Editorial Type:
Article
Article Type:
Research Article

On the Dynamics of Indian Ocean Teleconnections into the Southern Hemisphere during Austral Winter

Z. E. Gillett aSchool of Earth, Atmosphere and Environment, Monash University, Melbourne, Victoria, Australia
bClimate Change Research Centre, University of New South Wales, Sydney, New South Wales, Australia
cARC Centre of Excellence for Climate Extremes, University of New South Wales, Sydney, New South, Wales, Australia

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H. H. Hendon aSchool of Earth, Atmosphere and Environment, Monash University, Melbourne, Victoria, Australia
cARC Centre of Excellence for Climate Extremes, University of New South Wales, Sydney, New South, Wales, Australia
dBureau of Meteorology, Melbourne, Victoria, Australia

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J. M. Arblaster aSchool of Earth, Atmosphere and Environment, Monash University, Melbourne, Victoria, Australia
cARC Centre of Excellence for Climate Extremes, University of New South Wales, Sydney, New South, Wales, Australia
eNational Center for Atmospheric Research, Boulder, Colorado

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H. Lin fRecherche en prévision numérique atmosphérique, Environment and Climate Change Canada, Dorval, Quebec, Canada

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D. Fuchs bClimate Change Research Centre, University of New South Wales, Sydney, New South Wales, Australia
cARC Centre of Excellence for Climate Extremes, University of New South Wales, Sydney, New South, Wales, Australia

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Online Publication:
16 Sep 2022
Print Publication:
01 Sep 2022
DOI:
https://doi.org/10.1175/JAS-D-21-0206.1
Page(s):
2453–2469
Free access

Abstract

Stationary Rossby waves, forced by the Indian Ocean dipole (IOD), have an important role in Southern Hemisphere (SH) weather and climate, including promoting Australian drought and driving Antarctic sea ice variations. However, the dynamics of these teleconnections are not fully understood. During winter, the subtropical jet (STJ) should prohibit continuous propagation of a stationary Rossby wave into the SH extratropics due to the negative meridional gradient of absolute vorticity (β*) on its poleward flank. The mechanisms that enable this teleconnection are investigated using observational and reanalysis datasets, a hierarchy of atmospheric model experiments and Rossby wave diagnostics. We conduct 90-member simulations using the Community Atmosphere Model, version 5, with an imposed local diabatic heating anomaly over the eastern Indian Ocean. We find an initial zonal propagation along the STJ waveguide, but after about 10 days, a poleward-arcing wave train appears in the extratropics that has the characteristics of the observed IOD teleconnection. Our results suggest that the Rossby wave can overcome the negative β* barrier by (i) propagating directly poleward in the midtroposphere and thus avoiding this evanescent region in the upper troposphere, (ii) partly propagating directly through this barrier, and (iii) propagating around this barrier farther upstream to the west. A transient eddy feedback, previously postulated to be the key mechanism to allow the stationary Rossby wave to appear on the poleward side of the negative β* region, reinforces the response but is not a requisite, which we confirm through comparison with a simplified linear model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zoe Gillett, zoe.gillett@unsw.edu.au

Abstract

Stationary Rossby waves, forced by the Indian Ocean dipole (IOD), have an important role in Southern Hemisphere (SH) weather and climate, including promoting Australian drought and driving Antarctic sea ice variations. However, the dynamics of these teleconnections are not fully understood. During winter, the subtropical jet (STJ) should prohibit continuous propagation of a stationary Rossby wave into the SH extratropics due to the negative meridional gradient of absolute vorticity (β*) on its poleward flank. The mechanisms that enable this teleconnection are investigated using observational and reanalysis datasets, a hierarchy of atmospheric model experiments and Rossby wave diagnostics. We conduct 90-member simulations using the Community Atmosphere Model, version 5, with an imposed local diabatic heating anomaly over the eastern Indian Ocean. We find an initial zonal propagation along the STJ waveguide, but after about 10 days, a poleward-arcing wave train appears in the extratropics that has the characteristics of the observed IOD teleconnection. Our results suggest that the Rossby wave can overcome the negative β* barrier by (i) propagating directly poleward in the midtroposphere and thus avoiding this evanescent region in the upper troposphere, (ii) partly propagating directly through this barrier, and (iii) propagating around this barrier farther upstream to the west. A transient eddy feedback, previously postulated to be the key mechanism to allow the stationary Rossby wave to appear on the poleward side of the negative β* region, reinforces the response but is not a requisite, which we confirm through comparison with a simplified linear model.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Zoe Gillett, zoe.gillett@unsw.edu.au
Keywords: Atmospheric circulation; Planetary waves; Stationary waves; Jets; Climate variability; Cool season

1. Introduction

Tropical convection anomalies, such as those driven by anomalous sea surface temperatures (SSTs) associated with El Niño–Southern Oscillation (ENSO) and the Indian Ocean dipole (IOD), have important influences on the atmospheric circulation at both tropical and extratropical latitudes. The Matsuno–Gill (Matsuno 1966; Gill 1980) model describes the equatorially trapped response to steady equatorial heating, consisting of a Kelvin wave to the east of the heating and Rossby waves to the west. This thermally direct Rossby wave response has a deep baroclinic structure with upper-level anticyclones and lower-level cyclones straddling the equator (e.g., Jin and Hoskins 1995). Away from the equator, equivalent-barotropic Rossby waves propagate poleward and eastward (e.g., Hoskins and Karoly 1981). They develop because tropical heating induces upper-level divergence that causes vortex stretching and also advects mean vorticity out of the tropics (e.g., Sardeshmukh and Hoskins 1985), thus producing a Rossby wave source (RWS) in the subtropical westerlies. Therefore, these wave trains enable anomalous tropical convection within the upper-tropospheric easterlies to influence extratropical climate (e.g., Karoly 1989; Li et al. 2015a).

The theory for the initiation (e.g., Sardeshmukh and Hoskins 1985) and propagation (e.g., Hoskins and Karoly 1981) of stationary Rossby waves, from a steady source, is well established for zonally symmetric flow but it also appears to work for zonally asymmetric flows (e.g., Hoskins and Ambrizzi 1993). During SH winter [June–August (JJA)], the major zonal asymmetry of the zonal winds is the subtropical jet (STJ), which extends from the eastern Indian Ocean (EIO) to the western Pacific near 27°S (e.g., Gillett et al. 2021). It strongly influences both the RWS due to the maximum in the meridional gradient of absolute vorticity β*=β−∂2U¯/∂y2  (where β = ∂f/∂y, f is the Coriolis parameter, and U¯ is the local background zonal wind) along the jet and the dispersion of Rossby waves because it acts as a strong waveguide (e.g., Hoskins and Ambrizzi 1993; Ding et al. 2012; Li et al. 2015b; Yiu and Maycock 2019). However, there are still outstanding questions about the role of the STJ for shaping tropically forced Rossby waves.

Based on observational analyses, Cai et al. (2011) argued for the existence of a continuous Rossby wave train propagating from SST anomalies in the equatorial EIO to the SH extratropics during winter (see their Fig. 9a). However, stationary Rossby waves are reflected toward higher stationary total wavenumber:
Ks=β*U¯
(Hoskins and Ambrizzi 1993) and from Eq. (1), they can only propagate where β*>0 and the flow is westerly (U¯>0). Climatologically, Ks decreases toward the poles, thus Rossby waves are typically reflected equatorward at high latitudes and are absorbed when they hit their low latitude critical line. During winter, β* becomes negative on the poleward side of the STJ between ∼60°E–120°W (e.g., Hoskins and Ambrizzi 1993; Li et al. 2015a; McIntosh and Hendon 2017; O’Kane et al. 2017), where there is strong anticyclonic shear (∂2U¯/∂y2) that can overcome β. Consequently, Ks becomes undefined and should prevent continuous linear propagation of a stationary Rossby wave originating in the tropics to its north and west: the wave should be reflected to the tropics. Therefore, it is unclear how tropical Indian Ocean convective anomalies can impact extratropical latitudes south of Australia, as indicated earlier by Cai et al. (2011).

