskins et al., 1983). The E-vector is defined as E time average and the prime a deviation from this average (i.e. the transient part). The x-component of this vector provides information on the eddy anisotropy with eastward (westward) pointing vectors indicating a meridional (zonal) orientation. The y-component is equal but opposite of the eddy poleward momentum flux and is related to the tilt of the eddies. This implies that for strongly  and the anisotropy axes. tilted eddies there is an angle between E Under certain approximations the propagation characteristics of transient disturbances can be  If the contours of mean absolute vorticity, ζ¯ , make only small angles with the inferred from E.  and the relative group zonal direction, there is a simple relationship between cg , ∇ ζ¯ and |E|, ¯  ¯ velocity, cg − v, subtends an angle with E equal to that made by the ζ -contours. Kiladis (1998)  for 6–30-days filtered 200 hPa winds and found large south- or calculated mean wintertime E southeastward pointing vectors near the western end of the Pacific westerly duct (his Fig. 10a). This indicates equatorward propagating, positively tilted, meridionally elongated eddies. One

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 and relatively large zonal should bear in mind, however, that due to the large y-components of E  deviates from cg − v¯ and can only convey a rather qualitative picture. ζ¯ -gradients in this region, E Nevertheless Matthews and Kiladis (1999a,b) were able to demonstrate that increased Evectors are associated with higher eddy kinetic energy and larger OLR variance on intraseasonal  timescales, the latter being a likely indication for the occurrence of TPs. In addition the E-field is sensitive to changes in the large-scale circulation associated with interannual variations related  to ENSO and intraseasonal variations related to the MJO. The E-fields in these studies indicate little cross-equatorial propagation in the intraseasonal frequency band consistent with Yang and Hoskins (1996, see Section 4).  that is often used for wave diagnostics in midlatitudes Another interesting characteristic of E  approximates the effective westerly momentum flux in a non-divergent, barotropic, is that E frictionless flow, given that −∂xx u v can be neglected (Hoskins et al., 1983). In the westerly duct regions, however, poleward momentum fluxes can be expected to be large and therefore one  here. should refrain from this interpretation of E 4.2. Modelling results The problem of tropical–extratropical interactions has also been addressed with the help of numerical models of different complexity. Most of the earlier work is based on steady state divergent barotropic (i.e. shallow water) models. For instance, Webster and Holton (1982) perturbed different idealized, zonally symmetric and asymmetric basic states with zonal wavenumbers k = 1, 3 and 6 at 20◦ N. They found that equatorward energy dispersion is restricted to corridors of lowlatitude westerlies as predicted by stationary Rossby-wave theory (see Section 4.1.1) and that the scales of motion of the perturbations have to be considerably smaller than the basic state scale (i.e. the width of the westerly duct). The latter is in agreement with WKBJ theory. The amplitude of the response in the deep Tropics depends strongly on the magnitude of the westerlies. Hoskins and Ambrizzi (1993) conducted similar experiments with a realistic (i.e. mean wintertime) 300 hPa basic flow and found stationary waves dispersing into and out of the westerly duct regions in the equatorial Pacific and Atlantic from both hemispheres (their Fig. 13). Yang and Hoskins (1996) repeated these experiments for non-stationary disturbances and found no equatorward propagation in the case of eastward phase speeds (wave periods 7 and 14 days, their Figs. 13 and 14). This is again consistent with the theory presented in Section 4.1.2. Blackwell (2000) presents a barotropic modelling study directly related to TPs. Using a 200 hPa January mean flow as a basic state he places a mass sink (i.e. convergent forcing) in the eastern portion of the climatological ridge over the central Pacific Ocean. As a consequence the advection of vorticity through the perturbation divergent winds leads to an amplification and zonal contraction of the trough to the east of the ridge, which eventually results in a circulation similar to the upper-level flow associated with observed TPs (e.g. Fig. 1). Blackwell (2000) argues that the lowlatitude convergence is driven by large-scale cold advection and subsidence in association with extratropical wave train activity. The former argument contradicts the assumption that barotropic mechanisms are dominant. In the author’s view this raises the question of how appropriate the chosen forcing and the conclusions derived from this study are for the real atmosphere. In recent years higher-complexity models have been applied to the investigation of tropical–extratropical interactions. For example, Yang and Hoskins (1996) repeated their barotropic modelling experiments with a dry, 15-sigma level primitive equation baroclinic model in T31 horizontal resolution and were able to confirm their general conclusions. With a similar model Matthews and Kiladis (1999a) compared simulations for two different realistic basic

