Reviewer Comment on:  Weather persistence on subseasonal to seasonal timescales: a methodological review

Authors: Alexandre Tuel and Olivia Martius

Submitted to: egusphere 2023 111

Summary

The 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 ‘self-similarity of system values x(𝑡) with a metric’ but this notion can be confused with geometric self-similarity 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 Long-range 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 power-law 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 co-occurring 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_X0 is the residence time for state x₀.

    Review of "Veather persistence on sub-seasonal 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/quasi-stationarity 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

 subsub-subsections). 

 1. Perhaps to aid readers, especially early career researchers, an

  extra figure showing a tree-like 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, thirs-order 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 

  'quasi-stationary' 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

              anti-persistence.

          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_0|x_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 1-day 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 inter-event times

            5.2 Stochastic modeling of recurrence

               5.2.1 Events series

               5.2.2 Recurrence plots  

 References

 ----------  

   Baur F, 1951: Extended-range weather forecasting. In: T. F. 

      Malone, ed. Compendium of Meteorology, Amer. Met. Soc., 

      Boston MA, pp. 814-33.

   Chapman C C, D P Monselesan, J S Risbey, M Feng, and B M Sloyan,

      2022: A large-scale 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, 

      6724-6738.

   Hannachi A, 2010: On the origin of planetary-scale extratropical 

      winter circulation regimes. J. Atmos. Sci., 67, 1382-1401.

   Hannachi A, 2014: Intermittency, autoregression and censoring: a 

      first-order AR model for daily precipitation. Meteorol. Appl., 

      21, 384-397.

   Hannachi A, and N Trendafilov, 2017: Archetypal analysis: mining 

      weather and climate extremes. J. Climate, 30, 6927-6944.

   Kooperberg C, and F O'Sullivan, 1996: Prediction oscillation 

      patterns: A synthetic of methods for spatial-temporal 

      decomposition of random fields. J. Amer. Stat. Assoc., 91, 

      1485-1496.

   Pires C, and A Hannachi, 2021: Bispectral analysis of nonlinear 

      interaction, predictability and stochastic modelling with 

      application to ENSO. Tellus A, 73, 1-30.

   Stephenson D B, A Hannachi, and A O'Neill, 2004: On the existence 

      of multiple climate regimes. Q. J. R. Meteorol. Soc., 130, 

      583-605.