Closer inspection of the wintertime IOD-induced Rossby wave train (McIntosh and Hendon 2017) suggests that the group velocity goes to zero as it encounters the region where β*<0, with some evidence of reflection to the tropics. However, McIntosh and Hendon (2017) noted amplification of the wave train along this region and the appearance of an additional RWS to its south. Subsequently, they proposed that the wave train continues into the higher latitudes because of a secondary RWS poleward of the STJ that arises from a barotropic transient eddy feedback in the extratropical storm track and excites a wave train that propagates along the midlatitude eddy-driven jet (EDJ) waveguide. When combined with the wave train equatorward of the STJ, it gives the appearance of a continuous wave train emanating from the tropical Indian Ocean, as envisioned by Cai et al. (2011). However, this theory has yet to be substantiated with targeted experimentation.

Stationary Rossby wave propagation is also prohibited in the upper-tropospheric equatorial easterlies. Studies have demonstrated that cross-equatorial propagation can still occur due to the establishment of a RWS (e.g., Sardeshmukh and Hoskins 1985), and also by including the background meridional flow in the barotropic dispersion relation, which enables direct propagation when it is sufficiently strong by acting as a one-way tunnel (e.g., Schneider and Watterson 1984; Li et al. 2015c; Zhao et al. 2015).

The time-mean response to tropical heating is well established in linearized models (e.g., Hoskins and Karoly 1981; Branstator 1983) and in atmospheric general circulation models (AGCMs; e.g., Yiu and Maycock 2019). However, few studies have explored the time-dependent response in an AGCM, which has the advantage of revealing how the time-mean response is established. Therefore, we analyze the temporal evolution of the response to switched-on tropical heating in a comprehensive AGCM and a linear model. We focus on the austral winter months when the STJ is strongest to examine its role in producing the effective RWS and providing reflective effects. Our goal is to elucidate how the wave train that emerges from the tropical Indian Ocean can traverse the β*<0 region and thus to better understand the mechanism of the teleconnection from the Indian Ocean to the SH extratropics during winter.

This teleconnection is not just of academic interest as it promotes Australian drought (e.g., Ummenhofer et al. 2009; King et al. 2020), bushfires (e.g., Cai et al. 2009) and temperature extremes (e.g., McKay et al. 2021), variations in Antarctic sea ice extent (e.g., Meehl et al. 2019; Purich and England 2019; Wang et al. 2019), and influences the Antarctic stratosphere (e.g., Lim et al. 2020; Rao et al. 2020). Therefore, it is pertinent to have an improved understanding of its dynamics.

2. Data and numerical experiments

a. Observational and reanalysis datasets

Wintertime teleconnections between the tropical Indian Ocean and SH extratropics are analyzed using observational and reanalysis datasets from 1979 to 2019. Monthly mean heights and winds are taken from the Japanese 55-year Reanalysis (JRA-55; 1.25° grid; Kobayashi et al. 2015). Gridded (2.5°) monthly mean outgoing longwave radiation (OLR) is used to monitor tropical convection variations and is taken from Liebmann and Smith (1996).

Gridded (1°) monthly mean SST is obtained from the merged Hadley-NOAA/Optimal Interpolation SST analyses (hereafter Hadley-OI; Hurrell et al. 2008). The dipole mode index (DMI; Saji et al. 1999) is used as an indicator for the IOD and is calculated as the anomalous (from the monthly climatology) SST difference between the tropical western Indian Ocean (WIO; 10°S–10°N, 50°–70°E) and EIO (10°S–0°, 90°–110°E) using Hadley-OI. We do not linearly remove the effect of ENSO from the DMI as in Cai et al. (2011) because the indices are weakly correlated in winter, and the IOD wave train pattern is similar with and without the removal of ENSO (Cai et al. 2011).

To develop the observed IOD teleconnection, the detrended and normalized austral winter seasonal-mean DMI is regressed against detrended OLR, heights and winds. The regressed height and wind anomalies are also used to derive the diagnostics described in section 2d. Statistical significance of the regressed anomalies is assessed using a two-tailed t test assuming 40 degrees of freedom.

b. Community Atmosphere Model

1) Model description

We use the National Center for Atmospheric Research Community Atmosphere Model, version 5.1 (CAM5; Neale et al. 2012). CAM5 is the atmospheric component of the Community Earth System Model (CESM1.2.2; Hurrell et al. 2013) and is coupled to an active land model (Community Land Model CLM4; Oleson et al. 2010) with prescribed SSTs and sea ice concentrations from Hadley-OI. CAM5 is run with a 0.9° × 1.25° horizontal grid and 30 hybrid sigma–pressure levels.

2) Experimental setup

A control simulation uses repeating monthly varying SSTs and sea ice averaged over 1982–2001 to represent present-day climate. Other boundary conditions (greenhouse gases, ozone, aerosols, etc.) are prescribed to be year 2000 conditions. We generated a control ensemble by integrating CAM5 30 times for one year starting from 1 January 2000 initial conditions, with a small change to the initial atmospheric temperature applied on the first day using the “pertlim” parameter following Kay et al. (2015). We output a restart file on the first of June, July, and August for each of these 30 integrations. This provides 90 independent initial conditions across the three start dates and thus samples the full winter variability.

The CAM5 control simulates a reasonable wintertime STJ with similar magnitude and structure to that depicted with JRA-55 [see Fig. S1 in the online supplemental material, which displays the observed and simulated terms in Eq. (1)]. The large β* associated with the STJ is slightly narrower meridionally in CAM5 (Fig. S1e) than observed (Fig. S1d), which leads to a narrower STJ waveguide (Fig. S1h). However, the β*<0 region on the poleward flank of the STJ is well represented (Fig. S1h).

We create a 90-member, 30-day sensitivity experiment using these restarts by adding a prescribed diabatic heating anomaly. It is imposed in the temperature tendency equation at each 30-min time step in the radiative heating subroutine in CAM5 following Dixit et al. (2018). This heating is designed to mimic the additional heating during the IOD and is preferred over specified SST anomalies, which have been shown to not always produce a localized convective heating response (e.g., Trenberth et al. 2015). The specified heating takes an elliptical form in the horizontal (e.g., Barsugli and Sardeshmukh 2002) and half sine wave in the vertical (e.g., Meehl et al. 2008) defined by the following function:
δf(σ,λ,ϕ)=Ah(λ,ϕ)υ(σ),
where
h(λ,ϕ)={cos⁡2(π2 λ−λcλw)cos⁡2(π2 ϕ−ϕcϕw),|λ−λc|<λw, |ϕ−ϕc|<ϕw0,otherwise
and
υ(σ=pps)={sin⁡[π(p−10 000)(ps−10 000)],p>10 000 Pa0,p≤10 000 Pa,
which is a function of the sigma level (σ, where p is local pressure and ps is surface pressure), longitude (λ), and latitude (ϕ); A is the maximum amplitude of the heating; (λc, ϕc) is the central point; and λw and ϕw are the zonal and meridional half widths of the anomaly. For our main EIO experiment, we set (λc, ϕc) = (100°E, 5°S), λw = 20° and ϕw = 10° based on the eastern pole for the DMI. We set A to 5 K day−1 (patch average ∼1.2 K day−1) as in previous studies (e.g., Branstator 2014; Meehl et al. 2016). At the center, this rate produces the same vertically integrated latent heating as an ∼11.9 mm day−1 (patch average ∼3.1 mm day−1) precipitation anomaly. A is stronger than typical in winter as the IOD magnitude is largest in spring (Zhao and Hendon 2009). We compared different values of A (1 and 2.5 K day−1; not shown), and the response scales approximately linearly for positive imposed heating. The strong amplitude of the heating and size of the patch helps to ensure that the CAM5 response is statistically significant. Similar results are obtained if the size of the patch is decreased (not shown). The horizontal distribution of the imposed heating in the midtroposphere is shown in Fig. 1a and the vertical profile averaged over the patch is shown in Fig. 1b (red curve). We also conduct a WIO simulation where (λc, ϕc) = (60°E, 0°).
Fig. 1.
Fig. 1.

