Kp Index Research Articles

One‐Day Forecasting of Global TEC Using a Novel Deep Learning Model

AbstractIn this study, we make a global total electron content (TEC) forecasting using a novel deep learning method, which is based on conditional generative adversarial networks. For training, we use the International GNSS Service (IGS) TEC maps from 2003 to 2012 with 2‐h time cadence. Our model has two input images (IGS TEC map and 1‐day difference map between the present day and the previous day) and one output image (1‐day future map). The model is tested with two data sets: solar maximum period (2013–2014) and solar minimum period (2017–2018). Then, we compare the results of our model with those of 1‐day Center for Orbit Determination in Europe (CODE) prediction model. Our major results can be summarized as follows. First, we successfully apply our model to the forecast of global TEC maps. Second, our model well predicts daily TEC maps with 1 day in advance using only previous TEC maps. The averaged root mean square error, bias, and standard deviation between AI‐generated and IGS TEC maps are 2.74 TECU, −0.32 TECU, and 2.59 TECU, respectively. Third, our model generates some peak structures around equatorial regions. Fourth, our model shows better performance than 1‐day CODE prediction model during both solar maximum and minimum periods. Fifth, another model with additional input data Kp index gives a slight improvement of the results. Our study shows that our deep learning model based on an image translation method will be effective for forecasting of future images using previous data.

An APS index theorem for even-dimensional manifolds with non-compact boundary

An APS index theorem for even-dimensional manifolds with non-compact boundary

Ionospheric total electron content response to annular solar eclipse on June 21, 2020

The effects of physical events on the ionosphere structure is an important field of study, especially for navigation and radio communication. The paper presents the spatio-temporal ionospheric TEC response to the recent annular solar eclipse on June 21, 2020, which spans across two continents, Africa and Asia, and 14 countries. This eclipse took place on the same day as the June Solstice. The Global Navigation Satellite System (GNSS) based TEC data of the Global Ionosphere Maps (GIMs), 9 International GNSS Service (IGS) stations and FORMOSAT-7/COSMIC-2 (F7/C2) were utilized to analyze TEC response during the eclipse. The phases of the TEC time series were determined by taking the difference of the observed TEC values on eclipse day from the previous 5-day median TEC values. The results showed clear depletions in the TEC time series on June 21. These decreases were between 1 and 9 TECU (15–60%) depending on the location of IGS stations. The depletions are relatively higher at the stations close to the path of annular eclipse than those farther away. Furthermore, a reduction of about −10 TECU in the form of an equatorial plasma bubble (EPB) was observed in GIMs at ~20° away from the equator towards northpole, between 08:00–11:00 UT where its maximum phase is located in southeast Japan. Additionally, an overall depletion of ~10% was observed in F7/C2 derived TEC at an altitude of 240 km (hmF2) in all regions affected by the solar eclipse, whereas, significant TEC fluctuations between the altitudes of 100 km − 140 km were analyzed using the Savitzky-Golay smoothing filter. To prove TEC depletions are not caused by space weather, the variation of the sunspot number (SSN), solar wind (VSW), disturbance storm-time (Dst), and Kp indices were investigated from 16th to 22nd June. The quiet space weather before and during the solar eclipse proved that the observed depletions in the TEC time series and profiles were caused by the annular solar eclipse.

A new method to subtract dayglow for auroral observation of SSUSI in LBH ranges based on the improved AURIC

A new method to remove the dayglow components for auroral observations from the Special Sensor Ultraviolet Spectrographic Imager (SSUSI) aboard the Defense Meteorological Satellite Program (DMSP) F16 in Lyman-Birge-Hopfield (LBH) ranges based on the improved Atmospheric Ultraviolet Radiance Integrated Code (AURIC) algorithm is proposed in this study. This method is developed by determining the coefficients between the dayglow intensities calculated by the improved AURIC algorithm and the dayglow components from SSUSI in the whole 2005. The least-square polynomials are used to fit the calculations to the observations and the coefficients of the polynomials are divided by Ap indices and solar zenith angles (SZA). This algorithm can be used to simulate the dayglow intensity in the northern polar region at an altitude of 110 Km. Three examples with Ap indices 5, 27, 154 are tested to verify the effectiveness of the algorithm. The consistency between the original AURIC and the improved AURIC at nadir direction, the derived auroral images and the simulated dayglow images, also the fitting precisions and deviations between the dayglow intensities from improved AURIC and the dayglow intensities from SSUSI, demonstrate that this method is feasible and reliable. The proposed method provides us with a useful tool to separate the dayglow and aurora for space FUV observation.

