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1. Introduction An important feature of midlatitude atmospheric dynamics is the existence of upper-tropospheric Rossby waves with synoptic- to planetary-scale wavenumbers. Often a Rossby wave is not strictly circumglobal; rather, its amplitude is spatially inhomogeneous with a relative maximum at a specific location decaying to smaller values at larger distances. This gives rise to so-called Rossby wave packets [RWPs; for a recent review see Wirth et al. (2018) ]. A key feature of RWPs is the
1. Introduction An important feature of midlatitude atmospheric dynamics is the existence of upper-tropospheric Rossby waves with synoptic- to planetary-scale wavenumbers. Often a Rossby wave is not strictly circumglobal; rather, its amplitude is spatially inhomogeneous with a relative maximum at a specific location decaying to smaller values at larger distances. This gives rise to so-called Rossby wave packets [RWPs; for a recent review see Wirth et al. (2018) ]. A key feature of RWPs is the
1. Introduction Precipitation over the tropical belt (∼20°N/S) is organized over a wide range of spatial and temporal scales. Among the organized precipitation systems, we see mesoscale convective systems (MCSs), synoptic-scale convectively coupled waves (CCWs), and planetary-scale disturbances such as the Madden–Julian oscillation (MJO; Takayabu 1994 ; Wheeler and Kiladis 1999 ; Wheeler et al. 2000 ; Kiladis et al. 2009 ; Zhang et al. 2020 ). Over the tropical Western Hemisphere
1. Introduction Precipitation over the tropical belt (∼20°N/S) is organized over a wide range of spatial and temporal scales. Among the organized precipitation systems, we see mesoscale convective systems (MCSs), synoptic-scale convectively coupled waves (CCWs), and planetary-scale disturbances such as the Madden–Julian oscillation (MJO; Takayabu 1994 ; Wheeler and Kiladis 1999 ; Wheeler et al. 2000 ; Kiladis et al. 2009 ; Zhang et al. 2020 ). Over the tropical Western Hemisphere
average. To identify when and how the intrinsic limit might impact the skill of future forecasting systems, it is necessary to understand the transition in error growth processes as initial condition accuracy improves. Sun and Zhang (2016) investigated predictability by means of idealized baroclinic wave experiments with a variety of initial condition perturbations. They found that for small-amplitude initial condition perturbations, rapid error growth on convective scales is triggered, which is
average. To identify when and how the intrinsic limit might impact the skill of future forecasting systems, it is necessary to understand the transition in error growth processes as initial condition accuracy improves. Sun and Zhang (2016) investigated predictability by means of idealized baroclinic wave experiments with a variety of initial condition perturbations. They found that for small-amplitude initial condition perturbations, rapid error growth on convective scales is triggered, which is
phase. Beyond this synoptic-scale phase saturation at long lead times (beyond 2 weeks), the results of Buizza and Leutbecher (2015) indicate that there is still forecast skill for large-scale fields. To investigate error growth up to the planetary scale, we employ a complementary diagnostic that filters out phase information and identifies the envelope of the upper-level Rossby waves. This diagnostic is based on finite-amplitude local wave activity (LWA) in the primitive-equation, isentropic
phase. Beyond this synoptic-scale phase saturation at long lead times (beyond 2 weeks), the results of Buizza and Leutbecher (2015) indicate that there is still forecast skill for large-scale fields. To investigate error growth up to the planetary scale, we employ a complementary diagnostic that filters out phase information and identifies the envelope of the upper-level Rossby waves. This diagnostic is based on finite-amplitude local wave activity (LWA) in the primitive-equation, isentropic
1. Introduction Rossby waves are a dominant feature of the midlatitude upper-tropospheric circulation at synoptic to planetary scales ( Rossby 1940 ; Haurwitz 1940 ). Owing their existence to the rotation and the spherical shape of Earth, they take the form of large-scale meanders in the westerly winds ( Rhines 2015 ). On the weather time scale, Rossby wave activity typically varies in longitude and time and tends to organize in the so-called Rossby wave packets (RWPs), rather than
1. Introduction Rossby waves are a dominant feature of the midlatitude upper-tropospheric circulation at synoptic to planetary scales ( Rossby 1940 ; Haurwitz 1940 ). Owing their existence to the rotation and the spherical shape of Earth, they take the form of large-scale meanders in the westerly winds ( Rhines 2015 ). On the weather time scale, Rossby wave activity typically varies in longitude and time and tends to organize in the so-called Rossby wave packets (RWPs), rather than
