Proposal of new models of the bottom-side B0 and B1 parameters for IRI

The time series of hourly electron density profiles N(h) obtained from 27 ionosonde stations distributed world-wide have been used to obtain N(h) average profiles on a monthly basis and to extract the expected bottom-side parameters that define the IRI profile under quiet conditions. The time series embrace the time interval from 1998 to 2006, which practically contains the entire solar cycle 23. The Spherical Harmonic Analysis (SHA) has been used as an analytical technique for modeling globally the B0 and B1 parameters as general functions on a spherical surface. Due to the irregular longitudinal distribution of the stations over the globe, it has been assumed that the ionosphere remains approximately constant in form for a given day under quiet conditions for a particular coordinate system. Since the Earth rotates under a Sun-fixed system, the time differences have been considered to be equivalent to longitude differences. The time dependence has been represented by a two-degree Fourier expansion to model the annual and semiannual variations and the year-by-year analyses of the B0 and B1 have furnished nine sets of spherical harmonic coefficients for each parameter. The spatial–temporal yearly coefficients have been further expressed as linear functions of Rz12 to model the solar cycle dependence. The resultant analytical model provides a tool to predict B0 and B1 at any location distributed among the used range of latitudes (70°N–50°S) and at any time that improves the fit to the observed data with respect to IRI prediction.     

The variability and IRI2007-predictability of hmF2 over South Africa

This paper presents an investigation into the variability and predictability of the maximum height of the ionospheric F2 layer, hmF2 over the South African region. Data from three South African stations, namely Madimbo (22.4°S, 26.5°E, dip angle: −61.47°), Grahamstown (33.3°S, 26.5°E, dip angle: −64.08°) and Louisvale (28.5°S, 21.2°E, dip angle: −65.44°) were used in this study. The results indicate that hmF2 shows a larger variability around midnight than during the daytime for all seasons. Monthly median hmF2 values were used in all cases and were compared with predictions from the IRI-2007 model, using the URSI (Union Radio-Scientifique Internationale) coefficient option. The analysis covers the diurnal and seasonal hourly hmF2 values for the selected months and time sectors e.g. January, July, April and October for 2003 and 2005. The time ranges between (03h00–23h00 UT; LT = UT + 2h) representing the local sunrise, midday, sunset and midnight hours. The time covers sunrise, midday, sunrise, and midnight hours (03–06h00 UT, 07–11h00 UT, sunrise 16–18h00 UT and 22–23h00 UT; LT = UT + 2h). The dependence of the results on solar activity levels was also investigated. The IRI-2007 predictions follow fairly well the diurnal and seasonal variation patterns of the observed hmF2 values at all the stations. However, the IRI-2007 model overestimates and underestimates the hmF2 value during different months for all the solar activity periods.     

Low solar activity variability and IRI 2007 predictability of equatorial Africa GPS TEC

Diurnal, seasonal and latitudinal variations of Vertical Total Electron Content (VTEC) over the equatorial region of the African continent and a comparison with IRI-2007 derived TEC (IRI-TEC), using all three options (namely; NeQuick, IRI01-corr and IRI-2001), are presented in this paper. The variability and comparison are presented for 2009, a year of low solar activity, using data from thirteen Global Positioning System (GPS) receivers. VTEC values were grouped into four seasons namely March Equinox (February, March, April), June Solstice (May, June, July), September Equinox (August, September, October), and December Solstice (November, December, January). VTEC generally increases from 06h00 LT and reaches its maximum value at approximately 15h00–17h00 LT during all seasons and at all locations. The NeQuick and IRI01-corr options of the IRI model predict reasonably well the observed diurnal and seasonal variation patterns of VTEC values. However, the IRI-2001 option gave a relatively poor prediction when compared with the other options. The post-midnight and post-sunset deviations between modeled and observed VTEC could arise because NmF2 or the shape of the electron density profile, or both, are not well predicted by the model; hence some improvements are still required in order to obtain improved predictions of TEC over the equatorial region of the Africa sector.     

