GPS coordinate estimates by a priori tropospheric delays from NWP using ultra-rapid orbits

High accuracy GPS positioning estimates using scientific GPS software through three different processing strategies were compared. The two Italian baselines in a time period of 5 months during 2004 made a calculus data set. For high accuracy GPS differential positioning the use of global tropospheric delay models can be replaced by the implementation of other techniques. The GPS coordinate can be repeated when the tropospheric delay is calculated in Near-Real Time (NRT) from a Numerical Weather Prediction (NWP) model. For the NRT approach IGS ultra-rapid orbits instead of precise orbits were used. Concerning coordinate repeatability, the NWP-based strategy with tropospheric error adjustment appeared more accurate (at the submillimetric level) than a standard GPS strategy. Furthermore, several hundreds km long baselines demonstrated the standard deviation at the level of millimeters (from 4.2 to 7.6 mm). Practically, the NWP-based strategy offers the advantage of tropospheric delay estimations closer to realistic meteorological values. The application of a more accurate meteorology leads to satisfactory coordinate estimations, and vice versa well-defined GPS estimations of coordinates may serve as the additional meteorological parameters source. Mailing address: Dr. Mauro Boccolari, Dipartimento di Ingegneria dei Materiali e dell’Ambiente (DIMA), Università degli Studi di Modena e Reggio Emilia, Via Vignolese 905, 41100 Modena, Italy; e-mail: boccolari.mauro@unimore.it


Introduction
When GPS satellite signals are transmitted through the atmosphere they are affected by the media.In the neutral atmosphere refraction is a function of the meteorological conditions such as pressure, temperature and humidity along the signal path, and this effect is referred to in GPS terminology as the tropospheric delay.
In the GPS positioning process this effect represents an important error source introducing primarily biased station heights and scale biases of estimated baseline length (Beutler et al., 1988).
Usually, GPS software employs global tropospheric models (based on a standard atmosphere) to handle this effect.Instead global, other meteorologically based tropospheric delay models can be implemented, applying observational data sources.The tropospheric delay calculated from a Numerical Weather Predictions (NWP) analysis and/or forecast was already tested, (e.g., Cucurull et al., 2002;Jensen et al., 2002;Fazlagic´, 2003).In Cucurull et al. (2002) MM5 model forecasts are applied in GIPSY software precise point positioning to estimate the hourly improvement of geodetic vertical coordinate in 24-h reference solutions.In Jensen et al. (2002) NWP zenith delays are used within a GPS static positioning processing to correct

