Zenith Hydrostatic Delay Research Articles

Empirical model for mean temperature and assessment of precipitable water vapor derived from GPS

The estimation of Precipitable Water Vapor (PWV) derived from Global Positioning System (GPS) data at the IGS site WUHN is assessed by comparing with PWV obtained from radiosonde data (No.57494) in Wuhan. The applicability of Saastamoinen (SAAS) , Hopfield and Black models used for estimating Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD) and different models is verified in the estimation of GPS-derived PWV for the applied area. The experimental results demonstrated that: 1) the precision of PWV estimated from Black model used for calculating ZHD (ZHD B ) is lower than that of SAAS (ZHD SAAS ) model and Hopfield model (ZHD H ) with the RMS of 4. 16 mm; 2) the RMS of PWV estimated from SAAS model used for calculating ZWD (SAAS) is 3.78 mm; 3) the well-known Bevis model gives similar accuracy compared with the site-specific models for T m in terms of surface temperature ( T s ) and surface pressure ( Ρ s ) , which can reach the accuracy inside 1 mm in the GPS-derived PWV estimates.

Applicability of methods for estimating GPS precipitable water in the Qinghai-Tibet Plateau

Atmospheric weighted mean temperature (Tm) and zenith hydrostatic delay (ZHD) are key parameters in determining the accuracy of GPS precipitable water (PW) estimations. Using radiosonde profiles with a high vertical resolution of 10–30m, we calculated Tm, ZHD and PW and investigated the applicability of the modeled Tm and ZHD, including the GPS PW obtained with them, in the Qinghai-Tibet Plateau (QTP). It is found that (1) the bias and RMS error of the Bevis Tm model in the QTP are less than 5% and 2%, respectively, with a diurnal variation that is small in the morning and large otherwise. (2) The ZHD models have an RMS error within 1% in the QTP, which is smaller than that in the plain of Central China, which is within 1.5%. The ZHD bias of the Saastamoinen model is less than 0.5% in the QTP, smaller than those of the Hopfield and Black models. The diurnal variations of the modeled ZHD bias and RMS error are complex in the QTP, varying with the ZHD model and station. (3) The relative RMS error of GPS PW increases with the station altitude, with a range of 12–66% in the QTP and within 8% in the plain of Central China. The diurnal variations of the GPS PW bias and RMS error in the QTP are similar to those of the modeled ZHD. (4) The accuracy of GPS PW is mainly affected by the ZHD model, and a good Tm can improve the accuracy of GPS PW in the QTP.

The temporal variation of mean gravity of atmosphere

One of the precise widely used global Zenith Hydrostatic Delay (ZHD) model is based on the gravity value at the centroid of the atmospheric column at the station of observation and gravity value at the centroid is constant in this model for a specific location throughout the year. However, as the content and extent of atmosphere varies temporally, its centroid and consequently gravity value at the centroid also varies. Apart from this, the actual atmospheric condition of different region is not alike. Therefore, there is a need to develop a regional mean gravity model and development of such model has been discussed in this paper. To obtain the mean gravity model, first a regional model of centroid height of atmospheric column was developed as a function of the surface pressure and temperature. It was developed by multiple regressions between estimated centroid of the atmosphere and surface pressure, surface temperature using radiosonde data of five radiosonde stations spread over the Indian subcontinent. Three years radiosonde data from 2006 to 2008 was used for each station. The root mean square error in estimating centroid of the atmospheric column is about ±326 m, which is negligible considering the variability of the atmosphere and its content. The centroid height model has been used to formulate the mean gravity model, considering uniform lapse rate in gravity with height. It is found that proposed mean gravity model provides temporal variation of mean gravity values at the centroid and thus matches with the reality. The interesting advantage of the developed model is that the model shows diurnal variation of mean gravity. The accuracy of ZHD has shown of the order of about 0.3mm using the developed regional mean gravity model. However, already developed ZHD model has shown a slight inferior result compared to the developed model. These models have shown accuracy of about 0.8mm and 0.6mm.

