The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data

The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth’s gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.     

The effect of spatial truncation error on variance of gravity anomalies derived from inversion of satellite orbital and gradiometric data

The spatial truncation error (STE) is a significant systematic error in the integral inversion of satellite gradiometric and orbital data to gravity anomalies at sea level. In order to reduce the effect of STE, a larger area than the desired one is considered in the inversion process, but the anomalies located in its central part are selected as the final results. The STE influences the variance of the results as well because the residual vector, which is contaminated with STE, is used for its estimation. The situation is even more complicated in variance component estimation because of its iterative nature. In this paper, we present a strategy to reduce the effect of STE on the a posteriori   variance factor and the variance components for inversion of satellite orbital and gradiometric data to gravity anomalies at sea level. The idea is to define two windowing matrices for reducing this error from the estimated residuals and anomalies. Our simulation studies over Fennoscandia show that the differences between the 0.5°×0.5°$0.5°\times 0.5°$ gravity anomalies obtained from orbital data and an existing gravity model have standard deviation (STD) and root mean squared error (RMSE) of 10.9 and 12.1 mGal, respectively, and those obtained from gradiometric data have 7.9 and 10.1 in the same units. In the case that they are combined using windowed variance components the STD and RMSE become 6.1 and 8.4 mGal. Also, the mean value of the estimated RMSE after using the windowed variances is in agreement with the RMSE of the differences between the estimated anomalies and those obtained from the gravity model.     

Probing the method of correcting Faraday rotation in vector magnetograms

By analyzing the vector magnetograms of Huairou Solar Observing Station (HSOS) taken at the line center (0.0 Å) and the line wing (−0.12 Å) of FeI λ5324.19 Å, we make an estimate of the measured errors in transversal azimuths (δ?) caused by Faraday rotation. Since many factors, such as the magnetic saturation and scattered light, can affect the measurement accuracy of the longitudinal magnetic field in the umbrae of sunspots, we limit our study in the region ∣B_z∣ < 800 G. The main mean azimuth rotations are about 4°, 6°, 7° and 9°, while ∣B_z∣ are in the ranges of 400–500 G, 500–600 G, 600–700 G and 700–800 G, respectively. Moreover, we find there is also an azimuth rotation of about 8° at the wavelength offset −0.12 Å of the line compared against a previous numerical simulation.     

Quantifying the role of solar radiative forcing over the 20th century

The 20th century temperature anomaly record is reproduced using an energy balance model, with a diffusive deep ocean. The model takes into account all the standard radiative forcings, and in addition the possibility of a non-thermal solar component. The model is parameterized and then optimized to produce the most likely values for the climate parameters and radiative forcings which reproduce the 20th century global warming. We find that the best fit is obtained with a negligible net feedback. We also show that a non-thermal solar component is necessarily present, indicating that the total solar contribution to the 20th century global warming, of ΔT_solar = 0.27 ± 0.07 °C, is much larger than can be expected from variation in the total solar irradiance alone. However, we also find that the largest contribution to the 20th century warming comes from anthropogenic sources, with ΔT_man = 0.42 ± 0.11 °C.     

Studies of electron and ion temperatures at 500 km altitude during sunrise using Indian SROSS C2 satellite

Solar dependence of electron and ion temperatures (T_e and T_i) in the ionosphere is studied using RPA data onboard SROSS C2 at an altitude of ∼500 km and 77°E longitude during early morning hours (04:00–07:00 LT) for three solar activities: solar minimum, moderate and maximum during winter, summer and equinox months in 10°S–20°N geomagnetic latitude. In winter the morning overshoot phenomenon is observed around 06:00 LT (T_e enhances to ∼4000 K) during low-solar activity and to T_e ∼ 3800 K, during higher solar activity. In summer, it is observed around 05:30 LT, but the rate of T_e enhancement is higher during moderate solar activity (∼2700 K/hr) than the low-solar activity (∼1700 K/hr). During equinox, this phenomenon is delayed and is observed around 06:00 LT (∼4200 K) during all three activities.     

The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery

The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities.     

Semi-stochastic modification of second-order radial derivative of Abel–Poisson’s formula for validating satellite gravity gradiometry data

The geoid can be used to validate the satellite gravity gradiometry data. Validation of such data is important prior to their downward continuation because of amplification of the data errors through this process. In this paper, the second-order radial derivative of Abel–Poisson’s formula is modified stochastically to reduce the effect of the far-zone geoid and generate the second-order radial derivative of geopotential at 250 km level. The numerical studies over Fennoscandia show that this method yields the gradients with an error of 10 mE and when the long wavelength of geoid is removed from the estimator and restored after the computations (remove–compute–restore) the error will be in 1 mE level. We name this method semi-stochastic modification. The best case scenario is found when the degree of modification of the integral formula is 200 and the long wavelength geoid to degree 100 is removed and restored. In this case the geoid should have a resolution of 15′ × 15′ and the integration should be performed over a cap size of 3°.     

