Bayesian approach to ionospheric imaging with Gaussian Markov random field priors

Ionosfääri on noin 60–1000 kilometrin korkeudella sijaitseva ilmakehän kerros, jossa kaasuatomien ja -molekyylien elektroneja on päässyt irtoamaan auringon säteilyn ja auringosta peräisin olevien nopeiden hiukkasten vaikutuksesta. Näin syntyneillä ioneilla ja vapailla elektroneilla on sähkö- ja magneettikenttien kanssa vuorovaikuttava sähkövaraus. Ionosfäärillä on siksi merkittävä rooli radioliikenteessä. Se voi mahdollistaa horisontin yli tapahtuvat pitkät radiolähetykset heijastamalla lähetetyn sähkömagneettisen signaalin takaisin maata kohti. Toisaalta ionosfääri vaikuttaa myös sen läpäiseviin korkeampitaajuuksisiin signaaleihin. Esimerkiksi satelliittipaikannuksessa ionosfäärin vaikutus on parhaassakin tapauksessa otettava huomioon, mutta huonoimmassa se voi estää paikannuksen täysin. Näkyvin ja tunnetuin ionosfääriin liittyvä ilmiö lienee revontulet. Yksi keskeisistä suureista ionosfäärin tutkimuksessa on vapaiden elektronien määrä kuutiometrin tilavuudessa. Käytännössä elektronitiheyden mittaaminen on mahdollista mm. tutkilla, kuten Norjan, Suomen ja Ruotsin alueilla sijaitsevalla EISCAT-tutkajärjestelmällä, sekä raketti- tai satelliittimittauksilla. Mittaukset voivat olla hyvinkin tarkkoja, mutta tietoa saadaan ainoastaan tutkakeilan suunnassa tai mittalaitteen läheisyydestä. Näillä menetelmillä ionosfäärin tutkiminen laajemmalla alueella on siten vaikeaa ja kallista. Olemassa olevat paikannussatelliitit ja vastaanotinverkot mahdollistavat ionosfäärin elektronitiheyden mittaamisen alueellisessa, ja jopa globaalissa mittakaavassa, ensisijaisen käyttötarkoituksensa sivutuotteena. Satelliittimittausten ajallinen ja paikallinen kattavuus on hyvä, ja kaiken aikaa kasvava, mutta esimerkiksi tarkkoihin tutkamittauksiin verrattuna yksittäisten mittausten tuottama informaatio on huomattavasti vähäisempää. Tässä väitöstyössä kehitettiin tietokoneohjelmisto ionosfäärin elektronitiheyden kolmiulotteiseen kuvantamiseen. Menetelmä perustuu matemaattisten käänteisongelmien teoriaan ja muistuttaa lääketieteessä käytettyjä viipalekuvausmenetelmiä. Satelliittimittausten puutteellisesta informaatiosta johtuen työssä on keskitytty etenkin siihen, miten ratkaisun löytymistä voidaan auttaa tilastollisesti esitetyllä fysikaalisella ennakkotiedolla. Erityisesti työssä sovellettiin gaussisiin Markovin satunnaiskenttiin perustuvaa uutta korrelaatiopriori-menetelmää. Menetelmä vähentää merkittävästi tietokonelaskennassa käytettävän muistin tarvetta, mikä lyhentää laskenta-aikaa ja mahdollistaa korkeamman kuvantamisresoluution.Ionosphere is the partly ionised layer of Earth's atmosphere caused by solar radiation and particle precipitation. The ionisation can start from 60 km and extend up to 1000 km altitude. Often the interest in ionosphere is in the quantity and distribution of the free electrons. The electron density is related to the ionospheric refractive index and thus sufficiently high densities affect the electromagnetic waves propagating in the ionised medium. This is the reason for HF radio signals being able to reflect from the ionosphere allowing broadcast over the horizon, but also an error source in satellite positioning systems. The ionospheric electron density can be studied e.g. with specific radars and satellite in situ measurements. These instruments can provide very precise observations, however, typically only in the vicinity of the instrument. To make observations in regional and global scales, due to the volume of the domain and price of the aforementioned instruments, indirect satellite measurements and imaging methods are required. Mathematically ionospheric imaging suffers from two main complications. First, due to very sparse and limited measurement geometry between satellites and receivers, it is an ill-posed inverse problem. The measurements do not have enough information to reconstruct the electron density and thus additional information is required in some form. Second, to obtain sufficient resolution, the resulting numerical model can become computationally infeasible. In this thesis, the Bayesian statistical background for the ionospheric imaging is presented. The Bayesian approach provides a natural way to account for different sources of information with corresponding uncertainties and to update the estimated ionospheric state as new information becomes available. Most importantly, the Gaussian Markov Random Field (GMRF) priors are introduced for the application of ionospheric imaging. The GMRF approach makes the Bayesian approach computationally feasible by sparse prior precision matrices. The Bayesian method is indeed practicable and many of the widely used methods in ionospheric imaging revert back to the Bayesian approach. Unfortunately, the approach cannot escape the inherent lack of information provided by the measurement set-up, and similarly to other approaches, it is highly dependent on the additional subjective information required to solve the problem. It is here shown that the use of GMRF provides a genuine improvement for the task as this subjective information can be understood and described probabilistically in a meaningful and physically interpretative way while keeping the computational costs low

