Rossby Wave Train Teleconnections and Atmospheric Blocking

Rossby Wave Train Teleconnections and Atmospheric Blocking describe the large-scale dynamical processes by which localized tropical or extratropical heating anomalies excite dispersing packets of upper-tropospheric planetary Rossby waves across thousands of kilometers, and by which those waves amplify, break non-linearly, and stall into persistent, quasi-stationary high-pressure atmospheric blocks that obstruct the normal eastward progression of mid-latitude synoptic cyclones for 5 to 30 days. Within synoptic-dynamic meteorology, climate predictability, and earth system science, teleconnections explain how convective heating anomalies associated with the Madden–Julian Oscillation (MJO) in the Indo-Pacific warm pool, the Pacific Meridional Mode, or the Indian Summer Monsoon and Findlater Jet reorganize 500 hPa and 200 hPa geopotential height fields over North America, Europe, and Eurasia within 1 to 2 weeks. When a dispersing Rossby wave train undergoes large-amplitude wave breaking or eddy vorticity feedback, it establishes an Omega block, Rex (dipole) block, or high-latitude Greenland/Ural ridge, driving persistent summer heatwaves, agricultural droughts, and winter polar cold-air outbreaks while coupling vertically with the stratospheric Brewer–Dobson Circulation.

As formulated by Brian J. Hoskins and David J. Karoly (1981) and extended by Regina R. Sardeshmukh and Hoskins, stationary and low-frequency planetary Rossby waves propagate horizontally along great-circle rays governed by the barotropic conservation of absolute vorticity (ζ + f). In a divergent tropical atmosphere where deep cumulonimbus convection releases latent heat and drives upper-tropospheric divergence (D = ∇ · v_χ > 0 at 200 hPa), the generation of planetary wave activity is quantified by the Rossby Wave Source (RWS):

S = − ζ_a D − v_χ · ∇ζ_a = − ∇ · (v_χ ζ_a)

where ζ_a = ζ + f is the absolute vorticity and v_χ is the divergent outflow wind vector at the tropopause level (~200 hPa). Because planetary vorticity f and its meridional gradient β = ∂f/∂y are small near the equator but large near the flanks of the subtropical westerly jet stream (25°–35° latitude), divergent upper-level outflow (v_χ) streaming poleward from tropical MJO or El Niño convective clusters strongly advects absolute vorticity across the sharp vorticity gradient of the subtropical jet (−v_χ · ∇ζ_a), generating a concentrated Rossby wave source in the subtropics.

Dispersion Relation, Phase Velocity, and Group Velocity

For a barotropic Rossby wave of zonal wavenumber k and meridional wavenumber l embedded in a basic-state westerly flow U, the dispersion relation for frequency ω, zonal phase speed c_x, and energy-propagating group velocity c_g = (c_gx, c_gy) is:

c_x = ω / k = U − β_M / (k² + l²) c_gx = ∂ω / ∂k = U + [β_M (k² − l²)] / (k² + l²)², c_gy = ∂ω / ∂l = [2 β_M k l] / (k² + l²)²

where β_M = β − ∂²U/∂y² is the meridional gradient of absolute vorticity. Consequently, a stationary Rossby wave train (c_x = 0, so total wavenumber K_s = √(k² + l²) = √(β_M/U)) has zero phase speed—its troughs and ridges remain locked in place—yet possesses a positive eastward and poleward group velocity (c_gx > 0, c_gy ≠ 0) of 20 to 35 m/s (~2,000–3,000 km/day). Wave energy radiates poleward along a great-circle arc until it reaches a high-latitude turning latitude (where l → 0 because K_s decreases poleward as β diminishes), refracting equatorward back toward the subtropics to trace classic arching teleconnection patterns such as the Pacific–North American (PNA) pattern and the circumglobal waveguide teleconnection trapped along the Asian–North American jet.

First defined synoptically by Daniel F. Rex (1950) and adapted into objective geopotential-height gradient reversal indices by Stefano Tibaldi and Franco Molteni (1990), atmospheric blocking occurs when the normal meridional gradient of 500 hPa geopotential height (Z₅₀₀)—which normally slopes downward from south to north, supporting mid-latitude westerly winds via geostrophic balance—reverses sign between 40°N and 60°N (GHGS = [Z₅₀₀(φ₀) − Z₅₀₀(φ_s)] / (φ₀ − φ_s) > 0) across at least 15° of longitude for 5 or more consecutive days.

Potential Vorticity (PV) Inversion and Wave Breaking

From the perspective of Ertel Potential Vorticity (PV) on upper-tropospheric isentropic surfaces (such as the 320 K to 350 K potential temperature surfaces near the dynamic tropopause, defined by PV = 2 PVU where 1 PVU = 10^-6 K m² kg^-1 s^-1), an atmospheric block is a large, isolated anomaly of low-PV air (PV < 0.5–1.0 PVU in the Northern Hemisphere) extracted from the subtropical upper troposphere and injected poleward to 55°–75°N.

