Thermosphere joint observations by TM-1 constellations and Swarm-B during the April 2023 geomagnetic storm

The response of thermosphere density to geomagnetic storms is a complicated physical process.Multi-satellite joint observations at the same altitude but different local times(LTs)are important for understanding this process;however,until now such studies have hardly been done.In this report,we analyze in detail the thermosphere mass density response at 510 km during the April 23−24,2023 geomagnetic storm using data derived from the TM-1(TianMu-1)satellite constellation and Swarm-B satellites.The observations show that there were significant LT differences in the hemispheric asymmetry of the thermosphere mass density during the geomagnetic storm.Densities observed by satellite TM02 at nearly 11.3 and 23.3 LTs were larger in the northern hemisphere than in the southern.The TM04 dayside density observations appear to be almost symmetrical with respect to the equator,though southern hemisphere densities on the nightside were higher.Swarm-B data exhibit near-symmetry between the hemispheres.In addition,the mass density ratio results show that TM04 nightside observations,TM02 data,and Swarm-B data all clearly show stronger effects in the southern hemisphere,except for TM04 on the dayside,which suggest hemispheric near-symmetry.The South-North density enhancement differences in TM02 and TM04 on dayside can reach 130%,and Swarm-B data even achieve 180%difference.From the observations of all three satellites,large-scale traveling atmospheric disturbances(TADs)first appear at high latitudes and propagate to low latitudes,thereby disturbing the atmosphere above the equator and even into the opposite hemisphere.NRLMSISE00 model simulations were also performed on this geomagnetic storm.TADs are absent in the NRLMSISE00 simulations.The satellite data suggest that NRLMSISE00 significantly underestimates the magnitude of the density response of the thermosphere during geomagnetic storms,especially at high latitudes in both hemispheres.Therefore,use of the density simulation of NRLMSISE00 may lead to large errors in satellite drag calculations and orbit predictions.We suggest that the high temporal and spatial resolution of direct density observations by the TM-1 constellation satellites can provide an autonomous and reliable basis for correction and improvement of atmospheric models.

The dawn−dusk asymmetry in mesosphere and lower thermosphere temperature disturbances during geomagnetic storms at high latitude

Utilizing observations by the Sounding of the Atmosphere using Broadband Emission Radiometry(SABER)instrument,we quantitatively assessed the dawn-dusk asymmetry in temperature disturbances within the high-latitude mesosphere and lower thermosphere(MLT)during the main phase of geomagnetic storms in this study.An analysis of five geomagnetic superstorm events indicated that during the main phase,negative temperature disturbances were more prevalent on the dawn side than on the dusk side in the high-latitude MLT region.Results of a statistical analysis of 54 geomagnetic storm events also revealed a notable disparity in temperature disturbances between the dawn and dusk sides.At high latitudes,38.2%of the observational points on the dawn side exhibited negative temperature disturbances(less than−5 K),whereas on the dusk side,this percentage was only 29.5%.In contrast,at mid-latitudes,these proportions were 34.1%and 36.5%,respectively,showing no significant difference.We also conducted a statistical analysis of temperature disturbances at different altitudes,which revealed an increase in the proportion of warming disturbances with altitude.Conversely,the proportion of cooling disturbances initially rose with altitude,reaching a peak around 105 km,and subsequently decreased.These temperature disturbance differences could be explained by the day-night asymmetry in vertical wind disturbances during storm conditions.

Responses of the field-aligned currents in the plasma sheet boundary layer to a geomagnetic storm

Geomagnetic storms can result in large magnetic field disturbances and intense currents in the magnetosphere and even on the ground.As an important medium of momentum and energy transport among the solar wind,magnetosphere,and ionosphere,field-aligned currents(FACs)can also be strengthened in storm times.This study shows the responses of FACs in the plasma sheet boundary layer(PSBL)observed by the Magnetospheric Multiscale(MMS)spacecraft in different phases of a large storm that lasted from May 27,2017,to May 29,2017.Most of the FACs were carried by electrons,and several FACs in the storm time also contained sufficient ion FACs.The FAC magnitudes were larger in the storm than in the quiet period,and those in the main phase were the strongest.In this case,the direction of the FACs in the main phase showed no preference for tailward or earthward,whereas the direction of the FACs in the recovery phase was mostly tailward.The results suggest that the FACs in the PSBL are closely related to the storm and could be driven by activities in the tail region,where the energy transported from the solar wind to the magnetosphere is stored and released as the storm is evolving.Thus,the FACs are an important medium of energy transport between the tail and the ionosphere,and the PSBL is a significant magnetosphere–ionosphere coupling region in the nightside.

