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Franziska Teubler
and
Michael Riemer

Abstract

Rossby wave packets (RWPs) have been associated with increased atmospheric predictability but also with the growth and propagation of forecast uncertainty. To address the important question of under which conditions RWPs imply high and low predictability, a potential vorticity–potential temperature (PV–θ) framework is introduced to diagnose RWP dynamics. Finite-amplitude RWPs along the midlatitude waveguide are considered and are represented by the synoptic-scale, wavelike undulations of the tropopause. The evolution of RWPs is examined by the amplitude evolution of the individual troughs and ridges. Troughs and ridges are identified as PV anomalies on θ levels intersecting the midlatitude tropopause. By partitioning the PV-tendency equation, individual contributions to the amplitude evolution are identified. A novel aspect is that the important role of the divergent flow and the diabatic PV modification is quantified explicitly. Arguably, prominent upper-tropospheric divergent flow is associated to a large extent with latent-heat release below and can thus be considered as an indirect diabatic impact. A case study of an RWP evolution over 7 days illustrates the PV–θ diagnostic. In general, baroclinic coupling and, important, the divergent flow make contributions to the amplitude evolution of individual troughs and ridges that are comparable in magnitude to the wave’s group propagation. Diabatic PV modification makes a subordinate contribution to the evolution. The relative importance of the different processes exhibits considerable variability between individual troughs and ridges. A discussion of the results in light of recent studies on forecast errors and predictability concludes the paper.

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Michael Riemer
and
Frédéric Laliberté

Abstract

This study introduces a Lagrangian diagnostic of the secondary circulation of tropical cyclones (TCs), here defined by those trajectories that contribute to latent heat release in the region of high inertial stability of the TC core. This definition accounts for prominent asymmetries and transient flow features. Trajectories are mapped from the three-dimensional physical space to the (two dimensional) entropy–temperature space. The mass flux vector in this space subsumes the thermodynamic characteristics of the secondary circulation. The Lagrangian diagnostic is then employed to further analyze the impact of vertical wind shear on TCs in previously published idealized numerical experiments. One focus of this analysis is the classification and quantitative depiction of different pathways of environmental interaction based on thermodynamic properties of trajectories at initial and end times. Confirming results from previous work, vertical shear significantly increases the intrusion of low–equivalent potential temperature ( ) air into the eyewall through the frictional inflow layer. In contrast to previous ideas, vertical shear decreases midlevel ventilation in these experiments. Consequently, the difference in eyewall between the no-shear and shear experiments is largest at low levels. Vertical shear, however, significantly increases detrainment from the eyewall and modifies the thermodynamic signature of the outflow layer. Finally, vertical shear promotes the occurrence of a novel class of trajectories that has not been described previously. These trajectories lose entropy at cold temperatures by detraining from the outflow layer and subsequently warm by 10–15 K. Further work is needed to investigate in more detail the relative importance of the different pathways for TC intensity change and to extend this study to real atmospheric TCs.

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Michael Riemer
,
Marlene Baumgart
, and
Sven Eiermann

Abstract

During extratropical transition (ET), tropical cyclones exert a significant impact on the midlatitude circulation. Archetypical features of this impact are jet streak formation, amplification of the downstream trough, and modification of the associated downstream cyclogenesis. This study investigates the relative importance of the jet streak and the upper-level trough for cyclone development by quantifying the respective contributions to midtropospheric vertical motion using the Q-vector partitioning by J. C. Jusem and R. Atlas. Their framework is here extended from quasigeostrophic theory to alternative balance. The Q vector under alternative balance involves the nondivergent wind, instead of the geostrophic wind, and therefore represents more accurately the balanced dynamics associated with vertical motion, in particular downstream of ET where the flow often exhibits significant curvature associated with the amplified trough.

An idealized ET scenario and three real cases, the cyclones downstream of Hanna (2008), Choi-wan (2008), and Jangmi (2009), are analyzed. In all cases, the trough plays a prominent role in cyclone development. The jet streak plays a prominent, favorable role in the idealized ET scenario and downstream of Hanna. In contrast, the role of the jet streak downstream of Choi-wan is clearly of secondary importance. Interestingly, downstream of Jangmi the jet streak has a prominent but detrimental impact. It is concluded that amplified jet streaks associated with ET have the potential to be of significant importance for downstream cyclone development. The few cases considered in this study, however, point to a large case-to-case variability of the role of the jet streak.

