Dependence of the Solar Wind Plasma Density on Moderate Geomagnetic Activity Elucidated by Potential Learning

Dependence of the Solar Wind Plasma Density on Moderate Geomagnetic Activity Elucidated by Potential Learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Dependence of the Solar Wind Plasma Density on Moderate Geomagnetic Activity Elucidated by Potential Learning Ryozo Kitajima, Motoharu Nowada, Ryotaro Kamimura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3657665/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, the relationship between a moderate range of geomagnetic activity, represented by the K p index (2- – 5+), and solar wind conditions were revealed based on Potential Learning (PL), a newly developed neural network, and dependence of particular solar wind plasma density on moderate geomagnetic conditions was discussed. It has poorly been understood from what stage of geomagnetic activity the solar wind density begins to control the K p level. We utilized the PL protocols that were improved for the research of space plasma physics in our previous study. As a result, we succeeded in specifying the most influential solar wind parameters at an extremely low (0–1+) and high (6- – 9) K p ranges under southward interplanetary magnetic field (IMF) conditions. The IMF three components (B x , B y , and B z ), solar wind flow speed (V x ) in geocentric solar magnetospheric (GSM) coordinates, and solar wind plasma density (N p ) obtained from the OMNI solar wind database (1998–2019) were used as input parameters for PL. Based on PL, the solar wind velocity is the most significant parameter for the moderate K p range under southward IMF conditions and the solar wind number density is the second most influential parameter. Based on the examination of the statistical relationship between the solar wind speed and plasma density under extremely low, high, and moderate K p ranges using the PL database, geomagnetic conditions remain high while the plasma number density becomes large, even if the solar wind velocity decreases (or remains similar). This shows that both solar wind velocity and plasma number density govern geomagnetic activity, following the relational equation between K p index and the solar wind plasma parameter. We investigated the relation between the solar wind velocity and plasma density and revealed that the solar wind density begins to affect the K p level from moderate geomagnetic activity level (2- – 5) based on PL and incidental statistical studies using PL input data. Our results would greatly help understand general relationship between solar wind conditions and geomagnetic activity under various IMF conditions. Space weather modeling Solar wind conditions Geomagnetic activity Potential Learning Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The terrestrial magnetosphere is always exposed to the high-speed plasma streams originating from the sun (referred to as solar wind) and changes dynamically because of the interactions with solar wind plasmas and magnetic fields, so-called interplanetary magnetic field (IMF e.g., Black, 1967 ; Glassmeier et al., 2009 ; Glassmeier and Vogt, 2010 ). Therefore, geomagnetic disturbances strongly depend on solar wind conditions. Magnetic reconnection occurring on the boundary region between geomagnetic field and IMF is the main driver enhancing the geomagnetic activity, because this process is caused by the breaking down of the geomagnetic field frozen-in condition, caused by reconnecting the geomagnetic field with the field lines of IMF, and leads to magnetic disturbances in the magnetosphere. The K p index is a widely accepted parameter for measuring the global geomagnetic activity, which can be obtained based on the weighted average of the geomagnetic activity indices ( K indices) at 13 geomagnetic observatories worldwide (Bartels, 1949 ) with a 3h time resolution. It has been well-known that there is good correlation between K p and solar wind parameters at L1 (Lagrange) point, which were revealed by Wing et al. ( 2005 ), Wintoft et al. ( 2017 ), Zhelavskaya et al. ( 2019 ), Shprits et al. ( 2019 ), and references therein. Newell et al. ( 2008 ) succeeded in formulating the K p index which has the functions of the IMF and energy coupling functions, which show quantitative entry amount of solar wind electromagnetic energy to the magnetosphere using the IMF and solar wind plasma moments as proposed by Newell et al. ( 2007 ). An early study of Snyder et al. ( 1963 ) and recent Elliott et al. ( 2013 ) statistically revealed that a close relationship exists between K p and the solar wind velocity. Nevertheless, it has been difficult to estimate the geomagnetic activity level using the solar wind parameters. Recently, machine learning (or deep learning), such as neural network (NN) with the input parameters of the IMF and solar wind plasma approaches have been utilized to predict geomagnetic activity (Boberg et al., 2000 ; Wing et al., 2005 ). Boberg et al. ( 2000 ) developed a multi-layer feed-forward network and evaluated their network algorithm in terms of “training,” “validation,” and “test” with the correlation coefficient and root-mean-square error (RMSE). Bala and Reiff ( 2012 ) exploited the K p index forecasting model based on a NN and compared several K p forecasting patterns with inputs of various IMF and solar wind plasma conditions. They identified significant differences in the RMSE and correlation coefficients between the models. Another machine learning technique, such as a support vector machine (SVM), was applied to build a K p prediction model by Ji et al. ( 2013 ). The performance of the SVM-based forecasting model was evaluated by comparisons with the K p prediction models which were developed based on a NN. They constructed forecasting models for K p values exceeding 6. As another K p forecasting model, Tan et al. ( 2018 ) developed and evaluated a forecasting model for K p that considered the forecasting error of the K p index with long short-term memory (LSTM), constructed by recurrent NNs (RNNs; Hochreiter and Schmidhuber, 1997 ). In their forecasting model, they used the solar energy input function, that is, a coupling function and associated viscous term, proposed by Newell et al. ( 2008 ), were used as the input parameters of the solar wind conditions besides the IMF and solar wind plasma data. Kitajima and Nowada et al. ( 2022 ; hereafter referred to as KN2022) examined the relationship between solar wind conditions and extremely low ( K p = 0–1+) and high geomagnetic activity ( K p = 6+ – 9) under southward IMF conditions using long-term solar wind OMNI and K p databases. In their study, a newly developed NN, potential learning (PL), was applied for the first time to time-series data in space plasma, and a K p classification model was constructed to extract the most significant solar wind parameter, that is, input parameter with a value of the highest potentiality that would drive large geomagnetic disturbances. They succeeded in extracting the solar wind velocity as the most influential parameter that is closely related to extremely low and high K p conditions. Their results obtained by PL were also consistent with the relation between solar wind parameters and K p , which can be described by the empirical equations derived by statistical data analysis (Newell et al., 2008 ). In this study, we discuss the relationship between solar wind conditions and moderated ( K p = 2- – 5+) and extremely high ( K p = 6- – 9) geomagnetic conditions under southward IMF, making full use of the features of PL, that is, the availability to identify the most significant or influential parameter to the output parameters from the input parameters. Furthermore, by extracting the most significant solar wind parameter(s) and comparing the results obtained in this study with those from KN2022, we elucidated the ultimate solar wind parameter(s) governing the geomagnetic activity under southward IMF conditions when the magnetosphere is easily disturbed. The data, compilation, and methodology used in this study are described in Section 2 . The results obtained based on the PL and incidental statistical analyses using the PL database are presented in Section 3 . The discussion and summary are provided in Section 4 . 