By the invertibility principle of potential vorticity (Hoskins, McIntyre, & Robertson, 1985), a deep upper-tropospheric negative PV anomaly induces a warm-core, equivalent-barotropic anticyclonic circulation extending throughout the depth of the troposphere down to the surface, capped by an elevated tropopause (13–15 km high instead of 9–10 km). Because planetary Rossby phase propagation moves westward relative to the mean flow (c_x − U = −β/K²), a large-amplitude blocking ridge adjusts its horizontal scale so that westward Rossby phase propagation exactly balances eastward advection by the background westerly flow (c_x ≈ 0).

Why Blocks Persist: Synoptic Eddy Vorticity Shutoff Valve and Latent Heat Release

A stationary blocking anticyclone subject to radiative cooling and surface Ekman friction would decay within 5 to 7 days without continuous replenishment of low-PV air. Blocks persist for 2 to 4 weeks through two non-linear self-maintenance mechanisms:

1. Upstream Synoptic Eddy Straining (Shutts–Illari–Marshall Mechanism): As fast-moving, high-frequency synoptic baroclinic eddies (weather systems with periods of 2–6 days) approach the western flank of a stationary block where the westerly jet splits into northern and southern branches, the diffluent deformation field stretches the eddies meridionally and compresses them zonally. This eddy straining cascades energy upscale into the stationary block and deposits anticyclonic (low-PV) eddies into the northern blocking center and cyclonic (high-PV) eddies into the southern cut-off low, continuously recharging the dipole against dissipation.
2. Diabatic Warm-Conveyor-Belt (WCB) Outflow: As documented by Stephan Pfahl, Madonna, and Heini Wernli (2015), 30% to 45% of the low-PV air masses entering Northern Hemisphere blocking anticyclones originate from moist ascending warm conveyor belts in upstream extratropical cyclones; latent heat release from cloud condensation inside the rising airstream destroys potential vorticity below the level of maximum heating and injects fresh low-PV air directly into the upper-tropospheric blocking ridge.

Blocking anticyclones are the proximate dynamical cause of the most persistent mid-latitude weather anomalies:

• Summer Heat Domes: Beneath a stationary Omega block (such as the June 2021 Pacific Northwest heat dome, the 2003 European heatwave, or the 2010 Russian block), adiabatic subsidence warms the air column by compression, suppresses cloud formation, and dries out surface soils, triggering land–atmosphere sensible-heat feedback loops.
• Winter Cold-Air Outbreaks and Stratospheric Vortex Disruption: On the eastern flank of a Greenland block (negative North Atlantic Oscillation) or Alaskan/Ural block, northerly flow advects Arctic air equatorward into Europe, East Asia, or North America, while stationary wave numbers k = 1 and k = 2 propagate upward into the stratosphere to accelerate the Brewer–Dobson Circulation and trigger Sudden Stratospheric Warmings.

How can a Rossby wave train have zero phase speed while its energy travels eastward at 2,500 km per day?

Rossby waves are dispersive waves, meaning their phase velocity (the speed of individual ridges and troughs) differs from their group velocity (the speed at which wave energy travels). For a stationary planetary wavelength (~5,000–7,000 km), westward Rossby phase propagation exactly cancels the eastward background westerly wind (c_x = 0), so the individual troughs and ridges remain anchored over the same longitudes while new troughs and ridges amplify successively downstream at the eastward group velocity (c_gx > 0).

How does the tropical Madden–Julian Oscillation (MJO) control blocking over North America and Europe two weeks later?

When the active convective phase of the MJO moves across the eastern Indian Ocean and Maritime Continent (MJO Phases 2–4) or the western Pacific (Phases 6–8), upper-tropospheric divergent outflow at 200 hPa impinges on the subtropical East Asian jet stream, creating a strong Rossby Wave Source. The resulting Rossby wave train propagates across the North Pacific and North America over 7 to 14 days, systematically favoring either positive PNA / positive NAO zonal flow or negative NAO Greenland blocking two weeks after the tropical MJO pulse.

What is the difference between an Omega block and a Rex block?

An Omega block consists of a single central warm-core high-pressure ridge flanked on both its western and eastern bases by two closed low-pressure cyclones, so the 500 hPa height contours trace the Greek letter Ω. A Rex block (or dipole block) consists of a high-latitude anticyclone stacked directly north of a lower-latitude cut-off cyclone along the same meridian, forcing the westerly jet stream to split around a figure-eight circulation with easterly winds blowing between the northern high and southern low.

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2. Rex, D. F. (1950). Blocking action in the middle troposphere and its effect upon regional climate. I. An aerological study of blocking action. Tellus, 2(3), 196–211. https://doi.org/10.3402/tellusa.v2i3.8546
3. Shutts, G. J. (1983). The propagation of eddies in diffluent jetstreams: Eddy vorticity forcing of 'blocking' flow fields. Quarterly Journal of the Royal Meteorological Society, 109(462), 737–761. https://doi.org/10.1002/qj.49710946204
4. Woollings, T., Barriopedro, D., Methven, J., Son, S.-W., Martius, O., Harvey, B., Sillmann, J., Lupo, A. R., & Seneviratne, S. (2018). Blocking and its response to climate change. Current Climate Change Reports, 4(3), 287–300. https://doi.org/10.1007/s40641-018-0108-z