the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Weather persistence on subseasonal to seasonal timescales: a methodological review
Alexandre Tuel
Olivia Martius
Abstract. Persistence is an important concept in meteorology. It refers to surface weather or the atmospheric circulation either remaining in approximately the same state (stationarity) or repeatedly occupying the same state (recurrence) over some prolonged period of time. Persistence can be found at many different timescales; however, the subseasonal to seasonal (S2S) timescale is especially relevant in terms of impacts and atmospheric predictability. For these reasons, S2S persistence has been attracting increasing attention by the scientific community. The dynamics responsible for persistence and their potential evolution under climate change are a notable focus of active research. However, one important challenge facing the community is how to define persistence, from both a qualitative and quantitative perspective. Despite a general agreement on the concept, many different definitions and perspectives have been proposed over the years, among which it is not always easy to find one’s way. The purpose of this review is to present and discuss existing concepts of weather persistence, associated methodologies and physical interpretations. In particular, we call attention to the fact that persistence can be defined as a global or as a local property of a system, with important implications in terms of methods but also impacts. We also highlight the importance of timescale and similarity metric selection, and illustrate some of the concepts using the example of summertime atmospheric circulation over Western Europe.

Notice on discussion status
The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.

Preprint
(9224 KB)

The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
(9224 KB)  Metadata XML
 BibTeX
 EndNote
 Final revised paper
Journal article(s) based on this preprint
Alexandre Tuel and Olivia Martius
Interactive discussion
Status: closed

RC1: 'Comment on egusphere2023111', Anonymous Referee #1, 24 Feb 2023
Reviewer Comment on: Weather persistence on subseasonal to seasonal timescales: a methodological review
Authors: Alexandre Tuel and Olivia Martius
Submitted to: egusphere 2023 111
SummaryThe authors present a manuscript for a review article on persistence as the occurrence of approximately constant or recurrent atmospheric states in the subseasonal to seasonal (S2S) time range. Persistence determines damages, challenges understanding and promises predictab ility. The review considers various aspects of persistence: definitions, methodologies, and examples encompassed by this rather general notion
In their review, the authors undertake a challenge when they combine meteorological observations and a mathematical d efinition in terms of advanced statistical and dynamical approaches. While a general definition of persistence is already hard, the related notion recurrence is even more difficult to grasp and to distinguish. Not surprisingly, the review is weak when the authors attempt the almost impossible task to provide a comprehensive theoretical framework, but it gets stronger when it resorts to methodologies and meteorological examples. In particular t he variety of examples and their properties show the width of the seem ingly simple no tion persistence.The authors are well aware of the difficulties involved and do not hide that. The review is wor th to read for two reasons: the collection of method ologies th at have been sugge sted to analyze persistence, and the huge amount of examples. In summary the authors provide a broad and useful overview with a lot of insight. Below I mention some aspects that I noticed.
Specific comments
Line 55: Since persistence needs a timescale for the definition this question is somehow circular: ‘At which timescale(s) does the persistence occur? There could be reference to Section 3.4.
Line 124, Eq (x(t))_{t} ∈ R^{m} what is the meaning of the subscript t together with the argument t? This should be explained.
Line 126, I recommend to use ‘state space’ instead of phase space (the often used notion phase space is reserved for Hamiltonian systems).
Line 136: To characterize the difference between precipitation and temperature an autocorrelation time would be appropriate here. This is better than ‘inertia’ since it is difficult to associate precipitation with an inertia, while temperature, on the other hand, has something like an inertia due to the heat capacity.
Lines 143, 155 in Section 3.1 Global, state and episodic persistence. It seems that global and state persistence are different concepts. Global persistence appears nothing else than stationarity which includes recurrence. Why is global persistence ‘strongly related to intrinsic system predictability’? Maybe these definitions could be useful: Does persistence of a state x(t) mean dx(t)/dt=0. And could global persistence be defined in terms of integrals or averages like d<x(t)>/dt=0? And are conservation laws useful?
Line 184: What is a ‘symmetrically, persistent state’?
Line 188: How can this sentence be understood: ‘However, state persistence only characterizes the average behavior of system states.’
Line 201: Section 3.2
Here is a good opportunity to define Lagrangian stationarity of a quantity ѱ(x,t) along a flow u, by ∂ѱ/∂t + u∙∇ѱ = 0, in comparison to the Eulerian stationarity with ∂ѱ/∂t = 0.
Line 216: The authors write ‘selfsimilarity of system values x(𝑡) with a metric’ but this notion can be confused with geometric selfsimilarity used in the definition of fractal objects for example. Or is that what the authors intend?
Line 300: write what the symbol E(…) denotes.
Line 348: On Longrange memory: mention the absence of a timescale.
Line 360: Write that the Hurst exponent H and d are related by H=2d+1, see the Table 1 in Franzke et al. (2020).
Line 382: Written is: ‘If temporal dependence is present’. This is unclear. Eq. (10) is the result a powerlaw in of ρ (Eq.(6)), line 350.
Line 490: Section 4.2.4. The role of the extremal index θ is difficult here. In extreme value statistics the extremal index is the inverse time scale with cooccurring extreme events, used to eliminate short term variability and to combine events. Why is this index a measure of stationarity? Is it correct that short term excursions are allowed with θ in Eq (13)?
Line 569: Please write that R_{X}_{0} is the residence time for state x_{0}.
 AC1: 'Reply on RC1', Alexandre Tuel, 27 Mar 2023