Analysis of Anomalous Enhancement in TEC and Electron Density in the China Region Prior to the 17 March 2015 Geomagnetic Storm Based on Ground and Space Observations

Total Electron Content(TEC)and electron density enhancement were observed on the day before 17 March 2015 great storm in the China Region.Observations from ground-and space-based instruments are used to investigate the temporal and spatial evolution of the pre-storm enhancement.TEC enhancement was observed from 24°N to 30°N after 10:00 UT at 105°E,110°E and 115°E longitudes on March 16.The maximum magnitude of TEC enhancement was more than 10 TECU and the maximal relative TEC enhancement exceeded 30%.Compared with geomagnetic quiet days,the electron density of Equatorial Ionization Anomaly(EIA)northern peak from Swarm A/C satellites on March 16 was larger and at higher latitudes.NmF2 enhanced during 11:30—21:00 UT at Shaoyang Station and increased by 200%at~16:00 UT.However,TEC and electron density enhancement were not accompanied by a significant change of hmF2.Most research has excluded some potential mechanisms as the main driving factors for storm-time density enhancements by establishing observational constraints.In this paper,we observed pre-storm enhancement in electron density at different altitudes and Equatorial Electrojet(EEJ)strength results derived from ground magnetometers observations suggest an enhanced eastward electric field from the E region probably played a significant role in this event.

Observations of equatorial plasma bubbles during the geomagnetic storm of October 2016

We investigated the variations of equatorial plasma bubbles(EPBs)in the East-Asian sector during a strong geomagnetic storm in October 2016,based on observations from the Beidou geostationary(GEO)satellites,Swarm satellite and ground-based ionosonde.Significant nighttime depletions of F region in situ electron density from Swarm and obvious nighttime EPBs in the Beidou GEO observations were observed on 13 October 2016 during the main phase.Moreover,one interesting feature is that the rare and unique sunrise EPBs were triggered on 14 October 2016 in the main phase rather than during the recovery phase as reported by previous studies.In addition,the nighttime EPBs were suppressed during the whole recovery phase,and absent from 14 to 19 October 2016.Meanwhile,the minimum virtual height of F trace(h’F)at Sanya(18.3°N,109.6°E,MLAT 11.1°N)displayed obvious changes during these intervals.The h’F was enhanced in the main phase and declined during the recovery phase,compared with the values at pre-and post-storm.These results indicate that the enhanced nighttime EPBs and sunrise EPBs during the main phase and the absence nighttime EPBs for many days during the recovery phase could be associated with storm-time electric field changes.

On the loss mechanisms of radiation belt electron dropouts during the 12 September 2014 geomagnetic storm

Radiation belt electron dropouts indicate electron flux decay to the background level during geomagnetic storms,which is commonly attributed to the effects of wave-induced pitch angle scattering and magnetopause shadowing.To investigate the loss mechanisms of radiation belt electron dropouts triggered by a solar wind dynamic pressure pulse event on 12 September 2014,we comprehensively analyzed the particle and wave measurements from Van Allen Probes.The dropout event was divided into three periods:before the storm,the initial phase of the storm,and the main phase of the storm.The electron pitch angle distributions(PADs)and electron flux dropouts during the initial and main phases of this storm were investigated,and the evolution of the radial profile of electron phase space density(PSD)and the(μ,K)dependence of electron PSD dropouts(whereμ,K,and L^*are the three adiabatic invariants)were analyzed.The energy-independent decay of electrons at L>4.5 was accompanied by butterfly PADs,suggesting that the magnetopause shadowing process may be the major loss mechanism during the initial phase of the storm at L>4.5.The features of electron dropouts and 90°-peaked PADs were observed only for>1 MeV electrons at L<4,indicating that the wave-induced scattering effect may dominate the electron loss processes at the lower L-shell during the main phase of the storm.Evaluations of the(μ,K)dependence of electron PSD drops and calculations of the minimum electron resonant energies of H+-band electromagnetic ion cyclotron(EMIC)waves support the scenario that the observed PSD drop peaks around L^*=3.9 may be caused mainly by the scattering of EMIC waves,whereas the drop peaks around L^*=4.6 may result from a combination of EMIC wave scattering and outward radial diffusion.

