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Extended neutrospheric modelling for the GNSS-based determination of high-resolution atmospheric water vapor fields
Abstract and Figures
Signals of global navigation satellite systems (GNSS) are delayed by propagating through the Earth's electrically neutral atmosphere. This delay term plays an important role in GNSS positioning and has been taken into account in high-precision geodetic applications. The neutrospheric delay can be subdivided into a dry and a complementary wet component. The wet component amounts to typically less than 10% of the total neutrospheric delay and can be used to determine high-resolution atmospheric water vapour fields based on extended neutrospheric modelling. The approach outlined in the present paper combines empirical neutrospheric a priori model, site-specific neutrosphere parameters and residuals of GNSS phase observations. Using so-called single-layer models, the derived atmospheric water vapour fields are two-dimensionally reconstructed and visualised. Applying this extended neutrospheric model to generate water vapour fields within a regional GNSS network, the results indicate that both the temporal and the spatial resolution of the determined water vapour fields are improved in comparison to the conventional neutrospheric modelling.
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... Global Navigation Satellite Systems (GNSS), however, have been considered since the 1990s as an efficient microwave-based tool for atmospheric sounding (Bevis et al., 1992;Rocken et al., 1995). Since then, numerous methods have exploited the GNSS observations to produce estimates of the integrated atmospheric water vapor and to generate water vapor maps (Luo et al., 2008;Jade and Vijayan, 2008;Karabatić et al., 2011). InSAR and GNSS, signals are affected in a similar way by the atmosphere (Onn and Zebker, 2006). ...
... Another approach proposed by Katzfuss and Cressie (2009) targets determination of the covariance parameters using the algorithm of maximum likelihood estimation (MLE). Furthermore, they estimated the covariance parameters using the expectation-maximization (E-M) algorithm (Dempster et al., 1977) to reduce the computational burden. ...
... That means || [t+1] − [t] || < b should hold for a small enough and positive value of b. Following Katzfuss and Cressie (2009), b is assigned a value of 10 −6 r 2 . The starting choice of K and σ 2 ζ should be valid; strictly speaking, K [0] must be symmetric and positivedefinite and σ 2 ζ [0] must be positive; i.e., K [0] = 0.9 · var( Z)I r and σ 2 ζ [0] = 0.1 · var( Z). ...
Data fusion aims at integrating multiple data sources
that can be redundant or complementary to produce complete, accurate
information of the parameter of interest. In this work, data fusion of
precipitable water vapor (PWV) estimated from remote sensing observations and
data from the Weather Research and Forecasting (WRF) modeling system are
applied to provide complete grids of PWV with high quality. Our goal is to
correctly infer PWV at spatially continuous, highly resolved grids from
heterogeneous data sets. This is done by a geostatistical data fusion
approach based on the method of fixed-rank kriging. The first data set
contains absolute maps of atmospheric PWV produced by combining observations
from the Global Navigation Satellite Systems (GNSS) and Interferometric
Synthetic Aperture Radar (InSAR). These PWV maps have a high spatial density
and a millimeter accuracy; however, the data are missing in regions of low
coherence (e.g., forests and vegetated areas). The PWV maps simulated by the
WRF model represent the second data set. The model maps are available for
wide areas, but they have a coarse spatial resolution and a still limited
accuracy. The PWV maps inferred by the data fusion at any spatial resolution
show better qualities than those inferred from single data sets. In addition,
by using the fixed-rank kriging method, the computational burden is
significantly lower than that for ordinary kriging.
... Global Navigation Satellite Systems (GNSS), however, have been considered since the 1990s as an efficient microwave-based tool for atmospheric sounding (Bevis et al., 1992;Rocken et al., 1995). Since then, numerous methods have exploited the GNSS observations to produce estimates of the integrated atmospheric water vapor and to generate water vapor maps (Luo et al., 2008;Jade and Vijayan, 2008;Karabatić et al., 2011). InSAR and GNSS, signals are affected in a similar way by the atmosphere (Onn and Zebker, 2006). ...