RC2: 'Comment on egusphere2023111', Abdel Hannachi, 03 Apr 2023
Review of "Veather persistence on subseasonal to seasonal
timescales: a methodological review" by Tuel and Martius,
submitted to Geoscientific Model Development.The authors attempt to provide a 'comprehensive' review of weather
persistence on S2S timescales. The authors start by stating the
origin of persistence, i.e. stationarity/quasistationarity or
recurrence, along with the different methodologies. Stationarity
is then described in terms of globality (eg autocorrelation),
states (eg patterns) and episodic events. Lastly, they describe
recurrence as another facet of persistence via various
aspects/measures.
Recommendation
The paper exposes the subject of persistence in a detailed fashion.
It is quite useful to researchers working on S2S predictability,
especially early career scientists (eg PhD students).
I support its publication in Geoscientific Model Development
subject to some minor changes as detailed below.
Major Comments
The authors have put great effort in an attempt to bring together
all the different blocs of persistence. Persistence is a loose
concept as there is no definite definition for it, and the authors
propose to bring together its different facets. I had to go more
than once to get a clear picture of the different bits and pieces.
For example, in the 6 sections there are 13 subsections (excluding
subsubsubsections).1. Perhaps to aid readers, especially early career researchers, an
extra figure showing a treelike diagram linking the different
concepts of persistence would be welcome.2. Some related papers are missing from this review. Two particular
references related to persistence and therefore predctability:
predictive oscillation patterns (Kooperberg and O'Sullivan 1996),
and a related paper: optimally interpolated patterns (Hannachi
2008), making use of the power spectra (ie autocorrelation.)In global stationarity, thirsorder statistics based, eg on
bispectrum (Pires and Hannachi 2021) would complement the
persistence description.In relation to extremes and persistence archetypal analysis
Hannachi and Trendafilov 2017, Chapman et a. 2022) also identifies
'quasistationary' states or regimes.
Minor Comments
1. Pg 1, abstract: delete acronym S2S. It is abbreviated in
section 1.2. Pg 3, l75: you mean Fig. 1c.
3. Pg7, l175: delete 'of'
4. Pg 13, eq (15): may be use 0<\alpha<1 to include the case of
antipersistence.
l358: add the following reference on short timescale of
precipitation (Hannachi 2014).
l367,369: may be 'persistence' is more convenient here
than 'stationary'.
5. Pg 14, last paragraph 4.1.2: Fig.3 does not seem to have been
mentioned.6. Pg 15, l407: consider adding an earlier reference of Baur (1951)
on Grosswetterlagen.7. Pg18, l461: add "by projecting simplified dynamics (eg quasi
geostrophy) onto the leading modes of variability of the
GCM simulation" after "January conditions".8. Pg 20, eq (13): x is not specified, and I think there is some
confusion in the original reference (Faranda et al.) I
think x represents the log of the distance between state
at time t {\bf x}(t) and {\bf x}_0.9. Pg 23, eq(21): my understanding is that \alpha is a probability
(P(x_0) = P(x_{t+1}=x_0x_t=x_0)), therefore eq(21) < 0,
and also log(\alpha)<0, please clarify.10. Pg 31, l646: Ripley's K function was considered in Stephenson
et al. (2004), and Hannachi (2010).11. Pg 31, l686: " ... as the variance of successive event counts
over an interval of ..."12. Pg 37, l791: full stop before 'Note'
l793: 'too'
l801: use 'measures' instead of 'metrics'Fig. 15: are a, b,c 1day apart?
Section 5: I suggest renumbering/relabelling the subsections as:
5.1 Diagnostic methods
5.1.1 Window counts
5.1.2 Dispersion metrics
5.1.3 Ripley's K function
5.1.4 Distribution of interevent times
5.2 Stochastic modeling of recurrence
5.2.1 Events series
5.2.2 Recurrence plotsReferences
Baur F, 1951: Extendedrange weather forecasting. In: T. F.
Malone, ed. Compendium of Meteorology, Amer. Met. Soc.,
Boston MA, pp. 81433.
Chapman C C, D P Monselesan, J S Risbey, M Feng, and B M Sloyan,
2022: A largescale view of marine heatwaves revealed by
archetype analysis. Nature Communication, 13, 7843.
Hannachi A, 2008: A new set of orthogonal patterns in weather
and climate: optimally interpolated patterns. J. Climate, 21,
67246738.
Hannachi A, 2010: On the origin of planetaryscale extratropical
winter circulation regimes. J. Atmos. Sci., 67, 13821401.
Hannachi A, 2014: Intermittency, autoregression and censoring: a
firstorder AR model for daily precipitation. Meteorol. Appl.,
21, 384397.
Hannachi A, and N Trendafilov, 2017: Archetypal analysis: mining
weather and climate extremes. J. Climate, 30, 69276944.
Kooperberg C, and F O'Sullivan, 1996: Prediction oscillation
patterns: A synthetic of methods for spatialtemporal
decomposition of random fields. J. Amer. Stat. Assoc., 91,
14851496.
Pires C, and A Hannachi, 2021: Bispectral analysis of nonlinear
interaction, predictability and stochastic modelling with
application to ENSO. Tellus A, 73, 130.
Stephenson D B, A Hannachi, and A O'Neill, 2004: On the existence
of multiple climate regimes. Q. J. R. Meteorol. Soc., 130,
583605.Citation: https://doi.org/10.5194/egusphere2023111RC2  AC2: 'Reply on RC2', Alexandre Tuel, 02 May 2023
Interactive discussion
Status: closed