Heating in the CAM5 EIO experiment. (a) The shading and contours show the 500-hPa horizontal structure of the heating imposed at each time step (K day−1). (b) Vertical structure of the heating imposed at each time step averaged over the patch (15°S–5°N, 80°–120°E; red curve). The 30-day- and patch-averaged induced heating anomaly due to moist processes (DTCOND; purple curve) and total induced diabatic heating anomaly (black curve). The total induced heating rate in CAM5 is the sum of the temperature tendency due to DTCOND, vertical diffusion (DTV), longwave heating (QRL), solar heating (QRS), and orographic wave drag (TTGWORO).

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

The model responds to the imposed heating by producing additional enhanced rainfall primarily collocated with the imposed heating but also nonlocally. The total heating diabatic anomaly (i.e., sensitivity experiment minus control) averaged over the 30-day integration is shown in Fig. S2. Compensating downward motion occurs primarily to the west but also to the east (Fig. S2). The vertical profile of the induced diabatic heating anomaly averaged over the patch and 30-day period is overlaid in Fig. 1b (black curve). It shows that this induced heating is about twice as large as the imposed heating and is dominated by the induced latent heating anomaly (DTCOND; purple curve). Also important for our understanding of the induced RWS, these induced heating anomalies rapidly develop (even by day 1 it is of comparable magnitude as the imposed heating) and appears to saturate by day 3 (not shown). It is also clear in Fig. 1b that the vertical profile of the induced total heating anomaly has the shape of the induced DTCOND (i.e., it peaks above 500 hPa), although the imposed heating anomaly peaks below 500 hPa. Limited experimentation using a deeper prescribed heating profile (not shown) reveals little sensitivity of the response, presumably because the total heating anomaly is dominated by DTCOND that chooses its own profile irrespective of the prescribed profile.

The experiment design using 90 pairs of experiment and control simulations allows for the depiction of the daily (0000 UTC) evolution of the forced response to anomalous heating. However, later in the integration (beyond ∼2 weeks), the experiment and control responses for individual initial conditions become very different, therefore a much larger sample size is required to recover the forced component. Hence, we focus on the daily evolution during the first two weeks of the integration, which is the typical time for the high-latitude response to be established (e.g., Jin and Hoskins 1995), and average over the final two weeks to better extract the time-mean response.

Our focus is on the response to an imposed positive heating anomaly, but we also performed limited experimentation with a negative heating anomaly (not shown). For the first week, the negative heating produces a similar structure to the response to positive heating but with reversed sign. However, the magnitude of the induced negative heating anomaly is much weaker (∼2–3 times) than in the positive case, which results presumably from the positive-only nature of rainfall (i.e., the maximum negative rainfall anomaly is limited by the background rainfall rate). Hence, later in the integration, the negative heating results are noisier than the positive heating results and it is harder to recover the forced component. Therefore, we have not undertaken further analysis of potential nonlinearities in this study.

c. Linear simple general circulation model

1) Model description

The comprehensive AGCM (CAM5) results are compared to similar experiments using a linear simplified AGCM (SGCM; Hall 2000). The SGCM is a dry primitive equation atmospheric model that is linearized about an “observed” three-dimensional climatological basic state for the austral winter season. This basic state is the time mean of a long integration of the nonlinear version of the model with a prescribed constant forcing, which is calculated from observed daily data and acts to maintain the observed basic state. The basic state of the model is therefore close to the observed basic state. However, it may not be exactly the same because the time-mean of the eddy fluxes in the model is not constrained to be identical to the observations, thus resulting in slight biases in the mean flow. The SGCM is run at triangular 31 resolution (∼3.75°) and 10 sigma–vertical levels.

2) Experimental setup

The SGCM is converted into a linear perturbation model and is run on a time-independent basic state (perpetual JJA; e.g., Lin et al. 2010; Lin and Brunet 2018). Similar to the CAM5 simulations, a thermal forcing is applied centered on the equator that follows an elliptical form in the horizontal and half sine wave in the vertical, but which follows υ(σ) = (1 − σ)sin[π(1 − σ)] and peaks at σ = 0.35. The vertical profile is the same as in Lin and Brunet (2018; see their Fig. 2) but A = 4.5 K day−1. Here λw = 40° and ϕw = 11°, thus λw is double the length used in the CAM5 simulations. However, the similarity of the SGCM and CAM5 responses suggests that this difference has little impact on our results. Nonetheless, Ambrizzi and Hoskins (1997) found that zonal elongation of an applied forcing increased the amplitude of meridional propagation, which we have not explored further. As this is a linearized model, the response scales with the magnitude of the prescribed heating and is identical but opposite-signed to prescribed negative heating. Like the CAM5 simulation, we archive instantaneous daily output for 20 days after the heating is switched on and conduct experiments for a heating patch centered at (100°E, 0°).

d. Rossby wave diagnostics

1) Rossby wave source

Following Sardeshmukh and Hoskins (1985), the total RWS is given by
RWS=−Vχ⋅∇η−ηD,
where η is the absolute vorticity, Vχ is the divergent component of the horizontal wind vector, and D is divergence of the horizontal wind. The anomalous RWS is well approximated by its two linear components: S1=−Vχ′⋅∇η¯ which is advection by the anomalous divergent wind of the background absolute vorticity gradient and S2=−η¯D′ which is vortex stretching in response to anomalous subtropical convergence of the divergent winds (Qin and Robinson 1993). The overbar denotes the time mean for the observational analysis and the ensemble mean of the control experiments, and the prime represents the deviation from this mean (sensitivity experiment minus control for the model runs). S1 was shown by Sardeshmukh and Hoskins (1985) to be particularly effective for producing a RWS in extratropical westerlies when the anomalous heating occurred within upper-level tropical easterlies. A spectral filter at truncation T21 was applied to spatially smooth the RWS following Sardeshmukh and Hoskins (1984). Negative RWS values indicate a cyclonic tendency in the SH, while positive values indicate an anticyclonic tendency.

