DISSERTATION Tropospheric delay parameters derived from GNSS-tracking data

of a fast-moving fleet of trains

Ausgeführt zum Zwecke der Erlangung des akademischen Grades eines Doktors der

technischen Wissenschaften unter der Leitung von

Ao.Univ.Prof. Dipl.-Ing. Dr.techn. Robert Weber

am E 120-4

Department für Geodäsie und Geoinformation

eingereicht an der Technischen Universität Wien

Fakultät für Mathematik und Geoinformation

von

Matthias Aichinger-Rosenberger Matr.Nr: 00926550 Ried 14/7 6306 Söll

Wien, Februar 2021 (Unterschrift Verfasser/in) (Unterschrift Betreuer/in)

i

“Wonach du sehnlich ausgeschaut, Es wurde dir beschieden. Du triumphierst und jubelst laut Jetzt hab ich endlich Frieden! Ach, Freundchen, rede nicht so wild, Bez¨ahme deine Zunge! Ein jeder Wunsch, wenn er erf¨ullt, Kriegtaugenblicklich Junge.” —Wilhelm Busch (1832-1908) ii Acknowledgements

Theverse on the previous page, composed by thefamousGermanwriterWilhelm Busch, Ihad stumbled upon awhile agoinsomeold bookathome. From there on,I knew thatIneeded to add it to this thesis as an opening line since there’spractically no better way of describing myacademiccareer over the years. And as I’mwriting this and therebyfinish this chapter,there’s already somethingnew and exciting coming up forthe future. Nevertheless before that is nowthe time to thank everybodywho made this thesis and my PhD studies possible. First and foremost, Iwouldliketothank Prof. Robert Weber, who served as my supervisorand mentor not only forthis thesis but at allaspectsofuniversitylife. Thanks forgiving me the opportunity to jointhe research divisionand pursue such an interesting PhDstudy. Furthermore thanks to: Johannes B¨ohm,again forthe chance to start an academic career at TU Wien and forcompetent advice with his expertknowledge in atmosphericmodelling and space geodesy. MarcusFranzGlaner,for thegreatcamaraderieand collaborationatworkand numerous precious advices and discussions on GNSS,PPP andeven notvery ”work-specific passions” likedistance running. GregorM¨o ller, foralot of expert advice on all thingsconcerning GNSS (and GNSS Meteorology in particular) as well as the greatcollaboration not limitedbyour relatively short time at theinstitutetogether. Natalia Hanna, foralot of expertadvice on dataassimilationand carrying out the assimilation testsfor thisthesis. Zoreh Adavi,for providing ray-traced troposphericdelays forthe validation of the results. In generaltoall other colleagues at the research divisionand the institutewho Ihad thepleasuretoknowand workwith. Although my time thereended already ayearago, Ireally enjoyedevery dayofitand will alwaysbegrateful forthisexperience.

iii iv

Finally Iwould liketothankmyfamily: Eva, foryourlove andcontinuous support, withoutwhich this thesis would not have been possible/finished in such ashort timeframe. Ilove you. Paula and Fiona, the greatest giftsofmylife. Iloveyou too. My parents, brothers and all other relatives who supportedmeand kept me motivated over all those yearsI’ve nowspent studying. Abstract

Watervapourdenotes one of the most importantparametersutilizedfor describing the stateand evolution of the atmosphere. Therefore, detailed knowledgeofits distribution is of immense importance forweather forecasting. Furthermore, it is also themost effective greenhouse gas and highlyvariable in both space andtime. Thus, it is obvious that high resolutionobservations arecrucialfor accurate precipitation forecasts, especially forshort-termpredictionofsevereweather. Althoughnot intentionally built forthis purpose, GlobalNavigation Satellite Systems(GNSS)have proventomeet those requirements. The derivation of meteorologicalparameters fromGNSSobservations is based on the fact that electromagnetic signals aredelayedwhen travelling through the atmosphere. Parametrisations of these delays, most prominentlythe Zenith Total Delay (ZTD) parameter, havebeen studied extensively and proventoprovide substantial benefits foratmospheric research and especially NumericalWeather Prediction(NWP) model performance.Typically,regional/globalnetworks of static reference stationsare utilizedtoderiveZTD alongwith other parametersofinterest in GNSS analysis (e.g. station coordinates).Results areused as acontributing data source fordetermining the initialconditions of NWP models, aprocess referred to as Data Assimilation (DA).

Thisthesisgoesbeyond the approach outlined above, showing howreasonable troposphericparameters canbederived from highly-kinematic, single-frequency (SF) GNSSdata. This data wasgathered on trains ofthe Austrian FederalRailways(OBB¨ ) and processed using the Precise Point Positioning (PPP) technique. The special natureofthe observations yieldsanumber of additionalchallenges, from appropriate pre-processing and extended outlier detection, to advanced strategies in the PPP setup and forusage in DA procedures. Furthermore, since only SF dataisprovided, the treatmentofthe ionosphere represents one of the major challenges of thisstudy. Therefore different strategies havebeeninvestigated and shown to provide satisfactory results, suitable forZTD estimation. Despite thesechallenging circumstances, reasonable results forZTD estimatescould be

v vi obtained forthe analysed test cases investigating different PPP processing strategies. For validation of the results, comparisons with ZTD calculated using data from ERA5, the latest reanalysis of the European Centre forMedium-RangeWeather Forecasts (ECMWF),werecarried out. They yield very highcorrelation and an overall agreement fromthe lowmillimetre-rangeupto5centimetre, depending on solution and analysed travelling track. First tests of assimilation into aNWP modelagain showthe reasonable qualityofthe resultsasbetween 30-100 %ofthe observations areaccepted by the model. Furthermore guidelines to an operationalprocessingand possibleextensions to advancedtroposphericparameters were outlined, in order to exploitthe huge benefits (horizontal/temporal resolution)ofthis specific dataset foroperational weather forecasting. Kurzfassung

Atmosph¨a rischem Wasserdampf kommtdurch seineRolle als wichtigstesTreibhausgas und seine gleichzeitig r¨aumlichund zeitlich hoch variable Verteilung eine besondere Bedeutung inder Meteorologie zu.Dadurch ist auch verst¨a ndlich dassein m¨oglichst dichtes Beobachtungsnetz f¨ur die Niederschlagsvorhersage von entscheidender Bedeu- tung ist.Wenn auch urspr¨unglich nicht zu diesem Zweck entwickelt,k¨o nnen Global Navigation SatelliteSystems (GNSS)hier Abhilfe schaffen. Die Bestimmung von atmosph¨a rischen Wasserdampfmengen mit GNSS basiert dabei auf dem Sachverhalt dass elektromagnetische Signaleauf ihremWeg durch die Atmosph¨a re durch die Pr¨a senz vonWasserdampf verz¨o gert werden. Parametrisierungen dieser Verz¨ogerung, wie der Zenith Total Delay(ZTD),k¨o nnen aus Netzwerken fixer Stationen in der GNSSAuswertung, zusammen mit z.B. Stationskoordinaten, bestimmt werden. Die gewonnenen Resultatewerden typischerweise alskomplement¨a rer Datensatzzur Bestimmung der Anfangsbedingungen in numerischen Wettermodellen verwendet, ein Prozessder Datenassimilation bezeichnet wird.

Die vorliegende Arbeit geht ¨u berdiese Ans¨a tze hinausindem sie die Nutzbarkeit von Einfrequenz-GNSS-Daten, welche in einem hoch kinematischen Umfeld beobachtet wurden, zur Bestimmung vonZTD zeigt. Dabei handelt es sich um Lokalisierungs- daten vonZ¨u gen der Oster¨ reichischen Bandesbahnen (OBB¨ ), welche mittels Precise PointPositioning (PPP) ausgewertet wurden. Die große Anzahl der bereitsmit GNSSEmpf¨a ngernausgestatteten Z¨uge verspricht dabei eine noch nieerreichte r¨aumliche (und auch zeitliche) Aufl¨osung vonZTD Daten ¨u berganz Oster¨ reich. Die speziellen Eigenschaften der Daten bringen allerdings eine Reihe vonHerausforderungen mitsich, voneiner deutlich aufwendigeren Ausreißerkorrektur bishin zu speziellen Prozessierungs- und Assimilierungsans¨a tzenwelche in dieser Arbeit getestet wurden. Durch die Verwendung vonEinfrequenz-Daten kommt der Korrektur von ionosph¨a rischen Laufzeitverz¨ogerungen eine besondershohe Bedeutung zu.Aus diesem Grund wurden hierf¨u rmehrere verschiedene Ans¨a tze getestet, welche alle zufriedenstellende Ergebnisse

vii viii liefern konnten. Trotz dieser herausfordernden Voraussetzungenkonnten durchwegs realistische Ergeb- nisse f¨ur dieanalysierten Testf¨alleerzielt werden. Vergleiche mit ausatmosph¨arsichen Reanalyse-Daten (ERA5)des European Centre forMedium-Range Weather Forecasts (ECMWF) gerechneten ZTDs zeigen eine sehr hohe Korrelation und mittlere Abwe- ichungen vomunteren mm-Bereichbis zu 5cm, abh¨a ngigvon verwendeterSoftwareund Teststrecke. Erste Tests von Assimilation in ein numerisches Wettermodell zeigendass, abh¨a ngig vonL¨o sung und Strecke, 30 -100%der Beobachtungen vomModell akzeptiert werden.Dar¨u berhinaus wurde auch noch eine Strategief¨u rdie Implementierung dieser Idee im operationellen Betrieb entwickelt bzw. vorgeschlagen, um die großen Vorteile dieser Datens¨a tze (sehr hohe r¨aumliche/zeitliche Aufl¨osung)f¨u rdie operationelle Wettervorhersage nutzbar zu machen. Contents

Acknowledgements iii

Abstract v

Kurzfassung vii

Contents viii

1Introduction 1 1.1Thesis contribution...... 3 1.1.1 Goals ...... 4 1.2 Thesis outline ...... 5

2GlobalNavigation Satellite Systems 7 2.1Principles of GNSS positioning ...... 8 2.2 GNSS types...... 8 2.2.1 GPS ...... 9 2.2.2 GLONASS ...... 12 2.2.3 Galileo ...... 13 2.3 Precise Point Positioning ...... 14 2.3.1 Observation equations ...... 15 2.3.2 Errorsources ...... 15 2.3.3 LinearCombinationsofGNSS Observations ...... 19 2.3.4 Integerambiguityresolution ...... 22 2.3.5 Kinematic PPP...... 22

3Physicsofthe atmosphere 23 3.1General overview ...... 23 3.1.1 Optical propertiesand energy budget ...... 23 3.1.2Atmosphericcomposition ...... 24

ix x CONTENTS

3.2Vertical structure andlayers of theatmosphere ...... 25 3.2.1 Hydrostatic balance ...... 25 3.2.2 Vertical structureofpressure/density...... 26 3.2.3 Vertical distributionoftemperature ...... 27 3.2.4 Atmospheric layers ...... 27 3.3 Water vapourinthe atmosphere ...... 29 3.3.1 Watervapourmeasures ...... 30 3.4 Precipitation ...... 32 3.4.1 Numerical modellingofprecipitation ...... 33

4Signalpropagation in the atmosphere 35 4.1 Maxwellequations ...... 35 4.2 Path delays ...... 36 4.2.1 Ionospheric delay...... 37 4.2.2 Troposphericdelay...... 39

5GNSS Meteorology 45 5.1History ...... 45 5.2 GNSS-based troposphereproducts forNWP ...... 46 5.2.1 Ground-based products ...... 47 5.2.2 Space-based products...... 49 5.3 Estimation oftroposphericparameters using PPP ...... 50 5.3.1 Kinematic platforms ...... 52

6GNSS dataprocessing 53 6.1Data sources ...... 53 6.1.1 Greenlight ...... 53 6.1.2 Railway track database...... 55 6.1.3 EPOSA ...... 55 6.2 Pre-Processing...... 56 6.2.1 DilutionofPrecision ...... 56 6.2.2 Multipathanalysis...... 57 6.2.3 Cycle slip detection ...... 58 6.2.4 Data cleaning ...... 59 6.3 Parameter estimation in PPPprocessing ...... 59 6.3.1 Least-squaresadjustment ...... 60 6.3.2 Kalman Filtering ...... 62 CONTENTS xi

6.4 SEID...... 63 6.4.1 Accuracy of SEID model ...... 65 6.4.2Kinematicimplementation ...... 66 6.5 Processingscheme: CSRS ...... 66 6.6 Processingscheme: PPP-Wizard ...... 67 6.7 Processingscheme: GAMP using SEID...... 68 6.7.1 GAMP ...... 69 6.8 Processingscheme: Height-constrained PPP ...... 69 6.9 Filteringmethods and performance metrics...... 71 6.9.1 Moving averagefiltering ...... 71 6.9.2 Error metrics forperformance evaluation...... 72

7ZTD validation and assimilation 75 7.1Validation using ERA5 reanalysis products ...... 76 7.1.1 ERA5...... 76 7.1.2 ZTD calculationfromERA fields...... 77 7.1.3Quality of ERA5-derived ZTD...... 78 7.2 Basicsofdata assimilation ...... 80 7.2.1 DA techniques ...... 81 7.3 Assimilation of GNSS data in NWP...... 83 7.4 Assimilation andverification methodology...... 84 7.4.1 Model descriptionand setup ...... 84

8Results 87 8.1Overviewofconducted casestudies ...... 87 8.1.1 Test cases ...... 88 8.1.2PPP processing settings...... 89 8.2 Case study 1: 11.05.2017 ...... 92 8.2.1 Rawdataquality...... 92 8.2.2 PPP noise analysis ...... 93 8.2.3ZTD validation...... 95 8.3 Case study 2: 28.09.2017 ...... 100 8.3.1 Rawdataquality...... 100 8.3.2 PPP noise analysis...... 101 8.3.3 SEIDprocessing...... 104 8.3.4 ZTD validation ...... 106 8.4 Case study 3: 29.11.2019...... 110 xii CONTENTS

8.4.1Raw dataquality...... 110 8.4.2 PPP noiseanalysis ...... 112 8.4.3 ZTD validation ...... 113 8.5 Case study 4: 01.12.2019 ...... 116 8.5.1 Rawdataquality...... 116 8.5.2 PPP noise analysis...... 118 8.5.3 ZTD validation ...... 122 8.6 ZTD sensitivityanalysis ...... 124 8.6.1 Impact of GLONASS observations...... 124 8.6.2 Elevation cut-off ...... 127 8.6.3 Estimationofhorizontal gradients ...... 129 8.6.4 Mis-modelling of ionosphere using SEID ...... 131 8.6.5Altitude-dependency of estimation errors...... 132 8.7 Assimilation tests in WRF...... 135 8.7.1 WRFsetup ...... 135 8.7.2 Influenceofhorizontal resolution...... 135 8.7.3 Assimilation test:CS3 ...... 138 8.7.4 Assimilation test:CS2 ...... 138

9Towards real-timeprocessing 143 9.1Requiredadaptations forNRT GNSS processing ...... 144 9.1.1 Data transmission ...... 144 9.1.2 Orbit/clock products ...... 144 9.1.3 Processingsoftware ...... 144 9.1.4 Outputinterval ...... 145 9.1.5 Data format of NRTproducts...... 146 9.2 Purposedworkflowfor NRT processing ...... 146 9.2.1 SF-PPP using regionalionosphere maps ...... 146 9.2.2 DF-PPP usingSEID model ...... 146 9.3 Requirements forNWP assimilation and applications ...... 148 9.3.1 DA configuration ...... 148 9.4 Extension to advanced troposphericparameters ...... 150

10 Conclusions and outlook 151

Acronyms 157

Bibliography 171 CONTENTS xiii

Curriculum Vitae 187 xiv Chapter 1

Introduction

In times of extreme weather eventsand climate change, monitoring of the Earth’sat- mosphere is becoming amorecrucialtaskthan ever before. One of the most important, yetalso at least understood ingredientsofthis complex system is water vapour. It is not only the keyparameter in formationofcloudsand thus precipitation, but also the most importantgreenhouse gasaffecting global warming. In relationtoits importance, observationsofatmosphericwatervapourare relatively sparse. Radiosondes and other measurement techniques aretypically used to observe itsconcentration and distribution, but these techniques often suffer fromlow temporal and horizontal resolution, e.g.pro- viding measurements only once aday. This is wherethe field of Global NavigationSatelliteSystems(GNSS)can provide an alternative. Theretrieval of watervapourfrom GNSS signals relies on the fact that electromagneticwavesare delayedontheir way through theatmosphere. In terms of the neutral atmosphere, this delayoriginatesdue to the presence of waterand thus can be interpreted as ameasureofwatervapourinthe columnabove the receiver. Tropospheric parameters, derived fromGNSSsensors,are awell-established datasource forNumericalWeather Prediction (NWP) nowadays. The widespreadusage of GNSS systems formultiple fields of applicationprovides ahuge amount of observations avail- able forthe meteorological community.Basedonthe concept of GNSS Meteorology, outlined by Bevisetal. (1992), tropospheric delays areestimated operationally both in national and international networks, likethe European EGVAP network (Guerovaetal. 2016). Assimilation of these observations in NWP models is nowadays awidely-used technique to improveprecipitation andcloud cover forecasts. Several new developments havebeen achieved in the last twodecades, e.g. the establishmentofGNSS station networksused solely foratmosphericmonitoring or the usabilityofthe Galileosystem. Tropospheric estimatesare typicallyderived within adouble-difference (DD) network

1 2 Introduction solution,which can providethe high accuracy needed in NWP (∼ 1cmfor ZTD).This approach provides the most accurate results but has the downside of being cost-intensive since only high-end infrastructurecan be used and alargernumber of referencestations is needed forastable solution. Aside of this ‘classical’ approach, severalauthors havealso studied the potential of low-cost GNSS receiversinterms of tropospheric monitoring.Therefore, Precise Point Positioning (PPP)denotes the most promisingapproach forprocessingnowadays, espe- cially when resultshave to be availablein(near)real-time.The processing does not need any data fromreference stations and thus computational speed is increased remarkably. Another advantage is the fact that troposphericestimates fromPPP arenot biasedby correlations as typicallyintroduced in small-scale local station networks when applying DD processing (M¨oller 2017). These can prevent the detection of local (site-specific) watervapourtrends/anomalies and therefore can be problematicfor investigation very small-scale weather phenomena.However,when using PPP,high qualityinformation of satellite orbits and clocks (provided by institutionslikethe International GNSS Service (IGS)) is mandatory to obtain resultswith high accuracy. Low-cost receivers often only provide single-frequency (SF)observations. Amajorprob- lemwhen working with SF data is the treatment of the non-neutral atmosphere, the so-called ionosphere. For dual-frequency (DF) observations its effect can be eliminated by building the appropriatelinearcombination usingobservations on two frequencies. However, this is notpossiblewith SF observations and thus theeffect must be modelled. If ionospheric delaysand other majorerror sourcescan be modelled with sufficient accu- racy,moststudies showpromisingresults in terms of positioning as well as tropospheric monitoring. Until today, most studies concentratedonmeasurements from staticreceivers due more trivial data processingand more controllable measurement conditions. Gao et al. (2006)developed areal-time SF-PPPsystemand tested it in both road and marineenvironments. Both test scenarios achieved decimetreaccuracy in kinematic pro- cessingmode. de Bakker and Tiberius (2017)demonstrated lane identification and mappingonamo- torway using SF-PPP.Performance wasfound to be strongly dependent on the number of available satellites. Deng et al. (2009)densified an already existing station networkwith SF receivers and retrieved tropospheric delays using staticPPP in post-processing mode. In order to deal withthe ionospheric influence, they developedthe Satellite-specific Epoch-differenced Ionospheric Delay(SEID) model, which uses information fromsurrounding reference sta- 1.1Thesis contribution 3 tions to generate syntheticobservationsonasecond frequency forthe SF receiver. This approachprovided promisingresults andwill be tested in the course of this study as well. Krietemeyer et al. (2018)studiedthe feasibility of using low-cost receivers to increasethe density of GNSS networks forretrievalofPrecipitable WaterVapour(PWV). They pro- cessed oneyearofGNSS data fromanIGS station and two co-located single-frequency stations also by using the SEID algorithm to correct forthe ionospheric influence. Mendez Astudilloetal. (2018)carriedout aperformance assessment of three PPP on- lineservices and three softwarepackagesconcerningZTD estimation.Inthis context, they compared ZTDestimates from PPP processing to those obtained from the IGS tropospheric products. The resultsindicate that the online PPP services performance is better than thoseofselected PPPsoftwarepackages in all cases. Zhaoetal. (2019)estimated both PWV from low-cost multi-GNSS receivers in static mode. They retrieved ZTDs with an accuracy betterthan 10 mm compared with tro- posphere productspublished by IGS and about 3mmfor PWV compared to radiosonde results. Only very fewstudies have investigated the possibilityofmonitoring tropospheric pa- rametersfrom kinematic platforms. Most of these kinematic studies used maritime environments(shipborne (Rocken et al. (2005), Bonifaceetal. (2012), Fujita et al. (2008), Kealyetal. (2012)) and buoys(Chadwell and Bock (2001), Dodson et al. (2001)) or airborne data (Skone et al. (2006)).Uptill now, theonly investigation on train-borne GNSS data wascarriedout by Webb et al. (2016), who analysedZenith Wet Delay(ZWD) forover adecade of continuous observationsoverarangeofaltitudes on theSnowdon Mountain Railway,locatedinSnowdonia NationalPark, NorthWales. Theyfound an improvement of amulti-system GNSS solution in kinematic PPP,with an agreement of 11.6 mm forthe multi-GNSSsolution compared to 16.2 mm forthe GPS-only solutioninZWD.

1.1 Thesiscontribution

Thisstudy goes one step beyond the studies presented before by making useofthe kinematic PPP approach to derive tropospheric parametersfrom SF observationstaken on fast-movingtrains. These trains areequippedwith dual-system SF receivers, which currently areable to track GPS and GLONASS signals. In afuture state the receivers will be switched to GPS/GALILEO capability. Data is gathered on different railway tracks over Austria in the course of theproject Greenlight,led by theAustrianFederalRailways (OBB¨ ). 4 Introduction

Ahigher number of challenges is faced due to the fast movement of the sensorand a large number of obstructed areas on the track (e.g. tunnels). The potentialbenefits areavery highspatial and temporal resolution forobservations gathered attrain tracks covering huge partsofAustria and neighbouring countries. Moreover, ahighnumber of trains (∼ 1400) is already equipped withGNSS sensors and up to 200vehicles more are planned in the course of the next year. In particularthis thesis aims to answer the following questions:

• Can reliable troposphericestimates be derivedfrom GNSStrackingdataoffast- moving trains?

• Which pre-processing steps arerequired to prepare the obtained tracking data for PPPprocessing (cycle slip detection, multipath, ionospheric corrections)?

• Which dataprocessing scheme(s) is/areadequate to obtain results comparableto independent ZTD sources (NWP,ray-tracing)?

• Whatisthe quality of the derived dataand is it sufficient to be incorporatedinto an NWPdata assimilation system?

• Can the estimation and assimilationbecarried out in a(near) real-time (NRT) operational mode?

First investigations, as presented in Aichinger-Rosenberger and Weber (2020), already indicatedthe possibility to deriveZTD estimates of reasonable quality, even forrailway tracks in highlychallenging environments. This thesis extends these investigations fora number of test tracks and processing schemes, analyses specific sensitivities in the GNSS processingand presents first testsofZTD assimilation into aNWP model.

1.1.1Goals

Directly linked to thosequestions raised aboveare the following goals of the thesis:

1. Goals related to GNSS processing:

• Data cleaning:Implement astrategyfor datacleaning, mostly concerning cycle slips and multipath

• GNSS data processing: Find the best possible processing scheme(s) forthe given GNSS observations,especially taking into account adequate modelling of ionospheric corrections 1.2Thesis outline 5

• Tropospheric estimation: Estimate tropospheric parameters(ZTD) using the developedprocessingscheme(s)

• Qualityassessment: Assessthe limits of reachable qualityfor tropospheric parameter estimates using these processing scheme(s) by comparison to NWP-derived and ray-tracedtropospheric delays

• Processing of test cases (train tracks): Process data foranumber of casestudies(availabletrain tracks) in post-processing mode withfocus on tropospheric estimation

• NRT GNSS data processing: Provide strategy and theoretical basis of possible extension frompost-processing to NRT operation

2. Goals related to NWP data assimilation:

• Observation qualitycheck: Assess if qualityofestimates is sufficient to enter the model

• Assimilation casestudies: Assimilation of GNSS troposphericestimates from moving trains intoaNWP model

1.2 Thesisoutline

Chapter 2 gives an introductiononthe most importantaspects of existing GNSS,the physical/geometrical principles behind them and their usage in different scientific and real-world applications. Chapter 3 summarizes information on theEarth’satmosphere and it’s governingpro- cesses whichare of importance forthisstudy. Chapter 4 introduces the theoretical background and physical laws behind the propaga- tionofelectromagnetic signals travelling through the atmosphere. Chapter 5 takesacloser look on thehistory and thelatest scientific achievements in the specific field of GNSS Meteorology. Chapter 6 describes the different processing schemes forGNSS data used in this study. Adetailed description of processing setups is given forall deployedapproaches. Further- more the utilized dataand necessary pre-processing steps areintroduced. Chapter 7 introduces the methods and datasets used forassessing the reached quality of thetropospheric estimates derivedinChapter 6.Resultsofthis validation procedure can serveasanindication forthe usabilityofthe results forassimilation. Furthermore it dealswith assimilationprocedure of the ZTD estimates, derived fromthe processing 6 Introduction schemesintroduced in Chapter 6,intoaNWP model. Therefore ashort introduction to the mathematicalbackground ofdataassimilation andthe utilized NWP model is given. Chapter 8 providesthe resultsfrom all test cases conducted. Resultsofdata processing (in termsofZTD andheightestimatesmainly) areshown as well as validation and as- similation results. Chapter 9 aims to serveasanoutlook to apossibleNRT operational mode forGNSS tracking data processing. Therefore the theoretical frameworkand ideas forimplemen- tation as well as challenges of this approach will be examined. Chapter 10 concludes the thesis with adiscussionand summary of the main findings. Furthermoreanoutlook on futureimplementations of this research idea is provided, whichincorporatesrecommendationsfrom Chapter 9. Chapter 2

Global Navigation Satellite Systems

Global Navigation Satellite Systems (GNSS) have revolutionised anumber of scientific re- search fields as well as practical applications over thelastdecades (Aichinger-Rosenberger 2018). Originally startingasacompletely military system, it wasopened forpublic usage in 1983. Since then,ithas been extensively used and studied in the scientific andthe public societyand awidespread field of applications has emerged over thelastyears. Thefollowing points denote just asmall selection of topics which rely on or areclosely related to GNSS:

• Navigation: reaching frompedestriantoautomotive/railway/aviation usage

• High-precisionpositioning

• High-precisiontiming applications

• Assisted/Autonomous driving

• Geomonitoring: detection of plate tectonics, earthquakes, landslides

• Atmospheric monitoring:weather forecasting, climateresearch

Thefollowing section introduces the principle of GNSS positioning, which providesthe foundation forall applications mentioned above.Basedonthis principle the observation equations areformulated and thetypical error sourcesare described. Furthermore the differenttypes of GNSS areoutlined. At last,the mainprocessingscheme used in this study is outlined, Precise Point Posi- tioning (PPP). There, adetailed descriptionofthe observables, governing equations and estimated parameters of the approach is given. Benefits and weaknesses of the technique as well as typical error sourcesinfluencing its performance areoutlined.

7 8 GlobalNavigation SatelliteSystems

2.1 PrinciplesofGNSSpositioning

The basic principle of GNSS positioning relies on very precise propagation time measure- ments foranelectromagnetic signal travelling fromasatellite to areceiver.Through exact knowledge of thispropagationtime Δt thegeometric distance r from satellite to receiver results from

r = c(Tu − Ts)=cΔt, (2.1) where c denotesthe speed of light, Tu the system time at which the signalleft the satellite and Ts the system time when it reaches the receiver. However, sincethe receiver and satellite clocks arenot synchronizedthe measurementsofpropagation time will be biased. Thus thecalculateddistance will not be thereal geometric distance r but the so-called pseudorange ρ.Itisgiven by

s ρ = r + c(δtu − δt ), (2.2)

s where δtu is the offset of the receiverclock fromsystem time and δt is theoffset of the satellite clock from system time. Since on boardofthe satellites atomic clocks areused, the error in the satelliteclock is marginal compared to the receiver clock. Moreover it typicallycancels through observation differencing or can be modelled using accurate correctionmodels (see Section 2.3 formoredetails).Therefore only δtu is left in Equation 2.2,

ρ = r + cδtu, (2.3) whichnow consists of four unknowns (X,Y and Zcoordinate of receiverposition and re- ceiver clock error). Thus, pseudorangeobservations from at least four satellites (ρ1,.., ρ4) enable thecalculationofthe receiver coordinates. Additionalobservations result in an over-determined problemwhich is typically solved by least-squares adjustment. Geometrically this concept corresponds to the intersectionofthe surfaces of spheres, which havethe measured pseudoranges as radius. This is indicated in Figure 2.1,sim- plified to the 2D case (using circles instead of spheres). Typically only three satellites would be sufficient to calculate the 3D receiver position, as threespheres would intersect in one point on Earth. Nevertheless, introducingthe receiver clock error as an unknown likementioned before gives aminimumnumber of four satellitesneeded.

2.2 GNSS types

Since the start of their public availability in 1983, multipleGNSStypes havebeen built up. These include the AmericanGPS, RussiansystemGLONASS, European system 2.2GNSS types 9

Figure 2.1: Geometric conceptofGNSSpositioning, shown here inthe 2D case. Takenfrom B¨ohringer (2008)

Galileo andthe Chinese system Beidou. The first three mentioned systems aredescribed in more detail in the nextsection.

2.2.1 GPS

Since the early 1960s, several U.S governmentorganizations,including theDepartment of Defence (DOD),were interested in developing asatellite systemfor three-dimensional position determination(Kaplan and Hegarty2006)asthe successorofthe already oper- ating TransitSatelliteNavigationSystem. Theaim wastosecure the following attributes forthe system:

• global coverage

• continuous/all-weather operation

• abilitytoservehigh-dynamic platforms

• high accuracy 10 GlobalNavigation SatelliteSystems

Component Frequency

Fundamental frequency f0 =10.23MHz

Carrier L1 154·f0 =1575.42 MHz

Carrier L2 120·f0 =1227.60 MHz

Carrier L5 115·f0 =1176.45 MHz

Table 2.1: Components andfrequencies forcivil use of GPSsignal

In 1969, the Defense Navigation SatelliteSystem (DNSS) program wasestablished, an efforttoconcentratethe contributions of different organisations. As aresult, the Navstar Global Positioning System (GPS) (DoD 2020), aspace-borne positioning system for military purposes, wasfinally introduced in 1973. From thenonittookanother 10 years until the system became open to civil users in 1983.Since then GPS has been running as adual-use system, forboth military andcivil purposes.

GPS signals

GPS satellites use the so-called code divisionmultiple access (CDMA) technique to broadcastrangingcodes and navigation messages. Every satelliteemits an individual Pseudo Random Noise (PRN) code using this technique. These codes were initially solely modulatedontwo frequencies L1 (1575.42 MHz)and L2 (1227.6 MHz), which aremultipliersofthe fundamental frequency 10.23 MHz.Onto L1, Course/Acquisition (C/A) code and Precise(P1)codeismodulated as well as Precise (P2) code onto L2. In the course of the GPS modernization program anew third civil frequency L5 wasintroduced. This opened multiplenew possibilities of carrier phase combinations, especially useful forthe resolution of ambiguities and elimination of the ionosphericdelay. Table 2.1 shows an overviewofcarrierfrequencies used for(civil) GPS. In contrast to L5,the L3 =1381.05 MHz andL4=1379.913 carrier frequencies are only used formilitary purposes(Hofmann-Wellenhof et al. 2012). Since first tests of GPS revealed much betteraccuracy than originally expected, techniques likeSelective Availability(SA)were used to ensure superiorityofthe military over the civil user.This technique incorporatede.g. manipulation of orbital and satellite clock information for civil users to worsen positioning resultsuntil its use wasfinally terminated in May2000. However, encrytion of varioussignals formilitarypurposes(Anti-Spoofing)isstillinuse.

System components

In literature,GPS is usually described as asystems comprised of three different segments: 2.2GNSS types 11

• Space segment

• Control segment

• User segment

The space segment represents the satellite constellation, which consists nominallyof 24 operationalsatellites placedinsix nearly circularorbitsinclined by 55◦ with an altitude of about20200kmabove the Earth’ssurface (Karabatic 2011). This number of 24 satelliteswas reachedinJuly 1995and therebythe space segment became fully operational. Different typesofsatellites havebeen developedinthe course of the last 20-30years,which aresplit in differentblocks. By March 2019, 31 operationalsatellites areavailable anddelivering datadowntoEarth.

The control segment is build upon amaster control station, located in Colorado Springs, USA. This master station is responsible forcontrolling the satellites and keeping the system operating. This includes maintaining the satellites in their proper orbital positions (called stationkeeping)and monitoring satellite subsystem healthand status (Kaplan and Hegarty2006). In addition, five monitoring stations and anumber of ground antennas areemployed. Themonitoring stations makecontinuous measurements to all visiblesatellites and send this data to the master station. There, orbit and clock parametersare calculated and forwarded to theground antennas, which upload thepa- rameters three timesaday.Using this data, the navigation message forGPS is generated.

The user segment incorporateseveryuser of the system and is split into two dif- ferent categories, civil and military users. As already mentioned in the beginning of this chapter,the number of applicationsfor civil use haveincreased heavily over the last yearsand continuetodo so.They reach fromclassical tasks likepositioning, navigation or monitoring to meteorological and climatological applications. In principle, one distinguishes between single- and multi-frequency receivers depending on howmany frequency bandsobservations canbetaken.

GPSreference system

GPS coordinates aredefined in thethe DOD’s World Geodetic System1984 (WGS-84) (National Imagery and Mapping Agency 2000), whichrepresents the standard physical model of the Earth used forGPS applications(Kaplan and Hegarty2006). Alist of the defining parametersofthe underlyingreferenceellipsoid is givenisTable 2.2. 12 GlobalNavigation SatelliteSystems

Parameter andValue Description a =6378137.0 m Semi-majoraxisofthe ellipsoid f =1/298.257223563 Flattening of the ellipsoid −5 −1 ωE =7.292115·10 rad s Angular velocityofthe Earth µ =3986004.418·108 m3 s−2 Earth’s gravitational constant

Table 2.2: Defining parameters of WGS-84, taken from Hofmann-Wellenhof et al. (2012)

2.2.2GLONASS

Globalnaya navigatsionnaya sputnikovaya sistema (GLONASS)isthe Russian counterpart to theAmerican GPS system. LikeGPS originally designed as afully military service, its development started already in 1976.In1982 thefirst satellites were launched and in 1995 the full constellation wascompleted. Thelatterwas alsothe year in which the system became publicly available.Atthe end of the nineties, the capacityofthe system declined more and more due to lack of financial supply.This continued until 2001, when the restoration of thesystembecame one the top priorities of the Russian government. GLONASSismanaged by theRussianSpace Forces and operatedbytheCoordination Scientific Information Center of the Ministry of Defense of the RussianFederation (Xu 2007).

GLONASS signals

Just likeGPS, GLONASSsatellites transmittwo typesofsignals,astandard-precision (C/A code) and ahigh-precision signal (P code). In contrasttothe CDMA tech- niqueused by other GNSS systems, GLONASS uses frequency divisionmultiple access (FDMA), which means thateach satellitecan be identified by its ownuniquecarrier frequencies. These carrier frequencies (in MHz) aredefined by

G1=1602.0+0.5625k G2=1246.0+0.4375k where k denotesthe frequency channel. In the course of modernization, the CDMA technique is being investigated since 2008. Thisisexpected to provide multiple benefits forinteroperability with othersystems.Inaddition,anew signal on the third carrier as well as asecond civil signalonG2should be established. Since November 2018 24 GLONASS satellites areoperational andthusfulloperationalcapability(FOC) is reached. 2.2GNSS types 13

GLONASSreference system

Theterrestrialreference frame used by GLONASS is the ”PZ-90” (Earth Parameters 1990 –Parametry Zemli1990), whichuses the meanposition from1990to1995for the precise locationofthe North Pole. In contrast to this, WGS-84 as GPS reference system uses the location of the North Pole in 1984. The new version PZ-90.11 is broadcasted since 31 December 2013. It is aligned to theInternational TerrestrialReference System at epoch2011.0 at the centimeter level.

2.2.3 Galileo

Galileo is the European alternative to GPS and GLONASS, established by the European Union (EU) through acooperation of theEuropean Commission (EC), the European Space Agency(ESA) and at alaterstage the European GNSS Agency (GSA). Up to date (December 2020), thesystemconsists of 24 operationalsatellites.Infull operational mode observations from30satellitesshould become available to users. Contrary to itscounterparts GPS and GLONASS,Galileoisintended primarily forcivilian use, as basic (lower-precision) services will be free and open to everyone. From 2022 on,also high precision positioning will become available forusers with multiple signal receivers,the Galileo High-Accuracy Service(HAS).