( Matsuno 1966 ). Two other major wave types have been observed in the tropical belt that are not obtained from the shallow-water equations: the Madden–Julian oscillation (MJO; Madden and Julian 1971 ) and westward traveling tropical disturbances (TDs) including easterly waves ( Riehl 1945 ). All these waves are collectively termed “tropical waves” in this paper. The spatiotemporal scales range from planetary and 30–90 days in the case of the MJO to synoptic and 1–3 days in the case of inertio
( Matsuno 1966 ). Two other major wave types have been observed in the tropical belt that are not obtained from the shallow-water equations: the Madden–Julian oscillation (MJO; Madden and Julian 1971 ) and westward traveling tropical disturbances (TDs) including easterly waves ( Riehl 1945 ). All these waves are collectively termed “tropical waves” in this paper. The spatiotemporal scales range from planetary and 30–90 days in the case of the MJO to synoptic and 1–3 days in the case of inertio
. 2019 ), as well as extreme precipitation and/or flooding ( Blackburn et al. 2008 ; Schubert et al. 2011 ; Hirata and Grimm 2016 ; de Vries 2021 ). Rossby waves manifest as meridional undulations in the extratropical atmospheric circulation, resulting from the conservation of a dynamical property known as potential vorticity (PV); PV is a function of both relative and planetary vorticity, and of static stability. Owing to the rotation and the sphericity of Earth, planetary vorticity increases
. 2019 ), as well as extreme precipitation and/or flooding ( Blackburn et al. 2008 ; Schubert et al. 2011 ; Hirata and Grimm 2016 ; de Vries 2021 ). Rossby waves manifest as meridional undulations in the extratropical atmospheric circulation, resulting from the conservation of a dynamical property known as potential vorticity (PV); PV is a function of both relative and planetary vorticity, and of static stability. Owing to the rotation and the sphericity of Earth, planetary vorticity increases
.0.CO;2 . 10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2 Hoskins , B. J. , and T. Ambrizzi , 1993 : Rossby wave propagation on a realistic longitudinally varying flow . J. Atmos. Sci. , 50 , 1661 – 1671 , https://doi.org/10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2 . 10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2 Huntingford , C. , D. Mitchell , K. Kornhuber , D. Coumou , S. Osprey , and M. Allen , 2018 : Assessing changes in risk of amplified planetary waves in a
.0.CO;2 . 10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2 Hoskins , B. J. , and T. Ambrizzi , 1993 : Rossby wave propagation on a realistic longitudinally varying flow . J. Atmos. Sci. , 50 , 1661 – 1671 , https://doi.org/10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2 . 10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2 Huntingford , C. , D. Mitchell , K. Kornhuber , D. Coumou , S. Osprey , and M. Allen , 2018 : Assessing changes in risk of amplified planetary waves in a
wavenumber, which measures the number of full wavelengths as one goes around the globe. Planetary-scale Rossby waves are typically characterized by zonal wavenumbers , whereas synoptic-scale Rossby waves are characterized by higher wavenumbers. Another idealized incarnation of a Rossby wave would be a single trough or ridge being equivalent to a single dipole of υ . However, except in very rare cases, a Rossby wave appears neither as a purely sinusoidal circumglobal wave nor as a single trough or ridge
wavenumber, which measures the number of full wavelengths as one goes around the globe. Planetary-scale Rossby waves are typically characterized by zonal wavenumbers , whereas synoptic-scale Rossby waves are characterized by higher wavenumbers. Another idealized incarnation of a Rossby wave would be a single trough or ridge being equivalent to a single dipole of υ . However, except in very rare cases, a Rossby wave appears neither as a purely sinusoidal circumglobal wave nor as a single trough or ridge
Waves to Weather (W2W) is a collaborative research center formed to investigate the limits of predictability of weather. Our ability to make forecasts up to a week or more in advance contributes to a strong economy and protects human life and property. Although we commonly speak of “weather,” particularly high-impact weather events take many different forms that result from different physical processes. The most destructive weather disasters in recent years have been associated with floods and
Waves to Weather (W2W) is a collaborative research center formed to investigate the limits of predictability of weather. Our ability to make forecasts up to a week or more in advance contributes to a strong economy and protects human life and property. Although we commonly speak of “weather,” particularly high-impact weather events take many different forms that result from different physical processes. The most destructive weather disasters in recent years have been associated with floods and