Response of the Ionospheric F_2-region Over Irkutsk and Hainan to Strong Geomagnetic Storms

The ionospheric responses to two strong storms on 17-19 August 2003 and 22-23 January 2004 are studied,using the data from Irkutsk(52.5°N,104°E) and Hainan(19.5°N,109°E) ionospheric stations.The analysis of variations in relative deviations of the critical frequency △f_0F_2 revealed that at middle latitudes(Irkutsk) negative disturbances were observed in the summer ionosphere; positive and negative ones,in the winter ionosphere during the main and recovery phases respectively.At low latitudes(Hainan),the disturbances were positive in all the cases considered. Mechanisms of the disturbances were analyzed with the aid of empirical models of the neutral atmosphere NRLMSISE-00 and thermospheric wind HWM07.The main factors determining △f_0F_2 variations at middle latitudes during the storms were demonstrated to be the disturbed equatorward thermospheric wind transporting the disturbed atmospheric composition,the increase in the atomic oxygen concentration,and the passage of internal gravity waves.At low latitudes,the effects associated with neutral composition variations are less significant than those of the thermospheric wind and electric fields.

Ionospheric disturbances following the March 2015 geomagnetic storm from GPS observations in China

When strong solar activities and geomagnetic storms happen, satellite communications and navigation system will be strongly disturbed. It is of great significance to monitor ionospheric disturbances,because empirical models cannot capture ionospheric anomalous disturbances well. Nowadays, dualfrequency GPS(Global Positioning System) observations can be used to estimate the ionospheric total electron content, correct the ionospheric delay and analyze the response of the ionosphere to geomagnetic storms. In this paper, the ionospheric response to the geomagnetic storm occurred in March 2015 is investigated using GPS observations provided by Crustal Movement of Observation Network of China. The result shows that this storm increases the electron density in the ionosphere quickly and disrupts the structure of the northern equatorial anomaly region at the beginning. In the main process stage, compared with that in the quite periods, the VTEC(Vertical Total Electron Content)around the longitude of 120°E decreases by 50% and the amount of depletion is larger in the high latitude region than that in the low latitude region. We also find the height of the peak electron density in F2 layer increases during the geomagnetic storm from the electron density profiles derived from GPS occultation mission.

Statistical study on great geomagnetic storms during solar cycle 23

Characteristics of great geomagnetic storms during solar cycle 23 were statistically investigated. Firstly, we focused on the uniqueness of solar cycle 23 by analyzing both the great storm number and sunspot number from 1957 to 2008. It was found that the relationship between the sunspot number and great storm number weakened as the activity of the storms strengthened. There was no obvious relationship between the annual sunspot number and great storm number with Dst≤-300 nT. Secondly, we studied the relationship between the peak Dst and peak Bz in detail. It was found that the condition Bz〈-10 nT is not necessary for storms with Dst≤-100 nT, but seems necessary for storms with Dst≤-150 nT. The duration for Bz≤-10 nT has no direct relationship with the giant storm. The correlation coefficient between the Dst peak and Bz peak for the 89 storms studied is 0.81. After removing the effect of solar wind dynamic pressure on the Dst peak, we obtained a better correlation coefficient of 0.86. We also found the difference between the Dst peak and the corrected Dst peak was proportional to the Dst peak.

Assessment of the predictive capabilities of NIGTEC model over Nigeria during geomagnetic storms

The Nigerian Total Electron Content(NIGTEC)is a regional neural netwo rk-based model developed by the Nigerian Centre for Atmospheric Research to predict the Total Electron Content(TEC)at any location over Nigeria.The addition of the disturbance storm time(Dst)index as one of NIGTEC’s input layer neurons raises a question of its accuracy during geomagnetic storms.In this paper,the capability of NIGTEC in predicting the variability of TEC during geomagnetic storms has been assessed.TEC data predicted by NIGTEC is compared with those derived from Global Navigation Satellite System(GNSS)over Lagos(6.5°N,3.4°E)and Toro(10.1°N,9.120 E)during the intense storms in March 2012 and 2013.The model’s predictive capability is evaluated in terms of Root Mean Square Error(RMSE).NIGTEC reproduced a fairly good storm time morphology in VTEC driven by the prompt penetration electric field and the increase in thermospheric O/N2.Nevertheless,it failed to predict the increase in TEC after the intense sudden impulse of 60 nT on 8 March 2012.And it could not capture the changes in VTEC driven by the storm time equatorward neutral wind especially during 18:00-24:00 UT.Consequently,the RMSEs were higher during this time window,and the highest RMSE value was obtained during the most intense storm in March 2012.

