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An accurate estimation of the Thermospheric Neutral Density (TND) is important for predicting the orbit of satellites and objects, for example, those with the altitude of less than 1000 km. Models are often used to simulate TNDs but their accuracy is limited due to uncertainties. Satellite missions such as CHAMP, GRACE, GOCE, Swarm, and GRACE-FO or the Satellite Laser Ranging (SLR) missions can be used to estimate along-track TNDs. However, spatial and temporal coverage of these space borne TNDs is restricted to the mission design. To make the best use of the modelling tools and measurements, we applied these along-track TND measurements within the sequential Calibration and Data Assimilation (C/DA) framework proposed by (Forootan et al., 2022, doi:10.1038/s41598-022-05952-y). The C/DA is used to re-calibrate the NRLMSISE00 model, which is called “C/DA-NRLMSISE00”, whose outputs fit well to the introduced space-borne TNDs. The C/DA-NRLMSISE00 is applicable for forecasting TNDs and individual neutral mass compositions at any predefined vertical level (between ~100 and ~600 km) with user-defined spatial-temporal sampling. Seven periods (between 2003 - 2020) with considerable geomagnetic activity are selected for our investigations because most of the available models lack accuracy to provide reasonable TND simulations. Independent comparisons are performed with the space-borne TNDs that were not used within the C/DA framework, as well as with the outputs of other thermospheric models such as Jacchia-Bowman 2008 (JB2008) and the High Accuracy Satellite Drag Model (HASDM) database. The numerical results indicate that indeed the new model is suitable for producing multi-level global thermospheric neutral density fields.

An accurate estimation of ionospheric variables such as the total electron content (TEC) is important for many space weather, communication, and satellite geodetic applications. Empirical and physics-based models are often used to determine TEC in these applications. However, it is known that these models cannot reproduce all ionospheric variability due to various reasons such as their simplified model structure, coarse sampling of their inputs, and dependencies to the calibration period. Bayesian-based data assimilation (DA) techniques are often used for improving these model’s performance, but their computational cost is considerably large. In this study, first, we review the available DA techniques for upper atmosphere data assimilation. Then, we will present an empirical decomposition-based data assimilation (DDA), based on the principal component analysis and the ensemble Kalman filter. DDA considerably reduces the computational complexity of previous DA implementations. Its performance is demonstrated by updating the empirical orthogonal functions of the empirical NeQuick and the physics-based TIEGCM models using the rapid global ionosphere map (GIM) TEC products as observation. The new models, respectively, called ‘DDA-NeQuick’ and ‘DDA-TIEGCM,’ are then used to predict TEC values for the next day. Comparisons of the TEC forecasts with the final GIM TEC products (that are available after 11 days) represent an average 42.46% and 31.89% root mean squared error (RMSE) reduction during our test period, September 2017.

The upper part of the Earth’s atmosphere is important for the ground-based and satellite radio communications and navigation. It consists of free electrons and ions, mainly ionized by solar radiation. The free electrons in the ionosphere strongly impact the propagation of radio waves. Therefore, modelling and predicting ionosphere are important for many space weather and geodetic applications. In this study, we apply geometry-free multi-GNSS approach enabling the simultaneous retrieval of vertical total electron content (VTEC). Unlike previous studies, multiple frequency GNSS receivers of smartphones and more accurate geodetic receivers are used to understand how various code/phase observations could be combined. The smartphone observations are typically less precise and affected by multipath and they contain frequent cycle slips. Various combinations of the ionospheric observations, using both code and phase measurements, are tested to understand how to mitigate the challenges and to account for the measurements’ quality. Finally, the advantages and disadvantages of these combinations are explained. Keywords: Smartphone, Vertical Total Electron Content, Multi-frequency GNSS