... Another approach proposed by Katzfuss and Cressie (2009) targets determination of the covariance parameters using the algorithm of maximum likelihood estimation (MLE). Furthermore, they estimated the covariance parameters using the expectation-maximization (E-M) algorithm (Dempster et al., 1977) to reduce the computational burden. ...
... That means || [t+1] − [t] || < b should hold for a small enough and positive value of b. Following Katzfuss and Cressie (2009), b is assigned a value of 10 −6 r 2 . The starting choice of K and σ 2 ζ should be valid; strictly speaking, K [0] must be symmetric and positivedefinite and σ 2 ζ [0] must be positive; i.e., K [0] = 0.9 · var( Z)I r and σ 2 ζ [0] = 0.1 · var( Z). ...
... Reanalysis models assimilate nonhomogenized radiosonde temperature and relative humidity data, which might result in inhomogeneities in the output products (Wang et al., 2016). Global Positioning System (GPS), the first of the Global Navigation Satellite Systems (GNSS), has been used since the 1990s for providing accurate estimates of the atmospheric variables (Alshawaf et al., 2015;Bender et al., 2008;Gendt et al., 2004;Jade & Vijayan, 2008;Luo et al., 2008). As of today, ground-based time series of tropospheric products estimated using geodetic techniques such as GPS and very long baseline interferometry are relatively long and can be used for estimating climatic trends (Alshawaf et al., 2017;Balidakis et al., 2018;Gradinarsky et al., 2002;Haas et al., 2003;Nilsson & Elgered, 2008). ...
For more than two decades, Global Positioning System (GPS) tropospheric delays have successfully been exploited to monitor the tropospheric water vapor in near real time and reprocessing mode. Although reprocessed data are considered reliable for climatic research, it is important to address the often present gaps, inhomogeneities, and to use a proper model to describe the stochastic part of the time series so that trustworthy trends are estimated. Having relatively long time series, daily reprocessed tropospheric Zenith Total Delay, precipitable water vapor (PWV), and gradients from the Tide Gauge benchmark monitoring network are used in this work to estimate climatic trends. We use a first‐order autoregressive model AR(1) to describe the residuals after the trend estimation so that a correct trend uncertainty is estimated. Using the same model, we obtain the number of years of PWV data required to estimate statistically significant trends. For comparison, we produce tropospheric parameters at each Tide Gauge station based on ERA‐Interim refractivity fields. We found that 83% of 64 GPS stations show a positive PWV trend below 1 mm/decade independent of the time interval, with approximately half of the trends indicated significant. There is a strong correlation (86%) between the Global Navigation Satellite Systems and ERA‐Interim PWV trends. The trends tend to increase when moving east and south on the European map. The results show a percentage change of PWV of 3–8% per a degree Celsius rise in temperature. The number of years required to detect significant PWV trends varies between 30 and 40 years.
... While other observation systems such as radiosondes and microwave radiometers provide PWV measurements that are limited in the temporal and (or) spatial resolutions, ground-based GNSSs provide time series of accurate PWV estimates with 15 min (for this work) sampling at dense GNSS networks, without significant additional costs. Since Bevis et al. (1992) presented the Global Positioning System (GPS) as an efficient meteorological tool, GNSS data have been increasingly used for estimating atmospheric parameters, particularly precipitable water vapor (Gendt et al., 2004;Luo et al., 2008;Jade and Vijayan, 2008;Bender et al., 2008;Alshawaf et al., 2015). GNSS-Published by Copernicus Publications on behalf of the European Geosciences Union. ...