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states and found enhanced upper-level stationary wave dispersion into the more intense Pacific westerly duct during La Ni˜na conditions, which is in close agreement with the observed interannual variability of low-latitude disturbances and TPs (Sections 2.2 and 3.1). Held et al. (2002) employed a primitive equation model with a zonal mean January basic state and showed that the linear and non-linear stationary wave response to observed extratropical heating includes strongly positively tilted wave trains towards low latitudes. Finally, in a perpetual January simulation with a full General Circulation Model (GCM) with 19 vertical levels and T42 horizontal resolution Slingo (1998) detected realistic energy dispersion into the Pacific westerly duct. She claims that this behaviour is strongly dependent on the model’s ability to produce a realistic basic state over this region. This result agrees well with findings of Kiladis and Feldstein (1994). 4.3. Vertical structure The theoretical, modelling and observational results described above are derived from barotropic approaches or concentrate on upper-levels. In this subsection the vertical structure of the disturbances will be discussed. Fig. 6 is taken from a study by Tomas and Webster (1994) who used one-point correlation techniques based on 6–30-days filtered isentropic PV fields during winter to examine wave propagation through the Pacific westerly duct at different vertical levels. The vertical cross-sections shown in Fig. 6 follow a southeastward-oriented line from a point to the south of Kamchatka across the tropical Pacific into the Atlantic near the southern Argentinean coast (part of this line is displayed in Fig. 7b). The base point for the correlation computation is located at 200 hPa near Hawaii (marked ‘B’ in Figs. 6 and 7b). Simultaneous correlations reveal a wave train with weak baroclinic tilt in the extratropics and a nearly equivalent barotropic structure at low latitudes (Fig. 6a). The 3-day lag correlations shown in Fig. 6b clearly demonstrate that the disturbances are propagating southeastward across the

Fig. 6. Vertical structure of wave trains across the Pacific westerly duct following a line from 45◦ N, 160◦ E to 45◦ S, 60◦ W (see Fig. 7b). The displayed one-point correlations were calculated from December–February 6–30-days filtered isentropic potential vorticity for a base grid point located at 22.5◦ N, 165◦ W, 200 hPa (filled circle). Field points lead the base point by (a) 0 days (simultaneous) and (b) 3 days. Contour interval is 0.1; the zero contour is omitted. Dashed lines depict isentropes except for the solid 315-K contour. Regions with mean easterlies are grey-shaded. Data basis are the ECMWF analyses 1980–1989. (From Tomas and Webster, 1994. Reprinted with permission from the American Meteorological Society.)

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westerly duct into the SH. The most striking result is the absence of strong signals in the region of low-level mean easterlies at low latitudes (grey-shaded in Fig. 6). This is consistent with the linear Rossby wave arguments given in Section 4.1 and is further corroborated by the fact that the propagation characteristics and shape of disturbances on the 315-K isentropic level (bold line in Fig. 6) suggest critical line absorption of wave energy (not shown; see Tomas and Webster, 1994, their Fig. 9). Modelling results by Slingo (1998, her Fig. 9) and Held et al. (2002, their Fig. 11b) also show weak wave signals at lower-levels in connection with, respectively, convection over the Pacific westerly duct and stationary wave trains excited by extratropical heating. Fig. 7 summarizes results from observational work by Kiladis and Weickmann (1992b, 1997) that relates wintertime OLR anomalies over the Pacific and Atlantic westerly ducts to streamfunction anomalies at 200 and 850 hPa using the same intraseasonal frequency band as Tomas and Webster (1994). The upper-level signals (depicted by thick black lines in Fig. 7) have already been discussed in detail in Section 3.2 (see Fig. 4 for the Pacific westerly duct) and we will concen-

Fig. 7. Vertical structure of wave trains related to a −1 standard deviation in OLR in the westerly duct regions: (a) Eastern Atlantic (base region 0◦ N–10◦ N, 20◦ W–10◦ W) and (b) central Pacific (base region 5◦ N–15◦ N, 160◦ W–150◦ W). Thick black lines schematically depict upper-level wave trains based on 200 hPa streamfunction and wind anomalies; filled circles indicate the respective local maxima and minima. Thin contours show 850 hPa streamfunction every 2 × 105 m2 s−1 , with the zero contour omitted. The shading outlines regions of OLR anomaly less than −10 W m−2 . All data were 6–30-days bandpass-filtered. Data basis are the NCEP operational analyses December–February 1984/1985–1992/1993. In addition, the black line and letters in (b) indicate the location of the cross-section shown in Fig. 6 with the correlation maxima and minima from Fig. 6a. The figures are based on Figs. 5 and 6 from Kiladis and Weickmann (1997).