Exploiting the reflected signals from the surface of the Earth to provide information about the reflecting surface is the primary concept of GNSS Interferometric Reflectometry (GNSS-IR). One of the most common usages of GNSS-IR is the estimation of the absolute vertical distance from a GNSS antenna to the reflective surface. In this work, the authors present a developed MATLAB-based GNSS software, namely, GNSS-IR-UT that translates the various signal from different systems such as GPS (L1, L2 and L5), GLONASS (G1, G2 and G3), Galileo (E1, E5a, E5b, E5 and E6), and BeiDou (B1, B2 and B3), more precisely the signal-to-noise ratio (SNR) data, into the reflection height. This user-friendly software permits users to evaluate a variety of processing options and parameters in height calculation by taking advantage of the Graphic User Interface (GUI) of MATLAB. In this software, to extract the dominant frequency in reflectometry concept, the Least Square Harmonic Estimation (LS-HE) has been used for the first time. Moreover, besides the reflectometry applications, the users can use some parts of this software in working with GNSS data for their specific usage. All in all, we aimed at providing a new, easy to use, and powerful software to the scientific community to make it easy for new users of the GNSS-IR concept.

Today, satellite altimetry is capable of observing the instantaneous sea level and is regarded as a standard tool in the study of waters level variations on both regional and global scales. In this research, we have introduced a software package under MATLAB called ATSAT, which is used to process the satellite altimetry data. ATSAT is able to process the observations of five satellites, namely Jason-1, Jason-2, Jason-3, Saral and Sentinel-3. This software program has certain capabilities: 1) Reading the observations related to the five satellites in the NetCDF format 2) Producing the time series obtained from the observations of each satellite at any desired point 3) Analyzing the outlier detection in the time series 4) Estimating the weight matrix pertinent to each time series using the Least Square Variance Components Estimation (LS-VCE) method 5) Considering the two noise models of White and White + Flicker for the variance components estimation and formation of the weight matrix for each time series 6) Estimating the average water level, as well as the amplitude of 22 main tide components at any desired point 7) Extracting the available frequencies in each time series using the Least Square Harmonic Estimation (LS-HE) method in the two modes of univariate and multivariate, and finally 8) Calculating the radial orbital error using the crossover adjustment.

Atmospheric drag has a direct relationship with the thermospheric neutral density (TND) and represents a considerable impact on the precise orbit determination (POD) and prediction of low Earth orbit (LEO) satellites, for example those with the altitude of less than 1000 km, as well as space debris. The distribution of TND combined with the solar and geomagnetic activity has a direct impact on the electron distribution in the ionosphere. The latter is important for medium- and long-range high frequency communication, positioning, and over-the-horizon radar systems. New capabilities to understand, model and predict thermosphere variables are typically provided by models; however, the quality of them is limited due to their imperfect structure and uncertainty of their inputs. In this study, we present various data assimilation frameworks to take advantage of freely available accelerometer derived TNDs from GRACE, GRACE-FO and Swarm missions. This is realized by (1) formulating ensemble Kalman filter (EnKF)-based calibration and data assimilation (C/DA) procedures to update the model's states (and simultaneously calibrates its key parameters if needed); and (2) an empirical decomposition-based data assimilation is applied to merge satellite derived along-track estimates with global model derived TND simulations. The results of these two frameworks are then evaluated against independent measurements. The technical challenges and benefits are discussed in detail.

An accurate simulation global thermospheric neutral density (TND) on various altitudes is important for geodetic and space weather applications. In addition, this is essential for designing the low-Earth-orbit (LEO) missions, predict their missions’ lifetime and performing a reliable attitude control. Although empirical and physics-based models typically simulate TND variations, the quality of these models is limited due to various structural simplifications and the uncertainty of inputs. Here, we present an ensemble Kalman filter (EnKF)-based calibration and data assimilation (C/DA) technique that updates the model's states and simultaneously calibrates its key parameters. The proposed approach provides the opportunity to improve the now-cast and forecast skills of the NRLMISISE-00 and NRMSIS-2.0 models through re-calibrating the model’s key parameters including those controlling the influence of solar radiation and geomagnetic activity as well as those related to the calculation of exospheric temperature.In this research, TND estimates from on-board accelerometer measurements of GRACE, GRACE-FO and Swarm are ingested as observations into the NRLMSISE-00 and NRLMSIS-2.0 models based on the C/DA. The newly calibrated model, called here ‘C/DA-NRLMSISE’, is then used to simulate global maps of TND as well as individual neutral mass densities covering the altitudes of 300-600 km. Various investigations are performed to test the temporal and vertical consistency of the TND outputs from C/DA-NRLMSISE.

