Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

Range and range rate measurements play an important role in geodetic applications of electromagnetic waves (terrestrial as well as from space, including Very Long Baseline Interferometry (VLBI)) Recent developments of measuring, techniques have led to the situation that the measuring accuracy is no longer the limiting factor in the final accuracies of range and range rate measurements. The main error stems now from the influence of the atmosphere and from assumptions and approximations in context with the derivation of refractive index used to describe the wave propagation properties of the atmosphere. Only in the case that the geometrical optics approximation holds is it possible to calculate or to measure range error for wave propagation in the atmosphere of the earth (troposphereand ionosphere) from knowledge of the refractive index as a function of space (location) and time. Otherwise we have to consides additionally scattering and/or diffraction effects. A discussion of the formulae for the refractive indices in the troposphere and in the ionosphere is followed by a review of the propagation of electromagnetic waves described by the geometrical optics approximation and on the limitations, of geometrical optics. A comprehensive discussion of range errors in the non-ionized atmosphere (troposphere) and in the ionosphere follows. For this purpose we use the elevation of the “ray” at a ground station for division into four domains: a) vertical incidence (as a special case), b) elevation between 90° and 30°, c)elevation between 30° and 5°, d) elevation smaller than 5°.     

Phase acceleration: a new important parameter in GPS occultation technology

Based on 40 years of radio-occultation (RO) experiments, it is now recognized that the phase acceleration of radio waves (equal to the time derivative of the Doppler shift), derived from analysis of high-stability Global Positioning System (GPS) RO signals, is as important as the Doppler frequency. The phase acceleration technique allows one to convert the phase and Doppler frequency changes into refractive attenuation variations. From such derived refractive attenuation and amplitude data, one can estimate the integral absorption of radio waves. This is important for future RO missions when measuring water vapor and minor atmospheric gas constituents, because the difficulty of removing the refractive attenuation effect from the amplitude data can be avoided. The phase acceleration technique can be applied also for determining the location and inclination of sharp layered plasma structures (including sporadic E _s layers) in the ionosphere. The advantages of the phase acceleration technique are validated by analyzing RO data from the Challenging Minisatellite Payload (CHAMP) and the FORMOSA Satellite Constellation Observing Systems for Meteorology, Ionosphere, and Climate missions (FORMOSAT-3/COSMIC).     

A VLBI Delay Model for Radio Sources at a Finite Distance

A relativistic delay model for Earth-based very long baseline interferometry (VLBI) observation of sources at finite distances is derived. The model directly provides the VLBI delay in the scale of terrestrial time. The effect of the curved wave front is represented by using a pseudo source vector K = (R ₁ + R ₂)/(R ₁ + R ₂), and the variation of the baseline vector due to the difference of arrival time is taken into account up to the second-order by using Halley’s method. The precision of the new VLBI delay model is 1 ps for all radio sources above 100 km altitude from the Earth’s surface in Earth-based VLBI observation. Simple correction terms (parallax effect) are obtained, which can also adopt the consensus model (e.g. International Earth Rotation and Reference Frames Service conventions) to finite-distance radio source at R > 10 pc with the same precision. The new model may enable estimation of distance to the radio source directly with VLBI delay data.     

大气折射对光学卫星遥感影像几何定位的影响分析

采用ISO国际标准大气模型和Owens大气折射系数算法,根据大气层内不同纬度和海拔高度处的大气折射系数分布规律,把地球大气简化为对流层和同温层的双层均匀球形大气,从在轨光学卫星CCD探元视线出发,使用视线跟踪几何算法,计算不同侧视角下大气折射产生的几何位置偏差。结果表明,大气折射几何偏差随卫星观测角的增加而非线性迅速增加。当卫星运行在650km的太阳同步轨道,侧视30°成像时,大气折射产生约2.5m的几何偏差;卫星侧视45°成像时,大气折射产生约9m的几何偏差。在高分辨率敏捷卫星成像和宽视场卫星遥感图像的严密几何定位处理中,使用本文提出的大气折射几何偏差算法和严密几何定位大气折射校正模型,在地心地固坐标系下补偿严密几何模型中存在的大气折射偏差,能够进一步提升高分辨率卫星遥感图像的无控几何定位精度,应用于我国高分系列卫星遥感图像地面几何定位处理。     

GPS radio holography as a tool for remote sensing of the atmosphere, mesosphere, and terrestrial surface from space

