1. 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
GNSS4SWEC 3rd Workshop, March 8-10, 2016, Reykjavik, Iceland 1

2. 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

3. 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)

4. 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

5. 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, , 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

6. 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)

7. 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 ( ) for all altitudes and global grid:
Douša J, Eliaš M (2014), An improved model for calculating tropospheric wet delay, Geoph. Res. Lett. 41

8. 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

9. 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 ( :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

10. Surface ZWD models - zonal dependence
Global ERA-Interim data ( :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

11. 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,

12. 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,

13. 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
--> 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
Václavovic P, Douša J (2015), Backward smoothing for precise GNSS applications, Advances in Space Research, Volume 56, Issue 8, 15 October 2015, Pages
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

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

15. 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

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

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

18. 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

19. 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

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 ( )
LD14102 – Czech Ministry of Education, Youth and Science ( )
Trop4LAS – European Space Agency ( )
DARTMA – European Space Agency ( )
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
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