1. Introduction

Global positioning system (GPS) ground-based receivers can work as meteorological sensors. The GPS signal from the satellite to the ground receiver is delayed by the ionosphere and the neutral atmosphere. The ionospheric refraction, due to free charged particles, is frequency dependent, and its effect on a radio signal can be almost cancelled out through observations at two different frequencies (viz., around 1.5 and 1.2 GHz) by constructing the iono-free linear combination (Hoffmann-Wellenhof et al. 1997). On the other hand, the influence of the neutral atmosphere cannot be cancelled due to its nondispersive behavior. While the variation of the refraction index in the troposphere is due to temperature, pressure, and water content (Thayer 1974), the zenith total delay (ZTD)—that is, the delay of the neutral atmosphere—can be split into a hydrostatic part, a function of the surface pressure (Saastamoinen 1972), and a component that depends on the content of water vapor and temperature. The estimate of the hydrostatic zenith delay, derived from surface pressure, can be subtracted, leaving the effect of the wet zenith delay, which is proportional to the integrated precipitable water vapor (IPWV). The dimensionless constant of proportionality (Askne and Nordius 1987; Elgered et al. 1991) is a weak function of the weighted mean temperature of the atmospheric column and can be related to the surface temperature by a linear relationship (Bevis et al. 1992).

In the framework of the Meteorological Applications of GPS Integrated Column Water Vapor Measurements in the Western Mediterranean (MAGIC) project (Haase et al. 2001), GPS zenith tropospheric delays have been, since January 1999, routinely delivered and monitored at the Centro di Geodesia Spaziale of the Italian Space Agency (ASI) in Matera, for a network covering the central Mediterranean area. The network has a higher resolution over the Italian territory due to the fact that all the available Italian GPS permanent stations are included in the analysis. In mid-2001 a near-real-time (NRT) datastream was developed and, since then, has provided GPS ZTD estimates for meteorological applications on an hourly basis.

The general requirements for a climatological and meteorological GPS zenith total delay estimation are reported in the next section. In section 3 the ASI processing system, which monitors ZTD for climate studies, and its long-term internal validation, are discussed. Section 4 provides a technical description of the near-real-time datastream for meteorological applications. Also discussed in the same section are comparisons between the zenith total delay estimates obtained in the operational phase by the two datastreams previously presented. Furthermore, an intriguing correlation between height coordinates and zenith total delay residual time series has been detected. This correlation is thoroughly explained in section 4, as well.

2. Requirements for a climatological and meteorological GPS ZTD estimation

The main applications for the GPS estimated tropospheric parameters are long-term monitoring and study of the dynamics of the derived IPWV, and assimilation into numerical weather prediction (NWP) models of IPWV or ZTD. The requirements for meteorological and climatological ZTD estimations have been thoroughly discussed within the European Cooperation in the Field of Scientific and Technical Research (COST) action 716, “Exploitation of ground based GPS for climate and numerical weather prediction application” (http://www.oso.chalmers.se/∼kge/cost/Oslo_WGmeetings.pdf) (Elgered 2001; Van der Marel 2000).

As far as climate applications are concerned, long time series (>10 yr) of GPS estimates have to be achieved, while a long-term stability is necessary. The required standard deviation after removal of long-term bias is 6–30 mm in ZTD (Van der Marel 2000). The GPS final orbits, provided by the International GPS Service (IGS), with a delay of 2 weeks, can be used since the timeliness requirement is 1–2 months. In order to perform an operational weather forecast, it is required that 75% of the observations are available within 1 h, 45 min. Therefore, a fast and reliable data flow from GPS observations to ZTD estimation has to be set up (see Fig. 1), and predicted GPS orbits can be used. The IGS UltraRapid orbits, delivered twice a day, have enough accuracy (∼25 cm or better; Springer and Hugentobler 2001) for meteorological application, although “bad” orbits, due to unpredictable nonconservative forces, may occur. The strategy based merely on the quality index provided with the predicted orbits cannot ensure the required accuracy. As a result, several approaches have been developed in order to handle the “bad” satellites: orbit relaxation by estimating along-track orbit parameters for all satellites (Kruse et al. 1999), an iterative process for orbit improvement/relaxation (Ge et al. 2000), and bad satellite detection and removal that is based on residual analysis (Springer and Hugentobler 2001).