Estimation of tropospheric wet delay from GNSS measurements

The determination of the zenith wet delay (ZWD) component can be a difficult task due to the dynamic nature of atmospheric water vapour. However, precise estimation of the ZWD is essential for high-precision Global Navigation Satellite System (GNSS) applications such as real-time positioning and Numerical Weather Prediction (NWP) modelling.The functional and stochastic models that can be used for the estimation of the tropospheric parameters from GNSS measurements are presented and discussed in this study. The focus is to determine the ZWD in an efficient manner in static mode. In GNSS, the estimation of the ZWD is directly impacted by the choice of stochastic model used in the estimation process. In this thesis, the rigorous Minimum Norm Quadratic Unbiased Estimation (MINQUE) method was investigated and compared with traditional models such as the equal-weighting model (EWM) and the elevationangle dependent model (EADM). A variation of the MINQUE method was also introduced. A simulation study of these models resulted in MINQUE outperforming the other stochastic models by at least 36% in resolving the height component. However, this superiority did not lead to better ZWD estimates. In fact, the EADM provided the most accurate set of ZWD estimates among all the models tested. The EADM also yielded the best ZWD estimates in the real data analyses for two independent baselines in Australia and in Europe, respectively.The study also assessed the validity of a baseline approach, with a reduced processing window size, to provide good ZWD estimates at Continuously Operating Reference Stations (CORS) in an efficient manner. Results show that if the a-priori station coordinates are accurately known, the baseline approach, along with a 2-hour processing window, can produce ZWD estimates that are statistically in good agreement with the estimates from external sources such as the radiosonde (RS), water vapour radiometer (WVR) and International GNSS Service (IGS) solutions. Resolving the ZWD from GNSS measurements in such a timely manner can aid NWP model in providing near real-time weather forecasts in the data assimilation process.In the real-time kinematic modelling of GNSS measurements, the first-order Gauss- Markov (GM) autocorrelation model is commonly used for the dynamic model in Kalman filtering. However, for the purpose of ZWD estimation, it was found that the GM model consistently underestimates the temporal correlations that exist among the ZWD measurements. Therefore, a new autocorrelation dynamic model is proposed in a form similar to that of a hyperbolic function. The proposed model initially requires a small number of autocorrelation estimates using the standard autocorrelation formulations. With these autocorrelation estimates, the least-squares method is then implemented to solve for the model’s parameter coefficients. Once solved, the model is then fully defined. The proposed model was shown to be able to follow the autocorrelation trend better than the GM model. Additionally, analysis of real data at an Australian IGS station has showed the proposed model performed better than the random-walk model, and just as well as the GM model. The proposed model was able to provide near real-time (i.e. 30 seconds interval) ZTD estimates to within 2 cm accuracy on average.The thesis also included an investigation into the several interpolation models for estimating missing ZWD observations that may take place during temporary breakdowns of GNSS stations, or malfunctions of RS and WVR equipments. Results indicated marginal differences between the polynomial regression models, linear interpolation, fast-Fourier transform and simple Kriging methods. However, the linear interpolation method, which is dependent on the two most recent data points, is preferable due to its simplicity. This result corresponded well with the autocorrelation analysis of the ZWD estimates where significant temporal correlations were observed for at most two hours.The study concluded with an evaluation of several trend and smoothing models to determine the best models for predicting ZWD estimates, which can help improve real-time kinematic (RTK) positioning by mitigating the tropospheric effect. The moving average (MA) and the single-exponential smoothing (SES) models were shown to be the best-performing prediction models overall. These two models were able to provide ZWD estimates with forecast errors of less 10% for up to 4 hours of prediction

