The association of the residual error of dual-frequency Global Navigation Satellite Systems with ionospheric turbulence parameters

The effects of ionospheric scintillation on the residual error of the dual-frequency Global Navigation Satellite System are investigated. For the ordinary and extraordinary waves the scalar wave equations are obtained to a high-frequency approximation from the Maxwell equations. The solution for these scalar equations to the second-order Rytov approximation made it possible to determine the residual error up to the third order taking into account the ionospheric anisotropy and diffraction effects appearing when the signal is propagating through a turbulent ionospheric plasma. It is shown that the third-order effects, associated with scintillation, that is, with the propagation of the signal through a randomly inhomogeneous ionosphere, can be dominant and exceed second-order effects associated with the influence of the geomagnetic field. We investigate the association of the residual error with such parameters of ionospheric turbulence as the variance, and the inner and outer scales.     

地基GNSS VTEC约束的大气掩星电离层误差修正方法

介绍了一种考虑电离层沿GNSS掩星射线路径分布不对称且兼顾一阶和二阶项的大气掩星电离层误差修正新方法,它综合地基GNSS VTEC的水平变化信息和电离层模式的垂直变化信息,在沿"入射线"与"出射线"双边局部球对称假设下,估算GNSS掩星射线路径上的电子密度;进而计算一阶和二阶项弯曲角电离层误差廓线.采用太阳活动低年的2008年7月15日和太阳活动较高年的2013年7月15日两天的MetOp-A和GRACE掩星观测资料和IGS的GNSS VTEC数据,计算了GNSS大气掩星弯曲角一阶和二阶项电离层误差廓线.对比分析表明：新方法经验模型和理论模型的二阶项弯曲角电离层残差,以及经验模型与实测数据的一阶和二阶项弯曲角电离层误差均具有良好的一致性,因此该方法可用于L2信号数据质量较差或L2信号中断的掩星事件,同时修正大气掩星一阶和二阶电离层误差,从而提高弯曲角精度和掩星观测资料的利用率.     

Assessment of NeQuick ionospheric model for Galileo single-frequency users

The ionosphere is the main error source in GNSS measurements and in extreme cases can degrade the positioning significantly, with errors exceeding 100 m; therefore, modelling and predicting of this type of error is crucial and critical. The ionospheric effect can be reduced using different techniques, such as dual-frequency receiver or suitable augmentation system (DGPS, SBAS); the aforesaid approaches involve the use of expensive devices and/or complex architectures. Single frequency stand-alone receivers are the cheapest and most widespread GNSS devices; they can estimate and partially correct the error due to the ionosphere, through adequate algorithms, which use parameters broadcasted by the navigation message. The aim of this paper is performance assessment of the ionospheric model NeQuick, adopted by the European GNSS Galileo for single frequency receivers. The analysis is performed in measurements domain and the data are collected in different geographical locations and in various geomagnetic conditions.     

从电离层垂直反射的二次回波的統計特性

在地面上用无线电方法研究电离层时,通常只利用电离层反射的一次回波,但是利用二次回波来研究电离层也是可能的。利用二次回波提供的补充知识,特別是利用一次和二次回波的同时观测结果的相互对比,在某些情况下,对电离层物理和电波传播的研究,具有特别的意义。在这篇文章中,将对垂直採测时从电离层反射的二次回波波場和振幅的统计特性,以及一次和二次回波之间的统计联系,进行一些理论上的计算;并根据这些计算结果,讨论一下利用二次回波研究电离层和电波传播吋的若干问題。     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

Dynamics of field-aligned currents reconstructed by the ground-based and satellite data

Parameters of field-aligned currents reconstructed by ground-based measurements of magnetic field in the Scandinavian countries (IMAGE) and ionospheric conductivity for specific events of the 6 and 8 December 2004 are represented here. Ionospheric conductivity was calculated from precipitating electron flux measured at DMSP-13 satellite and electron density EISCAT incoherent scattering radar direct measurements. There is a high correlation between field-aligned currents, calculated from DMSP-13 satellite data and field-aligned currents calculated from radar measurements for the December 6, 2004 in the presence of developed ionospheric current system. The comparison of field-aligned currents, reconstructed by the proposed method, with the currents calculated by the variation of magnetic field on the DMSP satellites, confirms correctness of the offered algorithm.     

Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α²-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.     

High spatial and temporal resolution observations of an impulse-driven field line resonance in radar backscatter artificially generated with the Tromsø heater

The CUTLASS Finland HF radar has been operated in conjunction with the EISCAT Tromsø RF ionospheric heater facility to examine a ULF wave characteristic of the development of a field line resonance (FLR) driven by a cavity mode caused by a magnetospheric impulse. When the heater is on, striating the ionosphere with field-aligned ionospheric electron density irregularities, a large enough radar target is generated to allow post-integration over only 1 second. When combined with 15 km range gates, this gives radar measurements of a naturally occurring ULF wave at a far better temporal and spatial resolution than has been achieved previously. The time-dependent signature of the ULF wave has been examined as it evolves from a large-scale cavity resonance, through a transient where the wave period was latitude-dependent and the oscillation had the characteristics of freely ringing field lines, and finally to a very narrow, small-scale local field line resonance. The resonance width of the FLR is only 60 km and this is compared with previous observations and theory. The FLR wave signature is strongly attenuated in the ground magnetometer data. The characterisation of the impulse driven FLR was only achieved very crudely with the ground magnetometer data and, in fact, an accurate determination of the properties of the cavity and field line resonant systems challenges the currently available limitations of ionospheric radar techniques. The combination of the latest ionospheric radars and facilities such as the Tromsø ionospheric heater can result in a powerful new tool for geophysical research.     

Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model

Higher-order approximation techniques for estimating stochastic parameter of the non-homogeneous Poisson (NHP) model are presented. The NHP model is characterized by a two-parameter cumulative probability distribution function (CDF) of sediment displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of the average rest period and step length of sediment particles, respectively. Difficulty of estimating the parameters has, however, restricted the applications of the NHP model. The approximation techniques are proposed to address such problem. The basic idea of the method is to approximate a model involving stochastic parameters by Taylor series expansion. The expansion preserves certain higher-order terms of interest. Using the experimental (laboratory or field) data, one can determine the model parameters through a system of equations that are simplified by the approximation technique. The parameters so determined are used to predict the cumulative distribution of sediment displacement. The second-order approximation leads to a significant reduction of the CDF error (of the order of 47%) compared to the first-order approximation. Error analysis is performed to evaluate the accuracy of the first- and second-order approximations with respect to the experimental data. The higher-order approximations provide better estimations of the sediment transport and deposition that are critical factors for such environment as spawning gravel-bed.     

Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model

Higher-order approximation techniques for estimating stochastic parameter of the non-homogeneous Poisson (NHP) model are presented. The NHP model is characterized by a two-parameter cumulative probability distribution function (CDF) of sediment displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of the average rest period and step length of sediment particles, respectively. Difficulty of estimating the parameters has, however, restricted the applications of the NHP model. The approximation techniques are proposed to address such problem. The basic idea of the method is to approximate a model involving stochastic parameters by Taylor series expansion. The expansion preserves certain higher-order terms of interest. Using the experimental (laboratory or field) data, one can determine the model parameters through a system of equations that are simplified by the approximation technique. The parameters so determined are used to predict the cumulative distribution of sediment displacement. The second-order approximation leads to a significant reduction of the CDF error (of the order of 47%) compared to the first-order approximation. Error analysis is performed to evaluate the accuracy of the first- and second-order approximations with respect to the experimental data. The higher-order approximations provide better estimations of the sediment transport and deposition that are critical factors for such environment as spawning gravel-bed.     

On effective conductivity of the ionosphere with random irregularities

The influence of stochastic irregularities of the ionosphere on its effective conductivity has been estimated. The study was carried out for large scale inhomogeneities and quasistationary electromagnetic fields. It is found, that Pedersen conductivity sharply increases in a strong geomagnetic field even for small stochastic ionospheric irregularities of the electron density. This peculiarity has to be taken into account during analysis of ionospheric and magnetospheric measurements.     