2) Wave activity flux

The Rossby WAF is used to explore horizontal propagation of stationary Rossby waves. The WAF is parallel to the group velocity of stationary Rossby waves for a slowly varying background flow (Plumb 1985). Following Takaya and Nakamura [2001, Eq. (38)]:
W=p cos⁡ϕ2|V¯|{U¯a2 cos⁡2ϕ[(∂ψ′∂λ)2−ψ′ ∂2ψ′∂λ2]+V¯a2 cos⁡2ϕ[∂ψ′∂λ ∂ψ′∂ϕ−ψ′∂2ψ′∂λ∂ϕ]U¯a2 cos⁡ϕ[∂ψ′∂λ ∂ψ′∂ϕ−ψ′∂2ψ′∂λ∂ϕ]+V¯a2(∂ψ′∂ϕ)2−ψ′∂2ψ′∂ϕ2},
where p is local pressure divided by 1000 hPa, |V¯| is the magnitude of the horizontal background wind vector, a is Earth’s radius, ψ is the quasigeostrophic streamfunction, and other variables/notation are defined above. We use the geostrophic approximation to derive the streamfunction; therefore, we only display WAF poleward of 5° latitude.

e. Eddy feedback

We calculate the barotropic feedback of the transient eddies onto the mean flow anomaly to examine the mechanism postulated by McIntosh and Hendon (2017) as outlined in section 1. Following Hoskins et al. (1983), it is calculated as the divergence of the transient eddy vorticity flux and is converted to a height (Z) tendency by application of the inverse Laplacian operator
(∂Z∂t)eddy=fg ∇−2[−∇⋅V″ζ″¯],
where ζ is the relative vorticity, g is the gravitational acceleration, and other variables/notation are defined above. The double prime indicates a high-pass filter, which is calculated with JRA-55 by retaining periods of less than 7 days using a Lanczos filter with 31 weights (Duchon 1979) and with the CAM5 output by simply removing the 7-day running mean. For CAM5, V″ζ″¯ was calculated separately for the sensitivity and control ensemble members and the ensemble-mean difference was computed before calculating the divergence.

3. Results

a. Observed Indian Ocean teleconnection

We first review the observed wintertime teleconnection driven by the IOD (e.g., Cai et al. 2011; McIntosh and Hendon 2017). Figure 2 shows the regression coefficients of austral winter mean fields onto the negative DMI (one standard deviation anomaly). The negative phase of the IOD, which has anomalously warm SSTs in the EIO and anomalously cool SSTs in the WIO, is associated with enhanced convection over the EIO (negative OLR values shaded in blue in Fig. 2a), flanked by weaker suppressed convection to the west and east (positive OLR values shaded in red). The enhanced EIO convection leads to increased upper-level divergent outflow toward the south (vectors in Fig. 2a) and an anticyclonic S1 RWS (solid blue contours in Fig. 2a) in the subtropics to the west of Australia. A weaker cyclonic S2 RWS (dashed orange contours) occurs farther to the south due to convergence of this upper-level outflow near 30°S. An opposite-signed S1–S2 couplet also forms downstream (east) of the first couplet over southeastern Australia, with a strong anticyclonic S2 RWS (solid orange contours), which is discussed in section 3b.

Fig. 2.
Fig. 2.

Regression onto the negative of the DMI during austral winter using JRA-55 (1979–2019) for (a) outgoing longwave radiation (OLR) anomaly (shading, W m−2), 250-hPa divergent wind anomaly (vectors, scale in bottom right, m s−1, vectors with magnitude less than 0.2 m s−1 are not displayed), 250-hPa Rossby wave source (RWS) advection term S1 (blue contours, positive solid, and negative dashed, zero contour omitted, interval is 10−11 s−2 from −3 × 10−10 s−2 to 3 × 10−10 s−2), and 250-hPa RWS stretching term S2 (orange contours, positive solid, and negative dashed, zero contour omitted, interval is 10−11 s−2 from −3 × 10−10 s−2 to 3 × 10−10 s−2). In the SH, positive RWS indicates anticyclonic tendency and negative RWS indicates cyclonic tendency. (b) 250- and (c) 750-hPa geopotential height (Z, shading, m) and horizontal wave activity flux (WAF; vectors, scale in bottom right, m2 s−2, vectors with magnitude less than 0.02 m2 s−2 are not displayed) anomalies, respectively. (d) 250-hPa eddy-induced geopotential height tendency (shading, m day−1). The light green contours in (b)–(d) enclose regressed values of geopotential height in (b)–(c) and eddy feedback in (d) where p < 0.10 calculated using a two-sided t test. The RWS and eddy feedback fields have been smoothed with the Hoskins spectral filter.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

The anticyclonic S1 term maximizes to the west of Australia in association with large β* (Fig. S1d) in the upper troposphere due to the presence of the STJ and appears to be the primary trigger for the southeastward-propagating wave train (Fig. 2b). The wave train splits into two near New Zealand, with one branch extending in the west–east direction along the STJ waveguide and the other taking a great circle route to higher latitudes but is reflected by the EDJ waveguide near 60°S. These waveguides are illustrated in Fig. 3a by the two local maxima of Ks at 250 hPa during austral winter. Superposition of the 250-hPa WAF on Ks (Fig. 3a) suggests that the wave train avoids the undefined Ks region south of Australia, with evidence of along-jet WAF and return equatorward WAF in the central Pacific, although there is a hint of some WAF crossing this β*<0 region to the south of Australia. The extratropical wave train is equivalent-barotropic, with the same-signed height anomalies at 250 (Fig. 2b) and 750 hPa (Fig. 2c). Motivated by McIntosh and Hendon (2017), we also compute the transient eddy feedback (Fig. 2d), which contributes constructively to the wave train centers in the mid- to high southern latitudes. The peak magnitude (∼4–4.5 m day−1) suggests that it would have to act for ∼3 days to account for the height anomaly south of Australia (Fig. 2b).

Fig. 3.
Fig. 3.

The stationary Rossby wavenumber (Ks, dimensionless) during JJA derived from JRA-55 at (a) 250 and (b) 750 hPa. White shading indicates where Ks is undefined due to easterly winds (enclosed by green contours) and where the meridional gradient of absolute vorticity (β*) is reversed (enclosed by magenta contours). Wave activity flux (WAF) vectors are duplicated from Fig. 2.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

In summary, the region where β*<0, described in section 1, is clear at 250 hPa (white shading enclosed by magenta contours, Fig. 3a) but is absent at 750 hPa (Fig. 3b) and the waveguide (maximum in Ks) along the STJ in the upper troposphere is also clear in Fig. 3a. There is some evidence of the WAF emerging from the tropical IO to converge and also reflect away from β*<0 in the upper troposphere. However, some WAF appears to propagate through this barrier, counter to the expectation of linear Rossby wave theory. We thus explore further how the extratropical wave train depicted in Fig. 2 is established in our model experiments.

b. Evolution of the response to eastern Indian Ocean heating in CAM5

To explore the development of the IOD wave train, we examine the daily evolution of the forced response to imposed, switched-on diabatic heating in the EIO in CAM5 (Fig. 1). The 250-hPa height (shading) and horizontal WAF (vectors) anomalies are shown in Fig. 4 for every other day. The direct tropical response resembles the Matsuno–Gill pattern with anticyclonic anomalies straddling the heating to the west and a Kelvin wave front emerging along the equator to the east. It is interesting to observe that the Kelvin wave takes ∼11 days to reach South America, whereas a dry first baroclinic wave should encircle the entire globe in ∼10 days (e.g., Wheeler and Nguyen 2015). Inspection of the rainfall anomalies along the equator (not shown) reveal that the leading edge of this Kelvin wave is associated with a negative rainfall anomaly, suggestive that it is better described as being convectively coupled and therefore travels eastward much slower than a dry wave with the same deep baroclinic structure (e.g., Wheeler et al. 2000).

Fig. 4.
Fig. 4.