GPS radio occultation (RO) signals are highly coherent and precise, and thus sufficient for holographic investigation of the atmosphere, ionosphere, and the Earth's surface from space. In principle, three-dimensional radio-holographic remote sensing is possible by using new radio holographic equations to retrieve the radio field within the atmosphere from a radio field known at some interface outside the atmosphere. A simplified two-dimensional form of the radio-holographic equations which are developed under an assumption of local spherical symmetry can be used to obtain two-dimensional radio images of the atmosphere and terrestrial surface. To achieve this, radio holograms recorded by a GPS receiver onboard a low earth orbit (LEO) satellite at two GPS frequencies can be used and focused synthetic aperture principle applied. Analysis of GPS/MET RO data is presented to show the effectiveness of a radio-holographic approach. It is shown that the amplitude of GPS radio signals (in addition to phase data) can be used to obtain detailed altitude profiles of the vertical gradient of refractivity in the atmosphere and electron density in the mesosphere. The results demonstrate the applicability of GPS radio holography for a detailed global study of the natural processes in the atmosphere and mesosphere. Electronic Publication     

Modelling of radiation transfer in Earth’s hazy atmosphere and calculation of path radiances in IRS LISS-I Bands

A model (named ATMRAD) of radiation transfer in the Earth’s hazy atmosphere based on simplistic solution of radiation transfer equation and tropical model atmosphere is developed to estimate path radiance for correction of remote sensing multispectral data. The atmosphere is assumed to be cloud free and plane-parallel stratified with various quatities specified for 46 layers in its 100 km assumed thickness and model altitude profiles of haze aerosols specified for 23 km and 5 km visibility ranges. Altitude profiles of haze for any intermediate visibility ranges are deduced from linear mixing of the two profiles for 23 and 5 km visibilities. Deirmendjian size distribution function is assumed for aerosols. The radiation transfer calculations have been performed for 126 wavelengths in 0.25 to 3.0 μm range by considering Rayleigh and Mie Scatterings by air molecules and aerosols; and absorption by atmospheric gases. The model calculations have been carried out for path radiances in bands of IRS LISS-I sensor for different visibility ranges and solar illumination angles.     

The effects of atmospheric turbulence on telescopic observations

Telescopic observations to terrestrial and extraterrestrial objects are affected by atmospheric turbulence. The structure of atmospheric turbulence is reviewed in tems of the refractive index structure parameter. The mean and fluctuating refraction effects of the turbulent atmosphere on the propagation of electromagnetic waves are addressed. The known formulae for the variance and the spectrum of the angle-of-arrival fluctuations are presented and experimental results are summarised. The angular resolution is compared with the pointing precision of a telescope for visual observations through a turbulent atmosphere. The ultimate precision of direction measurements is shown to be a function of instrumental design parameters, the strength of atmospheric turbulence, and the length of the averaging period.     

Analysis on the global morphology of stratospheric gravity wave activity deduced from the COSMIC GPS occultation profiles

Monthly mean global morphologies of potential energy density E _p from stratospheric gravity waves are revealed by observations of COSMIC GPS radio occultation. The E _p is obtained from vertical wavelengths ranging from 2 to 10 km over cells of 1° × 2° in latitude and longitude. The computed values confirm previous results and obtain new ones. The large gravity wave E _p values found in the tropics between 25°N and 25°S could be mainly due to the strong tropical cumulus convection; July values are larger than those for January (2007). In mid and high latitudes, the most prominent features of the northern winter hemisphere are the enhanced densities above the Eurasian continent and the North Atlantic and the depressed E _p values above the North Pacific and North America for which topography, wind sources and wind filtering may be responsible. In southern winter hemisphere, large E _p values are found around 180° and 300° longitudes that are likely due to the topography of the Antarctic plateau, the Antarctic Peninsula and South America. Enhanced E _p values are found over Scandinavia. However, there is no clear evidence to show that gravity waves are localized over the Rocky Mountains, the Himalayas and the Andes. Topography and planetary wave modulations are proposed to interpret the large-scale longitudinal variations and inter-hemisphere asymmetry of the GW activity.     

The use of atmospheric dispersion in optical distance measurement

The development of lasers, new electro-optic light modulation methods, and improved electronic techniques have made possible significant improvements in the range and accuracy of optical distance measurements, thus providing not only improved geodetic tools but also useful techniques for the study of other geophysical, meteorological, and astronomical problems. One of the main limitations, at present, to the accuracy of geodetic measurements is the uncertainty in the average propagation velocity of the radiation due to inhomogeneity of the atmosphere. Accuracies of a few parts in ten million or even better now appear feasible, however, through the use of the dispersion method, in which simultaneous measurements of optical path length at two widely separated wavelengths are used to determine the average refractive index over the path and hence the true geodetic distance. The design of a new instrument based on this method, which utilizes wavelengths of6328 ? and3681 ? and3 GHz polarization modulation of the light, is summarized. Preliminary measurements over a5.3 km path with this instrument have demonstrated a sensitivity of3×10 ⁻⁹ in detecting changes in optical path length for either wavelength using1-second averaging, and a standard deviation of3×10 ⁻⁷ in corrected length. The principal remaining sources of error are summarized, as is progress in other laboratories using the dispersion method or other approaches to the problem of refractivity correction.     