Validation of B0 and B1 in the IRI 2001 model at low solar activity for Ilorin an equatorial station

A new set of data obtained at low solar activity from Ilorin, Nigeria (geog. latitude 8.5°N, geog longitude, 4.6°E, dip 4.1°S) is used to validate the IRI 2001 model at low solar activity. The results show in general a good agreement between model and observed B0 at night but an over estimation during daytime. The overestimation is greatest during the morning period (0600LT–1000LT). The model prediction for B1 is fairly good at night and during the day. A dependence of B0 on solar zenith angle χ is observed during the daytime. A formulation of the form B0 = A[cos(χ)ⁿ] is therefore proposed. Values of the constants n and A were determined for the period of low solar activity for this station.     

Comparison between observed ionospheric foF2 and IRI-2001 predictions over periods of severe geomagnetic activities at Grahamstown,South Africa

The observed ionospheric F2 critical frequency (foF2) values over a South Africa mid-latitude station, Grahamstown, (geographic coordinates: 33.3°S, 26.5°E), were analysed and compared with International Reference Ionosphere (IRI) model, using the CCIR (Comite´ Consultatif International des Radio communications) and URSI (Union Radio-Scientifique Internationale) coefficients, during four geomagnetically disturbed days in the year 2000. These days are April 5, May 23, August 10 and September 15. The data were analysed for five days around the storm day. Comparisons between the IRI-2001 predicted foF2 values, using both CCIR and URSI coefficients and the observed values are shown with their root-mean-square error (RMSE) and the relative deviation module mean (rdmm) for the various storm periods. The CCIR option performed more accurately than the URSI option.     

Variations in the ionospheric scale height parameter at the F2 peak over Grahamstown,South Africa

The Grahamstown, South Africa (33.3°S, 26.5°E) ionospheric field station operates a Lowell digital pulse ionospheric sounder (Digisonde) whose output includes scaled parameters derived from the measured ionogram. One of these output parameters is the ionospheric scale height parameter (H), and this paper presents an analysis of the seasonal, diurnal, and solar activity variations of this parameter over the Grahamstown station. Ionosonde data from three years 2002, 2003, and 2004 were used in this study. The data was subjected to a general trend analysis to remove any outliers and then the monthly median data were used to explore the different variations. The results of this analysis were found to be similar to what has already been presented in the literature for low latitude stations, and are presented as well as the correlation at this mid-latitude station between the H parameter, the IRI shape parameter (B0), and the peak electron density (NmF2).     

A 12 year comparison of MIDAS and IRI 2007 ionospheric Total Electron Content

Data assimilation in conventional meteorological applications uses measurements in conjunction with a physical model. In the case of the ionised region of the upper atmosphere, the ionosphere, assimilation techniques are much less mature. The empirical model known as the International Reference Ionosphere (IRI) could be used to augment data-sparse regions in an ionospheric now-cast and forecast system. In doing so, it is important that it does not introduce systematic biases to the result. Here, the IRI model is compared to ionospheric observations from the Global Positioning System satellites over Europe and North America. Global Positioning System data are processed into hour-to-hour monthly averages of vertical Total Electron Content using a tomographic technique. A period of twelve years, from January 1998 to December 2009, is analysed in order to capture variations over the whole solar cycle. The study shows that the IRI model underestimates Total Electron Content in the daytime at solar maximum by up to 37% compared to the monthly average of GPS tomographic images, with the greatest differences occurring at the equinox. IRI shows good agreement at other times. Errors in TEC are likely due to peak height and density inaccuracies. IRI is therefore a suitable model for specification of monthly averages of Total Electron Content and can be used to initialise a data assimilation process at times away from solar maximum. It may be necessary to correct for systematic deviations from IRI at solar maximum, and to incorporate error estimation into a data assimilation scheme.     