RC1: 'Comment on egusphere2023111', Anonymous Referee #1, 24 Feb 2023
Reviewer Comment on: Weather persistence on subseasonal to seasonal timescales: a methodological review
Authors: Alexandre Tuel and Olivia Martius
Submitted to: egusphere 2023 111
SummaryThe authors present a manuscript for a review article on persistence as the occurrence of approximately constant or recurrent atmospheric states in the subseasonal to seasonal (S2S) time range. Persistence determines damages, challenges understanding and promises predictab ility. The review considers various aspects of persistence: definitions, methodologies, and examples encompassed by this rather general notion
In their review, the authors undertake a challenge when they combine meteorological observations and a mathematical d efinition in terms of advanced statistical and dynamical approaches. While a general definition of persistence is already hard, the related notion recurrence is even more difficult to grasp and to distinguish. Not surprisingly, the review is weak when the authors attempt the almost impossible task to provide a comprehensive theoretical framework, but it gets stronger when it resorts to methodologies and meteorological examples. In particular t he variety of examples and their properties show the width of the seem ingly simple no tion persistence.The authors are well aware of the difficulties involved and do not hide that. The review is wor th to read for two reasons: the collection of method ologies th at have been sugge sted to analyze persistence, and the huge amount of examples. In summary the authors provide a broad and useful overview with a lot of insight. Below I mention some aspects that I noticed.
Specific comments
Line 55: Since persistence needs a timescale for the definition this question is somehow circular: ‘At which timescale(s) does the persistence occur? There could be reference to Section 3.4.
Line 124, Eq (x(t))_{t} ∈ R^{m} what is the meaning of the subscript t together with the argument t? This should be explained.
Line 126, I recommend to use ‘state space’ instead of phase space (the often used notion phase space is reserved for Hamiltonian systems).
Line 136: To characterize the difference between precipitation and temperature an autocorrelation time would be appropriate here. This is better than ‘inertia’ since it is difficult to associate precipitation with an inertia, while temperature, on the other hand, has something like an inertia due to the heat capacity.
Lines 143, 155 in Section 3.1 Global, state and episodic persistence. It seems that global and state persistence are different concepts. Global persistence appears nothing else than stationarity which includes recurrence. Why is global persistence ‘strongly related to intrinsic system predictability’? Maybe these definitions could be useful: Does persistence of a state x(t) mean dx(t)/dt=0. And could global persistence be defined in terms of integrals or averages like d<x(t)>/dt=0? And are conservation laws useful?
Line 184: What is a ‘symmetrically, persistent state’?
Line 188: How can this sentence be understood: ‘However, state persistence only characterizes the average behavior of system states.’
Line 201: Section 3.2
Here is a good opportunity to define Lagrangian stationarity of a quantity ѱ(x,t) along a flow u, by ∂ѱ/∂t + u∙∇ѱ = 0, in comparison to the Eulerian stationarity with ∂ѱ/∂t = 0.
Line 216: The authors write ‘selfsimilarity of system values x(𝑡) with a metric’ but this notion can be confused with geometric selfsimilarity used in the definition of fractal objects for example. Or is that what the authors intend?
Line 300: write what the symbol E(…) denotes.
Line 348: On Longrange memory: mention the absence of a timescale.
Line 360: Write that the Hurst exponent H and d are related by H=2d+1, see the Table 1 in Franzke et al. (2020).
Line 382: Written is: ‘If temporal dependence is present’. This is unclear. Eq. (10) is the result a powerlaw in of ρ (Eq.(6)), line 350.
Line 490: Section 4.2.4. The role of the extremal index θ is difficult here. In extreme value statistics the extremal index is the inverse time scale with cooccurring extreme events, used to eliminate short term variability and to combine events. Why is this index a measure of stationarity? Is it correct that short term excursions are allowed with θ in Eq (13)?
Line 569: Please write that R_{X}_{0} is the residence time for state x_{0}.
 AC1: 'Reply on RC1', Alexandre Tuel, 27 Mar 2023