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Tobias Selz
,
Michael Riemer
, and
George C. Craig

Abstract

This study investigates the transition from current practical predictability of midlatitude weather to its intrinsic limit. For this purpose, estimates of the current initial condition uncertainty of 12 real cases are reduced in several steps from 100% to 0.1% and propagated in time with a global numerical weather prediction model (ICON at 40 km resolution) that is extended by a stochastic convection scheme to better represent error growth from unresolved motions. With the provision that the perfect model assumption is sufficiently valid, it is found that the potential forecast improvement that could be obtained by perfecting the initial conditions is 4–5 days. This improvement is essentially achieved with an initial condition uncertainty reduction by 90% relative to current conditions, at which point the dominant error growth mechanism changes: With respect to physical processes, a transition occurs from rotationally driven initial error growth to error growth dominated by latent heat release in convection and due to the divergent component of the flow. With respect to spatial scales, a transition from large-scale up-amplitude error growth to a very rapid initial error growth on small scales is found. Reference experiments with a deterministic convection scheme show a 5%–10% longer predictability, but only if the initial condition uncertainty is small. These results confirm that planetary-scale predictability is intrinsically limited by rapid error growth due to latent heat release in clouds through an upscale-interaction process, while this interaction process is unimportant on average for current levels of initial condition uncertainty.

Significance Statement

Weather predictions provide high socioeconomic value and have been greatly improved over the last decades. However, it is widely believed that there is an intrinsic limit to how far into the future the weather can be predicted. Using numerical simulations with an innovative representation of convection, we are able to confirm the existence of this limit and to demonstrate which physical processes are responsible. We further provide quantitative estimates for the limit and the remaining improvement potential. These results make clear that our current weather prediction capabilities are not yet maxed out and could still be significantly improved with advancements in atmospheric observation and simulation technology in the upcoming decades.

Open access
Christian Euler
,
Michael Riemer
,
Tobias Kremer
, and
Elmar Schömer

Abstract

Extratropical transition (ET) of tropical cyclones involves distinct changes of the cyclone’s structure that are not yet well understood. This study presents for the first time a comprehensive Lagrangian description of structure change near the inner core. A large sample of trajectories is computed from a convection-permitting numerical simulation of the ET of Tropical Storm Karl (2016). Three main airstreams are considered: those associated with the inner-core convection, inner-core descent, and the developing warm conveyor belt. Analysis of these airstreams is performed both in thermodynamic and physical space. Prior to ET, Karl is embedded in weak vertical wind shear and its intensity is impeded by excessive detrainment from the inner-core convection. At the start of ET, vertical shear increases and Karl intensifies, which is attributable to reduced detrainment and thus to the formation of a well-defined outflow layer. During ET, the thermodynamic changes of the environment impact Karl’s inner-core convection predominantly by a decrease of θe values in the inflow layer. Notably, notwithstanding Karl’s weak intensity, its inner core acts as a “containment vessel” that transports high-θe air into the increasingly hostile environment. Inner-core descent has two origins: (i) mostly from upshear-left above 4-km height in the environment and (ii) boundary layer air that ascends in the inner core first and then descends, performing rollercoaster-like trajectories. At the end of the tropical phase of ET, the developing warm conveyor belt comprises air masses from several different source regions, and only partly from the cyclone’s developing warm sector, as expected for extratropical cyclones.

Open access
Tobias Kremer
,
Elmar Schömer
,
Christian Euler
, and
Michael Riemer

Abstract

Major airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories [O(106)]. A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in physical space, and use Fréchet distance, which emphasizes differences in trajectory shape, as a similarity metric. To make feasible the use of this elaborate metric, data compression is introduced that approximates the shape of trajectories in an optimal sense. To make clustering of large numbers of trajectories computationally feasible, we reduce dimensionality in distance space by so-called landmark multidimensional scaling. Finally, k-means clustering is performed in this low-dimensional space. We investigate the extratropical transition of Tropical Storm Karl (2016) to demonstrate the applicability of our clustering procedure. All identified clusters prove to be physically meaningful and describe distinct flavors of inflow, ascent, outflow, and quasi-horizontal motion in Karl’s vicinity. Importantly, the clusters exhibit gradual temporal evolution, which is most notable because the clustering procedure itself does not impose temporal consistency on the clusters. Finally, TC problems are discussed for which the application of the clustering procedures seems to be most fruitful.

Open access
Christopher A. Davis
,
Sarah C. Jones
, and
Michael Riemer

Abstract

Simulations of six Atlantic hurricanes are diagnosed to understand the behavior of realistic vortices in varying environments during the process of extratropical transition (ET). The simulations were performed in real time using the Advanced Research Weather Research and Forecasting (WRF) model (ARW), using a moving, storm-centered nest of either 4- or 1.33-km grid spacing. The six simulations, ranging from 45 to 96 h in length, provide realistic evolution of asymmetric precipitation structures, implying control by the synoptic scale, primarily through the vertical wind shear.

The authors find that, as expected, the magnitude of the vortex tilt increases with increasing shear, but it is not until the shear approaches 20 m s−1 that the total vortex circulation decreases. Furthermore, the total vertical mass flux is proportional to the shear for shears less than about 20–25 m s−1, and therefore maximizes, not in the tropical phase, but rather during ET. This has important implications for predicting hurricane-induced perturbations of the midlatitude jet and its consequences on downstream predictability.