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trate on the lower-level here. For the Atlantic, the 850 hPa streamfunction contours show a wave train whose circulation centres correspond nicely to their upper-level counterparts (filled circles; Fig. 7a). In the extratropics there is a distinct northwestward baroclinic tilt with height, while structures are more barotropic in the subtropics and Tropics. The vertical tilt of the disturbances is in line with our discussion of Fig. 6. The relatively strong signal at lower-levels over the Atlantic agrees with the stationary wave response to extratropical heating in a modelling study by Held et al. (2002, their Fig. 11b). The low-level streamfunction pattern over the Pacific appears more complicated (Fig. 7b). While the cyclonic circulation over the western Pacific shows a close correspondence with the upper-level trough to the west, a large anticyclone dominates the circulation farther to the south and east and stretches across the northern part of the upper-trough in the subtropics. Kiladis (1998, his Figs. 3 and 7c) and Kiladis and Weickmann (1992b) (their Fig. 5) show that midand low-level cold advection/anomalies are associated with the northerly flow along the eastern side of this anticyclone. The same authors also find a surge in the trade winds and enhanced near-surface convergence in the convectively active region (grey-shaded in Fig. 7b). Kiladis and Weickmann (1997) remark that convection in off-equatorial southerly flow between a cyclone to the west and an anticyclone to the east is reminiscent of an equatorial Rossby wave, suggesting a possible explanation of the observed low-latitude pattern. It is clear from Fig. 7b that the very complex three-dimensional circulation associated with low-latitude convection over the central Pacific cannot be attributed to linear Rossby wave propagation from the extratropics alone and needs further study. To the best of the author’s knowledge a detailed analysis of the reasons for the discrepancy in low-level structures between the two westerly duct regions has not yet been undertaken. PV considerations offer a possible way to explain the lack of a significant cyclonic signal at lower-levels over the Pacific. The depth of influence of an upper-PV anomaly is related to fL/N, where f is the Coriolis parameter, L the characteristic horizontal scale and N is the BruntV¨ais¨al¨a frequency (Eq. 33b in Hoskins et al., 1985). Generally the dependence on f implies that disturbances become more vertically constrained at low latitudes in agreement with Fig. 6. The usually relatively large N in the subtropics and the decreasing L of the often stretched-out PV streamers or cut-offs could lead to an even smaller influence depth. Only the latter two factors, of course, come into question to explain differences between the two ocean basins at the same latitude. One problem with using the formula for the influence depths given above is that its derivation relies on a balance between the mass and momentum fields and constant mass between two isentropic surfaces in a given domain (Hoskins et al., 1985). This might not always be justified in the Tropics, where diabatic processes can be dominating. Therefore the relationship should be applied with some caution. 4.4. Baroclinic and diabatic processes at higher latitudes As shown in the previous subsection, the extratropical portions of wave trains propagating into the Tropics display a westward and poleward tilt with height, indicative of baroclinic growth (Figs. 6 and 7). In the following we will discuss the importance of baroclinic and diabatic processes for the wave trains from a PV perspective. Fig. 8 shows an example of a distinct PV streamer that is about to penetrate to low latitudes to the west of West Africa and instigate convection and heavy precipitation there (Knippertz and Martin, 2006). The large PV gradients and wind vectors along the east coast of North America indicate a strong upstream jet, consistent with the composite of low-latitude PV streamers shown in Fig. 3. An unusually strong jet upstream of

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Fig. 8. Example of upstream influences on low-latitude potential vorticity (PV) streamer formation over the North Atlantic at 00 UTC 08 January 2002. Thin isopleths show PV every 1 PVU starting with 2 PVU and vectors show total winds greater than 15 m s−1 (scale in bottom right corner) on the 325-K isentropic level. Shading indicates negative diabatic PV tendencies in the 200–250 hPa layer (legend below figure; in PVU day−1 ). A filled circle and number indicate the position and core pressure (in hPa) of a selected surface low-pressure system. (Slightly modified after Knippertz and Martin, 2006.)

low-latitude upper-troughs has been found in other observational and modelling studies (Kiladis and Weickmann, 1992b, their Fig. 4; Slingo, 1998, her Fig. 16). In the exit region of the jet there is a rapidly deepening and northeastward moving surface cyclone (depicted by a filled circle in Fig. 8) in agreement with results by Kiladis (1998, his Fig. 3). The intense baroclinic development over the northwestern Atlantic leads to a rapid amplification of the downstream PV wave with a large breaking ridge at midlatitudes and a south- or southeastward moving PV streamer (not shown). Fig. 2 exemplifies the final stage of such a development for a PV streamer over the Pacific (see also Kiladis and Weickmann, 1992b, their Fig. 6). The occurrence of wave breaking in association with convection in the Atlantic westerly duct is corroborated by the large northeastward extension of the anticyclonic 850 hPa streamfunction anomaly into Europe in Fig. 7a, a signature of which is also evident in the Pacific TP composite by Iskenderian (1995) (his Fig. 5). In agreement with that, Postel and Hitchman (2001) find distinct upstream baroclinicity in a detailed case study of a North Pacific Rossby wave-breaking event. The evolution described above has some resemblance to the so-called LC1 baroclinic wave lifecycle as simulated with a dry, frictionless primitive equation model by Thorncroft et al. (1993). Shapiro et al. (2001) observe that such LC1 developments are more common during La Ni˜na cool seasons over the eastern North Pacific. This is fully consistent with the interannual variability in the frequency of low-latitude disturbances and TPs (see Sections 2.2 and 3.1). There are also indications for an influence of diabatic processes associated with the abovedescribed baroclinic developments. The grey shading in Fig. 8 delineates regions of negative PV tendencies resulting from latent heat release in the cloud head of the intensifying surface cyclone to the west. Knippertz and Martin (2005, 2006) argue that the locally substantial diabatic upper-PV reduction might support the ridge amplification and breaking over the North Atlantic, as well as the subsequent streamer formation farther east. Numerical sensitivity experiments by Massacand