RC2: 'Comment on egusphere2023111', Abdel Hannachi, 03 Apr 2023
Review of "Veather persistence on subseasonal to seasonal
timescales: a methodological review" by Tuel and Martius,
submitted to Geoscientific Model Development.The authors attempt to provide a 'comprehensive' review of weather
persistence on S2S timescales. The authors start by stating the
origin of persistence, i.e. stationarity/quasistationarity or
recurrence, along with the different methodologies. Stationarity
is then described in terms of globality (eg autocorrelation),
states (eg patterns) and episodic events. Lastly, they describe
recurrence as another facet of persistence via various
aspects/measures.
Recommendation
The paper exposes the subject of persistence in a detailed fashion.
It is quite useful to researchers working on S2S predictability,
especially early career scientists (eg PhD students).
I support its publication in Geoscientific Model Development
subject to some minor changes as detailed below.
Major Comments
The authors have put great effort in an attempt to bring together
all the different blocs of persistence. Persistence is a loose
concept as there is no definite definition for it, and the authors
propose to bring together its different facets. I had to go more
than once to get a clear picture of the different bits and pieces.
For example, in the 6 sections there are 13 subsections (excluding
subsubsubsections).1. Perhaps to aid readers, especially early career researchers, an
extra figure showing a treelike diagram linking the different
concepts of persistence would be welcome.2. Some related papers are missing from this review. Two particular
references related to persistence and therefore predctability:
predictive oscillation patterns (Kooperberg and O'Sullivan 1996),
and a related paper: optimally interpolated patterns (Hannachi
2008), making use of the power spectra (ie autocorrelation.)In global stationarity, thirsorder statistics based, eg on
bispectrum (Pires and Hannachi 2021) would complement the
persistence description.In relation to extremes and persistence archetypal analysis
Hannachi and Trendafilov 2017, Chapman et a. 2022) also identifies
'quasistationary' states or regimes.
Minor Comments
1. Pg 1, abstract: delete acronym S2S. It is abbreviated in
section 1.2. Pg 3, l75: you mean Fig. 1c.
3. Pg7, l175: delete 'of'
4. Pg 13, eq (15): may be use 0<\alpha<1 to include the case of
antipersistence.
l358: add the following reference on short timescale of
precipitation (Hannachi 2014).
l367,369: may be 'persistence' is more convenient here
than 'stationary'.
5. Pg 14, last paragraph 4.1.2: Fig.3 does not seem to have been
mentioned.6. Pg 15, l407: consider adding an earlier reference of Baur (1951)
on Grosswetterlagen.7. Pg18, l461: add "by projecting simplified dynamics (eg quasi
geostrophy) onto the leading modes of variability of the