Capturing the essential spatial variability in distributed hydrological modelling: Hydraulic roughness

The spatial variability of each parameter affecting storm runoff must be accounted for in distributed modelling. The objective of the work reported here is to assess the effects of using distributed versus lumped hydraulic roughness coefficients in the modelling of direct surface runoff. A spatially variable data set composed of Manning roughness coefficients is used to model direct surface runoff. To assess the information content (as measured by entropy) of spatially variable data and its significance in distributed modelling, various degrees of smoothing are applied. The error resulting from smoothing the hydraulic roughness coefficients is determined by modelling overland flow using a finite element solution. The Manning roughness coefficients were taken from field measurements of the Manning roughness coefficient at 0.6 m on a 14 m hillslope. These values were then used in a numerical simulation of outflow hydrographs to investigate the dependence of error on spatial variability. Our study focuses on the characteristics of spatial data used in distributed hydrological modelling. The field sites have fractal dimensions of ≈? 1.4, which is close to a Brownian variation. The sampling interval that captures the essential spatial variability of the Manning roughness coefficient does not seem to matter due to its Brownian variation in the field sites. Hence due to the nearly uniform random distribution, measurements at 0.6 m intervals are not necessary and larger intervals would yield results that are just as acceptable provided the mean value together with a uniformly random distribution is maintained for any size of finite element or sampling resolution. Because detailed measurements of hydraulic roughness are not practically available for deterministic catchment modelling, it is important to know that larger sampling resolutions may be used than 0.6 m.     

Electric field enhancement in an auroral arc according to the simultaneous radar (EISCAT) and optical (ALIS) observations

The character of a change in the ionospheric electric field when several auroral arcs crossed the region of radar measurements has been analyzed. In one case the plasma conductivity and electric field normal component in an arc increased as compared to their undisturbed values. In another case the field and conductivity changed traditionally (in antiphase). Arcs with an increased field were previously classified as correlating arcs, but their existence was subsequently open to question during optical observations. The usage of the ALIS system of digital cameras made it possible to decrease the errors introduced by optical equipment. The measurements in the vicinity of correlating arcs were performed when these arcs were generated, and a traditional arc was a completed formation. In an originating arc, the field value can depend not only on the ionospheric plasma conductivity but also on the processes in the magnetospheric-ionospheric system resulting in the field enhancement.     

Reaction of the ionospheric <Emphasis Type="Italic">F</Emphasis>1 region to disturbances in October and November 2003 (analysis from Irkutsk digisonde measurements)

We consider the ionospheric response at heights of 120–220 km to geomagnetic disturbances in October and November 2003, which caused a strongly pronounced decrease in the electron content in the noted height range. For this disturbance period, using a technique of the authors, midday variations of the relative content of atomic and molecular oxygen at a height of 120 km were estimated. This estimation was performed with the help of ionospheric measurements (by a digital ionosonde) conducted at the Institute of Solar-Terrestrial Physics of the Russian Academy of Sciences from 2003 to 2006. Comparison of these values with similar values from the mass spectrometer-incoherent scatter (MSIS)-86 model showed that our estimates during disturbance days were two times less. This study continues research into the field of using ionospheric measurements to estimate the relative gas composition of the thermosphere at heights below the maximum of the F2 layer.     

Two-dimensional electric field measurements in the ionospheric footprint of a flux transfer event

Line-of-sight Doppler velocities from the SuperDARN CUTLASS HF radar pair have been combined to produce the first two-dimensional vector measurements of the convection pattern throughout the ionospheric footprint of a flux transfer event (a pulsed ionospheric flow, or PIF). Very stable and moderate interplanetary magnetic field conditions, along with a preceding prolonged period of northward interplanetary magnetic field, allow a detailed study of the spatial and the temporal evolution of the ionospheric response to magnetic reconnection. The flux tube footprint is tracked for half an hour across six hours of local time in the auroral zone, from magnetic local noon to dusk. The motion of the footprint of the newly reconnected flux tube is compared with the ionospheric convection velocity. Two primary intervals in the PIFs evolution have been determined. For the first half of its lifetime in the radar field of view the phase speed of the PIF is highly variable and the mean speed is nearly twice the ionospheric convection speed. For the final half of its lifetime the phase velocity becomes much less variable and slows down to the ionospheric convection velocity. The evolution of the flux tube in the magnetosphere has been studied using magnetic field, magnetopause and magnetosheath models. The data are consistent with an interval of azimuthally propagating magnetopause reconnection, in a manner consonant with a peeling of magnetic flux from the magnetopause, followed by an interval of anti-sunward convection of reconnected flux tubes.     