Occurrence of sporadic-E layer over the ionospheric station of Rome: Analysis of data for thirty-two years

Hourly systematic measurements of the highest frequency reflected by the sporadic-E layer (foEs) recorded at the Rome ionospheric observatory (Italy, 41.8° N, 12.5° E), were considered during the period January 1976–December 2007, to calculate the percentage of occurrence of sporadic-E layer with frequencies foEs greater than a given threshold value f_T, P(foEs > f_T).     

Variation of ionospheric total electron content in Taiwan region of the equatorial anomaly from 1994 to 2003

The ionospheric total electron content (TEC) in the northern hemispheric equatorial ionospheric anomaly (EIA) region is studied by analyzing dual-frequency signals of the Global Position System (GPS) acquired from a chain of nine observational sites clustered around Taiwan (21.9–26.2°N, 118.4–112.6°E). In this study, we present results from a statistical study of seasonal and geomagnetic effects on the EIA during solar cycle 23: 1994–2003. It is found that TEC at equatorial anomaly crests yield their maximum values during the vernal and autumnal months and their minimum values during the summer (except 1998). Using monthly averaged I_c (magnitude of TEC at the northern anomaly crest), semi-annual variations is seen clearly with two maxima occurring in both spring and autumn. In addition, I_c is found to be greater in winter than in summer. Statistically monthly values of I_c were poorly correlated with the monthly Dst index (r = −0.22) but were well correlated with the solar emission F_10.7 index (r = 0.87) for the entire database for the period during 1994–2003. In contrast, monthly values of I_c were correlated better with Dst (r ? 0.72) than with F_10.7 (r ? 0.56) in every year during the low solar activity period (1994–1997). It suggests that the effect of solar activity on I_c is a longer term (years), whereas the effect of geomagnetic activity on I_c is a shorter term (months).     

Quantifying the relationship between the measurement precision and specifications of a UV/visible sensor on a geostationary satellite

To investigate the feasibility of new satellite observations, including air quality (AQ) observations from geostationary (GEO) orbit, it is essential to link the measurement precision (ε) with sensor specifications in advance. The present study attempts to formulate the linkage between ε and specifications of a UV/visible sensor (signal-to-noise ratio (SNR), full width at half maximum (FWHM) of the slit function, and sampling ratio (SR)) on a GEO satellite. A sophisticated radiative transfer model (JACOSPAR) is used to calculate synthetic radiance spectra that would be measured by a UV/visible sensor observing the atmosphere over Tokyo (35.7°N, 139.7°E) from GEO orbit at 120°E longitude. The spectra, modified according to given sensor specifications, are analyzed by the differential optical absorption spectroscopy technique to estimate the ε for slant column densities of O₃ and NO₂. We find clear relationships: for example, the ε of the O₃ slant column density (molecules cm⁻²) and SNR at 330 nm are linked by the equation log(ε) = −1.06 · log(SNR) + 20.71 in the UV region, and the ε of the NO₂ slant column density and SNR at 450 nm are linked by log(ε) = −0.98 · log(SNR) + 18.00, at a FWHM = 0.6 nm (for the Gaussian slit function) and SR = 4. The relationships are mostly independent of other specifications (e.g., horizontal and temporal resolutions), as they affect ε primarily through SNR, providing constraints in determining the optimal SNR (and alternatively FWHM and SR) for similar UV/visible sensors dedicated for AQ studies.     

One dimensional blood flow in a planetocentric orbit

All life on earth is accustomed to the presence of gravity. When gravity is altered, biological processes can go awry. It is of great importance to ensure safety during a spaceflight. Long term exposure to microgravity can trigger detrimental physiological responses in the human body. Fluid redistribution coupled with fluid loss is one of the effects. In particular, in microgravity blood volume is shifted towards the thorax and head. Sympathetic nervous system-induced vasoconstriction is needed to maintain arterial pressure, while venoconstriction limits venous pooling of blood prevents further reductions in venous return of blood to the heart. In this paper, we modify an existing one dimensional blood flow model with the inclusion of the hydrostatic pressure gradient that further depends on the gravitational field modified by the oblateness and rotation of the Earth. We find that the velocity of the blood flow V_B is inversely proportional to the blood specific volume d, also proportional to the oblateness harmonic coefficient J₂, the angular velocity of the Earth ω_E, and finally proportional to an arbitrary constant c. For c = −0.39073 and ξ_H = −0.5 mmHg, all orbits result to less blood flow velocities than that calculated on the surface of the Earth. From all considered orbits, elliptical polar orbit of eccentricity e = 0.2 exhibit the largest flow velocity V_B = 1.031 m/s, followed by the orbits of inclination i = 45°and 0°. The Earth’s oblateness and its rotation contribute a 0.7% difference to the blood flow velocity.     

