the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Probabilistic modelling of substorm occurrences with an echo state network
Ryuho Kataoka
Masahito Nosé
Jesper W. Gjerloev
Abstract. The relationship between solar wind conditions and substorm activity is modelled with an approach based on an echo state network. Substorms are a fundamental physical phenomenon in the magnetosphere–ionosphere system, but the deterministic prediction of substorm onset is very difficult because the physical processes that underlie substorm occurrences are complex. To model the relationship between substorm activity and solar wind conditions, we treat substorm onset as a stochastic phenomenon and represent the stochastic occurrences of substorms with a nonstationary Poisson process. The occurrence rate of substorms is then described with an echo state network model. We apply this approach to two kinds of substorm onset proxies. One is a sequence of substorm onsets identified from auroral electrojet intensity and the other is onset events identified from Pi2 activity. We then analyse the response of substorm activity to solar wind conditions by feeding synthetic solar wind data into the echo state network. The results indicate that the effect of the solar wind speed is important, especially for Pi2 substorms. A Pi2 pulsation can often occur even if the interplanetary magnetic field (IMF) is northward, while the activity of auroral electrojets is depressed during northward IMF conditions. We also observe spiky enhancements in the occurrence rate of substorms when the solar wind density abruptly increases, which might suggest an external triggering due to a sudden impulse of solar wind dynamic pressure. It seems that northward turning of the IMF also contributes to substorm occurrences, though the effect is likely to be minor.
Shin'ya Nakano et al.
Status: open (until 20 Jun 2023)
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RC1: 'Comment on angeo-2023-9', Anonymous Referee #1, 28 Mar 2023
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General comments
This paper presents a novel probabilistics model to estimate the occurence rate of substorm onsets based on solar wind parameters. Accurate prediction of substorm onset time and location is important, because substorms are a fundamental part of the dynamics of the solar wind-magnetosphere-ionosphere system and responsible for many space weather -related disturbance. Because physics-based models cannot yet perform this task reliably, development of empirical models, such as the model presented in this paper, is a worthy topic. The presented model does not consider the onset location but is shown to make a decent job of estimating the occurrence rate of onsets and produces interesting results on the effect of solar wind parameters on the substorm onset occurrence rate. The study is generally well-written and concise, but I think it would benefit from a more extensive comparison with existing methods to show that the developed method produces improved results.
Specific comments:
The question the current paper does not answer is: Does the new method give better results than existing methods, such as the method by Maimiti et al. (2019) or identification of substorm onsets from predicted AE indices? Such a comparison would be very useful, and in case larger statistics are considered to be too much work for the present paper, I'd like to see how the other methods perform in the example event at least.
Technical corrections:
Lines 39-40: "a nonstationary Poisson process" Please provide a reference.
Line 49: "DP2 type convection" Please provide a reference.
Line 60: Please define "p".
Line 81: "OMNI" Please provide a reference.
Line 274: "marginai" should be "marginal"Fig. 2 and 3: I suggest combining these figures to avoid repeating the same data and to make comparison of the two predictions easier.
Fig. 7 and 8: I suggest combining these figures as well. What is the meaning of the shaded area? What are the arrows in Fig. 8? This information should be given in the caption.
Citation: https://doi.org/10.5194/angeo-2023-9-RC1 -
AC1: 'Reply on RC1', Shinya Nakano, 06 Apr 2023
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We are grateful to the referee for the comments.
The referee suggests that we should compare our method with other existing method or identification of substorm onsets from predicted AE indices.
According to this suggestion, we tried to identify substorm onsets from the predicted SML index obtained with the echo state network (ESN) developed in our previous study (Nakano and Kataoka, 2022). As our previous study predicted the SML index with 5-minute resolution, we identified an onset using the following criteria:
1. SML(t0+5min) - SML(t0) < -45nT,
2. SML(t0+5min) + SML(t0+10min) + SML(t0+15min) + SML(t0+20min) + SML(t0+25min) - SML(t0) < -100nT,
which are similar to the criteria used by Newell and Gjerloev (2011). As a result, we identified only 246 onsets during the four years from 2015 to 2018, while we identified 4515 onsets from the 5-minute values of the actual SML index during the same period using the same criteria. As shown in Figure 1, many of negative SML spikes due to substorm onsets were not reproduced by the predicted SML index, and many of substorm onsets cannot be identified from the predicted SML index. We therefore believe that the proposed approach is more suitable for analysing substorm activity.
As the referee points out, Maimaiti et al. (2019) also predicted substorm onsets from solar wind data. However, their method addresses a slightly different task from our method. Maimaiti et al. predicted a substorm occurrence for next 60 minutes from the time history of solar wind data. They thus attempted to predict a substorm onset without using the solar wind data just before the onset. On the other hand, our purpose is to model the response to given solar wind inputs. We use the solar wind data with 5-minute resolution until the time interval of the onset to calculate the probability of the substorm occurrence. Another difference is in data selection. Maimaiti et al. selected the data so that the number of onset cases is equal to that of non-onset cases, which is favourable to attain a high F1 score. However, the number of onset cases is actually much less than that of non-onset cases. If a probabilistic model is trained by a data set in which onset cases and non-onset cases are equalised, it would provide a biased result when the occurrence rate is calculated. Our study uses the entire data from 2005 to 2014 except for spin-up periods due to data missing, which is appropriate to evaluate the occurrence rate of substorm onsets. It is therefore difficult to compare the two methods using the same metric.
The referee also suggest that we should provide references for a nonstationary Poisson process, the DP2 type convection, and the OMNI solar wind data. A description on a nonstationary Poisson process is found in the textbook by Daley and Vere-Jones (2003). We will cite this textbook. We will also cite the document by King and Papitashvili as a reference to the OMNI solar wind data. The description on the DP2 type convection is found in the paper by Kamide and Kokubun (1996). We will revise the sentence from Line 47 as follows:
"However, since the events determined from the auroral electrojet intensity may contain non-substorm events such as DP2 type convection enhancements (e.g., Kamide and Kokubun, 1996), an increase of the auroral electrojet does not necessarily indicate a substorm onset."
The referee recommends us to combine Figures 2 and 3 and to combine Figures 7 and 8. We think Figures 2 and 3 should not be combined because Figure 3 shows the analysis of Pi2 substorm onsets which are not yet explained in Section 4. However, we will combine Figures 7 and 8. We thank the referee for the helpful suggestion.
We are also grateful for pointing out the errors in Lines 64 and 274. We will correct them.
References:Daley, D. J. and Vere-Jones, D.: An introduction to the theory of point processes: Volume I: Elementary theory and method, 2nd ed., Springer, New York, 2003.
King, J. and Papitashvili, N.: One min and 5-min solar wind data sets at the Earth's bow shock nose, available at https://omniweb.gsfc.nasa.gov/html/HROdocum.html, last access: 4 April 2023.
Citation: https://doi.org/10.5194/angeo-2023-9-AC1
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AC1: 'Reply on RC1', Shinya Nakano, 06 Apr 2023
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Shin'ya Nakano et al.
Shin'ya Nakano et al.
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