Air Force Institute of Technology Research Report 2020

This Research Report presents the FY20 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document

Local Ensemble Transform Kalman Filter for Earth-System Models: An application to Extreme Events

abstract: Earth-system models describe the interacting components of the climate system and technological systems that affect society, such as communication infrastructures. Data assimilation addresses the challenge of state specification by incorporating system observations into the model estimates. In this research, a particular data assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is applied to the ionosphere, which is a domain of practical interest due to its effects on infrastructures that depend on satellite communication and remote sensing. This dissertation consists of three main studies that propose strategies to improve space- weather specification during ionospheric extreme events, but are generally applicable to Earth-system models: Topic I applies the LETKF to estimate ion density with an idealized model of the ionosphere, given noisy synthetic observations of varying sparsity. Results show that the LETKF yields accurate estimates of the ion density field and unobserved components of neutral winds even when the observation density is spatially sparse (2% of grid points) and there is large levels (40%) of Gaussian observation noise. Topic II proposes a targeted observing strategy for data assimilation, which uses the influence matrix diagnostic to target errors in chosen state variables. This strategy is applied in observing system experiments, in which synthetic electron density observations are assimilated with the LETKF into the Thermosphere-Ionosphere- Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm. Results show that assimilating targeted electron density observations yields on average about 60%–80% reduction in electron density error within a 600 km radius of the observed location, compared to 15% reduction obtained with randomly placed vertical profiles. Topic III proposes a methodology to account for systematic model bias arising ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap- plied with the TIEGCM during a geomagnetic storm, and is used to estimate the spatiotemporal variations of bias in electron density predictions during the transitionary phases of the geomagnetic storm. Results show that this strategy reduces error in 1-hour predictions of electron density by about 35% and 30% in polar regions during the main and relaxation phases of the geomagnetic storm, respectively.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

Local Ensemble Transform Kalman Filter for Earth-System Models: An application to Extreme Events

abstract: Earth-system models describe the interacting components of the climate system and technological systems that affect society, such as communication infrastructures. Data assimilation addresses the challenge of state specification by incorporating system observations into the model estimates. In this research, a particular data assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is applied to the ionosphere, which is a domain of practical interest due to its effects on infrastructures that depend on satellite communication and remote sensing. This dissertation consists of three main studies that propose strategies to improve space- weather specification during ionospheric extreme events, but are generally applicable to Earth-system models: Topic I applies the LETKF to estimate ion density with an idealized model of the ionosphere, given noisy synthetic observations of varying sparsity. Results show that the LETKF yields accurate estimates of the ion density field and unobserved components of neutral winds even when the observation density is spatially sparse (2% of grid points) and there is large levels (40%) of Gaussian observation noise. Topic II proposes a targeted observing strategy for data assimilation, which uses the influence matrix diagnostic to target errors in chosen state variables. This strategy is applied in observing system experiments, in which synthetic electron density observations are assimilated with the LETKF into the Thermosphere-Ionosphere- Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm. Results show that assimilating targeted electron density observations yields on average about 60%–80% reduction in electron density error within a 600 km radius of the observed location, compared to 15% reduction obtained with randomly placed vertical profiles. Topic III proposes a methodology to account for systematic model bias arising ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap- plied with the TIEGCM during a geomagnetic storm, and is used to estimate the spatiotemporal variations of bias in electron density predictions during the transitionary phases of the geomagnetic storm. Results show that this strategy reduces error in 1-hour predictions of electron density by about 35% and 30% in polar regions during the main and relaxation phases of the geomagnetic storm, respectively.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