Springer and Hugentobler (2001) proved that these different approaches provide similar results and that the detection and removal of bad satellites, based on the observation phase postfit residuals, are relatively easy and can be fully automated in a near-real-time ZTD process estimation.

The required absolute accuracy for a meteorological ZTD estimation is about 6 mm, corresponding to approximately 1-mm IPWV. Furthermore, it is important that surface meteorological instruments are collocated with a GPS receiver. In order to compute the hydrostatic component of the delay [zenith hydrostatic delay (ZHD)] by applying the Saastamoinen (1972) equation, barometric measurements are necessary. To guarantee an accuracy of 1 mm for ZHD, a 0.4-mb accuracy for pressure measurements is required. The main uncertainty in the conversion of zenith wet delay (ZWD) into IPWV is related to the computation of the mean temperature. Bevis et al. (1992) found a linear relationship between the mean temperature of the atmosphere and the surface temperature; for an operational meteorological service an accuracy of 1 K for temperature measurements is essential. There are different techniques for assimilation of GPS atmospheric parameters into numerical weather prediction models, such as nudging (Kuo et al. 1993), which requires the IPWV, and the 3D-VAR and 4D-VAR techniques (Kuo et al. 1996), which are able to directly assimilate GPS ZTD estimates with no need of other transformations, thus avoiding errors due to uncalibrated barometers and assumptions on the atmospheric state in the computation of the mean temperature.

One of the main issues for an operational use of ground-based GPS meteorology is the reliability and latency of the hourly data. GPS data should be available shortly after they are collected, and the data transmission connection should ensure regular data flows in order not to degrade the solutions useful for operational meteorology.

Another important step to be taken when setting up an operational weather forecast is computation of the atmospheric volume observed by a single GPS receiver, in order to establish a network with enough GPS receivers to sound the whole atmosphere in the concerned area. Considering a single-layer model of the atmosphere, a GPS cutoff angle of 10°, and a tropospheric height of 5 km, we can ascertain that the area seen by a single GPS receiver is a cycle of 27-km radius. This means that to sound different tropospheric volumes the concerned area could be divided into a grid of 50 km × 50 km. Nevertheless, this is a rather optimistic conclusion. Actually, a denser network (down to 30 km × 30 km) is needed because of the complex topography of the earth's surface, even if what really dictates the station grid is the spatial scale of the atmospheric structure one wishes to determine.

3. Climatological ZTD monitoring

In the central Mediterranean area, GPS zenith total delays for climate studies have been routinely delivered and monitored since January 1999. An operative datastream has been developed, in the framework of the MAGIC project, at the Centro di Geodesia Spaziale of the ASI in Matera, in order to provide daily estimates of GPS ZTD. (Figure 2 shows 3-yr ZTD time series estimates for the Matera site.) Throughout the whole of 1999, a high correlation is found when comparing GPS and very long baseline interferometry (VLBI) zenith tropospheric delay estimates relevant to the three Italian collocated stations, Matera, Medicina, and Noto (Pacione et. al. 2002). The validation of the GPS-derived zenith total delay has been performed according to independent techniques such as ground-based microwave radiometer (WVR) and radiosonde observation (raob). The epoch campaign carried out during 1999 at Cagliari Astronomical Station, Sardinia (see Fig. 5 for its geographical location), allows us to compare GPS, and ground-based microwave radiometer and radiosonde integrated precipitable water vapor relying on monthly, seasonal, and annual bases, providing hints regarding GPS long-term stability. On an annual basis the comparison analysis of IPWV estimation between WVR and GPS has shown a standard deviation equal to 0.136 cm with a bias of −0.049 cm, while raob and GPS IPWV have a 0.193-cm standard deviation and a bias of −0.022 cm. A better coherence is found between the two microwave sensors, and the largest standard deviation occurs in comparisons involving raob (Westwater et al. 2000). More details on this campaign as well as on achieved outcomes can be found in Pacione et. al. (2002).

