Developing troposphere augmentation corrections and their use in GNSS positioning Jan Douša, Michal Eliaš, Pavel Václavovic Geodetic Observatory Pecný (GOP), RIGTC, The Czech Republic Kryštof Eben, Jaroslav Resler, Pavel Krč Institute of Computer Sciences (ICS), Academy of Science of the Czech Republic jan.dousa@pecny.cz GNSS4SWEC 3rd Workshop, March 8-10, 2016, Reykjavik, Iceland 1

Motivation Troposphere affects satellite-based positioning & navigation: via 1) signal delay and 2) bending of signal trajectory high correlation exists between troposphere, clocks and heights in most situations we are interested in ‘geodetic’ parameters (position) approximations used in GNSS model – ZHD, ZWD, MF, GRD, ...  improvements in resolution, accuracy and timeliness of NWP models suggest to enhance modelling of troposphere in specific applications Climatology data Blind modelling Meteorological data Augmentation Observed data In situ modelling

Troposphere model development The goal: to exploit NWM 3D data field for user troposphere corrections  Model simplification via vertical, spatial and temporal approximations Meteo/observable parameterization model (classical) User/troposphere parameterization model (new) Flexible/combined parameterization model (new) Vertical scaling vertical approximations Horizontal/temporal interpolations (reference surface)

Improved vertical approximations vertical parameter approximation (from data in NWM profile) T – linear decrease  β [K/km] E – exponential decrease  λ [-] ZWD – exponential decrease  ϒ [-] Basic idea: ZWD vertical profile (integrated value) is generally more stable! E and ZWD decays can be compared or even substituted Note: figure below shows an extreme case of vertical profile for various parameters

Improved vertical approximations ZWD vertical profile follows partial water vapour pressure decrease, we thus introduced a similar relation for ZWD using γ [-] decay parameter γ [-] definition useful for substitution or combination of both λ and γ ! ‘equivalency’ in using P and H (geopotential height) Note: modified MOPS/UNB3 uses e (not e/T) ZWD dependency in vertical approx. Douša and Eliaš, 2014 compare to MOPS / UNB3 by Collins and Langley 1997 ! Smith 1966 Dousa and Elias 2014 Table shows r.m.s. of ZWD differences [mm] at various altitudes (ERA-Interim, 2015-06-06, 0 UTC) Height 0-1 km 1-2 km 2-3 km 3-4 km 4-5 km 5-6 km 6-7 km 7-8 km MOPS 11.4 20.7 20.2 19.9 15.3 13.2 10.4 7.9 10.8 19.1 18.6 18.0 13.6 8.7 6.5 GOP f(P) 8.2 7.4 5.5 5.6 5.0 3.7 GOP f(H) 8.3 5.7 Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

Common ZWD models (empirical/analytical) Hopfield [1969]: Saastamoinen [1972]: Chao [1973]: Ifadis [1986]: Askne & Nordius [1987]: All empirical models performs worse than AN (Radiosonde Praha-Libus, 2007)

Improved ZWD model of Askne-Nordius WV (water vapour) pressure decay (λ) is difficult to estimate (sensitive to inversions, ...), but represents a parameter that may be observed in situ ZWD decrease better follows the exponential decay (no inversions, ...) For taking advantage of WV & ZWD decay parameters, we estimated an optimal combination ratio for calculating modified λ’ parameter for the model of Askne-Nordius (1987) Combination ratio (w) and its vertical change were estimated using the ERA- Interim (1990-2013) for all altitudes and global grid: Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

Combination ratio for λ and γ decays Difference in λ and γ (E/ZWD pow-fit) Ratio estimated globally from Askne-Nordius vs. Integrated ZWD Estimates of combination ratio and lapse rate including uncertainties Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

