| 16 Jul 2026
Potential vorticity modification by turbulence in the upper troposphere and lower stratosphere – Part 1: Mechanistic understanding in an upper-level jet-front system
Abstract. Turbulence has been recognised as an important non-conservative process that modifies potential vorticity (PV) in the upper troposphere and lower stratosphere (UTLS) since the 1970s from research flight measurements. While recent studies based on numerical simulations affirmed the significance of turbulence in changing the PV distribution in the UTLS, the understanding of the underlying mechanism and properties of the PV modification by turbulence remains limited. Therefore, a comprehensive and detailed analysis is required to determine if turbulence may systematically modify PV, which would permit an important up-scale dynamical influence. In this study, we develop an analytical framework and perform a numerical simulation using the Integrated Forecasting System (IFS) model from the European Centre for Medium-Range Weather Forecasts to provide insight into turbulence-induced PV modification. Inspired by the coherent signal near an upper-level jet-front system in the simulation, we first employ an idealised quasi-two-dimensional framework to explore the characteristics of PV modification by turbulence. Both the turbulent heat and the momentum fluxes cause a transfer of PV away from the turbulent zone in most situations, leading to the formation of a tripole pattern of instantaneous PV tendencies. The relevance of the idealised framework to realistic atmospheric flows is validated in the IFS simulation, which features prominent PV tendency tripoles in the frontal zones associated with the upper-level jet stream, consistent with the theory. Material PV changes along air parcel trajectories are further examined by accumulating the instantaneous PV tendencies due to different non-conservative processes in the simulation along the flow. In the vicinity of the upper-level jet-front system, turbulence is shown to be the dominant contributor to accumulated PV changes, which are organised into tripolar bands along the jet axis. By analysing vertical profiles of the atmospheric conditions traced along individual trajectories, air parcels are found to travel consistently through the PV tendency tripoles induced by turbulence. This allows them to steadily accumulate PV changes, which ultimately form the observed tripolar bands. Our results thus (i) provide a mechanistic explanation for the emergence of the tripolar PV tendency pattern due to turbulence with the idealised framework, (ii) demonstrate the possibility of turbulence in systematically modifying PV in the UTLS, which may influence the flow evolution subsequently, and (iii) highlight the importance of the upper-level jet-front systems in providing the spatial and temporal coherence required for the organised behaviour of turbulence in modifying PV. This study therefore advances our understanding of PV modification by turbulence in the UTLS and provides the foundation for future studies, e.g., on the relevance of turbulence to forecast errors and flow dynamics in the UTLS.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Weather and Climate Dynamics.
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General:
This manuscript deals with the generation of bands of potential vorticity (PV) in the upper troposphere and lower stratosphere (UTLS) resulting from non-conservative processes like diabatic heating or turbulence. There are two parts: part 1 uses an idealized framework and argues why turbulence due to strong vertical shear of the ambient wind can lead to tripolar structures in the generated PV field. Part 2 goes on and considers an upper-tropospheric jet-front system in a NWP model simulation with the goal to show that these processes do actually occur in the real world. In this part, the computation of trajectories serves as a bridge between the instantaneous PV tendencies from the idealized framework and the observed patterns in the realistic case, where PV anomalies arise from an accumulation of PV anomalies along trajectories.
The science question behind this manuscript is sound and relevant. I also trust that the computations have been done carefully and are valid. Therefore, I think that the work merits publication. Also, I think that the focus on an upper-level jet-front system in this manuscript is justified, as this is a prototypical flow situation in which one may expect these tripolar patterns. Not surprisingly, the authors hint (in their discussion section) at the fact that the PV patterns turn more complex in more generic flow situations. But I think that’s fine, since one should be allowed to pick prototypical situations in an attempt to advance theoretical understanding.
Yet, I think that the paper does not live up to its potential. This is mostly related to the quality and the style of the text. The text would be well suited for a person who is part of the PhD committee of the first author and has followed the progress of the work over several years. By contrast, the general reader would appreciate (and sometimes need) a presentation on a higher level of abstraction, which assumes a less detailed a-priori familiarity with the topic. Given the text as it is right now, it is rather difficult to find out what is new and why this paper is so important. In particular, the conceptual sections could and should be made more compelling and more lucid. In my eyes such a revision would imply a fairly thorough rewrite of the entire text. Below I provide examples of such issues to clarify what I mean. However, this is not an exhaustive list, which means that addressing each individual issue will not be sufficient to address my criticism.
Major issues
The PV changes due to turbulent fluxes of heat and momentum in Fig. 4d and 4e look rather blobby, and it is only after both are combined that a tripole-like structure becomes apparent (Fig 4f). Is this a miracle, or is there an easy way to understand this? Does it mean that there is a hidden (so far undetected) constraint? Would a different perspective be more illuminating by revealing such a hidden constraint? I my eyes this issue is relevant to the paper, because if this is just a lucky coincidence of this particular case, it would not serve the purpose of corroborating the arguments from the idealized-conceptional part of the paper.
Along similar lines, I find the near-cancellation between the two non-advective fluxes rather dangerous, because it undermines the generalizability of the results from the case study: you may have just been lucky with your choice of the case. Do you provide only a “more nuanced understanding” of a single case, or are the results of more lasting value?
It would help me (and possibly other readers) if you interpret or frame your findings on a more abstract level, like for instance: a monopol in turbulence (a single turbulent layer) creates a dipole in the tendencies of u and theta (your Fig 2), and this in turn creates a tripole in the PV tendency (your Fig 4). Your important contribution is then the fact that there may be near cancellations between the non-advective fluxes of momentum and heat, but nevertheless one obtains a tripole in the end. As I mentioned above, the latter appears somewhat as a miracle.