The GNSS tomography provides the opportunity to estimate atmospheric wet refractivity, which is important for precise positioning and navigation, as well as for constraining weather and climate models. The GNSS-derived water vapor is often estimated by implementing voxel-based inversions, but this technique is numerically unstable due to the high number of unknown parameters especially in networks covering large areas or when the spatial resolution increases. To mitigate this problem, in this study, we introduce functional based 3 and 4 dimensional (3D and 4D) inversion formulations. Here, the horizontal changes are modelled by the spherical cap harmonic functions. For the vertical component, empirical orthogonal functions derived from ERA5 (Empirical Reanalysis Fifth generation) are applied as background model. The time-dependency is accounted for by applying polynomial spline functions. Numerical results are based on a network of about 190 GPS stations in Germany during 15 days in summer and winter of 2018. Observations from 8 radiosonde stations are applied for comparisons. Our results indicate that the functional tomography is effective and retrieves wet refractivity indices with the mean RMSE (Root Mean Square Error) of about 1.9 ppm. These values are found to be up to 22% smaller than those derived by comparing ERA5 with the radiosonde data.

Drought is one of the most common natural phenomena. Many indices using multiple data types have been created, and their success at recognizing periods of extreme wetness and dryness has been well documented. The merit of the method is the utilization of terrestrial water storage (TWS) variations from Gravity Recovery and Climate Experiment (GRACE) quantification of drought intensity. Alongside with these observations, we add precipitation data to equations. In this study, we analyze Merged-dataset Drought index (MDI) using GRACE-derived TWSA and precipitation in Iran, where most of the area is desert and mountain in the middle and South of the country. Our sample period is from January 2003 to December 2014. MDI shows a strong correlation with existing drought indices, especially with the Palmer Drought Severity Index (PDSI). Based on the obtained results, MDI indicates a moderate Drought event in 2008 and 2012–2015, which is compatible with the recorded result of PDSI. The longest drought took 22 months (from January 2008 to October 2009). Interestingly, the coefficient of correlation between MDI and PDSI is 0.67.

Using a coastal Global Navigation Satellite System (GNSS) station, one can measure sea surface height (SSH) using GNSS Interferometric Reflectometry (GNSS-IR) technique as it gives vertical distance between the antenna and the reflective surface in a height reference frame. In this study, Signal-to-Noise Ratio (SNR) data of a GPS station located in Honolulu, Hawaii, were observed over a one-month period to estimate the amplitude of the dominant tidal constituents. SSH values acquired from GNSS-IR are then compared to traditional tidal observations obtained from a nearby tide-gauge station. Obtaining a Root Mean Square Error (RMSE) of 11.5 cm and a correlation of 0.87 between SSH values obtained from GNSS-IR and tide-gauge, we estimated the amplitudes of dominant tidal constituents (M2, S2, K1, P1, 01) with maximum and minimum amplitude differences of 2.38 and 0.28 cm, respectively. Next, a set of control points around the GNSS station were chosen and the FES2012 global tide model was used to calculate the amplitudes of those constituents one more time. The maximum and minimum differences in amplitude obtained from the tide-gauge station and the FES2012 model were 3.65 and 0.31 cm, respectively. This study suggests that the GNSS-IR technique can be used as a tool for estimating tidal constituents over a short period of time in the order of one month.