Development of a site-specific ZHD model using radiosonde data

Estimation of precipitable water vapor (PWV) in the atmosphere using ground based GPS (Global Positioning System) data requires an appropriate model for computation of zenith hydrostatic delay (ZHD). Presented herein is a site-specific ZHD model (SSM) for a station at New Delhi, India. The model has been developed by regressing one-year atmospheric vertical profile data collected through radiosonde. The model based on surface atmospheric pressure at the station, has been validated invoking data of three more years. The ZHD values estimated through the model disagree at the 0.3 mm level with ZHD values obtained from raytracing of radiosonde data. Further, Saastamoinen ZHD model provides an error about 0.23 mm rms while about 0.19 mm by the developed model (SSM). Thus, developed SSM can be used for precise estimation of PWV.

Precipitable water vapor estimates from homogeneously reprocessed GPS data: An intertechnique comparison in Antarctica

[1] Homogeneously reprocessed GPS data offer the possibility of an accurate, stable, and increasingly long-term record of integrated precipitable water vapor (PW) of particular value in data sparse regions. We present such a global reanalysis of GPS data, focusing on 12 Antarctic sites. We show stepwise improvements of GPS zenith total delay (ZTD) estimates upon adoption of each of (1) absolute antenna phase centre variations, (2) VMF1 tropospheric mapping functions, and (3) an accurate model of a priori zenith hydrostatic delay (ZHD) from observed surface meteorological data. The cumulative effect of these three additions to the analysis is a systematic decrease in the magnitude of GPS estimates of ZTD by an average of ∼11 mm ZTD (∼1.8 mm PW). The resultant GPS PW data set for 2004 shows a mean bias to radiosonde measurements of -0.48 mm PW. Our conclusion is that, in Antarctica at least, a proportion of the widely observed bias between GPS and radiosonde measurements can be explained by earlier GPS analysis deficiencies. We also compare our GPS PW measurements with AIRS and MODIS level 2 PW products. The GPS agreements with AIRS and MODIS are comparable. Reanalyzed GPS gives typically larger measurements than AIRS with a mean site bias of 0.58 mm PW and a mean rms of 1.24 mm PW. By contrast, the GPS measurements are typically smaller than those from MODIS, with a mean site bias of -0.35 mm PW and rms of 1.42 mm PW. PW estimates from reprocessed GPS solutions using state-of-the-art models now have greater potential for assimilation into regional or global numerical weather models.

Lower atmospheric anomalies following the 2008 Wenchuan Earthquake observed by GPS measurements

The Mw=8.0 Wenchuan Earthquake occurred on May 12, 2008 at the Longmen Shan fault, the western Sichuan Basin, China, killing more than ten thousand people in several cities and causing large economic losses. Global Positioning System (GPS) observations have provided unique insights on this event, including co-seismic ionospheric disturbances, co-/post-seismic crustal deformations and fault slip distributions. However, the processes and the driving mechanisms are still not clear, particularly possible seismo-lower atmospheric–ionospheric coupling behaviors. In this paper, the lower atmospheric (tropospheric) variations are investigated using the total zenith tropospheric delay (ZTD) from GPS measurements around this event. It has the first found co-seismic tropospheric anomalies during the mainshock with an increase and then a decrease, mainly in the zenith hydrostatic delay component (ZHD), while it is also supported by the same pattern of surface-observed atmospheric pressure changes at co-located GPS site that are driven by the ground-coupled air waves from ground vertical motion of seismic waves propagation. Therefore, the co-seismic tropospheric disturbances (CTD) indicate again the acoustic coupling effect of the atmosphere and the solid-Earth with air wave propagation from the ground to the top atmosphere.