An assimilation test, as well as sensitivity experiments to verify the impact of GPS precipitable water on the precipitation forecast over the Mediterranean area, have been performed (Faccani et al. 2002, manuscript submitted to J. Appl. Meteor.) considering the intensive observation period IOP7 (17–19 October 1999) as a case study. During the last stage of this event, a line of thunderstorms occurred over the northern Tyrrhenian Sea and across the Italian regions, producing precipitation over central and southern Italy. The resulting model using upper-air, surface, and GPS precipitable water observations shows an improvement of the high-resolution precipitation forecast over the area where the GPS receivers are located.

The GPS internal validation of zenith tropospheric delay is carried out taking into account two independent 2.5-yr ZTD time series (January 1999–May 2001) assessed, respectively, by ASI and the Centre National de la Recherche Scientifique (CNRS) Géosciences Azur (http://kreiz.unice.fr/magic) in the framework of the MAGIC project. The comparison of the results achieved by using different GPS data analysis software and approaches shows a bias of ±5 mm (∼±1 mm of IPWV), more stable for the last year (Fig. 3), and a standard deviation ranging from 4 to 15 mm (Fig. 4), in line with the requirements described in section 2. Such comparisons can be considered as good tests of the long-term internal consistency of the GPS solutions. The reasons for the “jump” that occurred on 1 January 2000—as reported in Fig. 3—are presently under investigation; possible causes could be connected to station coordinate errors and to a change in the terrestrial reference frame.

The postprocessing GPS data reduction is performed on a daily basis, in a fully automatic way, with a 2-week latency. The GPS ground network (Fig. 5) covers central and southern Europe. Over Italy it has a spatial resolution higher than in other regions since all available Italian permanent sites are included in this analysis. Most of the stations belong to the European Reference Frame (EUREF)/IGS network (http://epncb.oma.be). The analysis is carried out by using GPS-Inferred Positioning System and Orbit Analysis Simulation Software (GIPSY-OASIS II) package (Webb and Zumberge 1997) and the precise point positioning approach (Zumberge et al. 1997), and fixing Jet Propulsion Laboratory (JPL) fiducial-free satellite orbits, clocks, and earth orientation parameters. ZTDs estimated with a sampling rate of 5 min are averaged over 15 min and converted into a standard meteorological data format. The main features of the analysis are reported in Pacione et al. (2001). The main strategy changes are application of the ocean loading corrections and estimation of the tropospheric horizontal gradient, the effects of which on ZTD estimates are discussed respectively in sections 3a and 3b.

The main goal of the postprocessed solutions is to provide both ZTD estimates for climate applications and station coordinates, which will be fixed, in the meteorological solutions when enough accuracy is reached. As for meteorological applications, we need to monitor the terrestrial reference frame. The weak point of the proposed approach is its high dependence on the availability of JPL products. As a matter of fact, to avoid any nuisances we are obliged to apply the same models used to compute the fixed orbits, earth orientation parameters, and satellite clocks.

b. Tropospheric gradient estimation

The mathematical model applied for the GPS propagation delay, which takes into account the azimuthally inhomogeneous atmosphere, is (Bar-Sever et al. 1998)

View Expanded

where ɛ is the satellite elevation angle; ϕ is the satellite azimuth angle measured eastward from the north; m_h(ɛ), m_w(ɛ), and m_Δ(ɛ) are the mapping functions; and G = (G_N, G_E) is the gradient vector, with G_N and G_E its components in the north and east directions, respectively. The gradients represent real atmospheric features due to the inhomogeneousness of the atmosphere and are not artifacts caused by other errors such as multipath or GPS orbits (Bar-Sever et al. 1998). The cotɛ factor accounts for the increase in horizontal change of refractivity along the signal path as the elevation decreases (MacMillan 1995). As far as the mapping functions are concerned, we chose m_h(ɛ), m_w(ɛ), and m_Δ(ɛ) equal to Niell's (1996) dry, wet, and dry mapping functions, respectively.