GPS coordinate estimates by a priori
tropospheric delays from NWP using ultra-rapid orbits Mauro Boccolari, Slobodan Fazlagic ´and Renato Santangelo Dipartimento di Ingegneria dei Materiali e dell'Ambiente (DIMA), Università degli Studi di Modena e Reggio Emilia, Modena, Italy Abstract High accuracy GPS positioning estimates using scientific GPS software through three different processing strategies were compared.The two Italian baselines in a time period of 5 months during 2004 made a calculus data set.For high accuracy GPS differential positioning the use of global tropospheric delay models can be replaced by the implementation of other techniques.The GPS coordinate can be repeated when the tropospheric delay is calculated in Near-Real Time (NRT) from a Numerical Weather Prediction (NWP) model.For the NRT approach IGS ultra-rapid orbits instead of precise orbits were used.Concerning coordinate repeatability, the NWP-based strategy with tropospheric error adjustment appeared more accurate (at the submillimetric level) than a standard GPS strategy.Furthermore, several hundreds km long baselines demonstrated the standard deviation at the level of millimeters (from 4.2 to 7.6 mm).Practically, the NWP-based strategy offers the advantage of tropospheric delay estimations closer to realistic meteorological values.The application of a more accurate meteorology leads to satisfactory coordinate estimations, and vice versa well-defined GPS estimations of coordinates may serve as the additional meteorological parameters source.
Following the GPS coordinate analysis suggested by Fazlagic ´(2003), coordinates of two Italian sites (Genoa and Venice), for the time period of 5 months using three different processing strategies are examined.
Ways of tropospheric delay handling may determine different approaches.The three strategies for the coordinate estimates applied in this work were: -[MET] Meteorological strategy: by introduction of Zenith Tropospheric Delay (ZTD) a priori calculated from meteorological dataanalysis and forecasts by a NWP model, without any further tropospheric delay error adjustment; -[STD] Standard strategy: by ZTD a priori obtained by the global Saastamoinen model (Saastamoinen, 1972) followed by the tropospheric delay error adjustment; -[MIX] Mixed strategy: by introduction of ZTD a priori calculated from meteorological data, like in the MET strategy, but with afterward tropospheric error adjustment, as in the STD strategy.
Also (Kleijer, 2004) discussed the differences between the approach based on ZTD «tropospheric-fixed» model, and other «tropospheric float model» techniques.
Differential positioning with GPS Bernese Software 4.2 (Hugentobler et al., 2001) is applied in this work, taking a GPS observation window of 12 h at first, and then using a shorter observation window of 6 h.In this paper only results obtained with the 6-h window are shown: the wider 12-h window results do not offer significant differences.
The two independent baselines, for Venice and Genoa GPS sites, are created by the introduction of the third (fixed) GPS site, the IGS (International GPS Service) station of Medicina.
It is well known that in high accuracy positioning the prevailing source of error is originated by satellite orbits so the introduction of precise ephemeredes is suggested.Since a Near Real Time (NRT) approach is important for meteorology purposes, IGS ultra-rapid orbits (Springer and Hugentobler, 2001) are introduced instead of IGS Final orbits.In 2004 IGS ultra-rapid orbits were available twice daily offering a good accuracy (about 25 cm was indicated in http://igscb.jpl.nasa.gov).

Data sources and baselines definition
The GPS sites Venice (VENE) and Genoa (GENO) were selected (both with long time stable record, located in the same tectonic plate in Northern Italy and belonging to EPN -European Reference Frame Permanent Network).
Looking for a reference spot the station of Medicina (MEDI-IGS station, located in Northern Italy) appeared convenient.Thus two independent baselines were formed: Venice-Medicina (VE-ME) and Genoa-Medicina (GE-ME).
Figure 1 shows the map featuring the three GPS stations.The baseline lengths are 115351.7578m for Venice-Medicina and (almost twice longer) 217154.4860m for Genoa-Medicina respectively.The Bernese processing was set up to: elevation cut-off at 15°; Quasi-Ionosphere-Free (QIF) algorithm in baseline mode as ambiguity resolution strategy; ionosphere-free linear combination to mitigate ionosphere dispersion; no ocean loading (its effect for the test sites and for the limited testing period was evaluated to be of the submillimeter order); tropospheric model (when used): Saastamoinen; automatic processing with the Bernese Processing Engine (BPE).
The following two datasets were retrieved: -GPS hourly observations (for all three stations), from Agenzia Spaziale Italiana (ASI), appropriately merged to obtain a 6 h (and 12 h) window observation session (ftp://geodaf.mt.asi.it).
-The most recent GPS ultra-rapid orbits available (and Earth Rotation Parameter files) from IGS data center (ftp://igs.ifag.de).
Also, for the two meteorologically based strategies (MET and MIX) the Deutscher Wetterdienst (DWD) Local Model (LM) (DWD, 2003) analysis and forecasts interpolated over the selected sites data were retrieved.DWD data were available twice daily, where each data set is referred to 00 UTC analysis or 12 UTC analysis plus forecasts up to 48 h.DWD data refer both to the surface level and to upper air levels.
Figure 2 presents a synthetic flow chart with input and output data for all three strategies.