The development of space-geodetic observation techniques has brought out a wide range of applications such as positioning and navigation, where the Global Navigation Satellite System (GNSS) is the main tools to provide surveying measurements in these applications. Though GNSS signals enable the calculation of receiver's position, some errors restrict their accuracy. Among these errors, the ionospheric delay is considered as an important error source in the Standard Point Positioning (SPP) applications. Empirical ionospheric models such as Klobuchar, International Reference Ionosphere (IRI), and NeQuick are often applied for computing the Total Electron Content (TEC) within ionosphere and its equivalent delays. However the simulation and forecasting skills of these models are limited due to the simplified model structures and model sensitivity to the calibration period. In this study, we present a novel sequential Calibration approach based on the Ensemble Kalman Filter (C-EnKF) to improve the performance of TEC estimations for SPP applications. To demonstrate the results, the IRI model is used as our basis and the TEC estimates from 56 IGS stations in Europe are applied as observation. The C-EnKF is applied to calibrate some selected model parameter so that IRI can be tuned over Europe. The numerical assessments are performed against the TEC estimates from dual frequency GNSS measurements and against the final IONEX products (that are available with 11 days delays). Based on the forecasting results (during September 2017), we show that the accuracy of TEC estimates from the C-EnKF is improved in the range of 3.7-64.87% compared to IRI. Keywords: Ionosphere, Sequential Calibration, Ensemble Kalman Filter (EnKF), IRI, Total Electron Content (TEC), Standard Point Positioning (SPP), GNSS

Global ionosphere maps (GIM) are generated on daily basis at the Center for Orbit Determination in Europe (CODE) using data from about 200 GNSS sites of the International GNSS Service (IGS) and other institutions. These measurement are used to numerically model the vertical total electron content (VTEC) in a solar-geomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. In this study, an efficient method is developed and applied to densify the GIM model in a region of interest using the TEC measurements of local networks. Our approach follows a Bayesian updating scheme, where the GIM data are utilized as a prior information in the form of Slepian-coefficients in the region of interest. These coefficients are then updated by the GNSS measurements in a Bayesian framework that considers both the uncertainty of a priori information and the new measurements. Numerical application is demonstrated using a GNSS network in South America. Our results indicate that by using 62 GNSS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the Bayesian-derived VTEC estimates in a Standard Point Positioning (SPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were found to be ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.Key words: Bayesian densification, Slepian Functions, Spherical Harmonics, Ionospheric modelling, VTEC, SPPs

SUMMARY Improving thermospheric neutral density (TND) estimates is important for computing drag forces acting on low-Earth-orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs for the precise orbit determination experiments. However, it is known that simulating TNDs are of limited accuracy due to simplification of model structure, coarse sampling of model inputs and dependencies to the calibration period. Here, we apply TND estimates from accelerometer measurements of the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE) missions as observations to improve the NRLMSISE-00 model, which belongs to the mass spectrometer and incoherent scatter family of models. For this, a novel simultaneous calibration and data assimilation (C/DA) technique is implemented that uses the ensemble Kalman filter and the ensemble square-root Kalman filter as merger. The application of C/DA is unique because it modifies both model-derived TNDs, as well as the selected model parameters. The calibrated parameters derived from C/DA are then used to predict TNDs in locations that are not covered by CHAMP and GRACE orbits, and forecasting TNDs of the next day. The C/DA is implemented using daily CHAMP- and/or GRACE-TNDs, for which compared to the original model, we find 27 per cent and 62 per cent reduction of misfit between model and observations in terms of root mean square error and Nash coefficient, respectively. These validations are performed using the observations along the orbital track of the other satellite that is not used in the C/DA during 2003 with various solar activity. Comparisons with another empirical model, that is, Jacchia-Bowman, indicate that the C/DA results improve these quality measurements on an average range of 50 per cent and 60 per cent, respectively.

Several least-squares adjustment techniques were tested for dam deformation analysis. Deformation monitoring had only been studied horizontally. Simulated observations were first performed ...