Improved ZWD model of Askne-Nordius Differences of ZWDs: Calculated: using A-N model using λ, γ, and λ’ = f(λ,γ) Reference: numerically integrated ZWD using a full NWM profile ERA-Interim (2005-06-05:00) ZWD using λ fit via E (pow-fit) ZWD using combination of λ, γ (ratio 64.5%) GOP Modified Askne-Nordius model ZWD using γ fit via ZWD (pow-fit) Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

Surface ZWD models - zonal dependence Global ERA-Interim data (2005-06-05:00) Latitudinal dependence for ZWD calculated at the surface Reference values – integrated ZWD Compared values – ZWD calculated using the model of Askne and Nordius: ZWD from λ pow-fit via partial WV pressure data ZWD from λ log-fit via partial WV pressure data ZWD from λ pow-fit via ZWD data ZWD from λ log-fit via ZWD data optimally combined λ pow-fit via partial WV pressure and ZWD data Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

Tropospheric corrections modes Four modes were distinguished: BM – blind mode using climatological data only - blind model corrections () AM – augmented mode using actual NWM data - augmented corrections () SBM – site mode with in situ observations () + BM model corrections () SAM – site mode with in situ observations () + AM model corrections () Model parameter BM AM SBM SAM Pressure P [Pa] / / / WV pressure E [Pa] - / - / / / Mean temperature Tm [K] Zenith wet delay ZWD [m] / - / - - / - Tm lapse rate βm [K/km] WV decay rate λ [-] ZWD decay rate ϒ [-] ZHD (Saastamoinen 1972) ZWD (Askne-Nordius 1987) ZWD (AN / Douša-Eliaš 2014) ZWD (GOP/Douša-Eliaš 2014) Douša J, Eliaš M, Veerman H, van Leeuwen S, Zelle H, de Haan S, Martellucci A, Perez OA (2015), High accuracy tropospheric delay determination based on improved modeling and high resolution Numerical Weather Model, Proceedings of ION GNSS, 3734-3744

Assessment of tropo correction models/modes KNMI’s Harmonie Local Area Model × EUREF GNSS product … at the surface and in 1 km, 2 km, 5 km and 10 km (De Bilt location, the Netherlands) ERA-Interim × IGS GNSS product … at the surface, globally Model mode Mean bias Mean std dev Blind 2.4 mm 35.2 mm Site -5.6 mm 26.3 mm Augmented 3.2 mm 10.5 mm Site+Augmented 3.8 mm 13.3 mm Douša J, Eliaš M, Veerman H, van Leeuwen S, Zelle H, de Haan S, Martellucci A, Perez OA (2015), High accuracy tropospheric delay determination based on improved modeling and high resolution Numerical Weather Model, Proceedings of ION GNSS, 3734-3744

Further developments & software Enhancements of troposphere augmentation model & use Gradients estimated from ZHD+ZWD tropo data grid at the user side Estimation and use of optimal λ × ϒ combination ratio Derivation of ZWD, E, ZHD, P scale heights using λ, ϒ decay parameters Combination of NWM troposphere corrections with GNSS ZTD estimates Use cases on exploitation of external troposphere corrections G-Nut generic library for GNSS application developments http://www.pecny.cz --> G-Nut software G-Nut/Shu – tropospheric AM models based on NWM data G-Nut/ShuGNSS – combination of NWM AM model + GNSS ZTDs G-Nut/Apep – time-series analysis tool for BM model development G-Nut/Tefnut – troposphere monitoring - (near) real-time, post-processing G-Nut/Geb – precise point positioning (PPP) - static/kinematic, real-time/offline Václavovic P, Douša J, Györi G (2013), G-Nut software library - state of development and first results, Acta Geodyn Geomater, Vol. 10, No. 4 (172), pp. 431-436 Václavovic P, Douša J (2015), Backward smoothing for precise GNSS applications, Advances in Space Research, Volume 56, Issue 8, 15 October 2015, Pages 1627-163 Douša J, Václavovic P (2014) Real-time zenith tropospheric delays in support of numerical weather prediction applications. J Adv Space Res, (available online 1 March 2014) 13 13 13