(a)–(e) Evolution every other day of the 250 hPa geopotential height (m, shading) and wave activity flux (WAF; vectors, scale in bottom right, m2 s−2, vectors with magnitude less than 0.5 m2 s−2 are not displayed) anomalies from the CAM5 EIO experiment minus control. (f) As in (a)–(e), but for the mean over days 17–30 of the integration. The thick magenta contour indicates the zero contour of β*, which encloses the region of β*<0 poleward of the subtropical jet. β* is calculated using the ensemble-mean of the 90-member EIO sensitivity experiment.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Away from the equator the initial response in the first week appears as a wave train developing from west to east in the upper troposphere with a wavelength of approximately 90° longitude (Figs. 4a–c). This rapid eastward propagation occurs along the STJ waveguide (Fig. S1h). The wave appears to respond to the presence of the β*<0 region (magenta contours) as it is reflected away from this region toward the STJ waveguide and the equator. This initial wave train is largely confined to the upper troposphere (cf. Figs. 4a–c with Figs. 5a–c and 6a–c, which show versions of Fig. 4 at 550 and 750 hPa, respectively), consistent with the confinement of the mean-state westerlies in the vicinity of the STJ to the upper troposphere.

Fig. 5.
Fig. 5.

As in Fig. 4, but for 550 hPa. β* is positive in the subtropics at 550 hPa.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Fig. 6.
Fig. 6.

As in Figs. 4 and 5, but for 750 hPa. β* is positive in the subtropics at 750 hPa.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

A second more poleward wave train with equivalent-barotropic structure becomes prominent in the second week of the integration (Figs. 4–6d–e). It appears to escape into the extratropics, arcing poleward and eastward to higher latitudes and then reflecting back to lower latitudes, reminiscent of a great circle path. This wave train is substantially established by day 11 (Fig. 4e), and the day 17–30 mean (Fig. 4f) resembles the observed IOD wave train (Fig. 2b).

The RWS reveals the apparent origin of the extratropical height response. The S1 and S2 RWS at day 3 are displayed in Fig. 7a, along with the anomalous divergent wind and OLR. We examine the RWS early in the integration (e.g., Li et al. 2015a) to highlight the direct forcing from the imposed heating instead of the vorticity response that develops as the Rossby wave modifies the divergence and vorticity fields later in the integration (altering S2, in particular, as discussed below). Decreased OLR (shading) in the EIO develops over the imposed heating, which is locally largely balanced by upward motion, as confirmed in Fig. 8 that displays the vertical velocity at 400 hPa early in the integration (negative omega i.e., upward motion is shaded in blue). Due to the presence of the STJ and the associated maximum in β* (Figs. S1b,e), the southward divergent flow (vectors) induces a strong anticyclonic S1 RWS anomaly (solid blue contours) directly south of the imposed heating west of Australia (Fig. 7a). There is some opposite-signed S2 RWS (dashed orange contours) on its southwestern flank where the divergent outflow converges and sinks, but the S1 term dominates. We show the total anomalous RWS in Fig. 7b to emphasize that it is dominated by the linear S1 term, consistent with Sardeshmukh and Hoskins (1985). This S1 source appears to be the primary forcing that enables the tropical heating anomaly to excite a poleward-propagating Rossby wave outside of the tropics.

Fig. 7.
Fig. 7.

(a) Rossby wave initiation on day 3 at 250 hPa from the CAM5 EIO experiment minus control. Outgoing longwave radiation (OLR) anomalies are shaded (W m−2). Rossby wave source (RWS) advection term S1 is in blue contours (positive solid and negative dashed, zero contour omitted, interval is 0.3 10−10 s−2 from −3 × 10−10 to 3 × 10−10 s−2) and RWS stretching term S2 is in orange contours (positive solid and negative dashed, zero contour omitted, interval is 0.3 10−10 s−2 from −3 × 10−10 to 3 × 10−10 s−2). In the SH, positive RWS indicates anticyclonic tendency and negative RWS indicates cyclonic tendency. Divergent wind anomalies are shown as vectors (scale in bottom right, m s−1, vectors with magnitude less than 1 m s−1 are not displayed). Zero β* (magenta contour) as in Fig. 4a. (b) The total RWS (positive solid and negative dashed, zero contour omitted, interval is 0.3 10−10 s−2 from −3 × 10−10 to 3 × 10−10 s−2). The RWS fields have been smoothed with the Hoskins spectral filter.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Fig. 8.
Fig. 8.

Omega anomalies (shading, hPa s−1) at 400 hPa from the CAM5 EIO experiment minus control. Anomalies have been smoothed with the Hoskins spectral filter.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Subsequently by days 3–5, a positive S2 anomaly develops over southern and eastern Australia, which acts to extend eastward the anticyclonic S1 anomaly. This anticyclonic S2 term is associated with upward motion that develops over southern Australia (Fig. 8), which can be deduced to occur from the omega equation (e.g., Hoskins and James 2014). As the wave train disperses eastward, a cyclonic center in the upper troposphere develops over southeastern Australia (Fig. 4). This cyclonic anomaly in the presence of the strong vertical shear of the mean zonal wind in the STJ will induce upward motion in the midtroposphere. Therefore, this S2 anomaly appears to develop in response to strong induced ascent over eastern Australia (Fig. 8b) rather than a direct RWS associated with the imposed heating.

The largest total diabatic heating anomaly (Fig. S2) occurs in the same location as the imposed heating but there is also anomalous negative heating in the equatorial WIO, creating a zonal dipole-like pattern, similar to the pattern expected during the negative IOD. In the zonal mean, the imposed heating causes the tropics and SH subtropics to warm and subsequently appears to drive a local Hadley response that shifts the STJ poleward over the Indian Ocean (not shown). We have conducted an experiment where the zonal-mean heating is prescribed to be zero (i.e., by applying compensating cooling in the latitude band of the heated region but outside the source region) and the response is similar, indicating that this mean-state change does not substantially affect wave propagation.

c. Possible pathways to overcome the undefined β* region

After examining the initiation of the wave response to imposed EIO diabatic heating and the evolution of the upper-tropospheric response, we now explore possible pathways that could enable the Rossby wave train to overcome the β*<0 barrier and propagate into SH extratropics.

The first consideration is that the β*<0 region is meridionally narrow, therefore possibly violating the assumptions of linear WKB theory that the mean state varies slowly compared to the scale of the waves. It is possible that the impinging Rossby wave does not even “feel” the β*<0 region and propagates directly across it. However, it is clear from the initial evolution of the wave train that it is reflected, at least partially, away from this region (Fig. 4). Therefore, we can conclude that the wave train does indeed know about the β*<0 region, but this does not preclude the possibility that some activity does indeed propagate across it, which we address below.

Second, it is possible that the wave train propagated largely unimpeded at lower levels of the troposphere where β*>0. The β*<0 barrier is vertically shallow and is confined to the upper troposphere. Below ∼350 hPa (Fig. 3b shows Ks at 750 hPa in JRA-55), Rossby waves should be able to propagate freely to higher latitudes. In the first 10 days at 250 hPa (Figs. 4a–d), most of the WAF has a strong zonal component due to the β*<0 region that reflects this wave activity toward the STJ waveguide, although there is some evidence of continuous southward propagation. Therefore, in the upper troposphere, the height anomalies appear to be largely prohibited from reaching the SH extratropics. At 550 (Fig. 5) and 750 hPa (Fig. 6), however, there is evidence of direct propagation of WAF from the EIO to the south of Australia. Although the RWS to the west of Australia is weaker in the mid- to lower troposphere (not shown), the upper-tropospheric RWS projects onto the barotropic mode, thus initiating Rossby waves that have amplitude at levels below the level of maximum forcing. Figures 5 and 6, therefore, provide evidence of direct and uninhibited propagation of the forced anomalies in the mid- to lower troposphere, below the β*<0 barrier.