THE EFFECT OF ALTITUDE ON TRAVERSE ERRORS

Abstract

I. These notes are the results of following up in some detail the well-known fact that the horizontal distance between two points at altitude h is greater, by an amount proportional to h, than the distance between the corresponding points at sea-level. Traverses based on rectangular coordinates are considered, with special reference to the residual errors left after adjusting the misclosures of such traverses without first eliminating errors due to altitude.     

利用一维变分同化方法从地基GPS相位延迟中获取大气折射率

GPS信号相位延迟中包含很多大气信息,通过一定的方法可以从中获取有价值的大气参数。基于地基GPS相位延迟数据,提出了一种结合经验模式的一维变分同化获取大气折射率的方法。利用GPS相位延迟模拟数据进行同化试验,讨论了背景误差的设置对同化结果的影响,采用实测个例对该方法进行了验证。结果表明,该一维变分同化方法可行,并可获取高精度的0~60 km大气折射率。低层大气背景误差设置的准确程度会对整个高度范围内的同化效果产生影响。首次将同化获取的大气折射率应用于无线电波折射修正,取得了很好的修正效果,修正精度可达1 mm量级。     

利用FY-3C折射率对大气边界层高度的反演与分析

2013年中国发射了首颗进行全球导航卫星系统(global navigation satellite system,GNSS)掩星观测的气象卫星风云3号C星(Fengyun-3C,FY-3C),且已发布自2014年6月以来的FY-3C掩星大气产品,但目前还未见将其应用于大气边界层的相关研究.首次尝试利用FY-3C折射率...     

Ground- and space-based GPS data ingestion into the NeQuick model

This paper presents a technique for ingesting ground- and space-based dual-frequency GPS observations into a semi-empirical global electron density model. The NeQuick-2 model is used as the basis for describing the global electron density distribution. This model is mainly driven by the F2 ionosphere layer parameters (i.e. the electron density, N _m F2, and the height, h _m F2 of the F2 peak), which, in the absence of directly measured values, are computed from the ITU-R database (ITU-R 1997). This database was established using observations collected from 1954 to 1958 by a network of around 150 ionospheric sounders with uneven global coverage. It allows computing monthly median values of N _m F2 and h _m F2 (intra-month variations are averaged), for low and high solar activity. For intermediate solar activity a linear interpolation must be performed. Ground-based GNSS observations from a global network of ~350 receivers are pre-processed in order to retrieve slant total electron content (sTEC) information, and space-based GPS observations (radio occultation data from the FORMOSAT-3/COSMIC constellation) are pre-processed to retrieve electron density (ED) information. Both, sTEC and ED are ingested into the NeQuick-2 model in order to adapt N _m F2 and h _m F2, and reduce simultaneously both, the observed minus computed sTEC and ED differences. The first experimental results presented in this paper suggest that the data ingestion technique is self consistent and able to reduce the observed minus computed sTEC and ED differences to ~25–30% of the values computed from the ITU-R database. Although sTEC and ED are both derived from GPS observations, independent algorithm and models are used to compute their values from ground-based GPS observations and space-based FORMOSAT-3/COSMIC radio occultations. This fact encourages us to pursue this research with the aim to improve the results presented here and assess their accuracy in a reliable way.     

Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT

When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT). Results of a regional gravity field recovery in a 10^o×20^o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights.     

TABULAR AZIMUTH

Abstract

In a known latitude Φ the azimuth A of a heavenly body, of known declination δ, is determinable if its altitude h is measured by a theodolite or other instrument. The azimuth of course is that for the instant of observation.     