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et al. (2001) do indeed demonstrate an influence of upstream diabatic heating on a streamer over the Mediterranean. This idea is also corroborated by large upper-level divergence and negative OLR anomalies over the extratropical North Pacific in composite studies by Kiladis (1998, his Fig. 4), Kiladis and Weickmann (1992b) (their Fig. 4b) and Iskenderian (1995) (his Fig. 5b). Also consistent with these results are frequent observations of elongated cloud bands upstream of TPs in satellite studies (Fig. 1; Gray and Clapp, 1978; McGuirk et al., 1987). In conclusion, the studies mentioned in this subsection point to the fact that baroclinic and diabatic processes over the midlatitude western Atlantic and Pacific play an important role for the generation of disturbances that then propagate as Rossby waves towards the westerly duct regions. In the author’s view the understanding of the described processes would greatly benefit from a quantitative analysis of the relative importance of latent heat as an energy source for low-latitude PV streamers. 5. The role of tropical convection Rather different views exist in the literature with respect to the physical processes involved in the statistical relation between convection/TPs and upper-level troughs at low latitudes (see Sections 2.3 and 3.2). The key question is whether the observed lifting is a result of dynamical forcing, convective heating or some interaction between them. Some authors regard convection as negligible or only passively responding to extratropical forcing. Blackwell (2000), for example, simulates TP-like circulations in a dry barotropic model and concludes that moist convective processes are not important for TP formation. However, a convincing physical explanation of the prescribed forcing in his model is not provided (see Section 4.2), so that, in the author’s view, the study cannot rule out an influence of convection in the real atmosphere. Several observational studies postulate that positive vorticity advection (PVA) ahead of the lowlatitude upper-troughs quasi-geostrophically (QG) forces ascent and thereby triggers the eruption of cloud plumes (McGuirk et al., 1988; Kiladis, 1998). Explicit calculations of QG forcing for three cases of TPs and precipitation over West Africa by Knippertz and Martin (2005), however, make for relatively small values of forced uplift at mid-tropospheric levels compared to midlatitudes. As discussed in Section 4.4, this might be related to the small influence depth of low-latitude PV anomalies, implying that the ascent will be confined to upper-levels. This idea is consistent with observations by Kiladis (1998, his Fig. 8) and modelling results by Slingo (1998), who finds that only a convective parameterization scheme that responds to upper-level forcing can realistically reproduce observed tropical–extratropical interactions in a GCM. Another factor of potential importance for convection is the relatively small static stability below a positive upper-PV anomaly (Kiladis and Weickmann, 1992b; Kiladis, 1998). With the help of idealized thermal profiles Juckes and Smith (2000) demonstrate the vertical destabilization of the atmosphere through the arrival of an upper-trough. Fig. 3, however, shows that a large portion of the OLR signal is relatively remote from the upper-PV trough, suggesting an influence of other mechanisms. At lower-levels, the observed intensification of the trade winds (see Section 4.3) might enhance near-surface convergence and thereby support convection (see Kiladis and Weickmann, 1992b; Knippertz, 2005). It is, however, unclear whether these trade surges are forced by the extratropics, by tropical waves or whether they are merely the mass-conservation response to the convective updrafts triggered by other processes. With respect to the formation of the elongated cloud plumes connecting the Tropics and extratropics (i.e. TPs), poleward advection of convectively generated cirrus from the ITCZ by the strong