Estimation of the elastic Earth parameters (h2, l2) using SLR data

We present results for the global elastic parameters h₂ and l₂ derived from the analysis of Satellite Laser Ranging (SLR) data. SLR data for the two satellites LAGEOS 1 and LAGEOS 2 observed during 2.5 years from January 3, 2005 until July 1, 2007 with 18 globally distributed ground stations were analysed using different approaches. The analysis was done separately for the two satellites and approaches to estimate the two elastic parameters independently and together were performed. We do a sequential analysis and study the stability of the estimates as a function of length of the data set used. The adjusted final values for h₂ equal to 0.6151 ± 0.0008 and 0.6152 ± 0.0008, and those for l₂ equal to 0.0886 ± 0.0003 and 0.0881 ± 0.0003 for LAGEOS 1 and LAGEOS 2 tracking data are compared to other independently derived estimates. These parameters and their errors achieve stability at about the 24 and 27 month time interval for h₂ and l₂, respectively.     

Using the radial basis function neural network to predict ionospheric critical frequency of F2 layer over Wuhan

Neural networks (NNs) have been applied to ionospheric predictions recently. This paper uses radial basis function neural network (RBF-NN) to forecast hourly values of the ionospheric F₂ layer critical frequency(f_oF₂), over Wuhan (30.5N, 114.3E), China. The false nearest neighbor method is used to determine the embedding dimension, and the principal component analysis (PCA) is used to reduce noise and dimension. The whole study is based on a sample of about 26,000 observations of f_oF₂ with 1-h time resolution, derived during the period from January 1981 to December 1983. The performance of RBF-NN is estimated by calculating the normalized root-mean-squared (NRMSE) error, and its results show that short-term predictions of f_oF₂ are improved.     

Comparison of ionospheric F2 peak parameters foF2 and hmF2 with IRI2001 at Hainan

Monthly median values of foF2, hmF2 and M(3000)F2 parameters, with quarter-hourly time interval resolution for the diurnal variation, obtained with DPS4 digisonde at Hainan (19.5°N, 109.1°E; Geomagnetic coordinates: 178.95°E, 8.1°N) are used to investigate the low-latitude ionospheric variations and comparisons with the International Reference Ionosphere (IRI) model predictions. The data used for the present study covers the period from February 2002 to April 2007, which is characterized by a wide range of solar activity, ranging from high solar activity (2002) to low solar activity (2007). The results show that (1) Generally, IRI predictions follow well the diurnal and seasonal variation patterns of the experimental values of foF2, especially in the summer of 2002. However, there are systematic deviation between experimental values and IRI predictions with either CCIR or URSI coefficients. Generally IRI model greatly underestimate the values of foF2 from about noon to sunrise of next day, especially in the afternoon, and slightly overestimate them from sunrise to about noon. It seems that there are bigger deviations between IRI Model predictions and the experimental observations for the moderate solar activity. (2) Generally the IRI-predicted hmF2 values using CCIR M(3000)F2 option shows a poor agreement with the experimental results, but there is a relatively good agreement in summer at low solar activity. The deviation between the IRI-predicted hmF2 using CCIR M(3000)F2 and observed hmF2 is bigger from noon to sunset and around sunrise especially at high solar activity. The occurrence time of hmF2 peak (about 1200 LT) of the IRI model predictions is earlier than that of observations (around 1500 LT). The agreement between the IRI hmF2 obtained with the measured M(3000)F2 and the observed hmF2 is very good except that IRI overestimates slightly hmF2 in the daytime in summer at high solar activity and underestimates it in the nighttime with lower values near sunrise at low solar activity.     