Galileo signals

The Galileo system transmitsthree different signals: • E1

• E5 consistingofE5a andE5b

• E6

SimilartoGPS, these carriers arebased on thefundamentalfrequency f0 =10.23 MHz. In order to enable services like open,Search-And-Rescue (SAR), commercial or public regulated services,eachsatellitewill broadcastdifferent navigation messages (Karabatic 2011). An overview of all available carrier frequencies can be foundinTable 2.3. Whentakingacloser look on the chosen frequencies it can be noticed thatE1and E5a coincide withGPS signalsL1and L5, as well as E5b with the GLONASSG3carrier. This is not pure coincidence but chosen forthe sakeofbetterinteroperabilitywith the competing systems. Despite this benefit, it is also accompanied by thepossibleproblem of interference between the systems, which is avoided by using different modulation schemes forGalileo. 14 GlobalNavigation SatelliteSystems

Component Frequency

Fundamentalfrequency f0 =10.23MHz

Carrier E1 154·f0 =1575.42 MHz

Carrier E6 125·f0 =1278.75 MHz

Carrier E5 116.5·f0 =1191.795 MHz

Carrier E5a 115·f0 = 1176.45 MHz

Carrier E5b 118·f0 = 1207.14 MHz

Table 2.3: Components and frequencies of Galileo signal

2.3 Precise PointPositioning

Precise Point Positioning (PPP) is aGNSS-based positioning technique which uses un- differenced single- or dual-frequency carrier phase and/orpseudorangemeasurements from asingle receiver (Hinterberger 2016). Itsmainadvantage is independence of addi- tionaldata from (nearby)reference stations, unlikeotherprominent techniques such as Real Time Kinematic (RTK). Instead, precise orbit and clock information as provided by e.g. theInternationalGNSSservice (IGS) is utilized to ensure high-quality results. Using dual-frequency observationsincombination with finalorbit/clocksolutions, centimetre- level accuracy can be reached.This potential wasfirstshown by Zumberge et al. (1997) and since then PPPhas become one of the most promising topics in GNSSresearch. Huge scientific effortshave been put into certain aspects like ambiguityresolution(AR) or thecorrectmodelling of satellite and/orreceiver hardwarebiases. Especially AR has been the topic of anumber of studies, since in classicalPPP usuallyareal-valued con- stant is estimated as phase bias instead of the integer ambiguity. Overcoming this issue denotes one of the most promisingmeans to improvethe accuracy of results even further. Nevertheless, the technique stilldeals with anumber of restrictions which currentlylimit its potential andusage. The most prominent oneisthe often longer convergence time of the solutioncompared to RTK. In the following acomprehensivelist of advantages and disadvantages of PPPisgiven:

• Only asparse globalstation networkneeded (for computation of orbit/clock in- formation),which also implies cost-effectiveness (+)

• No simultaneousobservations (from nearbystation)required (+)

• No errorsintroduced from observationsatreference stations (networkeffects) (+)

• Error sources arerepresented as state-space correction models and notasrange 2.3Precise PointPositioning 15

corrections in the observation space (+)

• Globally available/valid corrections (+)

• Reduced computationaleffortsdue to smaller data amount which also implies faster availabilityofthe results (+)

• Longconvergence time (-)

• Complicated observationmodeling (-)

• Challengeofinteger ambiguityresolutionfor highest accuracy (-)

• High-rate and high-qualitysatellite clock information required (-)

2.3.1 Observation equations

The observation equations forthe PPP algorithmare,writtenseparately forpseudorange s observations Pr,ν

s s s Pr,ν = ρr − cδt + cδtr + δion,ν + δtro + P,ν (2.4)

s and phase observations Lr,ν

s s s s Lr,ν = ρr − cδt + cδtr − δion,ν + δtro + λνBr,ν + L,ν. (2.5)

Here thesubscript r denotes aGNSS receiver, s asatelliteand ν the corresponding s frequency.Furthermore ρr denotes the geometric distance between satelliteand receiver, s c the speed of light, δt and δtr theclock errorsofsatellite andreceiver, δion,ν the

(slant) ionosphericdelay on thecorresponding frequency, δtro the(slant) tropospheric s delay, λν Br,ν thefloat ambiguity forphase observations and P,ν/L,ν areadditional error terms (e.g. multipath)for thecorresponding observation type.

2.3.2 Errorsources

Thissectionaims to give an overviewonsome of thedifferent error terms containedas in Equation 2.4 and 2.5.Avisual overview is given in Figure 2.2,which shows the most prominent delays/influences encountered forGNSS measurements. 16 GlobalNavigation SatelliteSystems

Figure 2.2: Component anderrorsources in pseudorange measurements, taken from Sanz Subirana et al. (2013)

Relativistic effects

Highly accurate timing capabilities arethe cornerstone of the GNSS positioningtech- nique.Thereforesatellites carryatomic clocks on board, which provide highlyaccurate timestamps forsignals leaving the satellite. Furthermore also on the receiver side, espe- cially forhigh-grade (geodetic) receivers, accuratetiming using precise clocks need to be ensured best as possible. The synchronisation of satellite and receiver clock denotes afundamentalrequirement forGNSSpositioning. Thistime transfer between satellite and receiver is influenced by relativistic effects, which can be split up intotwo parts (as originally defined by Einstein):

• General Relativityeffect: The gravitationalfieldofthe Earthinfluences theclock frequency differently forclocks in space and on Earth.

• SpecialRelativityeffect: The travelspeed of the satellites relativeto users/receivers manifests in aclock shift (time dilatation effect).

The combined effect results in ashift of the center frequency f0 given by: Δf f − f v2 ΔU v2 GM 1 1 = 0 = + = + E ( − ) (2.6) 2 2 2 2 f0 f0 2c c 2c c rs rE v denotes the satellite clock velocityrelativetothe ground receiver, c thespeed of light and ΔU the difference in gravitational potential between satellite and receiver. 2.3Precise PointPositioning 17

Integrating the aboveequationresultsinaclock correction of 38.6microseconds per day(Karabatic 2011). It is worth mentioninghere that the two relativisticeffects counteract each other.Due to GeneralRelativity, clocks on boardofthe satellites runfaster with increasingaltitude (approximately 45 microsecondsper day). SpecificRelativityonthe other handstates that the (relatively) moving clocks on boardofthe satellites run slowerthan their companions on ground. The combined effect is known as the ’factory offset’ which is appliedtothe satellite clocks before the satellitelaunch.

Another related effecttobeconsidered in the frameworkofhigh-precision appli- cations is the Sagnac effect.Itisaresult of the Earth’srotation takingplace while the GNSSsignalistraveling fromsatellitetoreceiver. The travel time correctioncan be calculated as v · ( r − r ) δt = R S (2.7) c 2 where v is thegeocentric velocityvectorofthe receiver and rR and rS arethe geocen- tricvectors ofreceiver and satellite. The correction due to the Sagnac effect can be considered software-internally in PPP processing.

Multipath

The Multipath effect occurswhen aGNSS signalisreflected off an object,such as the wall of abuilding before it is received at the antenna.These reflected signals can distort the code correlation peak andresult in arangingerror. Multipathdenotesone of the dominant error sources in GNSS positioning,especially in heavily obstructed (e.g.urban) areas. This is worsened by thefactthat modelling its influence on measurementsisa very challenging taskand completeelimination of theeffect is still practicallyimpossible forhighly dynamic environments(autonomousdriving,railway). However advancements in antenna designand specific filteralgorithms havemadeiteasier to recognizeand correct especially Non-Line-of-sight multipath. Multipath is ahighly localized error whichdoesnot cancel through differencing and therefore must be considered as themajorsource of errorinmany high precision ap- plications.Iteffects both code andcarrier phase measurements, wherethe introduced errorscan reach up to 150 meters forcodeobservations and up to 5cmfor carrierphases. Moreover, multipath can prevent coordinate convergence in PPPprocessing. Therefore it denotes one the most challenging error sources in GNSS processing, especiallyfor dynamic applications. 18 GlobalNavigation SatelliteSystems

Antenna phase center offsets

GNSS measurements refer to the phase centersofthe antenna of satelliteand receiver respectively.Offsets and variations in the locationofthe phase centerstherefore directly influence the accuracy of processing results. The effects to be considered are:

• Satellite antenna phase center (APC) offset and variation: This holdsfor orbital information in the broadcastnavigationmessages. However, precise orbitsinstead arereferred to the center of mass of the satellite, which makes acorrection to the phase center necessary forprecisePPP applications.

• Receiver APC offset and variation: As forthe satelliteantenna,the measurements arealso referred to the phase center of the receiverantenna.Since this location is not asuitable reference, apointtied to the baseofthe antenna,denoted as antenna reference point (ARP),isused instead.Information on the antenna phase center offset between theAPC and ARPnormallyare provided by the manufacturers or can be obtained from the IGS. Usually the receivercoordinates arereferred to a monument marker or to an external bench mark. The computed coordinates in the IGS SINEX files arereferred to the monumentmarker. Thesite eccentricity vectorbetween the ARP and the monument marker is also given inthe SINEX file, in up,north and east coordinates.

Phasewind-up correction

The phase wind-upeffect affects only the phase measurements and depends on the mutual orientationofthe satelliteand the receiver antennas. Phase wind-up arises due to the nature of the GPS signals as right-hand circularly polarized radio waves.For a static receiver, likethe receivers of areference network, thewind-up effect is due to the satellite orbitalmotion.Usually satellites undergo onlyslowrotationsinorderto keep their solarpanels pointing to the sun direction. This causes aphase variation, whichismisunderstood as arange variation.However,the satellitesalso undergo rapid rotationsinthe case of eclipse and noon seasons. During such an event the rotation of the antenna can reach up to one revolution, which corresponds to an increasein the carrier phase measurement of one cycle, within less than half an hour.For double- difference positioning on distances less thanfew hundreds of kilometres the carrier phase wind-up effect can be neglected. However, forlongerbaselines and in undifferenced point-positioning, thiseffect has to be taken intoaccount.Neglecting the effect and fixing orbits and clocks willleadtopositioning errors in thedm-level (Kouba andH´e roux 2001). 2.3Precise PointPositioning 19

Following Karabatic (2011), the computation of the phase wind-up can be carried out using the formulaspresentedbyWu et al. (1992):

D · D δφ = sign()arccos( ), (2.8) |D ||D | where = k·(D ×D ), k denotes the satellite-receiver unit vectorand D , D the effective dipole vectors of satelliteand receiver. Thelattercan be derivedfromthe satellite’s (x, y, z)and receiver’s unit vectors (x, y,z)intheir respectivebodycoordinate system:

D = x − k(k · x) − k × y, (2.9) D = x − k ( k · x ) − k × y . (2.10)

2.3.3 LinearCombinations of GNSS Observations

In GNSS data processing it is common practicetocombine simultaneous observations us- ing linearcombinations(LC). Different typesofcombinationsexistfor different purposes, the most important ones areintroducedinthe following.Inthe subsequent formulas observations ontwo frequencies areassumed. The equations can be generalized to any pair of signals at different frequencies offered by theGNSS systems.

Ionosphere-free linearcombination

Undoubtedly the most importantLCinGNSSprocessingisthe Ionosphere-free linear combination (IF-LC), whichbuildsthe basis formost processing strategies. It utilizes the dispersive nature of the ionosphereinorder to mitigate its first-order effects (up to 99.9%)byacombination of two-frequency carrier phase (orcode) observations. For carrier phase it reads 1 L = (f2L − f2L ), (2.11) IF 2 2 1 1 2 2 f1 − f2 and forpseudorange observations 1 P = (f2P − f2P ). (2.12) IF 2 2 1 1 2 2 f1 − f2

Especially LIF denotes the commonobservable in (DF) data processingtechniques like PPP. However, there arealso problems encountered in GNSS processing when using this LC. The two most common ones are:

• Difficult ambiguity fixing 20 GlobalNavigation SatelliteSystems

• Highernoiselevel: The IF-LC shows an increased noiselevel compared to the

originalcarrier frequencies (∼ factor3comparedtoL1). Further detailsonthis aregiven in Section 2.3.3.

Geometry-free linearcombination

As acounterpart of theIF-LC,the geometry-free LC (GF-LC or L4)exposes theiono- spheric delaybyremoving all non-dispersiveparts. ThereforethisLCisoften used for the estimation of ionosphere models, as also in this study forthe SEIDalgorithm (see Chapter 6). The GF-LC is formed by thedifference between twomeasurements on dif- ferent frequencies, with allnon-frequency dependent errors, such as satellite, receiver clock and geometry(orbit and station coordinates) cancelling. For phase observations, the GF-LC can be formulated as:

LGF = L4 = L1 − L2, (2.13) and forpseudorangeobservations it reads

PGF = P4 = P2 − P1. (2.14)

As mentioned above, the GF-LC extracts the ionospheric delayand therefore the basis of many ionospheric modelling algorithms.

Wide-lane linearcombination

The Wide-lane LC (LWL)isprimarily designed to construct an observationwith alarger wavelength, whichcan be beneficial forcycleslip detectionand ambiguityfixing. It is derived by f1L1 −f2L2 LWL = (2.15) f1 −f2

Narrow-lane linearcombination

The Narrow-lane LC (LNL)provides anobservation with shorter wavelength andalower noise level compared to the originalcarriers. It allows to increase precision in ambiguity fixed processing (M¨oller 2017).

f1L1 + f2L2 LNL = (2.16) f1 + f2

Melbourne-W¨ubenna linearcombination

The Melbourne-W¨u bbena LC (LMW), proposedbyMelbourne (1985), can be seen as an extension to the WL-LC. In addition to the phase observations forming the first 2.3Precise PointPositioning 21

Observable Wavelength Noise level Multipath level

P1,2 19.0/24.2 cm σcode = ±15cm mpcode = ±150m

L1 19.0 cm σL1 = ±1 − 2mm mpL1 = ±5cm

L2 24.2 cm 1.3 · σL1 1.3 · mpL1

LIF 0.6 cm 3.2 · σL1 4.5 · mpL1

LGF ∞ 1.6 · σL1 2.3 · mpL1

LWL 86.2 cm 6.4 · σL1 9.1 · mpL1

LNL 10.7 cm 0.8 · σL1 1.1 · mpL1

LMW 86.2 cm ∼ σcode 9.1 · mpL1

Table 2.4: Overview on noise andmultipathcharacteristicsofGNSS observables, most infor- mation takenfrom M¨oller (2017). part of the equation, code observationsare used in the second part to mitigatethe ionospheric effects. Thus, the LMW is free from ionospheric delays,geometry, clock, and tropospheric effects. Thedisadvantage of theinclusion of code observations in the LC is thesignificant increase of the observation noise and the multipatheffects. However, in thefuture, advanced code modulations withsignificantly improved noise characteristics will considerably reduce the noiseofthis combination.The Melbourne-W¨u bbena LC is formed as follows:

1 1 L = (f L − f L ) − (f P + f P ) (2.17) MW 2 2 1 1 2 2 1 1 2 2 f1 − f2 f1 + f2

Expectfor multipath and measurement noise, LMW covers solely the wide-lane ambiguities. Therefore it can be used forcycleslip detection, which is exploited in the pre-processing of reference station datafor the SEIDalgorithm as described in Chapter 6.Inthe caseoflow multipath, lowcodenoiseand real-value widelane ambiguities, the LMW is directly used forthe resolutionofwide-lane ambiguities (Sch¨onemann 2014).

Anumber of other useful LCscan be found in GNSS literature, e.ginGlaner (2017).

Noise characteristics

As already seen before forthe IF-LC, some LCsshowundesirable effectsbyintroducing a higher noise level in the data processing compared to observations on theoriginal carrier frequencies (L1/P1 and L2/P2). Thereforeanoverview on thenoise characteristics of different combinations ofGNSS observationsisgiven in Table 2.4. 22 GlobalNavigation SatelliteSystems

2.3.4Integer ambiguityresolution

Although integer ambiguityestimation is not carried out within this study it should still be mentioned hereasakeyingredient forhigh-accuracy applications. If centimetre- accuracy level is required forthe position solution, fixing of the phase ambiguities to integer values is essential.For PPP processing, integer resolution is achieved by ap- plyingimproved satellite products, where phase delays areseparated from theinteger ambiguities (Hinterberger2016). In general two approaches can be distinguished:

• Ge et al. (2008): Decompositionofundifferenced ionosphere-free ambiguities into wide-lane and narrow-lane part.

• Laurichesse et al. (2009): Undifferenced ambiguities were directlyfixed to integers.

For adetailed discussion of thoseapproaches and furtherconsiderations on integer am- biguityresolution see e.g. Hinterberger (2016)orGlaner et al. (2020).

2.3.5Kinematic PPP

Kinematic PPPisapromisingprocessingtechnique foranumber of applications which do not allow forthe assumption of astatic roverposition,asdeployedin(standard) static PPP. Kinematic GPS PPP wasfirst investigated by Kouba and H´eroux (2001)and found well suited forpositioning of moving vehicles as needed e.g. in autonomous driving or agricultural applications. Although reachable accuracy is still lowerthanfor techniques likeRTK positioning, the simplicityofthe approach in terms of data requirements still is apromisingfeaturefor alot of users. Overthe last decade, different applications and processing strategies (e.g.concerning GNSS systems or orbit/clock products used) havebeen investigated. Alkan et al. (2017)used kinematic GPS/GLONASS PPP formarine applicationsand found an accuracy level of centimetre- to decimetre-level even in challenging conditions as well as improvementsinsolution availabilitythrough theusage of GLONASSobser- vations. Katsigiannietal. (2019)examined the performance of the Galileo-only PPP and PPP-AR solutionsinpost-processing kinematic mode. Resultsindicate millimetre- to centimetre-level accuracy of the PPPsolution, especially forPPP-AR processing. Yu andGao (2017)studied the benefit of using multi-GNSSobservationsand found an significant enhancement in availabilityand accuracy of the positioningsolution. More- over they also found an increase in convergence performancefor all three coordinate components. Chapter 3

Physicsofthe atmosphere

This sectionaims to give an overviewonthe principles and parameters,which areex- ploited to drawconclusions on thecurrent stateofthe atmosphere. In order to get a first glance of the medium that is investigated in the course of thisstudy,somegeneral information is provided here.

3.1 General overview

The term Atmosphere referstothe gaseous envelopeofthe Earth or anyother celestial body(M¨oller 2017). Theatmosphere of theEarth is theresult of volcanicfumigation approximately four billion yearsago.Without this formation process, life would not have been able to establish itselfonthe planet due to anumber of reasons. This layer(or at leastits bottom end) is where weather andclimatic phenomenatakeplace, which areof larger interest thanever in achanging climate as experienced today. In the following,somebasicinformation on optical properties, chemicalcomposition andvertical structure of theatmosphere is summarized. This short overview is strongly based on Wallace and Hobbs (2006), whoprovide adetailed description not only on these introduction topics but on all majorfields of atmospheric research in general.

3.1.1 Optical properties and energy budget

The optical properties ofthe Earth’s atmosphere can briefly be summarized by two main properties:

• Transparency forincoming solar(short-wave) radiation

• Opaqueness foroutgoing (long-wave) radiation emitted by theEarth’s surface

23 24 Physicsofthe atmosphere

Process Radiation fraction Solarirradiation (short-wave) absorbed at surface +161 W/m2 Thermal emissionbythe Earth’ssurface -396 W/m2 Long-wave downwardradiation (e.g. fromclouds) +333 W/m2 Net radiation +98 W/m2

Table 3.1: Net radiation budgetofthe Earth, M¨oller (2017)

These propertiesmanifest themselves in awarming of the Earth’ssurface compared to temperatures to be expected from classical(blackbody) radiative transfer theory.This behaviour is what is commonly referred to as the Greenhouse Effect. Considerations on the energy budget of thewhole Earth system aretherefore closely linked to theseproperties.The derivation of thesystems energy budget relies on the conceptofblackbodyradiation.The termblackbodydescribes asurface whereall incoming energy is absorbed.Its flux density(i.e. irradiance) F is given by the Stefan- Boltzmannlaw

F = σT 4, (3.1) with σ =5.67 · 10−8 Wm−2K−4 being the Stefan-Boltzmann constant and T the temperatureofthe surface. Inserting the relevant parametersfor theEarth givesthe netradiationbudget outlined in Table 3.1.The remaining excess of 98 W/m2 in the budget is compensated by non- radiativeprocesses likesensible (e.g. convection) or latent heatfluxes (e.g. melting processes).

3.1.2Atmospheric composition

The Earth’s atmosphere is composed of amixtureofdifferent gases. The dominant ones include hydrogen (H), carbon dioxide (CO2)and methane (CH4). Togetherwith ozone (O3), they denote the most important greenhouse gases.This means that their molecularstructure allowsthem to effectivelytrapoutgoing long-wave radiation, and therefore cause the greenhouse effect. The dominant gasesinterms of concentration in the atmosphere arediatomic nitrogen

(N2)and oxygen(O2). Togetherthey account forover 99 %offractional concentration by volume. Adetailed overviewofthe major constituents of the atmospherecan be found in Table 3.2. 3.2Vertical structure andlayersofthe atmosphere 25

Constituent Molecularweight Fractional concentration by volume

Nitrogen(N2)28.013 78.08 %

Oxygen(O2)32.000 20.95 % Argon (Ar) 39.950.93 %

Water vapour (H2O) 18.02 0-5%

Carbon dioxide (CO2) 44.01 380 ppm Neon (Ne) 20.18 18 ppm Helium (He) 4.00 5ppm

Methane (CH4) 16.04 1.75ppm

Nitrous oxide (N2O) 56.03 0.3 ppm

Ozone (O3) 56.03 0.3ppm

Table 3.2: Fractional concentrations of gaseousatmospheric constituents with respect to dry air,withimportant greenhouse gases marked bold. Takenfrom Wallaceand Hobbs (2006)

3.2 Verticalstructure and layers of the atmosphere

This section discussesthe vertical distributionofthree essentialatmosphericvariables: pressure, temperatureand watervapour. Thereforethe concept of hydrostaticbalance is introduced which allowsfinding the relationship withair density andatmosphericpres- sure. Basedonthe described distributions (mainlyonthat of temperature), distinctive layers areintroduced in which the atmosphereiscommonly divided. Due to its importance forthis study,watervapourand itsdistribution and characteristics arediscussed separately in Section 3.3.

3.2.1 Hydrostaticbalance

Assuming astaticatmosphere, pressureonevery vertical level only depends on the weight of the (fluid) layers aboveit. This is what is commonlyreferred to as hydrostatic balance.Imagineavertical columnofair as shown in Figure 3.1.Itisobvious that both pressure p and density ρ are(at least) dependent on height z.For asmall changein height δz the corresponding pressurechange δp is

∂p δp = δz. (3.2) ∂z

The assumptionofastatic(i.e not accelerating)vertical column implies that the net force on it must be zero. This netforce consistsofthe following vertical forces (negative signindicatesdownwardforce) 26 Physicsofthe atmosphere

Figure 3.1: Avertical columnofair of density ρ,horizontal cross-sectional area δA, height δzand mass M= ρδAδz. The pressure on thelower surface is p,the pressure on theupper surface is p+δp.

• gravitational force Fg = −gM = −gρδAδz,

• pressureforce acting at the topface, FT = −(p + δp)δA,and

• pressureforce acting at the bottom face, FB = pδA.

Setting the net force Fg +FT +FB =0oneobtains δp+gρδz =0andbyusingEquation 3.2 finds ∂p + gρ =0, (3.3) ∂z theequation of hydrostatic balance.Itdescribes the decrease in atmosphericpres- sure withheight, i.e with decreasing weight of theoverlyinglayers. The assumptionof negligiblevertical acceleration of the air columnisanappropriate oneinmost circum- stances. Exceptions aresmall-scale phenomena likeconvection, tornados, or turbulence in atmosphericboundary layer(ABL).

3.2.2Vertical structure of pressure/density

An importantinformation Equation 3.3 withholds is the actualvalueofp(z).Therefore the equation of state of airisused to rewriteEquation 3.3 to ∂p gp = − , (3.4) ∂z RT where T is theatmospheric temperatureand R=8314.459 J/(kmolK) the idealgas constant. 3.2Vertical structure andlayersofthe atmosphere 27

For an isothermal atmosphere (T = T0 = const.)Equation 3.4 reads ∂p gp p = − = − , (3.5) ∂z RT0 H where theconstant H = RT0/g is calledthe scale height.The resulting pressure p at height z then is (−z) p(z)=pse H , (3.6) where ps = p(z =0)is thepressure at thesurface z =0.Equation 3.6 describesthe exponentialdecrease of pressurewith height. The isothermal assumption delivers quite reasonable results forthe structurewhich is actuallyobserved. In the more realistic case of an non-isothermal atmosphere,where temperature T (z) andscale height H(z) areafunction of height too, pressure p(z) is foundas

(− z dz ) p(z)=pse 0 H(z) . (3.7)

3.2.3 Verticaldistribution of temperature

Temperatureprofilesshowlarge variationsespecially in vertical direction throughoutthe whole atmosphere. The vertical structurehowever, is somehowsimilar everywhere and thusitisconvenient to introducea’typical’ profile. For the sake of simplicityonly this profile will be introduced here. However, it should be mentioned that both vertical and horizontal deviations fromthis profile exist. The vertical ones forexampleare connected to the meteorological termofstability,especially in the ABL. The typical mid-latitude vertical temperature profile is showninFigure 3.2.Itconfirms thehighvariations in theprofile andit’s rather complicatednature.The extreme values of the profile can be used to distinguishbetween fourlayers, which represent different temperature tendencies and therefore different physicalconditionsand properties. These layers areintroduced in detail in thenextsection.

3.2.4 Atmospheric layers

Starting fromtop to bottom, thefirstlayer of the atmosphereiscalled Thermosphere.

This is the region wherehighly energetic UV radiation is absorbed, mainly by O2 and

CO2.Atthe top (bordertofreespace),temperature is very highand decreases down to 90 km height where it stays fairly constant down to the Mesopause. Below, temperatureincreases again throughout the whole Mesosphere down to the Stratopause at 50 km height. This maximum is directlyconnected with themaximum in the absorption of mid-wavelength UV radiation by stratosphericozone (O3). 28 Physicsofthe atmosphere

Figure 3.2: Typical atmospheric temperature profilefromU.S.standard atmosphere, taken from Wallace and Hobbs (2006)

However themaximum in the ozone concentration is observed at lowerheights(20-30 km)inthe Stratosphere,causedbythe fact thatthe ozone is veryopaque to UV.In principle the wholeexistence of thelayerisdue to the existence of this high ozone con- centration. The air is typically verydry andtemperaturedecreases throughout thelayer down to the Tropopause. The tropopause is locatedbetween 8-15 km, the actual height depends both on lati- tudeand season. It marks the typicalupper height limit forexistenceofwaterinall forms (and therefore e.g. of clouds) in theatmosphere. The layerfrom theredownto the surfaceofthe Earthiscalled Troposphere.Here, temperature increases again by typically 70-80 Kelvin fromthe tropopause down to the surface. Practically allphysical phenomena thatwegroupunder the term’weather’ aretakingplace within this layer. Thisisdirectly linked to thefact that, as already mentioned above,nearly all wateris concentrated here. 3.3Water vapourinthe atmosphere 29

3.3 Water vapour in the atmosphere

Aconstituentofspecial interest forthis study is watervapour. Although it only accounts forabout 0.25%ofthe atmospheric mass, it denotes akey component of the system due to its high spatial and temporal variabilityand itsroleasagreenhouse gas. Water vapour is often concentrated verylocally in the atmospheredue to to the factthat it remains thereonlyabout 8-10 days.Thisresidence time is based on the total mass of waterinthe atmosphere (around 30 kg/m2 whichcorrespondstoaglobal waterlayer of around 3cm) and amean rainfallrate of roughly 0.3cm/day(Wallace and Hobbs 2006). The amount of watervapourwhich can be conserved in the atmosphere at a certain temperature is given by theClausius-Clapeyron relation 1 Δe L M s ∼ v w . (3.8) ∗ 2 es ΔT 1000R T

Thereby es represents the watervapourpressureatsaturation level, T thetemperature, ∗ Lv the latent heat of vaporization, Mw themolecularweight of H2O and R the universalgas constant. Thisrelation has amassiveimpact on the evolution of climate change, as it implies that witharising globaltemperaturethe atmosphereiscapable of capturingmore watervapourand therefore also alargeramount of energy.This willagain amplify the temperature increase through the greenhouse effect and isexpected to also lead to increasing activityinall kinds of severeweather eventsrelated to the precipitation (tropical storms, floods, extreme precipitation events,...).

In general,waterappears in the troposphereinthree different forms:

• solid: snow, hail, graupel, ice

• liquid:rain, clouds, fog

• gaseous: watervapour

As mentioned earlier,watervapourshows strong variations in spatial andtemporal directions. This is in completecontrasttodry air which has no significant variation in composition withlatitude or height (Smith and Weintraub 1953). Thesestrong variationsalsomakeitdifficult to measureormodel its local or global distribution. Typicalinstrumentstodosoare hygrometers,with whom measurementsatsurface as well as vertical profilesfrom radiosondescan be derived. It becomes obvious that the horizontal (and temporal) resolution of thosemeasurements is rather poor anddefinitely not sufficient to describesuch strong variability. 30 Physicsofthe atmosphere

Overthe last decades more and more possibilitiestomeasurewatervapour(or related parameters) indirectly with satellites havebeeninvestigated. Nowadays anumberof satellite missions carry suitable instruments likeinterferometers, operating fromoptical to microwave regions.Although originally not designed forsuch purposes, GNSS can alsobeadded to this list. This fact has given risetoanew, cost-effectiveand all-weather operating sourceofobservations.

3.3.1Water vapour measures

Amountsofwatervapourare usuallymeasured as afractionofmoistair compared to dryair. In the following,somemeasures which can reflect the watervapourcontentof the atmosphereare introduced.

Mixing ratio

One possible measurefor thewatercontent of air is the mixing ratio w.Itisdefined by the quotient of watervapourmass perunit mass of dry air m ρ w = v = v , (3.9) md ρd where mv,md denote the mass and ρv,ρd thedensityofwatervapourand dryair.The partialpressure of watervapor e and dry air Pd can be calculated by applyingthe equation of state

e = ρvRvT, (3.10)

Pd = ρdRdT. (3.11)

−1 −1 −1 −1 Here Rv =287.06 ± 0.01 Jkg K and Rd =461.525 ± 0.003 Jkg K denote the specific gas constantsofwatervapourand dry air. By usingEquations 3.10 and 3.11, an alternativeformulation forthe mixing ratio can be found: e/R T e e w = v = ≈ , (3.12) (P − e)/RdT P − e P where = Rd/Rv =0.622.Itshould be mentioned here that the approximationin Equation 3.12 is convenient because the partial pressuretypically only accounts for about 1% of the total pressure.

Specific humidity

As an alternativetothe mixing ratio, the measureofspecific humidity q canbeused: ρ q = v ≈ w. (3.13) ρm 3.3Water vapourinthe atmosphere 31

Here thedensityofmoistair (i.ethe mixtureofdry air andwatervapor) ρm is used and therefore q is approximately equal to w.

One canalso applythe equation of state formoist air which leads to

P = ρmRdTv, (3.14) where Tv is the virtual temperature

Tv =(1+0.61w)T, (3.15) given in Kelvin. It denotes the temperaturethat dryair at pressure P would havewhen its densitywouldequal that of moist air at temperature T ,pressure P ,and mixing ratio w (Haltiner and Martin 1957). With Equation 3.15 one can account forthe presence of moisture in theair.

Relative humidity

Finally,the humiditycontainedinair can also be expressed in relative terms to areference state. This is referred to as relative humidity.Itrepresentsthe ratio (expressed in percentage) of the actualmixing ratio w to the so-called saturation mixing ratio ws with respect to aplane watersurface (Wallace and Hobbs 2006), where the later denotes the ratio of masses between saturated and dry air.The expression forrelativehumidity reads w e RH =100 ∼ 100 , (3.16) ws es where w is theactualand ws the saturation mixing ratio. e and es arethe corresponding watervapour pressures. 32 Physicsofthe atmosphere

3.4 Precipitation

In meteorology, the term precipitation describes any product of the condensation of atmospheric watervapourthatfallsunder gravity from clouds. The main forms arerain, snow,graupeland hail. Precipitation occurswhen local moist air cools, becomes saturated withwatervapor and is no longer able to maintain itslevel of water vaporingaseous form. Processes which can lead to this cooling are:

• an airmasscools adiabatically through rising motion(e.g.lifting on mountain ranges) or

• an airmass cools through radiative processes, or ground contact with cold terrain.

Therefore, it can originate fromanumber of different atmospheric processes which define its type.The three most importanttypes are:

1. Cyclonic precipitation

2. Convective precipitation

3. Orographic precipitation

Cyclonic (orfrontal)precipitation is theresult of frontalsystems associated with extratropical cyclones, which form when warm, tropicalair meets cooler air.Air masses of different densities (moistureand temperaturecharacteristics) meet, and warmer air is forced to rise. This creates an effectofsaturation and, if conditions arefavourable, causes precipitation. Convectiveprecipitationoccurs when air rises verticallythroughthe mechanism of convection, i.e. rising of heated airand cloud formation within aconditionallyunstable atmosphere. Convective precipitation is typically avery local phenomenon, lasting over justashorttime but usually at high intensity. Orographicprecipitation is somehowsimilartothe cyclonic type,exceptthat the rising motion is caused by an orographic obstacle(e.g. amountain ridge).

Figure 3.3 showsatypical climatology of precipitation derived from different data sources (reanalysis data, observations) forthe period1981-2010. Thetypical maxima areobserved in the tropics, wherelarge-scale convectionprocesses lead to huge amounts of rainfall. These processesare strongly connected to significant patterns in globalcirculation, likethe so-called Hadley circulation which bringsair masses towards 3.4Precipitation 33

Figure3.3: Climatological average precipitationrate(mm/day)for 1981-2010 from ERA-Interim,Global Precipitation Climatology Cen- tre(GPCC),Global Precipitation Climatology Project(GPCP) and E-OBS (European Observations)taken from https://climate.copernicus.eu/ monthly-summaries-precipitation-relative-humidity-and-soil-moisture the equator andthereforealso causes the constantlyeast-directed trade winds (Passat winds).

3.4.1 Numerical modelling of precipitation

Quantitativeprecipitationforecasting (QPF) has been amajor challenge in the framework of NWP over the last years. Still, especially cases of convective precipitation in summer remainaproblematic topic inthis scientific area. The main problemisattached to thefact that parametrizations of deep convection used in NWPmodels arenot able to reproduce convectivesystems in needed detail, as outlined by Wulfmeyer et al. (2008). Improvementscan be achievedbyusingnon-hydrostaticconvection-permitting models 34 Physicsofthe atmosphere and increasing horizontalresolutionasshown by e.g. Ducrocq et al. (2002). Performance of models using parametrizations fordeep convectionstill performpoorinsimulating heavyand highly localized precipitation and therefore high resolution to explicitly resolve theseprocessesisneeded. This holds especially forcomplex terrain, where much more small-scale structures havetoberesolved. Of majorinterestfor QPF arethe mesoscale initialconditions andinparticular, the initial moisture field. This is where GNSS datacan provide valuableaid formodels through DA.Lots of efforts havebeenmadebyinternational NWP centres investigating optimal combinations of observations and model output forDAsystems. Nowadays these high- resolutionsystems,based on non-hydrostatic convectionresolving models with rapid update cycles, areoperational in several meteorological centres (Yanetal. 2009). Chapter 4

Signal propagation in theatmosphere

AGNSS signal recorded at the Earth’s surface has to travel through the atmosphereon theway from satellitetoreceiver. It’sconcretepath andvelocityistherebydetermined by multiple physical principles andparameters. This chapter introduces the physical laws determining signal propagation, distinctivelayersand their characteristics and howthe influences of the atmosphere on the GNSS signalcan be modelled.

4.1 Maxwell equations

In 1862, J. C. Maxwell introduced aset of equations which describe the propagation of electromagneticwaves,the so-called Maxwell equations (Jackson1999). Thegeneral Maxwell equations read

∇·E= (4.1) ∂B ∇×E=− (4.2) ∂t ∇·B=0 (4.3) ∂E ∇×B=µJ + µ , (4.4) ∂t where E is theelectric field, the totalcharge and the electric permittivityofthe medium, B themagneticfield, µ the permeability and J = κ·E thecurrent electric den- sitywith κ as the electric conductivity. In anon-conductingmedium like thetroposphere

35 36 Signal propagation in the atmosphere

κ and arezero and Equations 4.1 become:

∇·(E)=0 (4.5) ∂B ∇×E=− (4.6) ∂t ∇·B=0 (4.7) ∂E ∇×B=µ , (4.8) ∂t Assuming only small spatialand temporal variations in µ and ,one can combine these equations intoawave equationfor theelectric field (B¨ohm 2004). ∂2E n2 ∂2E ∇2E = µ = (4.9) ∂t2 c2 ∂t2 √ where c =1/ 0µ0 denotes the speed of light in vacuum and n therefractiveindex. This refractive index n is thekey parameter to describethe propagationofanelectro- magnetic signal through the atmosphere. In the troposphereitisveryclose to one, and therefore it is good practice to usetorefractivity N instead, which is defined by

N =(n−1) · 106. (4.10)

In general N is acomplex number andcan be separated intothree parts

N = N0 + N (ν) − iN (ν). (4.11)

The realpartconsistsofnon-dispersive part N0 andadispersive part N (ν).Itcauses refraction and thepropagation delayofelectromagnetic signals. On the other hand, the imaginary part iN (ν) accountsfor absorption and is directly related to the absorption coefficient α 4πνN(ν) α(ν)=10−6 . (4.12) c While α is important in many other remotesensing techniques, it is typically not relevant forspace geodetic measurements like GNSS or VLBI, where the travel time of the signal is observed. This is due to the fact that absorption does not affect the propagation delay of thesignal.