Tropospheric delay modeling
In high accuracy differential positioning based on the carrier phase observable, as in the GPS Bernese Software, the slant tropospheric delay between a GPS receiver k and a GPS satellite i is estimated as where ZTD apr, k is the Zenith Tropospheric Delay according to the a priori model (or other data source) specified; ZTDk(t) is the (time dependent) zenith tropospheric parameter for station k, which corrects the previous term; z k i is the zenith distance; fapr is the mapping function of the a priori model; is the mapping function used for the parameter estimation.For NWP-based strategies (MET and MIX), ZTDapr, k were calculated from DWD/LM, using ZTD expressed by means of a sum of different contributions (Thayer, 1974).The largest atmospheric delay results from hydrostatic constituents (Zenith Hydrostatic Delay -ZHD).ZHD (in meters) is calculated as (Davis et al., 1985) (3.2) where p s, is the surface air pressure (in hPa) and f is a function depending by the geographical latitude φ and ellipsoidical height h.The sites selected for this work present f(φ, h) values close to one.The second largest contributor to tropospheric delay is water vapor, which corresponds to Zenith Non Hydrostatic Delay (ZNHD), given in meters, as reported in Vedel et al. (2001) (3.3)where q is specific humidity (kg/kg), T is the temperature (K), p is the upper-air pressure (in hPa), Rd is the dry air specific constant (Rd =287.05Jkg −1 K −1 ); g is gravity acceleration (fixed constant to 9.81 ms −2 ); ε is the ratio between the dry air and water vapor molar mass; k 1, k2, k3 are coefficients (Bevis et al., 1994) (k1=77.6K/hPa, k2=70.4K/hPa, k3=3.739⋅10 5 K 2 /hPa).
On the other hand, the DWD data set provides all meteorological parameters necessary to calculate the tropospheric delay contribution.
Very low contributions to the atmospheric refractivity are due to nongaseous atmospheric constituents, hydrometeors and other particulates (Solheim et al., 1999).The delay due to hydrometeors (ZHMT), can be expressed in (meters) as (3.4) where CW is the cloud water content (kg/kg) in the atmosphere and ρair is the air density.The cloud water content available from DWD data permitted us also to consider even this usually neglected contribution.
In STD strategy, ZTDapr, k is calculated by Bernese using the Saastamoinen equation where p s, Ts and es are the surface air pressure (in hPa), the surface air temperature (in K) and the surface partial water vapor pressure (in hPa) respectively.In Bernese ps, Ts and es are set to constant values.
Table I, referring to eq. (3.1) presents a review of ZTD apr, k sources and ZTDk(t) approaches for all three strategies.
Mapping function in eq.(3.1), when used, was always the zenith angle cosine.

Results on coordinate repeatability impact
For the total sum of 608 sessions obtainable to estimate (4 coordinate sets for 152 days), just the number of coordinates estimates as given in table II, were suitable for processing, due to poor availability of data (observations, orbits or meteorological data lack).
Estimated global Cartesian coordinates (X, Y, Z ) for Genoa and Venice, together to the local coordinates: Up (U), North (N) and East (E); with respect to the corresponding estimated coordinates mean values are discussed.
Table III shows the Cartesian coordinates (X, Y, Z ) mean biases between different strategies for Genoa and Venice.It can easily be seen that the biases corresponding to MIX-STD comparison are minimal with respect the two other comparisons involving MET strategy.In conclusion, the MIX and STD strategy was equivalent with respect to coordinate repeatability.The MET strategy shows that avoiding tropospheric error delays estimation is not sufficiently correct.
Table V shows baseline length mean values ( ) and their standard deviations ( ).The repeatability of baseline lengths with respect to the reference station of Medicina for all three strategies shows a good agreement, varying only from a submillimetric to a millimetric level.The standard deviations of the baseline lengths, with almost doubled values for Genoa with respect to Venice, are consistent with the baseline length differences.
The standard deviation values showed the convenience of MIX strategy, achieving results very close to the STD strategy, again with differences at the submillimetric level.Figures 3 and 4 show the smoothing curves (quadratic fit) of local coordinates (U, N, E) time series for all three strategies.(The MIX strategy curve is in red color, the STD strategy is in blue and the curve of the MET strategy is in the black color).Generally, all three MIX and the STD curves follow an analogous pattern, while the MET strategy Up curve shows expected meteorological variability dependence (cm range against mm range for N and E components).
Moreover, it is necessary to confirm that the reciprocal position of the three sites were considered time stationary.However, from the EUREF improved time series (http://epncb.oma.be) the kinematical displacements of the local coordinates of three sites appear about 0-3 mm/yr.