The Italian GPS stations in Cagliari, Matera, Medicina, and Noto are for point-positioned estimating and not estimating the gradient vector. To sense the gradients, low-elevation observations should be included. Unfortunately, we are compelled to use a cutoff angle of 15° in the data reduction since no observations have been recorded down to this elevation angle at that time. In Fig. 8 the two ZTD time series for Cagliari relevant to April 1999 are shown. The zenith total delay obtained by modeling the inhomogeneousness of the atmosphere in the azimuth direction is ∼1.5 mm (i.e., ∼0.2 mm of IPWV), which is higher but less scattered than the one obtained by neglecting this inhomogeneousness (see Bar-Sever et al. 1998). The variability of the two gradient components is at the millimeter level, and comparisons with VLBI estimates (Pacione et. al. 2002) have shown a bias of about 2 mm with a standard deviation ranging from 0.5 to 10 mm, in accordance with other values available in literature.

It has been shown by Bar-Sever et al. (1998) and Rothacher et al. (1998) that estimating the gradients improves the multiday repeatability of the station coordinates. In conclusion, it is recommended to model them, since one of the goals of the postprocessed solutions is to provide accurate station coordinates to be set as a priori values in the near-real-time datastream.

4. Meteorological ZTD estimation

The GPS data of a European network of 30 stations, covering the central Mediterranean area, are analyzed in order to deliver ZTD within 1 h, 45 min once the hourly files are closed. The Italian stations included in the analysis provide hourly data, with a 10-min latency, directly to the ASI Geodetic Data Archiving Facilities (GeoDAF; http://geodaf.mt.asi.it), where they are archived and made available to users. The hourly data of the other involved stations are retrieved by the IGS data center and are available with a latency ranging from few minutes up to 20 min. GIPSY-OASIS II software is used for data reduction with a standard technique of network adjustment. The IGS UltraRapid orbits, available 3 h after both UTC midnight and UTC noon, are kept fixed but checked, and “bad” satellites are automatically excluded based on the analysis of postfit phase observation residuals, as suggested by Springer and Hugentobler (2001). A 24-h sliding window for data handling is applied, which means that the Receiver Independent Exchange (RINEX) data of the last hour are merged with the previous 23 h into a single file in order to have enough data to yield robust results. A sampling rate of 5 min and a cutoff angle of 10° are applied. The zenith wet delay is estimated every 5 min with a stochastic model (random walk) and a constraint of 20 mm/. The station coordinates are kept fixed to values provided by combining 1 month of the postprocessed solutions, described in section 2, with repeatability at the centimeter level or even better. They are updated every 30 days in order to take into account the tectonic movements of the area. The phase ambiguities are estimated as a float, and the satellite and station clocks are estimated with respect to one reference clock (usually Wettzell). The Niell (1996) mapping function and the ocean-loading corrections are applied. The ZTD estimates of the last hour are derived from the 24-h batch; they are averaged to a 15-min sampling rate, put into COST format (Offiler 2001), and sent to the U.K. Met. Office. Finally, a dynamic Web page (http://geodaf.mt.asi.it/GPSAtmo/ground.html) is updated with the latest results. The processing starts 18 min after every hour, and it takes about 40 min for 30 stations on an HP workstation with 512-Mbytes RAM. It lasts more than its nominal CPU time if a bad satellite or bad station is detected and removed, based on postfit phase observation residuals causing an overlap of 2-hourly solutions. Actually, the amount of processed data versus latency is a delicate balance for planning an operational stage of ground-based GPS meteorology. This system has been run since June 2001, delivering up to now about 80% of the solutions (Fig. 9). As for operational weather forecasting, 75% of data must reach the meteorological agencies within 1 h, 45 min. The histogram displayed in Fig. 10 shows the number of GPS hourly files analyzed for each station during the June 2001–September 2002 period. Note that an 80% average is available to the data center to be analyzed in the NRT mode, and that 20% of data arrive too late or are lost, causing an unpredictable instability in the ground network and, consequently, in the ZTD estimates, since a processing window and a network approach are applied. The GPS-derived ZTD has the potential to become a significant source of data for operational weather forecasting, provided that it can be available in NRT with a minimum accuracy degradation compared to postprocessed products. For this purpose, a subset of 19 stations with postprocessed and near-real-time solutions are compared by computing monthly bias and standard deviation. The ZTD bias (Fig. 11) ranges from −6 to 12 mm (from −1 to 2 mm of IPWV), showing a periodic behavior. The origin of this time-varying behavior has been thoroughly investigated. No particular signature has been found when comparing IGS UltraRapid orbits to JPL fiducial-free satellite orbits. On the contrary, an intriguing correlation has been detected comparing height coordinates and zenith total delay residual time series. Blewitt and Lavallée (2001) pointed out that GPS coordinate time series have annual signals with typical amplitudes of several millimeters, a significant component of which is due to crustal motion forced by surface loading (Van Dam et al. 2001). The vertical velocities of 12 European stations are obtained with a least squares fit of the weekly EUREF height time series (Bruyninx et al. 2001) from July 1996 up to August 2002, assuming that they can be modeled as a linear function of time plus a sinusoidal signal of semiannual and annual periods. On the other hand, the ZTD residual time series are modeled as a sinusoidal function of semiannual and annual periods, the amplitude and phase of which are estimated in a least squares sense. The estimated signals in the height and in the ZTD residual time series are summarized in Table 1. It can be shown that the estimated annual signals have an amplitude of ∼5 mm both in the heights and in the ZTD residual time series and with the same phase. A phase lag of π between the ZTD and the height is expected since the two parameters anticorrelated. Through our analysis, a phase delay of ∼1 radiant (see Table 1) is detected. The origin of such a discrepancy deserves investigation. Nevertheless, part of such a phase lag can be explained since in the near-real-time datastream the site coordinates are set to the previous month—that is, with a phase lag of ∼0.5 radiant—and are updated every 30 days. So, half of the phase lag remains to be explained. It is worthwhile to investigate the matter in the follow-on of the present paper. On the basis of this result, our concern is that once the station coordinates, and the meteorological solutions are set, only the linear trend is modeled, neglecting the annual and semiannual signatures. Such mismodeling causes, as a matter of fact, the pattern of the bias shown in Fig. 11. Therefore, a possible solution is that, for any GPS site with at least a 2.5-yr-long time series (Blewitt and Lavallée 2001; Vespe et al. 2001), site velocities, initial position, and annual and semiannual signatures have to be taken into account for setting the terrestrial reference frame in the NRT solutions.