In this study, we present a data processing framework to apply measurements of the Global Navigation Satellite System (GNSS) technique for analyzing and predicting the movements of civil structures such as bridges. The proposed approach reduces the noise level of GNSS measurements using the Kalman Filter (KF) approach and enables the estimation of static, semi-static, and dynamic components of the bridge’s movements using a series of analyses such as the temporal filtering and the Least Squares Harmonic Estimation (LS-HE). The numerical results indicate that by using a RTK-GNSS system the semi-static component is extracted with a Standard Deviation (STD) of 0.032, 0.048, and 0.06 m in the North, East, and Up (NEU) directions, while that of the dynamic component is 0.004, 0.003, and 0.01 m, respectively. Comparing the dominant frequencies of the bridge movements from LS-HE with those of the permanent stations provides information about the bridge’s stability. To predict its deflection, the Neural Network (NN) technique is tested to simulate the time-varying components, which are then compared with the safety limits, known by its design, to assess the structural health under usual load. In this study, we present a data processing framework to apply measurements of the Global Navigation Satellite System (GNSS) technique for analyzing and predicting the movements of civil structures such as bridges. The proposed approach reduces the noise level of GNSS measurements using the Kalman Filter (KF) approach and enables the estimation of static, semi-static, and dynamic components of the bridge’s movements using a series of analyses such as the temporal filtering and the Least Squares Harmonic Estimation (LS-HE). The numerical results indicate that by using a RTK-GNSS system the semi-static component is extracted with a Standard Deviation (STD) of 0.032, 0.048, and 0.06 m in the North, East, and Up (NEU) directions, while that of the dynamic component is 0.004, 0.003, and 0.01 m, respectively. Comparing the dominant frequencies of the bridge movements from LS-HE with those of the permanent stations provides information about the bridge’s stability. To predict its deflection, the Neural Network (NN) technique is tested to simulate the time-varying components, which are then compared with the safety limits, known by its design, to assess the structural health under usual load

A new approach is presented to improve the spatial and temporal resolution of the Vertical Total Electron Content (VTEC) estimates for regional positioning applications. The proposed technique utilises a priori information from the Global Ionosphere Maps (GIMs) of the Center for Orbit Determination in Europe (CODE), provided in terms of Spherical Harmonic (SH) coefficients of up to degree and order 15. Then, it updates the VTEC estimates using a new set of base-functions (with better resolution than SHs) while using the measurements of a regional GNSS network. To achieve the highest accuracy possible, our implementation is based on a transformation of the GIM/CODE VTECs to their equivalent coefficients in terms of (spherical) Slepian functions. These functions are band-limited and reflect the majority of signal energy inside an arbitrarily defined region, yet their orthogonal property is remained. Then, new dual-frequency GNSS measurements are introduced to a Least Squares (LS) updating step that modifies the Slepian VTEC coefficients within the region of interest. Numerical application of this study is demonstrated using a synthetic example and ground-based GPS data in South America. The results are also validated against the VTEC estimations derived from independent GPS stations (that are not used in the modelling), and the VTEC products of international centres. Our results indicate that, by using 62 GPS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the new VTEC estimates in a Precise Point Positioning (PPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were &sim, 23% and 25% for a day with moderate solar activity while 26% and &sim, 35% for a day with high solar activity, respectively.

Observing global terrestrial water storage changes (TWSCs) from (inter-)seasonal to (multi-)decade time-scales is very important to understand the Earth as a system under natural and anthropogenic climate change. The primary goal of the Gravity Recovery And Climate Experiment (GRACE) satellite mission (2002–2017) and its follow-on mission (GRACE-FO, 2018–onward) is to provide time-variable gravity fields, which can be converted to TWSCs with ∼ 300 km spatial resolution; however, the one year data gap between GRACE and GRACE-FO represents a critical discontinuity, which cannot be replaced by alternative data or model with the same quality. To fill this gap, we applied time-variable gravity fields (2013–onward) from the Swarm Earth explorer mission with low spatial resolution of ∼ 1500 km. A novel iterative reconstruction approach was formulated based on the independent component analysis (ICA) that combines the GRACE and Swarm fields. The reconstructed TWSC fields of 2003–2018 were compared with a commonly applied reconstruction technique and GRACE-FO TWSC fields, whose results indicate a considerable noise reduction and long-term consistency improvement of the iterative ICA reconstruction technique. They were applied to evaluate trends and seasonal mass changes (of 2003–2018) within the world’s 33 largest river basins.