Characterizing Auroral‐Zone Absorption Based on Global Kp and Regional Geomagnetic Hourly Range Indices

AbstractIncreased ionization in the auroral oval leads to the absorption of high‐frequency radio waves in the auroral zone, or auroral absorption. Auroral absorption is typically characterized by global geomagnetic activity indices, such as the Kp index. In this paper the hourly range of the magnetic field (HR) is examined as an alternative to the 3‐hr Kp index for describing the dynamic and localized features of auroral absorption represented by the hourly range of absorption (HRA). Kp, magnetometer, and riometer data were examined for a 3‐year period for stations spread across typical auroral latitudes. A general linear relationship was shown to exist between Kp and LOG10(HRA) for Kp < 4; for Kp ≥ 4 the correlation was weaker. A stronger linear correlation was demonstrated between LOG10(HRA) and LOG10(HR) for HR > 50 nT, characterized by a correlation coefficient of R = 0.63. Increased variability in the relationship between HRA and Kp was attributed to the following factors: the variability of the magnetic field within the 3‐hr window characterized by the Kp index, which was better represented by a 1‐hr HR; the dependence of the Kp index on subauroral magnetic data, which is not subject to the geomagnetic variations typically experienced within the auroral region; and reduced statistics for Kp > 6.

Calcium Citrate Versus Calcium Carbonate in the Management of Chronic Hypoparathyroidism: A Randomized, Double-Blind, Crossover Clinical Trial.

ABSTRACTIn hypoparathyroidism (HypoPT), calcium supplementation is virtually always required, although the disease is likely to be associated with an increased risk of nephrolithiasis. The use of calcium citrate (Ca‐Cit) theoretically could have a positive impact on the nephrolithiasis risk because citrate salts are used to reduce this risk. Our objective was to evaluate the potential therapeutic advantage of Ca‐Cit in comparison with calcium carbonate (CaCO3) in HypoPT, on nephrolithiasis risk factors, as well as to their ability to maintain desirable serum calcium levels. We also evaluated these preparations on quality of life (QOL). This randomized, double‐blind, crossover trial recruited 24 adults with postsurgical chronic hypoparathyroidism at Campus Bio‐Medico University of Rome. Participants were randomized 1:1 to Ca‐Cit or CaCO3 for 1 month and then crossed over to the other treatment for another month. The primary outcomes were changes in albumin‐adjusted serum calcium and in ion activity product of calcium oxalate levels (AP[CaOx] index). Secondary efficacy outcomes included changes in SF‐36 survey score, fatigue score, constipation, and adverse events. No difference in terms of AP(CaOx) index was observed between the two groups. However, Ca‐Cit was associated with a significant reduction in the oxalate/creatinine ratio compared with CaCO3 (−2.46 mmol/mol [SD 11.93] versus 7.42 mmol/mol [SD 17.63], p = 0.029). Serum calcium and phosphorus concentration was not different between the two calcium preparations. Ca‐Cit was associated with less constipation (p = 0.047). No difference was found in QOL scores. Although Ca‐Cit did not modify the AP(CaOx) index when compared with CaCO3, it was associated with a reduction in urinary oxalate excretion that could have a potential beneficial effect on nephrolithiasis risk. These results are likely to have clinical implications in HypoPT, particularly those who do not tolerate CaCO3 and those affected by nephrolithiasis. A longer‐term experience is needed to confirm these findings. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Suicides and Mortality from Cardiovascular Diseases Due to Space-Weather Factors in High Latitudes

The aim of this study is to identify the impacts of the main space-weather factors on suicides and cardiovascular (CVD) mortality in Murmansk oblast (northwestern Russia). Data on a total of 908 suicides and 9057 CVD deaths in the town of Kirovsk (67.6 N; 33.7 E) have been analyzed for the period from 1948 to 2010. The main space-weather factors we consider are solar proton events (SPEs) and geomagnetic disturbance determined by the geomagnetic Ap index. As a result of the application of modern methods of spectral and wavelet analysis (MTM spectra, wavelet decomposition, and cross-wavelet spectra), periodicities corresponding to the main 11-year cycle of solar activity and its 2nd harmonic (5.5 years) are revealed. The results of calculating the wavelet coherence indicate the existence of a close relationship between variations in mortality rates and the main factors of space weather. In the case of CVD, although the influence of geomagnetic disturbance on the mortality rate is present, it is not significant compared with socioeconomic factors.