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winds at the outflow level is commonly regarded the dominant factor. TP progression rates, however, do not always match the wind speed at the respective level, and TP cloud bands have been observed to result from consolidation due to both advection and a dynamic component related to the STJ (McGuirk et al., 1987, 1988; Mecikalski and Tripoli, 1998; Knippertz, 2005). Especially in the poleward section of TPs significant influences of QG forcing can be expected. There are also indications that the convection actively influences the upper-level circulation. Kiladis (1998) argues that the enhanced convective updrafts drive an anomalous “local Hadley circulation”, i.e. a circulation in the meridional–vertical plane over a restricted longitudinal stretch. The poleward-directed upper-level branch of this cell contributes to an acceleration of the STJ in the region of the cloud band and the downstream ridge (see also McGuirk et al., 1987; Knippertz, 2005). If convection does occur underneath the upper-PV anomaly, the associated latent heating generates negative PV tendencies near the tropopause and accelerates the decay of the uppertrough (Kiladis, 1998). Another line of arguments is concerned with inertial (in)stability at the outflow level and its relation to the intensification of convection. In an idealized modelling study Blanchard et al. (1998) demonstrate that regions of negative absolute vorticity (in the NH) act to intensify the divergent upper-level outflow from convection, particularly at low latitudes, where geostrophic adjustment is slow. Even in a region of initially weak inertial stability non-linear interactions between convective outflow and the ambient flow can eventually render the upper-level circulation inertially unstable, leading to a positive feedback cycle that aids upscale growth of the convection. In the right entrance region of the STJ streaks usually accompanying low-latitude troughs and TPs, regions of negative absolute vorticity are common due to the small f and large anticyclonic (i.e. negative) shear vorticity. The upper-level cross-equatorial flow found in several studies (Fig. 1; Iskenderian, 1995, his Fig. 5; Kiladis and Weickmann, 1992b, their Fig. 4) is likely to advect negative absolute vorticity from the SH to the eastern side of the NH upper-trough as evident from Fig. 2. This region often appears to be involved in TP genesis, even though it is relatively remote from the direct dynamical influence of the NH upper-level high-PV anomaly. Motivated by such observations Mecikalski and Tripoli (1998) investigated the role of inertial instability for TP genesis. Introducing a new diagnostic parameter termed ‘inertial available kinetic energy (IAKE)’, they quantify the kinetic energy lost or gained when convective outflow, driven by the energy released in the updraft, expands quasi-horizontally into the surrounding upper-tropospheric environment. IAKE is highly sensitive to convective-scale processes like the difference in vertical stability between the region above the convective heating and the surrounding environment, and the convective transport of horizontal momentum (see also Mecikalski and Tripoli, 2003). Since the effect can only come into play, when deep convection is already established, a combined measure of positive IAKE, high surface equivalent-potential temperature and near-surface convergence is proposed as an indicator for TP genesis. The results discussed above do not allow a straightforward conclusion on whether TPs mainly owe their existence to dynamical lifting related to the upper-trough or to tropical convection. Therefore Knippertz (2005) calculated a large number of trajectories from within the TP shown in Fig. 1, two of which are shown exemplarily in Fig. 9 together with total and ageostrophic wind vectors along the trajectories. The southern portion of the TP originates in tropical convection over South America and experiences large ageostrophic acceleration. This contribution appears to agree with the mechanism proposed by Mecikalski and Tripoli (1998). The northern portion of the TP consists of trajectories along the anticyclonic flank of the STJ which experience weak dynamical lifting over the Atlantic. Finally, the clouds over northwestern Africa are related to weak QG forcing, and weak vertical and inertial stability (see Knippertz and Martin, 2006 and

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Fig. 9. Tracks of two exemplary trajectories within a tropical plume over the North Atlantic between 26 March and 01 April 2002. Grey-shading represents model clouds at 00 UTC 31 March from a simulation of the event using the University of Wisconsin Nonhydrostatic Modelling System. Before this time trajectories are solid and dashed afterwards; 00- and 12-UTC trajectory positions are marked by grey filled circles, additional 06- and 18-UTC positions by open circles; black numbers indicate the calendar day for the 00-UTC positions. Black and grey vectors indicate total and ageostrophic winds, respectively, according to the scale in the lower right corner. (From Knippertz, 2005.)

Section 6). This indicates that several of the processes discussed above are of importance in different parts of the TP at different stages of the evolution. 6. Poleward moisture fluxes and non-ITCZ precipitation As shown in many studies of the general circulation the mean transport of atmospheric water vapour within the Hadley cell is equatorward. In contrast, transient disturbances are generally associated with moisture fluxes in the poleward direction, in particular in the midlatitude storm track regions. The penetration of transient disturbances into low-latitudes, as observed in the westerly duct regions, can therefore lead to transports of moist static energy against the direction of the stationary circulation as shown by Trenberth and Stepaniak (2003) (their Fig. 6). The following section describes observations of such moisture fluxes related to low-latitude troughs and discusses the implications for precipitation away from the ITCZ region. A crucial problem in this context is the roughly exponential decrease of moisture content with height in the atmosphere and the concentration of transient disturbances to upper-levels (see previous sections). Therefore only systems whose circulation reaches deep enough into the troposphere and far enough equatorwards to tap into the low- or midlevel tropical moisture reservoir, can in fact instigate a considerable poleward water vapour flux. Due to the often-weak surface depressions underneath low-latitude upper-disturbances (see Section 4.3) equatorward trade winds (and moisture transports) might prevail in the lowest layers, while above the planetary boundary layer moisture is transported poleward (see Knippertz and Martin, in press). Such midlevel moisture exports from the Tropics have been detected with the help of trajectories, water vapour images and vertically integrated water vapour fluxes (Ziv, 2001; Fink and Knippertz, 2003; Knippertz, 2003; Knippertz et al., 2003; Knippertz and Martin, 2005, in press; Bao et al., 2006).

