Developments towards use of external tropospheric models in GNSS positioning and navigation

Transcription

1 Developments towards use of external tropospheric models in GNSS positioning and navigation Jan Douša, Michal Eliaš Geodetic Observatory Pecný, RIGTC, Czech Republic Florian Zus Deutsches GeoForschungsZentrum Potsdam, Germany EUREF Symposium 2014 Vilnius, (jan.dousa@pecny.cz) 1

2 Outline Introduction Improved tropospheric wet delay modelling Advanced NWM products for geodetic applications ZWD vertical modelling & improved Askne-Nordius model Tropospheric model in precise point positioning Mapping functions Horizontal gradients Summary 2

3 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 in GNSS model - ZHD+ZWD, MFs, HORIZ GRADIENTS,.. improvements in resolution, accuracy and timeliness of NWP models suggest to enhanced modelling of troposphere in specific applications Climatology data blind modelling Meteorological data augmentation Observed data in situ modelling

4 Tropospheric path delays in GNSS processing Tropospheric delay in GNSS is often modelled using zenith parameters mapped into an actual slant delay with mapping functions DT ( z ) = ZHD mf H ( z ) + ZWD mfw ( z ) +... separation of zenith total delay was introduced by Davis (1985) hydrostatic component kr ZHD = d P0 gm non-hydrostatic ( wet) component æ ö k e ZWD = 10-6 ç k 2' + 3 ò dh Tm ø h 0 T è by using Tm - mean temperature e dh h0 T Tm = e ò h0 T 2 dh ò Mean ZHD value : 2.3 m in zenith ~ 90% of the total path delay Mean ZWD value : 0-50 cm in zenith ~ 10% of the total path delay

5 Focus on ZWD modeling Askne Nordius [1987]: derived an analytical formula for ZWD calculation assumption that the partial water vapour pressure decreases with height much faster than the total pressure and follows an exponential decay l +1 (Smith, 1966): e æpö =ç e0 è P0 ø æ k ö Rd ZWD = 10 ç k2' + 3 es Tm ø (l + 1) g m è with l» 3.0 [-] æ ' k3 ö e ZWD = 10 ç k2 + ò dh Tm ø h 0 T è where Rd is dry gas constant, gm is mean gravity, ki are empirical coefficients, Tm is the mean temperature (Davis 1985): -6 æ b Rd ö Tm = Ts ç1 ( l + 1) g m ø è -6 using T lapse rate: T = T0 - b (h - h0 ) Such model for calculation of surface ZWD is very sensitive to λ The model was adopted for Minimum Observation Performance Standards

6 Other ZWD (empirical) models Hopfield [1969]: Saastamoinen [1972]: Chao [1973]: Ifadis [1986]: H we ZWD = 10 N ws 5 æ 1255 ö ZWD = ç es è Ts ø e e0 0 ZWD = a T0 T03 2 ZWD = ( PS ) es es TS All empirical models performs worse than AN (Radiosonde Praha-Libus, 2007)

7 Selected tropospheric models TU Vienna: VMF1 (actual mapping function) ah, aw, ZHD, ZWD (2 2.5 ), orography, 6H resolution GMF (blind mapping function) VMF1 fitted by spherical harmonics (9 9), mean and annual terms, fixed phase offsets GPT (used together with GMF) ERA 40 P, T - spherical harmonics (9 9), mean sea level mean and annual terms, fixed phase offsets GPT2 (includes mapping function) ERA Interim P, T, β, e, ah, aw (5 5 ), ETOPO5, mean, annual/semi-annual terms, estimated phase offsets GPT2w (GPT2 and water vapour decrease factor) ERA Interim P, T, β, e, Tm, λ, ah, aw (1 1 ),ETOPO5, mean, annual/semi-annual terms, phase offsets University of New Brunswick: UNB3 (adopted as MOPS model for SBAS) P, T, e, β, λ - mean + annual terms (latitude belts), mean sea level VMF1-UNB NCEP The VMF1 concept adopted

8 Reduction of NWM data to ZHD/ZWD Blind model (temporal) vs. Augmented model (actual weather) 3D to 2D data reduction + vertical parameterization 8