The emergence of an equivalent-barotropic structure in the SH extratropics poleward of the β*<0 region could also be facilitated by induced vertical motion resulting from the cyclonic anomaly centered over southeast Australia developing in the presence of the strongly vertically sheared STJ. As the initial wave train disperses eastward, the cyclonic center develops over southeastern Australia (Fig. 4) and upward motion develops over central-eastern Australia at days 3 and 5 (Figs. 8b and 8c). As discussed above, this induced upward motion can be understood from the omega equation (e.g., Hoskins and James 2014): a cyclonic anomaly in the presence of a strong vertical shear of the mean zonal wind will induce upward motion below it. This vertical motion acts as an anticyclonic S2 RWS in the upper troposphere over south-central Australia (Fig. 6a). The expected response to this anticyclonic RWS in the extratropical upper troposphere is a cyclonic anomaly upstream and an anticyclone downstream so that vortex stretching associated with the anticyclonic S2 RWS can be balanced by zonal advection by the strong westerly flow (e.g., Hoskins and Karoly 1981). Such a response would facilitate the emergence of the deep barotropic structure of the cyclonic anomaly to the south of Australia (and south of β*<0). Yang and Hoskins (2017) provided a similar argument to explain the formation of equivalent-barotropic waves in the tropical Western Hemisphere.

These ideas are summarized in Fig. 9, which shows the vertical structure of the height anomalies approximately following the ray path by tracing the centers of the anomalies from Figs. 4–6. The subtropical-midlatitude anticyclonic anomaly (shading) at 110°E is primarily confined to the mid- to upper troposphere (changes sign below 500 hPa), with the maximum anomaly between 150 and 200 hPa. The mid–high-latitude cyclonic anomaly that develops at 130°E by days 5 and 7 appears to do so mainly below the β*<0 region (magenta contour), with the maximum anomaly shifted toward lower levels near 300–400 hPa. Subsequently, the anticyclonic anomaly that develops farther poleward and downstream extends farther upward into the upper troposphere, suggesting that there is direct propagation under the β*<0 region, which then remerges with deep equivalent-barotropic structure at high latitudes where there is no β*<0.

Fig. 9.
Fig. 9.

Following the ray as it moves poleward and eastward every other day from (a) day 3 to (f) day 13 of the CAM5 EIO experiment minus control. Anomalous geopotential height (shading, m) and zero β* (magenta contour). The height anomalies are shown in three sections: averaged over 100°–120°E for 20°–40°S, 120°–140°E for 40°–55°S, and 170°–190°E for 55°–70°S [heading above the (a)–(c) indicates the central longitude]. β* is calculated using zonal wind averaged over 90°E–180° from the EIO experiment.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

The third possibility is that the wave propagated directly across β*<0 in opposition of linear theory. Although most of the upper-tropospheric WAF is trapped along the subtropical waveguide during the development phase of the extratropical wave train (Fig. 4), there is also some evidence of continuous poleward propagation across the β*<0 region that emerges from the anticyclonic center to the west of Australia. This suggests that this region is not entirely impermeable to wave propagation, probably because it is meridionally narrow. The strong reflection away from the β*<0 region suggests that over-reflection could be a mechanism that enables direct propagation across this region. Classical studies such as Lindzen and Tung (1978) show that if a meridionally propagating Rossby wave encounters a region where β*<0, over-reflection occurs (i.e., the wave extracts energy from the mean flow), and wave propagation is possible on either side of this region. Our case should meet the conditions for over-reflection: the RWS occurs in a region where propagation is possible (along the STJ) and there is a region where β*<0 with an embedded zero-wind latitude (i.e., a critical latitude; e.g., Branstator 1983).

We also consider the possibility that the inclusion of the mean meridional wind could allow the Rossby wave to propagate directly across the β*<0 region (e.g., Li et al. 2015c; Zhao et al. 2015, 2019). Zhao et al. (2015) and others demonstrate that the mean meridional wind modifies the meridional group propagation behavior to be in the same direction as the meridional wind, thus enabling a stationary Rossby wave to overcome a critical latitude. However, studies have not explored how the meridional wind influences stationary Rossby wave propagation in regions where the zonal wind is nonzero and β*<0. Near the STJ, the zonal gradient of absolute vorticity (qx¯) is small (assumed to be zero) and is negligible compared to the meridional gradient (qy¯; like β* but with additional terms to include a meridional component). Therefore, the meridional component of the group velocity [Eq. (11b) in Zhao et al. (2015)] can be in either direction (northward or southward) and is modified by the background meridional wind. However, the zonal wind is an order of magnitude larger than the meridional wind, so the waveguide effect along the STJ dominates the wave propagation behavior. At the region where qy¯=qx¯=0, the meridional group propagation reduces to the background meridional wind; therefore, a Rossby wave cannot exist. Importantly, in the Australian sector during winter, the mean meridional wind is equatorward; thus, it seems unlikely that the mean meridional wind can promote poleward propagation of the Rossby wave across the β*<0 region.

We also computed the WAF using the Plumb (1985) definition, which does not include variations in the background meridional wind, and they are nearly identical to the WAF in Fig. 4, thus providing further evidence that the background meridional wind is not important for poleward propagation in our experiments. In this section, we have provided evidence of possible pathways to explain this apparent disagreement between theory and observations and three more possible pathways are described below.

Another possibility is that the extratropical wave train can emerge from the tropics on the upstream side (to the west) of the β*<0 region. In the WIO (west of approximately 90°E), the β*<0 barrier does not exist (Fig. 4 and Fig. S1h). The tropical-subtropical height response to imposed EIO heating is strong in this region (Fig. 4) and therefore some of the wave activity may avoid the barrier and propagate freely into the SH upstream of the β*<0 region. In Fig. 4, it appears that the tails of the extratropical height anomalies originate from farther west [e.g., day 7 (Fig. 4c)] and by day 11 (Fig. 4e), it is clear that the subtropical height response has extended into the west, with clear evidence of WAF emanating from this region. The key S1 RWS also extends to the west of the main β*<0 region (Fig. 7a) and can trigger poleward-propagating waves that can reach the extratropics.

The pathway around to the west of the β*<0 region is conclusively demonstrated with the WIO experiment (60°E, 0°). A direct pathway to higher latitudes on the westward side of the β*<0 region is clear in Fig. 10. This WIO wave train has similar characteristics as the EIO wave train but is translated westward by ∼40°. Note, that the overall response is weaker for the WIO heating than the EIO heating because of the smaller β* to the south of the heating in the WIO (Fig. S1e). Thus, divergent outflow results in a weaker S1 RWS than for heating farther to the east. However, this result confirms that the wave train can emerge into the extratropics around the west of the β*<0 region. We would expect the effect of this pathway to weaken as the forcing is moved farther east to be more in line with the β*<0 region.

Fig. 10.
Fig. 10.

As in Fig. 4, but for the CAM5 WIO experiment minus control.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

It is also possible that the wave train itself acts to reduce the β*<0 region. This is apparent in Fig. 4, whereby the days 17–30 mean (Fig. 4f), the β*<0 south of Australia has disappeared. This occurs because the cyclonic anomaly in the Australian region acts to weaken the zonal winds to the south of the jet, thus reducing the negative gradient of the zonal winds on its poleward flank. Hence, the wave itself could act to promote poleward propagation. However, the poleward wave train is well established before the barrier appears to start to vary and decay on day 9 (Fig. 4d). Therefore, we do not consider the possible induced leaky nature of the barrier to be a mechanism for the wave to reach the SH extratropics in our simulations per se, but it could contribute to the large amplitude of the extratropical response. It further could add to an asymmetry between the positive and negative heating responses, with negative heating acting to reinforce the β*<0 region and thus reducing the extratropical response.