A discussion of height reductions for Zenith Hydrostatic Delays derived from weather models

A discussion of height reductions for Zenith Hydrostatic Delays derived from weather models

Effect of broadcast and precise satellite orbits in the estimation of Zenith tropospheric delay and integrated precipitable water vapour from GPS

Global Positioning System (GPS) estimates the total delay in zenith direction by the propagation delay of the neutral atmosphere in presence of water vapour present in the troposphere. This total delay has been treated as a nuisance parameter for many years by the geodesists. The above delay have two parts dry delay and wet delay and known as Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD) respectively. The Integrated Precipitable Water Vapour (IPWV) is estimated through ZWD overlying the receiver at ground-based station. The accuracy of the above said estimates depends on the quality of the predicted satellite orbits, which are not the same for each individual satellite. India Meteorological Department (IMD) is operationally estimating the IPWV on near real time basis at five places and matches fairly well (error ~6.7 mm) with Radisonde (RS) data. This paper examine the effect of International GPS Service (IGS) predicted precise orbits and near real time predicted rapid or broadcast orbits supplied by the Scripps Orbit and Permanent Array Center (SOPAC) on Zenith Total Delay (ZTD) and IPWV estimates by calculating the mean Bias and Root Mean Square Error (RMSE) for ZTD and IPWV in mm for all the five stations. The observed bias for ZTD is almost of the order of less than 1 mm in most cases and RMSE is less than 6 mm. Similarly the bias observed in the case of derived IPWV is almost negligible and RMSE is less than 1 mm.

Assessment of ECMWF-derived tropospheric delay models within the EUREF Permanent Network

The Global Positioning System (GPS) observations from the EUREF Permanent Network (EPN) are routinely analyzed by the EPN analysis centers using a tropospheric delay modeling based on standard pressure values, the Niell Mapping Functions (NMF), a cutoff angle of 3° and down-weighting of low elevation observations. We investigate the impact on EPN station heights and Zenith Total Delay (ZTD) estimates when changing to improved models recommended in the updated 2003 International Earth Rotation and Reference Systems Service (IERS) Conventions, which are the Vienna Mapping Functions 1 (VMF1) and zenith hydrostatic delays derived from numerical weather models, or the empirical Global Mapping Functions (GMF) and the empirical Global Pressure and Temperature (GPT) model. A 1-year Global Positioning System (GPS) data set of 50 regionally distributed EPN/IGS (International GNSS Service) stations is processed. The GPS analysis with cutoff elevation angles of 3, 5, and 10° revealed that changing to the new recommended models introduces biases in station heights in the northern part of Europe by 2---3 mm if the cutoff is lower than 5°. However, since large weather changes at synoptic time scales are not accounted for in the empirical models, repeatability of height and ZTD time series are improved with the use of a priori Zenith Hydrostatic Delays (ZHDs) derived from numerical weather models and VMF1. With a cutoff angle of 3°, the repeatability of station heights in the northern part of Europe is improved by 3---4 mm.

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.

Atmospheric effects and spurious signals in GPS analyses

Improvements in the analyses of Global Positioning System (GPS) observations yield resolvable millimeter to submillimeter differences in coordinate estimates, thus providing sufficient resolution to distinguish subtle differences in analysis methodologies. Here we investigate the effects on site coordinates of using different approaches to modeling atmospheric loading deformation (ATML) and handling of tropospheric delays. The rigorous approach of using the time‐varying Vienna Mapping Function 1 yields solutions with lower noise at a range of frequencies compared with solutions generated using empirical mapping functions. This is particularly evident when ATML is accounted for. Some improvement also arises from using improved a priori zenith hydrostatic delays (ZHD), with the combined effect being site‐specific. Importantly, inadequacies in both mapping functions and a priori ZHDs not only introduce time‐correlated noise but significant periodic terms at solar annual and semiannual periods. We find no significant difference between solutions where nontidal ATML is applied at the observation level rather than as a daily averaged value, but failing to model diurnal and semidiurnal tidal ATML at the observation level can introduce anomalous propagated signals with periods that closely match the GPS draconitic annual (∼351.4 days) and semiannual period (∼175.7 days). Exacerbated by not fixing ambiguities, these signals are evident in both stacked and single‐site power spectra, with each tide contributing roughly equally to the dominant semiannual peak. The amplitude of the propagated signal reaches a maximum of 0.8 mm with a clear latitudinal dependence that is not correlated directly with locations of maximum tidal amplitude.