4.2 Path delays

As already indicated in the last section, electromagneticsignals aredelayeddue to their travel throughthe Earth’satmosphere. When investigating the different atmospheric phenomena and propertieswhich lead to this behaviour it is reasonabletoseparate the atmosphereinto (atleast) two parts,the ionosphere and the troposphere. 4.2Pathdelays 37

4.2.1 Ionosphericdelay

Theionosphere is defined as the ionized part of the atmosphere, which extends from about 60 to 1000kmheightabove ground. Theionization of particlesiscaused by incoming solarradiation,leading to alarge number of free electrons in the layer. The wholeionosphericlayer is typically split intodifferent partswhich areindicated by Figure 4.1.How many layers canbedistinguished variesfromday (four) to nighttime (two), again relatedtothe amount of solarradiation.These are: D, E, F1 andF2, the

Figure 4.1: Ionosphericlayers present at day- and nighttime and their respective heights, takenfrom https://commons.wikimedia.org/w/index.php?curid=7009115 latter being largely responsiblefor theionosphericeffects which typically affect GNSS applications. Typical verticalprofiles of electron densityfor Vienna and different seasons (January and July)atday and night-time areshown in Figure 4.2.Large differences for dayand night-time areindicated, which areamplified in the winter season. Thepeaks of the profilesaround 300kmare alllocatedinthe F/F2 region(compare to Figure 4.1), explaining its importance forGNSS applications which wasoutlined before. Theelectron density is normally expressed in terms of Total Electron Content (TEC) units, which is denoted as the electron content Ne along the raypath from satellite (S)toreceiver (R)

R TEC = Neds. (4.13) S In general we distinguish between vertical total electron content (VTEC)and TEC along theray path, slanttotalelectron content (STEC). Since TECvalues arenormally pro- vided as VTEC,amappingfunction hastobeused to gain the STEC foracertain signal 38 Signal propagation in the atmosphere

Figure 4.2: Ionospheric electron density profiles computed from the International Reference Ionosphere(IRI) modelfor Vienna in 2017, takenfrom Magnet (2019). from asatellite VTEC STEC = (4.14) cos z with R2 sin2 z cos z = 1 − , (4.15) (R + H)2 where z is the elevationangle of the satellite, R is the mean radius of the Earthand H is the effectiveionosphericheight, i.e.the height of the layerassumed to contain all electrons. TEC values understandably showastrong dependence on time of dayaswell as elevation of the satellite. Furthermore duetoinfluence of the Earth’s magnetic field, it is alsoa function of latitude.

Correcting forionospheric delays

For GNSS signals, the ionosphereisadispersivemedium,meaningthe propagation velocityisfrequency-dependent.Therefore the formulationsofthe ionospheric delayfor phase andgroupmeasurementsread 40.31 40.31 Δρ = − N ds = − STEC (4.16) ion,ph f 2 e f 2 40.31 40.31 Δρ = N ds = STEC, (4.17) ion,gr f 2 e f 2 where f is the frequency of the signal, Ne is the number of free electrons, ds is the signal pathand STEC denotes the slant totalelectroncontent along the raypath of 4.2Pathdelays 39

Figure4.3: VTECmap for26.02.2010, 12 UTC derived usingthe Klobuchar model. Typical maximums in VTEC arevisible at lowlatitudes.Taken from Najman and Kos (2014) the signal. The constant40.31 can be calculated from the physical quantities electron mass, electron charge, and the permittivityoffreespace. In the case to DF observations the dispersive nature of the ionosphere canbeexploited by building the IF-LC introduced in Section 2.3.3.Itallows forthe completeelimination of (first order) ionospheric delayand much betteraccuracy of thegained parameters. For positioning with SF receivershowever, using Equations 4.16 is of great importance in terms of accuracy.They allowthe user to correct forthe path delayusing TEC values andthe well-known carrier frequencies.TEC information canbeobtained from various sources including:

1. Global VTEC models

2. Regional VTEC models

3. Ionospheric prediction models

4. Empirical models

4.2.2 Troposphericdelay

In contrast to the ionosphere, thetroposphere is anon-dispersive medium forelectro- magnetic waves up to 15 GHz. No larger number of charged particles is present in the layerand therefore all carrier frequencies aredelayedbythe same amount. Although the magnitude of the delayistypically much smaller,the non-dispersivenature does not allowelimination by building linearcombinations. Thetroposphericdelayisusuallysplit up intotwo parts (Davis et al.1985): 40 Signal propagation in the atmosphere

• Hydrostaticpart: mainly determined by atmosphericpressure

• Wetpart: delaydue to amount of watervapour

Furthermoreone can distinguish between delays in differentdirections.This is typically donefor the zenith direction(zenith delay)and elevation direction of each satellite (slant delay). In the following these kind of delays areintroduced in detail and some recipes fortheir modelling and estimation aregiven.

Zenith delay

The Zenith Total Delay (ZTD) represents the full delayinzenith direction, due to the presence of the troposphere. The definition of the ZTD reads (Jinand Luo2009):

∞ Δρz = c · τ =10−6· N(s)·ds, (4.18) 0 where c is the speed of light in avacuum, τ is thedelaymeasured in seconds, and N is the neutral atmospheric refractivity, where neutraladdresses the non-ionized component of the atmosphere. Again following e.g. Jin andLuo (2009) N can also be computed by: P P N = k · ρ + k · w + k · w (4.19) 1 2 3 2 Zw · T Zw · T where ki(i =1,2,3) areconstants, ρ the total mass densityofthe atmosphere, Pw the partial pressure of watervapor, Zw acompressibilityfactorclose to unityaccounting for the small departures of moist airfromanideal gas, and T the temperatureinKelvin.

The term can be split up intoahydrostatic (dry) and awet proportion, Nh (addressing the first term of 4.19)and Nw (addressing theother two terms of 4.19). As indicated in Figure 4.4,these twoquantities differ substantially in both magnitude and variability. The dry part is fargreaterinmagnitude andshows acontinuous decay with height, whereas the wetpartisofsmaller magnitude but very variable in both time and space.Its fluctuationsdepend heavilyonatmospheric conditions (water vapour pressure, temperature) as Equation 4.19 and Figure 4.4 indicate. Twoeffects have to be considered, when evaluating the integralinEquation 4.18.At first, propagation speed is decreasingwith increasing density, which representsthe main influence on thesignal. Secondly,the signalpropagation is determined by Fermat’s principle, stating thatthe signal pathisnot necessarily astraight (G)but bent line (S) as indicated in Figure 4.5.This effect can be accounted forbyextending Equation 4.18 to ∞ Δρz = c · τ =10−6· N(s)·ds + S − G. (4.20) 0 4.2Pathdelays 41

Figure4.4: Height profilesofthe hydrostatic (Nh)and wetcomponent (Nw)ofthe refractivity

N fortwo different days, originating fromthe same timeofthe dayand station. Nh shows a continuous curve, Nw high variabilityintimeand space. Takenfrom Nilssonetal. (2013).

Figure4.5: Path of aGNSS signal trough the troposphere.The actual pathSislongerthan the geometric path Gdue to thebending effect and arrives at adifferentelevation e0.Taken from Nilssonetal. (2013).

In practical applications the effect is only relevant forobservations gatheredatvery lowelevations. The magnitude of the full tropospheric path delayistypicallyinthe metre-range,although reaching up to ten times higher values at very lowelevations.

As mentioned before, the ZTD can, just as the refractivity, be split up intotwo parts, the Zenith Hydrostatic Delay (ZHD) and the Zenith WetDelay (ZWD). The ZHD is defined as the integral over the hydrostatic refractivity along thesignal path: ∞ z Δρh = Nh(s) · ds (4.21) 0 and can be modelled by only usingsurface pressure, station heightand latitude, following simple models like Saastamoinen (1972), as shown in Equation 4.22: K ·R ·p Δρz =10−6· 1 d s (4.22) h −6 gm·(1 − 0.00266 · cos(2 · Φ) − 0.28 · 10 · H) 42 Signal propagation in the atmosphere

where K1 is therefractivityconstantofdry air, Rd is thespecific gasconstant of dry air, and ps is the surface pressure. ps is corrected forlocal gravityeffects by using mean gravity gm,station latitude Φ andthe station height above the geoid H. ZWD can then be derivedasthe simpledifference between ZTD and ZHD as

z z z Δρw =Δρ −Δρh. (4.23)

It representsthe tropospheric delayofthe GNSS signal caused by watervapour andcan be transformed into precipitable watervapor (PWV)by

z PWV =Π·Δρw, (4.24) where theconversion factor Π equates to

−6 k3 −1 Π=(10 · ρ · Rv · ( + k2)) , (4.25) Tm ◦ with ρ being the density of liquid waterat0C, Rv the specific gasconstant forwater vapour, Tm the weighted mean temperatureofthe atmosphere, k2 = k2 − mk1 and m the ratio of the molarmassesofwatervapourand dry air.

Slant delay

The tropospheric delayinline-of-sight direction is called Slant Total Delay (STD). It is obtained by ascalingofthe zenith component with geometric factors, the so-called mapping functions which areagainsplit up intohydrostatic and wetpart. As afirst approximation, with evenly stratified atmosphere and no earth curvatureassumed, one can write (Karabatic 2011)the STDas 1 Δρs=Δρz , (4.26) sin where Δρs is thetroposphericslant delay, Δρz is thetroposphericzenith delayand is the elevation angle of the satellite. The factor 1/sin() denotes acrude basic version of amapping function whichdoesnot account forazimuthal asymmetry.Simple approaches likethisone deliverreasonable STDresults only forelevations above 10◦.For lowerelevation angles anumber of more sophisticatedmapping functions were developed overthe course of the last 40 years. The next section aims to giveashort overview over them.

Mappingfunctions

Mapping functions condense informationabout the variability of delays over the whole elevation range (Landskron and B¨ohm2017). This information is typically expressed by 4.2Pathdelays 43 thethree mappingfunction coefficients a, b and c of acontinued fractionform(Marini 1972) 1 mf()= a (4.27) sin + b sin + c sin + sin +... These coefficients, independent of theazimuthangle, aredetermined forthe hydrostatic andthe wetpartseparately.This can be done by fitting them to different sources of observations/model data:

• Standardatmospheres: e.g. Chao (1974)

• Radiosondedata: Niell (1996)

• NWP data: Niell (2000)and B¨ohm et al. (2006).

Marini (1972)conducted thefirst tryoutsofverification against astandard atmosphere. Here, he foundanagreement betweenthem betterthan 0.3% down to elevationsof1◦. However, acomparison with radiosonde databyNiell (1996)showedlarge deviations of range corrections in both lowelevations and even in zenith direction. Herring (1992)introduced aslightly different fraction form compared to Marini (1972), shown in Equation 4.28. 1+ a 1+ b m()= 1+c (4.28) sin + a sin + b sin +c In 1996, Niell (1996)developedthe Niell mapping function(NMF) which is based on the continuous fraction form shown in Equation 4.28.The coefficients a and b areonly dependent on dayofyear(DOY) and the station latitude and height.For theNorthern Hemisphere they arederived from meteorological profiles of the US Standard Atmosphere (see Chapter 3,Figure 3.2). Since the millennium anumber of NWP-based mapping functions havebeen developed: In 2000, Niell (2000)introduced the Isobaric Mapping Function(IMF), which arebased on the relation of hydrostatic mapping function coefficients withgeopotentialheight at isobaric surfaces. The coefficients arederived from 6-hmodel output of aglobal NWM. Basedonthisconcept theViennaMappingFunctions (VMF) were introducedbyB¨ohm andSchuh (2004), which were able to overcome some limitations of IMF, especially in the wetpart. Thesubsequent Vienna Mapping Functions 1(VMF1) by B¨ohmetal. (2006)are regarded as themostaccurate mapping functions nowadays and areapplied by numerous research centers and other agencies worldwide (Landskronand B¨ohm2017). Analogouslyfor NorthAmerica,the UNB-VMF1 (Santos et al. 2012)use the same model but NWM 44 Signal propagation in the atmosphere data fromthe National Centersfor EnvironmentalPrediction (NCEP) and the Canadian MeteorologicalCenter. The latest versionofthe VMFseriesisVMF3 (Landskron andB¨o hm 2017), which introduced some refinements, especially forvery lowelevation angles. Chapter 5

GNSS Meteorology

Thischapter aims to giveashort overview on thehistoryofGNSS Meteorologyand the different approaches used nowadays.EspeciallyinEurope anumber of dense station networks, initially built up forpositioningservices, were utilized fortropospheric moni- toringoverthe last decade. Someofthese networks arealso described in the following chapter. Furthermore an introduction to the means of using this datainweather forecasting shall be given. In this context different strategiesfor assimilation of GNSS products into numericalweather models (NWM) areoutlined. Most information is based on Guerova et al. (2016), whogiveavery detailed insight into thecurrent stateand futureprospects of GNSS Meteorology.

5.1 History

Theterm GNSS Meteorology wasfirst used by Bevis et al. (1992), who presented the basic concept of the technique in theearly nineties. GNSS Meteorologyuses the tropospheric delays introduced in Section 4.2.2 to derive estimatesofwatervapour content, which canbeused in NWP dataassimilation.Figure 5.1 illustrates thebasic principle of the approach hereonce again. Since the rise of GNSS as an accuratepositioning andnavigation system, many station networks havebeen established worldwide. Data fromthese networksare oftenfree of charge forscientific research and therefore also exploited to deriveinformation on atmospheric conditions. The first continuous GPSnetworkbuilt up formeteorological purposes alone wasthe GPS-IPW Networkofthe National Oceanicand Atmospheric Administration (NOAA) ledbytheir ForecastSystemLaboratory in the USAinthe 1990s(Wolfe andGutman 2000). In the course of the last decade, thetechnique has

45 46 GNSS Meteorology

Figure5.1: Basic illustrationofthe GNSS Meteorology concept. Individual STDsare mapped to ZTD forasingle station.Taken from Guerova et al. (2016). become more feasible and more and more observations areavailable forassimilation. In Europe, thisfact relies heavily on the set-upofdifferentresearch programstoinvestigate the usabilityofGNSS-derived information in meteorology.The first one of those was founded by TheEuropean Cooperation in Science and Technology (COST) andwas called ”COST Action 716: Exploitation of ground-based GPS forclimate and numerical weather prediction applications” (Elgered 2001). Following up, the project “Targeting Optimal UseofGPS Humiditymeasurementsinmeteorology (TOUGH)” wasconducted from2003 to 2006 (Huang et al.2003). Based on thesuccess ofthe priorresearch, the EUMETNET EIG GNSS watervapourprogramme (E-GVAP) wasestablished in 2005. It consists of aseries of research projects all devotedtothe useofnearreal-time (NRT) tropospheric GNSS data forNWP.Anumber of analysis centersfrom all over EuropecontributetoE-GVAP by providing delayestimates forforecast validation, NRT monitoring and researchprojects. Figure 5.2 givesanoverview on thetimeline of European projects mentioned above.In addition to research projects embedded in the projects mentioned above, several other research studies havebeen carried out.

5.2 GNSS-based troposphere products forNWP

As already outlined in the previous section, tropospheric products from GNSS haveat- tractedincreasing interest of the meteorological communityover thelast decade. This 5.2GNSS-based troposphere productsfor NWP 47

Figure 5.2: TimelineofEuropean projects in thefieldofGNSS Meteorology from 1996 - 2016. Takenfrom Guerova et al. (2016)

went fromsmall case studies withonlyfew GNSS observations available forassimilation, to operational usageof(at leastZTD)products in most NWP models today. Nowadays they areawell-established and valuableobservation source fordata assimilation in NWP models.The field of GNSS meteorologytherefore denotes astronginteractionand co- operationbetween GNSS expertsand meteorologists,aiming to increase availabilityand qualityofthe observationsaswell as proper usage inapplications. Due to the varietyofproducts it is reasonable to giveashort overview on themost pop- ularones used in NWP in this section. In avery basicmanner, products can be grouped in ground-based (GNSS meteorology) and space-based (GNSS RadioOccultation).Al- though ashort introduction on GNSS RadioOccultation (GNSS-RO) is provided,this section focuses mainly on ground-based products.

5.2.1 Ground-based products

Zenith Total Delay/Integrated Water Vapour

Up to date, ZTDisstill themost commontropospheric product fromGNSSprocessing. ThemajorityofNWP nowadays is able to assimilate ZTD observationsorquantities derived from it, likeIntegrated WaterVapour(IWV). Table 5.1 gives an overviewof popularNWP models which use ZTD/IWV. Nevertheless other techniques and quan- tities, such as GNSS Tomography and usageofSTDs,are exploited quite frequently nowadays.Especially STDcurrentlydenotes ascientific focus of the communitysince the slant estimates contain alargeramount of information as theraysalso experience horizontal variationsofatmosphericconstituents. 48 GNSS Meteorology

Model QuantityAssimilation strategy WRF ZTD/STD4D-Var COSMO IWV/STD 4D-Var AROME ZTD/STD3D-Var ECMWF (IFS) ZTD 4D-Var

Table 5.1: Overview of assimilation strategies used forGNSS-derived tropospheric products in popularNWP models: WRF(Weather Research and Forecasting),COSMO (Consortium forSmall-scale Modeling), AROME(Application of Research to Operations at MEsoscale)and IFS (Integrated Forecasting System,operated at ECMWF) model

GNSS Tomography

GNSS Tomography makes use of existing GNSS infrastructure(satellites andnetworks of geodeticreference stations) in order to deriveaspatially resolvedwatervapourfield. Therefore, alarge number of slant delays areestimated from anetworkofground stations using double-difference networkprocessing (M¨oller 2017)orPPP (Zhao et al. 2018). Sinceevery satellite-stationcombination givesanintegral measurefor watervapour concentration along theray path, adense observationfield can be created given a sufficient number of ground stations(see Figure 5.3). This tomography area is then usually divided into3Dcubes called voxels. Thenatomographic reconstruction (as commonly known fromseismology) is carried out using these slant delayobservations to derive a3Dfield of wetrefractivityand ultimately atmosphericwatervapour. The main challenge of the approach is the ill-posed nature of the mathematicalproblem behind the technique. This originatesfrom alimited spatial resolutionofsatellitesand ground stationsand therefore, especially forahigh resolutionfield, not everyvoxel will be intersected by asignal ray. Thus, from mathematicalpoint of view, asingulardesign matrix has to be inverted to solve the equation system. Therefore, specialalgorithmsfor under-determinedsystemshave to be applied. Recent investigations deal forinstance withdifferent parametrization methods forcomputing thedesignmatrix. Adavi et al. (2020)studied theeffect of introducing ray-tracing methods(seee.g. Hofmeister (2016)) forcomputing the length of rays passing through avoxel as well as theimpact of considering the topography of thetomography model area. They found improvements of about 5ppm in mean deviation of wetrefractivitytoradiosonde measurements. Assimilation of tomography products into NWMs wasalso shown to be beneficial by a number of studies, e.g. Hanna et al. (2019)who used aROassimilation operatorto assimilate refractivityfields. 5.2GNSS-based troposphere productsfor NWP 49

More detailed insights on the principles, benefits andrestrictions of the technique of the aregivene.g. by M¨oller (2017).

Figure 5.3: Principle of GNSStomography,taken from Dong and Jin (2018)

5.2.2 Space-based products

GNSSRadioOccultation(GNSS-RO) denotes the most prominent space-based technique forestimation of meteorological information about thelower(troposphere)aswell as the higher atmosphere(ionosphere). Thetechnique is based on using GNSS measurements received by low-Earth orbiting (LEO) satellitestoprofile the Earth’s atmosphere with high verticalresolution and global coverage. Beginnings of radio occultation techniques go back to the 1960s where they were used to study atmospheres of the outer planets of the solarsystem.Overthe last decades it wasincreasingly used to probethe Earth’s atmosphere also. As radiosignals from theGNSS satellites pass throughthe atmosphere, molecules and electrons bend their paths andslowtheir propagation.The benefits as well as disadvan- tages of GNSS-RO arelisted in thefollowing:

• Assuredlong-term stability (+)

• All-weather operation (+)

• Global 3D coverage (+)

• Vertical resolution:100 minthe lowertroposphere (+) 50 GNSS Meteorology

• Compact, low-power, low-cost sensor (+)

• Highaccuracy:Averaged profilesto<0.1 K(+)

• Fairly lownumber of soundings perLEO (depending on GNSS systems used): ∼ 600 perday (-)

• Poorspatialresolution(300 kmhorizontal) (-)

Figure 5.4: Basic principle of GNSS RO, Source: ECMWF

Nowadays GNSS RO is extensively used in forNWP andclimateresearch (Anthes 2011). Different scientific programslikethe COSMIC mission havebeen builtupinorder to es- tablish global data coverage. Furthermore many low-orbiting satellites originally launched forgravityfield observation likeCHAMP or GRACE havebeen used forRO(see e.g. Wickert et al. (2009)).

5.3 Estimation of tropospheric parameters using PPP

Tropospheric parametersare typically derived together withstation coordinates and the receiver clock error in GNSS analysis. The mathematicalmeans to carry outthis task willbeintroduced in Chapter 6,Section 6.3 in from of standard methods for parameter estimation. Nevertheless, it should already be noted here that estimated tropospheric parametersare typically strongly correlated with the other parameters estimated, especiallytothe height coordinate and thereceiver clock error. Timeseries of height andZTD typically showahighanti-correlationand therefore theirrespective estimation errors arealsodependent on each other. If ZTDs areestimated in GNSS analysis, the respectivestationsheight coordinates aredecreased by amagnitude of 5.3Estimation of tropospheric parameters usingPPP 51

3-3.5 × ZTD (Beutler etal. 1989). As shown in Beutler et al. (1989)orKrawinkel et al. (2014), thetransfer ratiobetween heightcoordinate andZTD residual is constant and corresponds to approximately -3:1. The exact ratio between heightand ZTD error is dependent on the elevation cut-off used in processing.The lowerthe cut-off elevation angle used in processing,the more efficiently ZTD canbedecorrelated fromthe height coordinate. Nevertheless, observations from such lowelevations areoften notavailable or significantly affected by multipath and therefore havetobeused withcaution,especially in kinematic scenarios.

Over the last yearsPPP is becoming an increasingly used technique fortropo- sphericparameter estimation. Although DD networksolutions arestill considered in alot of operationalprocessingatdifferentdata centers, anumber of authors have already shown promisingresultsfor PPP processing approaches. The analysis centers at GFZ and NGAA (GNSS AC collaboration between Chalmers Technical University and Swedish Meteorological andHydrological Institute) developedtheir owntechniques forproviding globalorbit andclock products in supportofPPP (Guerova et al. 2016). Tropospheric products derived from real-time PPP processing areofhigh interest for NWP models and fornowcasting of severe weather events (Guerovaetal. 2016). Simeonovetal. (2016)evaluatedIWV fromWRF with PPPresults over Bulgaria and found good agreement between thedatasets. Stepniakand Bock (2018)compared oneyearofGPS PPPand DD resultsinterms of ZTD and found that PPP processing might be abeneficialapproach compared to DD, especiallyinthe presence of outliers arising fromdefects in thebaseline geometry. In Austria, first studies were conducted by Karabatic (2011), who found slightly worse resultsfor ZWD fromPPP compared to those fromDDprocessing forasubset of stations of theEPOSA network. Nevertheless thepossible benefits of PPP processing likeshorter latency time could already be outlined by thestudy.Since then several research projects on similartopicswereconducted at the research division Higher Geodesy at TU Wien which indicated that shorter latency is often equally importantas highest precision,for typicalNWP applications. 52 GNSS Meteorology

5.3.1Kinematic platforms

This section is specifically devoted to GNSS Meteorology (i.e. ZTDestimation) in kinematic GNSS scenarioslikewhen utilizing air-orshipborne receiver data. Kinematic GNSS must deal with the dynamics of areceiver,and the problemofbeing unable to constrain the position solution to asingle location. This reduces the redundancy of the system and therefore tends to worsen the accuracy of the tropospheric estimates. Only very few studies havebeenconducted in this directionofresearch up till now. Rocken et al. (2005)used DD relativesolutionswith levered ZTDestimates, where ZTDatastaticreference site is fixed and only the difference of akinematic roverto thisreference is estimated. Shipborne studies were carried out by Dodson et al. (2001) and Kealy et al. (2012), using alevered approach to obtain an agreement of 1-2mmin ZTDand 2.2mminPWV. Chadwell and Bock (2001)processed anetwork-equivalent double-differenced ambiguity-fixed solution foraGPS buoy andobtained an agreement of 1.5 mm PWVwith radiosonde launches few kilometres away.

An extensionofthese studies to the railway domainand therefore to highly kine- matic conditions (up to 200km/h travelling speed) is carried out in this thesis,using specific processing(Chapter 6), validationand assimilation methods (Chapter 7). Chapter 6

GNSS data processing

The following section gives adetailed overviewofall processing steps carried out on the rawGNSS tracking-data.Therefore the chapter covers an introductiononthe utilized datasets, continueswith extensivepre-processing procedures,the actualPPP algorithm applied and finally discusses suitable post-processing strategies. For certain tasks (e.g. pre-processing)multiple approaches were tested andaquantitative evaluation of their weaknessesand strengths is provided.

6.1 Data sources

Thissection introduces the data utilized in GNSS processing within this study.This ranges fromthe actualGNSS measurements takenontrains to thereference station data andtrackdatabaseused forspecific processing strategies.

6.1.1 Greenlight

Greenlight is aproject by theAustrian Federal Railways(OBB¨ )which dealswith accurate trainpositioningtosupportanumber of applicationsfrom improvedpassenger informa- tion to security activities. Thebasicidea is to build and operate an integration platform (Greenlight gateway)for different OBB¨ systems established in-house. This providesthe chance of developing new functions fortrain positioning aswellasfor thein-house pas- senger information system (AURIS). Figure 6.1 gives an overview of the workflow and over all systems working together on the Greenlight gateway.The basic workflowcan be summarized as the following:

1. Observations from GNSS arerecorded by an antennainstalled on the top of train traction vehicles.

53 54 GNSS dataprocessing

2. From thecentral reference station database (TEPOS) correctiondataare broad- casted to the receiver.

3. RTK-Positions arecalculatedatthe receiverand position dataare broadcasted back to TEPOS viaGSM.

4. Positiondataare forwarded from TEPOS to theARAMIS (Advanced Rail- way Automation Management Information System)and AURIS (Automatisches Reisenden-Informationssystem) systems.

5. In the Greenlight gateway the position dataislinkedtodata from the route systems andthe raildatabase.This is complemented by additionaldatafor locations with lowornoreception.

Figure6.1: Overview of systems working together in Greenlight, courtestyofDI(FH) Manfred St¨a ttner, OB¨ BInfrastrucktur

In 2016inthe course of the Greenlightproject, OBB¨ startedtoequip theirfleet of trains with multi-GNSS receivers with the aimofonline-positioning. The receivers are capable of logging GPS and GLONASS L1 observationsatanupdate rate of 1Hz. The upcoming generationofreceiverswill be GPS and Galileo L1 capable and in futurealso DF capabilityiscontemplated.Today,morethan 1400 vehicles arealready equipped withsuch single-frequency receivers, providing decimetrelocalisation of the fast-moving traction vehiclesgained by RTK-positioning and referencing to the EPOSA correction service. In parallel, thereceivers also allow to store rawGNSS observation dataofall 6.1Datasources 55 train travels within aperiodofuptothree weeks. These data,acquired foranumber of days,formthe foundation of all results shown in thenext chapters.

6.1.2 Railway trackdatabase

Furthermore, OBB¨ generously providedacoordinate database fortwo of theinvestigated railway tracks (Salzburg-Klagenfurt/Innsbruck -Graz). In the first place, this data areusedfor quality checks of thePPP solutions in terms of positioning performance. Secondly,the height information from the databaseisutilizedfor aheight-constrained PPP approach (see Section 6.8 fordetailed information).

6.1.3 EPOSA

Datafrom the AustrianGNSS reference station networkEPOSAisutilized forcorrecting the train-tracking GNSS datafor ionosphericinfluence (using the SEIDalgorithm,see Section 6.4). Therefore ashort introduction to the networkand its characteristics is given in the following. The GNSS networkconsists of 38 stations, which aredistributed all over Austria

Figure 6.2: Reference station network of EPOSA. The colourofthe triangles denotesthe company operatingthe station. Takenfromhttp://www.eposa.at/

(Figure 6.2). EPOSA originated fromacooperation of different Austrian companies and startedoperating in autumnof2009.Maingoal is to provide GNSS users with real- time correction data, by using all available GNSS systems,athighest possible reliability and guaranteed quality. Thereference station network(Figure 6.2)was builtupin 56 GNSS dataprocessing consideration of several criteria likepresentinfrastructure, stabilityofreference points, distribution ofstationsand distances in between and obstructionfreehorizon. Every reference station is equipped with both aGPS and aGLONASS receiver (in afuture state also Galileo).The research divisionHigher Geodesy at the TU Vienna provides quality controlfor all stationdata on aregular basis. Furthermorethe network is utilized forestimation of troposphericparameterswhich aredeliveredtothe AustrianCentral Institute of Meteorology and Geodynamics (ZAMG) forassimilation intothe NWPmodel AROME.

6.2 Pre-Processing

Duetothe highlykinematic and multipath-pronenatureofthe utilized data, adata pre-processing is necessary before starting theactualestimation.Therefore, acycleslip correction is applied in order to correct phase measurements. Since different methods exist forthis task, aselectionof2-3 strategies will be investigated. Furthermore, the ionosphere has to be accounted forsince the observationsare only single-frequency.Here two different approaches will be implemented.The first oneuses existing ionospheric TEC models to calculaterange corrections forthe observations.Different models are availableatboth global andregionalscale. At the researchdivisionHigher Geodesy,the globalmodel GIOMO (Magnet 2019)and the regionalmodel Regiomontan (Boisits et al. 2020)are available.These models were notusedinthisstudy due to partlyexpensive implementationinthe utilized softwarepackagesbut might be in further studies on this topic. In the second approach, the utilized SF datawillbeextended to DF observations using the SEID algorithm in order to apply the ionospheric correction by building aIF-LC in the PPP processing later on.

6.2.1DilutionofPrecision

The geometry of the satellites (i.e. howthe user sees them) affectsthe positioning error (SanzSubirana et al.2013). This influence canbequantified by theso-calledDilution Of Precision (DOP) parameters. They aredefined as (e.g. Sanz Subirana et al. (2013)):

• Geometric Dilution Of Precision:

GDOP = qxx + qyy + qzz + qtt (6.1) 6.2Pre-Processing 57

• Position Dilution Of Precision: PDOP = qxx + qyy + qzz (6.2)

• Horizontal Dilution Of Precision: √ HDOP = qnn + qee (6.3)

• Vertical DilutionOfPrecision: √ VDOP = quu (6.4)

• Time Dilution Of Precision: √ TDOP = qtt (6.5) where qxx,qyy,qzz and qtt represent the diagonalentries of the cofactormatrix (see Section 6.3 fordetailed description) related to the 3D-coordinates in ageocentric earth- fixed frame (subscripts xx, yy and zz)aswell as the receiver clock error(subscript tt). On the other hand, HDOP andVDOP aredefined in alocal level frame and therefore qnn,qee and quu refer to thediagonalentries of the cofactor matrix related to the 3D- coordinates in thisrespectiveframe. GDOP is presentedtogether withthe number of visible satellites in the first analyses of the rawdata in Chapter 8.Bothparametershelp to quantify the environmental conditions along the investigated tracks in terms of satellite geometry. Thereforethey provideafirst indication ofthe resulting quality to be expected from PPP processing andhelp top identify possibly critical sections along the routes where results might be degraded or unreliable.

6.2.2 Multipath analysis

Train-borneGNSSreceiver observations aretypically multipath afflicted due to the per- manentlychanging and often challengingenvironment.Therefore amultipathanalysis wascarried out, in order to get an idea of the quality of theraw observationsand iden- tify particularly critical sections on the investigated tracks. The procedure chosen in the course of this studyuses the pseudo-multipath or Code-Minus-Carrier (CMC)observable:

CMCs = Ps − Ls (6.6) where P s and Ls denotecode/pseudorange and carrier phase measurements (in meter) from each satellite. It representsajudicious linearcombination of the GPS observables 58 GNSS dataprocessing

Method Accuracy Computational cost Additional requirements Phase-code affected by code noise lowno Phase-phase wavelengthdependent medium DF observations Doppler Integration affected by high dynamics lowno Inertialaided highmedium INS system (costs,quality, ...) Time-differencing proportional to order of time series highDFobservations in somecases Double-differencing varieswith algorithm complexity high no

Table 6.1: Overview on methodsfor cycle slipdetection (Farooq et al.2018). and produces an observable containing abiasedestimate of the pseudorangemultipath and afew small additional terms (Bisnath andLangley2001). Thepseudo-multipathobservable gives agood representation of code multipath, as the magnitude of the carrier-phase multipath in Equation 6.6 is much smaller than the corresponding pseudorange terms.

6.2.3Cycleslipdetection

A cycle slip denotes ajump in the accumulated carrier phase observation by an integer number of cycles.Its occurrence affects not only thecurrent measurement,but also the following epochs and therefore can substantially degrade positioning accuracy.

SF observations

Although generally considered difficult, cycle slip detectionand correction forsingle frequency receivers has recently received attention due to thelarge number of evolving applications for low-costmass-marketsingle frequency receivers. AccordingtoHofmann- Wellenhof et al. (2012), three sources of cycle slips can be identified:

1. Physical obstructions,blocking the signal,

2. Lowsignal to noise ratio,

3. Failureinthe receiver software.

Avarietyoftechniques forcycleslip detectionand correction exist forbothDFand SF observations. Farooq et al. (2018)giveagoodoverviewonthe current status of methodsfor SF dataand the categorisation in Table 6.1 is based on their explanations. In thisstudy,Doppler Integrationand the Time-differencing approach were testedfor pre-processing of rawtracking data. Doppler-Integrationwas foundunsuitablefor the testedcases sincethe receiver dynamics were toohigh at typical travelling speeds (mean around 100km/h). 6.3Parameter estimationinPPP processing 59

Althoughcomputationallyquite expensive (depending on theorder of differencing),time- difference-based approaches were found to be most useful forthe investigated SF data.

DF observations

For DF data likefrom theEPOSA stations or generated withthe SEID algorithm, phase- phase combinations likethe MW-LC(see Section 2.3.3)wereutilized. TheGF-LCcould also be used foridentifying cycle slips forreference station data. Based on computed values of these LCs, abnormallylarge valuesinepoch-differences areidentified as cycle slips and corrected or excluded fromprocessing (depending on the softwareimplemen- tation). Bothmethods aree.g. realized indifferent softwarepackageswhich were used forprocessing.

6.2.4 Data cleaning

Since the train data is pronetomultiple error sourcesoutlined above,aqualitycheck has to be carried out and faulty data has to be rejected in the best possibleway. This qualitycheck must also be appliedtothe DF reference station data. An important prerequisite forapplying SEIDsuccessfully to aSFstationistohave themostconsistent andclean reference station data possible. Therefore apre-processing of thisdata was carried out in order to detect outliers and cycle slips, which denote amajorerrorsource forSEID. This pre-processing is done using goGPS (HerreraOlmo et al. (2015)and Realini and Reguzzoni (2013)),anopen-source satellite positioning software package written in MATLAB.The methods describedabove were utilized forthisstep.

6.3 Parameter estimation in PPP processing

From the equations presented in Chapter 2,Section 2.3 the wanted set of parameters (typically 3D coordinates, receiverclock error and ZTD)can be derived. Since typically redundant observationsare available, an appropriate technique foranoptimal estimation of the parameter set has to be applied. Beside optimal resultsofthe unknown parameters, another huge benefit of such tech- niques is that additionally errorestimates forthese parameterscan be calculated by introducing astochasticmodel in the estimation. The errorestimates aretypically de- scribed by the covariance (orvariance-covariance) matrix of the respective parameters. Therefore thecalculation of the covariance matrix of the wanted parametersisalso in- 60 GNSS dataprocessing troduced forthe respectiveapproachespresentedinthe following. The two (most common) techniques forparameter estimationinGNSS processing are introduced in the following:

• Least Squares (LSQ) adjustment

• KalmanFiltering

6.3.1Least-squares adjustment

The most commontechnique forparameter estimation in GNSS positioning is theclas- sicalLSQ adjustment,which is stillutilized in anumber of GNSS softwarepackages nowadays.Inthis study,LSQ adjustment is used forparameter estimation within the CSRS-PPP (see Section 6.5)softwareand therefore the basic principle is introduced in the following. Using the notation of Hofmann-Wellenhofetal. (2012)and Magnet (2019), the basic functionalrelationship of LSQ reads:

L + v = φ(x) (6.7) where L([n × 1]) denotethe measured observations (with n being the number of obser- vations), v theerrorvectorand φ(x) the functionalrelation between the observations and the parameterstobeestimated. x = x0 + dx denotes the vectorofunknown parameterswith x0 being approximatevalues and dx the difference to their estimated values. Linearisation of Equation 6.7 gives

L + v = φ(x0)+Ax (6.8) with A being the design matrix,which contains the partial derivatives of φ(x) with respect to the unknown parameters ( ∂φ(x)). Equation 6.8 cannow be solved for v, ∂x resulting in:

v = Ax − (L − φ(x0)) = Ax − l (6.9) with l = L − φ(x0) being the difference between measured and computed observations, the so-called residuals. In the generalleastsquares approach all measurementsare given thesameweight,not considering a-priori qualityinformation forthe observations which might be available. Thisisgenerallynot suitable forareal-world scenario where notall themeasurements willhaveequal qualityand therefore equal error.Inordertocopewiththisproblem, and 6.3Parameter estimationinPPP processing 61 to furthermore get an errorestimation forthe unknown parameters, astochastic model is employedbyintroducing the weighting matrix P :

−1 2 −1 P = Qll = σ0Σll (6.10) where Qll denotes thecofactormatrix, σ0 the a-priori variance factor and Σll the covariance matrix. Differentmeasurement weighting schemes havebeen introduced in GNSS processing over the yearslikee.g.