Ground-based GNSS (Global Navigation Satellite System) has efficiently been used since the 1990s as a meteorological observing system. Recently scientists have used GNSS time series of precipitable water vapor (PWV) for climate research. In this work, we compare the temporal trends estimated from GNSS time series with those estimated from European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA-Interim) data and meteorological measurements. We aim to evaluate climate evolution in Germany by monitoring different atmospheric variables such as temperature and PWV. PWV time series were obtained by three methods: (1) estimated from ground-based GNSS observations using the method of precise point positioning, (2) inferred from ERA-Interim reanalysis data, and (3) determined based on daily in situ measurements of temperature and relative humidity. The other relevant atmospheric parameters are available from surface measurements of meteorological stations or derived from ERA-Interim. The trends are estimated using two methods: the first applies least squares to deseasonalized time series and the second uses the Theil–Sen estimator. The trends estimated at 113 GNSS sites, with 10 to 19 years temporal coverage, vary between -1.5 and 2.3 mm decade-1 with standard deviations below 0.25 mm decade-1. These results were validated by estimating the trends from ERA-Interim data over the same time windows, which show similar values. These values of the trend depend on the length and the variations of the time series. Therefore, to give a mean value of the PWV trend over Germany, we estimated the trends using ERA-Interim spanning from 1991 to 2016 (26 years) at 227 synoptic stations over Germany. The ERA-Interim data show positive PWV trends of 0.33 ± 0.06 mm decade-1 with standard errors below 0.03 mm decade-1. The increment in PWV varies between 4.5 and 6.5 % per degree Celsius rise in temperature, which is comparable to the theoretical rate of the Clausius–Clapeyron equation.
... water vapor (Gendt et al., 2004;Luo et al., 2008;Jade and Vijayan, 2008;Bender et al., 2008;Alshawaf et al., 2015). GNSSbased estimates of zenith total delay or PWV have been used to improve the numerical weather prediction (NWP) models (Bock et al., 2005;Bennitt and Jupp, 2012). ...
Ground-based GNSS (Global Navigation Satellite Systems) have efficiently been used since the 1990s as a meteorological observing system. Recently scientists used GNSS time series of precipitable water vapor (PWV) for climate research. In this work, we use time series from GNSS, European Center for Medium-Range Weather Forecasts Reanalysis (ERA-Interim) data, and meteorological measurements to evaluate climate evolution in Central Europe. The assessment of climate change requires monitoring of different atmospheric variables such as temperature, PWV, precipitation, and snow cover. PWV time series were obtained by three methods: 1) estimated from ground-based GNSS observations using the method of precise point positioning, 2) inferred from ERA-Interim data, and 3) determined based on daily surface measurements of temperature and relative humidity. The other variables are available from surface meteorological stations or received from ERA-Interim. The PWV trend component estimated from GNSS data strongly correlates with that estimated from the other data sets. The linear trend is estimated by straight line fitting over 30 years of seasonally-adjusted PWV time series obtained using meteorological measurements. The results show a positive trend in the PWV time series at more than 60 GNSS sites with an increase of 0.3–0.6 mm/decade. In this paper, we compare the results of three stations. The temporal increment of the PWV correlates with the temporal increase in the temperature levels.
... All Rights Reserved. observations to produce estimates of the atmospheric water vapor, which are exploited to build water vapor maps [Luo et al., 2008;Jade and Vijayan, 2008;Karabatić et al., 2011]. InSAR and GNSS signals are affected in a similar way by the atmosphere [Onn and Zebker, 2006]. ...
Over the past twenty years, repeat-pass spaceborne Interferometric Synthetic Aperture Radar (InSAR) has been widely used as a geodetic technique to generate maps of the Earth's topography and to measure the Earth's surface deformation. In this paper, we present a new approach to exploit microwave data from InSAR, particularly Persistent Scatterer InSAR (PSI), and Global Navigation Satellite Systems (GNSS) to derive maps of the absolute water vapor content in the Earth's atmosphere. Atmospheric water vapor results in a phase shift in the InSAR interferogram, which if successfully separated from other phase components provides valuable information about its distribution. PSI produces precipitable water vapor (PWV) difference maps of a high spatial density, which can be inverted using the least squares method to retrieve PWV maps at each SAR acquisition time. These maps do not contain the absolute (total) PWV along the signal path, but only a part of it. The components eliminated by forming interferograms or phase filtering during PSI data processing are reconstructed using GNSS phase observations. The approach is applied to build maps of absolute PWV by combining data from InSAR and GNSS over the region of Upper Rhine Graben in Germany and France. For validation, we compared the derived PWV maps with PWV maps measured by the optical sensor MERIS. The results show strong spatial correlation with values of uncertainty of less than 1.5 mm. Continuous grids of PWV are then produced by applying the kriging geostatistical interpolation technique that exploits the spatial correlations between the PWV observations.