对流层传播延迟改正

介绍了流层大气折射对GPS信息的影响及修正方法，着重讨论了各种天顶延迟计算方法和投影函数模型；通过试算，并分析比较这些模型的差异，得出了一些有益的结果。     

Impact of tropospheric modelling on GNSS vertical precision: an empirical analysis based on a local active network

The troposphere affects Global Navigation Satellite System (GNSS) signals due to the variability of the refractive index. Tropospheric delay is a function of the satellite elevation angle and the altitude of the GNSS receiver and depends on the atmospheric parameters. If the residual tropospheric delay is not modelled carefully a bias error will occur in the vertical component. In order to analyse the precise altimetric positioning based on a local active network, four scenarios in Southern Spain with different topographical, environmental, and meteorological conditions are presented, considering both favourable and non-favourable conditions. The use of surface meteorological observations allows us to take into account the tropospheric conditions instead of a standard atmosphere, but introduces a residual tropospheric bias which reduces the accuracy of precise GNSS positioning. Thus, with short observation times it is recommended not to estimate troposphere parameters, but to use an a priori model together with the standard atmosphere. The results confirm that it is possible to achieve centimetre-scale vertical accuracy and precision with real time kinematic positioning even with large elevation differences with respect to the nearest reference stations. These numerical results may be taken into consideration for improving the altimetric configuration of the local active network.     

Adaptive mapping functions to the azimuthal anisotropy of the neutral atmosphere

The anisotropy of propagation of radio waves used by global navigation satellite systems is investigated using high-resolution observational data assimilations produced by the European Centre for Medium-range Weather Forecast. The geometry and the refractivity of the neutral atmosphere are built introducing accurate geodetic heights and continuous formulations of the refractivity and its gradient. Hence the realistic ellipsoidal shape of the refractivity field above the topography is properly represented. Atmospheric delays are obtained by ray-tracing through the refractivity field, integrating the eikonal differential system. Ray-traced delays reveal the anisotropy of the atmosphere. With the aim to preserve the classical mapping function strategy, mapping functions can evolve to adapt to high-frequency atmospheric fluctuations and to account for the anisotropy of propagation by fitting at each site and time the zenith delays and the mapping functions coefficients. Adaptive mapping functions (AMF) are designed with coefficients of the continued fraction form which depend on azimuth. The basic idea is to expand the azimuthal dependency of the coefficients in Fourier series introducing a multi-scale azimuthal decomposition which slightly changes the elevation functions with the azimuth. AMF are used to approximate thousands of atmospheric ray-traced delays using a few tens of coefficients. Generic recursive definitions of the AMF and their partial derivatives lead to observe that the truncation of the continued fraction form at the third term and the truncation of the azimuthal Fourier series at the fourth term are sufficient in usual meteorological conditions. Delays’ and elevations’ mapping functions allow to store and to retrieve the ray-tracing results to solve the parallax problem at the observation level. AMF are suitable to fit the time-variable isotropic and anisotropic parts of the ray-traced delays at each site at each time step and to provide GPS range corrections at the measurement level with millimeter accuracy at low elevation. AMF to the azimuthal anisotropy of the neutral atmosphere are designed to adapt to complex weather conditions by adaptively changing their truncations.     

Fine-resolution forest tree height estimation across the Sierra Nevada through the integration of spaceborne LiDAR,airborne LiDAR,and optical imagery

ABSTRACT

Forests of the Sierra Nevada (SN) mountain range are valuable natural heritages for the region and the country, and tree height is an important forest structure parameter for understanding the SN forest ecosystem. There is still a need in the accurate estimation of wall-to-wall SN tree height distribution at fine spatial resolution. In this study, we presented a method to map wall-to-wall forest tree height (defined as Lorey’s height) across the SN at 70-m resolution by fusing multi-source datasets, including over 1600 in situ tree height measurements and over 1600?km² airborne light detection and ranging (LiDAR) data. Accurate tree height estimates within these airborne LiDAR boundaries were first computed based on in situ measurements, and then these airborne LiDAR-derived tree heights were used as reference data to estimate tree heights at Geoscience Laser Altimeter System (GLAS) footprints. Finally, the random forest algorithm was used to model the SN tree height from these GLAS tree heights, optical imagery, topographic data, and climate data. The results show that our fine-resolution SN tree height product has a good correspondence with field measurements. The coefficient of determination between them is 0.60, and the root-mean-squared error is 5.45?m.     

在大气折射延迟模型中避免采用大气分布模型的论证

天文大气折射是经典天体测量学和大地测量的一项误差源,大气折射延迟是空间大地测量技术中的一项重要误差源,它们的改正模型都直接与大气折射率和大气分布模型有关。文章简述了大气的垂直分布状况,以及大气折射率(或折射率差)因地和因方位而异的情况,分析了目前只能采用球对称大气分布模型的原因。论证了随测站和随方位而异的天文大气折射和电磁波大气折射延迟实测模型建立的必要性和可能性。实测模型已经包含了测站上空大气实际分布及其非球对称的特性,不必再去寻找或建立随地势而异和随季节而变的大气分布模型,避免了大气分布模型选择不当的影响,从而排除了空间大地测量技术中的一项主要误差源。