Global investigation of the ionospheric irregularities during the severe geomagnetic storm on September 7-8, 2017

In this study,the global effects of the severe geomagnetic storm on the Earth’s ionosphere on September5 e9,2017 with Coronal Mass Ejections(CMEs)associated with X-9.3 flares on September 6,2017 were investigated by the Rate of Total Electron Content(TEC)Index(ROTI).ROTI was used as a criterion of ionospheric irregularities that took place during the storm.This study was conducted with TEC values obtained from fifty stations connected to the International GNSS System(IGS)-GPS network for five different latitude regions.As a result,it was observed that the irregularities in the high latitude regions of the southern hemisphere were greater in number in comparison with those at the high latitude regions of the northern hemisphere during the storm.It was observed that these irregularities generally occurred during the main and recovery phases of the storm at all latitudes.The weak and moderate ionospheric irregularities that developed at high latitudes during the storm were more in the southern hemisphere.Especially,moderate ionospheric irregularities in high latitudes of both hemispheres took place in eastern longitudes(18 oE-160 oE).However,ionospheric irregularities in the mid-latitude regions were observed in more stations at the northern hemisphere than at the southern hemisphere.Generally,ionospheric irregularities during the storm developed at eastern longitudes in all sectors.

Correlating the interplanetary factors to distinguish extreme and major geomagnetic storms

We investigate the correlation between Disturbance Storm Time(Dst)characteristics and solar wind conditions for the main phase of geomagnetic storms,seeking possible factors that distinguish extreme storms(minimum Dst<−250 nT)and major storms(minimum Dst<−100 nT).In our analysis of 170 storms,there is a marked correlation between the average rate of change of Dst during a storm’s main phase(ΔDst/Δt)and the storm’s minimum Dst,indicating a fasterΔDst/Δt as storm intensity increases.Extreme events add a new regime toΔDst/Δt,the hourly time derivative of Dst(dDst/dt),and sustained periods of large amplitudes for southward interplanetary magnetic field Bz and solar wind convection electric field Ey.We find that Ey is a less efficient driver of dDst/dt for extreme storms compared to major storms,even after incorporating the effects of solar wind pressure and ring current decay.When minimum Dst is correlated with minimum Bz,we observe a similar divergence,with extreme storms tending to have more negative Dst than the trend predicted on the basis of major storms.Our results enable further improvements in existing models for storm predictions,including extreme events,based on interplanetary measurements.

Global distributions of storm-time ionospheric currents as seen in geomagnetic field variations

To investigate temporal and spatial evolution of global geomagnetic field variations from high-latitude to the equator during geomagnetic storms, we analyzed ground geomagnetic field disturbances from high latitudes to the magnetic equator. The daytime ionospheric equivalent current during the storm main phase showed that twin-vortex ionospheric currents driven by the Region 1 field-aligned currents （R1 FACs） are intensified significantly and expand to the low-latitude region of-30~ magnetic latitude. Centers of the currents were located around 70~ and 65~ in the morning and afternoon, respectively. Corresponding to intensification of the R1 FACs, an enhancement of the eastward/westward equatorial electrojet occurred at the daytime/nighttime dip equator. This signature suggests that the enhanced convection electric field penetrates to both the daytime and nighttime equa- tor. During the recovery phase, the daytime equivalent current showed that two new pairs of twin vortices, which are different from two-cell ionospheric currents driven by the R1 FACs, appear in the polar cap and mid latitude. The former led to enhanced north- ward Bz （NBZ） FACs driven by lobe reconnection tailward of the cusps, owing to the northward interplanetary magnetic field （IMF）. The latter was generated by enhanced Region 2 field-aligned currents （R2 FACs）. Associated with these magnetic field variations in the mid-latitudes and polar cap, the equatorial magnetic field variation showed a strongly negative signature, produced by the westward equatorial electrojet current caused by the dusk-to-dawn electric field.