2. Data and Methodology 2.1 Analysis of Large Databases In this study, we attempted to clarify the relationship between solar wind conditions and a moderate K p level, which ranges from 2- to 5, by developing a model that utilizes IMF and solar wind plasma parameters as inputs and classifies K p according to its magnitude (level). The analysis method used in this study is PL. We utilized the same procedure and algorithm as described in details in Kitajima and Nowada et al. ( 2022 ; hereafter, referred to as KN2022). PL consisted of five input and 192 output neurons in the knowledge acquisition phase and 192 intermediate and two output neurons in the prediction phase, which were determined by the sampled data size. The transfer function of intermediate neurons is a hyperbolic tangent function in the prediction phase and that of output neurons is a softmax function. 2.2 Database compilation We examined the relationship between solar wind conditions, represented with some physical parameters, and global geomagnetic activity using a large OMNI solar wind and geomagnetic activity index databases including records from 22 years, that is, from January 1, 1998, to December 31, 2019. Table 1 summarizes the five parameters used in this study to characterize solar wind conditions, which were used in this study. These input parameters were normalized in the range between 0 and 1 (x ’ ), which can be derived from the following equation: (x – min(x))/(max(x) – min(x)), where x is input parameter, and min(x) and max(x) are minimum and maximum input parameter values, respectively. We used the three components of IMF, solar wind plasma density, and solar wind velocity in geocentric solar magnetospheric (GSM) coordinates as the input parameters for the classifier built based on the PL algorithm. The time resolutions of the solar wind parameters and the K p index are 1 min and 3 h, respectively. We adjusted the time resolution difference between solar wind data and K p by calculating the 3-hour average of solar wind data. In case of the solar wind data greater than 40%, the data averages were not taken. We used only in-situ solar wind observation data, when the GSM-X component (sun-earthward directional component) of the satellite location was larger than the nominal bow shock nose location (~ 15 R E ), derived from the bow shock model proposed by Farris and Russell ( 1994 ). This is because we try to examine the dependence of solar wind conditions on moderate geomagnetic after excluding the influences from the Earth’s bow shock. In this study, we only used solar wind conditions and geomagnetic activity during southward (negative) IMF-B Z intervals as input parameters for PL, labelled as Bs in Table 1. The reasons for this selection are discussed in KN2022. Before the solar wind parameters were inputted to the PL classifier, the K p indices were categorized into positive and negative groups (targets). K p ranging from 6- to 9, which were identified as extremely high geomagnetic conditions, and associated solar wind data were categorized as positive target (group). In contrast, the K p index from 2- to 5+, defined as moderate geomagnetic activity, and associated solar wind parameters were classified as negative target (group). The positive (extremely high geomagnetic conditions) and negative (moderate geomagnetic conditions) targets were divided based on the K p levels. The total data point number was 30,541, including a positive (negative) target number of 803 (29,738). However, we randomly selected 803 points from 29,738 negative target data points, in order to equalize the data numbers between positive and negative targets. Finally, 1,606 positive and negative data points were utilized for the PL classifier. 3. Results 3.1 Model evaluation We calculated the values of four measures (accuracy, precision, recall, and F-measure) and evaluated the K p classification model using PL. Table 2 shows the calculation results of the four measures for extremely low and high K p cases, as shown in KN 2022, and those obtained in this study to compare the reliability of the classification model used in this study with that of the previously reported one. In the KN 2022 case, the value of “r” in the equation to derive the potentiality [see Eq. (3) in KN 2022] was 5 and the accuracy value was 0.9875, which was slightly smaller than that in multi-layer perceptron (MLP). In this study, the value of parameter “r” was 2 and the accuracy value was 0.9100, which was also smaller than that in MLP. This value was slightly smaller than that reported in KN2022; however, both accuracy values exceeded 0.9000. Therefore, we used the PL algorithm with the advantage that the most influential input parameter on the output parameter can be obtained, although only the precision value in PL (0.9276) is larger than that of MLP (0.9232). 3.2 Statistical distributions of solar wind plasma The occurrence histograms of the solar wind velocity (V X ) and plasma density (N P ), which were used as the input neurons of the PLs in KN2022 and in this study, are shown in Figs. 1 and 2 . Figure 1 shows that a velocity distribution peak can be found in the range of 300 km/s − 400 km/s at extremely low geomagnetic levels ( K p = 0–1+); in the velocity ranges of 400 km/s – 500 km and 500 km/s – 600 km/s, the peaks of the solar wind velocity can be seen in cases of moderate (2- – 5+) and extremely high K p (6- – 9). This proportional relation between solar wind velocity ranges and geomagnetic activity levels have already been revealed based on statistical studies using large-scale databases (Newell et al., 2008 ) and machine learning (PL) techniques (KN 2022). In the plasma density distributions shown in Fig. 2 , the main peak ranges of all K p levels do not significantly differ; they range within 10.0/cc. However, when the plasma density was higher than 10.0/cc, the plasma density occurrence abruptly decreased at extremely low K p compared with a relatively gradual decrease at extremely high and moderate K p levels. In the case of extremely high K p levels, active geomagnetic conditions should be predominantly supported by fast solar wind plasma velocity effects, as revealed by KN2022. In contrast, moderate geomagnetic activity has a solar wind range slower than that in the case of extremely large K p case and the plasma density distribution is broader than that in extremely low geomagnetic activity, suggesting that the solar wind velocity and high plasma density may contribute to the level of moderate geomagnetic activity. This has already been suggested by Newell et al. ( 2008 ) based on an equation showing the relationship between K p and solar wind parameters. However, it remains unclear how much the plasma density contributes to the geomagnetic activity level. To investigate this, we performed an analysis based on PL and investigated the significance of the plasma density at moderate K p levels. 3.3 Determination of influential solar wind parameter for moderate K p level Figure 3 shows the results of PL in KN2022 (panel a) and in this study (panel b) for the input parameters at r = 5 (KN 2022) and r = 2 (this study). In extremely high and low K p cases, PL selected the solar wind velocity as the highest potentiality parameter (~ 1.0000), indicating that the solar wind velocity can be the most significant parameter to govern extremely high and low geomagnetic conditions under southward IMF conditions. The second highest potentiality was assigned to the solar wind plasma density (0.1208); however, because this potentiality value was much smaller than that of the solar wind velocity, the impact of the plasma number density on these geomagnetic activity levels could be almost considered to be ignored. In addition, in this study, the solar wind velocity had the highest potentiality (1.0000), but the second highest potentiality value of the plasma density (0.4021) was 3.5 times higher than that of KN2022, suggesting that the plasma number density is a more influential solar wind parameter for moderate geomagnetic activity than for extremely high and low K p levels. The effect of the IMF, particularly the B X and B Y components, resulting in moderate geomagnetic activity, is much smaller than that of the solar wind plasma parameters or can be ignored, although the input parameters of all IMF components have small values of potentiality. 