Refraction Delay Research Articles

Atmospheric Refraction Delay Toward Millimeter‐Level Lunar Laser Ranging: Correcting the Temperature‐Induced Error With Real‐Time and Co‐Located Lidar Measurements

AbstractNext‐generation lunar laser ranging (LLR) aims for mm‐level accuracy, significantly promoting the study of gravitational physics. However, atmospheric refraction delay causes an unacceptable ranging error that can be efficiently corrected by neither the atmospheric delay models nor ray‐tracing calculation. Here we report on an improved ray‐tracing method, in which temperature profiles measured by radiosonde are replaced by those measured by a pure rotational Raman lidar, to realize real‐time and co‐located delay correction. Using 9‐night lidar observations, temperature‐induced delays of ±15 mm can be corrected for laser ranging, which is the largest residual in the LLR error budget.

On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations: the Seewinkel network

Microwave electromagnetic signals from the Global Navigation Satellite System (GNSS) are affected by their travel through the atmosphere: the troposphere, a non-dispersive medium, has an especial impact on the measurements. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The correlation structure of residuals from GNSS relative position estimation provides a unique opportunity to study specific properties of the turbulent atmosphere. Prior to such a study, the residuals have to be filtered from unwanted additional effects, such as multipath. In this contribution, we propose to investigate the property of the atmospheric noise by using a new methodology combining the empirical mode decomposition with the Hilbert–Huang transform. The chirurgical “designalling of the noise” aims to filter both the white noise and low-frequency noise to extract only the noise coming from tropospheric turbulence. Further analysis of the power spectrum of phase difference can be performed, including the study of the cut-off frequencies and the two slopes of the power spectrum of phase differences. The obtained values can be compared with theoretical expectations. In this contribution, we use Global Positioning System (GPS) phase observations from the Seewinkel network, specially designed to study the impact of atmospheric turbulence on GPS phase observations. We show that (i) a two-slope power spectrum can be found in the residuals and (ii) that the outer scale length can be taken to a constant value, close to the physically expected one and in relation with the size of the eddies at tropospheric height.

Determination of the Instantaneous Values of Astronomical Atmospheric Refraction and Local Observational Modeling

A new application of astronomical atmospheric refraction in space geodesy is utilized. It is pointed out that in order to meet the high needs of this new application there must be an effective method by means of which the instantaneous value of atmospheric refraction can be directly determined. An atmospheric refraction model fitting in the geographical environment surrounding the observing station is established and then transformed into the neutral atmospheric refraction delay correction model. In this article the necessary conditions for the determination of the value of atmospheric refraction are briefly described. A method for the direct determination of the values of instantaneous atmospheric refraction in various directions and at various zenith distances by taking advantage of the observational principle of the low latitude meridian circle, explored by the Yunnan Observatory, is expounded and the atmospheric refraction observational models built on the basis of stellar spectral type classification in the 4 directions of east, south, west and north and by making use of the observed data are given.

Path Bending Correction for Refraction Delay of Electromagnetic Waves

Focusing on lowering the cut-off elevation in the neutral atmosphere refraction delay correction and on raising the accuracy of the correction, we derive the formulae for calculating the correction for the bending of the light path caused by atmospheric refraction. This is the sort of correction that is given after the principal term in theoretical models of neutral atmospheric refraction delay correction, but is often neglected because it is a small quantity. However, in practice, for a not too low elevation like 15°, this term reaches 1 cm order of magnitude and can not be neglected. Li Yan-xing et al. specially gave a derivation of this correction and a computational method by successive approximation and some calculated values. Yan Hao-jian also proposed a formula of direct calculation but his calculated result was more than 3 times smaller than that of Li Yan-xing, which shows that further study of this correction is called for. Here we give a simple, convenient and reliable formula for calculating the correction.

Retrieval of the change of precipitable water vapor with zenith tropospheric delay in the Chinese mainland

As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTD) are analyzed from 28 permanent GPS sites in the Chinese mainland. The objectives are to estimate the GPS ZTD and their variability in this area. The differences between radiosonde precipitable water vapor (PWV) and GPS PWV have a standard deviation of 4 mm in delay, a bias of 0.24 mm in delay, and a correlation coefficient of 0.94. The correlation between GPS ZTD and radiosonde PWV amounts to 0.89, indicating that the variety of tropospheric zenith delay can reflect the change of precipitable water vapor. The good agreement also guarantees that the information provided by GPS will benefit the NWP models. The time series of GPS ZTD, which were derived continuously from 2002 to 2004, are used to analyze the change of precipitable water vapor in Chinese mainland. It shows that the general trend of GPS ZTD is diminishing from the south-east coastland to the north-west inland, which is in accordance with the distribution of Chinese annual amount of rainfall. The temporal distribution of GPS ZTD in the Chinese mainland is that the GPS ZTD reaches maximum in summer, and it reaches minimum in winter. The long term differences between the observational data sources require further study before GPS derived data become useful for climate studies.