Statistical Structure of Nighttime O2 Aurora From SABER and Its Dependence on Geomagnetic and Solar Activities in Winter

AbstractO2 aurora is one kind of important molecular aurorae that is not fully understood yet. It is hard to be investigated due to the contamination by nightglow. In this work, we studied O2 aurora based on the observations of O2 emission at 1.27 μm from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument during the nighttime over 18 years. The horizontal structure of O2 auroral zone is given for the first time, and the vertical profile of O2 auroral volume emission rate is obtained after removing O2 nightglow contamination. The O2 auroral intensity and the peak height and peak volume emission rate of the vertical profile averaged over the O2 auroral zone are studied in detail. For Kp Levels 1–5, the O2 auroral peak height varies between 104 and 112 km and is negatively correlated with the auroral intensity and peak volume emission rate. The O2 auroral intensity varies between 0.14 and 5.97 kR, and the peak volume emission rate varies between 0.97 × 102 and 41.01 × 102 photons cm−3 s−1. Furthermore, the dependences of the O2 aurora on geomagnetic and solar activities are analyzed. The O2 auroral intensity and peak volume emission rate exponentially increases with increasing Kp index, whereas the peak height decreases with increasing Kp index. The O2 auroral intensity and peak volume emission rate under solar minimum condition are larger than those under solar maximum condition. The peak height under solar minimum condition is lower than that under solar maximum condition.

Large Forbush Decreases and their Solar Sources: Features and Characteristics

One of the factors responsible for the wide variety of Forbush decreases is the different solar sources related to them. In this investigation the different features and characteristics of Forbush decreases, with emphasis on large Forbush decreases and their association with solar sources, are examined. Initially, a wider selection of events from the Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation of the Russian Academy of Sciences Forbush decreases database served as a starting point for this study, which was then narrowed down to a group of large Forbush decreases. According to the helio-longitude of the solar source, the events under study were separated into three subcategories: western ( $21^{\circ} \leq \mbox{helio-longitude} \leq 60^{\circ}$ ), eastern ( $-60^{\circ} \leq \mbox{helio-longitude} \leq -21^{\circ}$ ), and central ( $-20^{\circ} \leq \mbox{helio-longitude} \leq 20^{\circ}$ ). The selected events cover the period 1967 – 2017. The “Global Survey Method” was used for analyzing the aforementioned Forbush decreases, along with data on solar flares, solar-wind speed, geomagnetic indices (Kp and Dst), and interplanetary magnetic field. The superimposed epoch method was applied to display the temporal profiles for the selected events. This detailed analysis reveals interesting results concerning the features of cosmic-ray decreases in relation to the helio-longitude of the solar sources. Specifically, Forbush decreases related to central or eastern solar sources are more often observed, have a greater magnitude, and present a slower development than Forbush decreases related to western sources, which are rarer, have a smaller magnitude, and have a shorter lifespan. Nevertheless, regardless of the helio-longitude of the solar source, large Forbush decreases are accompanied by increased geomagnetic activity and increased anisotropy, including anisotropy before the events, which can serve as a typical precursor of Forbush decreases.

Forecasting the ionospheric F2 Parameters over Jeju Station (33.43°N, 126.30°E) by Using Long Short-Term Memory