Finally, the possibility proposed by McIntosh and Hendon (2017) is considered: the transient eddy feedback on the 250-hPa flow could act as an effective RWS on the poleward side of the β*<0 region. Figure 11 displays the anomalous feedback of the transient eddies on the 250-hPa mean flow, which is averaged over days 4–27 for brevity. The eddy feedback is largest at mid- to high latitudes to the south of Australia (Fig. 11) and is in-phase with the same-signed cyclonic height anomaly (Fig. 4), thus acting to strengthen this anomaly. It is in good agreement with the observed transient eddy feedback (Fig. 2d) and of comparable magnitude, i.e., the feedback in Fig. 11 acting for 3–4 days could produce the simulated height anomaly. In section 3d we assess whether this feedback is of first-order importance for allowing the wave train to propagate poleward of the β*<0 region when we examine the results from the linear SGCM, which expressly excludes this feedback.

Fig. 11.
Fig. 11.

The eddy-induced geopotential height tendency (m day−1) averaged over days 4–27 at 250 hPa from the CAM5 EIO experiment minus control.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

d. Comparison with a linearized simple model

Some of the ideas addressed above can be assessed by comparison to the linear SGCM. In this model, wave–mean-flow interactions and baroclinic eddy feedbacks do not occur. Figures 12 and 13 show the evolution of the 250- and 550-hPa height and WAF anomalies for the anomalous forcing at 100°E. We only display up to day 11 after which point the high-latitude response evolves very little and is maintained by dissipation. Like the CAM5 experiment, the mid–high-latitude wave train emerges after ∼5 days and has an equivalent-barotropic structure. In contrast to CAM5, in the upper troposphere, the equatorial Kelvin wave propagates faster but the rapid wave train response along the STJ waveguide and the apparent reflection from the β*<0 region are absent (Fig. 12). Instead, WAF appears to strongly converge into this region, where presumably linear dissipation acts to remove the accumulation of WAF. The different responses could be because the SGCM does not incorporate nonlinear interactions (transient flux divergence of eddy vorticity and steady nonlinear flux divergence; e.g., Hendon 1986; Ting and Yu 1998). For example, Bao and Hartmann (2014) suggested that extraction of eddy kinetic energy from the STJ is important for the subtropical response to tropical heating. It could also be related to the way the β*<0 region behaves. In CAM5, this region is reflective (Fig. 4), but in the SGCM it appears to act more dissipatively. Importantly, the WAF anomalies in the SGCM strongly indicate inhibited Rossby wave propagation in the upper troposphere where β*<0 (Fig. 12), with the WAFs appearing to strongly converge where β*<0 with little evidence of reflection.

Fig. 12.
Fig. 12.

Evolution every other day of the 250-hPa geopotential height (m, shading) and wave activity flux (WAF; vectors, scale in bottom right, m2 s−2, vectors with magnitude less than 0.1 m2 s−2 are not displayed) anomalies from the SGCM (100°E, 0°) experiment minus control. The zero contour of β* (thick magenta) is calculated using the SGCM basic state and encloses the region of β*<0 poleward of the subtropical jet.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Fig. 13.
Fig. 13.

As in Fig. 12, but for 550 hPa.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Nonetheless, by day 9 (Fig. 12e), a wave train similar to the observed (Fig. 2b) and simulated CAM5 wave trains (Fig. 4f) has developed. It is also apparent at the 550- (Fig. 13) and 750-hPa (not shown) levels, which closely resemble the CAM5 results (Figs. 5 and 6). Furthermore, the RWS anomalies in the SGCM (Fig. 14) are similar to CAM5 (Fig. 7), demonstrating that the wave train in the SGCM is also generated by the anticyclonic S1 RWS upstream of Australia.

Fig. 14.
Fig. 14.

Rossby wave source (RWS) anomaly on day 3 at 250 hPa from the SGCM (100°E, 0°) experiment minus control. RWS advection term S1 is in blue contours (positive solid and negative dashed, zero contour omitted, interval is 0.15 × 10−10 s−2 from −1.5 × 10−10 to 1.5 × 10−10 s−2) and RWS stretching term S2 is in orange contours (positive solid and negative dashed, zero contour omitted, interval 0.3 × 10−10 s−2 from −3 × 10−10 to 3 × 10−10 s−2). In the SH, positive RWS indicates anticyclonic tendency and negative RWS indicates cyclonic tendency. The RWS fields have been smoothed with the Hoskins spectral filter. Divergent wind anomalies are shown as vectors (scale in bottom right, m s−1, vectors with magnitude less than 0.5 m s−1 are not displayed). No OLR output.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

Compared to 250 hPa (Fig. 12), where strong WAF emanates from the tropical Indian Ocean but appears to have no direct pathway across β*<0, at 550 hPa (Fig. 13), there are vectors with relatively larger magnitude south of Australia, implying continuous Rossby wave propagation, and therefore supporting the pathway described in section 3c (direct propagation below β*<0). This pathway is less evident in the vertical profile of heights, displayed in Fig. 15 (note that the longitude sections in Fig. 15 are slightly different from Fig. 9; see caption), which lacks a clear downward shift in the centers of the anomalies below the β*<0 region that is apparent in CAM5 (Fig. 9). Instead, Fig. 15 seems to suggest that more wave activity propagates directly poleward at all levels in the SGCM as the height anomalies are close to equivalent barotropic throughout the entire hemisphere.

Fig. 15.
Fig. 15.

As in Fig. 9, but for the SGCM. The longitude sections are shifted slightly from Fig. 9 to 90°–110°E for 20°–40°S, 120°–140°E for 40°–55°S, and 180°–200°E for 55°–70°S.

Citation: Journal of the Atmospheric Sciences 79, 9; 10.1175/JAS-D-21-0206.1

In terms of a pathway around the western end of the β*<0 region, the mean state in the SGCM is biased [Fig. S1; see section 2c(1)], with an almost zonally symmetric undefined region across ∼35°S (Fig. 11). Therefore, in this model, the anomalies should be unable to propagate around this region farther upstream to the west.

The SGCM appears to capture the extratropical teleconnection associated with the IOD, suggesting that the transient eddy feedback is not required. However, there is some loss of magnitude in the height anomalies between Australian latitudes and farther south in the SGCM, indicating that the transient eddy feedback may still be important. This can be demonstrated by computing the efficiency of the tropical heating for producing the extratropical response, which we estimate by the magnitude of the cyclonic anomaly south of Australia on day 20 divided by the vertically- and patch-averaged anomalous heating in the eastern Indian Ocean. This ratio is 70 and 52 m K−1 day−1 in CAM5 and the SGCM, respectively. Thus, the nonlinear mode produces an ∼25% bigger extratropical response, which we tentatively attribute to the induction of the transient eddy feedback in the nonlinear model. However, other factors, such as nonlinear advection (e.g., Hendon 1986; Ting and Yu 1998) and the biased western end of the β*<0 region, which inhibits the anomalies from propagating around this region, may also contribute to the diminished magnitude of the extratropical height anomalies in the SGCM compared to the observations and CAM5.

In summary, the transient eddy feedback appears not to be required to establish the extratropical wave train across the β*<0 region. As the wave train cannot skirt to the west of this region, we thus conclude that the main pathway for the extratropical teleconnection is underneath the β*<0 region, which is an in-common mechanism in both models, and possibly also directly across this region. However, the lack of reflection at the β*<0 region in the SGCM suggests that over-reflection may not be the pathway for this to occur.

4. Conclusions and discussion

This study has investigated the dynamics of the wintertime teleconnection from the tropical Indian Ocean into the SH extratropics. Using both a linear model (SGCM) and an AGCM (CAM5), we conducted experiments with an imposed local atmospheric diabatic heating anomaly in the equatorial EIO at 100°E and examined the daily evolution from when the heating is switched on. In this way, we were able to understand the development of the tropically forced Rossby wave and how it can overcome the apparent barrier to stationary wave propagation caused by the strong wintertime STJ, where Ks vanishes on its poleward flank due to β*<0. These experiments therefore help us to understand the apparent disagreement between Ks theory (e.g., Hoskins and Ambrizzi 1993) and observations (e.g., Cai et al. 2011).