GPS Monitoring of the Tropical Storm Delta along the Canary Islands Track, November 28-29, 2005

In this article we analyze the variations of the Zenith Tropospheric Delay (ZTD) and its components, Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD) recorded by the GPS reference stations in the area of the Canary Islands during the passing of the tropical storm Delta on November 28 and 29, 2005. During this event, we observed that all GPS stations experienced significant increases of the ZWD value of over 100 mm and a decrease in the ZHD values of about 30 mm. The increase of the normal ZWD values was detected several hours prior to the manifestation of the weather phenomena on the ground. We also noticed a connection between the maximum ZWD values observed and the temporal distribution of the rain. The observed variations of the tropospheric slant directional gradients correlate significantly with the variations in direction and intensity of the observed winds. The relation noted between the ZWD values and the tropospheric slant delay gradients with meteorological observables highlights the convenience of using existing or new GPS networks when studying weather phenomena such as severe cyclones.

A web-based package for ray tracing the neutral atmosphere radiometric path delay

An online ray-tracing package has been developed to provide zenith and slant neutral atmosphere delays using RAdiosonde OBservation (RAOB) and numerical weather prediction (NWP) models to users worldwide to assist precise global navigation satellite systems positioning scenarios. The package includes a web interface, necessary scripts to access RAOB and NWP data, and ray-tracing software capable of using both types of data. In addition, global maps of zenith hydrostatic delay, zenith non-hydrostatic or wet delay, north–south, east–west and total gradient and comparison maps of the University of New Brunswick climate-based models, and values calculated from NWP models every 3h are also provided.In this paper, the theoretical aspects of ray tracing will be reviewed. The structure of the software and web page, validation of results using different data sources, and further development for gradient calculations are explained.

Empirical model for mean temperature for Indian zone and estimation of precipitable water vapor from ground based GPS measurements

Abstract. Estimation of precipitable water (PW) in the atmosphere from ground-based Global Positioning System (GPS) essentially involves modeling the zenith hydrostatic delay (ZHD) in terms of surface Pressure (Ps) and subtracting it from the corresponding values of zenith tropospheric delay (ZTD) to estimate the zenith wet (non-hydrostatic) delay (ZWD). This further involves establishing an appropriate model connecting PW and ZWD, which in its simplest case assumed to be similar to that of ZHD. But when the temperature variations are large, for the accurate estimate of PW the variation of the proportionality constant connecting PW and ZWD is to be accounted. For this a water vapor weighted mean temperature (Tm) has been defined by many investigations, which has to be modeled on a regional basis. For estimating PW over the Indian region from GPS data, a region specific model for Tm in terms of surface temperature (Ts) is developed using the radiosonde measurements from eight India Meteorological Department (IMD) stations spread over the sub-continent within a latitude range of 8.5°–32.6° N. Following a similar procedure Tm-based models are also evolved for each of these stations and the features of these site-specific models are compared with those of the region-specific model. Applicability of the region-specific and site-specific Tm-based models in retrieving PW from GPS data recorded at the IGS sites Bangalore and Hyderabad, is tested by comparing the retrieved values of PW with those estimated from the altitude profile of water vapor measured using radiosonde. The values of ZWD estimated at 00:00 UTC and 12:00 UTC are used to test the validity of the models by estimating the PW using the models and comparing it with those obtained from radiosonde data. The region specific Tm-based model is found to be in par with if not better than a similar site-specific Tm-based model for the near equatorial station, Bangalore. A simple site-specific linear relation without accounting for the temperature effect through Tm is also found to be quite adequate for Bangalore. But for Hyderabad, a station located at slightly higher latitude, the deviation for the linear model is found to be larger than that of the Tm-based model. This indicates that even though a simple linear regression model is quite adequate for the near equatorial stations, where the temperature variations are relatively small, for estimating PW from GPS data at higher latitudes this model is inferior to the Tm-based model.