Ionospheric models aim to simulate and predict variations in the ionosphere. In this study, we attempt to develop a regional ionospheric model to predict hourly the foF2s (peak frequencies of the F2 layer) and the hmF2s (peak heights of the F2 layer) over the Jeju station (33.43°N, 126.30°E) for up to 24 hours by using a deep learning method. For forecasting the F2 parameters, we adopt the method of long short-term memory (LSTM), which, unlike traditional neural networks, can shed light on sequential variation in time-series data. The inputs of the LSTM model are sequential data for the past 24 hours, which includes the sunspot number (SSN), the daily F10.7 solar flux, geomagnetic the Ap and Kp indices, the foF2 and the hmF2. The foF2 and the hmF2 data used to train the model are measured by the Jeju ionosonde, operated by the Korean Space Weather Center (KSWC) during the period from 2011 through 2016. To evaluate our model performance, we utilized the root mean square error (RMSE) and the correlation coefficient (CC) as the performance skill scores between the model prediction and the measurement during the 338 days of 2017–2018. The best foF2 model, having 21 hidden neurons and 3 batch sizes, performed with an RMSE of 0.65 MHz and a CC of 0.92 when compared with the value measured during the next hour. The best hmF2 model, having 41 hidden neurons and 24 batch sizes, preformed with an RMSE of 23.8 km and a CC of 0.80. When the forecasting steps were increased, the performances gradually deteriorated. The LSTM model results were compared with the results of the TIE-GCM and the IRI-2016 model for geomagnetically quiet and active periods. On geomagnetic quiet days, the LSTM model showed the best performance among the three models. When the RMSEs of the foF2 (hmF2) predictions were compared, the percentage improvements of the LSTM model were 45% (30%) or more than those of the other models during geomagnetically quiet days. On geomagnetic storm days, however, the LSTM model did not improve predictions any better than the IRI-2016 model, which may be due to the limited amount of training data under the storm condition.

Analytical Fast Magnetosonic Wave Model Based on Observations of Van Allen Probe

AbstractBased on observations of Van Allen Probe‐A during the period from 19 September 2012 to 28 February 2016, the relations of the fast magnetosonic (MS) wave amplitude Bw with kp index, the wave normal angle (WNA), and the wave normalized frequency (norF) are presented. Then, we establish an analytical regression model for MS wave amplitude as a function of geomagnetic storm activity (presented by kp index), L‐shell (L), magnetic local time (MLT), magnetic latitude (λ), and the characteristics of MS wave, that is, wave norF and WNA. From the analytical Bw models, we found MS wave amplitude Bw has a positive relation with the intensity of geomagnetic activities both inside and outside the plasmapause, while the Bw can reach higher values inside the plasmapause than it does outside the plasmapause as the kp index increases. The Bw distribution on the norF demonstrates that most of the wave energies are concentrated on the lower harmonics part, which results from the excitation mechanism of MS waves. In addition, the Bw distribution on the WNA shows that the waves with larger normal angles have higher values of wave amplitude. Our analytic MS wave model agrees with the observed distribution in 3‐D space of L, MLT, and λ well with high value of determine coefficient R2. The extended λ dimension will help us to calculate the more accurate bounced averaged diffusion coefficients during particles transit time.

The Solar Event of 14\u2009\u2013\u200915 July 2012 and Its Geoeffectiveness

During Solar Cycle 24, which started at the end of 2008, the Sun was calm, and there were not many spectacular geoeffective events. In this article, we analyze the geomagnetic storm that happened on 15 July 2012 during the 602nd anniversary of the Polish Battle of Grunwald, thus we propose this event to be called the “Battle of Grunwald Day Storm”. According to NOAA scale, it was a G3 geomagnetic storm with a southward component of the heliospheric magnetic field, Bz, falling to −20 nT, minimum Dst index of −139 nT, AE index of 1368 nT, and Ap index of 132 nT. It was preceded by a solar flare class X1.4 on 12 July. This geomagnetic storm was associated with the fast halo coronal mass ejection at 16:48:05 UT on 12 July, first appearance in the Large Angle and Spectroscopic Coronagraph C2, with a plane-of-sky speed of 885 km s−1 and maximum of 1415 km s−1. This geomagnetic storm was classified as the fourth strongest geomagnetic storm of Solar Cycle 24. At that time, a significant growth in the failures of the Polish electric transmission lines was observed, which could have a solar origin.