Constructing an Observational Model of the Neutral Atmospheric Refraction Delay from Measured Values of the Astronomical Refraction

Discussing the requirements for an accurate correction of the neutral atmospheric refraction delay for the Global Positioning System, our paper points out that the existing theoretical correction models and the old postprocessing methods cannot attain the anticipated accuracy because the atmospheric refraction index has not been directly determined precisely. It is necessary to adopt atmospheric refraction delay models to improve the correction accuracy. The models are dependent on the observing station and the observation azimuth. By the new method we propose in this paper, the observational data of astronomical refractions at different azimuths and different zenith distances are grouped according to azimuth and used to calculate the refractivity and mapping functions. As an example of the newmethod, we introduce the configuration of the Lower Latitude Meridian Circle and the measurement method of instantaneous astronomical refractions, and present the observational astronomical refraction model toward the east, south, west, and north of the Yunnan Observatory. We estimate that, without the use of any atmospheric distribution models, the correction accuracy of the zenith delay will be within 1 mm, the correction accuracy of the refraction delay at the lower elevation will be improved to a centimeter magnitude, and the cutoff elevation angle will be reduced to 5 degrees or less.

A Possible Means of Improving the Accuracy of Refraction Delay Correction of Neutral Atmosphere

The space geodetic technology requires an accurate model of correction of refraction delay by the neutral atmosphere that varies from one observing station to another, and from one azimuth to the next. It is pointed out that under the present condition the astronomical refraction can not yet be directly determined, any correction model because of its high dependence on the assumed atmospheric distribution, is incapable of achieving the required accuracy or of improving the cut-off altitude. In this paper, based on the special properties of the lower latitude meridian circle at Yunnan Observatory and our experience of determining atmospheric refraction therewith, a new method is proposed for improving the accuracy of refraction delay correction. Namely, the measured data of astronomical refraction of an observing station from near zenith to low altitudes in different azimuths are used to evaluate the refractivities and the parameters of the mapping functions, thereby establishing a model of atmospheric refraction delay correction that varies with the observing station and the azimuth. Since it is unnecessary for the new method to adopt any atmospheric distribution model, application of this new method will improve correction accuracy of refraction delay to better than 1mm at zenith and to centimeters at low altitudes, and improve the cut-off altitude to below 5 degrees.

On the reliability of establishing mapping functions with standard atmospheric model

With the ever increasing precision of space techniques, the study of the errors in atmospheric refractive delay has become one of the ways of improving the observational accuracy. In order to reduce the influence of selection of atmospheric profile on the mapping function of atmospheric refractive delay, the adopted atmospheric profile has gradually changed from the past standard atmospheric model to radiosonde atmospheric profiles. Using the data of two representative radiosonde stations, the mapping functions provided by standard atmospheric model is compared with the results of radiosonde observations. The reliability of the mapping function given by standard atmosphere is investigated, and the selection of geophysical parameters is briefly discussed.

Impact of GPS Zenith Tropospheric Delay data on precipitation forecasts in Mediterranean France and Spain

Forecasting precipitation in the western Mediterranean is difficult because of the interactions among dynamical forcing, orographic lifting and moisture advection from the warm Mediterranean Sea. Torrential rainfall events are not uncommon, especially during the autumn. This type of event motivated an effort to improve precipitation forecasting by incorporating additional information on the initial state of the humidity field from Global Positioning System measurements of refractive delay. In this study we process data from a network of sites in Western Europe and assimilate the data over a two week period into the HIRLAM numerical weather prediction model. The overall impact for the two week period is neutral, however, for a severe rain event taking place during that period, the forecasts show improved skill when including GPS data. The work implies that the GPS data have good potential for influencing numerical models in rapidly developing, high moisture flux situations.

Accuracy and Variability of GPS Tropospheric Delay Measurements of Water Vapor in the Western Mediterranean

Abstract As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTDs) are analyzed from 51 permanent GPS sites in the western Mediterranean. The objectives are to estimate the error statistics necessary for future assimilation of GPS ZTD data in numerical models and to investigate the variability of the data in this area. The time series, which were derived continuously from November 1998 to June 2001, are compared with independent equivalent values derived from radiosonde profiles and the High-Resolution Limited-Area Model (HIRLAM) NWP model. Based on over two years of data, the difference between radiosonde and GPS ZTD has a standard deviation of 12 mm of delay and a bias of 7 mm of delay. Some sites have biases as high as 14 mm of delay. The bimodal distribution of residuals, with a higher bias for daytime launches, indicates these biases may be due to radiosonde day–night ...