Ionospheric behavior of the F2 peak parameters foF2 and hmF2 at Hainan and comparisons with IRI model predictions

Monthly median values of foF2, hmF2 and M(3000)F2 parameters, with hourly time interval resolution for the diurnal variation, obtained with DPS-4 digisonde observations at Hainan (19.4°N, 109.0°E) are used to study the low latitude ionospheric variation behavior. The observational results are compared with the International Reference Ionospheric Model (IRI) predictions. The time period coverage of the data used for the present study is from March 2002 to February 2005. Our present study showed that: (1) In general, IRI predictions using CCIR and URSI coefficients follow well the diurnal and seasonal variation patterns of the experimental values of foF2. However, CCIR foF2 and URSI foF2 IRI predictions systematically underestimate the observed results during most time period of the day, with the percentage difference ΔfoF2 (%) values changing between about −5% and −25%, whereas for a few hours around pre-sunrise, the IRI predictions generally overestimate the observational ones with ΔfoF2 (%) sometimes reaching as large as ∼30%. The agreement between the IRI results and the observational ones is better for the year 2002 than for the other years. The best agreement between the IRI results and the observational ones is obtained in summer when using URSI coefficients, with the seasonal average values of ΔfoF2 (%) being within the limits of ±10%. (2) In general, the IRI predicted hmF2 values using CCIR M(3000)F2 option shows a poor agreement with the observational results. However, when using the measured M(3000)F2 as input, the diurnal variation pattern of hmF2 given by IRI2001 has a much better agreement with the observational one with the detailed fine structures including the pre-sunrise and post-sunset peaks reproduced reasonably well. The agreement between the IRI predicted hmF2 values using CCIR M(30,000)F2 option and the observational ones is worst for the afternoon to post-midnight hours for the high solar activity year 2002. During daytime hours the agreement between the hmF2 values obtained with CCIR M(30,000)F2 option and the observational ones is best for summer season. The discrepancy between the observational hmF2 and that obtained with CCIR M(30,000)F2 option stem from the CCIR M(3000)F2 model, which does not produce the small scale structures observed in the measured M(3000)F2.     

Pre-storm behaviour of NmF2 and TEC (GPS) over equatorial and low latitude stations in the Indian sector

The pre-storm behavior of NmF₂ and TEC over an equatorial station, Trivandrum (8.47°N, 76.91°E, dip 0.6°S) and a low latitude station, Waltair (17.7°N,83.3°E, dip 20°N) has been studied for a total of 18 strong geomagnetic storms with DST ? −100 nT. The simultaneous measurements of GPS-TEC and NmF₂ over Trivandrum and Waltair during the period 2000–2005 have been considered for the present study. It is found that there is a substantial increase in NmF₂ and TEC before the onset of the storm over Waltair, while the increase is not present at Trivandrum. The origin of pre-storm enhancements in electron density still remains unresolved owing to several conditions in their potential sources and occurrence mechanisms. In the present study an attempt is made to identify the possible mechanisms responsible for such enhancements in electron density of the F-region.     

Study of maximum electron density NmF2 at Karachi and Islamabad during solar minimum (1996) and solar maximum (2000) and its comparison with IRI

The monthly hourly medians of maximum electron density, N_mF₂, at two Pakistani ionospheric stations, Karachi and Islamabad, have been determined for solar minimum (1996) and solar maximum (2000) and compared with IRI predictions using the URSI coefficients. At night and pre-noon period the N_mF₂ values at both stations are almost equal during the 2 years. However, at post-noon the values at Karachi are considerably larger than those at Islamabad due to the equatorial or geomagnetic anomaly. Karachi (geomag. coord. 16.44°N, 139.08°E) lies near the region of the equatorial anomaly (+20 and −20 geomagnetic latitude), so most of the N_mF₂ values at Karachi are larger than those at Islamabad (geomag. coord. 24.46°N, 145.67°E). The maximum monthly values of N_mF₂ show a semi-annual variation at Karachi and Islamabad both during 1996 and 2000 as predicted by IRI.     