Evaluating the impact of CNES real-time ionospheric products on multi-GNSS single-frequency positioning using the IGS real-time service

Multi-global navigation satellite system (GNSS) real-time (RT) single-frequency (SF) positioning with a low-cost receiver has received increasing attention in recent years due to its large amount of possible applications. One major challenge in single-frequency positioning is the effective mitigation of the ionospheric delays since it is a dominant error source. Nowadays, a high-precision RT ionospheric vertical total electron content (VTEC) product is released by the Centre National d’Etudes Spatiales (CNES) through its real-time service (RTS). The effect of this product on RT single-frequency positioning needs to be investigated. In this study, we provide an evaluation of the quality of multi-GNSS CLK93 orbit and clock products through the comparison to the final precise products, and comprehensively evaluate the impact of CNES VTEC products on multi-GNSS RT-SF-SPP (Standard Point Positioning)/PPP (Precise Point Positioning) performances. Datasets from 46 Multi-GNSS Experiment (MGEX) stations and the CLK93 corrections for 14 consecutive days in 2019 are collected to process with different scenarios. Experimental results show that the CNES VTEC products can replace the final GIM products in the single- and multi-GNSS SF-SPP with the same positioning accuracy requirements during the period of mild solar activity (Kp index is less than 3). Regarding the kinematic RT-SF-PPP, the (re-)convergence also can be improved by adopting the prior CNES-VTEC constrains. Compared with the IF RT-SF-PPP with quad-constellation, the positioning accuracy of the CNES-VTEC-constrained RT-SF-PPP can be improved by about 10.30%, in which the average RMS can achieve 17.9, 19.8 and 32.3 cm in the North, East and Up components, respectively.Compared with the final precise products of GBM, the satellite orbit accuracy of CLK93 products is 4, 5, 12 and 16 cm for GPS, Galileo, GLONASS and BDS, respectively. As for the CLK93 satellite clock, its RMS accuracy of GPS, Galileo, GLONASS and BDS is 0.3, 0.4, 2.5 and 1.8 ns, respectively.

Analysis of various thermodynamic instability parameters and their association with the rainfall during thunderstorm events over Anakapalle (Visakhapatnam district), India

Thunderstorm events usually take place in cumulonimbus clouds which are complemented with intense rainfall and high-speed winds. In general, rainfall parameter has massive significance when compared to other parameters. In this paper, a group of thunderstorm-related stability parameters were analyzed for pre-monsoon season only. Later, we also tried to study the association between thunderstorm-related stability parameters and rainfall parameter in pre-monsoon season over Anakapalle (Visakhapatnam district) during 2001–2010. We have utilized ERA-Interim ECMWF reanalysis daily datasets for this study. We also tried to compare IMD thunderstorm occurrence days with NOAA CPC-calculated rainfall days in pre-monsoon season over Anakapalle region for every year during 2001–2010. Out of those parameters, upward vertical velocity, convective available potential energy, K-index (KI), humidity index and total totals index parameters have shown good thresholds supporting the rainfall activity during pre-monsoon season. Later, we have also attempted the prediction of DCI and KI parameters over Anakapalle region using artificial neural network (ANN) and auto-regressive moving average (ARMA) techniques. In comparison between the two techniques, ANN technique has shown good correlation with ERA-Interim ECMWF reanalysis data.

Generation of Non‐Substorm Pi2s at Low and Middle Latitudes

AbstractThis study analyzes the characteristics of non‐substorm Pi2 (impulsive pulsations [3–25 mHz]) from low and middle latitudes and investigates the trends of these oscillations. Pi2 events are identified from geomagnetic H‐component data from low and middle latitude observatories Hyderabad (HYB, L = 1.03) and Paratunka (PET, L = 2.1) respectively, during solar maximum period (2015–2016) for quietest geomagnetic conditions, with stringent criteria of interplanetary parameters and activity indices. Data from five high‐latitude stations from THEMIS ground magnetometer chain, covering all local time sectors are additionally analyzed to verify the absence of substorms, pseudo substorms, etc. which may also generate Pi2 signatures. Variation of non‐substorm Pi2 periods with geomagnetic activity index Kp and solar wind speed (Vsw) show inverse relations with Pi2 period at HYB. In addition, non‐substorm Pi2s are distributed equally in all local time sectors with ratio of second harmonic to fundamental Pi2 ranging within 1.3–2.2. These trends of non‐substorm Pi2s indicate plasmaspheric cavity resonance (PCR) as the dominant source at low latitude, confirmed using a theoretical model. In contrast, non‐substorm Pi2 periods do not show a steady trend with Kp and Vsw at midlatitude station PET. Local time variations show an increased period in the premidnight sector at PET. A close agreement between theoretical estimates and observed periods of non‐substorm Pi2‐s at PET, leads to the inference of Alfvenic nature of these modes, attributable to a resonant oscillation.