Discussion and Comparison of the Mapping Functions in Radio Frequencies

Some mapping functions in radio frequency are reviewed at the beginning of this paper. From the viewpoint of statistics and mathematics, the error sources of refractive delay computation are analyzed together with the ray tracing technique and radiosonde data application. The NMF model (Niell 1996) used globally distributed radiosonde network data and tabular coefficients in its continued fraction expression and, therefore, reached a high accuracy with wide latitude and meteorological parameter coverage (MacMillan and Ma 1997). The UNSW931 model (Yan and Ping 1995)introduced an improved continued fraction form, which was derived from the generator function method and had a good convergency at low elevation observations. The influences of ground meteorological records on the mapping functions are generally discussed. Comparisons among different mapping functions are performed together with radiosonde data. In order to fit the requirements of more accurate and lower elevation observations in future space technique applications, we suggest constructing a new mapping function, which will involve the main advantages of present models and improve or avoid inadequate expressions as far as possible.

New continued fraction form of the mapping functions of atmospheric refraction corrections

Abstract As basic research problems in practical astronomy and geodesy, the formulation of the mapping functions both of the refractive delay and of astronomical refraction are studied in an analytical manner in this paper. First, we have proved that the complementary error function can be related to expressions for the atmospheric refraction integrals of the signal delay and also of the signal bending angle as well. An improved continued fraction expansion of the complementary error function is then derived to describe the new mapping functions of the refractive delay and astronomical refraction at radio and optical frequencies, respectively. Not only do the new mapping functions have good convergence at an elevation coverage near to the horizon, but they can also be applied to various atmospheric profiles at high accuracy, better than 1 cm for refraction delay and better than 0.″3 for angular bending at an elevation angle near to 2°.5 or lower over a wide range of meteorological and geophysical conditions. Some extra corrections are also briefly summarized in this paper.

A method for improved microwave‐interferometer remote sensing of convective boundary layer turbulence using water vapor as a passive tracer

Water vapor column irregularities within the lower troposphere's convective boundary layer constitute a nearly passive tracer of turbulent air motions and eddy convection. Remote sensing of turbulence in this layer from the ground is done with microwave radars and with lidars. Microwave interferometry is also sensitive to vapor column fluctuations via the known relative refractive delay of water vapor compared to dry air. However, interferometric measurements are intrinsically nonlocal, yielding only the baseline difference (the difference of measurements at two ends of an interferometer baseline) of vapor column, and thus are not amenable to classical data‐reduction methods for fluid turbulence, other than the equal‐time structure function. In order to remove this limitation of interferometry we have developed a method to estimate the time‐lagged cross covariance of vapor‐column fluctuations over two sites using interferometry data. This effectively circumvents the limitation to baseline‐differenced vapor column data at least in statistical second moments. The method is illustrated with 15‐GHz data taken by the very large array.

The Generator Function Method of the Tropospheric Refraction Corrections

view Abstract Citations (22) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Generator Function Method of the Tropospheric Refraction Corrections Yan, Hoojian ; Ping, Jinsong Abstract Both the astronomical angular refraction and the refractive delay of tropospheric atmosphere can be calibrated by means of the generator function method of mapping functions. Based on the continued fraction expression of the complementary error function, the new mapping function forms of the tropospheric delay have been derived for the standard atmospheric model and Hopfield atmospheric profile, respectively. The accuracies of these new models are insured to be better than 1 cm to an elevation angle lower than 2°.5 over a wide range of meteorological conditions in comparison with ray-trace solutions. Publication: The Astronomical Journal Pub Date: August 1995 DOI: 10.1086/117574 Bibcode: 1995AJ....110..934Y Keywords: ATMOSPHERIC EFFECTS full text sources ADS |

Definition of Very Long Baseline Interferometry (VLBI) Group Delay and Relativistic Correction Model With Picosecond Precision

In this paper, the incorrect definition of VLBI coordinate time delay in solar system barycenter frame (B-frame) is clarified, thus correcting the error of sign of the individual term in VLBI relativistic time delay model of transformation published earlier. It is proved that the terms, i. e. the tropospheric refraction delay, the axis offset refraction delay, and the gravitational delay caused by the major planets which are respectively multiplied by the velocity and the acceleration vector of the geocenter, should be taken into account in the model mentioned above under the precision of 1 ps. Finally, the VLBI relativistic time delay model with precision of better than 1 ps is obtained.