• Elevationangle: measurementsatlow elevationtend to havelargermultipathand atmospheric delayerrors than measurementsathigh elevation

• Signal-to-noise (SNR) ratio: decreased SNR servesasanindicator fore.g.high multipath activity, which canbeappliedtofind an appropriate formulationofthe weighting matrix.

The actual(weighted) LSQ solution is foundbyaminimization of the term:

vT Pv =(xTAT −lT)P(Ax − l)=xTATPAx−xTATPl−lTPAx+lTPl, (6.11) which is achieved by calculating the first derivativewith respect to x andsetting it to zero: ∂vT Pv =2ATPAx−2ATPl=0 (6.12) ∂x This results in the normal equation:

(AT PA)x−ATPl=Nx−b (6.13) with N = AT PA being the normalequation matrix and b = AT Pl.IfNis regular (i.e.invertible),solving for x givesthe unknown parameter vectoras:

x =(ATPA)−1ATPl=N−1b (6.14)

An estimation of theaccuracyofthe derived parameterscan be found via their variance- covariance matrix which is derived by inversion of the normal-equationmatrix:

−1 Qxx = N (6.15)

Thereby theactual co-factors of theestimated parametersare foundonthe diagonal of

Qxx. 62 GNSS dataprocessing

In theconceptofsequential LSQ (as utilized in the CSRS-PPP package, see Section 6.5), theestimated parameter vectorserves an a-priori estimation of the unknown parameter vectorinthe nexttimestep. The same holds forthe stochastic model of thisapproachasthe variance-covariance matrixofthe last timestep can be utilized as a-priori information in the next timestep.

6.3.2Kalman Filtering

Another popularalgorithm forparameter estimationisthe KalmanFilter which wasde- veloped by Kalman (1960). It is widely used in signal processing, navigation, geosciences and numerousother scientificareas nowadays. Since it is alsoheavilyusedinthis thesis, amoredetailed description than forLSQ is giveninthe following. In ageneral mathematicalsense the algorithm belongs to aclass of Bayesian estimation techniques, the Minimum Mean Square Error (MMSE) estimators. In more detail, it de- notes the combinationofsequentialLinearMMSE(LMMSE) estimation withaso-called state-space model. This model accounts forthe dynamic evolutionofthe system over time, which is akey difference/advantage compared to classicalLSQ estimation. An observedset ofparametersatapoint in time n(the state vector)thereforeisdefined recursively by its priorstateatn−1and new observationscomingin. The formulation of the Kalman filter algorithm outlined in the following is based on Hlawatsch (2019). Thefollowing equations define this state-space model forthe Kalman filter algorithm:

y[n]=Hx[n]+ωn (6.16) x[n]=Ax[n − 1] + Bu[n], (6.17) where y[n] denote themeasured data(observations), x[n] thestate vectorattime n (orn-1 respectively), H the design matrix, A thetransitionmatrix, B the control-input model matrix, u[n] the control vector and ωn the observationnoise. The algorithm is asequential combination of aprediction and acorrectionstepfor the state vectorand the error covariance matrix.Written down the formalism looks like:

x[n|n − 1] = Ax[n − 1|n − 1] (6.18)

T T Ce[n|n − 1] = ACe[n − 1|n − 1]A + BQ B (6.19) T T −1 K[n]=Ce[n|n−1]Hn (HnCe[n|n − 1]Hn Cωn ) (6.20)

x[n|n]=x[n|n−1] + K[n](xn − Hnx[n|n − 1]) (6.21)

Ce[n|n]=(I−K[n]Hn)Ce[n|n−1] (6.22) 6.4SEID 63 where [n|n−1] denotes the index of aprediction and [n|n] the indexofacorrection step.

Ce the error covariance matrix of theestimated parameters, Q the covariance/correlation matrix of the control-input and I the identitymatrix. K denotes the Kalman gain matrix which represents the keyfeatureofthe Kalmanfilter determining the correction step for the predicted parameters, based on the qualityofthe estimations (Ce[n|n − 1])and of the incomingdata (Cωn ). Thepresented algorithmcan be extended foranumber of other common features like coloured observationnoiseorthe implementationofanon-linear state-space model, which is typically used in GNSS processing (e.g. in the GAMP softwareused in this study,see Section 6.7)and known as the Extended Kalman Filter (EKF).

6.4 SEID

As already mentioned before, the ionospheric delayonGNSS signals tracked by aSFre- ceiver cannotbeeliminated by forming linear combinations. Apossible solution therefore is to correct forthe ionospheric delayusing TEC grids from global or regional ionosphere models.Then corrections can be applied to pseudorange and phase observations using formulas 4.16. As an alternative to this approach, theSatellite-specific Epoch-differenced Ionospheric Delaymodel (SEID)was developed by Deng et al. (2009)atGeoForschungsZentrum

(GFZ) Potsdam.Itisbased on thegeometry-free LC L4,the so-called ionospheric observation

L4 = L1 − L2, (6.23) whichcorresponds to the phase observation difference between L1 and L2 mainly gov- erned by theionosphericrefraction.

Unfortunately this L4 quantity has the major drawback of still containing the phase am- biguityparameter.Inorder to get rid of it,the algorithm usesepoch-differences of L4,

δL4.For two consecutivetime steps i and i +1this quantityreads

δL4(i)=L4(i+1)−L4(i). (6.24)

Theionosphericlayer is represented by asinglelayer model, e.g. athin shell withan altitudeofabout 300 km aboveEarth’s surface.The spatial change of the delayisthen expressed by thepositions of theintercept pierce points(IPP) of thesignal pathand the layer(Deng et al. 2009). Thebasicassumption nowisthatthisepoch-difference of aspecific satellite, derived from DF stations,can be fitted to alinearfunction, e.g., a 64 GNSS dataprocessing plane. Using thenotation of Deng et al. (2009)this linearfitreads

δL4 = α0 + α1λ + α2θ, (6.25)

where θ is the latitude and λ thelongitude of their IPPs and α0,α1 and α2 arethe model parameterstobedetermined. From Equation 6.25 it is obvious that aminimum of three referencestationsisrequired to derive thosemodel parameters.Ingeneral ahigher number of stations is beneficial to derivemoreaccurate resultsand deal withpossibledata gaps at certain stations. In the case offour or more reference stations theparametersare estimatedbymeans of aleast-squares adjustmentfor each satellite at each epoch. This resultsinadifferent plane modelfor each satellite-epochcombination, which givesahint on the highcom- putationaldemandofthe approach forlarger datasets.

Figure 6.3: δL4 values[m] foranexampleepoch andall GPS satellites processedwithin the SEIDmodel.Larger valuesindicate possible outliers or cycle slipsinthe dataofthe respective satellite(e.g. G32 here).

Analysing the magnitudes of the computed δL4 values, as shown in Figure 6.3,can be beneficialfor detection of outliers and cycle slips affecting the utilized satellites at each epoch. In the processing carried out in thisstudy athresholdof±0.5 misapplied for δL4.Ifthis threshold is exceeded, thecorresponding satellite is excludedfrom the further processing. 6.4SEID 65

Using the generated model parameters at epochi,the epoch-differenced ionospheric cor- rection of any SF receiver inside the reference networkcan be calculated. The correction ˜ foraspecific epoch k, L4(i0,k),isthe sum of the epoch-differenced corrections from thefirst epoch i0 on, k−1 ˜ ˜ L4(i0,k)= δL4(i, i +1). (6.26)

i=i0 ˜ By meansofthisquantity, aconverted L2 observation(L2)can be derived using

˜ ˜ L2(k)=L1(k)−L4(i0,k). (6.27)

This basicallyrepresents the L1 observationwith theionospheric delay adjustedtoL2.

Althoughtheyare usuallysignificantly down-weighted or not used at allinPPP processing, pseudorange observations canbetreatedusing thesame procedure. The main difference to phase observations is the fact that here it is no longer necessary to operate with epoch-differences since no ambiguityparameter is present. Beside this the model is establishedinasimilarway as forthe carrier-phase,

P4 = β0 + β1λ + β2θ, (6.28) where β0,β1 and β2 arethe model parameters. P2 is then calculated by

P2 = P1 + P4 (6.29)

Theoriginal SF RINEX file is then extended by theconverted L2 and P2 observations andcan be used forDFprocessing in asoftware package of choice.

6.4.1 AccuracyofSEID model

Althoughadetailed accuracyanalysis of the ionospheric corrections providedbythe approach wasnot carriedout, the most importantfindings from Deng et al. (2009)are summarized here. ˜ Deng et al. (2009)analyzedthe accuracy of both theionosphericcorrections L4 and theSTECvalues derivedusingthe SEID model. Therefore four reference stations were utilized,three of themfor the computation of themodel parametersand one of them ˜ wasassumed to be aSFstation. The interpolated L4 wascompared to computations of the GF-LC at thisparticularreference station.Denoting the standard deviation ofthe ˜ interpolated L values as σ ˜ and the standard deviation of the GF-LC values as σ , 4 L4 L4 thefollowing conclusions could be drawnfrom these comparisons (Deng et al. 2009): 66 GNSS dataprocessing

• If the SF station is located inside atriangle builtupofthe three reference stations, √ σ ˜ has avalue between σ · 2/3 and σ · 2.E.g. a σ =3.3 mm gives a L4 L4 L4 L4 σ ˜ =2.7 -4.7 mm. L4 • TheinterpolationerrorinSTEC values derivedwith SEID equates to ∼±1mm under average ionosphericconditions.

• Underabnormalionosphericactivitythe STEC interpolationerrorisincreased up to ∼±4mm at lowelevations.

Although still problemsfor describing sudden abnormaloscillations in ionospheric con- ditions exist,the results under average conditions indicate good performance of the approach and suitabilityofstudies using SF GNSS likethis one here. Nevertheless the high travelling speeds of the trains analysed heremakesomeadaptations necessary which aredescribed in the following section.

6.4.2Kinematic implementation

Due to the highly kinematic natureofthe train tracking data,SEID has to be executed in kinematic mode. Thereforeafew adaptations have to be applied to thealgorithm, the most importantones arelisted below:

• Nearest reference stationschangewiththe trains movement, thereforethe list of used stations has to be updated in an appropriatetime step (e.g.one hour)

• IPPsofDFand SF stationschange with time/movement and havetobeadjusted (more frequentlythan in astatic scenario)

• Adoption of aweighting scheme based on the euclideandistance between train/receiverand reference station (the closer the reference station the larger the weight)

6.5 Processing scheme:CSRS

The CSRS-PPPonline softwarewas used to gain afirst solutionfor thechosen days. The following information is based on T´etreault et al. (2005), who giveadetailed overview of the softwarepackage.Here, only some importantcornerstones and aspects of func- tionalityand usage areoutlined. The online service forGPS userswas introducedin2003 by theGeodetic SurveyDivision of Natural Resources Canadaand facilitates access to the Canadian Spatial Reference 6.6Processing scheme:PPP-Wizard 67

System(CSRS).CSRS-PPPprocesses GPS observations from single or dual-frequency GPS receivers operating in static or kinematic mode (T´etreault et al. 2005). User po- sitionsare estimatedbasedonsatellite orbits established in the InternationalTerrestrial Reference Frame(ITRF). Theuser online serviceofCSRS only needsRINEX dataand areference e-mail address as input. Positioning mode then can be chosen between static and kinematicand the reference frame forthe output coordinates has to be selected (e.g.ITRF).Additionally an OceanTidal Loading (OTL)file can be introduced. Results arethen returned to the givenemailaddress in formoftext files containing positionand ZTD estimates as well as theiruncertainties. The service wasused to estimate position and ZTDfrom Greenlight RINEX datafor the chosen days. The main processing/setup options canbefound in Table 6.2.

Feature Functional model Undifferenced/Uncombined Measurements Code,Phase Constellations GPS, Glonass Frequency Single, Dual Orbits/Clocks IGS Ionosphere GIM Troposphere VMF1 Phase-Wind-Up Corrected Relativistic effects 2ndorder correctiononclocks, gravitational time delay

Table 6.2: Default settings andfeatures forthe CSRS-PPP package.

6.6 Processing scheme: PPP-Wizard

Another suitable PPPsoftwareused in this research is the Precise Point Positioning WithInteger and Zero-difference AmbiguityResolutionDemonstrator (PPP-Wizard). Thesoftwarewas developedatCentreNational d’Etudes Spatiales(CNES) and aims at providingzero-difference AR for(RT-) PPP. Detailed information on the packagecan be found in Laurichesse andPrivat (2015). Themainprocessing/setup optionsare outlined in Table 6.3.Amain advantage of PPP- Wizardisthe fact that SF dataaswell as (SEID-generated)DFdata can be processed in astraightforwardway.Furthermore thedelivered package contains not only executables 68 GNSS dataprocessing

Feature Functional model Undifferenced/Uncombined Measurements Code,Phase,Doppler Constellations GPS, Glonass fornow,ongoing Galileo and Beidou Frequency Single,Dual, Triple Orbits/Clocks EGNOS or IGS Ionosphere EGNOS (SF) /IF-LC (DF) Troposphere Saastamoinen Phase-Wind-Up Corrected Relativistic effects 2nd order correctiononclocks, gravitational time delay

Table 6.3: Defaultsettings andfeatures forthe PPP-Wizard software. but afully-portable C++library which could be extended in the course of further research on this topic.

6.7 Processing scheme:GAMP using SEID

In order to gain yetanother independent solution to compare with CSRS-PPPand PPP- Wizard, acombination of different software packagesand algorithms wasapplied. The basic idea behind thisapproach is to generate aDFRINEX file out of the givenSFfile using the SEID model, describedinSection 6.4.The generated DF observations are thenprocessed in kinematic PPPmodeusing the GAMP software(Zhou et al. 2018). Emphasizing the combination ofthe SEID algorithmwiththe GAMP software forPPP processing, the approach is referred to as SGAMP in the following. The concreteflow chart of the approach is shown in Figure 6.4.The mainprocessing steps arethe following:

1. Download suitable DF reference station data fromthe EPOSAnetwork

2. Pre-process DF reference station data using goGPS

3. Apply SEID in kinematic mode to the SF datausing the5-6 nearest reference stations

4. Process the generated DF observationsinkinematic PPP mode using GAMP

The entire algorithm wasimplemented in Python. Here the Georinex package (https://pypi.org/project/georinex/) wasusedfor easy reading of RINEX data. Param- eterestimationwas carried outwith thescipypackage(Virtanen et al.2020). Further 6.8Processing scheme:Height-constrained PPP 69

Figure 6.4: Flowchart of the SGAMP processing scheme as followedinthis study. details on the concrete implementation of the SEID model (e.g. chosen stations) are given in Section 8.3,where resultsofthe test case arepresented.

6.7.1 GAMP

The PPP softwareusedfor theSGAMP processingscheme wasthe GAMP software (Zhou et al.2018), an open-source package developedatGFZ. It is capable of carrying outmulti-GNSS PPP based on undifferenced and uncombined observations. The soft- wareisasecondary development which is based on RTKlib (Takasu and Yasuda 2009), but withmanyimprovements in terms of cycle slipdetection, receiverclock jumpre- pair,orhandlingofGLONASSpseudorangeinter-frequency biases.Anoverview of the processing capabilities of GAMP aregiven in Table 6.4.

6.8 Processing scheme: Height-constrained PPP

Parameter constraintshavebeenextensively used in GNSS processing (e.g. Xu (2016), Suya (2019), Gao et al. (2017)) as well as sensorfusion algorithms (Huang et al. (2018), Zhu et al. (2020)).Even thecaseofstaticPPP processing representsaconstrained so- lution as the coordinate solution is to some degree constrained to astationary site. In this study,atightconstraint on theestimated height coordinate is used to supportthe 70 GNSS dataprocessing

Feature Functional model Undifferenced/Uncombined Measurements Code,Phase Constellations GPS,Glonass, Galileo and Beidou Frequency Single, Dual Orbits/Clocks Final/rapid/ultra-rapid Ionosphere IF-LC (dual)orIono-model Troposphere NMF or GMF Phase-Wind-Up Corrected Relativistic effects 2nd order correction on clocks, gravitational time delay

Table 6.4: Defaultsettings andfeatures forthe GAMP PPPsoftware.

tropospheric estimation. The idea behind this approach is to achieve significantdecor- relation between ZTD and height estimates by using precise height information from aGNSS-independent source. Therefore heightsfrom an existing database of railway tracks alloverAustria,established by classicalsurveying methods(e.g. levelling), are used here. The database wasthankfully provided by OBB¨ .For more detailed information concerning this dataset see Section 6.1.2.Inthe following the actual implementation of the height-constraint is shortly introduced. The basicprocedure is just asimple correction of the height estimateinthe Kalman Fil- ter,byusing the height provided at thenearestpoint in the track database. Thisnearest point is determined by searching the closest point in the database to the state estimate of the 2D-coordinates (prediction step in the filter), based on euclideandistance. Additionally,aheight offset has to be applied since the coordinates of the database pointsdonot refertothe GNSSantenna but to (reference-) pylons along the railway tracks. Since no concrete values forthisoffsetwereavailable,one can either use the pylon heightsdirectly (this will result in amoreloosely constraint) or set adefault value. The latterapproach wascarried out here with adefault offset determined by using the median of calculated deviation between GNSS heights fromCSRS-PPP(lowest noise of allPPP solutions, seeChapter 8 fordetailed results) and pylons forthree of the four testcases(where trackdatabasewas available). This equates to an offset of ∼ 4 meters which wasapplied to the database heights. Moreover one candecidewhen to apply the correction: (1)alwaysor(2) basedonanac- curacy criterionrelativetothe track database. In this study,the correction/replacement 6.9Filteringmethodsand performancemetrics 71 of the height estimateisapplied when thefollowing condition is met:

|HGNSS − (HRDB + dH)| > 0.1m (6.30)

where HGNSS and HRDB arethe ellipsoidal heights fromGNSS and the track database respectively and dH is the applied offset between pylon and antenna.

6.9 Filtering methods andperformancemetrics

Despite the usage of an appropriate parameter estimation method(e.g. KalmanFilter or LSQ) ,the PPP solution can showaquite large amount of noise in the estimates. This is present especially within the convergence time of thefiltersinthe beginning of processing or afterdata gapswhere the solutionwas lost. In order to remove this noise andalsoquantify its magnitude, afiltering (i.e. asmoothing)ofthe parameter estimates is carried out. Additionally some commonstatistical measures, which areused to describethe results shown in Chapter 8,are presented. They serveasperformance indicators in caseof the noise level analysis of the PPP solutionsand the validation of ZTD solutions(as described in Chapter 7). Furthermore it should be noted herethat foreveryparameter estimation (i.e.PPP pro- cessing) errorestimates areavailablefrom the covariance matrix (asdetailedinSection 6.3). However,these formal errorsare often much toooptimistic when compared to results of avalidation using independent referencedata.Moreover, some PPP software packages (asCSRS-PPPorGAMP in this case) do not even provide such formal errors forZTD estimates. Therefore adetailed analysis of these formalerrors wasomitted and instead only comparisons with smoothed solutions (fornoiseanalysis/filtering) and reference datasets (ZTDderived fromERA5) arepresented forthis study.

6.9.1 Movingaverage filtering

The Moving Average (MA) filter is asimple LowPass FIR(FiniteImpulse Response) filter which is commonlyused forsmoothing timeseries of sampled data. It takes afinite number of samples (denotes as N here) of input at atime and takesthe average of those N-samples and produces asingle output point. This denotes avery simple LPF (LowPassFilter)structuretofilter unwanted noisycomponents from the analysed data. As the filter lengthincreases (the parameter N)the smoothness of the output increases, whereas the sharp transitions in the dataare made increasingly blunt. This implies that 72 GNSS dataprocessing thisfilter has excellent time domain response but apoorfrequency response. Important featuresofthe MA filter can be summarized as follows

• Thealgorithm computes the average of N-pointsand produces asingle output point

• Due to the computation/calculations involved, thefilter introduces adefinite amount of delay(N/2)

• Thefilter actsasaLowPassFilter (with poor frequency domainresponseand a good time domain response).

The mathematical formulation of a N-point discrete-time moving average filter with input represented by thevectorxand the averaged outputvectorreads

1 N−1 y[n]= x[n − k] (6.31) N k=0

As already indicated above, thiscalculation introduces adelayofN/2 in the timeseries which has to be accounted for. In the results shown later,atime shiftbyN/2 is carried out in ordertoget afiltered estimation of the right (corresponding)timeseries entry.

6.9.2Errormetrics forperformance evaluation

This section introduces the utilized statistical measures forthe quality assess- ment/validation and of theconducted case studies shown in the nextchapters. All measures shown hereare well-known and frequentlyusedingeosciences, therefore only a short description and analysis of advantages/disadvantagesisgiven here.For detailed in- formation onproperties, performance features and other feasible measures, Wilks (2011) provides an extensivediscussion. In the following five basic scalarmeasures of accuracy,used in thisstudy,are introduced. Although manymoreare available,all validation results(seeChapter 8)are expressed in terms of those due to reasons likeeasyunderstandingand implementation.

1. BIAS: 1 n BIAS = · y − r (6.32) n k k k=1 The Bias(or Mean Error)isgiven as the mean difference between the observed

(yk)and reference values (rk)ofatimeseries. Its unit is the same as forthe analysedparameters. 6.9Filteringmethodsand performancemetrics 73

2. Standard deviation:The standard deviation of atime series y is defined as the square root of its variance: 1 n σ = (y − y¯)2 (6.33) n − 1 k k=1

3. Root Mean Square Error:The Root MeanSquare Error(RMSE) denotes the square root of the Mean Squared Error (MSE), which is theaverage squared difference betweenthe reference and observationpairs: √ 1 n RMSE = MSE = · (y − r )2 (6.34) n k k k=1

4. Median:The Medianisdefined as the mid-element of amonotonicallyincreasing time series and represents the value separating the higher half from the lowerhalf of adatasample. Main advantage of the median compared to thearithmeticmean is its robustness to outliers in thedataset. n +1 median = y( ) (6.35) odd 2 y( n )+y(n +1) median = 2 2 (6.36) even 2

5. Pearsoncorrelation coefficient:The Pearson correlationcoefficient R canbe calculated as: Cov(X, Y ) R(X, Y )= , (6.37) Var(X) Var(Y) where X and Y arerandom variables.Itisaunitless quantityand takesvalues from -1 to +1. 74 GNSS dataprocessing Chapter 7

ZTDvalidation and assimilation

The quality of ZTD estimationsderived using the GNSS processing strategies outlined in Chapter 6 needs to be assessedusing independent data.This can be achieved by a comparisontodifferent datasets, including:

• ZTD calculated from NWP forecast/analysis fields

• ZTD calculated from reanalysis products

This studyutilizesthe latter methodtoget afirst quality estimation forthe derived ZTD results. The following chapter is structured as follows:

At first it introduces the independent datasourcesand themethodologybehind the ZTD calculation from these data. Results of these comparisons forall test cases areshown in Chapter 8.

Secondly,anintroduction to the basicprincipleofDAisgiven, andsome of the most prominent techniques forDA, likedifferent variationalmethods, areintroduced. Afterwards, the currentstate-of-the-art of assimilationofGNSS data in NWP is analysed. Finallythe proposed approach forDAwithin thisstudy is presented, introducing the utilized model, the techniques used and the methods forverificationofthe results.

75 76 ZTDvalidationand assimilation

Reanalysis Periodcovered Grid resolution Assimilation scheme IFS model cycle (year) FGGE 1979 208 km OI (1980) ERA-15 1979-1994 125 km OI 13r4(1995) ERA-40 1957-2002125 km 3D-Var 23r4 (2001) ERA-Interim 1979-201980km4D-Var31r2(2006) ERA5 1950-present 31 km 4D-Var 41r2 (2016)

Table 7.1: Detailed information on theproductline of reanalyses produced by ECMWF.

7.1 Validation using ERA5 reanalysisproducts

The validation of GNSS-ZTDestimates is carried out using the ERA5 reanalysis dataset (Hersbach et al.2020), provided by theEuropean Centre forMedium-Range Weather Forecasts(ECMWF). This sectionprovides some basic details on thedataset and the methods utilized to deriveZTD referencevalues from it. Most information is basedon Hersbach et al. (2020), whoprovide adetailed descriptionofthe products available and the methodology of its production.

7.1.1ERA5

The ERA5 reanalysis is thenewest product of the ERA family produced by ECMWF. This new reanalysis replaced the ERA-Interim reanalysis (spanning 1979onwards) which was initiated in 2006. ERA5 is based on the Integrated Forecasting System (IFS) Cy41r2 which wasoperational in 2016(Hersbach et al. 2020).The dataset provides hourly estimatesofalargenumberofatmospheric, land, and oceanic climate variables.The data is providedat30kmhorizontal resolution and 37 vertical levels from the surface up to aheight of 80 km. The first parts ofthe ERA5 dataset areavailable forpublicuse (1979towithin 5days of real time)since 2019. In its final state, the ERA5 reanalysis will represent adetailed record of the global atmosphere, land surface and ocean from 1950till today. Compared to its predecessorERA-Interim,asignificantlyenhanced horizontalresolution of 31 km (compared to 80 km forERA-Interim) is available forERA5 (see alsoTable 7.1). An example visualisation of 2m-temperature ERA5 datafor January2016 is shown in Figure 7.1. 7.1Validation usingERA5 reanalysis products 77

7.1.2 ZTD calculation from ERAfields

TheZTD calculation from theERA5 reanalysis fields follows the approach of Wilgan andGeiger (2018), who used temperature, pressure and specific humidityfields from the NWM COSMO-1, whichisthe operational NWM at MeteoSwiss, specifically designed to produce the weatherforecast in the challenging Alpine region (MeteoSwiss 2020). The approach uses the formulation of Essen and Froome (1951)for thetotal refractivity p e e N = k − k + k , (7.1) tot 1 T 2 T 3 T 2 where p denotes pressure, T thetemperature, e the partialwatervapourpressure and −1 −1 −1 k1 =77.689KhPa , k2 =71.2952KhPa and k3 =375463KhPa the optimal averagerefractivitycoefficients from R¨ueger (2002), empirically determined forthe L-bandfrequencies.

Corresponding ERA fields forpressure,temperatureand specific humid- ity(whichallows forcomputation of e,see Chapter 3)are obtained from https://cds.climate.copernicus.eu/.This way 4D fieldsofrefractivityare computed which allow forthe computationofZTDsthroughvertical integration, as shown in Equation 7.2. −6 ZTDERA =10 · Ntot, (7.2) where ZTDERA representsthe resulting3DZTD field and Ntot the4Drefractivity field calculated from ERA5 fields using Equation 7.1. In the case of discrete dataasgiven here forERA5, Equation 7.2 can be approximated by Equation 7.3: NL−1 N + N ZTD =10−6· i i+1 · δs , (7.3) ERA 2 i i=1 where Ni representsthe total refractivityatthe i-th vertical level,NL is thenumber of verticallevels of ERA5 and δsi representsthe geometric distance between i-th and (i+1)-th layer. Furthermore the delayatthe top level NL is derived using Equation 7.4 (Saastamoinen 1972): 1255 ZTDNL =0.002277 · (pNL +( +0.05) · eNL), (7.4) TNL where pNL, TNL and eNL represent therespectiveparametersatthe highest vertical levelofERA5. The total ZTD is then givenbyEquation 7.5:

ZTDtotal = ZTDERA + ZTDNL. (7.5) 78 ZTDvalidationand assimilation

The actual ZTD value foragiven point on thetrain-trajectory is foundvia linearinter- polation of the 3D ZTDtotal field.

7.1.3Quality of ERA5-derived ZTD

Since ERA5 is one of thenewest atmosphericreanalyses, not manystudies have alreadyassessed the qualityofZTD valuescalculatedfrom its data. Validation of temperature, windand humiditydatabefore theactual releaseofERA5 already indicate increased performancesince comparisons withradiosonde showanimproved fit for those parameters, at least in the troposphere(Hersbach et al. 2020). First assessmentsofZTD were presented by Jiang et al. (2020), whoevaluatedthe performance of ERA5-derived ZTD againstGNSS-ZTDover China using data from 219GNSSstationsfor theperiod2015to2016.They found an average biasand RMS between ERA5-ZTDand GNSS of 2.97 mm and 11.49mm, respectively. Ssenyunzi et al. (2020)investigated the performance of ERA5 forretrieval of PWV over theEast African tropical region and found RMS errorsbetween GNSS- and ERA5-derived PWV valuesare in the range of 1.35 mm to 2.25 mm withthe overall average value of 1.66 mm. Overall, these studies indicate comparable resultsfor GNSS and ERA5 regarding the investigated quantities. Moreover the ZTD/PWVestimatesfrom GNSS used in thestudies mentioned abovewere derived fromhigh-qualityDFGNSS data. This encourages the use of ERA5 as thereference data source forthe performance assessment of SF GNSS-ZTDestimates as carried out in thisstudy.

Nevertheless it should be mentioned here thatNWP-deriveddata likethe ERA5 reanalysis areanindependent source of ZTD, which implies that consistency with GNSS-derivedZTD cannotalwaysbeexpected. In particular, station and NWP-specific biases can occur,which arejustified by adeficiency of the NWP orographyrepresenta- tion (Kaˇc maˇr ´ı ketal. 2017). Therefore, when comparing GNSS ZTDtoNWP model products, abias should not be considered as aqualityindicator,because station-specific GNSS ZTD biases areremoved priortoZTD assimilation (Mile et al. 2019). 7.1Validation usingERA5 reanalysis products 79

Figure7.1: ERA5 global gridof2m-temperature forJanuary2016. Top: full reanalysis, bottom: ERA5-Landreanalysis. Takenfrom: https://climate.copernicus.eu/climate-reanalysis 80 ZTDvalidationand assimilation

7.2 Basics of data assimilation

NWP denotesaninitial value problemand therefore strongly relies on the quality of the initial modelstate.The process of acquiring the best possible initialstateiscalleddata assimilation.The current sectionprovidesasmalloverview of DA concepts and methods as implemented in NWP models. In astrictly mathematical sense DA denotes the process of obtaining the statistically best combination between model state and the available observationsatacertain period of time. This includes consideringthe uncertaintyofboth observationsand model predictions in the process. Common techniques to achievethis arevariationalmethods like3D- or 4D-Var,different typesofKalman Filtering or nudging.For most cases, like the variational methods, this best initial state is derived by acombination of observations with amodel field of the observed variable, just before thestart ofthe next forecast run. Thisprinciple is indicated in Figure 7.2 fora24-hour assimilationwindow. The

Figure7.2: The basic principle of DA and its main components outlined forthe temperature (T, y-axis) parameterand a24-hour assimilation window (x-axis): background forecast (blue), observations (green)and analysis (red). model field denotes ashort-termforecastfrom theprevious forecastcyclewhich is called first guess or background forecast.Based on modeland observation errorestimates the so-called analysis is calculated, which servesasthe initial state forthe next forecast step. The optimal analysis is obtained by minimizing acost function measuring the misfit 7.2Basics of data assimilation 81 between observation and prediction by anon-linearmodel, which hasthe basic form shown in Equation 7.6 1 J(x) =(x−x)TB−1(x−x )+ (H[x]−yT)R−1(H[x]−y). (7.6) b b 2

In theabove equation, x representsthe analysis vector(the initial atmosphericstate), xb the forecast background vectorand y theobservationvector. H denotes the observation operatortransforming model variables into observation space. R denotesthe observation error covariance matrix and B the background errorcovariance matrixwhich contain information about the errorsinthe observations and the background field andtheir respectivecorrelations. Thenext section introduces some prominent DA techniques which arebasedonEquation 7.6.

7.2.1 DA techniques

The most common analysis methods used by current NWM include:

• Variational methods (3D-Var and4D-Var)

• Ensemble KalmanFilter (EnKF)

Typicalimplementations of variationalmethods rely on single deterministic forecasts. In contrast to this, theEnKF uses an ensemble approach to evaluateand apply assimilation increments. Major advantagesofthis technique include ease of implementation (unlike 4D-Var,EnKF does not require an adjoint model) and the generationofuseful estimates of analysis uncertainties, which aredifficult to obtain when using variationaltechniques with singleforecasts(Fujiwaraetal. 2017). Aconceptualoverviewofthe most prominent methodsisgiveninFigure 7.3. 82 ZTDvalidationand assimilation

Figure 7.3: Simplified schematicrepresentations of fourdata assimilation strategies frequently-usedinNWP:(a) 3D-Var,(b) 3D-FGAT,(c) incremental 4D-Var,and (d) EnKF. Blue circles representobservations, redlines representmodel trajectories, and purple diamonds indi- cateanalyses. The dotted red lines in(b)represent linearly interpolatedorextrapolated forecast valuesused to estimate increments at observation times.The dashed red linesin(c)represent theinitial forecast, priortoiterative adjustments.These illustrations areconceptual anddo not accurately reflect themuch more complexstrategies used by reanalysis systems.Taken from Fujiwaraetal. (2017) 7.3Assimilation of GNSS data in NWP 83

7.3 AssimilationofGNSSdata in NWP

Thefollowing section introduces the current state-of-the-artand developmentsinthe field of GNSS DA in NWP.Alot of information presented here wasalready outlined in Aichinger-Rosenberger (2018).

Nowadays ZTDassimilation is possible forall operational models in Europe,with the exception of COSMO, whichuses the related measureintegrated water vapour (IWV). Theusage of GNSS forinvestigation on the watervapour field has been the topic of several studies over the last couple of years. Different weather phenomena havebeeninvestigated, focusing on short-termforecastsand severe events. Anumber of authors studied the relationshipbetween the watervapour field and the life cy- cle/intensityofprecipitation systems (Guerova et al.2016). Yanetal. (2009)showed that the assimilation of ZTD datainthe AROME modelinduces changes in the vertical structureoflow-to-middle tropospheric watervapour.These changes areconsistent with measurementsfrom radiosondeand airbornelidar. Seco et al. (2012)found a relationship between IWV (orrather ZTD)and precipitation intensityinthe north of Spain during theperiod 2002-2010. Furthermore evidence that watervapour playsa keypartasprecursor in the initiationoflocal convectionwas found by van Baelen et al. (2011). Graham et al. (2012)showedthat the large transfer of watervapour amount (e.g. between amountainous area and the flatland) in convective systems initiated by orographycan be detected in IWV/ ZTD. The link between the moisture field and lightning and thunderstorm activitywas established by de Haan (2008). This wasused by Brenotetal. (2013)toidentify conditions fordeep convection and provide anowcasting warning system. 84 ZTDvalidationand assimilation

7.4 Assimilationand verification methodology

This following sectiondescribes the assimilation and verification approachused within thisstudy.Due to the special nature of the GNSS dataand their noveltyinusage for NWP-DAdrag some simplifications and adaptations to common approaches withthem.

7.4.1Model description and setup

The Weather Research and Forecasting (WRF) Model is utilized forthis study.Itis an atmospheric modelling system designed forboth research and numerical weather prediction (Skamarock et al. 2019). As an open-sourcecommunitymodel it has been adopted forresearch at universities and governmental laboratories, foroperational forecastingbygovernmental andprivate entities, andfor commercial applications by industry.The development of WRF started around the years1995-2000 with the goals being to build asystemshared by researchand operations andtocreate a next-generationNWP capability.The resulting modelling system is nowadays acommon platform which canbeused and developedfurther by abroad research community.

Figure 7.4 shows the system componentsofthe advancedresearch version of WRF used forthis study.The mainfocus in this case lies on the WRFDAData Assimilation module (Barker et al. 2012), whichperforms all the necessary steps attached to the ZTD assimilation. Maingoalofall theassimilation tests carried out hereisthe assessment of the number of observations providingsufficient accuracy to be processed by theWRFDAmodule (i.e. passing its qualitycheck). This actually representsyet another type of validation forthe GNSS-ZTDestimates since they are compared to values calculated by the background state/forecastofthe model.