Hurricane vortices in the sample resist shear by either adjusting their vertical structure through precession (Helene 2006), forming an entirely new center (Irene 2005), or rapidly developing into a baroclinic cyclone in the presence of a favorable upper-tropospheric disturbance (Maria 2005). Vortex resiliency is found to have a substantial diabatic contribution whereby vertical tilt is reduced through reduction of the primary vortex asymmetry induced by the shear. If the shear and tilt are so large that upshear subsidence overwhelms the symmetric vertical circulation of the hurricane, latent heating and precipitation will occur to the left of the tilt vector and slow precession. Such was apparent during Wilma (2005).

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Paolo Ghinassi
,
Marlene Baumgart
,
Franziska Teubler
,
Michael Riemer
, and
Volkmar Wirth

Abstract

Recently, the authors proposed a novel diagnostic to quantify the amplitude of Rossby wave packets. This diagnostic extends the local finite-amplitude wave activity (LWA) of N. Nakamura and collaborators to the primitive-equations framework and combines it with a zonal filter to remove the phase dependence. In the present work, this diagnostic is used to investigate the dynamics of upper-tropospheric Rossby wave packets, with a particular focus on distinguishing between conservative dynamics and nonconservative processes. For this purpose, a budget equation for filtered LWA is derived and its utility is tested in a hierarchy of models. Idealized simulations with a barotropic and a dry primitive-equation model confirm the ability of the LWA diagnostic to identify nonconservative local sources or sinks of wave activity. In addition, the LWA budget is applied to forecast data for an episode in which the amplitude of an upper-tropospheric Rossby wave packet was poorly represented. The analysis attributes deficiencies in the Rossby wave packet amplitude to the misrepresentation of diabatic processes and illuminates the importance of the upper-level divergent outflow as a source for the error in the wave packet amplitude.

Open access
Volkmar Wirth
,
Michael Riemer
,
Edmund K. M. Chang
, and
Olivia Martius

Abstract

Rossby wave packets (RWPs) are Rossby waves for which the amplitude has a local maximum and decays to smaller values at larger distances. This review focuses on upper-tropospheric transient RWPs along the midlatitude jet stream. Their central characteristic is the propagation in the zonal direction as well as the transfer of wave energy from one individual trough or ridge to its downstream neighbor, a process called “downstream development.” These RWPs sometimes act as long-range precursors to extreme weather and presumably have an influence on the predictability of midlatitude weather systems. The paper reviews research progress in this area with an emphasis on developments during the last 15 years. The current state of knowledge is summarized including a discussion of the RWP life cycle as well as Rossby waveguides. Recent progress in the dynamical understanding of RWPs has been based, in part, on the development of diagnostic methods. These methods include algorithms to identify and track RWPs in an automated manner, which can be used to extract the climatological properties of RWPs. RWP dynamics have traditionally been investigated using the eddy kinetic energy framework; alternative approaches based on potential vorticity and wave activity fluxes are discussed and put into perspective with the more traditional approach. The different diagnostics are compared to each other and the strengths and weaknesses of individual methods are highlighted. A recurrent theme is the role of diabatic processes, which can be a source for forecast errors. Finally, the paper points to important open research questions and suggests avenues for future research.

Open access
Jacopo Riboldi
,
Christian M. Grams
,
Michael Riemer
, and
Heather M. Archambault

Abstract

The extratropical transition (ET) of tropical cyclones (TCs) can significantly influence the evolution of the midlatitude flow. However, the interaction between recurving TCs and upstream upper-level troughs features a large and partly unexplained case-to-case variability. In this study, a synoptic, feature-based climatology of TC–trough interactions is constructed to discriminate recurving TCs that interact with decelerating and accelerating troughs. Upper-level troughs reducing their eastward propagation speed during the interaction with recurving TCs exhibit phase locking with lower-level temperature anomalies and are linked to pronounced downstream Rossby wave amplification. Conversely, accelerating troughs do not exhibit phase locking and are associated with a nonsignificant downstream impact. Irrotational outflow near the tropopause associated with latent heat release in regions of heavy precipitation near the transitioning storm can promote phase locking (via enhancement of trough deceleration) and further enhance the downstream impact (via advection of air with low potential vorticity in the direction of the waveguide). These different impacts affect the probability of atmospheric blocking at the end of the Pacific storm track, which is generally higher if a TC–trough interaction occurs in the western North Pacific. Blocking in the eastern North Pacific is up to 3 times more likely than climatology if an interaction between a TC and a decelerating trough occurs upstream, whereas no statistical deviation with respect to climatology is observed for accelerating troughs. The outlined results support the hypothesis that differences in phase locking can explain the observed variability in the downstream impact of ET.

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