The variation of ionosonde-derived hmF2 and its comparisons with International Reference Ionosphere (IRI) and Empirical Orthogonal Function (EOF) over Pakistan longitude sector during solar cycle 22

Variations of maximum height of F2 ionospheric layer are analysed over ionospheric stations of Pakistan located at Islamabad (geog. coord. 33.75°N, 72.87°E), Multan (30.18°N, 71.48°E) and Karachi (24.95°N, 67.14°E) during the years, 1987 (LSA), 1990 (HSA) and 1993 (MSA) representing low, high and moderate solar activity years, respectively. Results showed that hmF2 in summer is higher than in winter during LSA and MSA at all stations. However, diurnal pattern is not consistently followed during winters of LSA and MSA. The lowest hmF2 values are observed around sunrise and sunset; whereas, higher values are observed around noon and midnight which may be due to upward and downward plasma drift velocity as diurnal behaviour of hmF2 is similar to diurnal behaviour of E×B drift. No specific latitudinal trend is observed in hmF2 during the period of this study over Pakistan which may be due to the combined effect of E×B drift and energy transferred to ionosphere by atmospheric planetary waves. Solar quiet current seems responsible for the variation of hmF2 over Multan and Islamabad. For Karachi equatorial electrojet seems controlling the daytime hmF2 during LSA. The hmF2 is found to have linear correlation with solar activity and this correlation is stronger with solar index F10.7 as compared to the sunspot numbers. The correlation coefficients for both solar indices are above 80%; whereas, geomagnetic indices Ap and Kp are weakly correlated having correlation coefficients less than 30%. Ionosonde-derived hmF2 are compared with regional model based on expansion of Empirical Orthogonal Function (EOF) with linear and spline interpolation of coefficients of time, seasons, magnetic dip & sunspot numbers and, global model, International Reference Ionosphere (IRI), with International Union of Radio Science (URSI) and Consultative Committee for International Radio (CCIR) options of IRI-2012 and AMTB-2013, SHU-2015 and BSE-1979 sub-models in combination with URSI and CCIR of IRI-2016 versions. The daytime hmF2 values over Pakistan modelled by AMTB of IRI-2016 (with URSI and CCIR) are found to be the most converging of all IRI options during all solar periods. AMTB-2013 also predicted nighttime values with least errors in most cases except during LSA. In addition, IRI showed better equinoctial and annual correlations with ionosonde-derived hmF2 as compared to EOF model. EOF based model showed higher nighttime Mean Absolute Errors (MAE) as compared to IRI. The lowest daytime and nighttime errors in hmF2 are observed over Multan during LSA shown by IRI-2016-AMTB-2013 (using URSI and CCIR) with MAE being 7.8 km and IRI-2016-SHU-2015 (using URSI and CCIR) with MAE being 4.7 km.

Heliospheric Modulation of GCR at Mid and High Latitudes

The variations of Galactic Cosmic Ray (GCR) as compared with the behaviour of various solar activity indices, heliospheric parameters and the geomagnetic index Ap during 1999-2015, which covers part of cycles 23 and cycle 24 have been studied. Two sets of data were considered, consisting respectively of all days of the month and the five quietest days. Neutron Monitor Stations of Moscow and Rome (mid latitude stations) and Inuvik and Oulu (High latitude stations) were employed. Cosmic Ray (CR) wave characteristics were obtained by the harmonics method. The mean, diurnal amplitude of the first, second, and third harmonics were calculated and profiled. Furthermore, correlation analysis was carried out to determine the association between parameters. Results showed that the total magnetic field BT and the sunspot number (SSN) showed the strongest association with CR in both quiet conditions and all day conditions considered. The higher harmonics showed a slightly stronger association with CR than lower harmonics. A time-lag of about 12-15 months was observed for SSN suggesting a potential for predicting CR flux, while the total magnetic field had a zero lag for all the heliospheric parameters considered.