Variability of the ionosphere over Irkutsk at low solar activity

Statistical and spectral analyses are performed to investigate variations of two ionosphere F2 layer key parameters, the critical frequency (foF2) and the peak height (hmF2), that were measured over Irkutsk (52.5°N, 104.0°E) from December 2006 to January 2008 under solar minimum. The analyses showed that both parameters contain quasi-harmonic oscillations with periods of T_n = 24/n hours (n = 1–7), among which the diurnal (n = 1) and semidiurnal (n = 2) ones are the strongest. Seasonal variations are explored of mean and median values, spectrum, amplitude, and phase of the diurnal and semidiurnal components of foF2 and hmF2.     

Use of principal component analysis in the identification of the spatial pattern of an ionospheric total electron content anomalies after China’s May 12, 2008, M = 7.9 Wenchuan earthquake

This paper uses principal component analysis (PCA) to determine the spatial pattern of total electron content (TEC) anomalies in the ionosphere post the China’s Wenchuan Earthquake of 12 May, 2008 (UTC) (M_w = 7.9). PCA and image processing are applied to the global ionospheric map (GIM) with transforms conducted for the time period 08:00–10:00 UT on 12 May 2008. Results show that at a height of approximately 200 km the anomaly is widespread and less intense; however, it becomes more localized with height reaching maximum intensity and localization at an altitude of 300 km. The spatial distribution is remarkably similar to that reported for a TEC anomaly previously identified as a precursor anomaly on May 9, 2008 for the same time period. Potential causes of the results are discussed with emphasis given to vertical acoustic gravity waves based on the spatial pattern identified.     

Equatorial Ionospheric Anomaly (EIA) and comparison with IRI model during descending phase of solar activity (2005–2009)

The ionospheric variability at equatorial and low latitude region is known to be extreme as compared to mid latitude region. In this study the ionospheric total electron content (TEC), is derived by analyzing dual frequency Global Positioning System (GPS) data recorded at two stations separated by 325 km near the Indian equatorial anomaly region, Varanasi (Geog latitude 25°, 16^/ N, longitude 82°, 59^/ E, Geomagnetic latitude 16°, 08^/ N) and Kanpur (Geog latitude 26°, 18^/ N, longitude 80°, 12^/ E, Geomagnetic latitude 17°, 18^/ N). Specifically, we studied monthly, seasonal and annual variations as well as solar and geomagnetic effects on the equatorial ionospheric anomaly (EIA) during the descending phase of solar activity from 2005 to 2009. It is found that the maximum TEC (EIA) near equatorial anomaly crest yield their maximum values during the equinox months and their minimum values during the summer. Using monthly averaged peak magnitude of TEC, a clear semi-annual variation is seen with two maxima occurring in both spring and autumn. Results also showed the presence of winter anomaly or seasonal anomaly in the EIA crest throughout the period 2005–2009 only except during the deep solar minimum year 2007–2008. The correlation analysis indicate that the variation of EIA crest is more affected by solar activity compared to geomagnetic activity with maximum dependence on the solar EUV flux, which is attributed to direct link of EUV flux on the formation of ionosphere and main agent of the ionization. The statistical mean occurrence of EIA crest in TEC during the year from 2005 to 2009 is found to around 12:54 LT hour and at 21.12° N geographic latitude. The crest of EIA shifts towards lower latitudes and the rate of shift of the crest latitude during this period is found to be 0.87° N/per year. The comparison between IRI models with observation during this period has been made and comparison is poor with increasing solar activity with maximum difference during the year 2005.     