An Improved Mean-Gravity Model for GPS Hydrostatic Delay Calibration

The determination of global positioning system (GPS) heights with submillimeter accuracy needs proper correction of tropospheric delay. In this letter, the modeling of zenith hydrostatic delay (ZHD) was addressed, considering that wet delay must be treated separately. ZHD is traditionally estimated from Saastamoinen's formula using a mean-gravity model and surface pressure observations. The uncertainty in ZHD associated with the mean-gravity model is about 0.3 mm. An improved parametric model is derived here, which yields an uncertainty in the ZHD less than 0.1 mm when the surface altitude lies in the range of 0-9 km. A second parametric model is derived for higher altitudes (such as above radiosonde observations or atmospheric models). Both parametric models depend on latitude, height, and time variables. This dependence is due to the link between the mean gravity and temperature profiles between the surface and ~80-km altitude. The uncertainty in the parametric models due to short-term temporal variability of the temperature profiles is shown to produce an uncertainty in ZHD smaller than 0.1 mm

GPS zenith delay sensitivity evaluated from high‐resolution numerical weather prediction simulations of the 8–9 September 2002 flash flood over southeastern France

Estimations of zenith total delays (ZTD) were obtained during postprocessing of a high‐resolution (2.4 km) nonhydrostatic atmospheric model (Méso‐NH). These estimations were used to determine their sensitivity with respect to formulations of atmospheric refractivity, the approximation of zenith hydrostatic delays (ZHD) deduced from ground pressure, and the contributions of hydrometeors. The factor κ for the conversion of zenith wet delay (ZWD) to integrated water vapor (IWV) was examined. Méso‐NH is applied here to the extreme flash flood event of 8–9 September 2002 in southeastern France. The use of the hydrostatic formulation (to infer ZHD) leads to an overestimation of up to 18 mm with respect to the vertical integration of refractivity. Delay contributions of hydrometeors simulated by the high‐resolution model reached more than 70 mm (≈11 kg/m2 IWV) in the heart of the convective cells in the case of the extreme flood event. The mean variations of IWV due to the use of different conversion factors (κ used to transform ZWD to IWV) are evaluated to be less than 0.3 kg/m2. This is less than the mean underestimation of IWV by 0.6 kg/m2 relative to the GPS‐like evaluation of IWV using the hydrostatic formulation and the ground temperature. In this study we also use GPS ZTD observations to validate three different numerical simulations of this extreme flood event. The simulation with the best fit to the GPS observations is also in best agreement with the surface rainfall measurements.

Review of GPS Satellite Surveying, third edition by Alfred LeickGPS Satellite SurveyingJohn Wiley & Sons0-471-05930-7$120

This book is a third edition recently updated to include new developments in global positioning system GPS theory that have occurred since the release of the second edition in 1995. The book highlights high-accuracy GPS positioning and is intended for use by surveyors, civil engineers, transportation engineers, geodesists, geologists, geographers, technicians, and students—basically anyone with a desire to learn how scientists use least-squares adjustments, geodesy, and various physical models to process data collected from existing and future global navigation satellite systems GNSS . The book consists of nine chapters and three appendixes, as well as an extensive list of bibliographic references and an index. Chapter 1 gives the history of GPS and presents a timeline of the major milestones. Chapter 2 discusses such geodetic reference systems as the international terrestrial reference frame, and the international celestial reference frame, and how to go from one to the other. It includes new material on the effects of polar motion, tectonic plate motion, solid earth tides, and ocean loading. It introduces the three-dimensional 3D geodetic model as the preferred, unifying model for combining satellite positioning with classical surveying measurements. It also discusses the geoid and reductions to the ellipsoid. Chapter 3 outlines basic satellite orbit theory such as the Keplerian elements and the major forces that perturb satellite orbits: variations in the earth’s gravity field, the attraction of the sun and moon, and solar radiation pressure. New sections have been added to address eclipse transits and yaw maneuvers by GPS satellites; the planned L2C-, L5-, and M-codes for GPS modernization; the Russian GLONASS navigation message; and the upcoming Galileo satellite system. Chapter 4 contains basically the same comprehensive treatment of least-squares adjustments covered in the second edition: stochastic and mathematical models, variance-covariance propagation, and the mixed adjustment model—together with the special cases of the observation equation and condition equation models, linearization, sequential solutions, minimal and inner constraints, properties of error ellipses, redundancy numbers, internal and external reliability, and data snooping. A short section has also been added on Kalman filtering; this section nicely defines the concepts behind Gauss–Markov processes, white noise, and random walk. Chapter 5 presents the observation equations for the many different types of pseudorange and carrier phase observables used with GPS. It discusses the single-, double-, and triple-differences for the carrier phases and adds new sections that describe the correction for the rotation of the earth during signal transmission and the P1-P2 and C1-P1 code biases needed to compute accurate pseudoranges for GPS. Chapter 6, on the troposphere and ionosphere, has been extensively rewritten to include additional material. The Saastamoinen equations for zenith hydrostatic delay and zenith wet delay are now given, together with the hydrostatic