顾及电离层变化的层析反演新算法

区别于以往GPS电离层层析研究主要关注迭代模型的思路,本文从两方面入手提高GPS电离层层析迭代算法的反演精度:一方面,顾及传统电离层层析迭代模型仅与对电子密度误差起放大作用的GPS射线截距权重相关的不足,提出考虑层析像素格网中的电子密度对GPS TEC的贡献建立新的迭代模型,在不同电子密度像素格网内重新分配GPS TEC实测值与其反演值之间的差距;另一方面,顾及电离层层析迭代算法中松弛因子对反演结果的影响,提出考虑电子密度变化构造新的松弛因子,抑制传播噪声对电子密度反演精度的影响.实验结果显示,相对于传统代数重构算法(ART),新方法反演的电离层电子密度剖面更接近于电离层测高仪观测的电子密度剖面,提高了电子密度反演精度.     

Determining the ionospheric irregularity velocity vector based on doppler measurements in the artificially modified <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> region of the polar ionosphere

The method for estimating the behavior of the ionospheric irregularity motion vector in the artificially disturbed HF ionospheric region has been proposed, and this behavior has been analyzed based on the simultaneous Doppler observations performed on several paths using the method of bi-static backscatter of diagnostic HF signals by small-scale artificial ionospheric irregularities. The Doppler measurements were performed during the modification of the auroral ionosphere by powerful HF radiowaves emitted by the EISCAT heating facility (Tromsø, Norway). It has been obtained that the dynamics of the ionospheric irregularity directions in the F region, calculated based on the Doppler measurements of the total vector of the ionospheric irregularity velocity above the Tromsø EISCAT radar at a frequency of 931 MHz, is in satisfactory agreement with such calculations performed using the three-position method.     

Algorithm of the problem of simulating the total wave field of the geomagnetic pulsation signal within the ionospheric transition layer

Summary This supplement to paper by Prikner and Vagner (1991) describes the optimum algorithm for the automated computer program of numerical simulation of the total wave field anywhere within the ionospheric filter. The matrix method of thin layers in an inhomogeneous, anisotropic and dissipative ionosphere has been applied. The application of this method enables in situ measurements of geomagnetic pulsations in the ionosphere to be compared with the results of the numerical simulation.     

A statistical survey of dayside pulsed ionospheric flows as seen by the CUTLASS Finland HF radar

Nearly two years of 2-min resolution data and 7- to 21-s resolution data from the CUTLASS Finland HF radar have undergone Fourier analysis in order to study statistically the occurrence rates and repetition frequencies of pulsed ionospheric flows in the noon-sector high-latitude ionosphere. Pulsed ionospheric flow bursts are believed to be the ionospheric footprint of newly reconnected geomagnetic field lines, which occur during episodes of magnetic flux transfer to the terrestrial magnetosphere - flux transfer events or FTEs. The distribution of pulsed ionospheric flows were found to be well grouped in the radar field of view, and to be in the vicinity of the radar signature of the cusp footprint. Two thirds of the pulsed ionospheric flow intervals included in the statistical study occurred when the interplanetary magnetic field had a southward component, supporting the hypothesis that pulsed ionospheric flows are a reconnection-related phenomenon. The occurrence rate of the pulsed ionospheric flow fluctuation period was independent of the radar scan mode. The statistical results obtained from the radar data are compared to occurrence rates and repetition frequencies of FTEs derived from spacecraft data near the magnetopause reconnection region, and to ground-based optical measurements of poleward moving auroral forms. The distributions obtained by the various instruments in different regions of the magnetosphere were remarkably similar. The radar, therefore, appears to give an unbiased sample of magnetopause activity in its routine observations of the cusp footprint.