A correction model for zenith dry delay of GPS signals using regional meteorological sites. GPS-based determination of atmospheric water vapour
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1 Geodetc Week 00 October 05-07, Cologne S4: Appled Geodesy and GNSS A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Xaoguang Luo Geodetc Insttute, Department of Cvl Engneerng, Geo- and Envronmental Scences, KIT KIT Unversty of the State of Baden-Wuerttemberg and Natonal Research Center of the Helmholtz Assocaton Motvaton GPS-based determnaton of atmospherc water vapour Based on delay estmaton of GPS sgnals Zenth total delay (ZTD Estmated wthn GPS data processng Ste-specfc troposphere parameters Temporally varable (parameter tme span, constrants Zenth dry delay (ZDD Calculated usng meteorologcal (MET data near GPS stes Near-ste MET data: observatons, numercal weather model Hghly correlated wth pressure of dry ar Zenth wet delay (ZWD: ZTD-ZDD water vapour content Problem: non-avalablty of near-ste MET data A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes
2 Correctng a pror ZDD ATM STD (T 0, p 0, rh 0 H 0 = 0 m Extrapolaton (T S, p S, rh S e.g., Berg (948 Ste alttude (H S above MSL (H 0 Regonal MET stes (e.g., DWD MET M (T M, p M, rh M measurements Ste alttude (H M above MSL (H 0 A pror ZDD (H S nvarable n tme e.g., Saastamonen (973 ZDD (MET M usng MET data A pror ZDD (H M extrapolaton Correcton value ZDD S = F(H S A heght-dependent correcton model ZDD M =ZDD(MET M -ZDD(H M = F(H M Fg. : Schematc llustraton of a correcton model for a pror ZDD usng regonal metrologcal stes MSL: mean sea level; Index S/M: GPS/metrologcal stes; DWD: Deutscher Wetterdenst A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Data base Tab. : DWD MET data (free of charge Ar pressure p M Temporal resoluton Ste alttude ( stes Tme nterval DOY hpa Temperature T M 0. C Rel. humdty rh M % 6 h m Tab. : MET data from GPS stes DWD MET ste GPS ste Fg. : Selected DWD meteorologcal statons and GPS stes wth MET data n the area of southwest Germany (dgtal elevaton model: ETOPO, Amante and Eakns 009 Ste dll efbg muej bfo H S [m] MET R data (GPS Rate 0 s 5 mn 0 s 5 s Unt p R : 0. hpa T R : 0. C rh R : 0. % (R: RINEX A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes
3 A lnear regresson model Lnear relatonshp between H M and ZDD M ZDD M = ZDD( METM ZDD( H M ZDDM = a H M + b, a, b : regresson coeffcents Estmaton of regresson coeffcents Classcal ordnary least-squares estmaton (OLSE Mnmsng the squared sum of v:= (a H M + b ZDD M Outler detecton based on studentsed resduals r s ( v rs ( = = ˆ σ ˆ σ T Outler detected at v Q 0 vv ~ τ f (, ( f rs ( ( : = ~ t f f rs ( Beckman and Trussell (974; Pope (976; Heck (980, 98 sgnfcance level α f T ( > t f, -α / A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes A lnear regresson model Estmaton of regresson coeffcents Bootstrap estmaton (e.g., Efron 98, chap. 5; Trauth 006, p. 66 ff Resamplng data wth replacement Applyng OLS estmaton to each resampled data set Parameter estmaton wth a samplng dstrbuton Tme-consumng computaton Leave-one-out (LOO cross valdaton (e.g., Trauth 006, p. 77 ff Temporarly removng the -th data pont (x, y Performng OLS regresson usng the remanng n data ponts Predctng the -th data pont based on the regresson model f (x Computng the -th dscrepancy between predcton and observaton Calculatng the mean error over all n data ponts (Allen 974 ˆ σ LOO n = n = ( y f ( x / A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes 3
4 Outler detecton OLS regresson DOY008:77, UT: 6 h Bootstrap estmaton Cross valdaton Fg. 3: Example of outler detecton and ts mpact on parameter estmaton A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Regresson coeffcents Slope a Intercept b Lnear model: ZDDM = a H M + b Fg. 4: Comparson of regresson coeffcents usng dfferent approaches for parameter estmaton (wthout outlers Consstent regresson coeffcents usng dfferent methods Relable results also provded by drect OLS estmaton (OLSE Key beneft of OLSE: fast computaton A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes 4
5 Model error (ME Fg. 5: Influences of precptaton on resdual standard devaton (parameter estmaton: OLSE ME: standard devaton of OLS resduals ME < 5 mm n most nstances Improved ME after outler elmnaton Larger ME values on wet days A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Model verfcaton GPS ste: dll, 8 m Ste: dll GPS ste: bfo, 647 m Ste: bfo Fg. 6: Model valdaton usng GPS stes wth meteorologcal data A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes 5
6 Model accuracy (MA MA: mean absolute devaton (MAD n = MAD = ZDD( MET R ( ZDD( H S + ZDDS ( n GPS ste wthmet Corrected ZDD(HS H : alttude of GPS ste wth meteorologcal data ( MET S Tab. : Accuracy assessment usng GPS stes wth meteorologcal data R GPS ste wth MET data dll efbg muej bfo Alttude above MSL [m] MAD [mm] ( ZDD S wth outler MAD [mm] ( ZDD S wthout outler Improvement -% 5% % 7% MA values near 5 mm n most cases Improved MA after elmnatng outlers A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Conclusons Problem: ZDD of GPS sgnals wthout near-ste MET data Soluton: a correcton model for a pror ZDD Usng regonal free avalable MET statons of DWD Lnear regresson between H M and ZDD M Parameter estmaton: OLSE, BOOT, CROS Outler detecton based on studentsed resduals from OLSE Consstent regresson coeffcents (OLSE: fast computaton Model qualty assessments Model error (ME: standard devaton of OLS resduals Sgnfcantly affected by precptaton Mean ME < 5 mm n the presented case study Model accuracy (MA: mean absolute devaton (MAD Usng 4 GPS stes wth MET data MAD(ZDD MET(GPS ZDD corrected Near 5 mm n most cases Consderably mproved ME and MA after outler elmnaton A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes 6
7 Outlook Model valdaton Usng more GPS stes wth MET data Incorporatng more regonal MET stes MET data wth hgher temporal resoluton Model extenson Consderng ste locaton Heght-dependent ( D locaton-dependent (3 D A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes Questons & comments Thank you very much for your attenton! A correcton model for zenth dry delay of GPS sgnals usng regonal meteorologcal stes 7
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