Response of the ionospheric F-region in the Brazilian sector during the super geomagnetic storm in April 2000 observed by GPS

The response of the ionospheric F-region in the equatorial and low latitude regions in the Brazilian sector during the super geomagnetic storm on 06–07 April 2000 has been studied in the present investigation. The geomagnetic storm reached a minimum D_st of −288 nT at 0100 UT on 07 April. In this paper, we present vertical total electron content (VTEC) and phase fluctuations (in TECU/min) from GPS observations obtained at Imperatriz (5.5°S, 47.5°W; IMPZ), Brasília (15.9°S, 47.9°W; BRAZ), Presidente Prudente (22.12°S, 51.4°W; UEPP), and Porto Alegre (30.1°S, 51.1°W; POAL) during the period 05–08 April. Also, several GPS-based TEC maps are presented from the global GPS network, showing widespread and drastic TEC changes during the different phases of the geomagnetic storm. In addition, ion density measurements on-board the satellite Defense Meteorological Satellite Program (DMSP) F15 orbiting at an altitude of 840 km and the first Republic of China satellite (ROCSAT-1) orbiting at an altitude of 600 km are presented. The observations indicate that one of the orbits of the DMSP satellite is fairly close to the 4 GPS stations and both the DMSP F15 ion-density plots and the phase fluctuations from GPS observations show no ionospheric irregularities in the Brazilian sector before 2358 UT on the night of 06–07 April 2000. During the fast decrease of D_st on 06 April, there is a prompt penetration of electric field of magnetospheric origin resulting in decrease of VTEC at IMPZ, an equatorial station and large increase in VTEC at POAL, a low latitude station. This resulted in strong phase fluctuations on the night of 06–07 April, up to POAL. During the daytime on 07 April during the recovery phase, the VTEC observations show positive ionospheric storm at all the GPS stations, from IMPZ to POAL, and the effect increasing from IMPZ to POAL. This is possibly linked to the equatorward directed meridional wind. During the daytime on 08 April (the recovery phase continues), the VTEC observations show very small negative ionospheric storm at IMPZ but the positive ionospheric storm effect is observed from BRAZ to POAL possibly linked to enhancement of the equatorial ionospheric anomaly.     

The LAGEOS satellites orbit and Yukawa-like interactions

LAGEOS II general relativity pericenter precession has been analysed in terms of the errors produced by the mismodelling of both the gravitational and non-gravitational perturbations acting on the satellite orbit. The accuracy in the pericenter determination may be considered as an upper-bound value for the estimate of the strength α of a possible new-long-range-interaction described by a Yukawa-like potential. In the present work we have focused on the constraints in α that can be obtained with the current best multi-satellites gravity field model EGM96 (α < 2.6 × 10⁻¹⁰) and also with the first promising models from the CHAMP (α < 1.8 × 10⁻¹⁰) and GRACE (α < 1.2 × 10⁻¹⁰) gravimetric missions. These results represent, potentially, an improvement of two or three orders-of-magnitude with respect to the best constraints obtained in the past with Earth–LAGEOS and Lunar–LAGEOS data (|α| < 10⁻⁵–10⁻⁸). The impact of the non-gravitational perturbations mismodelling in the final error budget has been determined together with the improvements obtainable in the constraint of the strength α with the proposed LARES satellite.     

Comparing IRI and a regional model with ionosonde measurements in Pakistan

We have used the technique of expansion in Empirical Orthogonal Functions (EOFs) to develop regional models of the critical frequencies of E and F₂ layers (f_oE, f_oF₂), peak height (h_mF₂), and semi-thickness of F₂ layer (Y_mF₂) over Pakistan. In the present study levels of solar activity specified by Smoothed Sunspot Number (R) from 10 to 200 are taken into account. The magnetic dip angle for the model ranges from 30° to 60°. We have compared the regional model and the International Reference Ionosphere (IRI) with measurements of three ionosondes in Pakistan. The model parameters f_oE and f_oF₂ are found overall comparable to the observed hourly median values during daytime at Karachi (geographic latitude = 24.95°N, longitude = 67.13°E, magnetic inclination = 37°), Multan (30.18°N, 71.48°E, 45°) and Islamabad (33.75°N, 73.13°E, 51.5°) during the years 1988, 1996 and 2000. For h_mF₂ the computed values by regional and IRI model for the year 1995 are found close to each other. However, for Y_mF₂the results are better during daytime as compared to nighttime.     

Coordinated in situ measurements of plasma irregularities and ground based scintillation observations at the crest of equatorial anomaly