Ground-based GNSS (Global Navigation Satellite Systems) have efficiently been used since the 1990s as a meteorological observing system. Recently scientists used GNSS time series of precipitable water vapor (PWV) for climate research. In this work, we compare the temporal trends estimated from GNSS time series with those estimated from European Center for Medium-Range Weather Forecasts Reanalysis (ERA-Interim) data and meteorological measurements. We aim at evaluating climate evolution in Germany by monitoring different atmospheric variables such as temperature and PWV. PWV time series were obtained by three methods: 1) estimated from ground-based GNSS observations using the method of precise point positioning, 2) inferred from ERA-Interim reanalysis data, and 3) determined based on daily in situ measurements of temperature and relative humidity. The other relevant atmospheric parameters are available from surface measurements of meteorological stations or derived from ERA-Interim. The trends are estimated using two methods, the first applies least squares to seasonally-adjusted time series and the second using the Theil-Sen estimator. The trends estimated at 113 GNSS sites, with 10 and 19 year temporal coverage, varies between −1.5 and 2 mm/decade with standard deviations below 0.25 mm/decade. These values depend on the length and the variations of the time series. Therefore, we estimated the PWV trends using ERA-Interim and surface measurements spanning from 1991 to 2016 (26 years) at synoptic 227 stations over Germany. The former shows positive PWV trends below 0.5 mm/decade while the latter shows positive trends below 0.9 mm/decade with standard deviations below 0.03 mm/decade. The estimated PWV trends correlate with the temperature trends.
In this chapter, Sect. 3.1 provides a brief introduction to the Global Positioning System (GPS). Next, Sects. 3.2 and 3.3 describe the mathematical models for GPS absolute and relative positioning, respectively. The mathematical models of GPS observations consist of a functional and a stochastic component. In contrast to the continuously improved functional model, the stochastic model characterising the statistical properties of GPS measurements is still a controversial research topic. Here the functional model is discussed with a special focus on the error sources considerably affecting GPS positioning quality, while the stochastic model is presented with respect to observation weighting and correlation structure.
High spatially and temporally variable atmospheric water vapour causes
an unknown delay in microwave signals transmitted by space-borne sensors. This
delay is considered as a major limitation in Interferometric Synthetic Aperture
Radar (InSAR) applications as well as high-precision applications of Global
Navigation Satellite Systems (GNSS). On the other hand, the delay could be
quantified to derive atmospheric parameters such as water vapour. Temporal
variability of water vapour is well estimated from ongoing GNSS measurements,
while InSAR provides information about the spatial variations of water vapour.
This project aims at assimilating InSAR phase observations and spatially-sparse
GNSS measurements for the determination of atmospheric water vapour. In this
contribution GNSS-based water vapour calculations and assessment of different
strategies are presented. Work in progress is also reported including some
preliminary results.
Data fusion aims at integrating multiple data
sources that can be redundant or complementary to produce
complete, accurate information of the parameter of interest.
In this work, data fusion of precipitable water vapor (PWV)
estimated from remote sensing observations and data from
the Weather Research and Forecasting (WRF) modeling system
is applied to provide complete, accurate grids of PWV.
Our goal is to infer spatially continuous, precise grids of
PWV from heterogeneous data sets. This is done by a geostatistical data fusion approach based on the method of fixedrank
kriging. The first data set contains absolute maps of atmospheric
water vapor produced by combining observations
from Global Navigation Satellite Systems (GNSS) and Interferometric
Synthetic Aperture Radar (InSAR). These PWV
maps have a high spatial density and an accuracy of submillimeter;
however, data are missing in regions of low coherence
(e.g., forests and vegetated areas). The PWV maps
simulated by the WRF model represent the second data set.