An investigation of ionospheric disturbances over South Africa during the magnetic storm on 15 May 2005

The effects of the 15 May 2005 severe geomagnetic storm on the South African ionosphere are studied using ground-based and satellite observations. Ionospheric disturbances have less frequently been investigated over mid-latitude regions. Recently, a number of studies investigated their evolution and generation over these regions. This paper reports on the first investigation of travelling ionospheric disturbances (TIDs) over mid-latitude South Africa. Using global positioning system (GPS)-derived total electron content (TEC) variations from the South African network of dual frequency GPS receivers, we were able to examine the effects of the disturbance on the TEC. During this storm, two TEC enhancements were observed at low- and mid-latitudes: the first enhancement was observed between 30–45°S geomagnetic latitudes associated with equatorward neutral winds and the passage of a TID, while the second TEC enhancement is associated with a second TID. In addition, the F-region critical frequency (foF2) values observed at two ionosonde stations show response features that differ from those of the TEC during the disturbance period. The dissimilarity between the TEC and the foF2 suggests that two competing drivers may have existed, i.e., the westward electric field and equatorward neutral wind effects.     

Longitudinal behaviors of the IRI-B parameters of the equatorial electron density profiles retrieved from FORMOSAT-3/COSMIC radio occultation measurements

The electron density profiles in the bottomside F₂-layer ionosphere are described by the thickness parameter B0 and the shape parameter B1 in the International Reference Ionosphere (IRI) model. We collected the ionospheric electron density (N_e) profiles from the FORMOSAT-3/COSMIC (F3/C) radio occultation measurements from DoY (day number of year) 194, 2006 to DoY 293, 2008 to investigate the daytime behaviors of IRI-B parameters (B0 and B1) in the equatorial regions. Our fittings confirm that the IRI bottomside profile function can well describe the averaged profiles in the bottomside ionosphere. Analysis of the equatorial electron density profile datasets provides unprecedented detail of the behaviors of B0 and B1 parameters in equatorial regions at low solar activity. The longitudinal averaged B1 has values comparable with IRI-2007 while it shows little seasonal variation. In contrast, the observed B0 presents semiannual variation with maxima in solstice months and minima in equinox months, which is not reproduced by IRI-2007. Moreover, there are complicated longitudinal variations of B0 with patterns varying with seasons. Peaks are distinct in the wave-like longitudinal structure of B0 in equinox months. An outstanding feature is that a stable peak appears around 100°E in four seasons. The significant longitudinal variation of B0 provides challenges for further improving the presentations of the bottomside ionosphere in IRI.     

电离层中释放六氟化硫的流场及试验效应模拟

在电离层中释放六氟化硫时,释放初期的六氟化硫流速及流量等条件是影响释放效应仿真的重要因素,对仿真结果的准确性具有一定的影响.传统的六氟化硫释放引起的电离层效应仿真中并未讨论.基于Fluent流场仿真软件,针对不同释放初始条件并结合六氟化硫容器的结构,对六氟化硫释放过程中温度、压强以及喷口流速、流量等参数变化情况进行仿真计算,得到了以上参量在释放过程中的变化情况,并将其作为电离层化学物质释放三维动力学模型的初始参数,获得了更加精确的六氟化硫电离层释放效应仿真结果.     

Variability of the behavior of the bottomside (B0, B1) parameters obtained from the ground-based ionograms at China’s low latitude station