ZTD operator

The WRFDAsystem used in thisstudy providesvariational3D/4D as well as hybrid vari- ational ensemble algorithms (Barker et al. 2012). Currently,itsupports the assimilation of surface,radiosonde, aircraft,wind profile observations, as well as atmospheric motion vectors,radar reflectivity, spectrometric, GPS radio occultation andGPS ground-based data (Rohm et al.2019). Aspecific observation operator, the GPSPWoperatordefines the forward, tangent linearand adjoint of Hfor the4D-Var and3D-Var case forZTD and PW.The ZTDforwardoperatorHreadsasfollows(Vedel and Huang 2004)with 7.4Assimilation andverification methodology 85

Figure 7.4: System components of Advanced Research WRF,taken from Barker et al. (2012). further corrections made by Yong-Run Guo and presented in Rohm et al. (2019):

ZTD(i, j)=ZHD(i, j)+ZWD(i, j) (7.7) k=kts (wdk p(i, j, k)q(i, j, k) wdk p(i, j, k)q(i, j, k) δh ZWD(i, j)= ( 1 + 3 ) (7.8) t(i, j, k) t2(i, j, k) aew k=kte where i, j and k arethe model node indices,p is pressure, q specific humidity, t temperature and δh is the height difference betweentwo consecutive model layers. −7 −3 Furthermore aew =0.622,aswell as wdk1=2.21 · 10 and wdk3 =3.73 · 10 are compressibilityconstants. ZHD is computed with theSaastamoinen model as given in Equation 4.22.

TheZTD operatordescribed abovewas used in the WRFDAmodule forthe as- similation tests carried out forthis study.Resultsachieved fortwo test tracks/cases can be found in Chapter 8,Section 8.7. 86 ZTDvalidationand assimilation Chapter 8

Results

Chapter 8 presents the main results of this study in the form of four case studies (i.e. test cases). The case studies comprise various train tracksasdetailed in Section 8.1 andsummarized in Table 8.1.The data on whichthe presented resultsare basedupon areraw GNSS observations withanupdate rate of 1Hz. They were gathered in the course of the Greenlightproject(seeSection 6.1.1)and thankfullyprovidedbyOB¨ B.

At first,the testcases(travellingroutesand dates) and the used processing schemes foreachcase as well as the applied processing settingsare detailedinSection 8.1. Main resultsofthe investigatedcasestudies arepresentedand discussed in Sections 8.2, 8.3, 8.4 and 8.5. Furthermore, Section 8.6 providessomeadditional ZTD comparisonswhich aimto investigatethe sensitivityofthe ZTD solution to changes in certain aspectsofthe processing settings (i.e. changes to the default settingsintroduced in Section 8.1.2). Finally,Section 8.7 discusses the findings of the first assimilation testscarried out using ZTD time series fromtwo of theconductedcase studies.

8.1 Overview of conducted case studies

In the following, an overview of the conducted case studies and the used processing settings is given. For the analysed test cases (Sections 8.2 - 8.5)the presentation of the resultsissplit into three sections:

1. Rawdata quality:Atfirst, some indicators of the quality of theobtained raw GNSS data areshown in this firstsection. The presented parameters arethe CMC observables (asintroduced in Section 6.2), the number of visible satellites as

87 88 Results

well as GDOP values. This sectionaimsfor afirst estimation of theobservation qualityand the identification of possibly critical sections along theinvestigated tracks wheredegradationofthe PPPsolution canbeexpected.

2. PPP noise analysis:This sectionpresents an analysisofPPP results(in terms of height coordinates and ZTD) fromtwo different processingschemes (CSRS-PPP andPPP-Wizard). Main goalisanestimation of the noiselevel of the respective PPP solutionfor theheight coordinate and ZTD. Therefore, acomparison between actual softwareoutput against asmoothed (i.e. filtered) solutioniscarried outfor these two parameters.The smoothed solution is computed using an MA-filter,as detailed in Chapter 6,Section 6.9.1.The time windowofthe MA-filter is chosen based on the following criteria:

• Adequate smoothing effect: smooth noise in the parametersasmuch as pos- sible without loosing information on variations originating fromtrain move- ment.Thereforeamean travelling speed of 100 km/h is assumed. • Output interval to be used later forNWP assimilation:Delivering datafor assimilation everysecondisnot suitable and wouldnot represent an added value to weather forecasts since tropospheric conditions do not change this fast.Furthermore theamountsofdata andthus the computationaleffort would be huge. Therefore agood compromise has to be found in order to use as much valuable data as possible in agiven DA setup.

Considering these criterialistedabove, atime windowoffive minutes waschosen. This corresponds to amean travel distance of ∼8kmwhich wasassumed not to showtoo largevariations in height or ZTD along the track (atleast under average conditions, might not be true in highly mountainousregions) in order to filter out only noise components.

3. ZTD validation:Inasecond step, the ZTD estimates derived from PPP process- ing (referred to as GNSS-ZTD) arevalidated using ZTD calculated from ERA5 reanalysis data (referred to as ERA5-ZTD) as outlined in Chapter 7.Herede- viations from ERA5-ZTD arecompared between different schemes. Results are analysedinterms ofthe standard error measures outlined in Section 6.9.2.

8.1.1Testcases

Four different testcases were investigated in the course of this study.Their main characteristics in terms of travellingroute aresummarized in the following descriptions 8.1Overview of conducted case studies 89 and in Table 8.1. CS1 uses data fromatraintravellingonthe route Salzburg -Vienna airport. Chal- lenging conditions areexperienced duetoanumber of urban areas and tunnelsalong the track, which degrade the PPPsolutionoreven accountfor acompleteloss of the solution. CS2 coversthe routeSalzburg -Klagenfurtwhich includes alot of mountainous areas andultimatelyapassing of the main alpine ridgeaswell as tunnels and some urban environments. CS3 and CS4 investigatealmost similar routes (Innsbruck -Liezen for CS3 and Innsbruck -Graz for CS4)which covermountainousareas foralmostthe whole time. These areas include avarietyofdifferent environmentslikebroad andnarrowvalleys as well as smaller alpine passes.

These case studies attempt to represent abroad range of challengingconditions forGNSS encountered in the railway domain allover Austria.

Test case Date RouteProcessing CS1 11.05.2017 Salzburg-Vienna airport CSRS-PPP/PPP-Wizard CS2 28.09.2017 Salzburg-Klagenfurt CSRS-PPP/PPP-Wizard/SGAMP CS3 29.11.2019 Innsbruck -W¨o rgl -Schwarzach/St.Veit -Liezen CSRS-PPP/PPP-Wizard CS 4 01.12.2019 Innsbruck -W¨o rgl-Schwarzach/St.Veit -Liezen -Graz CSRS-PPP/PPP-Wizard

Table 8.1: Overview of conducted case studies

8.1.2 PPP processingsettings

This section introduces the most importantsettings which were applied in PPPprocess- ing forthe test cases introduced in the last section. Table 8.2 presents the main PPP settings used andpossible differences between the processingschemes. GNSSdata forprocessingwereprovided by OBB¨ in fromofraw observations available everysecondinbinary format.These were converted to RINEX 2.11 format(Gurtner and Estey 2007)and fed to thePPP processing engines (see Sections 6.5, 6.6, 6.7 and 6.8). 3D-coordinates, receiver clock error andZWD were estimatedevery second in PPP processing. All processing schemes outlined in Chapter 6 were applied at leastfor one test case (an overview is giveninTable 8.1). In the following,these schemes arereferred to as:

• CSRS-PPP: CSRS-PPP

• GAMP using SEID model(as detailed in Section 6.7): SGAMP 90 Results

• PPP-Wizard: PPPW

• PPP-Wizard withheight-constraint (implemented as detailed in Section 6.8): PPPW-HC

Dependingonthe actual processing scheme either SF-orDF-PPP forGPS and GLONASSobservationswere used. IGS finalproducts were utilized forsatellite orbit and clock corrections. Ionospheric corrections areapplied forCSRS-PPP through IGS GIM broadcastTEC mod- els and forPPPWbyobtaining EGNOS (European Geostationary Navigation Overlay Service) corrections. Since the SGAMP scheme operatesinDF-PPPmode, the IF-LC is used here. The hydrostaticpartofthe tropsopheric delay(i.e. ZHD) is modelled using VMF1 grids forCSRS-PPP,with thesimpleSaastamoinen model (Equation 4.22)for PPPWand using theGlobal Mapping Function (GMF, Boehm et al. (2006)) forSGAMP.

For thea-priori constraint settingsofthe Kalman Filter (σL,σP ,σZWD,σPosition)arange of values is given since anumber of different setups were tried outand theoptimal settingsvarybetween the test tracks.

Both code and phase sigma (σP ,σL)were set to significantly higher values compared to their typically magnitude (see Chapter 2,Section 2.3.3). This accounts forthe rather lowqualityofthe rawGNSS data and the difficult environmental conditions (e.g. mul- tipath) they were gatheredin.

ZWD (σZWD)was setinthe range from5mm to 1cmdepending on the test case. Many different settings were tried outfor this parameter and the presented ones were foundtoprovide the best results in the ZTDvalidation.The chosen values aretypically of quite lowmagnitude, but showedreasonable resultsfor all testcases. Possible reason forthe good fit of thischoice couldbethe dry weather conditionsfor thetest dates (un- fortunately forthe assimilation studies, see also Section 8.7). Furthermore foralmost all testcases,the trains spent asignificant amount of time at fairly high altitude where the influence of watervapourisdecreasing,especially in stable and dryweather situations. 7.5◦ waschosen as thedefaultsetting forthe cut-off observationangle. Measurements from elevation angles belowthis value were notconsidered in the processing.However, Section 8.6 investigateschances in this as well as otherprocessingsettings andtheir influence on the ZTDsolutionperformance. 8.1Overview of conducted case studies 91

Parameter Setting Mode Kinematic SF-PPP (CSRS-PPP/PPPW)/DF-PPP (SGAMP) GNSS GPS +GLONASS Phase AmbiguitiesFloat Observation weighting Elevation-dependent Orbits IGS final Clocks IGS final IonosphereGIM broadcast (CSRS-PPP)/EGNOS (PPPW)/SEID(SGAMP) ZHD VMF1 (CSRS-PPP)/Saastamoinen (PPPW)/GMF (SGAMP) Elevation cut-off 7.5◦

σL 0.1 -0.5 m

σP 1-10m

σZWD 0.005-0.01 m

σPosition 10 -50m

Table 8.2: GeneralPPP settingschosenfor the test cases. 92 Results

8.2 Case study 1: 11.05.2017

The first test case (CS1) is basedontracking data fromarailjettrain travelling from SalzburgtoViennaairporton11.05.2017. The travellingroute,obtained from the CSRS-PPP coordinate solution, is shown in Figure 8.1.This first test trackcovers relatively moderateheight(i.e.ZTD)differences with asteadydecrease (increase) in height (ZTD) towards Viennaasindicated in Figures 8.4 and 8.5 in the following section. Nevertheless frequent encountering of urban areas and tunnels still produce challenging conditions of GNSS processing.

Figure8.1: Train-track covered forCS1 (Salzburg -Vienna airport) derived from CSRS-PPP processing.

8.2.1Raw data quality

At first, some qualityindicators of the data in form of multipath analysis and geometry parametersare showninFigures 8.2 and 8.3.Figure 8.2 shows the computed CMC observables along the CS1 route. Criticalsections, which areencountered while going through urban areas in the beginning(Salzburg) andtowardsthe end of the time series (Vienna), arevisible.These sections also exhibit aclearly increased parameter noise in the PPP solution, as shown in Figures 8.4 and 8.5 later. Furthermore, Figure 8.3 shows the number of observed satellites andcomputedGDOP along the track. The observeddecreases in satellite availabilityand increases in GDOP values matchwell withthe increased parameter noise in ZTD and heightcoordinateat the same time (Figures 8.4 and 8.5)aswell as increased multipath influence (Figure 8.2). In general, highvariabilityisobserved forboth satellite visibiltyand GDOP,which indicates the changing and challengingenvironments the GNSS receiver has to cope 8.2Casestudy 1: 11.05.2017 93

Figure 8.2: Code-Minus-Carrier (CMC) observables forCS1,shown areall visible GPS satel- lites. with.

Figure 8.3: Number of visiblesatellites (left) and GDOP values(right)along the CS1 route.

8.2.2 PPP noise analysis

As outlined in the introductionofthis chapter, an analysisofthe observed noise level forheight and ZTD time seriesofCSRS-PPP and PPPWiscarried outhere. Therefore asmoothed solution wasproduced using aMA-filter withatime windowoffive minutes 94 Results as detailed in Section 8.1.Figures 8.4 and 8.5 showacomparisonofprocessing results forZTD and height coordinate respectively,derivedfrom CSRS-PPP (top) and PPPW (bottom). Theactualoutput of the respective PPPengine (red) and the smoothed time series (blue) areshown forboth components.

Figure8.4: CS1 PPPZTD time seriesfromCSRS-PPP (top)and PPPW (bottom).The raw PPP ZTDestimatesare shown in red, theMA-smoothed (Interval 5min)inblue.

Figure 8.5: CS1 PPPellipsoidalheight timeseries from CSRS-PPP (top) and PPPW (bot- tom). Theraw PPPheightestimatesare shown in red,the MA-smoothed (Interval5min) in blue.

Thecomparison allowsaquantification of the observed parameter noise through standard deviation and RMS,asindicated by themagnitudeofthe red spikes which arevisible in 8.2Casestudy 1: 11.05.2017 95 the plots. The noise level in ZTD variesbyafactor of ∼7-10 between CSRS-PPP and PPPW, with CSRS-PPP showingmagnitudes at the millimetreand PPPW at the centimetre level forRMS andstandard deviation.Bias values arevanishingly small forZTD (10−3 - 10−4 cm), which is expected fromthe comparison between atime series and its MA- smoothed version.This fact therefore suggeststhat the time windowoffive minutesfor the MA-filter is an appropriate choice to filter noisefrom these time series. For theheight coordinate, thenoiselevel varies by afactorof∼2(forboth RMS and standard deviation) between the respectiveschemes. Standarddeviation andRMS are below10metres forCSRS-PPP (8.769/9.289) andbetween 15 -20metres forPPPW (17.586/19.690). In terms of median aclearadvantage of CSRS-PPPisevident, for both ZTD andheightcoordinate. Allperformancemeasures concerning the noiselevel of both solutions aresummarized in Table 8.3 and 8.4.

Processing schemeBias[cm] Standard deviation [cm]RMS [cm] Median [cm] CSRS-PPP 0.00040.3 0.3 0.03 PPP-Wizard -0.0012.0 2.3 0.39

Table 8.3: Performancemetrics forthe PPP noise analysis of CS1 forCSRS-PPP andPPPW. Measuresare computed forZTD differences between original PPP outputand smoothedso- lution.

Processing scheme Bias [m] Standard deviation [m] RMS[m] Median [m] CSRS-PPP -0.017 8.769 9.289 0.645 PPP-Wizard 0.011 17.586 19.690 4.240

Table 8.4: Performancemetrics forthe PPP noise analysis of CS1 forCSRS-PPP andPPPW. Measuresare computed forheight coordinate differencesbetween original PPP output and smoothed solution.

8.2.3 ZTD validation

For thevalidation of the ZTD estimates derived fromCSRS-PPP andPPPW, reference ZTD valueshave been calculated fromERA5 reanalysisdata foreach case study,using themethodology detailed in Chapter 7.Resultsfor CS1are shown in Figure 8.6.A similarpattern forboth GNSS- and ERA5-ZTD can be seen forthe latter part of thetime series. However, forthe first hour (12-13UTC), GNSS- and ERA5-derived 96 Results

ZTD time series deviate significantly from each other.While ERA5-ZTDshows a maximum forthis period,the almost exact oppositebehaviour (minimum) is found in the GNSS-ZTDsolutions. There aretwo possible explanations forthis: (1): very localized occurrence of high watervapouramount not captured by GNSS or (2): errors/artefacts in the corresponding ERA5 fields. The latter might be more likely, considering the dry weather conditions observed on this dayand the fact that both GNSS-ZTDsolutions areingood agreement with each other (similarpatterns and thushighcorrelationbetween them). Nevertheless it is interesting to notice that in the corresponding area along the track multiple lakes of varying size arelocated (seeFigure 8.1). This maylead to very localized, high amountsofwatervapouras well as possibleartefactsinmodelled humidityfields in the ERA5 reanalysis data. However further researchwouldbeneeded to back up one of those possibleexplanations.

Comparing the performanceofthe ZTDestimation between the two different softwarepackagesused, adiverse picturecan be drawn forthis test case. In the first part of thetrack(first hour approximately),the CSRS-PPP ZTD solutionoutperforms the PPPWsolution in terms of deviations from the ERA5-ZTDreference. However, this part represents the time where the significant deviations in thesignal patterns between GNSS and ERA5 areobserved and therefore deviations might be interpreted with caution. For thelatter (and time-wise much larger)part, whichshows highlycorrelated patternsbetween GNSS and ERA5, PPPWresultsare closertoERA5. This factisalso represented in lowerbias(by factor of ∼3) and RMS values (factorof∼1.5)compared to CSRS-PPPasindicated in Table 8.5.Standard deviations of ZTD differences to ERA5 arecomparable forbothschemes (around 4cm, see also Table 8.5). Figure 8.7 shows the distributions of ZTD differences to ERA5 forboth processing schemes. Clearly visibleisthe fairlylarge number of strongly positivevalues forboth schemes. Thisisalso reflected in the(strictlypositive) bias values, especiallyfor CSRS-PPP which has no larger negativedeviationstoERA5 likePPPW(see x-axis of Figure 8.7). The computed correlation coefficients and linearfits between GNSS-and ERA5-ZTD solutions areheavily influenced by thelarge deviationsobserved in thefirsthourofthis testcase. Both GNSS-ZTDsolutionsshowalmost no, to slightly negative correlation with ERA-ZTD,asshown inFigure 8.8.Since both GNSS-ZTDsolutions agree very well with each other and thispartofthe trackdoesnot denoteparticularly challenging environmentsfor GNSS, the more likely explanationare problems in the ERA5 dataset as already discussed above. 8.2Casestudy 1: 11.05.2017 97

Figure 8.6: Comparison between estimated GNSS-ZTD (CSRS-PPP (red)and PPPW (green)) and ERA5-ZTD (black) forCS1 (11.05.2017),Top:absolute values, bottom: ZTD differences between GNSS-ZTDwithrespect to ERA5-ZTD

Figure 8.7: Histograms of ZTD differences between GNSS-ZTDand ERA5-ZTD fortest case CS1. Left: CSRS, Right: PPPW. Alsoindicatedare bias and standard deviation (σ)ofthe respective solutions.

Theinfluence of the deviationsbetween GNSS-ZTDand ERA5-ZTD becomes even more evident when comparing Figure 8.8 to Figure 8.9,wherethe latter shows the correlationbetween the respectivetime series when excluding theproblematic part in 98 Results

Figure 8.8: Correlation between ZTD as estimated by each softwarepackage andthe ERA5 referencevalues forCS1, 11.05.2017: (left) CSRS-PPP and(right) PPPW .Terms Rand y representthe correlationcoefficient andthe linearfit, respectively. the beginning (12:00 -13:30). The correlationcoefficients aresignificantly improved and close to the high levels which arepresentfor the other test cases. On theother hand, the statistics of this shortened time series (Table 8.6)showincreased bias and RMS values. This is caused by thefact that the significant positive biases of both GNSS-ZTDtime series arenot compensated by thenegativebiases present in the beginning of the complete testdata.Acompleteoverviewofstatistical performance metrics forthe ZTDvalidation can be found in Table 8.5 (full time series) and 8.6 (excluding 12:00 -13:30). Apart from these deviations in the first hour,results fromCS1 in general arepromising sincethe patterns of GNSS-and ERA5-ZTD agree well forthe remainingpart. Neverthelessanon-negligible bias in centimetre-level is observedbetween GNSS- and ERA5-ZTDtime series.

Processing scheme Bias [cm] Standard deviation [cm] RMS [cm]Correlation CSRS-PPP 5.51 4.22 6.85 -0.19 PPP-Wizard 1.97 4.35 4.72-0.15

Table 8.5: CS1: Performancemetrics forthe ZTD validation against ERA-ZTDfor processing resultsofCSRS-PPP and PPPW. 8.2Casestudy 1: 11.05.2017 99

Figure 8.9: Correlation between ZTD as estimated by eachsoftwarepackage and the ERA5 reference values forCS1,excluding the firsthour of data (12:00-13:30): (left) CSRS-PPP and (right) PPPW .TermsRand yrepresent the correlation coefficient andthe linearfit, respectively.

Processingscheme Bias [cm]Standard deviation [cm]RMS [cm]Correlation CSRS-PPP 8.39 1.07 8.46 0.73 PPP-Wizard 4.95 0.91 5.03 0.75

Table 8.6: CS1 (excluding 12:30 -13:30): Performancemetrics forthe ZTD validationagainst ERA-ZTD forprocessing resultsofCSRS-PPPand PPPW. 100 Results

8.3 Case study 2: 28.09.2017

CS2 uses datacollected by aRailjet train on 28.09.2017, the travelling track (coordinate solutionfrom CSRS-PPP) is showninFigure 8.10.The trainstartedinMunich (around 06 UTC)and arrivedinSalzburg around08UTC.From there it passed thealpine ridge southwards towards Klagenfurt, where it terminated shortlybefore 12 UTC. Especially

Figure8.10: Train-trackcovered forCS2 (Munich -Klagenfurt shown here) derived from CSRS-PPP processing. the passing of thealpine ridge (whereheightsover 1000 meters arereached) makes thisaparticularly interesting test case. Therefore, the periodcovering thealpine pass- ing (Salzburg-Klagenfurt),which corresponds to 08-12 UTC,was selectedfor detailed analysisofthe results.

8.3.1Raw data quality

Discussion of the resultsagainstarts withanoverviewonmultipathand geometry in- dicators. Figure 8.11 shows theCMC observablesfor CS2 forall visible GPSsatellites. As forCS1, highmultipath influence is experienced especially within partswhere urban environments areencountered (inthe beginningSalzburg,atthe end Villach and Kla- 8.3Casestudy 2: 28.09.2017 101 genfurt).Furthermore smaller tunnels in the middle of the track can also be recognized, as nosolutionisavailable there.

Figure 8.11: CMC observables forCS2, shownare all visible GPS satellites.

Aquitecoherent picturetothe multipath levels shows Figure 8.12,which presents the number of observedsatellites and computed GDOPvalues along the track. Here sub- stantial spikes (lownumber of satellites) and ahigh GDOP indicate sections of distorted geometry and therefore challenging conditions of GNSSoperation. These sections match approximately with timesofhigh multipathinfluence (Figure 8.11)and increased pa- rameter noise (Figures 8.13 and 8.14).

8.3.2 PPP noise analysis

Similar analysis of theparameter noise level as already presented forCS1 wascarried out forCS2. Again the original PPP output fromCSRS-PPPand PPPWwas compared against asmoothed (again MA-filtered, again five minute time window) solution forZTD andheightcoordinate.The comparisons areshown in Figures 8.13 and 8.14. Overall the solutions drawasimilarpicture as thosefrom thefirst test case.Most statistical measures outlined in Tables 8.7 and 8.8 arecomparable,sometimes almost similartothose of CS1. The time series derived using PPPWagainshowsignificantly increased noiseand standard deviation compared to the CSRS-PP solution,especially in ZTD(by factor ∼3-4).Nevertheless the performance of thePPPW ZTD solution is 102 Results

Figure 8.12: Number of visiblesatellites (left)and GDOP values (right) along theCS2 route. remarkably increased compared to the resultsfrom CS1 (50%smaller standard deviation andRMS). Thenoiselevel of the height coordinate largely remainthe same, with RMS and standarddeviationinthe millimetre-range forCSRS-PPP andincentimetre-range forPPPW. This representsavery promisingfirst indication of reasonable performance of the results, especially forCSRS-PPP. For theheight coordinate, statistics arealmost equal to CS1. Again the PPPW time series exhibitsafactor2-3 larger noise comparedtoCSRS-PPP.This is also evident in the bias values(-0.002/-0.023),differing by afactor10between the solutions and indicating decreasing performance of the 5-minute MA-filter fortime series with increased noise as forthe PPPW solutioninthis case. Furthermore, at thehighest sectionofthe track verychallenging conditions or even GNSS-denied areas in form of tunnels areencountered, which manifests itself in some smaller jumps in theresultsofboth schemes. Nevertheless, areasonable solutionis recoveredquite fast forbothschemes after these discontinuities. As already outlined before, the multipath-prone sections(mostly at the beginning of the route)are alsovisible in terms of increased parameter noise, especially in the PPPW time series. Adetailed summary of statistics can be found in Table 8.7 and 8.8. 8.3Casestudy 2: 28.09.2017 103

Figure 8.13: CS2 PPPZTD time series fromCSRS-PPP (top) andPPPW (bottom). The rawPPP ZTDestimates areshown in red, the MA-smoothed (Interval 5min)inblue.

Figure8.14: CS2 PPPellipsoidal height timeseries from CSRS-PPP (top) andPPPW (bot- tom). Theraw PPP heightestimates areshown in red, the MA-smoothed(Interval 5min) in blue. 104 Results

Processing scheme Bias [cm]Standard deviation [cm]RMS [cm] Median [cm] CSRS-PPP 0.0040.3 0.3 -0.001 PPPW 0.01 1.0 1.3 0.012

Table 8.7: Performancemetrics forthe PPPnoise analysisofCS2 forCSRS-PPP and PPPW. Measures arecomputedfor ZTD differences between original PPP outputand smoothed so- lution.

Parameter Bias [m]Standard deviation[m] RMS [m] Median [m] CSRS-PPP -0.002 7.2697.801 0.004 PPPW -0.023 20.095 20.022 0.357

Table 8.8: Performancemetrics forthe PPPnoise analysisofCS2 forCSRS-PPP and PPPW. Measures arecomputed forheight coordinate differences between originalPPP output and smoothedsolution.

8.3.3SEID processing

CS2isthe case wherethe application of the SEID model is tested forionospheric mitiga- tion. Therefore datafrom anumber of reference stations wasutilized within themodel. The chosen stations arelisted in Table 8.9 and the track map withthe stations location indicated is showninFigure 8.15.Asvisible fromthe map and table, seven stations

Station Distance from reference point[km] Gummern 47.6 Oching S¨ud 4.9 R¨otenkogel 55.2 Saalfelden 66.0 Salzburg 62.4 Sillian66.2 Schladming 62.4

Table 8.9: Reference stations chosen for SEID processing forCS2. arechosen forthe SEID processing. The decision which and howmany stationsare se- lected is based onthe distance from adefined reference point. This reference point was determined in astaticway here as the midpoint (median) of the trajectory. Allstations within80kmdistance areselected. This threshold decision is based on formerstudies 8.3Casestudy 2: 28.09.2017 105

Figure 8.15: Train-track coveredfor CS2 withthe reference stations utilized forSEID pro- cessing showninblue dots. and clearly variableunder different circumstances (e.g. higher/lowernumber of stations available within shorterdistance, i.e. denser/lessdense reference station network). Thisisclearly asimplified approach forakinematicapplication and has to be redefined foroperationalprocessingtoakind of moving reference point, which is chosen fora suitable time step. Apossiblechoicefor this time step wouldbe, e.g. one hour since:

• EPOSAreference station data in RINEX format is providedatthis interval

• Ionospheric conditions might not changetremendously within this time step

Althoughthe second point might not alwaysbefulfilled, one hour still seems to be an adequate choiceconsideringaverageconditions at mid-latitudes. Nevertheless,this choice also limits theoutput interval forZTD results if the SEIDmodel is used and 106 Results therefore thetopic hastobeinvestigated further in detail.

8.3.4ZTD validation

This sectionprovides theresults ofthe ZTD validation forCS2. Thevalidation is car- ried out in asimilarway as forCS1,only with the difference that resultsfrom allfour processingschemes introduced in Chapter 6 were available and thus arepresented here.

Figure8.16: Comparison between estimated GNSS-ZTD (CSRS-PPP (red),SGAMP (blue) andPPPW (green) and PPPW-HC (lime)) and ERA5-ZTD(black) forCS2 (28.09.2017), Top: ZTD, bottom: differencesbetween GNSS-ZTD with respecttoERA5-ZTD

Figure 8.16 showsthe comparison ofGNSS-ZTDs andERA5-ZTD forthe chosentime- frame/routeinterms of ZTD values and ZTD differences of the different processing schemes (GNSS-ZTDs) to ERA5-ZTD. PPPW-HC performs best in the comparison, showingvery lowbias (0.1 cm) and RMS (1.2 cm) values as outlined in Table 8.10.These values arecomparabletoDFsolutions whichare commonly used in GNSS Meteorology and therefore representvery promising results fromthis type of processing. 8.3Casestudy 2: 28.09.2017 107

SGAMP also shows lowvalues forbiasand RMS(1.3/2.8 cm), but has an increased standard deviation (byafactor ∼2) compared to the other schemes. Nevertheless these resultsare able to indicate the potential of theSEIDmodel forSF-GNSS processing and applications likeGNSSMeteorology. CSRS-PPP shows results comparable to SGAMP in terms of bias (2.4cm) and similar forRMS (2.7 cm)and its solutionhas thelowest standard deviation of all solutions (1.2 cm).Comparedtothe resultsfrom CS1, an improvement of ∼50 %can be found in terms of bias. Compared to the results of the other schemes those fromPPPW show significantly worse performance in terms of differences to ERA5-ZTD. In the PPPW ZTD time series, a negativeoffset of about 5-10cmis present over the entireanalysed period. This is also visible in thedistributions of ZTD differences, shown in the respective histogramsin Figure 8.17.The pronounced advantage of the height-constrained PPPW (PPPW-HC) over the standard versionmightindicate aheight offset introduced in PPPW which can be erased by applying aheight-constraint as described in Section 6.8. Adetailed summary of performance metrics forthe ZTD validation aregiven in Table 8.10. Overall, the resultsfrom theCS2 ZTD validation outline the potential of the newly introduced processing schemes (SGAMP and PPPW-HC), which both areable to out- performthe ”standard” PPPsolutions from CSRS-PPPand PPPW.Especially the good performance of PPPW-HC encourages its usage forthe following test cases (CS3 and CS4)aswell as forfuture studies.

Processing scheme Bias [cm] Standard deviation [cm] RMS [cm] Correlation CSRS-PPP 2.4 1.2 2.7 0.99 SGAMP 1.32.5 2.8 0.95 PPPW -8.8 1.88.9 0.97 PPPW-HC 0.1 1.3 1.3 0.99

Table 8.10: CS2: Performancemetrics forthe ZTD validation against ERA-ZTD forprocess- ingresults of CSRS-PPP,SGAMP and PPPW andPPPW-HC. 108 Results

Figure 8.17: HistogramsofZTD differencesbetween GNSS-ZTD andERA5-ZTDfor test case CS2. Topleft: CSRS-PPP,Top right: SGAMP,Bottom left: PPPW, Bottom right: PPPW-HC. Also indicatedare bias and standard deviation (σ)ofthe respective solutions. 8.3Casestudy 2: 28.09.2017 109

Figure 8.18: Correlation between ZTD as estimated by each softwarepackage and theERA5 referencevaluesfor CS2, 28.09.2017. Topleft: CSRS-PPP,Top right: SGAMP,Bottom left: PPPW,Bottom right: PPPW-HC. Terms Rand yrepresent thecorrelationcoefficient andthe linearfit, respectively. 110 Results

8.4 Case study 3: 29.11.2019

CS3 uses datagathered fromarailjettrainon29.11.2019. This express trainwas travellingonthe routefrom Innsbruck down the Inn valley to W¨orgl, fromthere via Kitzb¨uhel over to Salzburg and finallyterminating in Liezen, Styria. Thisroute providesvery diverse conditions along the track with some prominent features like major cities (Innsbruck, Graz (only forCS4 then)), major(Inn Valley,Enns Valley) and very narrow alpine valleys (Brixen Valley,i.e.W¨o rgl-Kitzb¨uhel) as well as mountain passes (Grießen pass, Mandling pass). Therefore environmental conditions (multipath, shading, atmospheric conditions) arevery differentalong differentsections of the route which is also reflected in the results. The exact travelling track, as derived fromCSRS- PPP,isvisualized in Figure 8.19.

Figure 8.19: Train track of CS3(29.11.2019): Innsbruck -Woergl-Bischofshofen -Liezen

8.4.1Raw data quality

Figure 8.20 shows the computed CMC observables along the route. Althoughthe mag- nitudes arequite constantonamedium level (between +/- 5m)and comparable to the priortest cases, some larger spikes arevisible especially in the first section (likely urban environment in Innsbruck) and from 13:00UTC on,where the train entersmore mountainous regions. Figure 8.21 shows the number of observedsatellites andcomputed GDOP along the track, providing afirst estimation of thesatellitegeometryalong this route. Lookingat values of both availablesatellites and GDOP,one notices thatthe first section(more or less the Inn Valley) provides better geometry(GDOP < 2 forthe most part) and visibility of satellites (number of visible satellitesconstantly over 10)whereas theseparameters 8.4Casestudy 3: 29.11.2019 111

Figure 8.20: CMC observables forCS3, shownare all visible GPS satellites. aredegraded when entering more mountainousenvironmentsafterwards.

Figure 8.21: Number of visiblesatellites (left)and GDOP values (right) along the CS3 route. 112 Results

8.4.2PPP noise analysis

Analysis of the parameter noiselevels reveals similar results as forthe priorcases forthe most part.Figures 8.22 and 8.23 showthe comparisonbetween original PPPoutput andsmoothed solution forCSRS-PPP (top) and PPP-Wizard (bottom). As forthe othertest dates the general parameter noiseofthe solutions is quite low, except forafew larger deviations (spikes) which again directly match with higher multipath levels observed in Figure 8.20.The height solutions areable to describethe frequent terrain/elevation changes of the covered route realistically.

Figure8.22: CS3 PPPprocessingresults forZTD fromCSRS-PPP (top) and PPPW (bot- tom).The actual PPP output is shown in red,the MA-smoothed (Interval 5min) in blue.

Onemain difference to the former cases is the fact thatthe PPPWsolutionismore comparable to CSRS-PPPconcerningnoise level of both,ZTD andheight coordinate. Improvements when using CSRS-PPPinsteadofPPPW areonly about afactor1.5 - 2for CS3. This fact also manifests later in the ZTDvalidation,asthis also seems to influence the bias of the ZTDsolution. Bias valuesare almost equalfor both schemes, especiallyinZTD.However, theheight coordinates showanincreased bias (byafactor ∼10) forboth solutions(decimetre-level) compared to the priorcasestudies. Interestingly,this behaviour is not mapped to the ZTDbiases which areaslow as before (∼ 10−4 cm). In general, the magnitude of parameter noise is smaller than forthe previous cases. This may be attachedtothe routecharacteristics or to possibleusage of new equipment (receiver, antenna),asthe data from this testcasewas gatheredtwo yearsafter those of CS1 and CS2. However these assumptions were not investigatedfurther but might 8.4Casestudy 3: 29.11.2019 113

Figure 8.23: CS3 PPPellipsoidal height timeseries from CSRS-PPP (top) andPPPW (bot- tom). Theraw PPP output is shown in red, the MA-smoothed (Interval5min) in blue. be of interest forfuture studies using similardatasets. Detailed statistics of the noise analysis forCS3 aregiven in Table 8.11 and 8.12.

Processing schemeBias[cm] Standard deviation [cm]RMS [cm] Median [cm] CSRS-PPP -0.004 0.7 0.7 -0.001 PPP-Wizard -0.0051.2 1.2 -0.003

Table 8.11: Performance metrics forthe PPPnoise analysisofCS3 forCSRS-PPP andPPPW. Measuresare computed forZTD differences between original PPP outputand smoothedso- lution.

Processing scheme Bias [m] Standard deviation [m] RMS[m] Median [m] CSRS-PPP 0.154 23.343 23.3230.010 PPP-Wizard 0.188 39.974 39.9380.013

Table 8.12: Performancemetrics forthe PPP noise analysis of CS3 forCSRS-PPP and PPPW. Measures arecomputed forheight coordinate differences between original PPP output and smoothedsolution.

8.4.3 ZTD validation

As withthe priorcases, thevalidation of ZTD estimates is conducted using ZTD com- puted from ERA5 fields. Figure 8.24 shows the comparisonofGNSS-ZTDand ERA5- ZTDfor thistest track. Results show an excellent performance by CSRS-PPP, with 114 Results

Figure 8.24: Comparisonbetween estimated GNSS-ZTD(CSRS-PPP (red) and PPPW (green)) and ERA5-ZTD (black) forCS3 (29.11.2019),Top: ZTD, bottom: differences be- tween GNSS-ZTDwithrespect to ERA5-ZTD

differences to ERA5 ofteninthe mm-range andvery high correlation between the re- spectivetime series. The overall bias is only around2.7 mm,the medianeven inthe sub-millimetrerange andalsothe standard deviationisthe lowest of allschemes (6.1 mm). PPPW-HC has comparable resultsfor alarge part of the routebut some larger deviations to ERA5-ZTD can be seen around 13:30 to 14:30 which correspondstothe time with the worst geometry(Figure 8.21). Still, these issues aremorelikely attachedtoproblems in thetrackDBheights or originatefrom interpolationerrors madeinthe constraining process (wrong point/height stored in databaseischosen).This becomes clearbylook- ing at thePPPW solutionwhich actuallyshows asimilarpattern as ERA5-ZTD,also in thissection. Overallindeed, the PPPW standard versionagainshows an increased bias(by afactor 5-10) andRMS compared to CSRS-PPP and PPPW-HC, although this bias is generally lowerthan forthe priortest cases. 8.4Casestudy 3: 29.11.2019 115

Correlationwith ERA5-ZTDisagainvery highfor most schemes, as visible fromFigure 8.26.Only PPPW-HC results aredistorted by thedeviations around 13:30-14:30 (R =0.72 forPPPW-HC compared to R=0.97/0.98for CSRS-PPP/PPPW). Detailed statistics forthe ZTD validation ofCS3 canbefound in Table 8.13. Overall the results areagainverypromising, especially forCSRS-PPPand PPPW-HC, considering the challengingconditions of the route.