The model maps are available for wide areas, but they have
a coarse spatial resolution and a yet limited accuracy. The
PWV maps inferred by the data fusion at any spatial resolution
are more accurate than those inferred from single data
sets. In addition, using the fixed-rank kriging method, the
computational burden is significantly lower than that for or
dinary kriging.
We have used a ground-based microwave radiometer, known as a water vapor radiometer, to investigate the local spatial and temporal variation of the wet propagation delay for a site on the west coast of Sweden. The data were obtained from a wide range of azimuths and from elevation angles greater than 23.6° (air mass 2.5). Visual inspection of the data suggested a simple ``cosine azimuth'' variation, implying that a first-order gradient model was required. This model was adequate for short time spans up to approximately 15 min, but significant temporal variations in the gradient suggested to us that we include gradient rate terms. The resulting six-parameter model has proven adequate (rms delay residual ~1 mm) for up to 30 min of data. Assuming a simple exponential profile for the wet refractivity gradient, the estimated gradient parameters imply average surface wet-refractivity horizontal gradients of order of 0.1-1 N km-1. These gradients are larger, by 1-2 orders of magnitude, than gradients determined by others by averaging over long (~100-km) distances. This result implies that for applications that are sensitive to local gradients, such as wet propagation-delay models for radio-interferometric geodetic studies, the use of meteorological data from widely spread stations may be inadequate. The gradient model presented here is inadequate for times longer than about 30 min, even if no gradients are present, because of the complicated stochastic like temporal behavior of the wet atmosphere. When gradients are present, they can change magnitude by ~50% over 10-15 min. Nevertheless, our ability to fit the radiometer data implies that on timescales =23.6°, the local structure of the wet atmosphere can be described with a simple model. (The model is not limited to this range of elevation angles in principle.) The estimated gradient and gradient rate vectors have preferred directions, which indicates a prevailing structure in the three-dimensional temperature and humidity fields, possibly related to systematic behavior in large-scale weather systems and/or the local air-land-sea interaction at this site.
On 19 September 1996, a squall line stretching from Nebraska to Texas with intense embedded convection moved eastward across the Kansas-Oklahoma area, where special observations were taken as part of a Water Vapor Intensive Observing Period sponsored by the Atmospheric Radiation Measurement program. This provided a unique opportunity to test mesoscale data assimilation strategies for a strong convective event. In this study, a series of real-data assimilation experiments is performed using the MM5 four-dimensional variational data assimilation (4DVAR) system with a full physics adjoint. With a grid size of 20 km and 15 vertical layers, the MM5-4DVAR system successfully assimilated wind profiler, hourly rainfall, surface dewpoint, and ground-based GPS precipitable water vapor data. The MM5-4DVAR system was able to reproduce the observed rainfall in terms of precipitation pattern and amount, and substantially reduced the model errors when verified against independent observations. Additional data assimilation experiments were conducted to assess the relative importance of different types of mesoscale observations on the results of assimilation. In terms of the assimilation model's ability to recover the vertical structure of moisture and in reproducing the rainfall pattern and amount, the wind profiler data have the maximum impact. The ground-based GPS data have a significant impact on the rainfall prediction, but have relatively small influence on the recovery of moisture structure. On the contrary, the surface dewpoint data are very useful for the recovery of the moisture structure, but have relatively small impact on rainfall prediction. The assimilation of rainfall data is very important in preserving the precipitation structure of the squall line. All the data are found to be useful in this mesoscale data assimilation experiment. Issues related to the assimilation time window, weighting of different types of observations, and the use of accurate observation operator are also discussed.