VLBI Relativistic Time Delay Model with Picosecond Precision

The VLBI relativistic time delay model of transformation is reformuled with a precision of better than 1 ps, which is given as followswhere is geocentric newtonial potential, and are the barycentric velocity vector in B-frame and the geocentric velocity vector of antenna i. Ŝ is the unit vector of the direction from the barycenter of solar system to the source. c is the speed of light in vacuum. , where is the geocentric baseline vector. δtv can be expressed as in which and where Δtatm, Δtion and Δtaxo are the tropospheric, the ionospheric and the axio offset refraction delays respectively, and Δtgrav is called the gravitational time delay. A straightforward differentation of expression (1), the equation of d(dτ)/dt can be obtained. The included in the can be expressed as The orders of magnitude of the various correction terms in expression (4) and (5) are estimated respectively. Conclusion: expression (4) and (5) should be taken into account in the VLBI relativistic model of transformation for the 1 ps precision. Equation (1) and the expression of its differentation differ from all the models which have been published earlier.

Refraction and propagation delays in space geodesy

Abstract Many measurements to satellites, whether of direct scientific interest or merely for tracking purposes, require a knowledge of the atmospheric propagation delay which affects the observation, The delay has to be precisely determined for such purposes as geodetic or navigation positioning using the TRANSIT system or GPS (Global Positioning system) and gravity-field determination by precise orbit determination using satellite laser ranging. In particular, the high accuracy of satellite altimetry can be severely degraded by propagation delays not only in the altimeter measurement itself but also in the tracking-system observations. This paper describes the effects of the ionosphere and troposphere on both optical and microwave observations, and discusses both the instrumental and mathematic modelling approaches to the determination of the propagation delay, giving examples of the solution adopted for geodetic, surveying and navigation satellite observations.

A review of geodetic and geodynamic satellite Doppler positioning

Since 1967, when the U.S. Navy Navigation System was released to the general public, the accuracy of geodetic and geodynamic satellite Doppler positioning using satellite Doppler has improved steadily. This improvement is due mainly to refinements in hardware, refraction, and orbital modeling. Point positioning, using a minimum of 30 passes and the U.S. Defense Mapping Agency (DMA) precise ephemeris, has reached submeter accuracy. Relative positioning among several simultaneously observing stations separated by distances up to 250 km and using a minimum of 30 passes has a typical accuracy below 0.5 m (1σ). Current hardware design and errors in modeling of delays in the wet portion of the troposphere limit the achievable accuracy in relative positioning at the 0.1‐ to 0.5‐m (1σ) level, unless errors in receiver phase and tropospheric refraction delays are continuously measured (calibrated). Also, a crystal oscillator of lower short‐term stability (≥ 5 × 10−12/100 s) increases the Doppler data noise and causes a positive correlation persisting over several minutes. Geodetic and geodynamic Doppler data reductions usually involve meticulous modeling for instrumental, atmospheric, and orbital errors as well as careful Doppler data editing. A short‐arc orbit computation employed in such satellite Doppler reductions requires a gravitational potential expanded to at least degree and order 10 if the orbit shape accuracy is to be comparable to DMA precise ephemeris. Satellite Doppler positioning has had a significant impact on geodetic datum definition and the establishment of national and continental networks of unprecedented accuracy. Satellite Doppler methods, apart from providing one of the most accurate continuous methods of polar motion monitoring, have also been found useful in other geodynamical and ice motion studies. This review concentrates mainly on system performance, models, and computational methods.

A rapid seismic refraction delay time profiling technique for shallow bedrock studies

A seismic refraction delay time traversing technique, highly suitable for a speedy delineation of shallow bedrock topography, is described. This technique quickly brings out the bedrock profile without laborious computations and is less expensive for the purpose than the normal seismic refraction sounding method. The principle of the method is based on the determination of the overburden delay time associated with a ‘shot-detector’ arrangement with constant separation along a traverse. The effect of the lateral velocity inhomogeneities on the measured delay times and the method for correcting this effect has been described. A hammer-source single-channel seismic timer is ideally suitable for the survey.

A METHOD OF WEATHERING CORRECTION *

AbstractIn western Canada, the near surface weathered zone has variable velocity and is underlain by more uniform subweathering material. The uphole time is often used to compensate for the weathered zone, but there are limitations to its use.A method is proposed using the refraction delay time which is exactly proportional to the weathering correction time for several commonly assumed weathering velocity functions. The method does not require accurate determination of velocities or weathering depth nor even the depth of shot, yet is theoretically exact. A strip off time tr is used to replace the weathered zone mathematically with high velocity material where tr= zD/F, where D is the delay time and F the Blondeau factor.An algorithm using first break times is proposed that is amenable to computer use for determining D for each geophone point. F might be constant in some areas but is more likely a variable to be solved in an automatic static program. Thus, structure and residual statics can be handled at once.