A statistical analysis of the Kappa-type energy spectrum distribution of radiation belt electrons observed by Van Allen Probes

The energy spectrum of energetic electrons is a key factor representing the dynamic variations of Earth’s Van Allen radiation belts.Increased measurements have indicated that the commonly used Maxwellian and Kappa distributions are inadequate for capturing the realistic spectral distributions of radiation belt electrons.Here we adopt the Kappa-type(KT)distribution as the fitting function and perform a statistical analysis to investigate the radiation belt electron flux spectra observed by the Van Allen Probes.By calculating the optimal values of the key KT distribution parameters(i.e.,κandθ2)from the observed spectral shapes,we fit the radiation belt electron fluxes at different L-shells under different geomagnetic conditions.In this manner,we obtain typical values of the KT distribution parameters,which are statistically feasible for modeling the radiation belt electron flux profiles during either geomagnetically quiet or active periods.A comparison of the KT distribution model results with those using the Maxwellian or Kappa distribution reveals the advantage of the KT distribution for studying the overall properties of the radiation belt electron spectral distribution,which has important implications for deepening the current understanding of the radiation belt electron dynamics under evolving geomagnetic conditions.

Statistical Study of the Geoeffectivity of Halo Coronal Mass Ejections Associated with X-Class Flares during Solar Cycles 23 and 24

By analysing a long series of data (1996-2019), we show that solar cycle 23 was more marked by violent solar flares and coronal mass ejections (CMEs) compared to solar cycle 24. In particular, the halo coronal mass ejections associated with X-class flares appear to be among the most energetic events in solar activity given the size of the flares, the speed of the CMEs and the intense geomagnetic storms they produce. Out of eighty-six (86) X-class halo CMEs, thirty-seven (37) or 43% are highly geoeffective;twenty-four (24) or approximately 28% are moderately geoeffective and twenty-five (25) or 29% are not geoeffective. Over the two solar cycles (1996 to 2019), 71% of storms were geoeffective and 29% were not. For solar cycle 23, about 78% of storms were geoeffective, while for solar cycle 24, about 56% were geoeffective. For the statistical study based on speed, 85 halo CMEs associated with X-class flares were selected because the CME of 6 December 2006 has no recorded speed value. For both solar cycles, 75.29% of the halo CMEs associated with X-class flares have a speed greater than 1000 km/s. The study showed that 42.18% of halo (X) CMEs with speeds above 1000 km/s could cause intense geomagnetic disturbances. These results show the contribution (in terms of speed) of each class of halo (X) CMEs to the perturbation of the Earth’s magnetic field. Coronal mass ejections then become one of the key indicators of solar activity, especially as they affect the Earth.

Evolutions of equatorial ring current ions during a magnetic storm

In this paper, we present evolutions of the phase space density(PSD) spectra of ring current(RC) ions based on observations made by Van Allen Probe B during a geomagnetic storm on 23–24 August 2016. By analyzing PSD spectra ratios from the initial phase to the main phase of the storm, we find that during the main phase, RC ions with low magnetic moment μ values can penetrate deeper into the magnetosphere than can those with high μ values, and that the μ range of PSD enhancement meets the relationship: S(O^+) >S(He^+)>S(H^+). Based on simultaneously observed ULF waves, theoretical calculation suggests that the radial transport of RC ions into the deep inner magnetosphere is caused by drift-bounce resonance interactions, and the efficiency of these resonance interactions satisfies the relationship: η(O^+) > η(He^+) > η(H^+), leading to the differences in μ range of PSD enhancement for different RC ions. In the recovery phase,the observed decay rates for different RC ions meet the relationship: R(O^+) > R(He^+) > R(H^+), in accordance with previous theoretical calculations, i.e., the charge exchange lifetime of O^+ is shorter than those of H^+ and He^+.