Figure 8.25: Histograms of ZTD differencesbetween GNSS-ZTD andERA5-ZTD fortest case CS3. Left: CSRS, Right: PPPW.Also indicatedare bias and standarddeviation (σ)of the respective solutions. 116 Results

Figure 8.26: Correlation between GNSS-ZTDasestimated by eachsoftwarepackage andthe ERA5 reference valuesfor CS3, 29.11.2019: (left) CSRS-PPP,(middle) PPPW and (right) PPPW-HC.TermsRand yrepresent the correlation coefficient andthe linearfit, respectively.

Processing scheme Bias [cm] Standard deviation [cm]RMS [cm] Correlation CSRS-PPP -0.27 0.61 0.660.98 PPPW -2.87 1.64 2.95 0.97 PPPW-HC 0.57 0.80 1.68 0.72

Table 8.13: CS3: Performancemetrics forthe ZTD validationagainst ERA5-ZTD forpro- cessing resultsofCSRS-PPP,PPPW and PPPW-HC.

8.5 Case study 4: 01.12.2019

The fourth and lasttest case (01.12.2019) uses data from arailjet train moving on a route very similartothe one of CS3, exceptthat fromLiezen the train travelled on to Graz. It is also worth mentioning that the analysed time series representsanight travel, which might account forasmallerionospheric influence on the results. As mentioned withCS3, theroute provides diverseconditions withalarge number prominentfeatures alongthe track. The exact travelling track, as derived fromCSRS-PPP processing,isvisualized in Figure 8.27.

8.5.1Raw data quality

The analysis of multipath (CMC observables), presented in Figure 8.28,shows asimilar pictureasfor CS3 forthe most part. Some larger spikes arevisible, most prominently around 02:30 UTC andinthe last part of the route. As forCS3, they correspond 8.5Casestudy 4: 01.12.2019 117

Figure 8.27: Train track of CS4 (01.12.2019):Innsbruck -Woergl-Bischofshofen -Liezen - Leoben-Bruck/Mur -Graz

approximately with times when (1)ahighly mountainous area and (2) additionallymore urbanareas (when thetrainapproaches Graz)are entered. Thispicture is also consistent

Figure 8.28: CMC observables forCS4, shownare all visible GPS satellites.

with Figure 8.29,which shows the number of observed satellitesand GDOP along the track. The problematicareas can again be recognized in terms of higher GDOP values and adropinthe number of available satellites. 118 Results

Figure 8.29: Number of visiblesatellites (left)and GDOP values (right) along theCS3 route.

8.5.2PPP noise analysis

Again forthislasttest case anoiseanalysis forthe PPPschemes is carried out.Similar to CS3,the overall noise is again lowand again the CSRS-PPPsolutionshows better performance.Biasvalues areagain vanishingly smallfor ZTD(<10−4 cm) and height coordinate (millimetre-level),showing the feasibility of the smoothing time window. PPPW ZTD results arecomparable to thoseofCSRS-PPP forbias/medianbut with increased standard deviation and RMS (1.9 cm comparedto0.1 cm). Heightcoordinate results also reveals RMSand standard deviationvalues comparable to those derivedfor theprior test casesand again arelowerfor CSRS-PPP compared to PPPW.Thisisalso consistent with allpriortestcasesbut the deviations areagain smallerthan forthe first two cases (asfor CS3).Possiblereasons, as updated equipment (receiver/antenna) forthis performance havealready been discussed forCS3 but need further research as already mentioned.

Processing scheme Bias [cm]Standard deviation [cm] RMS[cm] Median [cm] CSRS-PPP -0.0001 0.1 0.1 -0.0008 PPP-Wizard -0.0002 1.9 1.9 -0.004

Table 8.14: Performance metricsfor thePPP noise analysis of CS4 forCSRS-PPP and PPPW. Measures arecomputedfor ZTD differences between original PPP outputand smoothed so- lution. 8.5Casestudy 4: 01.12.2019 119

Figure 8.30: CS4 PPPZTD time series fromCSRS-PPP (top) andPPPW (bottom). The rawPPP output is shown in red,the MA-smoothed (Interval 5min) in blue.

Figure8.31: CS4 PPPellipsoidal height timeseries from CSRS-PPP (top) andPPPW (bot- tom). Theraw PPP output is shown in red, the MA-smoothed (Interval5min) in blue.

Processing scheme Bias [m] Standard deviation [m] RMS[m] Median [m] CSRS-PPP 0.007 3.969 3.972 -0.001 PPP-Wizard 0.005 13.552 13.5640.018

Table 8.15: Performancemetrics forthe PPP noise analysis of CS4 forCSRS-PPP and PPPW. Measures arecomputed forheight coordinate differences between original PPP output and smoothedsolution. 120 Results

Comparison with RTK

CS4 (unfortunately) representsthe only test case where aRTK-derived coordinate solu- tionisavailableand therefore allows to compare its height coordinate solution to those derived from CSRS-PPP and PPPW.The RTK solutionwas alsoprovidedbyOB¨ B, together with theraw observations forthistest case. It has asimilar update rate as the PPPsolution(1Hz). ThiscomparisonispresentedinFigure 8.32 which shows time series of ellipsoidalheight from CSRS-PPP (red) and PPPW (green)aswell as the RTK solution(black).Com- parisonoforiginal processingoutput is shown in the top part as well as comparisonfor the MA-smoothedtime series in the bottompartofFigure 8.32.

Figure8.32: Comparison of ellipsoidal heightbetween PPPand RTK solutions forCS4 (01.12.2019): CSRS-PPP (red) /PPP-Wizard (green) /RTK solution(black).Original processing output timeseries shownontop, MA-filteredtime series at the bottom.

Resultsinformthe usual performance metrics fordifferences between thePPP heights and the RTK heightsare presentedinTables 8.16 (originaloutput) and 8.17 (filtered time series). Comparingthe resultsshown in the tables, the huge benefits of the smoothing become apparent. All performance metrics areimproved(up to factor5-10, on average by factor ∼2) by applying theMA-filter as described in Section 8.1.Filtered time series showdeviations (bias and median) in the decimetre-range forCSRS-PPP and lowmetre-range forPPPW, whichcorrespond to the current limits (aspresented in literature) forbothPPP and RTK in suchhighly kinematic scenarios. Comparing theoriginal outputofRTK andPPP solutionsyields bias, RMS and median values of approximately 2-2.5 metresand thus shows higher values than the expected 8.5Casestudy 4: 01.12.2019 121 qualityrange forkinematic SF-PPPprocessing (decimetre-range).Reasons forthis sub- stantialdifferences might be the different ionospheric mitigation strategies forSF-PPP andRTK (althoughcorrections using aTEC model arealreadyapplied forPPP).An- other possible explanation is thatthe RTK solution might not be referringtothe GNSS antenna but the actual receiver position (inside the train).Since no detailed documenta- tion wasprovidedfor the RTK datatheseassumptions couldnot be investigated further. Moreover,one noticesPPPW showing betteragreement forthe comparisonoforiginal processing output withRTK whereas CSRS-PPPshows smaller deviations in the case of smoothed time series. Overall these comparisons outline agood PPPperformance andshowresults comparable to the RTK height coordinatesolution,which alsoincreases theconfidence in theZTD results derived from PPP processing.

Processing scheme Bias [m] Standard deviation [m] RMS[m] Median [m] CSRS-PPP 2.449 6.782 7.397 2.162 PPPW 1.995 7.626 7.903 2.046

Table 8.16: Performancemetrics forthe PPP noise analysis of CS4 forCSRS-PPP and PPPW. Measures arecomputed forheightcoordinate differences between rawPPP output and the rawRTK solution.

Processing scheme Bias [m] Standard deviation [m] RMS[m] Median [m] CSRS-PPP -0.048 3.229 3.229 0.267 PPPW 1.538 4.517 4.772 1.505

Table 8.17: Performancemetrics forthe PPP noise analysis of CS4 forCSRS-PPP and PPPW. Measuresare computed forheight coordinate differences between smoothed PPPand RTK timeseries. 122 Results

8.5.3ZTD validation

The ZTD validation forCS4 providessome interesting results which deviate to some extend fromthe former cases. Its main results areshown in Figures 8.33 - 8.35.

Figure8.33: Comparison between estimated GNSS-ZTD (CSRS-PPP (red)and PPP-Wizard (green)) and ERA5-ZTD(black) forCS4 (01.12.2019), Top: absolute values, bottom: differ- ences between GNSS-ZTD with respecttoERA5-ZTD

Overall, the results areagainvery promising, withhighest bias andRMS values in the lowcentimetre-range. The maindeviation to priortest cases is the relativeperformanceofthe processing schemes. Especiallysurprising is the fact thatinthis case CSRS-PPP providesthe least accurate results, based on the validation with ERA5-ZTD. Furthermore, the standard PPPW this time shows lowest standard deviation of allthree schemes. As forCS2, the PPPW-HC processing performs best in terms of bias (1.64 cm)and RMS (1.87 cm) butimprovements comparedtothe standardversion (PPPW) aremarginal this time. Correlation of all schemes withERA5-ZTDisagainveryhighand the standard deviations (∼0.8-1.1 cm) arecomparable to CS3,see Figure 8.35. Adetailed summary of the statisticsdiscussed aboveisprovided in Table 8.18. 8.5Casestudy 4: 01.12.2019 123

Figure 8.34: Histograms of ZTD differencesbetween GNSS-ZTD andERA5-ZTD fortest case CS4. Left: CSRS, Right: PPP-Wizard.Alsoindicated arebias and standard deviation (σ)ofthe respectivesolutions.

Figure 8.35: Correlation between ZTD as estimated by each softwarepackage and theERA5 referencevaluesfor CS4, 01.12.2019: (left) CSRS-PPP,(middle)PPPW and (right) PPPW- HC. Terms Rand yrepresent the correlationcoefficient and thelinear fit, respectively.

Processing scheme Bias [cm] Standard deviation [cm] RMS [cm] Correlation CSRS-PPP 2.08 0.97 2.200.96 PPPW 1.77 0.85 1.89 0.96 PPPW-HC 1.64 1.07 1.87 0.96

Table 8.18: CS4: Performancemetrics forthe ZTDvalidation againstERA5-ZTD forpro- cessing resultsofCSRS-PPP,PPPW and PPPW-HC. 124 Results

8.6 ZTD sensitivityanalysis

In addition to the main resultsofthe four test casespresented before, this section in- vestigates theinfluence of certainadaptations in the processing settings of thepurposed approaches. Some of thosechanges areofparticularinterest forNRT processing ap- proachesdescribed in the next chapter. In the followingsection, only selected software packages (GAMP/PPP-Wizard) areuseddepending on their capabilities forfine-tuning of the processing.Asalready mentioned before, CSRS-PPPisnot configurable manually andtherefore not feasible forsuch typesofstudies. Aimofthisinvestigationsistoassess the sensitivityofthe ZTDsolutionconditional on theuse of specific data and settings in PPP processing.The following settings are assessedinthe course of this section:

• UsageofGLONASS observations

• Elevationcut-off

• Gradient estimation

• Mis-modelling of ionospheric delays using SEID

• Height-dependency of ZTD errors

Compared to themainresults fromthe case studies, adetailedsummary of statistical performance measuresisnot presented forthese sensitivitystudies. Insteadavisual comparisonand only afew keymetrics as performance indicators areused to emphasize possible benefits forcertain changes in processing.

8.6.1Impact of GLONASS observations

In the following, the impact of additional GLONASS observationsinPPP processing on the ZTD solutionisassessed using PPPW ZTDsolutions forCS3 and CS4, processed in GPS+GLONASS andGPS-only PPPmode. Typically GLONASS observations areoflowerqualitybut can stabilize solutions in crit- ical environmentswhereonly less GPS satellites areavailable. The resultsfrom GPS-only vs GPS+GLONASS processing forthe test cases CS3 and CS4 areshown in Figures 8.36 and 8.37 respectively, as forthe priorsections in terms of ZTDand differences to ERA5-ZTD. In both cases no significant impact of the additional observationscan be found. Thereare small deviations between the solutions which are visible in the difference plots, forexample around12:30 UTC in Figure 8.36.Most of 8.6ZTD sensitivityanalysis 125 these smalldeviations even indicate betterperformance of the GPS-only solution, which might indicaterather poorqualityofeither GLONASS observations or GLONASS cor- rectionproducts (e.gclock corrections). Bias, standarddeviation andRMS values are practically unchangedbyadding/removing GLONASS observations from theprocessing (see Tables 8.19 and 8.20). This disagrees withstudies like Webb et al. (2016), who found improvementsofabout 5mmonaverage when using GLONASSobservations additionally. However thesestudies used data fromhigh-gradeDFreceivers and envi- ronmental conditions were (while stillmountainous) notreallycomparable. For futureapplicationsitmight be interestingtoanalyse the performance of GPS+Galileo solutions as soon as the new generation of receivers is available withinthe Greenlight project.

Figure8.36: Comparison of GNSS-ZTDwith ERA5-ZTD with/withoutGLONASSobserva- tions forCS3: (1) GPS+GLONASS(dark green),(2) GPS-only (light green). Absolute ZTD values (top) andabsolutedifferences to ERA5-ZTD (bottom).

Setting Bias [cm]Standard deviation [cm]RMS [cm]Correlation GPS-only -2.88 0.84 3.00 0.97 GPS+GLONASS -2.89 0.83 3.00 0.97

Table 8.19: CS3: Performancemetrics forthe ZTDvalidation againstERA5-ZTD forpro- cessing resultsfor GPS-onlyand GPS+GLONASS 126 Results

Figure 8.37: Comparison of GNSS-ZTDwith ERA5-ZTD with/without GLONASS obser- vations forCS4: (1) GPS+GLONASS(dark green),(2) GPS-only (light green). ZTDvalues (top) and differences to ERA5-ZTD (bottom).

Setting Bias [cm]Standard deviation [cm] RMS[cm] Correlation GPS-only 1.76 0.87 1.96 0.97 GPS+GLONASS 1.770.85 1.97 0.97

Table 8.20: CS4: Performancemetrics forthe ZTD validationagainstERA5-ZTD forpro- cessing resultsfor GPS-only andGPS+GLONASS 8.6ZTD sensitivityanalysis 127

8.6.2 Elevation cut-off

Thissectioninvestigates the sensitivityofthe ZTDsolution to the applied elevation cut-off. Theonly softwarepackage where theelevation cut-off can be varied is GAMP and therefore only test case CS2 is analysed here. Three different solutions areproduced for5◦,7.5◦ (default) and 10◦ cut-off,where the last two versionswere found to be identicaland therefore areonly shown once. ZTD solutions in comparisontoERA-ZTD arepresented in Figure 8.38 andthe corresponding histograms of the ZTD differences in Figure 8.39. The results indicate avisible improvement/degradation of the solution with higher/lower cut-offsetting.This is most prominentinthe flatter/lower-altitude parts of the track (beginning andend sections) whichseems intuitive due to thefactthatonly there satellites at lowelevation will be visible/trackable. Largest improvements in those areas areinthe cm-range and therefore clearly beneficial forZTD estimates. The overall bias canbereduced by about2mm and standard deviation is reduced by 5.5 mm forthe higher elevation cut-off solutions(see Table 8.21). Moreover it is visible from Figure 8.39, thatthe computed differences to ERA5-ZTDfollowthe expected Gaussiandistribution to alargerdegree forthe higher cut-off. The sample sizeofZTD differences might be relativitysmall but nevertheless atrendofimprovement is already noticeable. However, overasmall part on the track between 10:00and 10:30the oppositebehaviour can also be recognized. Most likely this is due to an already considerably lownumber of satellites in view, which could already be seen fromFigure 8.12 in Section 8.3.

Theseresults maydisagree with commonstrategies used fortropospheric estimation from GNSS, whereusing lowercut-off settingsachieves abetter decorrelationofZTD from the height coordinateand therefore is expected to provide improvedresults. A more detailed discussion on this topicisgiven in the final conclusions in Chapter 10.

Setting Bias [cm]Standard deviation [cm]RMS [cm]Correlation Cut-off 5◦ 0.54 2.55 2.56 0.94 Cut-off 7.5/10◦ 0.38 2.01 2.01 0.96

Table 8.21: Performancemetrics forthe ZTDvalidation againstERA5-ZTDfor processing results for5◦and7.5/10◦ cut-off elevationangle settings. Investigatedtest case is CS2. 128 Results

Figure 8.38: Comparison of GNSS-ZTD with ERA5-ZTD fordifferent settings forelevation cut-off: (1) 5◦ (dark blue),(2) 10◦ (lightblue). Absolute ZTDvalues(top) andabsolute differences to ERA5-ZTD (bottom).

Figure8.39: Histograms of GNSS-ZTDdifferences to ERA5-ZTD fordifferent settings for elevation cut-off: (1) 5◦ (darkblue),(2)7.5/10◦ (light blue). 8.6ZTD sensitivityanalysis 129

8.6.3 Estimationofhorizontalgradients

Thissectioninvestigates the possible benefit of additionally estimating horizontal tropo- spheric gradients in PPP processing. The extension of the parameter estimation fortroposphericgradients is atypical pro- cedure in GNSS Meteorology.Manystudies have confirmed itsbeneficial effects on troposphere and/orposition solutions andtheir usabilityfor dataassimilation. Further- more they also enable the user to calculateslant delays foreach observedsatellite, a parameter which is of increasing interest in the scientific communitynowadays. However, in asituation likepresent withinthis study the expectedbenefits of estimating this additional parameter might be reduced or not present at all.Somedetailed thoughts on thistopic can be found in the nextchapter, Section 9.4 Howeveritshould be mentioned that the results shown in the following only assess the influence of additionalgradient estimation on the ZTD solution. No actualgra- dient parametersare analysed, nevertheless thismight be atopic forfutureinvestiga- tions/applications. Gradients were introduced in processing using the formulation of Chen and Herring (1997)and estimated every epochtogether with thecommonparameters (coordinates, receiver clockerror andZTD). Theresults from ZTD-only vs ZTDand gradients (ZTD+GRAD) processing forCS2 areshown in Figure 8.40 and the respective his- togram of thedifferences to ERA5-ZTD in Figure 8.41. As with the usageofGLONASS,nosignificant impact can be found and distributions of ZTD differences arepractically unchanged by additional gradientestimation (see Table 8.22)asindicated also in the visual comparison of the ZTD(difference) time series. This disagrees withmostliteratureonthis topic, afact that mightbeattachedtothe challenging conditions present in this study (especially forCS2 which is analysed here). For large partsofthe analysed track, satellitevisibilityisreduced and redundancy might not be sufficient to estimategradient parametersofgood qualityorincrease thequality of estimated ZTDs.

Setting Bias [cm] Standard deviation [cm] RMS [cm] Correlation ZTD-only 0.66 2.58 2.54 0.94 ZTD+GRAD 0.68 2.58 2.54 0.94

Table 8.22: Performancemetrics forthe ZTDvalidation against ERA5-ZTDfor processing results forZTD-only and ZTD+GRAD settings.Investigated test caseisCS2. 130 Results

Figure 8.40: Comparison of GNSS-ZTDwith ERA5-ZTD with/without gradient estimation: (1) ZTD+GRAD (dark blue),(2)ZTD-only (light blue). Absolute ZTD values (top) and absolute differences to ERA5-ZTD (bottom).

Figure8.41: Histograms of GNSS-ZTDdifferences [cm] to ERA5-ZTD with/withoutgradient estimation: (1) ZTD+GRAD (dark blue),(2) ZTD-only (light blue). 8.6ZTD sensitivityanalysis 131

8.6.4 Mis-modelling of ionosphere using SEID

Thissection addresses the problemofapossible miss-modelling of theionosphericdelay whenusing the SEIDmodel and itsinfluence on theZTD solution. Therefore adifferent sectionfrom thetrain trackofCS1 wasprocessed using (1)CSRS-PPP,(2) PPPW and additionally (3) SGAMP. The resultsare shown in Figure 8.42.

Figure 8.42: Comparison of GNSS-ZTD timeseriesfromCSRS-PPP (red), SGAMP (blue) and PPPW (green) for16:00 to 19:00, 11.05.2017 (date of CS1).

Adistinctivebiasofabout 5dmisvisible forthe SGAMP time series compared to the CSRS-PPP and PPPW results. HoweverERA5-ZTDwas notspecifically derived forthis period,i.e. afull validation asfor thecasestudies wasnot carried out. Neverthelessthe largebias present indicates problems in the SEID model, whosusage representsthe key difference to the otherschemes. Since these haveshown reasonable performance forall test cases and in particularalso CS1, this cross-comparison seems sufficient to estimate theinfluence of miss-modelling the ionsopheric delayusing SEID. As showninSection 6.4.1,the accuracy of the ionospheric modelling using SEID is stronglydependent on the quality of thephase observations (frombothDFand SF stations) used. In case thisqualityisdegraded by e.g.cycle slips, the model algorithm might not be able to mitigate these errors, especially in the caseoflarge cycleslips which 132 Results remain undetected. This is represented in the large offset the SGAMP ZTDtime series shows forthis case. Even though the GAMP PPPengine tries to detect and correct present cycle slips in DF-PPP porcessingusing theMW-LC, alarge bias is still presentinthe ZTD results. Processing details from SGAMP reveal that forover50%ofepochs cycle slips havebeen detected. Many of those detected cycle slips showmagnitudesfrom 10-50 mand where probably introducedbysingle, undetected cycle slips (inSForDFdata).Inextreme cases likethis one, they areable to propagatethrough the SEIDalgorithm or areeven amplified by it. Thisshows the immense importance of rigorouscycle slip detectionand quality control forthe retrieved GNSS rawdatabefore using them in the SEIDmodel. Cycle slips in DF data aregenerallyeasier to detect.This can either be done using common strategies as outlined in Section 6.2 or in the SEID algorithm by identifying abnormally large values of epoch-differenced GF-LCs (dL4),asshown in Figure 6.3.For SF data, the methods described in Section 6.2 have to be appliedprior to usage of thedata in SEID algorithm. AdetectionlaterinPPP processing using DF detectionmethods gets much more challenging since theobservations on both carrier frequencies arenot independent any more.

8.6.5Altitude-dependency of estimation errors

As alastpointofthe sensitivitystudiespresented here,anassessment of the error behaviour withvaryingaltitude is carried out. This denotes an interesting question which wasalready assessed by Webb et al. (2016)for asingle railway track in North Wales. They found no obvious degradation with altitude fordifferent estimation strategies. For this study,fourdifferent test cases areavailable forCSRS-PPPand PPPWand can be averaged. Nevertheless one hastokeep in mind thatthesetracks allcan have substantiallydifferent features (multipath, shadowing, satellitegeometryattraveltime, ...),alsoatequal altitudes. Therefore thisassessment can only serveasafirst indication forthe comparison of the solutions in this respect. The results presented in Figures 8.43 and 8.44 representdifferences between GNSS-ZTD (CSRS-PPP andPPPW)and ERA-ZTDfor altitudesfrom 200-1000meters(x-axis), averagedover the analysed railway tracksfor different processing strategies.

Figure 8.43 presentsthe errorevolution with height averaged over all four test cases/tracks. Overall results indicate better performance forPPPW at loweraltitudes 8.6ZTD sensitivityanalysis 133

(up to 450-500m). At higher altitudes the PPPW performanceslightly decreases compared to CSRS-PPP, whichshows better results fromthereon. In general, performance increases withincreasing altitude forbothsolutions. CSRS-PPP errors staypretty constant at the2-3 cm level for500 mupwards. Noticeableisalso a clearincrease in performance forbothGNSS-ZTD solutionsaround 400m.This might be due to statistical reasons(most of the covered tracks lie abovethese heights) or increased encountering of (more) challenging conditionsatthe loweraltitudes (urban parts, multipath,...). In addition, Figure 8.44 shows the results foreach case separately,which enables to

Figure 8.43: Absolute GNSS-ZTD differences[cm] with respecttoERA5-ZTD,averagedover all four test casesfor CSRS-PPP (red) and PPPW (green) over thecovered altituderange from200 -1000 mellipsoidalheight. analyse each track/route and its characteristics separately.This is of interest since, as outlined in the case studies before, ZTD resultscan differ significantly fromeachother forthe different tracks/dates. CS2 (28.09.2017, top left)and CS3 (29.11.2019,bottom right)confirmthe findings presented in the averaged solutionabove, i.e.better performance of CSRS-PPPat altitudes higherthan500 m. Again thedifference stays almost constant (especially visiblefor CS2) with increasing altitude. CS1(11.05.2017,top left) and especially CS4 (01.12.2019, bottomright) reveal differ- ent patterns in the comparison between CSRS-PPP andPPPW. PPPW outperforms CSRS-PPP over the first part of CS1.These results becomeclearwhen looking at the height distributionofthe route which staysunder 450mmostofthe time (essentially altitudes where PPPW has loweraverageerrors as well). 134 Results

Resultsfor CS4 differ fromthose of the other test cases by showing better performance forPPPW withincreasing altitude. Below approximately 700mboth solutions show almost equal performance, abovePPPW biases are ∼ 1cmlowerthan forCSRS-PPP. Reasonsfor this behaviour arechallenging to find, maybethe fact thatthis case representsanight travel(andthereforedifferent ionospheric conditions) plays arole.

Figure 8.44: Absolute ZTD differences [cm]with respect to ERA5-ZTD, shown forall four test cases separately forCSRS-PPP (red) andPPPW (green)over the covered altitude range from 200 -1000 mellipsoidal height.

Overall theassessment of this section canbesummarized by the following points:

• Overall performance slightly improveswith increasing altitude.

• CSRS-PPPoutperforms PPPW at altitudesabove 450m,while forlower altitudes PPPWperforms better.

• Onetest case (CS4),coveringanight-time travel showscompletelycontrary re- sults, withlower errorsfor PPPW at higher, and approximatelyequal performance of both solutions at loweraltitudes. 8.7Assimilation tests in WRF 135

8.7 AssimilationtestsinWRF

This lastsectioninChapter 8 provides theresultsofthe assimilation tests using the WRF model. These testsshouldnot be equated with full impact studies forZTD assimilation as foundinalot of theliteraturepresentedinSection 7.3.The setup is rather reduced and concentrates fully on investigating the required quality of GNSS-ZTD to enter the DA system and if this qualitycan be achievedbythe resultspresentedinthe last sections. Therefore afew considerations havetobenotedhere before resultsare presented:

• Due to both time andcomputational resourcesthe resultshere focus on the ac- tualDAprocedure. This means that only theWRFDAmodule wasrun andan assessment of thequantityofGNSS-ZTD observations entering the procedure (and therefore the models initial state) is presented.

• No actualforecast wasrun due to reasons mentioned aboveand also due to the unlucky coincidence that almost no precipitationhas been observed over Austria on the investigated days. This would makeithardtoverifyan(beneficial) impact on precipitation/moistureforecasts, even if the computational resources would have been available.

• FurthermoreGNSS-ZTDdataisonly available from one railway track peranalysed case study and therefore its impact on actual forecasts is assumed to be limited. However this will change as soon as datafrommultiple tracks can be obtained simultaneously.

• The assimilation runs of WRFDAwerecarried outbymycolleagueNatalia Hanna.

8.7.1 WRFsetup

TheWRF model domains utilized forthe testsare showninFigures 8.46 and 8.48.The parentdomain with 30 km horizontalresolution, shown in black, basically covers Central Europe and the first nested domain, shown in blue, with10kmresolution is fittedto theAustrianborders. Furthermoreathird,very small domainwith3kmresolution was addedinorder to copewith the mountainous terrainthat is covered by thetrainroute. Thegeneralsettings forthe assimilation testsare summarized in Table 8.23 below.

8.7.2 Influence of horizontal resolution

The most importantsetting forthe DA setup in conditions as present in this study (mountainous terrain+moderate/unknown qualityofobservation data) is the horizon- 136 Results

Parameter Setting PeriodsCS2/CS3(1heach) Horizontal resolution (d01,d02,d03) 30/10/3km Background data and boundary conditionsERA5 Observation interval (GNSS-ZTD) 60 s Assimilation method 4D-Var Assimilation window1h ObservationoperatorGPSZTD Observationerror(pre-defined in WRFDA) 0.5cm Error threshold 2.5 cm

Table 8.23: WRFDAsettings chosen forthe assimilation tests. tal resolutionofthe model domain. It determines the qualityofthe background/model topography which is crucialfor thecalculation of ZTD values in themodel domain (re- ferred to as WRF-ZTDfrom nowon). Since thequalitycheck is based on the deviation between GNSS-ZTDand WRF-ZTD, the accuracy of WRF-ZTDdirectly influences the results of the check and therefore the decisionwhich GNSS-ZTDobservationsare ac- cepted by WRFDA. Figure 8.45 displays thedeviations between WRF-ZTDand GNSS-ZTD fortwo different setups: (1) using twomodel domains with30/10kmhorizontal resolution (d01,d02), (2)using an additionalthird domain of 3kmresolution(d03), nestedinto the10km domain. In addition the error threshold forthe qualitycheck is also indicated. Obviously,the GNSS-ZTD deviations with respect to WRF-ZTD aremuch toolarge in setup(1), whereas forsetup (2)all observations areaccepted by WRFDA(in case (2)only 10 points in the domain were used!). This behaviour becomes intuitive when one keeps in mind the environment in which the data wasgathered.Even at the less problematic sections of the routes, e.g.broader valleys like theInn valley,great changes in topography can be experienced within afew kilometres horizontaldistance. In narrow alpinevalley or at passes, altitude changes from 500-1000mcan be found on less than akilometrehorizontaldistance, in extreme cases. If due to apoorhorizontal model resolutione.g.apoint on amountaintop is chosen instead of therespectivepoint on thetrack, ahuge error will be introduced in WRF-ZTD. Therefore it becomes clearthat in such environmentsahorizontalresolutionof10kmwill not be sufficient, afact that has been amajor problem in NWP forthe lastdecades and wasalso experienced here within the first try-outs. 8.7Assimilation tests in WRF 137

Figure8.45: Comparison of numbers of assimilated observationsfor twodifferentWRFDA setups: (1) usingtwo model domains with 30/10 km horizontal resolution (green),(2) using an additional third domain of 3kmresolution (blue), nestedintothe 10 km domain. Additionally the errorthreshold forthe qualitycheck is alsoshown in red. 138 Results

8.7.3Assimilation test: CS3

Figure8.46: Plot of theusedWRF model domains forCS3:parent domain (d01, black)and nested domains(d02and d03,blue and green).

The resultsofthe tests forCS3 arepresented in Figure 8.47.All importantDA settings(forbothtest cases)were already outlined in Table 8.23. In general, the CS3 test shows very promising results forboth,the CSRS-PPPand the PPPW solution.All observationsofCSRS-PPPgot assimilated (60/60points, right part) andshowcomparable or sometimes even smaller deviations to WRF-ZTDthan to ERA-ZTD. The PPPW performance is also on ahigh level with49/60, i.e. ∼ 81 %ofobservationsentering WRFDA. These resultsshowthe feasibility of using such GNSS-ZTDestimates forDAand back up the results derivedinthe validation in the last sections. This manifests in the unexpectedly large number of accepted observations (given the challenging conditions and low-cost equipment) as well as in the fact that CSRS-PPP outperforms PPPWbyasmall margin.

8.7.4Assimilation test: CS2

Although not chronologically,test case CS2isanalysed second here due to its more chal- lenging conditions and therefore also significantlydifferent results. Figure 8.48 shows 8.7Assimilation tests in WRF 139

Figure8.47: Observations assimilated forCS3 using WRFDAfor different processing schemes. Processingschemes shown are: PPPW (left) andCSRS-PPP (right). thethree model domains (30/10/3 km) and the actualtrack passed by the train. Before discussing thistest caseindetail, it should be noted herethat the chosen time slot forassimilation(from09-10 UTC)corresponds tothe most challenging part of the track, theactualpassing of the alpine ridge (see plotsshown in Section 8.3). This was chosen on purpose in order to investigate the DA procedure and observationusabilityin themostchallenging conditions possible. The resultsofthe tests forCS2 arepresented

Figure8.48: Plot of the used WRF model domains forCS3:parentdomain(d01, black) and nested domains(d02and d03, blue andgreen). 140 Results in Figure 8.49,intermsofthe number of GNSS-ZTD observations which successfully entered the WRFDAsystem. The topleft track therebyrepresentsthe reference, showing allinvestigated observation pointsinthe model (background state of the model, totalof56points).The other three parts showresultsfor SGAMP(topright), PPPW-HC (bottomleft) and PPPW (bottom right).CSRS-PPP is left out of this comparisonsince surprisingly no observationsofit passed the quality check of WRFDA. This behaviour seems anomalous when looking at resultsofthe validation presented in the last sectionsand even more so if one looks to the first assimilation test,shown in the priorsection. The other threeschemes also perform much worsethan it couldbeexpected when look- ing to the priortest case(CS3).Nevertheless fore.g. PPPW-HC still approximatelyhalf of the derivedGNSS-ZTDgot assimilated(29/56, ∼52%). For SGAMP21(37.5%) and forPPPW 14 (25%)observations passed the quality check. An interesting featureofthose resultsisalso the areal distribution of assimilated obser- vations foreach processing scheme. It showssomemajor differences in agreement with themodel state/background forecast. SGAMP and PPPW-HC seem to fit betterinthe firstpartofthe track (first half hour)whereas all accepted observationsfrom PPPW were gathered at the end of the track. The overall resultsofCS2 mightrepresent whatwas to be expected fromthe data in the firstplace (prior to the startofthisstudy) butthey aresomehow disturbing consid- ering the resultsofCS3, especially forCSRS-PPP.Mainsuspicion is that environmental conditions (concerning GNSS and DA)are evenmorechallenging forthis case thanfor the others. Thetest case representsthe passing of the mainalpine ridgeand therefore very mountainous terrain including heavily obstructed narrowvalleys, tunnels and large horizontal changes of topography.All these features mayplaytheir part in the results shown here. Some further discussiononthis topicwill be addressed in Chapter 10. 8.7Assimilation tests in WRF 141

Figure8.49: Observations assimilated using WRFDAfor differentprocessing schemes. Refer- ence observationsofmodel background areshown in blue, top left. Processing schemes shown are: SGAMP (top right),PPPW-HC (bottom left) andPPPW(bottom right). 142 Results Chapter 9

Towards real-time processing

This lastchapter aims to provide thebasis forafuturenearreal-time (NRT) applica- tion of the approach proposed in this thesis. Continuous provision of NRTtropospheric parametersfrom train-tracking datacould represent ahuge benefit forNWP,especially forvery short-term weather forecasts (called Nowcasting)whereobservations have to be availableinavery narrowtime window(i.e. with the shortestlatencytime possible). Adetailed discussion of these aspects is giveninSection 9.3. As first efforts were already started to be taken in form of aresearch project by the Research Division Higher Geodesy at TU Vienna,this chapter should serveasabasic guideline forchangestobeimplemented to the strategies given in this study. Withinthe course of E-GVAP,NRT-ZTD estimations arealreadyprovidedfor alarge number of stations (see Chapter 5). Even investigations on real-time retrieval of ZTD havebeen carried out,e.g. by Lu et al. (2017)who used IGS real-time product streams forPPP processing. Hadasetal. (2020)recently defined an advanced processing strat- egy,which reduced the aposteriori errorofestimatedZTD (formal error)by41% and deviations to final products from IGS by 17%. Their overall suggestions are:

• Apply inter-system weighting formulti-GNSS observations

• Usageofanelevation-dependent cosine-typeweighting function

• Estimatehorizontal gradients

Thesestudies couldprovidesomebasic strategies forNRT processing of Greenlight GNSS data on an operational basis. Nevertheless,refinements and adaptations accounting for the challenging environment and data qualityissues havetobeintroduced. The following sections outline some importantchanges which havetobemadetothe described post- processing approach conducted within this study, in order fit forNRT data processing.

143 144 Towards real-time processing

9.1 Requiredadaptations forNRT GNSS processing

In order to provide tropospheric products at the required timeintervals fornowcasting applications some changes to thecurrent implementation arenecessary.This concerns anumber of points of the whole approachwhich aredetailed in the following:

1. Data transmission

2. Orbit/clock products

3. Processing

4. Output interval

5. Data format results

9.1.1Data transmission

Since inthis thesis apost-processingapproachwas chosen, datatobeprocessedwas availablelong before start of computation. In contrast, forNRT processing aregular data retrieval has to be set up close after tracking. Solutionsfor this problemmight be aided by theenhancement of telecommunication networksto5Gtechnology in order to secure fast datatransfer from sensortoprocessing engine. Integration of cloud services fordata storage and processing might also be feasible since data amountswill be significantly dependent on the number of utilized trains.

9.1.2Orbit/clock products

Final orbit/clock solutions cannolonger be used since they arenot availableontime forprocessing.RTstreams(e.g. from IGS) or ultra-rapid orbit/clock productsare a possible substitute forthis problem. Nevertheless, adegradation to acertain degree must be expected compared to the presented results.

