the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by HF Radar, and its relation to wind regimes, using the maximum entropy principle
Sofia Flora
Laura Ursella
Achim Wirth
Abstract. Two years (2021–2022) of High Frequency Radar (HFR) sea surface current data in the Gulf of Trieste (Northern Adriatic Sea) are analysed. Two different time scales are extracted using superstatistical formalism: a relaxation time and a larger timescale over which the system is gaussian. A new analytical universality class of Probability Density Functions (PDFs) is proposed for ocean current data combining a gaussian PDF for the fast fluctuations and a convolution of exponential PDFs for the slowly evolving variance of the gaussian. The Gaussian PDF has maximum entropy for real-valued variables with a given variance. If a positive variable, as is a variance, has a specified mean, the maximum entropy solution is an exponential PDF. Here it is the sum of two exponentials, reflecting the two spatial degrees of freedom.
In the Gulf of Trieste there are three distinct main wind forcing regimes: Bora, Sirocco and low wind, leading to a succession of different sea current dynamics on different time scales. The universality class PDF successfully fits the observed data over the two observation years and also for each wind regime separately with a different variance of the variance PDF, which is the only free parameter in all the fits.
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Sofia Flora et al.
Status: open (until 08 Jun 2023)
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RC1: 'Comment on npg-2023-9', Anonymous Referee #1, 22 May 2023
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The authors apply the formalism of superstatistics to describe the probability densities of velocity fluctuations in ocean currents relevant to forecasting in a region of Italy (Gulf of Trieste). The manuscript is interesting for two main reasons. First, it provides new tools for the statistical description of weather-relevant data that may not be that well-known in that community. Second, it reveals a new kind of superstatistical model, although somewhat related to the inverse-gamma (inverse chi-squared) superstatistics which is one of the main models originally proposed by Beck and Cohen. I would suggest improving the manuscript by addressing the following points:
1) Present in more detail the new model proposed in the work, namely Eq. 8 (equivalently, Eq. 10) and its relation to the inverse chi-squared superstatistics, taking into account that 1/sigma^2 plays the role of the inverse temperature beta when superstatistics is applied as an extension of statistical mechanics. Also, it would benefit the manuscript to give a larger context to the uses of superstatistics, as something beyond the mere description of two different time scales.
2) Expand on the maximum entropy (MaxEnt) principle, a topic that may not be that well-known to the target audience, perhaps by providing the original point of view by E. T. Jaynes in that MaxEnt allows for the construction of minimally biased models given some piece of information.
3) Fix some problems in the figures where NaN appears in the labels (Figs. 3 and 4).
Citation: https://doi.org/10.5194/npg-2023-9-RC1 -
RC2: 'Comment on npg-2023-9', Anonymous Referee #2, 23 May 2023
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In the article the authors claim that "A new analytical universality class of Probability Density Functions (PDFs) is proposed for ocean current data combining a gaussian PDF for the fast fluctuations and a convolution of exponential PDFs for the slowly evolving variance of the gaussian". Experimental data and simulated data (Weather Research and Forecasting (WRF) model) are used to Justify the conclusions.
The topic seems to be interesting for the geophysics community and useful for NPG readers.To be more useful to the readers, I suggest the following point to be considered by the authors.
1- Please provide more details in the abstract sentence: "The Gaussian PDF has maximum entropy for real-valued variables with a given variance."
2- Still in the abstract, some explanation are given in next sentences but I belive it is not completely consistent.
"If a positive variable, as is a variance, has a specified mean, the maximum entropy solution is an exponential
PDF. Here it is the sum of two exponentials, reflecting the two spatial degrees of freedom."3- Bibliographical references presented in the introduction are outdated. Many works on methods based on entropy computation have been published and can be explored for a better explanation of the results.
4- Figure captions are not informative, only descriptive. Please describe the main points of each figure so that the information is self-consistent.
5- Figure 2 (b), in particular, is not explored at any time in the text.
6- The authors mention that ``It is interesting to see that, if the wind is strong enough, the main wind regimes are just Bora and Sirocco (Fig. 2b)'' But it is not clear how this information can be observed in fig. 2(b).7- Section 4 is heavily descriptive also. I believe that more discussions and details about the entropy maximization method can be presented. Even the concept of super statistics may not be fully understood by the geophysics community.
8- Some values do not appear in Figure 3. (delta case 128).
9- Figure 4 is not very informative. Perhaps it should be discussed further.
*In general, the article presents an analysis method that may be of interest to the geophysics community. After the suggested corrections/additions of information, I believe that the article may be accepted for publication.
Citation: https://doi.org/10.5194/npg-2023-9-RC2
Sofia Flora et al.
Sofia Flora et al.
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