Climatology of Lyapunov exponents: the link between atmospheric rivers and large-scale mixing variability

Garaboa-Paz, Daniel; Eiras-Barca, Jorge; Pérez-Muñuzuri, Vicente

doi:https://doi.org/10.5194/esd-8-865-2017

Articles | Volume 8, issue 3

https://doi.org/10.5194/esd-8-865-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

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https://doi.org/10.5194/esd-8-865-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 8, issue 3

Research article

|

26 Sep 2017

Research article |

| 26 Sep 2017

Climatology of Lyapunov exponents: the link between atmospheric rivers and large-scale mixing variability

Daniel Garaboa-Paz, Jorge Eiras-Barca, and Vicente Pérez-Muñuzuri

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Final revised paper (published on 26 Sep 2017)
Supplement to the final revised paper
Preprint (discussion started on 26 Jan 2017)
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Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Review', Anonymous Referee #1, 27 Feb 2017
- AC1: 'Answer to Referee 1', Vicente Perez-Munuzuri, 20 Apr 2017
RC2: 'referee's comment', Anonymous Referee #2, 28 Feb 2017
- AC2: 'Answer to Referee 2', Vicente Perez-Munuzuri, 20 Apr 2017

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (28 Apr 2017) by Valerio Lucarini

AR by Vicente Perez-Munuzuri on behalf of the Authors (07 Jun 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (13 Jun 2017) by Valerio Lucarini

RR by Anonymous Referee #1 (26 Jun 2017)

RR by Anonymous Referee #2 (11 Jul 2017)

Suggestions for revision or reasons for rejection

The authors have clarified the objectives of their study as well as the scope of their results. The manuscript is now much clearer to me. If I understand correctly, the manuscript uses the Lyapunov exponents at 850 hPa as a proxy of tropospheric mixing, and then characterize mixing in this way:

1. Link between mixing and baroclinic instabilities: The correlation between Eady growth rate (used as a proxy of baroclinicity) and FTLEs (used as a proxy of kinematic mixing) is found with a peak at 5 days of integration time for the FTLE. This value corresponds to the lifetime of extratropic cyclones, and therefore is intepreted as an indication of a mechanistic relation between baroclinic instabilities and tropospheric mixing.

2. link between mixing and modes of climate variability: the inter-annual variability of FTLEs show the typical spatial pattern of El Nino ("the warm pool"), hence in the tropics the authors make a link between mixing and ENSO.

3. link between mixing and atmospheric rivers: the authors show that over the the Atlantic the FTLE activity is above their local average in correspondence of land falling atmospheric rivers.

I find acceptable the use of FTLEs for representing tropospheric mixing, interesting the structure of the paper and in particular the characterisation of mixing in terms of baroclinic instabilities, modes of climate variability, and atmospheric rivers.

Considering that three different classes of processes are considered, the manuscript remains however extremely short. At the very least, there are two issues that should be addressed (and a deeper analysis would be very welcomed).

1. The comparison between Eady growth rates and FTLEs is made by correlating time averaged maps, in which most of the regional patterns are smoothed out. The longitudinal patterns are very weak compared to the latitudinal ones. The time-averaged latitudinal patterns are very simple: a minimum at the equator and a maximum at the middle latitudes. One can wonder whether the correlation is dominated just by these two large-scale extrema, or whether smaller scale features have also a role in the correlation. This can be found out relatively easy, by computing the average of the day-by-day correlation and not only the correlation of the averaged maps. The outcome of the analysis should help to further elaborate on the role of extratropic cyclones (which should have a stronger signature on the day-by-day correaltion).

2. The ENSO analysis is based just on the visual identification of a pattern over the equatorial Pacific. The presence of this pattern is intriguing, but in order to claim a a modulation of the FTLEs by ENSO and more in general a study of the link between climate variability and mixing variability, I would have expected at least a temporal correlation between FTLE activity over the warm pool and the ENSO index, for instance looking at the FTLEs interannual anomalies in the years with positive ENSO and the years with negative ENSO.

Other minor issues:

The use of FTLE to imply mixing has been done in the past, but is not trivial, as Lyapunov exponents are used in some cases to identify transport barriers and sometimes mixing. Can the authors clarify on this point in the text? Something like : "forward FTLEs act as a precondition for mixing by stretching and filamenting air parcels. For this reason, we use here FTLEs as proxies of mixing".

Climate sources: the authors use the expression "climate sources" that I find misleading. I would use "modes of climate variability".

Page 1:
L16: atmospheric mixing -> tropospheric mixing (?)

L21: due to climate sources: what is a climate source? I would rephrase as: "activity associated to climatic variability", or "activity associated to modes of climate variability"

L23: in the same way -> In particular

L21-23: "changes in the atmospheric circulation are important, affecting the transport of energy,
momentum and water vapour thus the mixing processes present in the atmosphere." This sentence should be rephrased (it is obvious that the atmospheric circulation affects transport of energy etc.).

the local mixing rates -> "the local stretching rates (typically, a precondition to mixing)"

L22: bloom -> I find this single reference about the ocean and plankton out of context.

Page 2

L28: "to support this idea": I do not understand exactly which idea. Please explicit it.

L29: we go though (through ??).. -> we analyse the effect of baroclinic instabilities..

"Therefore, we focus.." This sentence repeats the previous one.

"Note as well that there is some longitudinal variability in the mixing that arises from the longitudinal variability in the Lyapunov exponents." I found this sentence tautological, because the authors do not have indipendent estimations of mixing and Lyapunov exponents. They identify mixing and Lyapunov exponents. It is therefore not possible to make a causality link between the two.

L31 convergence -> confluence (in order to avoid the possible misunderstanding that convergence is divergence with a minus sign)

P5
L1: Please add a reference.

P6
L20: true-false -> presence - absence

"revealing how the climate sources affect mixing processes within a few days scale." I find this statement too bold in respect to what is actually shown in this paper. There is no mechanistic analysis of the relation between "climate sources" (see my comment above about this term) and mixing processes. Even the statistical analysis that is done only suggests some possible links between some atmospheric processes (barioclinic instabilities, ENSO, or atmospheric rivers) and mixing.

Page 7-8, final statement:

"atmospheric mixing, as shown in terms of large FTLE values, is a potential state variable to define the state of the atmosphere..." I find this statement too vague. Either the authors are able to elaborate more about the role of the FTLEs as state variable, or this sentence should be removed.

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ED: Publish subject to minor revisions (review by Editor) (17 Jul 2017) by Valerio Lucarini

AR by Vicente Perez-Munuzuri on behalf of the Authors (31 Jul 2017) Author's response Manuscript

ED: Publish as is (11 Aug 2017) by Valerio Lucarini

AR by Vicente Perez-Munuzuri on behalf of the Authors (23 Aug 2017)

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Short summary

For the first time, a climatology of Lyapunov exponents (FTLE) for the period 1979–2014 has been established. This climatology is able to reproduce the main large-scale structures observed in the troposphere. The mean FTLE has been shown to correlate with the baroclinic Eady growth rate within timescales of a few days. As a case study, the contribution of atmospheric rivers to this climatology and their contribution to rainfalls over the Sahara and UK regions have been studied.