9.1.3Processingsoftware

In the course of this work, interpreted programming languages whereused forpre- processing(Matlab) and implementationofSEID (Python).Suggestion foraNRT application is to use compiled languages to maximise processing speedand therefore 9.1Requiredadaptations forNRT GNSS processing 145 reduce latency time of theresults. Furthermore anumber of differentsoftwarepackages(in different processing steps)were used in thisstudy,which automatically leads to alot of workdue to data transfer between the softwareand processing steps. In the worst case, this mayalso lead to ad- ditional errors introduced in these transfer processes. In order to avoid these confusions it maybebeneficialtoimplement afull processing chain in one single softwarepackage. This should include all steps necessary fromdata retrieval to delivery to potential end users.Asalready mentioned above,animplementation in acompiled language (e.g. C++, C, Fortran)istobestrived for. Another possibility beside designing an own, new packagewould be theextension of open-source packages to some of those used in this study (PPP-Wizard,GAMP) or thePPP softwarepackage raPPPd,developed at the research divisionHigher Geodesy at TU Vienna, which is also part of theVienna VLBI and Satellite Software (VieVS)(B¨ohm et al. 2018).

9.1.4 Output interval

This representsakey point concerning the usageofthe produced datasets in DA setups forNWP.Awell-defined balance has to be found between different aspects like:

• Use as much valuabledataaspossiblefor DA

• Investigate howmuch more datastill representsabenefit forforecasts/verification results

• Investigate howmuch data can be gathered/processed/assimilatedwithout running into computational(resource)problems

Allthese aspects havetobeconsideredwhen defining an optimaloutput interval forthe ZTD data. This is clearly to be done in close cooperation with endusersofthe data (NWP users/operators likemeteorological institutes). Therefore, adefinite recommen- dation is beyond the scopeofthis thesis. Nevertheless, the investigated intervalofone minute ZTDoutput, as introduced in Section 7.4 should be mentioned here again.Its performance wasreasonable foran investigation of pre-study status likethis one here. As already mentioned before, alot of furtherresearch might be necessary on this, in order to derive thebest possible choice foranoperational implementation. 146 Towards real-time processing

9.1.5Data format of NRT products

Although thismight be aminorpoint, theformat in which resultsare providedtopossible usersshould still be discussedhere. Currently the only existing standard formatfor GNSS- derived tropospheric products is the COST-Format (E-GVAP 2014). All processing products established at the Research Division Higher Geodesy at TU Vienna aredelivered in this format. However due the specialnature of thedata (much higher time-resolutionpossible,but only from one receiver/train perfile) one might think about alternatives. Ahighly standardized and widely-used format,especially formeteorological applications, is the NETCDFformat.This one could easily be adoptedfor theneeds of this application and most meteorologicalmodels arefamiliarwith it. Nevertheless it might also be possible to redefine the COST-format based on the structureofthe train-borne ZTD estimates.

9.2 Purposedworkflow forNRT processing

In general,two options forNRT PPPprocessing of Greenlight GNSS data arediscussed in the following.They areclosely related to theapproaches outlined in this study for post-processing,with the relevant changes describedbefore.

• SF-PPPusing regional ionosphere maps

• DF-PPPusingSEID model

9.2.1SF-PPP usingregional ionosphere maps

Thiscan be referredtoasthe standard approachwhen working withSFGNSSobser- vations.Thereforeitwas also used formost processing carried out in this study and its performance is well documented fordifferent softwarepackagesinChapter 8. Nowadays anumber of different models areavailable forboth global andregionaliono- spheremodelling.Mostofthese providecorrectionsinformofVTEC mapswith about ± 1-2 TEC units accuracy,which can be mapped to the elevation of every satellite in view. Usingthese STEC values,aionospheric range correctioncan be applied.

9.2.2DF-PPP using SEID model

The alternative approach to theusage of TEC maps presented aboveisa”synthetic upgrade” to DF observations using the SEIDapproach (Deng et al. 2009). The SEID model wasalready introduced in detailbefore (Section 6.4), thus this section focuses 9.2Purposedworkflowfor NRT processing 147 on the implementationofaprocessing strategy comprising the SEIDalgorithm it as a prerequisite. Apossibleapproach forimplementation is shown using the flowchart in Figure 9.1.

Figure 9.1: PossibleFlowchart forSEIDDF-PPP processing in aNRT-implementation of ZTDestimation from Greenlight GNSS data.

1. In the first step the SF datafromthe train as well as DF reference station data have to be gathered. Ideally this process is carried out simultaneously,using the principles of Parallel I/O.

2. Then both datasets arepre-processed, containing steps introduced in Section 6.2, in order to secure only data of usable qualityentersthe SEIDmodel.Againit would be favourable to parallelizethis step forSF/DF data.

3. In the thirdstepcommonsatellites of SF and DF dataset aredetermined and the interpolation coefficients of the SEIDmodel can be calculated from the DF data.

4. These coefficients areapplied to the SF datainformofthe SEIDmodel, generating asecond frequency observation. 148 Towards real-time processing

5. This extended dataset is processed in PPP mode using the IF-LC in an epoch- wise manner. In thecasethat continuous data streams of SF/DF data can be established, the whole process could be repeatedepoch-wise,avoiding large I/O of RINEX datainthe process.

9.3 Requirements forNWP assimilationand applica- tions

NRT products (from GNSS or other sensors) areofimmense importance forNWP appli- cations, especially very short-termweather forecasting (Nowcasting) and severe weather warning systems. Nowcasting products forinstance need to be produced rapidly (ideally available to customerswithin15minutes of data time) (Ballard et al. 2016). Moreover it is also crucial to matchthe observations as closely as possible in the first hoursofthe forecast.Anumber of studies haveoutlined the benefits of NRT tropospheric param- etersfrom GNSS fornowcasting overthe last decade. An extended overview of those investigations wasalready given in Chapter 7,Section 7.3. As already mentioned the 4D-Var assimilation shall be utilized to exploitthe high tempo- ral resolution of the GNSS-ZTDestimates in an optimal way.The nextsections describe afeasible example setup to realizeanoperational mode of Greenlight-GNSS-ZTD as- similation foroperational nowcasting.

9.3.1DAconfiguration

The configuration of theDAsystem is akey point forensuring the greatestpossible benefit of the GNSS-ZTDestimates. In thisstudy,usage of the 4D-Var technique was purposed.Anumber of studies havealready investigated the potentialofthistechnique forshort-termweather forecasts and nowcasting (Ballard et al. (2016), Thiruvengadam et al. (2020), Li et al. (2018), ...). It wasshown by Li et al. (2018)that 4D-Var assimilationhas apositive impact on precipitationforecasting skills compared to the corresponding 3D-Var assimilationfor thewhole nowcast period (sixhours fromanalysis time) and forecasts forthe United Kingdomclearly benefited fromthe use of extra, higher time frequency observations in both 3D-Var and 4D-Var setups. An example 4D-Var setup proposed by Ballard et al. (2016)isshown in Figure 9.2.This setup wasused within theNowcasting Demonstration Project(NDP) forprecipitation forecastsduring the LondonOlympics 2012. Akey factor of the implementation, whichisalso showninFigure 9.2,isthe observa- 9.3Requirements forNWP assimilation andapplications 149

Figure9.2: ExemplaryDAconfiguration using 4D-Var technique. Takenfrom Ballard et al. (2016)

tion window, i.e. thetime windowfrom which observations can be used to determine the next analysis. The study suggests that hourly GNSS-ZTDdata fromreference stations typically arrived toolate forthe shown setup, which uses an observation windowof60minutes.This is afamiliar problem which the Research DivisionHigher Geodesy at TU Vienna frequentlyencountered in the productionofNRT estimates forZAMG from an Austrianreference station network (Weberetal. 2019). Such a drawback could be resolvedbythe Greenlight ZTDestimateswhich areavailable on a shorter time-scale (e.g.15minutes as proposed before).Therefore asimilarsetuplike shown abovecould be used in case of using 4D-Var forassimilation of the ZTDestimates.

Howeverarefined strategy definitionfor thisproblemisfar beyond the scopeof this thesis. Therefore this proposed suggestionshould only serve as areference point forpossiblefuture implementations. It depends largely on the actual NWMand its compatibility with such aDAsystemand thus has to be coordinated with the model operators. 150 Towards real-time processing

9.4 Extension to advanced troposphericparameters

In terms of data delivery, the current setup couldbeextended foradvanced tropospheric products, i.eslant delays and horizontal gradients. Estimationofhorizontalgradientswas alreadyinvestigated in the course of this thesis, see Section 8.6.Gradient estimation has shown to be beneficial forGNSS-ZTDquality(Zus et al. (2019a), Hadasetal. (2020), ...) as well as forvariational DA methods (Zusetal. (2019b)).However, in this study only the influence on ZTDestimation wasanalysed, notthe quality of theactual gradient estimations themselves. From theresults shown in Section 8.6,nobeneficial effect could be found on ZTDsolutionswhen extending the parameter estimationfor gradients. This disagrees withliteratureavailableuptill nowonthis topic (Zus et al. (2019a), Hadas et al. (2020)).Nevertheless, one has to keep in mind thatthese studies focused on static measurements, mostly fromhigh-quality data gathered at reference stations placed strategically.However, theinitialsituation forthe data usedinthis study is significantly different. Thismight concern the following considerations:

1. In challenging GNSS environments, like frequently encountered in the railway do- main, satellite visibilityand therefore geometryoften is degraded. Therefore re- dundancy is not alwayssufficient to provide high-qualityestimates or even provide asolutionatall. As typically the position solution is the one of most interest, otherparametersare often downgraded in the processing.

2. In the case of such highly kinematic observations it might be questionableifgra- dient parametersare as interesting formeteorological applications as in the static case. Thisaddresses the fact that the sensorismoving relatively to acertain atmospheric phenomena to be observed.Asmuchasthese relativechanges could be of interest, it could alsointroduce some interferences between these effects which might cancel out information which would be present in gradients of static station data.

Therefore reliablepredictions on the benefit of train-borne atmospheric gradientsfor NWPcan not be providedhere,i.e. more effortshavetobeput in such investigations in order to guarantee useful results. From atechnicalpoint of view the extension to gradients is not toomuch effort since manysoftwarepackagesalready include the possibility of gradient estimation. This can then easily be extended forSTD estimates, using ZTD and gradient estimations to derive slant delays in astraightforwardway,e.g. by implementationthe formulation of Chen and Herring (1997)asrealizedinthe softwareATom(M¨oller2017). Chapter 10

Conclusionsand outlook

This study assessed thefeasibilityofderiving tropospheric parametersfromlow-cost GNSS receivers operating on trains and their usabilityfor assimilationinNWP models. Overall goalwas aprove of concept forafull processing and analysis chain from data retrieval to processing, filtering and finally usage in aNWM. The datautilized in thisstudy originate fromGreenlight,aproject led by theAustrian Federal Railways, and were collected on anumber of trains operatingondifferent tracks all over Austria. Rawdataobtained from the trains wasprocessed and analysed in terms of position and especiallytropospheric parameters, in detail ellipsoidalheight and most importantlyZTD.

Firstkey points in thedata processingchain were asuitable pre-processing strat- egy which includes amultipath analysisand cycle slip detection. Furthermore the fact that only SF observationsare availablefromGreenlightnecessitates aseparate correctionofthe ionospheric influence. Therefore two different approaches were tested:

• Range correction usingTEC maps derived fromglobal ionospheremodels

• Generation ofDFdatausing the SEID model

Bothapproaches were found suitable to account forionospheric delays up to the accuracyrequired forZTD estimation.

Alldata were processed using akinematic PPP approach deriving position and ZTD estimates fromthe tracking data.Although this common generalapproach is taken forall test cases, different strategies forcertain processing aspectshavebeen tested and the difference in performance wasassessed.

151 152 Conclusions andoutlook

The utilizedsoftwarepackages were CSRS-PPP,PPP-Wizard andGAMP.All of them were able to provide reasonable height trajectories and ZTDestimates forall test cases.

In general,the resultsofthe case studies (TestcasesCS1,CS3,CS4) were anal- ysedinterms of three basic aspects:

1. Rawdataqualityand environmental conditions

2. Analysis of parameter noise level of the PPPsolutionsfor ZTD and height coor- dinate

3. ZTDvalidation usingERA5-ZTD

The first point includedananalysis of themultipathlevel (using CMC observables) as well as geometry indicators in form of GDOPvalues. As expected, results show increased multipath levels (up to 100-150 metres) and degraded geometry (GDOP > 4-5), especially fortracksections in urban and mountainous areas.

In the second step, the parameter noise of original PPP time series of ZTD and height coordinate wasassessed by comparisontosmoothed time seriesofthe respective parameters. This comparison wascarried out between the CSRS-PPP and the PPPW solution. This smoothed solution wasproducedusing aMA-filter with atime window of five minutes. The resultsindicate avery lownoise level forbothZTD and height coordinate. Average bias values areinthe sub millimetre-range forZTD andinthe millimetre-rangefor the height coordinate, indicating the suitabilityofthe chosentime window of five minutes forthe MA-filter.Standard deviationand RMS areincentimetre- (ZTD) and metre-range(height coordinate) and almost equal to each other for all test cases. CSRS-PPP shows significantly lowernoise levels (byafactor10onaverage)compared to PPPW forboth ZTD and height and all case studies.

Finally,results from four different processing schemes (based on the three soft- warepackagesmentioned above)havebeenvalidatedusing independent ZTDdata derivedfrom ERA5 reanalysis data:

• CSRS-PPP

• PPP-Wizard (PPPW)

• PPP-Wizard with heightconstraint(PPPW-HC) 153

• GAMP using SEIDmodel (SGAMP)

Statistical analysisofthose results revealed good to excellent agreementwith ERA-ZTD depending on the specific test case forbothprocessing schemes. Thesolutionsagree at thelow cm- to mm-level withZTD derivedfrom ERA5.Onaverage, asignificant superiorityofone solution has notbeenrecognized. Althoughonly part of the assessment fortest case CS2, the SGAMP approachshowed very promisingresultsfor this case. Results haveasignificantlylowerbias (1.34cm) compared to CSRS-PPP/PPPW (2.4/8.8cm) and the correlation withERA-ZTD is just as high as forthe other solutions. Thismakes it apromising candidatefor future investigations on this topic, although further experience and tests aredefinitely required. Furthermore the accuracy of GNSS-ZTD can be improvedbyapplying atight constraint on the heightcoordinate solution. Thiswas achieved using heightcoordinatesfrom the official trackdatabase of OBB¨ andanimplementationinthe Kalmanfilter process of the PPPWsoftware. Solutions showmedium to large improvementscomparedtothe standard PPPWversion andthe othersolutions. With even smaller errors thanSGAMP, this approachisdefinitely suitablefor further research and test processing with larger datasets.

In alastvalidation step,certain processing options were tested in terms of sen- sitivityand performance of the ZTD solution. The conducted tests accounted for:

• Benefit of GLONASS observations:Verylittle to zeroimpact has been found due to the inclusionofGLONASS observations. Thismight indicate questionable qualityofthe observations.Exceptionsare highly obstructed areas wherethey help to stillprovide asolution.

• Estimation of tropospheric gradients:Again no visibleimpact is present forthe conducted tests. Although possible benefits aredocumented in literature. They might not be present in the investigated cases due to thechallenging geometry, observation qualityand lowvisibilityofsatellites in general forcertain areas.

• Impact of elevation cut-off:Using only elevations equalorhigher than 7.5◦ showsclearbenefits forZTD accuracycomparedtoaninclusion of observations down to 5◦.These findings somehow contradict with thefact that tropospheric estimates can be decorrelated from the height coordinate more efficiently when using alowerelevation cut-off. Nevertheless the results presented within this 154 Conclusions andoutlook

study areassumed to be heavily affected by thespecific environments the datais collected in. High multipath influence on signals at lowelevations and alimited number of those observations due to shading effectsmight be themainreasons behind the improvements fromhigher cut-off settings.

• Mis-modelling of ionospheric delayusingSEID:The results showthe huge sensitivityofthe SEID model and its results to outliers and cycle slips in the utilized phase observations. If alarge number of cycle slips remains undetected in pre-processing,errors introduced in theZTD solution can reach decimetre-levels. Rigorous qualitycontrol andefficient cycle slip detectionmethods areofimmense importance whenusing theSEID model forionospheric mitigation.

• Altitude-sensitivityofZTD errors:The analysis of the resultsshows agenerally decreasing errorinZTD withaltitude for both investigated schemes (CSRS-PPP and PPPW). This might be attached to the fact that with increasing altitude the amount of watervapourand therefore ZWD decreases. This means the rela- tiveimpact of ZHD modelling on ZTD results is increased and this parameter is much easier to model than ZWD. On the other side, under normal circumstances mountainous terrainismorelikely encountered at higheraltitudes and therefore geometryand satellite availabilitysuffer as well as multipathinfluence is present more often. On average,the first of those two considerationsseems to be the more prominent one forthis study. Comparing the solutions from the schemes yieldsanadvantage forPPPWatalti- tudes below450 mand vice versa forCSRS-PPPabove thisaltitude.

Furthermore, first tests forassimilation of GNSS ZTD data derived from trains were conducted fortwo of thetest cases. Therefore the WRF model wasutilized anda 4D-Var assimilation scheme forone hour of GNSS-ZTD (with resolutionofone minute, i.e. 60 observations each case) wastested. Resultsare very promisingingeneral, but with distinctivedifferences between the test cases. These most likely depend on the complexityand challenges of the GNSS environment(mountainous terrain, GNSS-denied areas liketunnels, urban areas). For testcaseCS3, almostall GNSS-ZTD observations(CSRS-PPP: 100%, PPPW: 81%) passed thequalitycheck of the WRFDAmodule, which performs theassimilation procedurewithin the WRF. Test caseCS2 however showssignificantly worse results as formostofthe four tested processingschemes not even half of the observations were accepted. Thislikely reflects the fact thatthis case presents the most challengingroute to be analysed 155 within this study.Aninteresting behaviour alsoobserved here arelocal differences between processing solutionagainst WRF-ZTDs. For threeout of four schemes (CSRS- PPP,PPPW-HCand SGAMP) onlyobservationsinthe first part of the investigated trackwere assimilated, forPPPW onlyobservations from the end of the track. The turning point seemed to be theactual alpine passing (pointsofhighest altitude) where tunnels were encountered. It couldbeguessed that abias introduced after this tunnel passage causes thisdistinctive behaviour but further researchand casestudies are definitely needed to solve this issue, andfor DA of thoseGNSS-ZTDingeneral. Howeverthese testsdid not include actually running a(precipitation) forecast, due to, amongst other things, limited (computational) resources. Therefore this investigation can only serveasafirst indication of the usabilityofthe GNSS-ZTDestimates in aNWM.

Finally,the feasibilityofthe presentedapproaches foroperationalNRT process- ing of GNSS tracking datahas been analysed and some necessary adaptations to the presented processing schemes were outlined. Anumber of challenges will arise from the extensionofthe presented post-processing study to an operational mode and an extensive test period is required to back up the findings of this thesis. Nevertheless, this extension is possible and will be of great benefit forotherscientific studies and even operational usage. Also positioningapplications fortrainlocalisation systems likedeveloped within Greenlight will benefit fromimproved processing strategies and tropospheremodelling. First and foremost, the idea of having alarge fleet of trains (uptohundreds of vehicles) andusing each one of themasameteorologicalsensorfor aparameter as importantas watervapourwill definitely be of huge interest foratmospheric sciences.The horizontal and temporal resolution whichcan be providedisnot achieved by anyother sensorat themoment. Moreover,afirst indication thatthe results areofsufficient qualitywas already giveninthis study.This qualitywill also increase in future mainly due to better hardwareand more sophisticated processing approaches. The most importantbenefits will hopefully arise forthe productionofmoreaccurate weather forecastsused fornowcasting,severe weather warnings and anumber of other NWP products. 156 Conclusions andoutlook Acronyms

ABL Atmospheric Boundary Layer

APC Antenna Phase Center

AR AmbiguityResolution

ARP Antenna Reference Point

ARAMIS Advanced Railway Automation Management Information System

AROME Application of Research to OperationsatMEsoscale

AURIS AutomatischesReisenden-Informationssystem

BOC Binary Offset Carrier

CMC Code-Minus-Carrier

CNES Centre National d’Etudes Spatiales

COSMO Consortium forSmall-scaleModeling

CS Case Study

CSRS Canadian SpatialReference System

DA DataAssimilation

DD Double-Difference

DF Dual-Frequency

DOD Department of Defence

DOP DilutionofPrecision

EC European Commission

157 158 Conclusions andoutlook

ECMWF European Centerfor Medium-Range Weather Forecast

EGNOS European Geostationary Navigation Overlay Service

EKF Extended Kalman Filter

EPOSA EchzeitPositionierung Austria

ERA ECMWF Re-Analysis

ESA European SpaceAgency

FIR FiniteImpulseResponse

GFZ GeoForschungsZentrum

GIM Global IonosphereMap

GMF Global Mapping Function

GNSS Global Navigation SatelliteSystems

GLONASS Globalnaya navigatsionnaya sputnikovaya sistema

GPS Global Positioning System

GSA European GNSS Agency

GSM Global System forMobile

HAS High-Accuracy Service

IF-LC Ionosphere-Free Linear Combination

IFS Integrated Forecasting System

IGS International GNSSService

I/O Input/Output

IPP Ionospheric Pierce Point

ITRF International Terrestrial Reference Frame

IWV Integrated WaterVapour

LC LinearCombination 159

LEO LowEarth Orbiting

LMMSE Linear Minimum MeanSquare Error

LSQ LeastSquares

MA Moving Average

MSE Mean Square Error

MMSE Minimum MeanSquareError

MPM Millimeter-wave PropagationModel

NCEP National Centersfor Environmental Prediction

NRT Near-Real Time

NWM NumericalWeather Model

NWP Numerical Weather Prediction

OEBB Oesterreichische Bundesbahn

OTL Ocean TidalLoading

PPP Precise Point Positioning

PWV Precipitable WaterVapour

QPF Quantitative PrecipitationForecasting

RINEX Receiver Independent Exchange Format

RO RadioOccultation

RT Real Time

RTK Real Time Kinematic

RUC RapidUpdate Cycle

SA Selective Availability

SAR Search-and-Rescue

SBAS Satellite-based Augmentation System 160 Conclusions andoutlook

SEID Satellite-specific Epoch-differenced Ionospheric Delaymodel

SF Single-Frequency

STEC Slant Total Electron Content

TEC TotalElectronContent

TEPOS T-Kom Services Echtzeit-Positionierung

VieVS Vienna VLBIand SatelliteSoftware

VTEC Vertical Total ElectronContent

VMF Vienna Mapping Function

WGS-84 World Geodetic System84

ZHD Zenith Hydrostatic Delay

ZTD Zenith Total Delay

ZWD Zenith WetDelay List of Figures

2.1Geometric concept of GNSS positioning,shown here in the 2D case. Takenfrom B¨ohringer (2008)...... 9 2.2 Component and errorsources in pseudorange measurements, taken from SanzSubirana et al. (2013)...... 16

3.1 Avertical column of airofdensity ρ,horizontalcross-sectional area δA, height δzand mass M= ρδAδz. Thepressureonthe lowersurface is p,the pressureonthe upper surface is p+δp...... 26 3.2 Typical atmospherictemperatureprofile from U.S. standardatmosphere, taken from Wallace and Hobbs (2006)...... 28 3.3 Climatological average precipitationrate (mm/day) for1981-2010 from ERA-Interim, Global Precipitation Climatology Centre(GPCC), Global Precipitation Climatology Project (GPCP) and E-OBS (Euro- pean Observations)taken from https://climate.copernicus.eu/ monthly-summaries-precipitation-relative-humidity-and-soil-moisture 33

4.1 Ionospheric layers present at day- andnight- time and their respectiveheights, takenfrom https://commons.wikimedia.org/w/index.php?curid=7009115 ...... 37 4.2 Ionospheric electron densityprofilescomputed from the International Ref- erence Ionosphere(IRI) modelfor Vienna in 2017,taken from Magnet (2019)...... 38 4.3 VTEC map for26.02.2010, 12 UTCderived using the Klobucharmodel. Typical maximums in VTEC arevisible at lowlatitudes. Takenfrom Najman and Kos (2014)...... 39

4.4 Height profiles of thehydrostatic(Nh)and wetcomponent (Nw)ofthe refractivity N fortwo different days,originating fromthe same time of

the dayand station. Nh shows acontinuouscurve, Nw highvariability in time and space. Takenfrom Nilssonetal. (2013)...... 41

161 162 LIST OF FIGURES

4.5 Path of aGNSS signaltrough thetroposphere. Theactual path Sis longer thanthe geometric path Gdue to the bending effect and arrives

at adifferent elevation e0.Taken from Nilssonetal. (2013)...... 41

5.1 Basic illustration of the GNSS Meteorology concept. Individual STDs are mapped to ZTD forasingle station. Takenfrom Guerova et al. (2016). . 46 5.2TimelineofEuropean projects in the field of GNSS Meteorology from 1996-2016. Takenfrom Guerovaetal. (2016)...... 47 5.3 Principle of GNSS tomography,taken from Dong and Jin (2018).... 49 5.4 Basic principle of GNSS RO, Source: ECMWF ...... 50

6.1 Overviewofsystems working together in Greenlight, courtestyofDI(FH) Manfred St¨a ttner, OBB¨ Infrastrucktur...... 54 6.2 Reference station network of EPOSA.The colour of the triangles denotes the company operating the station. Takenfrom http://www.eposa.at/ . 55

6.3 δL4 values[m] foranexample epochand allGPS satellitesprocessed within the SEID model. Largervalues indicate possible outliers or cycle slips in thedata of therespectivesatellite (e.g. G32 here)...... 64 6.4 Flowchart of the SGAMP processing scheme as followedinthisstudy... 69

7.1 ERA5 global grid of 2m-temperaturefor January 2016.Top: full reanalysis,bottom: ERA5-Land reanalysis. Takenfrom: https://climate.copernicus.eu/climate-reanalysis...... 79 7.2 Thebasic principleofDAand its main componentsoutlined forthe temperature(T, y-axis)parameter anda24-hourassimilation window (x-axis): background forecast (blue), observations (green) and analysis (red)...... 80 7.3 Simplified schematicrepresentations of four data assimilation strategies frequently-used in NWP:(a) 3D-Var,(b) 3D-FGAT,(c) incremental4D- Var,and (d)EnKF. Bluecircles represent observations,red lines rep- resent model trajectories, and purple diamonds indicate analyses. The dotted red lines in(b)represent linearly interpolated or extrapolated fore- cast values used to estimateincrements at observation times.The dashed red lines in(c)represent the initial forecast, priortoiterative adjustments. Theseillustrations areconceptual and do not accurately reflect the much more complex strategies used by reanalysis systems.Taken from Fujiwara et al. (2017)...... 82 LIST OF FIGURES 163

7.4 System components of Advanced Research WRF,taken from Barker et al. (2012)...... 85

8.1 Train-track coveredfor CS1 (Salzburg-Vienna airport) derivedfrom CSRS-PPPprocessing...... 92 8.2 Code-Minus-Carrier (CMC) observables forCS1, shown areall visible GPS satellites...... 93 8.3 Number of visible satellites (left) and GDOP values (right) along the CS1 route...... 93 8.4 CS1 PPPZTD timeseries fromCSRS-PPP (top) andPPPW (bottom). Theraw PPP ZTD estimates areshown in red, the MA-smoothed (In- terval5min) in blue...... 94 8.5 CS1 PPPellipsoidal height time series from CSRS-PPP (top) and PPPW (bottom). The rawPPP height estimates areshown in red, the MA- smoothed (Interval 5min) in blue...... 94 8.6 Comparisonbetween estimated GNSS-ZTD (CSRS-PPP(red) and PPPW(green)) andERA5-ZTD(black) forCS1 (11.05.2017), Top: ab- solute values, bottom: ZTD differences between GNSS-ZTDwith respect to ERA5-ZTD ...... 97 8.7 Histograms of ZTD differences betweenGNSS-ZTDand ERA5-ZTD for test case CS1. Left: CSRS, Right:PPPW. Alsoindicated arebiasand standard deviation(σ)ofthe respective solutions...... 97 8.8 Correlationbetween ZTD as estimated by each softwarepackage and theERA5 reference values forCS1, 11.05.2017:(left) CSRS-PPPand (right)PPPW .Terms Rand yrepresent the correlationcoefficient and the linearfit, respectively...... 98 8.9 Correlationbetween ZTD as estimated by each softwarepackage andthe ERA5 reference valuesfor CS1, excluding thefirst hour of data (12:00- 13:30): (left) CSRS-PPP and(right)PPPW.Terms Rand yrepresent the correlationcoefficient and the linearfit, respectively...... 99 8.10 Train-trackcoveredfor CS2(Munich-Klagenfurtshown here) derived fromCSRS-PPP processing...... 100 8.11 CMC observables for CS2, shownare all visible GPS satellites...... 101 8.12 Number of visiblesatellites(left) andGDOP values (right) along the CS2 route...... 102 164 LIST OF FIGURES

8.13 CS2 PPP ZTDtime series from CSRS-PPP (top) and PPPW (bottom). The rawPPP ZTD estimatesare shown in red,the MA-smoothed (In- terval 5min) in blue...... 103 8.14 CS2 PPP ellipsoidal height time series fromCSRS-PPP (top) andPPPW (bottom).The rawPPP height estimates areshown in red, theMA- smoothed (Interval 5min) in blue...... 103 8.15 Train-trackcovered forCS2 with thereference stations utilized forSEID processing shown in blue dots...... 105 8.16 Comparisonbetween estimatedGNSS-ZTD (CSRS-PPP(red), SGAMP (blue) and PPPW (green) andPPPW-HC (lime)) andERA5-ZTD (black) forCS2 (28.09.2017), Top: ZTD, bottom:differences between GNSS- ZTD withrespect to ERA5-ZTD ...... 106 8.17 Histograms of ZTD differences between GNSS-ZTD and ERA5-ZTDfor test caseCS2.Top left: CSRS-PPP, Top right:SGAMP,Bottomleft: PPPW, Bottom right: PPPW-HC. Also indicated arebias andstandard deviation (σ)ofthe respectivesolutions...... 108 8.18 Correlationbetween ZTDasestimated by each softwarepackage andthe ERA5 reference values forCS2, 28.09.2017. Topleft: CSRS-PPP,Top right: SGAMP, Bottom left:PPPW, Bottomright:PPPW-HC. Terms Rand yrepresent the correlation coefficient and the linearfit, respectively. 109 8.19 TraintrackofCS3 (29.11.2019): Innsbruck -Woergl -Bischofshofen - Liezen...... 110 8.20 CMC observables forCS3, shown areall visible GPSsatellites...... 111 8.21 Number of visible satellites(left) and GDOP values (right) along the CS3 route...... 111 8.22 CS3 PPPprocessing results forZTD from CSRS-PPP(top) andPPPW (bottom).The actual PPPoutput is shown in red,the MA-smoothed (Interval 5min) in blue...... 112 8.23 CS3PPP ellipsoidal height time series fromCSRS-PPP (top) andPPPW (bottom).The rawPPP output is showninred, the MA-smoothed (Interval 5min) in blue...... 113 8.24 Comparisonbetween estimated GNSS-ZTD(CSRS-PPP (red) and PPPW (green)) and ERA5-ZTD (black) forCS3 (29.11.2019), Top: ZTD, bottom: differences between GNSS-ZTDwith respect to ERA5-ZTD114 LIST OF FIGURES 165

8.25 HistogramsofZTD differencesbetween GNSS-ZTD andERA5-ZTD for test case CS3. Left: CSRS, Right:PPPW. Also indicated arebiasand standard deviation(σ)ofthe respective solutions...... 115

8.26 Correlationbetween GNSS-ZTDasestimated by each softwarepackage andthe ERA5 reference values forCS3, 29.11.2019: (left) CSRS-PPP, (middle) PPPW and (right) PPPW-HC. Terms Rand yrepresent the correlation coefficient and the linearfit, respectively...... 116

8.27 Train trackofCS4 (01.12.2019): Innsbruck -Woergl -Bischofshofen - Liezen-Leoben -Bruck/Mur -Graz ...... 117

8.28 CMC observables for CS4, shownare all visible GPS satellites...... 117

8.29 Number of visiblesatellites(left) and GDOP values (right) along the CS3 route...... 118

8.30 CS4 PPP ZTD time series from CSRS-PPP(top) and PPPW(bottom). The rawPPP output is shown in red, the MA-smoothed (Interval5min) in blue...... 119

8.31 CS4 PPPellipsoidal height time series from CSRS-PPP (top) and PPPW (bottom). Theraw PPP output is shown in red, theMA-smoothed (Interval 5min) in blue...... 119

8.32 Comparison of ellipsoidalheight between PPPand RTK solutions forCS4 (01.12.2019): CSRS-PPP (red) /PPP-Wizard(green) /RTK solution (black). Original processing output time series shown on top, MA-filtered time series at the bottom...... 120

8.33 Comparison between estimated GNSS-ZTD(CSRS-PPP(red) andPPP- Wizard (green)) andERA5-ZTD (black) forCS4 (01.12.2019), Top: ab- solute values, bottom: differences between GNSS-ZTDwithrespect to ERA5-ZTD ...... 122

8.34 HistogramsofZTD differencesbetween GNSS-ZTD andERA5-ZTD for test case CS4. Left: CSRS, Right:PPP-Wizard. Also indicated arebias and standard deviation (σ)ofthe respective solutions...... 123

8.35 Correlationbetween ZTD as estimated by each software package and the ERA5 reference values forCS4, 01.12.2019:(left)CSRS-PPP,(middle) PPPW and (right)PPPW-HC. TermsRand yrepresent the correlation coefficient and the linearfit, respectively...... 123 166 LIST OF FIGURES

8.36 Comparison of GNSS-ZTD with ERA5-ZTD with/withoutGLONASSob- servations forCS3: (1) GPS+GLONASS (dark green),(2)GPS-only (light green). Absolute ZTDvalues (top) andabsolutedifferences to ERA5- ZTD (bottom)...... 125 8.37 Comparison of GNSS-ZTD with ERA5-ZTD with/withoutGLONASSob- servations forCS4: (1) GPS+GLONASS (dark green),(2)GPS-only(light green). ZTDvalues (top) anddifferences to ERA5-ZTD(bottom)....126 8.38 ComparisonofGNSS-ZTDwith ERA5-ZTD fordifferentsettings forel- evation cut-off: (1)5◦(dark blue),(2) 10◦ (light blue). Absolute ZTD values (top) andabsolute differences to ERA5-ZTD(bottom)...... 128 8.39 Histograms of GNSS-ZTDdifferences to ERA5-ZTD fordifferentsettings forelevationcut-off: (1)5◦(dark blue),(2) 7.5/10◦ (lightblue)...... 128 8.40 Comparison of GNSS-ZTD with ERA5-ZTDwith/without gradientesti- mation:(1) ZTD+GRAD (darkblue),(2) ZTD-only(lightblue).Abso- lute ZTDvalues (top)and absolutedifferences to ERA5-ZTD (bottom). 130 8.41 Histograms of GNSS-ZTD differences [cm]toERA5-ZTD with/without gradient estimation: (1)ZTD+GRAD (darkblue),(2) ZTD-only(light blue)...... 130 8.42 Comparison of GNSS-ZTDtime series from CSRS-PPP(red), SGAMP (blue) andPPPW(green)for 16:00 to 19:00,11.05.2017 (dateofCS1). 131 8.43 Absolute GNSS-ZTDdifferences [cm] with respect to ERA5-ZTD, av- eraged over allfourtest casesfor CSRS-PPP (red) andPPPW(green) overthe coveredaltitude range from 200 -1000 mellipsoidal height. ..133 8.44 Absolute ZTD differences [cm] with respect to ERA5-ZTD, shown forall four test cases separatelyfor CSRS-PPP (red) and PPPW(green) over thecovered altitude range from 200-1000 mellipsoidalheight...... 134 8.45 Comparison of numbers of assimilated observations fortwo different WRFDA setups: (1)using two model domains with30/10kmhorizontal resolution(green), (2) using an additionalthird domainof3kmresolution (blue),nested into the 10 km domain. Additionally the error threshold forthe qualitycheck is also shown in red...... 137 8.46 Plotofthe used WRFmodel domains forCS3: parent domain (d01, black) and nested domains (d02 and d03, blue and green)...... 138 8.47 Observationsassimilated forCS3 using WRFDAfor different processing schemes. Processing schemes shown are: PPPW(left) andCSRS-PPP (right)...... 139 LIST OF FIGURES 167

8.48 Plot of theused WRF model domains forCS3: parentdomain(d01, black) and nested domains (d02 and d03, blue and green)...... 139 8.49 Observationsassimilated using WRFDAfor different processingschemes. Reference observations of model background areshown in blue, top left. Processing schemes shown are: SGAMP (top right), PPPW-HC (bottom left) andPPPW(bottomright)...... 141

9.1 Possible Flowchart forSEID DF-PPP processinginaNRT- implementation of ZTD estimation from Greenlight GNSS data...... 147 9.2 Exemplary DA configuration using 4D-Var technique. Takenfrom Ballard et al. (2016)...... 149 168 LIST OF FIGURES List of Tables

2.1Components andfrequencies forcivil use of GPS signal ...... 10 2.2 Definingparameters of WGS-84,taken from Hofmann-Wellenhof et al. (2012)...... 12 2.3 Components and frequencies of Galileo signal...... 14 2.4 Overviewonnoiseand multipath characteristics of GNSS observables, most information takenfrom M¨oller (2017)...... 21

3.1 Net radiation budget of the Earth, M¨oller (2017)...... 24 3.2 Fractionalconcentrationsofgaseous atmosphericconstituents with re- specttodry air,withimportantgreenhouse gases marked bold. Taken from Wallace and Hobbs (2006)...... 25

5.1Overviewofassimilationstrategies used forGNSS-derived tropospheric products in popularNWP models: WRF(Weather Research and Fore- casting),COSMO (Consortiumfor Small-scale Modeling), AROME (Ap- plication of Research to OperationsatMEsoscale) andIFS (Integrated Forecasting System,operatedatECMWF) model ...... 48

6.1 Overviewonmethods forcycle slip detection(Farooq et al. 2018). ... 58 6.2 Default settings andfeatures forthe CSRS-PPPpackage...... 67 6.3 Default settings andfeatures forthe PPP-Wizard software...... 68 6.4 Default settings andfeatures forthe GAMP PPP software...... 70

7.1 Detailed information on theproduct line of reanalyses produced by ECMWF. 76

8.1Overviewofconducted casestudies ...... 89 8.2 GeneralPPP settings chosen forthe test cases...... 91 8.3 Performancemetrics forthe PPPnoiseanalysis of CS1 forCSRS-PPP andPPPW. Measuresare computed forZTD differences between original PPP output and smoothed solution...... 95

169 170 LIST OF TABLES

8.4 Performance metricsfor the PPPnoiseanalysis of CS1for CSRS-PPP and PPPW.Measures arecomputedfor height coordinatedifferences between original PPPoutput andsmoothed solution...... 95 8.5 CS1: Performancemetrics forthe ZTD validation against ERA-ZTDfor processing results of CSRS-PPPand PPPW...... 98 8.6 CS1(excluding12:30 -13:30): Performancemetrics forthe ZTD valida- tion against ERA-ZTD forprocessingresultsofCSRS-PPP andPPPW. . 99 8.7 Performance metricsfor the PPPnoiseanalysis of CS2for CSRS-PPP and PPPW.Measures arecomputedfor ZTD differences between original PPP output and smoothed solution...... 104 8.8 Performance metricsfor the PPP noise analysis of CS2 forCSRS-PPP and PPPW.Measures arecomputedfor height coordinatedifferences between original PPPoutput andsmoothed solution...... 104 8.9Reference stations chosen forSEID processing forCS2...... 104 8.10 CS2: Performance metrics forthe ZTD validation against ERA-ZTDfor processing results of CSRS-PPP, SGAMPand PPPW and PPPW-HC.. .107 8.11 Performance metrics forthe PPPnoise analysis of CS3 forCSRS-PPP andPPPW. Measures arecomputedfor ZTD differences between original PPP output and smoothed solution...... 113 8.12 Performance metrics forthe PPPnoise analysis of CS3 forCSRS-PPP andPPPW. Measuresare computed forheight coordinatedifferences between original PPPoutput and smoothed solution...... 113 8.13 CS3: Performance metrics forthe ZTD validation against ERA5-ZTDfor processing resultsofCSRS-PPP, PPPW and PPPW-HC...... 116 8.14 Performance metrics forthe PPPnoise analysis of CS4 forCSRS-PPP andPPPW. Measures arecomputedfor ZTD differences between original PPP output and smoothed solution...... 118 8.15 Performance metrics forthe PPPnoise analysis of CS4 forCSRS-PPP andPPPW. Measuresare computed forheight coordinatedifferences between original PPPoutput and smoothed solution...... 119 8.16 Performance metrics forthe PPPnoise analysis of CS4 forCSRS-PPP andPPPW. Measuresare computed forheight coordinatedifferences between rawPPP output and the rawRTK solution...... 121 8.17 Performance metrics forthe PPPnoise analysis of CS4 forCSRS-PPP andPPPW. Measuresare computed forheight coordinatedifferences between smoothed PPP and RTK time series...... 121 LIST OF TABLES 171

8.18 CS4:Performance metrics forthe ZTD validation against ERA5-ZTDfor processing resultsofCSRS-PPP,PPPW andPPPW-HC...... 123 8.19 CS3:Performance metrics forthe ZTD validation against ERA5-ZTDfor processing resultsfor GPS-only and GPS+GLONASS ...... 125 8.20 CS4:Performance metrics forthe ZTD validation against ERA5-ZTDfor processing resultsfor GPS-only and GPS+GLONASS ...... 126 8.21 Performance metrics forthe ZTDvalidation against ERA5-ZTD forpro- cessingresultsfor 5◦ and7.5/10◦ cut-off elevation angle settings.Inves- tigated test case is CS2...... 127 8.22 Performance metrics forthe ZTDvalidation against ERA5-ZTD forpro- cessingresults forZTD-only and ZTD+GRAD settings. Investigated test case is CS2...... 129 8.23 WRFDA settingschosen forthe assimilation tests...... 136 172 LIST OF TABLES Bibliography

Adavi,Z., W. Rohm,and R. Weber, 2020: Analyzingdifferent parameterizationmethods in gnss tomography using the cost benchmark dataset. IEEE Journal Of Selected Topics In Applied Earth Observations And RemoteSensing, 13,6155–6163, doi:10. 1109/JSTARS.2020.3027909.