4. Summary and Discussion Based on a new NN (PL), which previously succeeded in revealing the dependence of solar wind conditions on extremely low and high geomagnetic activities, we examined the relationship between the solar wind conditions and moderate geomagnetic conditions, and extracted the influential solar wind parameters for the moderate K p index range. In this study as well as in KN 2022, we utilized 22 years’ worth of normalized OMNI solar wind data obtained under the southward IMF conditions as the input parameters for the PL classifier. Using the large solar wind and K p databases, PL extracted the solar wind velocity and plasma number density as the parameters with the highest and second highest potentiality, respectively, as shown in Fig. 3 . Even under moderate geomagnetic and southward IMF-B z conditions, the solar wind velocity is the most significant parameter for the moderate geomagnetic activity as well as extremely low and high K p cases. Many previous studies (e.g., Snyder et al., 1963 ; Vasyliunas et al., 1982 ; Borovsky et al., 1998 ; Gholipour et al., 2004 ; Newell et al., 2007 , 2008 ; Elliott et al., 2013 ; Kitajima and Nowada et al., 2022 , and references therein) have been discussed the dependence of solar wind speed (V x ) on the geomagnetic activity based on in-situ observations and machine learning techniques. According to the empirical equation, that is, Eq. (1) proposed by Newell et al. ( 2008 ), which describes the relation between the solar wind parameters and K p index, and was proposed based on a statistical study, K p can be expressed as follows: \({K}_{p}=0.05+2.244\times {10}^{-4}\left(\frac{d{{\Phi }}_{MP}}{dt}\right)+2.844\times {10}^{-6}{{N}_{p}}^{\frac{1}{2}}{V}_{sw}^{2} \left(1\right)\) \(\frac{d{{\Phi }}_{MP}}{dt}= {V}_{sw}^{\frac{4}{3}}{B}_{t}^{\frac{2}{3}}{sin}^{\frac{8}{3}}\left(\frac{{\theta }_{clock}}{2}\right) \left(2\right),\) where N P , V SW , B T , and θ CLOCK indicate the solar wind plasma density, solar wind velocity, IMF intensity, and clock angle, defined by arctan (IMF-B Y /IMF-B Z ), respectively. K p can be a function of the two solar wind velocity terms with square and 3/4 power in the solar wind convection electric field, represented by the solar wind–magnetosphere coupling function, as described in Eq. (2, Newell et al., 2007 ). This result is the same as that reported in KN2022 and shows a good agreement with the most significant parameter extraction using PL (Fig. 3 ). However, in this case, the value of potentiality of the plasma density was much higher than that in case of KN2022, indicating that the moderate K p case may depend on the solar wind plasma density being stronger than at extremely low and high geomagnetic activity levels. We did not consider to add the solar wind–magnetosphere coupling function as the input parameter of the PL, because this term is not able to have the highest or second highest potentiality. The Eq. (2) shows that the coupling function mainly consists of the terms of solar wind velocity and IMF intensity. When considering which parameter more effectively depends on coupling function, the solar wind velocity and IMF intensity are proxy parameters of the solar wind dynamic pressure (kinetic energy) and magnetic pressure (magnetic energy), respectively. In general, the solar wind dynamic pressure is much more dominant than the magnetic pressure in solar wind. Furthermore, since the plasma number density is also a function of the solar wind dynamic pressure and resultant parameter with the second highest potentiality, the IMF intensity cannot become a significant parameter for (moderate) geomagnetic activity. Figure 4 shows the summary scatter plots of the relation between the solar wind velocity (horizontal axis) and plasma density (vertical axis) in each K p category using the negative and positive target data of PL in KN2022 (panel a) and in this study (panel b). In the extremely low (negative target, blue square) and high (positive target, green open circle) K p cases in KN2022, the distribution profiles between the two K p levels were clearly different. The solar wind velocity ranged from 400 km/s to ~ 1000 km/s in extremely high K p cases, while its range was 250 km/s to 600 km/s at extremely low geomagnetic activity levels. Interestingly, in the plasma density distribution, the main density distribution range was 0.0 /cc to 22.0/cc in extremely low K p cases, but the density broadly ranged from 0.0 /cc to 40.0/cc throughout the solar wind velocity range at extremely high geomagnetic activity levels. Even at ~ 400 km/s, although the density distribution range was 0.0/cc to 13.0/cc at the extremely low activity, it ranged from 1.0/cc to 30.0/cc in the extremely high K p case. This indicates that, the more geomagnetic activity increases, the more the solar wind plasma density contributes to the state of high geomagnetic activity. The same profile can be seen even between moderate (negative target) and extremely high K p (positive target) cases. The solar wind velocity ranged between 300 km/s and 750 km/s and the plasma density was distributed over the range of 0.0 /cc to 30.0 /cc at a moderate K p . At ~ 400 km/s, the corresponding density distribution ranges were almost the same for both moderate and extremely high geomagnetic activities and their maxima reached ~ 40.0/cc. In contrast, the density contribution to K p appeared to be smaller in the velocity range above ~ 500 km/s at the moderate K p values. These relationship among the solar wind velocity, plasma density, and K p index can approximated by Equations (1) and (2), as proposed by Newell et al. ( 2008 ), and can also be predicted by the results of machine learning using KN2022 and Fig. 3 . This study and its comparison with the result of KN2022 clarified that the contribution of the plasma density to the K p index becomes effective as the geomagnetic activity increases, being supported by the results of our Fig. 3 and its difference in the plasma density potentiality value, shown in Fig. 3 of KN2022. Particularly, we can find significant differences in the density distributions between three K p categories over the solar wind velocity range of 350 km/s to 600 km/s (Fig. 4 ). Furthermore, it was found that, from K p = 2- to 5 (moderate geomagnetic activity range), the plasma density begins to be an influential parameter for the geomagnetic activity, although the solar wind velocity is the most significant parameter for all geomagnetic activity levels, irrespectively of K p index values. In this study, we showed that PL extracts the solar wind velocity as the most significant solar wind parameter from the solar wind database when the K p index represents moderate and extremely high geomagnetic activity during southward IMF intervals. However, based on the comparison of the results obtained in this study with those derived under extremely low and high geomagnetic activities (KN2022), the plasma number density has the second highest potentiality, ~ 3.5 times higher than the potentiality of the density in the KN2022 case. The identical statistical analysis using negative and positive target data in PL reveled that the plasma number density becomes significant at moderate geomagnetic activity with a K p range of 2- – 5. Based on the results of this study and KN2022, under southward IMF conditions, global geomagnetic activity with K p index larger than 2- may be closely related to increases in the solar wind velocity and the plasma density. The results in this study will greatly help understand general relationship between solar wind conditions and geomagnetic activity under various IMF conditions with combination of the results on the relationship between solar wind conditions and geomagnetic activity under northward IMF conditions which will be studied in detail in near future. Abbreviations PL, potential learning; IMF, interplanetary magnetic field; RMSE, root-mean-square error; NN, (artificial) neural network; MLP, multi-layer perceptron; GSM coordinates, geocentric solar magnetospheric coordinates; SOM, self-organizing map. Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials Solar wind OMNI data were obtained from the Coordinated Data Analysis Web (https://cdaweb.sci.gsfc.nasa.gov/index.html) provided by GSFC/NASA. K p index data were provided by the World Data Center for Geomagnetism, Kyoto (http://swdcdb.kugi.kyoto-u.ac.jp/). Competing interests The authors declare that they have no competing interest. Funding M.N. was supported by a grant from the National Natural Science Foundation of China (NSFC 42074194). Authors’ contributions Motoharu Nowada conceived the project. Ryozo Kitajima performed all data analyses, created all the figures, and tuned the PL codes. Motoharu Nowada wrote and edited the manuscript. Ryotaro Kamimura developed the main engine of the PL program. Ryozo Kitajima and Motoharu Nowada equally contributed to this work and manuscript. All authors critically reviewed and revised the manuscript and approved the final version for submission. Acknowledgements We would like to thank Editage (www.editage.com) for English language editing. 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Planet Space Sci 30:359–365. https://doi.org/10.1016/0032-0633(82)90041-1 Wing S, Johnson JR, Jen J, Meng C-I, Sibeck DG, Bechtold K, Freeman J, Costello K, Balikhin M, Takahashi K (2005) Kp forecast models. J Geophys Res 110:A04203. https://doi.org/10.1029/2004JA010500 Wintoft P, Wik M, Matzka J, Shprits Y (2017) Forecasting Kp from solar wind data: Input parameter study using 3-hour averages and 3-hour range values. J Space Weather Space Clim 7:A29. https://doi.org/10.1051/swsc/2017027 Zhelavskaya IS, Vasile R, Shprits YY, Stolle C, Matzka J (2019) Systematic analysis of machine learning and feature selection techniques for prediction of the Kp index. Space Weather 17:1461–1486. https://doi.org/10.1029/2019SW002271 Tables Tables 1-2 is available in the Supplementary Files section. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3657665","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266891830,"identity":"0a337afe-c91a-4ddd-adc8-df667e63ea31","order_by":0,"name":"Ryozo Kitajima","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-7826-4802","institution":"Tokyo Polytechnic University - Atsugi Campus: Tokyo Kogei Daigaku","correspondingAuthor":true,"prefix":"","firstName":"Ryozo","middleName":"","lastName":"Kitajima","suffix":""},{"id":266891831,"identity":"db90b18b-2876-4e43-a31b-bddf2d027edc","order_by":1,"name":"Motoharu Nowada","email":"","orcid":"","institution":"Shandong University at Weihai","correspondingAuthor":false,"prefix":"","firstName":"Motoharu","middleName":"","lastName":"Nowada","suffix":""},{"id":266891832,"identity":"2e01298b-ea9f-4430-96e8-f2161c70a0e7","order_by":2,"name":"Ryotaro Kamimura","email":"","orcid":"","institution":"Tokai University - Shonan Campus: Tokai Daigaku","correspondingAuthor":false,"prefix":"","firstName":"Ryotaro","middleName":"","lastName":"Kamimura","suffix":""}],"badges":[],"createdAt":"2023-11-24 07:28:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3657665/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3657665/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49708542,"identity":"5e60383a-c95f-49ac-b643-6135153948e9","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":529295,"visible":true,"origin":"","legend":"\u003cp\u003eOccurrence distributions of the solar wind velocity in the negative and positive target databases of PL used in Kitajima and Nowada et al. (2022, referred to as KN 2022) and this study are shown. From panels a to c, histograms of the solar wind occurrence distributions under extremely low (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 0 to 1+), moderate (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e \u003c/sub\u003e= 2- to 5+), and extremely high (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 6- to 9) geomagnetic conditions are shown.\u003c/p\u003e","description":"","filename":"Figures202309221.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/1680f38cc4f9aa7d5666b3aa.jpg"},{"id":49708540,"identity":"e6ab753c-ab2b-42dc-a0e5-8a00cdae9bba","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":540698,"visible":true,"origin":"","legend":"\u003cp\u003eOccurrence distributions of the solar wind plasma density in the negative and positive target databases of PL used in KN2022 and this study are shown. Formats of the histograms shown from panels a to c are the same as those in Figure 1.\u003c/p\u003e","description":"","filename":"Figures202309222.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/8a36f77768bfbeeed1d787de.jpg"},{"id":49708544,"identity":"3fcc8f91-4a25-4471-81ca-12d91e895955","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":673750,"visible":true,"origin":"","legend":"\u003cp\u003eResults of PL which were obtained from KN2022 (panel a) and this study (panel b) are shown. Five OMNI solar wind parameters (IMF-B\u003csub\u003ex\u003c/sub\u003e, IMF-B\u003csub\u003ey,\u003c/sub\u003e V\u003csub\u003ex\u003c/sub\u003e, N\u003csub\u003ep\u003c/sub\u003e, and B\u003csub\u003es\u003c/sub\u003e) were chosen as PL input data. The horizontal and vertical axes represent the input potentiality and five solar wind parameters, respectively. The potentialities are shown in each histogram bar.\u003c/p\u003e","description":"","filename":"Figures202309223.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/30db64b45431ab25021d0734.jpg"},{"id":49708543,"identity":"7d9cc468-b109-4395-99a6-253475f92acb","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1626191,"visible":true,"origin":"","legend":"\u003cp\u003eScatter plots of the relations between the solar wind velocity (horizontal axis) and solar wind plasma number density (vertical axis) in cases of extremely low and high geomagnetic activity (panel a), and under moderate and extremely high geomagnetic conditions (panel b) are shown.\u003c/p\u003e","description":"","filename":"Figures202309224.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/7e3e2dc1e898c69cdc4f0129.jpg"},{"id":52977391,"identity":"6286de40-505b-4f5d-980d-0c9f13349c8f","added_by":"auto","created_at":"2024-03-19 09:30:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":493763,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/50cf6661-9b06-4d98-8629-cad033590d38.pdf"},{"id":49708541,"identity":"5f513410-e18d-4560-bcde-36338e3a9f65","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":119659,"visible":true,"origin":"","legend":"","description":"","filename":"Tables20230922.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/d4402b0654d83bae8e555147.pdf"},{"id":49708545,"identity":"e01d2bdc-5769-43e9-98a8-59025761fa45","added_by":"auto","created_at":"2024-01-16 19:25:26","extension":"jpg","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":971051,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3657665/v1/18546e5448d6aea43496c131.jpg"}],"financialInterests":"","formattedTitle":"Dependence of the Solar Wind Plasma Density on Moderate Geomagnetic Activity Elucidated by Potential Learning","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe terrestrial magnetosphere is always exposed to the high-speed plasma streams originating from the sun (referred to as solar wind) and changes dynamically because of the interactions with solar wind plasmas and magnetic fields, so-called interplanetary magnetic field (IMF e.g., Black, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1967\u003c/span\u003e; Glassmeier et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Glassmeier and Vogt, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Therefore, geomagnetic disturbances strongly depend on solar wind conditions. Magnetic reconnection occurring on the boundary region between geomagnetic field and IMF is the main driver enhancing the geomagnetic activity, because this process is caused by the breaking down of the geomagnetic field frozen-in condition, caused by reconnecting the geomagnetic field with the field lines of IMF, and leads to magnetic disturbances in the magnetosphere.