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The amount of water vapour transported, of course, depends on the characteristics of the involved tropical air masses and potentially on a modification through wave activity in the Tropics (e.g. African easterly waves, see Knippertz et al., 2003). Fig. 10 shows an example of such a midlevel poleward moisture export from a study by Knippertz and Martin (in press). An elongated band of relatively large water vapour fluxes at 700 hPa stretches from the northern edge of the tropical moisture reservoir northeastward into the southern USA (grey-shading and vectors in Fig. 10). It is related to a geopotential height minimum near 30◦ N, 123◦ W (solid isopleths). Note the sharp contrast in mixing ratio between the tropical reservoir and the “moist tongue” in the subtropics, and the dry subtropical air farther to the northwest (dashed lines). The relatively narrow filament of poleward water vapour fluxes is reminiscent of extratropical ‘warm conveyor belts’ (e.g. Browning, 1990), but the low-latitude feature in Fig. 10 is not related to a sharp thermal front and moisture transports occur in a quasi-horizontal fashion. Therefore Knippertz and Martin (in press) termed this feature a ‘moist conveyor belt’, a notation, which has before been suggested by Bao et al. (2006). Moisture transports associated with upper-troughs at low latitudes can occasionally lead to substantial precipitation away from the source regions close to the ITCZ. The situation shown in Fig. 10, for example, was related to significant precipitation in the semi-arid southwestern USA (Knippertz and Martin, in press). Knippertz and Martin (2005) investigated three extreme precipitation events in tropical and subtropical West Africa during the cool season. Their analysis yields a complex combination of different dynamical and thermodynamical factors that are schematically depicted in Fig. 11. It contains some of the elements already discussed in the context of TP formation in Section 5. The thick black lines in Fig. 11 display a slightly positively tilted upper-trough to the west of West Africa with a strong STJ streak at its eastern side (black arrow). A TP is aligned along the anticyclonic shear side of the jet (stippled region). The PVA associated with the upperlevel disturbance leads to relatively weak QG forcing for ascent at midlevels (dark grey-shading) and a small region of inertial instability is found along the equatorward side of jet (dashed line).

Fig. 10. Example of a moisture conveyor belt over the eastern Pacific at 12 UTC 11 November 2003. Solid isopleths depict geopotential height every 20 gpm and dashed isopleths mixing ratio every 2 g kg−1 . Vectors and shading show water vapour flux. The vertical level is 700 hPa. The employed data come from a simulation of the event using the University of Wisconsin Nonhydrostatic Modelling System. (Slightly modified after Knippertz and Martin, in press.)

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Fig. 11. Schematic depiction of the synoptic situation during precipitation events over West Africa in connection with tropical plumes. Thick black lines delineate the low-latitude upper-trough and the thick arrow indicates the associated subtropical jet streak. Thin grey arrows show midlevel moisture transports from the deep Tropics. Stippled regions indicate high clouds and hatching delineates the major precipitation zone. Light (dark) grey shading depicts the region of convective instability under the coldest air at upper-levels (positive QG forcing for midlevel ascent). The dashed lines bound a region of upper-level inertial instability along the anticyclonic shear-side of the jet. The figure is based on case studies by Knippertz and Martin (2005).

At lower-levels tropical moisture is transported poleward towards subtropical West Africa in a way similar to the situation shown in Fig. 10 (thin arrows in Fig. 11). This provides precipitable water and destabilizes the atmosphere (Knippertz and Martin, 2005, their Figs. 11c, 12c and 13c). The main precipitation zone is then located in a region with (1) large low- to midlevel moisture contents and low vertical stability, (2) QG forcing for lifting and/or (3) inertial instability at the outflow level of convection. Recall from the discussion in Section 5 that inertial instability can only come into play to support intensification, if deep convection has previously been initiated through some other mechanism like, for instance, daytime heating of land surfaces or orographic forcing. Trajectory analyses by Knippertz and Martin (2005, in press) reveal that the midlevel moisture transport from the deep Tropics is relatively slow, so that it requires a persistent disturbance or two disturbances in short succession to generate substantial precipitation. This observation offers a possible explanation for the rare occurrence of such extreme events. On the other hand, Knippertz (2003) showed with the help of trajectories that moisture transports from the Tropics are frequently involved in more moderate precipitation events in subtropical northwestern Africa, particularly in mountainous regions and during the transition seasons. A second cloud and precipitation zone is evident in Fig. 11 in the region of coldest air close to the axis of the upper-trough. Consistent with the arguments of, e.g., Kiladis (1998, see Section 5) the vertical destabilization of the atmosphere underneath the associated upper-PV anomaly can lead to localized vigorous convection in this region (see the case studies by Fink and Knippertz, 2003; Knippertz and Martin, in press). At times the convective clouds close to the rotation centre of the upper-level disturbances take the form of a comma, typical for a so-called subtropical cyclone (Fig. 11). This feature is relatively weak in the example shown in Fig. 1. Note that the two cloud and precipitation zones depicted in Fig. 11 are well separated from each other by a drier region along the cyclonic side of the STJ, where the weak QG forcing for lifting is not sufficient to generate clouds.