First comparison of in situ density fluctuations measured by the DEMETER satellite with ground based GPS receiver measurements at the equatorial anomaly station Bhopal (geographic coordinates (23.2°N, 77.6°E); geomagnetic coordinates (14.29°N, 151.12°E)) for the low solar activity year 2005, are presented in this paper. Calculation of the diurnal maximum of the strength of the equatorial electrojet, which can serve as precursor to ionospheric scintillations in the anomaly region is also done. The Langmuir Probe experiment and Plasma Analyzer onboard DEMETER measure the electron and ion densities respectively. Irregularities in electron density distribution cause scintillations on transionospheric links and there exists a close relationship between an irregularity and scintillation. In 40% of the cases, DEMETER detects the irregularity structures (dNe/Ne ? 5% and dNi/Ni (O⁺) ? 5%) and GPS L band scintillations (S4 ? 0.2) are also observed around the same time, for the low solar activity period. It is found that maximum irregularity intensity is obtained in the geomagnetic latitude range of 10–20° for both electron density and ion density. As the GPS signals pass through this irregularity structure, scintillations are recorded by the GPS receiver installed at the equatorial anomaly station, Bhopal it is interesting to note that in situ density fluctuations observed on magnetic flux tubes that pass over Bhopal can be used as indicator of ionospheric scintillations at that site. Many cases of density fluctuations and associated scintillations have been observed during the descending low solar activity period. The percentage occurrence of density irregularities and scintillations shows good correspondence with diurnal maximum of the strength of electrojet, however this varies with different seasons with maximum correspondence in summer (up to 66%) followed by equinox (up to 50%) and winter (up to 46%). Also, there is a threshold value of EEJ strength to produce density irregularities ((dNe/Ne)_max ? 5%) and for moderate to strong scintillations (S4 ? 0.3) to occur. For winter this value is found to be ∼40 nT whereas for equinox and summer it is around 50 nT.     

Intracellular molecular distributions in spacecraft experiments in orbit around Earth

It is possible that the nucleolous inside the cell plays the role of a “gravity receptor”. Furthermore, cells up to 10 μm in diameter can demonstrate some effect due to the redistribution of mitochondria or nucleolous. Effects of gravity should be present in various cell systems where larger objects such as the ribosomes move from cell to cell. In this paper we study the effects of gravity on cells. In particular, we examine the resulting intracellular molecular distribution due to Brownian motion and the ordered distribution of molecules under the action of gravity, where n₀ is the number per unit volume at certain level, and n is the number per unit volume above that level. This is an experiment that takes place at a certain orbital altitude in a spacecraft in orbit around Earth, where the acceleration due to the central field is corrected for the oblateness and also the rotation of the Earth. We found that equatorial circular and elliptical orbits have the highest n/n₀ ratios. This experiment takes place in circular and elliptical orbits, with eccentricities e = 0, 0.1 and involves a bacterial cell at an orbital altitude of 300 km. We found that n/n₀ = 1.00299 and 1.0037 respectively, which is still a 0.6–0.7 % higher than n/n₀ = 0.0996685 calculated on the surface of the Earth. Examining mitochondria in similar orbital experiments we found that equatorial orbits result to higher n/n₀ ratios. In particular, we found that n/n₀ = 8.38119, where an elliptical orbit of eccentricity e = 0.1 results to n/n₀ = 13.8525. Both are high above 100%, signifying the importance of Brownian motion over gravity. Our results are of interest to biomedical applications. Molecular concentrations are important for various processes such as the embryogenesis, positional homeostasis and its relation to cell energy expenditure, cell torque, cell deformation, and more. These results indicate that statistical molecular distributions play an important role for the recognition of a particular environment by the cell, in biological space experiment to come.     

Contribution of satellite laser ranging to combined gravity field models

In the framework of satellite-only gravity field modeling, satellite laser ranging (SLR) data is typically exploited to recover long-wavelength features. This contribution provides a detailed discussion of the SLR component of GOCO02S, the latest release of combined models within the GOCO series. Over a period of five years (January 2006 to December 2010), observations to LAGEOS-1, LAGEOS-2, Ajisai, Stella, and Starlette were analyzed. We conducted a series of closed-loop simulations and found that estimating monthly sets of spherical harmonic coefficients beyond degree five leads to exceedingly ill-posed normal equation systems. Therefore, we adopted degree five as the spectral resolution for real data analysis. We compared our monthly coefficient estimates of degree two with SLR and Gravity Recovery and Climate Experiment (GRACE) time series provided by the Center for Space Research (CSR) at Austin, Texas. Significant deviations in C₂₀ were noted between SLR and GRACE; the agreement is better for the non-zonal coefficients. Fitting sinusoids together with a linear trend to our C₂₀ time series yielded a rate of (−1.75 ± 0.6) × 10⁻¹¹/yr; this drift is equivalent to a geoid change from pole to equator of 0.35 ± 0.12 mm/yr or an apparent Greenland mass loss of 178.5 ± 61.2 km³/yr. The mean of all monthly solutions, averaged over the five-year period, served as input for the satellite-only model GOCO02S. The contribution of SLR to the combined gravity field model is highest for C₂₀, and hence is essential for the determination of the Earth’s oblateness.