\u003c/p\u003e \u003cp\u003eThe \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index is a widely accepted parameter for measuring the global geomagnetic activity, which can be obtained based on the weighted average of the geomagnetic activity indices (\u003cem\u003eK\u003c/em\u003e indices) at 13 geomagnetic observatories worldwide (Bartels, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1949\u003c/span\u003e) with a 3h time resolution. It has been well-known that there is good correlation between \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e and solar wind parameters at L1 (Lagrange) point, which were revealed by Wing et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), Wintoft et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), Zhelavskaya et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), Shprits et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and references therein. Newell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) succeeded in formulating the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index which has the functions of the IMF and energy coupling functions, which show quantitative entry amount of solar wind electromagnetic energy to the magnetosphere using the IMF and solar wind plasma moments as proposed by Newell et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). An early study of Snyder et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1963\u003c/span\u003e) and recent Elliott et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) statistically revealed that a close relationship exists between \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e and the solar wind velocity. Nevertheless, it has been difficult to estimate the geomagnetic activity level using the solar wind parameters.\u003c/p\u003e \u003cp\u003eRecently, machine learning (or deep learning), such as neural network (NN) with the input parameters of the IMF and solar wind plasma approaches have been utilized to predict geomagnetic activity (Boberg et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Wing et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Boberg et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) developed a multi-layer feed-forward network and evaluated their network algorithm in terms of \u0026ldquo;training,\u0026rdquo; \u0026ldquo;validation,\u0026rdquo; and \u0026ldquo;test\u0026rdquo; with the correlation coefficient and root-mean-square error (RMSE). Bala and Reiff (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) exploited the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index forecasting model based on a NN and compared several \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e forecasting patterns with inputs of various IMF and solar wind plasma conditions. They identified significant differences in the RMSE and correlation coefficients between the models.\u003c/p\u003e \u003cp\u003eAnother machine learning technique, such as a support vector machine (SVM), was applied to build a \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e prediction model by Ji et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The performance of the SVM-based forecasting model was evaluated by comparisons with the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e prediction models which were developed based on a NN. They constructed forecasting models for \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e values exceeding 6. As another \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e forecasting model, Tan et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) developed and evaluated a forecasting model for \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e that considered the forecasting error of the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index with long short-term memory (LSTM), constructed by recurrent NNs (RNNs; Hochreiter and Schmidhuber, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). In their forecasting model, they used the solar energy input function, that is, a coupling function and associated viscous term, proposed by Newell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), were used as the input parameters of the solar wind conditions besides the IMF and solar wind plasma data.\u003c/p\u003e \u003cp\u003eKitajima and Nowada et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; hereafter referred to as KN2022) examined the relationship between solar wind conditions and extremely low (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 0\u0026ndash;1+) and high geomagnetic activity (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 6+ \u0026ndash; 9) under southward IMF conditions using long-term solar wind OMNI and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e databases. In their study, a newly developed NN, potential learning (PL), was applied for the first time to time-series data in space plasma, and a \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e classification model was constructed to extract the most significant solar wind parameter, that is, input parameter with a value of the highest potentiality that would drive large geomagnetic disturbances. They succeeded in extracting the solar wind velocity as the most influential parameter that is closely related to extremely low and high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e conditions. Their results obtained by PL were also consistent with the relation between solar wind parameters and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e, which can be described by the empirical equations derived by statistical data analysis (Newell et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn this study, we discuss the relationship between solar wind conditions and moderated (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 2- \u0026ndash; 5+) and extremely high (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 6- \u0026ndash; 9) geomagnetic conditions under southward IMF, making full use of the features of PL, that is, the availability to identify the most significant or influential parameter to the output parameters from the input parameters. Furthermore, by extracting the most significant solar wind parameter(s) and comparing the results obtained in this study with those from KN2022, we elucidated the ultimate solar wind parameter(s) governing the geomagnetic activity under southward IMF conditions when the magnetosphere is easily disturbed.\u003c/p\u003e \u003cp\u003eThe data, compilation, and methodology used in this study are described in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The results obtained based on the PL and incidental statistical analyses using the PL database are presented in Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The discussion and summary are provided in Section \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. Data and Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Analysis of Large Databases\u003c/h2\u003e \u003cp\u003eIn this study, we attempted to clarify the relationship between solar wind conditions and a moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e level, which ranges from 2- to 5, by developing a model that utilizes IMF and solar wind plasma parameters as inputs and classifies \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e according to its magnitude (level). The analysis method used in this study is PL. We utilized the same procedure and algorithm as described in details in Kitajima and Nowada et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; hereafter, referred to as KN2022).\u003c/p\u003e \u003cp\u003ePL consisted of five input and 192 output neurons in the knowledge acquisition phase and 192 intermediate and two output neurons in the prediction phase, which were determined by the sampled data size. The transfer function of intermediate neurons is a hyperbolic tangent function in the prediction phase and that of output neurons is a softmax function.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Database compilation\u003c/h2\u003e \u003cp\u003eWe examined the relationship between solar wind conditions, represented with some physical parameters, and global geomagnetic activity using a large OMNI solar wind and geomagnetic activity index databases including records from 22 years, that is, from January 1, 1998, to December 31, 2019. Table\u0026nbsp;1 summarizes the five parameters used in this study to characterize solar wind conditions, which were used in this study. These input parameters were normalized in the range between 0 and 1 (x\u003csup\u003e\u0026rsquo;\u003c/sup\u003e), which can be derived from the following equation: (x \u0026ndash; min(x))/(max(x) \u0026ndash; min(x)), where x is input parameter, and min(x) and max(x) are minimum and maximum input parameter values, respectively. We used the three components of IMF, solar wind plasma density, and solar wind velocity in geocentric solar magnetospheric (GSM) coordinates as the input parameters for the classifier built based on the PL algorithm.