Increasing the quality of ionosphere modeling is crucial and remains a challenge for many geodetic applications such as GNSS Precise Point Positioning (PPP) and navigation. Ionosphere models are the main tool to provide an estimation of Total Electron Content (TEC) to be corrected from GNSS career phase and pseudorange measurements. Skills of these models are however limited due to the simplifications in model equations and the imperfect knowledge of model parameters. In this study, an ionosphere reconstruction approach is presented, where global estimations of geodetic-based TEC measurements are combined with an ionospheric background model. This is achieved here through a novel simultaneous Calibration and Data Assimilation (C/DA) technique that works based on the sequential Ensemble Kalman Filter (EnKF). The C/DA method ingests the actual ionospheric measurements (derived from global GNSS measurements) into the IRI (International Reference Ionosphere) model. It also calibrates those parameters that control the F2 layer’s characteristics such as selected important CCIR (Comité Consultatif International des Radiocommunicationsand) URSI (International Union of Radio Science) coefficients. The calibrated parameters derived from the C/DA are then replaced in the IRI to simulate TEC values in locations, where less GNSS ground-station infrastructure exists, as well as to enhance the prediction of TEC when the observations are not available or their usage is cautious due to low quality. Our numerical assessments indicate the advantage of the C/DA to improve the IRI’s performance. Values of the TEC-Root Mean Square of Error (RMSE) are found to be decreased by up to 30% globally, compared to the original IRI simulations. The importance of the new TEC estimations is demonstrated for PPP applications, whose results show improvements in navigation applications.Keywords: Ionosphere, Calibration and Data Assimilation (C/DA), IRI, Total Electron Content (TEC), Precise Point Positioning (PPP), GNSS

The Global Ionosphere Maps (GIMs) are generated on a daily basis at the Center for Orbit Determination in Europe (CODE) using the observations from about 200 Global Positioning System (GPS)/GLONASS sites of the International GNSS Service (IGS) and other institutions. These maps contain Vertical Total Electron Content (VTEC) values, which are estimated in a solar-geomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. Although these maps have wide applications, their relatively low spatial resolution limits the accuracy of many geodetic applications such as those related to Precise Point Positioning (PPP) and navigation. In this study, a novel Bayesian approach is proposed to improve the spatial resolution of VTEC estimations in regional and global scales. The proposed technique utilises GIMs as a prior information and updates the VTEC estimates using a new set of base-functions (with better resolution than that of spherical harmonics) and the GNSS measurements that are not included in the network of GIMs. To achieve the highest accuracy possible, our implementation is based on a transformation of spherical harmonics to the Slepian base-functions, where the latter is a set of bandlimited functions that reflect the majority of signal energy inside an arbitrarily defined region, yet they remain orthogonal within this region. The new GNSS measurements are considered in a Bayesian update estimation to modify those of GIMs. Numerical application of this study is demonstrated using the ground-based GPS data over South America. The results are also validated against the VTEC estimations derived from independent GPS stations.Key words: Spherical Slepian Base-Functions, Spherical Harmonics, Ionospheric modelling, Vertical Total Electron Content (VTEC)

An accurate estimation of the Thermospheric Neutral Density (TND) is important to compute drag forces acting on Low-Earth-Orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs (along-track of LEO satellites) for the Precise Orbit Determination (POD) experiments. However, recent studies indicate that the TNDs of available models do not perfectly reproduce TNDs derived from accelerometer observations. In this study, we use TND estimates from the Challenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) missions and merge them with the NRLMSISE00 from the Mass Spectrometer and Incoherent Scatter family. The integration is implemented by applying a simultaneous Calibration and Data Assimilation (C/DA) technique. The application of C/DA is advantageous since it uses model equation to interpolate and extrapolate TNDs that are not covered by CHAMP and GRACE. It also modifies the model's selected parameters to simulate TNDs that are closer to those of CHAMP and GRACE. The C/DA of this study is implemented daily using CHAMP- and/or GRACE-TNDs, while using the Ensemble Kalman Filter (EnKF) and Ensemble Square-Root Kalman Filter (EnSRF) as merger. Compared to the original model, on average, we found 27% (in the range of 2% to 56%) improvements in the estimation of TNDs. In addition, the results of the C/DA are compared with the TND outputs of the JB2008 model along the CHAMP and GRACE orbits, whose results indicate that the daily C/DA outputs are 60% closer to the observed TNDs (that are not used for the C/DA). Overall, our assessment indicates that EnSRF results in more realistic TND simulation and prediction compared to those derived from EnKF. We show that the improved TND estimates of this study will be beneficial for Precise Orbit Determination (POD) studies. Keywords: Thermosphere, Calibration and Data Assimilation (C/DA), NRLMSISE00, Ensemble Kalman Filter (EnKF), Ensemble Square-Root Kalman Filter (EnSRF)