9 Original and modified ZWD vertical reduction Collins and Langley [1997] UNB3 original reduction formula for ZWD Using E/T-depedence of slightly modified formulation of the model of Askne and Nordius, authors introduced vertical ZWD reduction for the blind UNB3 models: Tm + k3 ) Rd es ZWD = (l + 1) g m - Rd b Ts 10-6 (k æ b (h - h0 ) ö ZWD = ZWD0 ç 1 T0 è ø ' 2 ( l +1) g0-1 Rd b Modified UNB3 (and MOPS) reduction formula for ZWD Using E-depedence of the original model of Askne and Nordius we formulate modified vertical ZWD reduction: ZWD = 10-6 ( k2' + k3 / Tm ) Rd (l + 1) g m æ b ( h - h0 ) ö ZWD = ZWD0 ç1 T 0 è ø es ( l +1) g 0 Rd b Table shows r.m.s. of ZWD [mm] estimated for different altitudes (global analysis of ERA-Interim ) 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 Original Modified

10 Estimation of WV pressure decay parameter λ We can fit λ through full vertical profile via E - partial water vapour pressure (definition formula) ZWD - zenith wet delay (UNB3 original or modified formula) We can fit λ via Original equation (power function) Modified equations (logarithmic form) We can fit λ as Height dependent Pressure dependent Figure shows fitted λ via E, ZWD (ERA Interim :00)

11 Fitting of decay parameters Comparison of fitting λ through full vertical profile via E - partial water vapour pressure (definition formula) ZWD - zenith wet delay (UNB3 original or modified formula) Global ERA-Interim data ( :00) For non-linear fitting we applied Levenberg-Marquardt algorithm

12 New parameter for ZWD vertical reduction ZWD vertical dependence reflects approximately WV decrease, we thus proposed a similar exponential function for ZWD: e æpö =ç e0 è P0 ø l +1 ZWD æ P ö =ç ZWD0 è P0 ø g +1 definition useful for substitution or combination of both parameters We can express ZWD vertical decrease also with dependence on height when also applying non-zero temperature lapse-rate (β 0): æpö ZWD = ZWD0 ç è P0 ø g +1 æ b (h - h0 ) ö = ZWD0 ç 1 T 0 è ø Equivalency in using P and H - geopotential height (g +1) g0 Rd b

13 Assessment of new ZWD vertical approximation Global ERA-Interim data ( :00) - ZWD vertical reduced with λ and γ decay parameters compared to integrated ZWD - Fitted as a power function via partial WV pressure and ZWD data through all levels 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 Original Modified New f(p) New f(h) Table shows r.m.s. of ZWD differences [mm] at various altitudes Figure shows differences & r.m.s. from radiosonde profiles at Praha-Libuš

14 Partial WV pressure vs. Zenith wet delay Global ERA-Interim data ( :00) -- plots display global features of various observations/parameters Surface WV pressure E [hpa] Surface ZWD [mm] Surface pressure P [hpa] Surface ZTD [mm]

15 Estimated vertical decay parameters (for E, ZWD) Global ERA-Interim data ( :00) Fit λ via E γ via ZWD Log-fit Pow-fit Fitted λ via E (log-fit) Fitted γ via ZWD (log-fit) Fitted λ via E (pow-fit) Fitted γ via ZWD (pow-fit)

16 Surface ZWD assessment in global scope Global ERA-Interim data ( :00) Reference values integrated ZWD (full profile) Compared values ZWD calculated with model of Askne and Nordius: Fitted λ via E (pow-fit) Fitted λ via E & γ via ZWD (ratio 50.0%) Fitted γ via ZWD (pow-fit)

17 Improving ZWD model of Askne and Nordius Remark: WV pressure decay is difficult to estimate (inversions), but represent parameters that may be observed in situ (e.g. at surface) ZWD is integral following smoothly the expected exponential decay curve In order to take advantage of both WV pressure and ZWD decay parameters we fitted an optimal combination ratio for estimating modified λ parameter to be introduced into the model of Askne and Nordius æ æ k3 ö Rd b Rd ö -6 ' ZWD = 10 ç k2 + ' es, Tm = Ts ç1 - ' T ( l + 1) g ( l + 1) g m ø m m ø è è Estimated from ERA-Interim ( ), all altitudes and global grid points: w æ w ö l = l + ç g 100 è 100 ø ' w = (h - hsurface )... including dependence on height

18 Combination ratio for λ and γ decays Ratio estimated globally with Askne-Nordius ZWD vs. Integrated ZWD (on the ERA-Interim surface) Yearly estimates of combination ratio and lapse rate including uncertainties:

19 Surface ZWD assessment in global scope Global ERA-Interim data ( :00) Latitudinal dependence for ZWD calculated at the surface Reference values integrated ZWD (full profile) Compared values ZWD calculated using the model of Askne and Nordius: Fitted λ via E (pow-fit) Fitted γ via ZWD (pow-fit) Fitted λ via E & γ via ZWD (ratio 50.0%) Fitted λ via E & γ via ZWD (ratio 64.5%)

