Optimization of Tropospheric Delay Retrieval from Numerical Weather Prediction Models and Assimilation of Zenith Path Delays from Surrounding Reference Stations eingereicht von Anthony Joseph Kiroe Vollständiger Abdruck der bei der Fakultät für Luft- und Raumfahrttechnik der Universität der Bundeswehr München zur Erlangung des akademischen Grades eines Doktor der Ingenieurwissenschaften (Dr.-Ing.) eingereichten Dissertation. Vorsitzender: Prof. Dr.-Ing. Steffen Marburg 1. Berichterstatter: Prof. Dr.-Ing. habil. Torben Schüler Universität der Bundeswehr München Fakultät für Luft- and Raumfahrttechnik 2. Berichterstatter: Prof. Dr. techn. Johannes Böhm Technische Universität Wien Department of Geodesy and Geoinformation Die Dissertation wurde am 25.07.2014 bei der Universitat der Bundeswehr Munchen,Werner- Heisenberg-Weg 39, D-85577 Neubiberg eingereicht. Tag der mundlichen Prufung: 08.06.2015 Abstract The Global Navigation Satellite System (GNSS) is essential for the monitoring of earth deformation processes the results of which serve as vital inputs for the realization of geodetic reference systems. However, the accuracy and precision of GNSS positioning is compromised by tropospheric wet propagation delays. Compared to other GNSS error sources, wet tropospheric delay is small in magnitude. However, it is difficult to model due to its dependence on the temporally and spatially variable atmospheric water vapor. It therefore continuous to be the most challenging source of error on GNSS radio signals and the situation is likely to continue for years to come as the average global temperatures continue to rise. Consequently, solutions must be provided to supply sufficiently precise troposphere delay corrections. The use of surface meteorological data does not allow the precise prediction of wet delays. In fact, current troposphere delay models leave unmodelled errors of about 3 cm in the zenith direction. Numerical weather prediction (NWP) models can be used to integrate the refractivity profiles at an accuracy level of 1 cm in zenith direction. GNSS troposphere delay observations contain information on atmospheric water vapor. This can be used to derive the integrated water vapor above a given point. Owing to the water vapor information in the delay observations, the delay data can as well be ingested into an NWP model to improve forecasts, particularly precipitation forecasts. This thesis presents the results and discussions from several studies that seek to revisit the topics discussed in the preceding paragraphs. The accuracy of NWP-derived troposphere delays is assessed and precipitable water vapor estimated using different methods including GNSS, NWP and radiosonde is analyzed. Part of this study includes an assessment of the accuracy of the weighted mean temperature, an important parameter in the determination water vapor using GNSS observations. The study also seeks to assess the impacts of assimilating ground-based GNSS troposphere delay observations on short-range NWP forecasts. The entire study, therefore, involves lots of accuracy assessments that are done through validation studies by comparing NWP data with similar observations sourced from meteorological sensors and radiosonde. The studies discussed in the preceding paragraph are conducted on a region that falls in the mid- latitudes, i.e. central Europe, and are also implemented on a region falling in the African equatorial region, i.e. Kenya. i Contents List of Figures ......................................................................................................................................................................... v List of Tables ....................................................................................................................................................................... viii List of Abbreviations and Acronyms ................................................................................................................................... ix List of Symbols ...................................................................................................................................................................... xi 1. General introduction ..................................................................................................................................................... 1 1.1. GPS error sources ................................................................................................................................................. 1 1.2. Troposphere delay: a nuisance in GPS positioning, a blessing in meteorology ................................................... 5 1.3. Numerical weather prediction (NWP) models with relevance to troposphere delay ............................................ 7 1.3.1. The fundamental equations in NWP .......................................................................................................... 8 1.3.2. Grid-point NWP model description ......................................................................................................... 10 1.3.3. NWP model resolution ............................................................................................................................. 12 1.3.4. NWP model simulation ............................................................................................................................ 16 1.3.5. Assimilation of local observations including troposphere delays ............................................................ 18 1.3.6. Using NWP model data to estimate troposphere delays .......................................................................... 19 1.4. Ground-based sources of troposphere delay observations .................................................................................. 19 1.5. Research goal and objectives .............................................................................................................................. 20 1.6. Structure of the thesis ......................................................................................................................................... 21 1.7. Summary ............................................................................................................................................................ 22 2. Background study ........................................................................................................................................................ 23 2.1. Troposphere delay .............................................................................................................................................. 23 2.2. Precipitable water vapor and weighted mean temperature ................................................................................. 29 2.3. Advanced Research WRF (ARW) model grid.................................................................................................... 33 2.4. Troposphere delay formulation using ARW NWP model variables ................................................................... 36 2.4.1. Troposphere delays above NWP model orography.................................................................................. 37 2.4.2. Troposphere delays within NWP model orography ................................................................................. 38 2.4.3. Troposphere delays below NWP model orography ................................................................................. 39 2.4.4. Local acceleration due to gravity ............................................................................................................. 40 2.4.5. Total zenith path delay in terms of NWP model variables ....................................................................... 40 2.5. Precipitable water vapor formulation using NWP model variables .................................................................... 41 2.6. Total zenith path delay observations operator .................................................................................................... 42 2.7. Summary ............................................................................................................................................................ 43 3. General methodology ................................................................................................................................................... 45 3.1. Variables retrieval from NWP model output files .............................................................................................. 45 3.1.1. Antenna below model orography ............................................................................................................. 47 3.1.2. Antenna within model orography ............................................................................................................ 48 3.1.3. Variables at model half mass levels ......................................................................................................... 49 3.2. Study case: Central Europe ................................................................................................................................. 51 3.3. Study case: Kenya .............................................................................................................................................. 53 3.4. Summary ............................................................................................................................................................ 53 4. Validation