Atmospheric water vapor was measured with six Global Positioning System (GPS) receivers for 1 month at sites in Colorado, Kansas, and Oklahoma. During the time of the experiment from 7 May to 2 June 1993, the area experienced severe weather. The experiment, called “GPS/STORM,” used GPS signals to sense water vapor and tested the accuracy of the method for meteorological applications. Zenith wet delay and precipitable water (PW) were estimated, relative to Platteville, Colorado, every 30 min at five sites. At three of these five sites the authors compared GPS estimates of PW to water vapor radiometer (WVR) measurements. GPS and WVR estimates agree to 1–2 mm rms. For GPS/STORM site spacing of 500–900 km, high-accuracy GPS satellite orbits are required to estimate 1–2-mm-level PW. Broadcast orbits do not have sufficient accuracy. It is possible, however, to estimate orbit improvements simultaneously with PW. Therefore, it is feasible that future meteorological GPS networks provide near-real-time hig...
Using observations of global navigation satellite systems (GNSS) for precise point positioning the quality of the results is depending on the effects which are affecting the GNSS signals and on the data processing methods and strategies as well. The effects of the length of the processed baseline, multipath, weighting of observables, neutrospheric modelling, and ambiguity resolution strategies are analysed and quantified by means of root mean square values derived from double difference residuals. As an example, GPS data of the SAPOS® network of Baden-Württemberg in the time span DOY2004: 186-193 are analysed.
Spaceborne radar interferometric delay measurements were used to infer high-resolution maps of integrated atmospheric water
vapor, which can be readily related to meteorological phenomena. Maps of the water vapor distribution associated with a precipitating
cloud, a partly precipitating cold front, and horizontal convective rolls reveal quantitative measures that are not observed
with conventional methods, and suggest that such radar observations can be used for forecasting and to study atmospheric dynamics.
This paper presents a new model for the height profile of tropospheric refractivity N and expressions derived from it for computing corrections for satellite Doppler or range data. (N ≡ 106 (n - 1), where n is the index of refraction.) The model is theoretically based on an atmosphere with constant lapse rate of temperature, as will be shown. It treats the ‘dry’ and ‘wet’ components of N separately and represents each as a fourth-degree function of height above the geoid; each component profile starts with its locally observed surface value and decreases to zero at an effective height that is different for the two components. The height parameters were obtained by a least-squares fit to observed data. A latitude dependence has been found for the ‘dry’ height. The model has been found capable of closely matching any local average N profile observed in a world-wide sample of locations throughout the height range of meteorological balloon data (up to 24 km); samples are shown. The corrections based on it are readily evaluated and are finite and usable at all elevation angles. Their effectiveness is evidenced by figures showing two different kinds of observed data: first, Doppler residuals for several satellite passes without and with the use of the correction; and the ‘navigation’ error in station-to-orbit slant range from Doppler data, again without and with the correction. The use of the correction removed obvious systematic errors. The fact that satellite Doppler data display identifiable tropospheric effects is of interest with regard to future study of the troposphere.
We develop a formalism for parameterizing and evaluating the effects of lateral variations in the properties of Earth's atmosphere on the propagation of microwave signals. A parametric form is incorporated into our analysis of very long baseline interferometry (VLBI) data, and the estimated atmospheric delay gradients are compared with those calculated from three-dimensional weather analysis fields from the National Center for Environmental Prediction (NCEP). For a 12-day series of experiments in January 1994, the VLBI and the NCEP analyses show common atmospheric gradient delays with amplitudes of up to 30 mm at 10° elevation angle. Comparison of the characteristics over a longer period of time reveals common mean north-south gradients with amplitudes up to ~10mm at 10° elevation at midlatitudes. No discernible mean east-west gradients were found in either data set. The root-mean-square (RMS) variations of the gradient effects, determined from the NCEP analysis, are similar in the north-south and east-west directions, with a typical RMS scatter of 6-10 mm at 10° elevation. After accounting for gradients, detailed analysis of the January 1994 VLBI data shows clearly that the residual station height variations of ~10mm at Westford, Massachusetts, are almost totally explained by the effects of atmospheric pressure loading.