RT-Demo: NWM tropo model Provider: Institute of Computer Science (ICS), Czech Republic Software: G-Nut/Shu (GOP) Model: WRF 3.6 Domains: EU/CZ Resolution: 9×9/3×3 km Levels: 38 vertical Real-time monitoring: http://www.pecny.cz/COST/RT-TROPO

Combined NWM + GNSS model (initial results) New strategy developed for optimal combination of NWM and GNSS Benchmark data set and ICS WRF used for an initial assessment Assessment using GNSS control points (selected as 1/2 or 1/3 of all) NWM only: 1/1 control points NWM+GNSS: 1/3 control points NWM+GNSS: 1/1 control points NWM+GNSS:1/2 control points 16 16 16

NWM tropospheric corrections in kinematic PPP ZTDs from ERA Interim, G-Nut/Geb PPP kinematic positioning NWM’s ZTDs into PPP vs. loosely constrained tropo estimates (Geb) 17 17 17

Kinematic experiment Date: 28th May, 2015 Maximal rover velocity - 4 m/s 2400 m above ellipsoid ≈ 2000 m above the earth surface Duration of the experiment: ̃2 h 30 min Václavovic P, Douša J, Eliaš M (2015) - Kinematic GNSS experiment supported by external tropospheric corrections , Presented at the 5th Scientific Galileo Colloquium, Braunschweig

Initial results Reference solution: GPS+GLO, IGS RT products, backward smoother Convergence: shortened by introducing NWM & GLO Height estimates: Introducing corrections from NWM increased stability by de-correlating height & ZTD

Summary New parameter γ[-] for vertical ZWD approximation significantly improved vertical ZWD scaling (by a factor of 2-3) Combination of WV and ZWD decay improved the 25-years-old model of Askne and Nordius for ZWD calculation New concept is universal and accurate for parameterization of tropospheric correction models (incl. in-situ meteo data) New ZWD analytical model is accurate (1cm level globally at any altitude) compared to the standard Askne-Nordius model (2-3 cm) Various model variants and modes were developed and assessed Blind model: ~35 mm (ZTD/ZWD) Blind + site model: ~25 mm (ZTD/ZWD) Augmented model: ~10 mm (ZTD/ZWD) Augmented + site model: ~10 mm (ZTD/ZWD) Use cases of tropospheric correction in geodetic applications performed, ongoing development, study not yet fully completed 20 20 20

Thank you for your attention Acknowledgements: ECMWF for providing ERA-Interim re-analysis H. Veerman, S van Leeuwen, H Zelle (NLR, the Netherlands) S de Haan (KNMI, the Netherlands) A Martellucci, R O Perez (ESA/ESTEC, the Netherlands) Developments/assessments of models have been supported by P209/12/2207 – Czech Scientific Foundation (2011-2015) LD14102 – Czech Ministry of Education, Youth and Science (2014-2017) Trop4LAS – European Space Agency (2013-2015) DARTMA – European Space Agency (2014-2016) Related publications: Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41 Douša J, Eliaš M, Veerman H, van Leeuwen S, Zelle H, de Haan S, Martellucci A, Perez OA (2015), High accuracy tropospheric delay determination based on improved modelling and high resolution Numerical Weather Model, Proceedings of the ION GNSS, pp 3734-3744 Douša J, Václavovic P, Krč P, Eliaš M, Eben E, Resler J (2015), NWM forecast monitoring with near real- time GNSS products, In: Proceedings of the 5th Scientific Galileo Colloquium, Braunschweig, Oct 27-29 Douša J, Dick G, Kačmařík M, Brožková R, Zus F, Brenot H, Stoycheva A, Möller G, Kaplon J (2016), Benchmark campaign and case study episode in Central Europe for development and assessment of advanced GNSS tropospheric models and products, Atmos. Meas. Tech. Discuss., discussion paper, 2016