Geodetic Sciences

Space geodetic techniques, e.g., global navigation satellite systems (GNSS), Very Long Baseline Interferometry (VLBI), satellite gravimetry and altimetry, and GNSS Reflectometry & Radio Occultation, are capable of measuring small changes of the Earth�s shape, rotation, and gravity field, as well as mass changes in the Earth system with an unprecedented accuracy. This book is devoted to presenting recent results and development in space geodetic techniques and sciences, including GNSS, VLBI, gravimetry, geoid, geodetic atmosphere, geodetic geophysics and geodetic mass transport associated with the ocean, hydrology, cryosphere and solid-Earth. This book provides a good reference for geodetic techniques, engineers, scientists as well as user community

Air Force Institute of Technology Research Report 2019

This Research Report presents the FY19 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document

Publications of the Jet Propulsion Laboratory, July 1969 - June 1970

JPL bibliography of technical reports released from July 1969 through June 197

NASA's Upper Atmosphere Research Program UARP and Atmospheric Chemistry Modeling and Analysis Program (ACMAP): Research Summaries 1994 - 1996. Report to Congress and the Environmental Protection Agency

Under the mandate contained in the FY 1976 NASA Authorization Act, the National Aeronautics and Space Administration (NASA) has developed and is implementing a comprehensive program of research, technology, and monitoring of the Earth's upper atmosphere, with emphasis on the stratosphere. This program aims at expanding our understanding to permit both the quantitative analysis of current perturbations as well as the assessment of possible future changes in this important region of our environment. It is carried out jointly by the Upper Atmosphere Research Program (UARP) and the Atmospheric Chemistry Modeling and Analysis Program (ACMAP), both managed within the Science Division in the Office of Mission to Planet Earth at NASA. Significant contributions to this effort are also provided by the Atmospheric Effects of Aviation Project (AEAP) of NASA's Office of Aeronautics. The long-term objectives of the present program are to perform research to: understand the physics, chemistry, and transport processes of the upper atmosphere and their effect on the distribution of chemical species in the stratosphere, such as ozone; understand the relationship of the trace constituent composition of the lower stratosphere and the lower troposphere to the radiative balance and temperature distribution of the Earth's atmosphere; and accurately assess possible perturbations of the upper atmosphere caused by human activities as well as by natural phenomena. In compliance with the Clean Air Act Amendments of 1990, Public Law 101-549, NASA has prepared a report on the state of our knowledge of the Earth's upper atmosphere, particularly the stratosphere, and on the progress of UARP and ACMAP. The report for the year 1996 is composed of two parts. Part 1 summarizes the objectives, status, and accomplishments of the research tasks supported under NASA UARP and ACMAP in a document entitled, Research Summary 1994-1996. Part 2 is entitled Present State of Knowledge of the Upper Atmosphere 1996.- An Assessment Report. It consists primarily of the Executive Summary and Chapter Summaries of the World Meteorological Organization Global Ozone Research and Monitoring Project Report No. 37, Scientific Assessment of Ozone Depletion: 1994, sponsored by NASA, the National Oceanic and Atmospheric Administration (NOAA), the UK Department of the Environment, the United Nations Environment Program, and the World Meteorological Organization. Other sections of Part 11 include summaries of the following: an Atmospheric Ozone Research Plan from NASA's Office of Mission to Planet Earth; summaries from a series of Space Shuttle-based missions and two recent airborne measurement campaigns; the Executive Summary of the 1995 Scientific Assessment of the Atmospheric Effects of Stratospheric Aircraft, and the most recent evaluation of photochemical and chemical kinetics data (Evaluation No. 12 of the NASA Panel for Data Evaluation) used as input parameters for atmospheric models