The computerized ionospheric tomography is a method for imaging the Earth’s ionosphere using a sounding technique and computing the slant total electron content (STEC) values from data of the global positioning system (GPS). The most common approach for ionospheric tomography is the voxel-based model, in which (1) the ionosphere is divided into voxels, (2) the STEC is then measured along (many) satellite signal paths, and finally (3) an inversion procedure is applied to reconstruct the electron density distribution of the ionosphere. In this study, a computationally efficient approach is introduced, which improves the inversion procedure of step 3. Our proposed method combines the empirical orthogonal function and the spherical Slepian base functions to describe the vertical and horizontal distribution of electron density, respectively. Thus, it can be applied on regional and global case studies. Numerical application is demonstrated using the ground-based GPS data over South America. Our results are validated against ionospheric tomography obtained from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) observations and the global ionosphere map estimated by international centers, as well as by comparison with STEC derived from independent GPS stations. Using the proposed approach, we find that while using 30 GPS measurements in South America, one can achieve comparable accuracy with those from COSMIC data within the reported accuracy (1 × 1011 el/cm3) of the product. Comparisons with real observations of two GPS stations indicate an absolute difference is less than 2 TECU (where 1 total electron content unit, TECU, is 1016 electrons/m2).

Radio occultation (RO) is one of the most novel satellite approaches that can be used to study ionospheric electron densities, by combining the observations of global navigation satellite systems and low earth orbiting (LEO) satellites to determine ionospheric electron density profiles with high vertical resolutions. This study aims at developing a multi-dimensional model of the electron density derived from ionospheric GPS RO measurements by the FORMOSAT-3/COSMIC satellites. In order to develop a 4D local model for the electron density, a Slepian function was used to account for longitudinal and latitudinal variations, the B-spline was utilized for time variations and the Chapman profile function was used to express the height variations of the electron density, in this way the parameters of the Chapman function, namely the maximum electron density of the F2 layer (NmF2) and the corresponding F2 peak height (hmF2) were modeled. The coefficients of the two sets of the Slepian functions were estimated using the least-squares adjustment technique. In order to validate the accuracy of the proposed technique, two approaches are considered: (1) The estimated F2-peak values were compared with the IRI model and ionosonde stations values, (2) Comparing the modeled electron density profile against the one estimated using RO methods.

global ionosphere maps are generated on a daily basis at CODE using data from about 200 GPS/GLONASS sites of the IGS and other institutions. The vertical total electron content is modeled in a solargeomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. The spherical Slepian basis is a set of bandlimited functions which have the majority of their energy concentrated by optimization inside an arbitrarily defined region, yet remain orthogonal within the spatial region of interest. Hence, they are suitable for decomposing the spherical harmonic models into the portions that have significant strength only in the selected areas. In this study, the converted spherical harmonics to the Slepian bases were updated by the terrestrial GPS observations by use of the least-squares estimation with weighted parameters for local ionospheric modeling. Validations show that the approach adopted in this study is highly capable of yielding reliable results.

We present a method for PPP adjustment based on Recursive Least Square Estimation (RLSE). This method estimates the stochastic model of GPS, GLONASS, Galileo and BeiDou observations by using RLS-Variance Components Estimation (RLS-VCE). The accuracy and the convergence time of horizontal, altitudinal and three-dimensional components is compared by using both nominal and RLS-VCE method so that the estimated accuracy for these coordinate components in suggested method is more accurate than nominal method. The accuracy of horizontal, altitudinal and three-dimensional components in this method are 1.3, 1.25 and 1.8 cm respectively in comparison to nominal method with 4, 3.8 and 5.6 cm. By considering 15 cm as the convergence condition, convergence time is estimated 3 and 5.3 min for suggested and nominal methods respectively. The obtained RMSE after convergence time in proposed and nominal methods are 7.1 and 9.2 cm respectively. According to the presented results, when Multi-GNSS observations are combined, the lowest RMSE are estimated for the coordinate components. As time passes, the stochastic model becomes more stable, therefore, the presented method will be more accurate.