\u003c/p\u003e \u003cp\u003eThe time resolutions of the solar wind parameters and the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index are 1 min and 3 h, respectively. We adjusted the time resolution difference between solar wind data and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e by calculating the 3-hour average of solar wind data. In case of the solar wind data greater than 40%, the data averages were not taken. We used only in-situ solar wind observation data, when the GSM-X component (sun-earthward directional component) of the satellite location was larger than the nominal bow shock nose location (~\u0026thinsp;15 R\u003csub\u003eE\u003c/sub\u003e), derived from the bow shock model proposed by Farris and Russell (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). This is because we try to examine the dependence of solar wind conditions on moderate geomagnetic after excluding the influences from the Earth\u0026rsquo;s bow shock. In this study, we only used solar wind conditions and geomagnetic activity during southward (negative) IMF-B\u003csub\u003eZ\u003c/sub\u003e intervals as input parameters for PL, labelled as Bs in Table\u0026nbsp;1. The reasons for this selection are discussed in KN2022.\u003c/p\u003e \u003cp\u003eBefore the solar wind parameters were inputted to the PL classifier, the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e indices were categorized into positive and negative groups (targets). \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e ranging from 6- to 9, which were identified as extremely high geomagnetic conditions, and associated solar wind data were categorized as positive target (group). In contrast, the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index from 2- to 5+, defined as moderate geomagnetic activity, and associated solar wind parameters were classified as negative target (group). The positive (extremely high geomagnetic conditions) and negative (moderate geomagnetic conditions) targets were divided based on the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels.\u003c/p\u003e \u003cp\u003eThe total data point number was 30,541, including a positive (negative) target number of 803 (29,738). However, we randomly selected 803 points from 29,738 negative target data points, in order to equalize the data numbers between positive and negative targets. Finally, 1,606 positive and negative data points were utilized for the PL classifier.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Model evaluation\u003c/h2\u003e \u003cp\u003eWe calculated the values of four measures (accuracy, precision, recall, and F-measure) and evaluated the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e classification model using PL. Table\u0026nbsp;2 shows the calculation results of the four measures for extremely low and high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases, as shown in KN 2022, and those obtained in this study to compare the reliability of the classification model used in this study with that of the previously reported one. In the KN 2022 case, the value of \u0026ldquo;r\u0026rdquo; in the equation to derive the potentiality [see Eq.\u0026nbsp;(3) in KN 2022] was 5 and the accuracy value was 0.9875, which was slightly smaller than that in multi-layer perceptron (MLP). In this study, the value of parameter \u0026ldquo;r\u0026rdquo; was 2 and the accuracy value was 0.9100, which was also smaller than that in MLP. This value was slightly smaller than that reported in KN2022; however, both accuracy values exceeded 0.9000. Therefore, we used the PL algorithm with the advantage that the most influential input parameter on the output parameter can be obtained, although only the precision value in PL (0.9276) is larger than that of MLP (0.9232).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Statistical distributions of solar wind plasma\u003c/h2\u003e \u003cp\u003eThe occurrence histograms of the solar wind velocity (V\u003csub\u003eX\u003c/sub\u003e) and plasma density (N\u003csub\u003eP\u003c/sub\u003e), which were used as the input neurons of the PLs in KN2022 and in this study, are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows that a velocity distribution peak can be found in the range of 300 km/s \u0026minus;\u0026thinsp;400 km/s at extremely low geomagnetic levels (\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 0\u0026ndash;1+); in the velocity ranges of 400 km/s \u0026ndash; 500 km and 500 km/s \u0026ndash; 600 km/s, the peaks of the solar wind velocity can be seen in cases of moderate (2- \u0026ndash; 5+) and extremely high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e (6- \u0026ndash; 9). This proportional relation between solar wind velocity ranges and geomagnetic activity levels have already been revealed based on statistical studies using large-scale databases (Newell et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) and machine learning (PL) techniques (KN 2022). In the plasma density distributions shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the main peak ranges of all \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels do not significantly differ; they range within 10.0/cc. However, when the plasma density was higher than 10.0/cc, the plasma density occurrence abruptly decreased at extremely low \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e compared with a relatively gradual decrease at extremely high and moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the case of extremely high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels, active geomagnetic conditions should be predominantly supported by fast solar wind plasma velocity effects, as revealed by KN2022. In contrast, moderate geomagnetic activity has a solar wind range slower than that in the case of extremely large \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e case and the plasma density distribution is broader than that in extremely low geomagnetic activity, suggesting that the solar wind velocity and high plasma density may contribute to the level of moderate geomagnetic activity. This has already been suggested by Newell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) based on an equation showing the relationship between \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e and solar wind parameters. However, it remains unclear how much the plasma density contributes to the geomagnetic activity level. To investigate this, we performed an analysis based on PL and investigated the significance of the plasma density at moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Determination of influential solar wind parameter for moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e level\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the results of PL in KN2022 (panel a) and in this study (panel b) for the input parameters at r\u0026thinsp;=\u0026thinsp;5 (KN 2022) and r\u0026thinsp;=\u0026thinsp;2 (this study). In extremely high and low \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases, PL selected the solar wind velocity as the highest potentiality parameter (~\u0026thinsp;1.0000), indicating that the solar wind velocity can be the most significant parameter to govern extremely high and low geomagnetic conditions under southward IMF conditions. The second highest potentiality was assigned to the solar wind plasma density (0.1208); however, because this potentiality value was much smaller than that of the solar wind velocity, the impact of the plasma number density on these geomagnetic activity levels could be almost considered to be ignored.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn addition, in this study, the solar wind velocity had the highest potentiality (1.0000), but the second highest potentiality value of the plasma density (0.4021) was 3.5 times higher than that of KN2022, suggesting that the plasma number density is a more influential solar wind parameter for moderate geomagnetic activity than for extremely high and low \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels. The effect of the IMF, particularly the B\u003csub\u003eX\u003c/sub\u003e and B\u003csub\u003eY\u003c/sub\u003e components, resulting in moderate geomagnetic activity, is much smaller than that of the solar wind plasma parameters or can be ignored, although the input parameters of all IMF components have small values of potentiality.