In this paper, data of (B0, B1) parameters deduced from the electron density profiles that are inverted from the ionograms recorded at Hainan (19.4°N, 109.0°E), China during a three year period from March 2002 to February 2005 are used to study the diurnal and seasonal variation of (B0, B1) parameters at low latitude. The observational results are compared with the IRI2001 model predictions. Variability study of (B0, B1) in terms of percentage ratio of the inter-quartiles to the median values and correlative analysis between (B0, B1) parameters and other ionospheric characteristics such as hmF2 and M(3000)F2 are also made. Our present study showed that: (1) for daytime hours, the IRI2001 model results with new table option (B0_Tab) is in a better agreement with the observational results (B0_Obs) than the IRI2001 model results with Gulyaeva option (B0_Gul) for summer season, whereas B0_Gul is in a better agreement with B0_Obs than B0_Tab for winter season. For nighttime, in general, B0_Gul is in a better agreement with B0_Obs than B0_Tab. For other occasions, both B0_Tab and B0_Gul showed some systematic deviations from the observational ones. Moreover, the deviations of B0_Tab and B0_Gul from B0_Obs showed opposite trends; (2) the monthly upper (lower) quartiles of (B0, B1) parameter showed a good linear relationship with the monthly median values, this makes it possible to do the regression analysis between the monthly upper (lower) quartiles and the monthly median values, which can give a measure of the variability of these parameters. In terms of the percentage ratio of the inter-quartiles to the median values, the variability of B0 showed a diurnal variation ranging between 22% and 36% with maximum value occurring at pre-sunrise hours, whereas the variability of B1 showed a diurnal variation ranging between 15% and 30% with higher value by daytime than at night; (3) B0 shows high linear correlative relationships with hmF2 and M(3000)F2 for most of the local time period of a day except for a few hours around midnight, whereas B1 showed high linear correlations with B0, hmF2 for daytime hours, but not for nighttime hours. This suggests that it maybe is possible to obtain the synthetic database of (B0, B1) parameter or to construct the model of (B0, B1) using database of hmF2 or M(3000)F2 which is much easier to obtain from experimental measurements.     

Evolution of periodic orbits near the Lagrangian point L2

A study of the evolution of the periodic and the quasi-periodic orbits near the Lagrangian point L₂, which is located to the right of the smaller primary on the line joining the primaries and whose distance from the more massive primary is greater than the distance between the primaries, in the framework of restricted three-body problem for the Sun–Jupiter, Earth–Moon (relatively large mass ratio) and Saturn–Titan (relatively small mass ratio) systems is made. Two families of periodic orbits around the smaller primary are identified using the Poincaré surface of section method – family I (initially elliptical, gradually becomes egg-shaped with the increase in the Jacobi constant C and elongated towards the more massive primary) and family II (initially egg-shaped orbits elongated towards L₂ and gradually becomes elliptical with the increase in C). The family I in the Sun–Jupiter and Saturn–Titan systems contains two separatrix caused by third-order and fourth-order resonances, while the Earth–Moon system has only one separatrix which is caused by third-order resonances. Also in the Sun–Jupiter and the Saturn–Titan systems, family I merge with family II, around Jacobian constant 3.0393 and 3.0163, respectively, while in the Earth–Moon system, family II evolves separately from two different branches. The two branches merge at C = 3.184515. In the Earth–Moon system, the family II contains a separatrix due to third-order resonances which is absent in the other two systems.     

Symmetry,reduction and relative equilibria of a rigid body in the J2 problem

The J₂ problem is an important problem in celestial mechanics, orbital dynamics and orbital design of spacecraft, as non-spherical mass distribution of the celestial body is taken into account. In this paper, the J₂ problem is generalized to the motion of a rigid body in a J₂ gravitational field. The relative equilibria are studied by using geometric mechanics. A Poisson reduction process is carried out by means of the symmetry. Non-canonical Hamiltonian structure and equations of motion of the reduced system are obtained. The basic geometrical properties of the relative equilibria are given through some analyses on the equilibrium conditions. Then we restrict to the zeroth and second-order approximations of the gravitational potential. Under these approximations, the existence and detailed properties of the relative equilibria are investigated. The orbit–rotation coupling of the rigid body is discussed. It is found that under the second-order approximation, there exists a classical type of relative equilibria except when the rigid body is near the surface of the central body and the central body is very elongated. Another non-classical type of relative equilibria can exist when the central body is elongated enough and has a low average density. The non-classical type of relative equilibria in our paper is distinct from the non-Lagrangian relative equilibria in the spherically-simplified Full Two Body Problem, which cannot exist under the second-order approximation. Our results also extend the previous results on the classical type of relative equilibria in the spherically-simplified Full Two Body Problem by taking into account the oblateness of the primary body. The results on relative equilibria are useful for studies on the motion of many natural satellites, whose motion are close to the relative equilibria.