Sea level usually undergoes constant changes. Some of which such as tidal changes have been recognized as a part of the sea nature which possess a particular significance. In the present study, modeling of tidal variations of sea level in Persian Gulf and Oman Sea is conducted using a 22-years dataset from TOPEX/Poseidon, Jason-1 and Jason-2 altimetry missions in a conjunction with coastal tide gauge data. To do so, a time series is determined for every point of a satellite in the sea, which means that, in 772 effect points of the satellite altimetry and 7 coastal stations over sea surface, several maps, including sea level map, Datum chart map, and codomain maps of tidal components M2, S2, K1, and O1, have been presented through noise analysis and observation synthesis. In this regard, first, the structure of the functional models is investigated to examine the noise feature of satellite altimetry observations, assuming that the observations contain colored noise. It is assumed that the models are affected by combination of the following noises: 1) white-flicker-random walk, 2) white-flicker- autoregressive, 3) white-random walk-autoregressive, 4) white-flicker-random walk- autoregressive, 5) white-flicker, 6) white-random walk, 7) flicker-random walk. Here, for statistical models of 1 to 4, the variances of autoregressive and random walk noises are estimated to be negative which reveals the inappropriateness of the random model for altimetry observations. For statistical models of 5 to 7, the variances of these three models are estimated to be positive which reveals the appropriateness of these models. Accordingly, the analysis of maximum likelihood function for these three models was investigated. Our results show that the highest value of similarity function belongs to the structure of the second model, which indicates that the existing noise in the time series of satellite altimetry observations would be a combination of white and flicker noises. By obtaining an appropriate functional model for satellite altimetry observations, we analyzed and investigated two important components of the, mean sea level and datum chart. This analysis has been considered in two conditions: 1) the weight matrix of observations is of a unit matrix type, i.e. the existing noise model in observations is white noise, and 2) the weight matrix of observations is obtained by a combination of white and flicker noise. Finally, the resultant difference between two components of the mean sea level and the chart datum is presented. The obtained results suggest that using a precise noise model for observations at the highest level can lead to an approximate difference of +25 cm and -20 cm, and an approximate difference of 8 cm on average in comparison with the condition that observations of unit weight are used.

In order to study in the field of the dynamics and continuous variations in the ionosphere, the ionospheric measurement tools such as ionosondes, incoherent scatter radars, satellites, and Global Positioning System (GPS) networks should be used. Total Electron Content (TEC) is a key parameter in the investigation and identification of ionosphere layer. From observations of dual frequency GPS receivers, the ionospheric TEC can be extracted. Global Ionospheric Maps (GIM) are auxiliary Maps for a study on ionosphere layer in around the world. It is necessary to produce the regional TEC map for precise studying of the ionospheric TEC. Bernese software is used to extract TEC by dual frequency GPS receivers. Regional modeling of ionospheric TEC by Artificial Neural Network (ANN) is a significant domain for prediction TEC at both single and double frequency GPS receivers. Five locations in Iran during the period of 2006-2010 were identified and used in the development of an input space and ANN architecture for the TEC modeling. The input space included the day number (seasonal variation), hour (diurnal variation), sunspot number (a measure of the solar activity) and magnetic index (a measure of magnetic activity). Based on the results, the ANN have capability and flexibility to model and to predict TEC. TEC predicted by ANN A (NN TEC) and TEC obtained from the IRI2007 version of the International Reference Ionosphere (IRI TEC) are compared during equinoxes and solstices. Results show that ANN predicts GPS TEC more accurately than the IRI over Iran. The IRI-2007 model is not a suitable method to produce TEC over IRAN.