GCM simulation" after "January conditions".8. Pg 20, eq (13): x is not specified, and I think there is some
confusion in the original reference (Faranda et al.) I
think x represents the log of the distance between state
at time t {\bf x}(t) and {\bf x}_0.9. Pg 23, eq(21): my understanding is that \alpha is a probability
(P(x_0) = P(x_{t+1}=x_0x_t=x_0)), therefore eq(21) < 0,
and also log(\alpha)<0, please clarify.10. Pg 31, l646: Ripley's K function was considered in Stephenson
et al. (2004), and Hannachi (2010).11. Pg 31, l686: " ... as the variance of successive event counts
over an interval of ..."12. Pg 37, l791: full stop before 'Note'
l793: 'too'
l801: use 'measures' instead of 'metrics'Fig. 15: are a, b,c 1day apart?
Section 5: I suggest renumbering/relabelling the subsections as:
5.1 Diagnostic methods
5.1.1 Window counts
5.1.2 Dispersion metrics
5.1.3 Ripley's K function
5.1.4 Distribution of interevent times
5.2 Stochastic modeling of recurrence
5.2.1 Events series
5.2.2 Recurrence plotsReferences
Baur F, 1951: Extendedrange weather forecasting. In: T. F.
Malone, ed. Compendium of Meteorology, Amer. Met. Soc.,
Boston MA, pp. 81433.
Chapman C C, D P Monselesan, J S Risbey, M Feng, and B M Sloyan,
2022: A largescale view of marine heatwaves revealed by
archetype analysis. Nature Communication, 13, 7843.
Hannachi A, 2008: A new set of orthogonal patterns in weather
and climate: optimally interpolated patterns. J. Climate, 21,
67246738.
Hannachi A, 2010: On the origin of planetaryscale extratropical
winter circulation regimes. J. Atmos. Sci., 67, 13821401.
Hannachi A, 2014: Intermittency, autoregression and censoring: a
firstorder AR model for daily precipitation. Meteorol. Appl.,
21, 384397.
Hannachi A, and N Trendafilov, 2017: Archetypal analysis: mining
weather and climate extremes. J. Climate, 30, 69276944.
Kooperberg C, and F O'Sullivan, 1996: Prediction oscillation
patterns: A synthetic of methods for spatialtemporal
decomposition of random fields. J. Amer. Stat. Assoc., 91,
14851496.
Pires C, and A Hannachi, 2021: Bispectral analysis of nonlinear
interaction, predictability and stochastic modelling with
application to ENSO. Tellus A, 73, 130.
Stephenson D B, A Hannachi, and A O'Neill, 2004: On the existence
of multiple climate regimes. Q. J. R. Meteorol. Soc., 130,
583605.Citation: https://doi.org/10.5194/egusphere2023111RC2  AC2: 'Reply on RC2', Alexandre Tuel, 02 May 2023
Peer review completion
Journal article(s) based on this preprint
Alexandre Tuel and Olivia Martius
Alexandre Tuel and Olivia Martius
Viewed
HTML  XML  Total  BibTeX  EndNote  

335  225  18  578  8  9 
 HTML: 335
 PDF: 225
 XML: 18
 Total: 578
 BibTeX: 8
 EndNote: 9
Viewed (geographical distribution)
Country  #  Views  % 

Total:  0 
HTML:  0 
PDF:  0 
XML:  0 
 1
The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
(9224 KB)  Metadata XML