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Besides southwestern North America and West Africa the described mechanism appears to be relevant for the precipitation in other semi-arid subtropical regions such as the Middle East (Dayan and Abramski, 1983; Ziv, 2001) and Australia (Wright, 1997). 7. Conclusions and open questions The present paper has striven to give a broad overview of the processes involved in and associated with the penetration of wave disturbances from the extratropics into low latitudes. Observational studies with three different approaches were discussed: (1) satellite-based identification of elongated bands of middle and upper-level clouds connecting the Tropics and extratropics, usually referred to as ‘tropical plumes’ (TPs; Section 2); (2) identification of lowlatitude troughs or cut-offs from fields of isentropic PV (Section 3.1) and (3) correlations between low-latitude OLR anomalies and fields of streamfunction, wind or geopotential (Section 3.2). The latter approach usually involves a prior filtering or averaging. The different methods agree upon activity maxima over the low-latitude central and eastern North Pacific and the North Atlantic Oceans during the extended boreal cool season. Various studies present evidence for a connection of low-latitude disturbances, convection and TP formation with eastward and equatorward propagating upper-level wavetrains from the extratropics. These observational results are consistent with linear Rossby-wave theory that predicts a meridional propagation of stationary waves only into regions with mean low-latitude westerlies. A detailed discussion of various extensions to the theory and the necessary approximations, as well as a comparison to studies with numerical models of different complexity was provided in Sections 4.1 and 4.2. While theory, observations and modelling shows good agreement at uppertropospheric levels, low-level structures are generally less clear-cut and differ between the Pacific and Atlantic (Section 4.3). In the extratropics there are strong indications for intense baroclinic and diabatic processes that serve as a sources for wave energy, which subsequently propagates into the Tropics (Section 4.4). The exact physical relation between convection/TPs and upper-level disturbances is still a matter of debate and appears to vary (1) between different parts of the TP, (2) at different times of the evolution, and (3) from case-to-case (Section 5). If the disturbances are located close enough to the tropical moisture reservoir, both vertically and meridionally, they can instigate moisture exports to and precipitation in the subtropics, which can at times be very significant (Section 6). The results presented suggest that the TP and precipitation generation is related to a multitude of factors such as QG forcing related to upper-level PVA, vertical destabilization through upperlevel extratropical cold air, low- and midlevel moisture transports from the Tropics, an interaction between convection and inertial instability at the outflow level, local triggers, as well as a simple advection of convectively produced cirrus clouds (see Fig. 11). The importance of single factors is likely to vary strongly from case-to-case. The positive tilts of the described disturbances indicate poleward eddy momentum fluxes. Calculations by Kiladis and Feldstein (1994) show that transients contribute almost half of the zonal momentum budget in the subtropical Pacific. Together with their importance for moisture transports and precipitation this makes upper-troughs at low latitudes an important element of the general circulation of the atmosphere. A number of open questions remain to be addressed in future investigations: • In Section 4.4 mid-latitude sources for wave energy at low latitudes were discussed, but these are themselves subject to influences from the Tropics, providing the possibility of

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mutual interactions. In a GCM simulation Slingo (1998) detected a chain of events involving Asian cold surges, flaring of convection over Indonesia, intensification of the Asian jet, amplification of a Rossby wave train over the North Pacific, flaring of convection over the eastern Pacific and the excitation of an easterly wave in the Tropics (her Fig. 19). If not an artefact of the model, such a mechanism should operate on subseasonal timescales and it would be worth to examine its relation to the MJO, which was shown to modify the equatorward propagation of waves over the North Pacific (Matthews and Kiladis, 1999b). More generally, the relationship between tropical low-level easterly waves and upper-level troughs which is part of the interaction described by Slingo (1998) is not fully understood and merits further study. Another interesting point in this context is the observation that the momentum fluxes associated with the positively tilted troughs at low latitudes act as a brake to the equatorial westerlies, so that subsequent tropical–extratropical interactions might be inhibited. It seems plausible that this counterbalancing effect could contribute to subseasonal variability. The main focus of this study is on the western hemisphere during the cool season, when mean westerlies are observed at low latitudes. However, over the Indian Ocean equatorial winds at upper-levels often switch from strong westerlies to strong easterlies, e.g. in association with the MJO. Little is known about the effect this intraseasonal variation has on waves propagating into the region from higher latitudes. From a more theoretical point of view the effects of violations to the assumptions made in the linear Rossby-wave theory (e.g. the WKBJ approximation) should be further investigated (see Section 4). Non-linear effects (see Held et al., 2002) and the impacts of planetary wave reflection and absorption near critical lines (Abatzoglou and Magnusdottir, 2004) are still not fully understood. This might also provide an explanation for the observed differences in the vertical structure of the wave trains over the Pacific and Atlantic that have received little attention in the literature. Another interesting point for further study is the nature of the extratropical wave source, in particular the relative contributions of baroclinic and diabatic processes to the wave amplification and breaking. Sensitivity studies of this aspect using a numerical modelling approach are currently under way. In this paper a discrepancy in seasonality between TPs and wave activity was noted. In particular this refers to strong cloud band activity in boreal fall, when low-latitude westerlies are weak. Possible reasons for this observation are a relation to convective outflow from tropical cyclones or a larger moisture availability and poleward transport during fall, when the NH monsoon circulations still affect the outer Tropics. In general, more observational and modelling studies are needed to better quantify the influence of the physical processes involved in TP generation and precipitation, both with a case study and statistical approaches. This includes differences in the results obtained with unfiltered PV diagnostics and filtered streamfunction anomalies such as the different mean tilts of the disturbances mentioned in Section 3.2. Last but not least a thorough and quantitative analysis of the role upper-level disturbances at low latitudes play in the general circulation of the atmosphere is needed, in particular with respect to the poleward transport of moisture and momentum. Such investigations are currently undertaken by the author on the basis of the ERA-40 re-analysis dataset recently released by the ECMWF.