20 Surface ZWD assessment (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: a) b) c) d) e) 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

21 G-Nut software library & user applications G-Nut generic library for GNSS application developments Application tools available under GNU GPL v3 G-Nut/Tefnut troposphere monitoring - (near) real-time, post-processing G-Nut/Geb precise positioning - static/kinematic, real-time/offline G-Nut/Shu tropospheric models based on NWM data G-Nut/Anubis multi-gnss quality check monitoring tool Recent publications: Vaclavovic P, Dousa J, Gyori G (2013), G-Nut software library - state of development and first results, Acta Geodyn Geomater, Vol. 10, No. 4 (172), pp Dousa J, Vaclavovic P (2014) Real-time zenith tropospheric delays in support of numerical weather prediction applications. J Adv Space Res, (available online 1 March 2014) Vaclavovic P, Dousa J (2014), G-Nut/Anubis - open-source tool for multi-gnss data monitoring, In: IAG Symposia Series, Springer, Vol. 143, (accepted) 21

22 ZTDs from GNSS and numerical weather model ERA-Interim, IGS products and kinematic PPP by G-Nut/Geb PPP convergence time minutes applicable ZTD from NWM Potential for high-kinematic PPP (augmentation model) 22

23 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) 23

24 The assessment of the tropospheric models/products Gyori G, Dousa J (2014), GOP-TropDB developments for tropospheric product evaluation and monitoring design, functionality and initial results, In: IAG Symposia Series, Vol. 143, (accepted) 24

25 DNS sw: ultra-fast NWM data ray-tracing developed by F. Zus (GFZ) thousands of slant-delays/second (using 1 standard CPU) Zus F, G. Dick G, Douša J, Heise S, Wickert J(2014) The rapid and precise computation of GPS slant delays and mapping factors utilizing a numerical weather model, Radio Science, 49(3) With the highly efficient ray-tracing software we assessed: MF tuning (approximations): a) satellite altitude b) elevation angle c) altitude dependence Dts mf ( e 0 ) = z Dt dmf (e ) 1 = - mf (e ) dh sin(e ) All current MFs - height dependence for ZHD, but not ZWD Specific fit for ah, bh and ch coefficients (constant over a glob) Asymmetry modeling: a) horizontal gradients DT ( z0, A) = DT ( z0 ) + éëgn cos ( A ) + GE sin ( A ) ùû mf AZ ( A )

26 Altitude approximation of mapping function MF approximation errors: errors surface -> 2 km above surface Zus F, Dick G, Douša J, Wickert J (2014) Systematic errors of mapping functions which are based on the VMF1 concept, GPS solutions (accepted) 2

27 Gradients from NWM model(s) Global ERA-Interim model (plus comparison study with NCEP s GFS) Zus et al Atmospheric content of GPS slant total delays (presented at EGU 2014)

28 Summary (1) We introduced parameter for ZWD vertical approximation γ[-] that improved vertical reduction by a factor of 2-3 New ZWD vertical modelling improved the 25-years-old model of Askne and Nordius for ZWD calculation by applying ratio w = (h-hsurf) for optimal combination WV (λ) and ZWD (γ) decay parameters New concept of ZWD modelling achieves 1 cm accuracy in a global scope using 1 x1 ERA Interim, while the legacy concept 2-3 cm only The theoretical development is efficient, flexible and accurate for parameterization of a future augmentation and blind tropospheric models even supporting in-situ meteo observations Douša J, Eliaš M (2014) An improved model for calculating tropospheric wet delay (submitted to GRL after minor revision) 28

29 Summary (2) G-Nut sw library enables us to study the potential of NWM introduction to PPP (positive impact on height repeatability) We studied approximations in mapping functions and showed the deficiency mainly in the altitude dependence We studied the potential of tropospheric horizontal gradients estimated from the numerical weather model fields Outlook: We will evaluate accuracy of tropospheric corrections from selected numerical weather models in GOP-TropDB We will complete development of blind model and exploit the new concept in real-time positioning & reprocessing 29

30 Thank you for your attention The presented work has been supported by Czech Science Foundation (P209/12/2207) and ESA project Trop4LAS ( /12/NL/LvH) Further we acknowledge: COST Action 1206 (GNSS4SWEC) ECMWF for providing the ERA-Interim data set a fruitful discussions on the topic with S. Leeuwen, A. Martelluci, S. de Haan, H. Vedel 30