Accounting for Variability in ULF Wave Radial Diffusion Models

AbstractMany modern outer radiation belt models simulate the long‐time behavior of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle, and energy diffusion. Radial diffusion is an important process, often characterized by a deterministic diffusion coefficient. One widely used parameterization is based on the median of statistical ultralow frequency (ULF) wave power for a particular geomagnetic index Kp. We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to the diffusion coefficient through stochastic parameterization, constrained by statistical properties of its underlying observations. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. When temporal variability is included, ensembles exhibit greater diffusion with more rapidly varying diffusion coefficients, larger variance of the diffusion coefficients and for distributions with heavier tails. When we introduce spatial variability, the variance in the set of all ensemble solutions increases with larger spatial scales of variability. Our results demonstrate that the variability of diffusion affects the temporal evolution of phase space density in the outer radiation belt. We discuss the need to identify important temporal and length scales to constrain variability in diffusion models. We suggest that the application of stochastic parameterization techniques in the diffusion equation may allow the inclusion of natural variability and uncertainty in modeling of wave‐particle interactions in the inner magnetosphere.

THE WAY TO DETERMINE THE APPROXIMATELY HAIL'S DIMENSIONS

To determine those storms associated with the convective clouds is necessary a good knowledge of the vertical profile of the troposphere. To determine this parameter, it's essential to make the Skew-T diagrams. From these, we can extract useful information relating to the level of free convection (LFC), the equilibrium level (EL), and the maximum speed of the updraft. The parameter brought in the discussion is handy to hail's forecast. Therefore, based on this parameter, of the ascendant airflow flux, it can determine the dimension of the hail. Besides to determine the hail's sizes, from Skew-T diagram we can find other parameters, such as the Total Totals Index (TTI), this being useful to decide on the coverage rate of the storms, the K Index (KI) - helpful in the case of convections who occur in the same air-mass. The Skew-T diagrams are useful to determine the conductor flux's speed and direction; this is situated between 700 to 500 hPa geopotential heights. Noteworthy are the synoptically materials, by analyzing the way of disposing of the isobars who can be a good indicator of the severity of the storm. Also, the synoptically materials examine at the 500 hPa, 300 hPa, and 200 hPa geopotential to notice if occur the 'cut-off low' areas in the high troposphere. To see if a cloud system is dangerous of hail will be following the cloud's top temperature.

Chain of responses of geomagnetic and ionospheric storms to a bunch of central coronal hole and high speed stream of solar wind

Results of analysis of the proxy of Coronal Hole (CH) Power index, Pch, combined with the high speed streams HSS of solar wind for a period from 2011 to 2019 are presented. It is found that the long-term variation of Pch index shows a trend of growing Pch towards the minimum of solar cycle while most of other identities of solar activity tend to diminish. Superposition of fast solar wind of CH origin with slow SW of CME's origin synchronized with SC explains increasing/decreasing solar wind speed Vsw at L1 point. Total 136 geo-effective Pch/HSS storms are selected with 4 criteria: (1) 3-day increment ΔPch ≥ 90 i.u. where ΔPch = Pch(1d_dmax) – Pch(-3d_dmin); (2) the Pch event is consistent with data of VizieR catalogue of CHs; (3) during 1–4 days after Pch(1d_dmax) the jump of HSS solar wind speed ΔVsw exceeds 50 km/s where ΔVsw = Vswmax(t0 + Δt) - Vswmin(t0) for running time window Δt ≤ 24 h; (4) index kp ≥ 3 occurs during 48 h after zero time t0. Example of moderate storm on 27–28 September 2019 is provided to illustrate Pch/HSS related storm. The superposed epoch analysis is applied to the solar wind speed Vsw, geomagnetic AE, AU, AL, aa, ap, kp, Dst indices and planetary ionosphere TEC-based Wp index during time t0-24 h ≤ t < t0 + 48 h with zero time t0 = 0 at Vswmin. The indices are chained by increasing time lag (delay) of index peak observed after t0 for more than 50% of Pch/HSS storms while the percentage occurrence of peak indices for minimum lag Δt = 8 h after Vswmin was decreasing. The highest rank belongs to AU, kp, ap and aa indices which demonstrate more than 50% of storms with lag Δt = 8 h followed by AE, AL and Vswmax (Δt = 10 h), Wp index (Δt = 13 h) and Dst index (Δt = 15 h). The model relations indicate potential to derive predictions of chain of the peak storm indices in the solar wind, magnetosphere and ionosphere from 1 to 5 days in advance when the relevant increment of Pch index is observed.