The standard deviation (Fig. 12) significantly decreases from 2001 to 2002. The decrease in the standard deviation and in the bias amplitude is mainly due to the refinement of the processing. Two major changes occurred during the 16-month routine operation. The number of the analyzed stations increased from 17 (in June 2001) to 30 (in September 2002) just to ensure a better geometrical network configuration. Nevertheless, the main change concerns the handling of the station coordinates. During the year 2001, for each hourly batch processing, first the station coordinates were estimated relying on the available data and, afterward, they were fixed in the ZTD estimation. This approach has two drawbacks: it is too time-consuming, since every batch has to be run twice, and the coordinates fixed for ZTD providing are not very accurate, since they are estimated over only 24 h of data. The method described so far has been applied starting from January 2002, as can be clearly noted by looking at Figs. 11 and 12.

5. Summary

Two approaches for zenith total delay estimation, useful for climatological and meteorological applications, by processing data from a network of ground-based GPS receivers in the central Mediterranean area have been described. As far as the postprocessed ZTD estimates are concerned, they have been validated with respect to ground-based water vapor radiometer and radiosonde observations, as an indication of the GPS long-term stability. Two different GPS ZTD 2.5-yr-long time series (January 1999–May 2001) have been compared to get an idea of the GPS long-term internal consistency. The comparison of postprocessed versus near-real-time solutions, useful for evaluating the degradation of the accuracy of the latter, shows a ZTD bias ranging from −6 to 10 mm and a standard deviation from 20 to 5 mm, significantly decreasing during the 16 months of routine operation due to processing tuning. The origin of the time-varying behavior in the ZTD bias has been investigated by comparing EUREF height coordinates and zenith total delay residual time series. The comparison has shown that the signatures in the time series have the same amplitude but an unexpected phase delay of ∼1 radiant. Such a phase delay is partially explained by the strategy applied in setting the site coordinates, but it deserves to be carefully investigated. A possible way to overcome the problem is that when the terrestrial reference frame is fixed in the meteorological solutions, the annual and semiannual sinusoidal signals in the GPS coordinate time series are taken into account. Critical issues related to the routine operation, which could be useful when planning an operational stage of GPS ground-based meteorology, are identified and discussed.