Aichinger-Rosenberger, M., 2018: Usabilityofhigh-resolution GNSS-ZTDdata in the AROME model. M.S. thesis,University of Innsbruck, URL https://diglib.uibk. ac.at/urn:nbn:at:at-ubi:1-27392.

Aichinger-Rosenberger, M. and R. Weber, 2020: Tropospheric delayparameters derived from GNSS-trackingdata of afastmovingfleet of trains. 7th Internationalcolloquium on scientific and fundamental aspects of GNSS, 1.

Alkan, R. M.,M.H.Saka, .M.Ozulu,and V. ˙Il¸ci, 2017: Kinematic precise point po- sitioningusing GPS and GLONASS measurementsinmarine environments. Measure- ment, 109,36–43,doi:https://doi.org/10.1016/j.measurement.2017.05.054,URL http://www.sciencedirect.com/science/article/pii/S0263224117303421.

Anthes, R. A., 2011: Exploring Earth’satmosphere with radio occultation: contribu- tions to weather, climate andspace weather. AtmosphericMeasurement Techniques, 4(6),1077–1103,doi:10.5194/amt-4-1077-2011,URL https://amt.copernicus. org/articles/4/1077/2011/.

Ballard, S. P.,Z.Li, D. Simonin, and J.-F. Caron, 2016: Performance of 4D-Var NWP- based nowcasting of precipitationatthe Met Office forsummer 2012. Quarterly Jour- nal of the RoyalMeteorologicalSociety, 142 (694),472–487,doi:10.1002/qj.2665, URL https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/qj.2665.

Barker,D., et al., 2012: Theweather researchand forecasting model’scommu- nity variational/ensemble dataassimilationsystem: Wrfda. Bulletin of The Amer- ican MeteorologicalSociety-BULLAMER METEOROLSOC, 93,831–843, doi: 10.1175/BAMS-D-11-00167.1.

173 174 BIBLIOGRAPHY

Beutler, G., I. Bauersima, S. Botton, W. Gurtner,M.Rothacher,and T. Schildknecht, 1989:Accuracy and biasesinthe geodetic applicationofthe global positioningsystem. manuscripta geodaetica, 14 (1),28–35.

Bevis,M., S. Businger,T.A.Herring, R. A. Anthes,and R. H. Ware, 1992: GPS Mete- orology: RemoteSensingofAtmospheric Water VaporUsing theGlobal Positioning System. Geophys. Mag., 34,359–425.

B¨ohm, J., et al., 2018: Vienna VLBIand satellite software(VieVS) forgeodesy and as- trometry. Publications of the AstronomicalSocietyofthe Pacific, 130 (986),044 503, doi:10.1088/1538-3873/aaa22b.

Bisnath, S. and R. Langley,2001: Pseudorange Multipath MitigationByMeans of Multipath Monitoring and De-Weighting.

Boehm, J.,A.Niell, P. Tregoning, and H. Schuh, 2006: Global mapping function(gmf): Anew empiricalmapping function based on numerical weather model data. Schuh Geophys. Res. Lett, 25,doi:10.1029/2005GL025546.

B¨ohm,J., 2004: Troposph¨a rischelaufzeitverz¨ogerungeninder vlbi.Ph.D.thesis, Geod¨asieund Geophysik.

B¨ohm, J. and H. Schuh, 2004: Vienna MappingFunctions in VLBI analyses. Geophysical Research Letters, 31 (1029/2003GL018984).

B¨ohm,J., B. Werl,and H. Schuh, 2006: Troposphere mappingfunctions forGPS and very longbaselineinterferometry fromEuropean Centre forMedium-Range Weather Forecastsoperational analysis data. J. Geophys. Res, 111.

B¨ohringer,F., 2008: Gleisselektiveortung von schienenfahrzeugen mitbordautonomer sensorik. Ph.D. thesis,doi:10.5445/KSP/1000007317.

Boisits, J., M. Glaner,and R. Weber, 2020: Regiomontan: Aregionalhigh precision ionospheredelaymodel and its applicationinprecise pointpositioning. Sensors, 20, 2845, doi:10.3390/s20102845.

Boniface, K., C. Champollion, J. Chery,V.Ducrocq, C. Rocken, E. Doerflinger, and P. Collard, 2012:Potential of shipborne GPS atmospheric delaydata forpredictionof Mediterranean intenseweatherevents. Atmospheric Science Letters, 13 (4),250–256, doi:10.1002/asl.391. BIBLIOGRAPHY 175

Brenot,H., et al., 2013: Preliminary signsofthe initiationofdeep convectionbyGNSS. Atmos. Chem. Phys., 13,5425—-5449.

Chadwell, C. D. and Y. Bock, 2001: Direct estimation of absolute precipitable water in oceanic regionsbyGPS tracking of acoastal buoy. Geophysical Research Letters, 28 (19),3701–3704,doi:10.1029/2001GL013280.

Chao, C., 1974: The tropospherecalibration model forMariner Mars 1971. JPLTechnical Report,32–1587.

Chen, G. and T. A. Herring, 1997: Effects of atmospheric azimuthalasymmetry on the analysis of spacegeodetic data. JournalofGeophysicalResearch: Solid Earth, 102 (B9),20489–20 502,doi:10.1029/97JB01739,URL https://agupubs. onlinelibrary.wiley.com/doi/abs/10.1029/97JB01739.

Davis, J., T. Herring, I. Shapiro,A.Rogers, and G. Elgered, 1985: Geodesy by Ra- dio Interferometry: Effects of Atmospheric Modeling Errors on Estimates of Baseline Length. RadioScience, 20,1593–1607. de Bakker,P.and C. Tiberius, 2017: Real-time multi-GNSS single- frequency precise point positioning. GPS Solutions, 21,1791–1803, doi: 10.1007/s10291-017-0653-2, https://agupubs.onlinelibrary.wiley.com/ doi/pdf/10.1029/2019EA000650. de Haan, S.,2008: Meteorological applications of asurface networkofGlobal Positioning System receivers.Ph.D. thesis, Wageningen University.

Deng, Z.,M.Bender,G.Dick, M. Ge, and J. Wickert, 2009: Retrieving tropospheric delays fromGPS networksdensified withsingle frequency receivers. Geophysical Re- search Letters, 36,36, doi:10.1029/2009GL040018.

DoD, 2020: Global positioning system standard positioning service performancestan- dard. Assistantsecretary of defense forcommand, control, communications, and in- telligence.

Dodson, A., W. Chen, N. Penna, and H. Baker, 2001: GPS estimation of atmospheric watervapourfrom amoving platform. Journal of Atmospheric and Solar-Terrestrial Physics, 63,1331–1341, doi:10.1016/S1364-6826(00)00251-0.

Dong, Z. andS.Jin, 2018: 3-Dwatervapor tomographyinWuhanfrom GPS, BDSand GLONASS observations. RemoteSensing, 10,62, doi:10.3390/rs10010062. 176 BIBLIOGRAPHY

Ducrocq, V., D. Ricard, J. P. Lafore,and F. Orain, 2002: Storm-scale numerical rainfall prediction forfive precipitatingevents overFrance:Onthe importance of the initial humidity field. Weather andForecasting, 17,1236––1256.

E-GVAP,2014: COST-Format File Specificationfor Ground-based GNSS Delayand WaterVapourData. https://www.romsaf.org/egvap_cost.pdf.

Elgered, G.,2001: An overview of COST Action 716: exploitation of ground-based GPS forclimate and numerical weather prediction applications. Physics and Chemistryof theEarth, Part A: Solid Earth andGeodesy, 26(6-8),399–404.

Essen, L. andK.D.Froome, 1951: The Refractive Indices andDielectric Constants of Air andits Principal Constituents at24,000Mc/s. Proceedings of the Physical Society. Section B, 64 (10),862–875,doi:10.1088/0370-1301/64/10/303,URL https:// doi.org/10.1088%2F0370-1301%2F64%2F10%2F303.

Farooq,S.Z., D. Yang, T. Jin,and N. Echoda, 2018: Survey of Cycle SlipDetection and Correction Techniques forSingle Frequency Receivers.957–961, doi:10.1109/ICCT. 2018.8599879.

Fujita, M., F. Kimura, K. Yoneyama, and M. Yoshizaki, 2008: Verification of precipitable watervapor estimated from shipborne GPS measurements. Geophysical Research Let- ters, 35 (13),doi:10.1029/2008GL033764.

Fujiwara, M., et al., 2017: Introductiontothe SPARCReanalysis Intercomparison Project (S-RIP) and overview of thereanalysissystems. AtmosphericChemistry and Physics, 17,1417–1452, doi:10.5194/acp-17-1417-2017.

Gao, Y., Y. Zhang, and K. Chen, 2006: Development of aReal-Time Single-Frequency Precise Point Positioning System and Test Results.

Gao, Z., M. Ge, and W. Shen,2017: Ionospheric and receiver DCB-constrained multi- GNSS single-frequency PPP integrated withMEMS inertial measurements. Journalof Geodesy, 91,1351—-1366,doi:https://doi.org/10.1007/s00190-017-1029-7.

Ge, M.,G.Gendt, M. Rothacher,S.Changhong, andJ.Liu, 2008: Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning (PPP)with DailyObservations. JournalofGeodesy, 82,389–399, doi:10.1007/s00190-007-0187-4.

Glaner,M.F., 2017: Eigenschaften und Einsatzm¨oglichkeiten vonGPS und Galileo Signal-Linearkombinationen. M.S.thesis, Department f¨ur Geod¨asie und Geoinfor- BIBLIOGRAPHY 177

mation /H¨o here Geod¨asie,URL http://repositum.tuwien.ac.at/urn:nbn:at: at-ubtuw:1-96172.

Glaner, M. F., R. Weber, and S. Strasser,2020: PPP-AR with GPS and Galileo: As- sessing diverse approaches and satellite products to reduce convergence time. EGU GeneralAssembly Conference Abstracts,7792, EGU General Assembly Conference Abstracts.

Graham, E.,E.N.Koffi, and C. Matzler,2012: An observational study of air andwater vapourconvergence over the western Alps during summer and the development of isolated thunderstorms. Meteorologische Zeitschrift, 21,1–13.

Guerova, G., et al., 2016: Reviewofthe state-of-the-art and futureprospects of the ground-based GNSS meteorologyinEurope. Atmospheric Measurement Techniques Discussions, 9,doi:10.5194/amt-9-5385-2016.

Gurtner, W. and L. Estey,2007: Rinex: Thereceiverindependent exchangeformat version 2.11.Astronomical Institute, UniversityofBern,Bern.

Hadas,T., T. Hobiger, andP.Hordyniec, 2020: Considering different recent advance- ments in GNSS on real-time zenith troposphere estimates. GPS Solutions, 24,doi: 10.1007/s10291-020-01014-w.

Haltiner, G. J. and F. L. Martin, 1957: Dynamical andPhysical Meteorology.McGraw- Hill Book Company.

Hanna,N., E. Trzcina, G. M¨oller,W.Rohm, and R. Weber, 2019: Assimilation of GNSS tomography products intothe Weather Research and Forecasting model us- ing radio occultationdata assimilationoperator. Atmospheric Measurement Tech- niques, 12 (9),4829–4848, doi:10.5194/amt-12-4829-2019,URL https://www. atmos-meas-tech.net/12/4829/2019/.

Herrera Olmo, A., H. Suhandri, E. Realini, M. Reguzzoni, and M. C. d. Lacy, 2015: goGPS: open-sourceMATLABsoftware. GPS Solutions, 20,1–9,doi:10.1007/ s10291-015-0469-x.

Herring, T. A., 1992: Modelling atmosphericdelays in the analysis of space geodetic data. Symposium on Refraction of Transatmospheric Signalsin Geodesy, 36,157—- 164. 178 BIBLIOGRAPHY

Hersbach, H., et al.,2020: The ERA5 global reanalysis. Quarterly Journal of the RoyalMeteorological Society, 146 (730),1999–2049, doi:10.1002/qj.3803, https: //rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/qj.3803.

Hinterberger, F.,2016: Influence of GPS satelliteorbits andclock corrections on the estimation ofsingle difference uncalibrated phase delays.Ph.D.thesis, Technische Universit¨a tWien.

Hlawatsch,F., 2019: Lecture notesinParameter Estimation Methods.Institute of Telecommunications, TechnicalUniversityVienna.

Hofmann-Wellenhof, B.,H.Lichtenegger, and J. Collins, 2012: Global Positioning System:Theoryand Practice.Springer Vienna,URL https://books.google.at/ books?id=F7jrCAAAQBAJ.

Hofmeister,A., 2016: Determination of pathdelaysinthe atmosphere forgeodetic VLBI by means of ray-tracing. Ph.D. thesis, Department f. Geod¨asie u. Geoinformation /H¨o hereGeod¨asie, URL http://resolver.obvsg.at/urn:nbn:at:at-ubtuw: 1-3444.

Huang,G., K. Eckenhoff, and J. Leonard, 2018: Optimal-State-Constraint EKF forVisual-Inertial Navigation. In: Bicchi A., Burgard W. (eds)Robotics Re- search. Springer Proceedings in Advanced Robotics, 2,doi:https://doi.org/10.1007/ 978-3-319-51532-8 8.

Huang,X.Y., et al.,2003: TOUGH: Targeting optimaluse of GPS humiditymeasure- ments in meteorology. International WorkshoponGPS Meteorology.

Jackson,J.D., 1999: Classicalelectrodynamics.3ded.,Wiley.

Jiang, C., T. Xu, S. Wang, W. Nie, andS.Zhangzhen, 2020: Evaluation of Zenith TroposphericDelayDerived from ERA5Data over China Using GNSS Observations. Remote Sensing, 12,663, doi:10.3390/rs12040663.

Jin,S.and O. Luo, 2009:Variabilityand climatology of PWV from global13-yearGPS observations. IEEE Trans. Geosci. RemoteSens. 47 (7).

Kalman, R. E., 1960: Anew approach to linearfiltering and predictionproblems. Trans- actionsofthe ASME–JournalofBasic Engineering, 82 (Series D),35–45.

Kaplan,E.and C. Hegarty, 2006: Understanding GPS -Principlesand Applications. ArtechHouse. BIBLIOGRAPHY 179

Karabatic, A., 2011: Precis Point Positioning (PPP) -analternative technique forground basedGNSS tropospheremonitoring. Ph.D. thesis,Geod¨asieund Geophysik.

Katsigianni, G., F. Perosanz,S.Loyer, andM.Gupta,2019: Galileo millimeter-level kine- matic precise point positioning withambiguity resolution. Earth, Planets andSpace, 71,doi:10.1186/s40623-019-1055-1.

Kaˇc maˇr ´ı k, M.,etal., 2017: Inter-technique validationoftropospheric slanttotal delays. Atmospheric Measurement Techniques, 10 (6),2183–2208,doi:10.5194/ amt-10-2183-2017,URL https://www.atmos-meas-tech.net/10/2183/2017/.

Kealy,J., J. Foster,and S. Businger,2012: GPS meteorology: An investigationofocean- based precipitable water estimates. Journal of Geophysical Research: Atmospheres, 117 (D17),doi:10.1029/2011JD017422.

Kouba,J.and P. H´eroux, 2001: Precise Point Positioning Using IGS Orbit and Clock Products. GPS Solutions, 5,12–28, doi:10.1007/PL00012883.

Krawinkel, T.,N.Lindenthal, and S. Sch¨on,2014: Apparent coordinate changes of gps reference stations: Influence of evaluationstrategies andantenna changes. ZFV -Zeitschrift fur Geodasie, Geoinformation und Landmanagement, 139,252–263, doi: 10.12902/zfv-0027-2014.

Krietemeyer, A., M.-c.Ten Veldhuis, H. Marel, E. Realini, and N. vandeGiesen, 2018: PotentialofCost-Efficient SingleFrequency GNSS Receiversfor WaterVapor Moni- toring. RemoteSensing, 10,1493,doi:10.3390/rs10091493.

Landskron,D.and J. B¨ohm,2017: VMF3/GPT3: refined discrete and empirical tropo- spheremapping functions. Journal of Geodesy, 92,349—-360.

Laurichesse, D., F. Mercier, J.-P. Berthias, P. Broca, and L. Cerri, 2009: Integer Am- biguityResolutiononUndifferenced GPS Phase Measurements and Its Applicationto PPP and Satellite PreciseOrbitDetermination. Navigation, 56 (2),135–149, doi: 10.1002/j.2161-4296.2009.tb01750.x.

Laurichesse, D. and A. Privat, 2015: An Open-sourcePPP Client Implementationfor theCNES PPP-WIZARD Demonstrator.

Li,Z., S. P. Ballard, and D. Simonin, 2018: Comparisonof3D-Var and4D-Var dataassimilation in anNWP-based system forprecipitation nowcasting at the Met 180 BIBLIOGRAPHY

Office. Quarterly Journal of the RoyalMeteorological Society, 144 (711),404– 413, doi:10.1002/qj.3211, https://rmets.onlinelibrary.wiley.com/doi/pdf/ 10.1002/qj.3211.

Lu, C., X. Chen, G. Liu, G. Dick, J. Wickert,X.Jiang, Z. Kai,and H. Schuh, 2017: Real-Time Tropospheric Delays Retrieved from Multi-GNSS Observations andIGS Real-Time Product Streams. RemoteSensing, 9,1317, doi:10.3390/rs9121317.

Magnet,N., 2019: Giomo:Arobust modellingapproach of ionosphericdelays forGNSS real-time positioning applications. Ph.D. thesis, Department f¨ur Geod¨asie und Geoin- formation /H¨o here Geod¨asie, URL https://repositum.tuwien.ac.at/urn:nbn: at:at-ubtuw:1-124443.

Marini, J., 1972: Correctionofsatellitetracking datafor an arbitrary tropospheric profile. Radio Science, 7,223–231.

Melbourne,W., 1985: Thecasefor rangingingps based geodetic systems. Proceedings of1stInternational Symposium on Precise Positioning with the Global Positioning System,373–386.

Mendez Astudillo, J., L. Lau,Y.-T. Tang, and T. Moore, 2018: Analysing the Zenith TroposphericDelayEstimates in On-line Precise Point Positioning (PPP)Services and PPP SoftwarePackages. Sensors, 18,580, doi:10.3390/s18020580.

MeteoSwiss,2020: COSMO forecasting system. https://www. meteoswiss.admin.ch/home/measurement-and-forecasting-systems/ warning-and-forecasting-systems/cosmo-forecasting-system.html.

Mile,M., P. Ben´aˇcek, and S. R´ozsa, 2019: The use of GNSS zenith total delays in operational AROME/Hungary 3D-Var overacentralEuropean domain. Atmospheric Measurement Techniques, 12 (3),1569–1579,doi:10.5194/amt-12-1569-2019,URL https://www.atmos-meas-tech.net/12/1569/2019/.

M¨oller, G., 2017: Reconstruction of 3D wetrefractivityfields in the loweratmosphere alongbended GNSS signal paths. Ph.D. thesis,Department f¨ur Geod¨asie und Geoin- formation /H¨o here Geod¨asie, URL http://repositum.tuwien.ac.at/obvutwhs/ content/titleinfo/2268559.

Najman, P. and T. Kos,2014:Performance Analysis of EmpiricalIonosphere Models by Comparison withCODE Vertical TEC Maps,MitigationofIonospheric Threats to GNSS. BIBLIOGRAPHY 181

NationalImageryand Mapping Agency,2000: Departmentofdefense world geodetic system1984:its definition and relationships with local geodetic systems.Tech. Rep. TR8350.2, National Imageryand Mapping Agency,St. Louis,MO, USA. URL http: //earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html.

Niell, A., 1996: Global mapping functions forthe atmospheredelayatradio wavelengths. J. Geophys. Res., 101,3227–3246.

Niell,A., 2000: Improvedatmosphericmapping functions forVLBI andGPS. Earth Planets Space, 52,699–702.

Nilsson, T.,J.B¨o hm,D.Wijaya,A.Tresch, V. Nafisi, and H. Schuh, 2013: Path Delays in theNeutral Atmosphere.In: B¨ohmJ., SchuhH.(eds) Atmospheric Effects in Space Geodesy.Springer Atmospheric Sciences. Springer, Berlin,Heidelberg,73–136.

Realini, E. and M. Reguzzoni, 2013: goGPS: Open Source Softwarefor Enhancing the Accuracy of Low-cost Receivers by Single-frequency Relative Kinematic Positioning. Measurement Science and Technology, 24,115 010, doi:10.1088/0957-0233/24/11/ 115010.

R¨ueger, J.,2002: Refractive IndexFormulaefor Radio Waves. Proc. FIGXXIIInterna- tional Congress, Washington, D. C.

Rocken, C., J. Johnson, T. VanHove, andT.Iwabuchi, 2005: Atmospheric watervapor andgeoid measurements in the open ocean with GPS. Geophysical Research Letters, 32 (12),doi:10.1029/2005GL022573.

Rohm, W., J. Guzikowski, K. Wilgan, and M. Kryza, 2019: 4DVARassimilation of GNSS zenith path delays andprecipitable waterinto anumerical weather prediction modelWRF. Atmospheric Measurement Techniques, 12 (1),345–361,doi:10.5194/ amt-12-345-2019,URL https://www.atmos-meas-tech.net/12/345/2019/.

Saastamoinen,J., 1972: Contributions to the theory of atmospheric refraction. Bull. Geodesique, 105,13–34.

Santos,M., D. McAdam, and J. B¨ohm, 2012: Statusand Validation of the UNB- VMF1. EGU General Assembly Conference Abstracts,13759, EGUGeneralAssembly Conference Abstracts.

Sanz Subirana, J., J. M. Juan Zornoza, and M. Hern´a ndez-Pajares, 2013: GNSS Data Processing, Volume I: Fundamentals and Algorithms. ESACommunications,ESTEC, Noordwijk, Netherlands. 182 BIBLIOGRAPHY

Sch¨onemann, E., 2014: Analysis of GNSS rawobservationsin PPP solutions. Ph.D. thesis, Technische Universit¨a tDarmstadt.

Seco, A.,etal.,2012:Rain pattern analysisand forecast model based on GPS estimated atmospheric watervapor content. Atmospheric Environment, 49,85–93.

Simeonov, T.,D.Sidorov, F. N. Teferle, G. Milev,and G. Guerova, 2016: Evalua- tion of IWV from thenumericalweather prediction WRF model withPPP GNSS processing forBulgaria. Atmospheric Measurement Techniques Discussions, 2016,1– 15, doi:10.5194/amt-2016-152,URL https://amt.copernicus.org/preprints/ amt-2016-152/.

Skamarock, W. C., J. B. Klemp,J.Dudhia,D.O.Gill, Z. Liu, J. Berner,and X. Huang, 2019: ADescription of theAdvancedResearch WRF Model Version 4. Tech. rep., NCAR. doi:10.5065/1dfh-6p97.

Skone, S., Y. Gao, O. Al-Fanek, W. Tao, Y. Zhang,P.H´e roux, and P. Collins, 2006: Atmospheric moisture estimation using GPSonamoving platform. 3,1891–1901.

Smith,E.K.and S. Weintraub, 1953: The Constants in the Equation forAtmospheric Refractive Index at Radio Frequencies. Journal of Research of the Notional Bureauof Standards, 50,39–41.

Ssenyunzi, R. C., B. Oruru,F.M.D’ujanga,E.Realini,S.Barindelli, G. Tagliaferro, A. vonEngeln, andN.van de Giesen, 2020: Performance of ERA5 data in retriev- ing Precipitable WaterVapour overEastAfricantropical region. Advances in Space Research, 65 (8),1877 –1893, doi:https://doi.org/10.1016/j.asr.2020.02.003.

Stepniak,K.and O. Bock, 2018: Comparisonoftroposphericestimatesfrom DD and PPP processing approaches forclimate monitoring. EGU General Assembly Conference Abstracts,14722, EGUGeneralAssembly Conference Abstracts.

Suya, G., 2019: Ionospheric-Constrained PPP using Triple-GNSS Constellations.

Takasu, T. and A. Yasuda, 2009: Development of thelow-cost RTK-GPS receiver with an open source program package RTKLIB. InternationalSymposiumonGPS/GNSS.

Thiruvengadam, P.,J.Indu, and S. Ghosh,2020:Significanceof4DVAR Radar DataAssimilation in Weather Research andForecastModel-Based Nowcasting Sys- tem. JournalofGeophysicalResearch: Atmospheres, 125 (11),e2019JD031 369, doi:10.1029/2019JD031369, https://agupubs.onlinelibrary.wiley.com/doi/ pdf/10.1029/2019JD031369. BIBLIOGRAPHY 183

T´etreault,P., J. Kouba,P.H´e roux, and P. Legree, 2005: CSRS-PPP:Aninternet service forGPS user accesstothe Canadian Spatial Reference frame. Geomatica, 59,17–28. van Baelen, J., M. Reverdy,F.Tridon,L.Labbouz, G. Dick, M. Bender, and M. Hagen, 2011: On the relationship between watervapour andevolution andthe lifecycleof precipitation systems. Q. J. R. Meteorol. Soc, 137,204–223.

Vedel, H. and X.-Y. Huang, 2004: Impact of GroundBasedGPS Data on Numerical Weather Prediction. Journalofthe MeteorologicalSocietyofJapan.Ser. II, 82 (1B), 459–472,doi:10.2151/jmsj.2004.459.

Virtanen, P.,etal., 2020:SciPy 1.0: Fundamental Algorithms forScientific Computing in Python. NatureMethods, 17,261–272, doi:10.1038/s41592-019-0686-2.

Wallace, J. M. and P. V. Hobbs, 2006: Atmospheric Science: An Introduction Survey. Elsevier, 255–280 pp.

Webb, S. R.,N.T.Penna, P. J. Clarke,S.Webster,I.Martin, and G. V. Ben- nitt, 2016: Kinematic GNSSEstimation of ZenithWet Delayover aRange of Altitudes. Journal of Atmospheric and Oceanic Technology, 33 (1),3–15,doi: 10.1175/JTECH-D-14-00111.1.

Weber, R., D. Landskron,N.Hanna, M. Aichinger-Rosenberger, andD.Horozovic, 2019: AtmosphereMonitoring by means of GNSS -Research Activities at TU Wien. Os¨ terreichische Zeitschrift f¨ur Vermessungund Geoinformation (VGI), 107 (2),78– 82.

Wickert, J., et al., 2009: GPS radio occultation: resultsfrom CHAMP,GRACE and FORMOSAT-3/COSMIC. Terrestrial Atmospheric and Oceanic Sciences, 20 (1),35– 50, doi:https://doi.org/10.3319/TAO.2007.12.26.01(F3C).

Wilgan, K. and A. Geiger, 2018: High-resolution models of tropospheric delaysand refractivity based on GNSS and numerical weather predictiondata foralpine regions in Switzerland. JournalofGeodesy,doi:10.1007/s00190-018-1203-6.

Wilks, D.S., 2011: Statistical methodsinthe Atmospheric Sciences.Elsevier, 255–280 pp.

Wolfe, D. E. andS.E.Gutman, 2000: Developing an Operational, Surface-Based, GPS, WaterVapor ObservingSystem forNOAA: NetworkDesign and Results. Journalof Atmospheric and Oceanic Technology, 17,426–440. 184 BIBLIOGRAPHY

Wu,J.T., S. C. Wu,G.A.Hajj, W. I. Bertiger, andS.M.Lichten, 1992: Effects of antenna orientation onGPS carrier phase. Astrodynamics1991,1647–1660.

Wulfmeyer,V., et al.,2008: Theconvective andorographicallyinduced precipitation study:Aresearch anddevelopment project of the World Weather ResearchPro- gramfor improving quantitativeprecipitation forecasting in low-mountain regions. Bull. Amer. Meteorol. Soc., 89(10),1477—-1486.

Xu, G.,2007: Gps: Theory,algorithms and applications. GPS: Theory,Algorithms and Applications,1–340, doi:10.1007/978-3-540-72715-6.

Xu, Y., 2016:GNSSPrecise PointPositioningwith Application of the Equivalence Principle. Ph.D. thesis, Technischen Universit¨at Berlin.

Yan, X., V. Ducrocq, G. Jaubert,P.Brousseau, P. Poli, C. Champollion, C. Flamant, and K. Boniface, 2009: The benefit of GPS zenith delayassimilation to high-resolution quantitative precipitation forecast. Acase-study from COPS IOP 9. Q. J. R. Meteorol. Soc., 135,1788—-1800.

Yu,X.and J. Gao, 2017: Kinematic Precise PointPositioning Using Multi-Constellation Global NavigationSatelliteSystem(GNSS)Observations. ISPRS International Journal of Geo-Information, 6,6,doi:10.3390/ijgi6010006.

Zhao,C., B. Zhang, W. Li, Y. Yuan,and M. Li, 2019: Simultaneous Retrieval of PWVand VTEC by Low-Cost Multi-GNSS Single-Frequency Receivers. Earth and Space Science, 6(9),1694–1709, doi:10.1029/2019EA000650, https://agupubs. onlinelibrary.wiley.com/doi/pdf/10.1029/2019EA000650.

Zhao, Q., Y. Yao, X. Cao, F. Zhou, and P. Xia, 2018: An Optimal Tropospheric Tomog- raphy MethodBased on the Multi-GNSS Observations. Remote Sensing, 10 (2), 2072–4292,doi:10.3390/rs10020234,URL https://www.mdpi.com/2072-4292/ 10/2/234.

Zhou, F., D. Dong,W.li, X. Jiang, J. Wickert, andH.Schuh, 2018: GAMP: An open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations. GPS Solutions, 22,doi:10.1007/s10291-018-0699-9.

Zhu, K.,X.Guo, C. Jiang,Y.Xue, Y. Li,L.Han, and Y. Chen, 2020:Mimu/odometer fusion with state constraintsfor vehicle positioning during beidou signal outage: Testing and results. Sensors(Basel,Switzerland), 20,doi:https://doi.org/10.3390/ s20082302. BIBLIOGRAPHY 185

Zumberge, J.,M.Heflin, D. Jefferson, M. Watkins, andF.Webb, 1997:PrecisePoint Positioning forthe Efficient And RobustAnalysis of GPS Datafrom Large Networks. Journal of Geophysical Research, 102,doi:10.1029/96JB03860.

Zus, F., J. Douˇs a, M. Kaˇc maˇr ´ı k, P. V´aclavovic,K.Balidakis,G.Dick, and J. Wickert, 2019a: Improving GNSS Zenith WetDelayInterpolationbyUtilizing Tropospheric Gradients: Experiments with aDense Station NetworkinCentral Europe in theWarm Season. RemoteSensing, 11 (6),doi:10.3390/rs11060674.

Zus, F.,J.Douˇs a, M. Kaˇc maˇr ´ı k, P. V´aclavovic,G.Dick, and J. Wickert,2019b: Esti- mating the Impact of Global Navigation SatelliteSystem HorizontalDelayGradients in Variational Data Assimilation. RemoteSensing, 11 (1),doi:10.3390/rs11010041. 186 CurriculumVitae

MatthiasAichinger-Rosenberger Ried 14/7, 6306 S¨oll Born on 30 June1990 in St.P¨olten, Austria

Educationand Professional training: 01/2020–Technical certifier forGNSS-basedapplicationsatNavCertGmbH, Mu- nich, Germany.

02/2018– Project assistant and Ph.D. student in the group of Prof. Dr. Robert 12/2019 Weberatthe Research division Higher Geodesy,Department of Geodesy and Geoinformation, TechnicalUniversityVienna.

2017–2018 Master thesis under the guidance of Prof. Dr. Mathias Rotach, Institute of Meteorologyand Geophysics, University of Innsbruck: Usability of high- resolution GNSS-ZTDdata in the AROME model.

2015–2018 Master studies at theUniversityofInnsbruck. Master of Science (M.Sc) in Atmospheric sciences.

2014–2015 Master thesisunder the guidance of Prof. Dr. Johannes B¨ohm and Dr. Michael Schindelegger, Institute of Geodesy and Geoinformation, Technical University Vienna: “Atmospheric contributiontodecadal-scale polarmotion variations from twentieth centuryreanalysis”.

2013–2015 Master studies at Technical UniversityVienna. Master of Science (Dipl.- Ing.) in Geodesy andGeoinformation.

2000–2008 Bunderealgymnasium,Krems. Matura.

Training courses:

“Parallel programming using MPI”, Vienna Scientific Cluster (VSC), 2019;

“Parallel I/O”,Vienna Scientific Cluster (VSC), 2019.

187