In section 4 I am asked several times to compare what I see on the plots with what I expect. But for me it was sometimes not clear what my expectation should be.
There seems to be an unresolved issue regarding previous work of Saffin et al. (2017). This somehow limits the value of the present work, as it remains unclear how generic the tripole patterns really are.
It is nice that you introduce the two-dimensional vectors H and M (eqn. 12). At the same time, you do not really stick to this formulation, like for instance in eqn. (14), which is formulated without any refence to H and M. I trust that all your calculations are OK, but it was somewhat confusing for me to shift back and forth between the different formulations.
Specific comments:
Line 34 “in local Cartesian coordinates”: Considering the Nabla symbol as an operator, there seems (at this stage) no need to refer to any specific coordinate system.
Line 45, “which induce a non-advective PV flux…”
Line 45, “…. and induce far-field effects….”: strictly speaking this cannot be understood at this point. It requires the additional concept of PV inversion for the balanced flow component to make sense --- which you have not talked about up to this point.
Line 50, “… influences the nonlinear evolution….”: is the evolution of linear waves unaffected?
Line 55/56, “radiation and turbulence…. cloud processes and convection”: these two pairs of mechanisms do not seem very distinct.
Line 120, “convection, cloud processes and turbulence”: not clear what exactly you mean by these three terms, moreover they do not seem mutually exclusive.
Line 157, not clear what feature you refer to by “tongue”.
Line 177, “…. based on reverse domain filling”: what is “reverse domain filling”?
Line 307, “below/above the heating maximum”: wouldn’t it be more relevant to frame this change in terms of the maximum of the turbulent flux (rather than the heating maximum)?
Line 315: I do not really see how the horizonal term creates a horizonal dipole. Can you explain? And: how do I have to visualize a “horizontal dipole superimposed on a vertical one”?
Line 329: can you tell the reader why the angle between m and theta surfaces is “usually acute”?! This seems rather central to this section and may not be obvious to everybody.
Line 336, then u-dot times theta-dot is positive…. but only above and below the turbulent layer, not right within the turbulent layer.
Line 370, “the scalar product”: which one, you have recently pointed out two scalar products in (17a) and (17b), and it is not clear which one you refer to. Possibly both?
Line 382, what does “divergent from isentropes” mean? (and similar for m-isopleths). Similarly on line 388 “diverges from the isotachs”.
The arrows in Fig. 4 are very small and hard to read (at least in the printed version).
Line 444, strictly speaking the plot only illustrates the “counteracting effect…. on the fluxes H and M”; PV modification is then given by the divergence of these fluxes, but for me it is hard to visualize the divergence in my head. Therefore, it is almost impossible for me to see from the plot what you ask the reader to see in the plot.
Line 453: does the reader know what the “typical vertical pattern” should look like? Similarly, “one may expect…”: are you sure the reader has the same picture in his/her head as you have? Actually, regarding the latter claim I am not sure whether I can follow you. It seems that (in my head!) I would have to evaluate the convergence of these fluxes, and this is not straightforward for me. Also, the computed DQ/Dt in panels 4d and 4e indicate a rather blobby picture, so I am not sure whether and to what extent this corresponds to my expectation (if I had any).
Paragraph starting on line 473: there seems to be conflicting information. On the one hand, Spreitzer obtained tripolar patterns while only considering turbulent fluxes of heat, while here you show that the turbulent fluxes of momentum are actually the key for producing the tripolar structures. Can you resolve? Is this simply a case-to-case variability? If so, then statements such as “turbulent momentum fluxes dominate” only apply to the respective case and do not, per se, have a more general validity.
Line 487, “instantaneous PV tendency field”: Just to be sure, when you talk about PV tendencies you always talk about material rates of changes, i.e., material tendencies, right? If this is so, it could and should be stated more clearly or more often. Later in line 495 you refer to material tendencies, but it seems that at this point you think more in terms of “accumulated” tendencies. In any case, both material tendencies and local rates of change can be studied either on an instantaneous basis or on an accumulated basis (parcel-based and grid-point-based, respectively). The issue of local rate of change versus material rate of change needs to be clearly distinguished from the concepts of instantaneous versus accumulated.
Line 505, “showing a decrease….”: but there seem to be just as many region close to the cut-off that show an increase?!
Line 517 (and later lines), “caused by …. “: a more careful wording would be “associated with….”
533, what is the “downstream flank of a cut-off”? To a first approximation a cut-off is azimuthally symmetric, which makes it difficult to define a downstream or an upstream direction.
Section 7.1: I got somewhat confused with this “summary”. There are tripolar patterns both in the vertical and in the horizontal (see, e.g., Figs 7 and 8 versus Fig. 6a), right? Could you more clearly distinguish between these two? Are both features related to turbulence?
Line 628, tropopause-relative versus turbulence-layer-relative: shouldn’t this essentially be the same, given that the turbulent layer is at a well-defined distance from the tropopause almost by design?!
Fig. 10: I am not happy with the dashed line, which is meant to indicate the “coherent direction”. To be sure, this is a quasi-three-dimensional visualization. But still, I thought that the “coherent direction” in this configuration corresponds with the jet axis, and in my eyes this is not what the dashed line indicates.
Lines 735-744 and Fig. 10: this section seems rather repetitive at this point. You may consider shifting the section to much earlier, after your idealized considerations and before you analyse the model data. This would facilitate the reader the see in the subsequent analysis what he/she is supposed to see.
Line 747, “aims at corroborating…”
Line 768, “flux is diverging from isentropes….”: what does this mean?
Fig B1 (and similar figures): the lines are so thin that it is hard to distinguish their colors.