The development of the simulated wave train in the 90-member CAM5 ensemble appears to follow a two-stage process. An initial Rossby wave train in the upper troposphere rapidly develops with primarily zonal propagation and is trapped along the STJ waveguide. There is clear evidence of the β*<0 region acting to reflect and trap the anomalies in the waveguide. After ∼7–10 days, a poleward-arcing wave train appears in the extratropics that mimics the observed IOD teleconnection, seemingly traversing the β*<0 region.

Analysis of the CAM5 simulations indicates that the Rossby wave train forced by imposed heating in the EIO appears to traverse the region of β*<0 in the following possible ways:

First, we show evidence of uninhibited propagation of WAFs underneath the β*<0 region in the mid- to lower troposphere. The re-emergence of an equivalent-barotropic structure in the mid- to high latitudes can be partly understood by induced vertical motion, because of the presence of strongly vertically sheared zonal wind, from the omega equation (Yang and Hoskins 2017).

Second, the Rossby wave appears to partly propagate directly through the β*<0 region. counter to the expectation from linear wave theory. This region is only meridionally narrow and does not appear to act as a concrete barrier. Over-reflection (e.g., Lindzen and Tung 1978), as a result of a region where β* changes sign, was suggested as a pathway to allow effectively direct propagation in CAM5. Furthermore, the narrowness of the β*<0 region relative to the scale of the waves possibly violates the WKB approximation of linear wave theory and could provide an additional explanation for the ability of the Rossby wave train to traverse this barrier. To this end, Wirth (2020) argues that stationary Rossby wave tracing theory is a poor diagnostic of waveguidability because the WKB assumption is often violated.

Third, the Rossby wave propagates around the upstream region of β*<0. This region is restricted to approximately 60°E–120°W on the poleward flank of the STJ. Therefore, some of the response likely originates in the tropical WIO and combines with the EIO wave train in the extratropics.

The strong coherence between the observational and CAM5 analysis and the consistent results with the SGCM provides evidence that the mechanisms outlined above operate linearly. McIntosh and Hendon (2017) proposed that a feedback from the transient eddies was the key mechanism to allow the stationary Rossby wave to appear on the poleward side of the β*<0 region. However, the SGCM captures the extratropical teleconnection without any eddy feedbacks, therefore nonlinear feedbacks only act to reinforce the magnitude of the mid–high-latitude height anomalies after it has already been established. In the SGCM, the upstream pathway cannot occur due to the biased mean state, resulting in the β*<0 region extending across the entire Indian Ocean to the central Pacific. The response is also more barotropic throughout the SH, with larger poleward propagation at all levels compared to CAM5.

Although we have assumed that the waves are stationary, our results should still be valid if we had assumed nonstationary wave propagation (Kω) because the only difference between stationary and nonstationary waves in Eq. (1) is in the denominator which becomes (U¯−c) for the nonstationary case. Hence the locations of waveguides associated with westerly jets are similar (e.g., Yang and Hoskins 1996; Rudeva and Simmonds 2021) and because the numerator (β*) does not change, a β*<0 region implies that both Kω and Ks are undefined.

While there are still some gaps between theory and observations, this study helps bring some of these ideas closer together and has helped refine linear stationary wave theory ideas. Studies have typically focused on horizontal propagation of stationary Rossby waves in the upper troposphere (e.g., Hoskins and Karoly 1981). By resolving vertical changes in the forced anomaly, this study provides evidence that the wave can penetrate under the β*<0 region and thus avoid the evanescent region. An issue is also related to the vertical structure of the forced anomaly, which has a deep baroclinic structure at lower latitudes and obtains an equivalent-barotropic structure in the midlatitudes. Previous studies have invoked vertical shear of the basic-state zonal wind to explain the vertical structure of the forced response to internal heating (e.g., Held et al. 1985; Lim and Chang 1986; Ting 1996). Vertical shear implies a conversion of the heat-induced baroclinic mode into barotropic anomalies and the vertical structure of the waves is determined by the shape of the basic-state winds (Held et al. 1985). However, these studies assume a zonal-mean basic state where the zonal wind is westerly everywhere, thus it is not clear how this thinking relates to a basic state where there exists a β*<0 region. The localized ascent over eastern Australia in a region of strongly sheared flow appears to support the development of an extratropical equivalent-barotropic structure, consistent with a mechanism outlined in Yang and Hoskins (2017).

Finally, our results demonstrate that teleconnections strongly depend on the mean state. The mean state can be defined in different ways, typically using a seasonal mean, and we have defined it on a daily scale using an ensemble mean. Ks is sensitive to the record length for the mean winds. When high temporal resolution data are used, there may be instances when wave propagation is possible in a region where it is usually prohibited (e.g., Rudeva and Simmonds 2021). This leaky behavior of the β*<0 region is apparent in the CAM5 simulations and could contribute to the development of the extratropical wave train. Furthermore, a comparison of the WIO and EIO teleconnections demonstrates that the WIO teleconnection can propagate freely to higher latitudes because β*>0 westward of the STJ and β* is still strong enough to generate an RWS. Hence simulated biases in the position and intensity of the STJ and EDJ (e.g., Simpson et al. 2020), and its associated transient eddy feedbacks, and the RWS (e.g., Nie et al. 2019) can impact the simulated IOD teleconnection with potential implications for climate prediction.

There are several possible extensions to this study. Future work could isolate the key pathway, such as by applying a localized sponge relaxation scheme outside the diabatic heating region, which dampens wave propagation in a selected direction (e.g., Shaman and Tziperman 2016). Furthermore, during boreal winter, a similar large region of undefined Ks exists on the poleward flank of the STJ in the west Pacific [e.g., see Fig. 2a in Soulard et al. (2021)]. It would be interesting to explore the dynamics of teleconnections to this region (e.g., Seo and Lee 2017).

Acknowledgments.

We acknowledge support from the Australian Research Council through the Centre of Excellence for Climate Extremes (CLEX; CE170100023). Z.E.G. was supported by an Australian Government Research Training Program Scholarship and a CLEX/Australian Bureau of Meteorology PhD Top-up scholarship. J.M.A. was partially supported by the Regional and Global Model Analysis component of the Earth and Environmental System Modeling Program of the U.S. Department of Energy’s Office of Biological and Environmental Research via National Science Foundation IA 1947282. Computing resources and services were provided by the National Computational Infrastructure, which is supported by the Australian government. The NCAR Command Language (http://www.ncl.ucar.edu) version 6.6.2 was used for data analysis and visualization. Z.E.G. thanks Vishal Dixit for providing the code to implement the heating in CAM5, and Deepashree Dutta for assistance in setting up CESM. The authors thank Steven Sherwood for discussions about experiment design, and Brian Hoskins and Isaac Held for insightful discussions about the results. We also thank Irina Rudeva and Matthew Wheeler for their comments on the first draft.

Data availability statement.

The JRA-55 dataset is available through the Collaborative REAnalysis Technical Environment–Intercomparison Project (CREATE-IT) website (https://esgf-node.llnl.gov/projects/create-ip/). The monthly mean OLR dataset is from the NOAA website (https://psl.noaa.gov/data/gridded/data.olrcdr.interp.html). The merged Hadley-NOAA/Optimal Interpolation SST dataset is available from its website (ftp://ftp.cgd.ucar.edu/archive/SSTICE/). Model output is available upon request.

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