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Summary and Discussion","content":"\u003cp\u003eBased on a new NN (PL), which previously succeeded in revealing the dependence of solar wind conditions on extremely low and high geomagnetic activities, we examined the relationship between the solar wind conditions and moderate geomagnetic conditions, and extracted the influential solar wind parameters for the moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index range. In this study as well as in KN 2022, we utilized 22 years\u0026rsquo; worth of normalized OMNI solar wind data obtained under the southward IMF conditions as the input parameters for the PL classifier.\u003c/p\u003e \u003cp\u003eUsing the large solar wind and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e databases, PL extracted the solar wind velocity and plasma number density as the parameters with the highest and second highest potentiality, respectively, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Even under moderate geomagnetic and southward IMF-B\u003csub\u003ez\u003c/sub\u003e conditions, the solar wind velocity is the most significant parameter for the moderate geomagnetic activity as well as extremely low and high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases.\u003c/p\u003e \u003cp\u003eMany previous studies (e.g., Snyder et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1963\u003c/span\u003e; Vasyliunas et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Borovsky et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Gholipour et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Newell et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Elliott et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kitajima and Nowada et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, and references therein) have been discussed the dependence of solar wind speed (V\u003csub\u003ex\u003c/sub\u003e) on the geomagnetic activity based on in-situ observations and machine learning techniques. According to the empirical equation, that is, Eq.\u0026nbsp;(1) proposed by Newell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), which describes the relation between the solar wind parameters and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index, and was proposed based on a statistical study, \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e can be expressed as follows:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K}_{p}=0.05+2.244\\times {10}^{-4}\\left(\\frac{d{{\\Phi }}_{MP}}{dt}\\right)+2.844\\times {10}^{-6}{{N}_{p}}^{\\frac{1}{2}}{V}_{sw}^{2} \\left(1\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{d{{\\Phi }}_{MP}}{dt}= {V}_{sw}^{\\frac{4}{3}}{B}_{t}^{\\frac{2}{3}}{sin}^{\\frac{8}{3}}\\left(\\frac{{\\theta }_{clock}}{2}\\right) \\left(2\\right),\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003ewhere N\u003csub\u003eP\u003c/sub\u003e, V\u003csub\u003eSW\u003c/sub\u003e, B\u003csub\u003eT\u003c/sub\u003e, and θ\u003csub\u003eCLOCK\u003c/sub\u003e indicate the solar wind plasma density, solar wind velocity, IMF intensity, and clock angle, defined by arctan (IMF-B\u003csub\u003eY\u003c/sub\u003e/IMF-B\u003csub\u003eZ\u003c/sub\u003e), respectively. \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e can be a function of the two solar wind velocity terms with square and 3/4 power in the solar wind convection electric field, represented by the solar wind\u0026ndash;magnetosphere coupling function, as described in Eq.\u0026nbsp;(2, Newell et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis result is the same as that reported in KN2022 and shows a good agreement with the most significant parameter extraction using PL (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). However, in this case, the value of potentiality of the plasma density was much higher than that in case of KN2022, indicating that the moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e case may depend on the solar wind plasma density being stronger than at extremely low and high geomagnetic activity levels. We did not consider to add the solar wind\u0026ndash;magnetosphere coupling function as the input parameter of the PL, because this term is not able to have the highest or second highest potentiality. The Eq.\u0026nbsp;(2) shows that the coupling function mainly consists of the terms of solar wind velocity and IMF intensity. When considering which parameter more effectively depends on coupling function, the solar wind velocity and IMF intensity are proxy parameters of the solar wind dynamic pressure (kinetic energy) and magnetic pressure (magnetic energy), respectively. In general, the solar wind dynamic pressure is much more dominant than the magnetic pressure in solar wind. Furthermore, since the plasma number density is also a function of the solar wind dynamic pressure and resultant parameter with the second highest potentiality, the IMF intensity cannot become a significant parameter for (moderate) geomagnetic activity.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the summary scatter plots of the relation between the solar wind velocity (horizontal axis) and plasma density (vertical axis) in each \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e category using the negative and positive target data of PL in KN2022 (panel a) and in this study (panel b). In the extremely low (negative target, blue square) and high (positive target, green open circle) \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases in KN2022, the distribution profiles between the two \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e levels were clearly different. The solar wind velocity ranged from 400 km/s to ~\u0026thinsp;1000 km/s in extremely high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases, while its range was 250 km/s to 600 km/s at extremely low geomagnetic activity levels. Interestingly, in the plasma density distribution, the main density distribution range was 0.0 /cc to 22.0/cc in extremely low \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e cases, but the density broadly ranged from 0.0 /cc to 40.0/cc throughout the solar wind velocity range at extremely high geomagnetic activity levels. Even at ~\u0026thinsp;400 km/s, although the density distribution range was 0.0/cc to 13.0/cc at the extremely low activity, it ranged from 1.0/cc to 30.0/cc in the extremely high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e case. This indicates that, the more geomagnetic activity increases, the more the solar wind plasma density contributes to the state of high geomagnetic activity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe same profile can be seen even between moderate (negative target) and extremely high \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e (positive target) cases. The solar wind velocity ranged between 300 km/s and 750 km/s and the plasma density was distributed over the range of 0.0 /cc to 30.0 /cc at a moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e. At ~\u0026thinsp;400 km/s, the corresponding density distribution ranges were almost the same for both moderate and extremely high geomagnetic activities and their maxima reached\u0026thinsp;~\u0026thinsp;40.0/cc. In contrast, the density contribution to \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e appeared to be smaller in the velocity range above ~\u0026thinsp;500 km/s at the moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e values.