ZTD comparison
As explained in the introduction, tropospheric errors adjustment is part of STD and MIX strategies, while in MET strategy tropospheric delays are fixed.
Table VI shows ZTD mean differences (biases) and standard deviations, averaged for a 6h estimation window.It can be seen that both ZTD biases and their standard deviations are minimal between two meteorologically based strategies (MET, MIX), but larger when the comparison is made to the STD strategy.That confirms that avoiding of the introduction of measured or modeled meteorological parameters (as in STD strategy) cannot provide an adequate ZTD estimation.Furthermore, comparing the standard deviations for both testing sites   From figs. 5 and 6 it can be noted that the two strategies MET and MIX proceed simultaneously, while the STD strategy moves rather linearly.Yet the coordinates obtained by either MIX or STD strategy are practically equal, leading to the assumption that NWP models applied in the MIX strategy gave a sufficient contribution.

Conclusions
In order to discuss the possible application of Numerical Weather Prediction (NWP) meteorological parameters in GPS elaboration, and vice versa accurate GPS elaboration as further information on meteorological fields, the three strategies for the GPS coordinate estimates are implemented.The so called MET and MIX strategies were based on the introduction of Zenith Tropospheric Delays (ZTD) calculated from NWP meteorological data while the STD strategy assumed the most used GPS elaboration mode based on ZTD obtained by a global model.STD and MIX strategies performed the estimation of both coordinates and tropospheric errors; while MET strategy produced only the coordinate estimation.For that purpose, two baselines formed by GPS sites of Venice, Genoa and Medicina, belonging to EPN in Northern Italy were tested.
Biases of global Cartesian coordinates values between various strategies and their standard deviations show that two strategies based on ZTD corrections (MIX and the STD) produce more adequate and similar results with respect to the third strategy (MET) based on the «errorless a priori» ZTD.The difference between MIX and STD strategy is generally at the submillimetric level, while for the MET strategy the difference with respect to other two strategies varies from millimetric to centimetric level.Also the standard variations values for three local coordinates confirm that both STD strategy and MIX strategy again gave comparable values.The dependence of tropospheric delay error modeling on the vertical local coordinate (Up) appears confirmed; the vertical components in MET strategy show the largest dispersion.
On the other hand, ZTD and their standard deviations are minimal between two meteorologically based strategies (MET, MIX), but much larger when the comparison is made between the STD strategy and the other two.Yet the coordinates obtained by either MIX or STD strategy are practically equal, leading to the assumption that NWP models applied in the MIX strategy gave a sufficient contribution.
We can conclude that reciprocally an accurate meteorology leads to a more precise coordinate estimation, and vice versa the well-defined GPS estimation of the coordinates may serve to take the place of lacking information on meteorological parameters.

Fig. 1 .
Fig. 1.The geographical map showing the GPS sites used in this work.

Fig. 3 .
Fig. 3. Smoothing curves of estimated local coordinates for Genoa for all strategies.

Fig. 4 .
Fig. 4. Smoothing curves of estimated local coordinates for Venice for all strategies.

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Genoa and Venice very small differences are verified.Figures5 and 6show ZTD 6-h averaged with smoothing curves.

Table I .
ZTD a priori sources and different estimation approaches.

Table IV .
Cartesian global coordinates and local coordinates standard deviations for Genoa and Venice and for all strategies.GPS coordinate estimates by a priori tropospheric delays from NWP using ultra-rapid orbits Also the data accuracy, represented in table IV by means of Cartesian global coordinates standard deviations (σX, σY, σZ) and local coordinates standard deviations(σUp, σNorth, σEast), indicates an equivalence between the MIX and STD strategies with respect to the repeatability.

Table II .
Number of coordinate estimates for each strategy and for each site.

Table III .
Cartesian coordinates mean biases for Genoa and Venice and for all strategies.
Mean baseline lengths and standard deviation values for all strategies.

Table VI .
Mean ZTD differences and standard deviation values, 6-h averaged.