Evidence of Correlation between High Frequency Geomagnetic Variations and Seismicity in the Caribbean

An analysis between the hourly distribution of earthquakes in three areas of the Caribbean and the high-frequency variations of the geomagnetic field is presented. The number of earthquakes selected for each zone is between 10,000 and 43,000, which guarantees a statistically significant distribution. The hourly distributions of seismicity in all areas show a bay-shape distribution with a significant increase in the number of earthquakes at night, from 11 PM to 5 AM. For example, in eastern Cuba 36.7% of earthquakes occur at that time, representing 11.7% over 25% in the absence of any time preference. Geomagnetic disturbances were compiled from several years to be able to make a statistically significant hourly distribution of their occurrence, being determined by sudden changes in the magnetic field at a short period of 1 minute. In this sense, geomagnetic data were processed between the years 2011-2016, recorded by the geostationary satellite GOES13 and the magnetic ground station SJG in San Juan, Puerto Rico. The result shows a significant correlation between hourly earthquakes distribution and high-frequency geomagnetic variations. The time-varying conductivity response of Earth’s interior also correlates with seismicity. The theory behind this correlation could be related to the piezoelectric phenomena and the electromagnetic force induced when the magnetic field is disturbed.

SZ-5 Cabin’s Height Changes during Three Super-storms in 2003

In this work,the daily height variations of SZ-5(Shenzhou-5) cabin from 22 October to 28 November in 2003 are analyzed,which includes the period of the Halloween Storm and the Great November Storm.The significant orbital decays have been observed at the end of October and in late November due to the great solar flares and the severe geomagnetic storms.According to the equation of the air-drag-force on a spacecraft and the SZ-5 orbital decay information,the relative daily average thermospheric density changes during the three 2003 super-storms are derived and the results are compared with the Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar Extended Model(NRLMSISE-00).The results show that the daily average thermospheric density(at the altitude of SZ-5,about 350 km) in storm time enhances to approximately 200% as much as that in the quiet time but the empirical model may somewhat underestimate the average thermospheric density changes and the daily contributions of geomagnetic storms to the density enhancements during these severe space weather events.

Current Status and Main Scientific Results of In-flight CSES Mission

The CSES(China Seismo-Electromagnetic Satellite)is the electromagnetism satellite of China’s Zhangheng mission which is planned to launch a series of microsatellites within next 10 years in order to monitor the electromagnetic environment,gravitational field.The CSES 01 probe(also called ZH-1)was launched successfully on 2 February 2018,from the Jiuquan Satellite Launch Centre(China)and is expected to operate for 5 years in orbit.The second probe CSES 02 is going to be launched in 2022.The scientific objectives of CSES are to detect the electromagnetic field and waves,plasma and particles,for studying the seismic-associated disturbances.To meet the requirements of scientific objective,the satellite is designed to be in a sun-synchronous orbit with a high inclination of 97.4°at an altitude around 507 km.CSES carries nine scientific payloads including Search-coil magnetometer,Electric Field Detector,High precision Magnetometer,GNSS occultation Receiver,Plasma Analyzer,Langmuir Probe,two Energetic Particle Detectors(including an Italian one),and Tri-Band Transmitter.Up to now,CSES has been operating in orbit for 2 years with stable and reliable performance.By using all kinds of data acquired by CSES,we have undertaken a series of scientific researches in the field of global geomagnetic field re-building,the ionospheric variation environment,waves,and particle precipitations under disturbed space weather and earthquake activities,the Lithosphere-Atmosphere-Ionosphere coupling mechanism research and so on.

Prediction of Partial Ring Current Index Using LSTM Neural Network

The local time dependence of the geomagnetic disturbances during magnetic storms indicates the necessity of forecasting the localized magnetic storm indices.For the first time,we construct prediction models for the SuperMAG partial ring current indices(SMR-LT),with the advance time increasing from 1 h to 12 h by Long Short-Term Memory(LSTM)neural network.Generally,the prediction performance decreases with the advance time and is better for the SMR-06 index than for the SMR-00,SMR-12,and SMR-18 index.For the predictions with 12 h ahead,the correlation coefficient is 0.738,0.608,0.665,and 0.613,respectively.To avoid the over-represented effect of massive data during geomagnetic quiet periods,only the data during magnetic storms are used to train and test our models,and the improvement in prediction metrics increases with the advance time.For example,for predicting the storm-time SMR-06 index with 12 h ahead,the correlation coefficient and the prediction efficiency increases from 0.674 to 0.691,and from 0.349 to 0.455,respectively.The evaluation of the model performance for forecasting the storm intensity shows that the relative error for intense storms is usually less than the relative error for moderate storms.