Characterization of Atmospheric Parameters using a Ground Based GPS Network in North Europe

We characterize the temporal and spatial variation of the Zenith Wet Delay (ZWD) and the Zenith Total Delay (ZTD), estimated using a network of Global Positioning System (GPS) receivers. This characterization is important for the improvement and validation of atmospheric water vapor models, applicable in GPS meteorology, as well as in the navigation. We treat the estimates of Zenith Hydrostatic Delay (ZHD) and ZWD as realizations of random walk stochastic processes and we derive the corresponding parameters for different locations and measurement techniques for data acquired at intervals of 1 to 3 hours. The monthly standard deviation (StD) of the ZTD is less than 50 mm and does not exhibit a strong seasonal signature over the period 1997-1998 for any of the studied GPS sites. However, the StDs of the pairwise-differenced ZTD time series show a seasonal dependence, mainly due to the spatial variations of the ZWD, which should be considered when GPS data are assimilated in weather prediction models. We show the differences in typical spatial characteristics of ZHD and ZWD for the winter and summer seasons in North Europe. Finally, we describe the use of temporal structure functions for detection of rapid changes in ZTD.

Zenith total delay study of a mesoscale convective system: GPS observations and fine-scale modeling

Zenith Total Delay (ZTD) observations and model calculations are used to analyze a mesoscaleconvective system which yielded a large amount of precipitation over a short period of time inthe north-western Mediterranean. ZTD observations are derived from the GPS signal delaywhereas the ZTD model results are calculated by means of the MM5 mesoscale model.Large values of the root-mean-square (rms) differences between the ZTD derived from theobservations and the modeling are found for the maximum activity of the mesoscale convectivesystem. It appears that the average bias between observations and modeling results is slightlyaffected (20%) by the passage of the storm system which is associated to the water vaporvariability of the atmosphere.We have analyzed the ZTD differences in terms of the two components: the Zenith HydrostaticDelay (ZHD) and the Zenith Wet Delay (ZWD). The hydrostatic error is mainly caused bythe differences between the elevation of the GPS stations and the model topography and isreduced when using a more accurate topography data set. We propose a correction for thiserror assuming hydrostatic equilibrium. The remaining average ZTD difference is associated tothe ZWD and is mainly generated by inaccuracies of the mesoscale model to predict the watervapor content during the rainfall event.

Preliminary evaluation of atmospheric mapping functions based on numerical weather models

Mapping of the zenith hydrostatic delay at radio frequencies to elevations as low as 3° has been improved by making use of the in situ atmosphere state. This information might be obtained from a numerical weather model, thus providing better atmosphere calibration on a global scale. The new model has been evaluated by comparing the repeatability of the lengths of baselines measured by Very Long Baseline Interferometry for a limited set of high accuracy experiments from 1994 January. The improvement compared to using the Niell 1996 mapping function, though significant, is less than expected, indicating other sources of unmodeled error.