\u003c/p\u003e \u003cp\u003eThese relationship among the solar wind velocity, plasma density, and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index can approximated by Equations (1) and (2), as proposed by Newell et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), and can also be predicted by the results of machine learning using KN2022 and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. This study and its comparison with the result of KN2022 clarified that the contribution of the plasma density to the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index becomes effective as the geomagnetic activity increases, being supported by the results of our Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and its difference in the plasma density potentiality value, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e of KN2022. Particularly, we can find significant differences in the density distributions between three \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e categories over the solar wind velocity range of 350 km/s to 600 km/s (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Furthermore, it was found that, from \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e = 2- to 5 (moderate geomagnetic activity range), the plasma density begins to be an influential parameter for the geomagnetic activity, although the solar wind velocity is the most significant parameter for all geomagnetic activity levels, irrespectively of \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index values.\u003c/p\u003e \u003cp\u003eIn this study, we showed that PL extracts the solar wind velocity as the most significant solar wind parameter from the solar wind database when the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index represents moderate and extremely high geomagnetic activity during southward IMF intervals. However, based on the comparison of the results obtained in this study with those derived under extremely low and high geomagnetic activities (KN2022), the plasma number density has the second highest potentiality, ~ 3.5 times higher than the potentiality of the density in the KN2022 case. The identical statistical analysis using negative and positive target data in PL reveled that the plasma number density becomes significant at moderate geomagnetic activity with a \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e range of 2- \u0026ndash; 5.\u003c/p\u003e \u003cp\u003eBased on the results of this study and KN2022, under southward IMF conditions, global geomagnetic activity with \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index larger than 2- may be closely related to increases in the solar wind velocity and the plasma density. The results in this study will greatly help understand general relationship between solar wind conditions and geomagnetic activity under various IMF conditions with combination of the results on the relationship between solar wind conditions and geomagnetic activity under northward IMF conditions which will be studied in detail in near future.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003ePL, potential learning; IMF, interplanetary magnetic field; RMSE, root-mean-square error; NN, (artificial) neural network; MLP, multi-layer perceptron; GSM coordinates, geocentric solar magnetospheric coordinates; SOM, self-organizing map.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSolar wind OMNI data were obtained from the Coordinated Data Analysis Web (https://cdaweb.sci.gsfc.nasa.gov/index.html) provided by GSFC/NASA. \u003cem\u003eK\u003csub\u003ep\u003c/sub\u003e\u003c/em\u003e index data were provided by the World Data Center for Geomagnetism, Kyoto (http://swdcdb.kugi.kyoto-u.ac.jp/).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM.N. was supported by a grant from the National Natural Science Foundation of China (NSFC 42074194).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMotoharu Nowada conceived the project. Ryozo Kitajima performed all data analyses, created all the figures, and tuned the PL codes. Motoharu Nowada wrote and edited the manuscript. Ryotaro Kamimura developed the main engine of the PL program. Ryozo Kitajima and Motoharu Nowada equally contributed to this work and manuscript. All authors critically reviewed and revised the manuscript and approved the final version for submission.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe would like to thank Editage (www.editage.com) for English language editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e1\u003c/sup\u003eDepartment of Engineering, Tokyo Polytechnic University, 5-45-1 Iiyama-minami, Atsugi, Kanagawa 243-0297, Japan. \u003csup\u003e2\u0026nbsp;\u003c/sup\u003eShandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University, 180 Wen-Hua West Road, Weihai City, Shandong Province 264209, China. \u003csup\u003e3\u003c/sup\u003eIT Education Center, Tokai University, 4-1-1 Kitakaname, Hiratsuka City, Kanagawa Prefecture 259-1292, Japan.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBala R, Reiff P (2012) Improvements in short-term forecasting of geomagnetic activity. 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Space Weather 17:1461\u0026ndash;1486. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/2019SW002271\u003c/span\u003e\u003cspan address=\"10.1029/2019SW002271\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1-2 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Space weather modeling, Solar wind conditions, Geomagnetic activity, Potential Learning","lastPublishedDoi":"10.21203/rs.3.rs-3657665/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3657665/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, the relationship between a moderate range of geomagnetic activity, represented by the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index (2- \u0026ndash; 5+), and solar wind conditions were revealed based on Potential Learning (PL), a newly developed neural network, and dependence of particular solar wind plasma density on moderate geomagnetic conditions was discussed. It has poorly been understood from what stage of geomagnetic activity the solar wind density begins to control the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e level. We utilized the PL protocols that were improved for the research of space plasma physics in our previous study. As a result, we succeeded in specifying the most influential solar wind parameters at an extremely low (0\u0026ndash;1+) and high (6- \u0026ndash; 9) \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e ranges under southward interplanetary magnetic field (IMF) conditions. The IMF three components (B\u003csub\u003ex\u003c/sub\u003e, B\u003csub\u003ey\u003c/sub\u003e, and B\u003csub\u003ez\u003c/sub\u003e), solar wind flow speed (V\u003csub\u003ex\u003c/sub\u003e) in geocentric solar magnetospheric (GSM) coordinates, and solar wind plasma density (N\u003csub\u003ep\u003c/sub\u003e) obtained from the OMNI solar wind database (1998\u0026ndash;2019) were used as input parameters for PL. Based on PL, the solar wind velocity is the most significant parameter for the moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e range under southward IMF conditions and the solar wind number density is the second most influential parameter. Based on the examination of the statistical relationship between the solar wind speed and plasma density under extremely low, high, and moderate \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e ranges using the PL database, geomagnetic conditions remain high while the plasma number density becomes large, even if the solar wind velocity decreases (or remains similar). This shows that both solar wind velocity and plasma number density govern geomagnetic activity, following the relational equation between \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e index and the solar wind plasma parameter. We investigated the relation between the solar wind velocity and plasma density and revealed that the solar wind density begins to affect the \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e level from moderate geomagnetic activity level (2- \u0026ndash; 5) based on PL and incidental statistical studies using PL input data. Our results would greatly help understand general relationship between solar wind conditions and geomagnetic activity under various IMF conditions.\u003c/p\u003e","manuscriptTitle":"Dependence of the Solar Wind Plasma Density on Moderate Geomagnetic Activity Elucidated by Potential Learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-16 19:25:21","doi":"10.21203/rs.3.rs-3657665/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5f0b3a6d-d879-45e6-b700-47fd65fea25c","owner":[],"postedDate":"January 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-10-19T05:31:42+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-16 19:25:21","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3657665","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3657665","identity":"rs-3657665","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}