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Acknowledgments The author is currently funded through the Emmy Noether programme of the German Science Foundation (DFG; Grant KN 581/2–3). I would like to thank Prof. Jonathan E. Martin and Prof. Emer. Stefan L. Hastenrath for hosting a 2-year post-doc stay at the Department of Atmospheric & Oceanic Sciences of the University of Wisconsin–Madison in 2003–2005, during which some of the results reported here were achieved. I also wish to acknowledge fruitful discussions with Francis Bretherton, Andreas Fink, George Kiladis, John Mecikalski, Klaus Weickmann and Heini Wernli. I am grateful to the helpful comments of two anonymous reviewers and to Darryn Waugh for providing an electronic version of Fig. 3. References Abatzoglou, J.T., Magnusdottir, G., 2004. Nonlinear planetary wave reflection in the troposphere. Geophys. Res. Lett. 31, L09101, doi:10.1029/2004GL019495. Bao, J.-W., Michelson, S.A., Nieman, P.J., Ralph, F.M., Wilczak, J.M., 2006. Interpretation of enhanced integrated watervapor bands associated with extratropical cyclones: their formation and connection to tropical moisture. Mon. Wea. Rev. 134, 1063–1080. Bjerknes, J., 1969. Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev. 97, 163–172. Blackwell, K.G., 2000. Tropical plumes in a barotropic model: a product of Rossby wave generation in the tropical upper troposphere. Mon. Wea. Rev. 128, 2288–2302. Blackwell, K.G., McGuirk, J.P., 1996. Tropical upper-tropospheric dry regions from TOVS and rawinsondes. J. Appl. Meteorol. 35, 464–481. Blad´e, I., Hartmann, D.L., 1995. The linear and nonlinear extratropical response of the atmosphere to tropical intraseasonal heating. J. Atmos. Sci. 52, 4448–4471. Blanchard, D.O., Cotton, W.R., Brown, J.M., 1998. Mesoscale circulation growth under conditions of weak inertial instability. Mon. Wea. Rev. 126, 118–140. Boyle, J.S., Chen, T.-J., 1987. Synoptic aspects of the wintertime East Asian Monsoon. In: Chang, C.P., Krishnamurti, T.N. (Eds.), Monsoon Meteorology. Oxford University Press, Oxford, pp. 125–160. Browning, K.A., 1990. Organization of clouds and precipitation in extratropical cyclones. In: Newton, C., Holopainen, E. (Eds.), Extratropical Cyclones: The Erik H. Palm´en Memorial Volume. American Meteorological Society, Boston, MA, pp. 129–153. Chang, C.-P., Erickson, J.E., Lau, K.M., 1979. Northeasterly cold surges and near-equatorial disturbances over the winter MONEX area during December 1974. Part I: synoptic aspects. Mon. Wea. Rev. 107, 812–829. Davis, N.E., 1981. Meteosat looks at the general circulation. III. Tropical–extratropical interaction. Weather 36, 168–173. Dayan, U., Abramski, R., 1983. Heavy rain in the Middle East related to unusual jet stream properties. Bull. Am. Meteorol. Soc. 64, 1138–1140. Erickson, C.O., Winston, J.S., 1972. Tropical storm, mid-latitude, cloud-band connections and the autumnal buildup of the planetary circulation. J. Appl. Meteorol. 11, 23–36. Ferranti, L., Palmer, T.N., Molteni, F., Klinker, K., 1990. Tropical–extratropical interaction associated with the 30–60 day oscillation and its impact on medium and extended range prediction. J. Atmos. Sci. 47, 2177–2199. Fink, A.H., Knippertz, P., 2003. An extreme precipitation event in southern Morocco in spring 2002 and some hydrological implications. Weather 58, 377–387. Gray, T.I., Clapp, P.F., 1978. An interaction between low- and high-latitude cloud bands as recorded on GOES-1 imagery. Bull. Am. Meteorol. Soc. 59, 808–809. Held, I.M., Ting, M., Wang, H., 2002. Northern winter stationary waves: theory and modeling. J. Clim. 15, 2125–2144. Hendon, H.H., Liebmann, B., Newman, M., Glick, J.D., Schemm, J., 2000. Medium-range forecast errors associated with active episodes of the Madden–Julian oscillation. Mon. Wea. Rev. 128, 69–86. Horel, J.D., Wallace, J.M., 1981. Planetary scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev. 109, 813–829. Hoskins, B.J., Karoly, D.J., 1981. The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci. 38, 1179–1196.

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