Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997–2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the “truth” signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.     

Is there utility in rigorous combinations of VLBI and GPS Earth orientation parameters?

Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame, the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local ties (including internal systematic effects within the techniques) will be critically important in such an effort.     

Combined Earth orientation parameters based on homogeneous and continuous VLBI and GPS data

The CONT02 campaign is of great interest for studies combining very long baseline interferometry (VLBI) with other space-geodetic techniques, because of the continuously available VLBI observations over 2 weeks in October 2002 from a homogeneous network. Especially, the combination with the Global Positioning System (GPS) offers a broad spectrum of common parameters. We combined station coordinates, Earth orientation parameters (EOPs) and troposphere parameters consistently in one solution using technique- specific datum-free normal equation systems. In this paper, we focus on the analyses concerning the EOPs, whereas the comparison and combination of the troposphere parameters and station coordinates are covered in a companion paper in Journal of Geodesy. In order to demonstrate the potential of the VLBI and GPS space-geodetic techniques, we chose a sub-daily resolution for polar motion (PM) and universal time (UT). A consequence of this solution set-up is the presence of a one-to-one correlation between the nutation angles and a retrograde diurnal signal in PM. The Bernese GPS Software used for the combination provides a constraining approach to handle this singularity. Simulation studies involving both nutation offsets and rates helped to get a deeper understanding of this singularity. With a rigorous combination of UT1–UTC and length of day (LOD) from VLBI and GPS, we showed that such a combination works very well and does not suffer from the systematic effects present in the GPS-derived LOD values. By means of wavelet analyses and the formal errors of the estimates, we explain this important result. The same holds for the combination of nutation offsets and rates. The local geodetic ties between GPS and VLBI antennas play an essential role within the inter-technique combination. Several studies already revealed non-negligible discrepancies between the terrestrial measurements and the space-geodetic solutions. We demonstrate to what extent these discrepancies propagate into the combined EOP solution.     

利用小波分解改进极移预报模型

高精度的日长（length of day,LOD）变化ΔLOD预报值在深空探测器跟踪、卫星自主导航和气候预测等领域具有重要作用。针对ΔLOD复杂的时变特性,首先,利用奇异谱分析（singular spectrum analysis,SSA）方法提取ΔLOD时间序列中的趋势项、周年项与半周年项等主成分,并基于SSA迭代插值算法对主成分进行外推;其次,采用差分自回归滑动平均（autoregressive integrated moving average,ARIMA）模型对扣除主成分的剩余项进行建模预测;最后,将SSA主成分外推值与ARIMA预测值相加获得ΔLOD预报值。选取国际地球自转与参考系服务组织发布的2000-01-01—2001-12-31的ΔLOD数据进行1~365 d跨度的预报实验,并将SSA+ARIMA预报结果与反向传播神经网络、广义回归神经网络和高斯过程等机器学习方法的预报结果进行对比分析。结果表明,SSA+ARIMA方法的预报精度优于几种机器学习方法,特别是中长期预报精度优势更为显著,其中,对于1~30 d短期和30~365 d中长期的预报,SSA+ARIMA方法的平均绝对预报误差相对于机器学习方法最大分别降低了39%和61%。

     

Polar motion of the triaxial nonrigid Earth and atmospheric excitation

The present study aims to extend the traditional rotation theory of the rotational-symmetric Earth to the triaxial Earth.We re-formulate the Liouville equations and their general solutions for the triaxial nonrigid Earth and find that the traditional theory intro-duces some theoretical errors in modeling the excitation functions.Furthermore,we apply that theory to the atmospheric excitation and find that theoretical errors should not be neglected given the present measurement accuracy.Thus we conclude that the traditional the-ory of the rotation of the rotational-symmetric Earth should be revised and upgraded to include the effects of the Earth’s triaxiality.     

A study on the reference frame consistency in recent Earth gravitational models

All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs, especially when their use is intended for high precision studies. Following the methodology described in an earlier paper by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model, the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae for the assessment of TRF inconsistencies among global geopotential models.     

EARTH ROTATION EQUATIONS CONTAINING BOTH NUTATION AND POLAR MOTION

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Possible improvement of Earth orientation forecast using autocovariance prediction procedures

 Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data, from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model. Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation residuals. Received: 22 October 1996 / Accepted: 16 September 1997     

同时顾及章动和极移的地球自转方程

通过引进章动坐标系相对惯性参照系的转动角速度随时间的变化,导出了一个可同时解出章动和极移的地球自转方程,用这个方程可同时研究地球的强迫和自由转动。与现行研究地球自转的惯用方法相比,该方法综合性强,易于理解。     

月球平均运动和地球自转速率长期变化的潮汐耗散

利用1983～1994年(共11年)期间,全球人卫激光测距(SLR)观测网对Lageos-1卫星的观测资料,估算二阶重力场系数和潮汐参数。SLR和卫星测高的潮汐解被用来计算月球轨道根数相对黄道坐标系的长期变化和地球自转速率的长期变化。SLR确定的总的潮汐耗散引起的月球平均运动的长期变化为-24.78″/世纪2,与激光测月结果（(-24.9±1.0)″/世纪2) 非常一致。日月潮汐引起的地球自转速率的长期变化为 -5.25×10-22rad /s2,顾及地球扁率变化（2）的非潮汐效应,对应的日长变化为1.49 ms/世纪,与1620年以来的天文月掩星结果（1.4 ms/世纪）十分相符。本文还联合卫星测高和人卫激光测距确定的潮汐解,在月球平均运动和地球自转速率的长期变化中,分离出固体地球和海洋的耗散效应。     

Combinations of Earth-orientation measurements: SPACE97, COMB97, and POLE97

Independent Earth-orientation measurements taken by the space-geodetic techniques of lunar and satellite laser ranging, very-long-baseline interferometry, and the global positioning system have been combined using a Kalman filter. The resulting combined Earth-orientation series, SPACE97, consists of values and uncertainties for universal time, polar motion, and their rates spanning the period 28 September 1976 to 3 January 1998 at daily intervals. The space-geodetic measurements used to generate SPACE97 have then been combined with optical astrometric measurements to form two additional combined Earth-orientation series: (1) COMB97, consisting of values and uncertainties for universal time, polar motion, and their rates spanning the period 20 January 1962 to 1 January 1998 at 5-day intervals, and (2) POLE97, consisting of values and uncertainties for polar motion and its rate spanning the period 20 January 1900 to 21 December 1997 at monthly intervals. Received: 10 August 1998 / Accepted: 31 May 1999     

On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs

In this paper, a new geometry index of very long baseline interferometry (VLBI) observing networks, the volume of network V, is examined as an indicator of the errors in the Earth orientation parameters (EOP) obtained from VLBI observations. It has been shown that both EOP precision and accuracy can be well described by the power law σ = aV ^c in a wide range of the network size from domestic to global VLBI networks. In other words, as the network volume grows, the EOP errors become smaller following a power law. This should be taken into account for a proper comparison of EOP estimates obtained from different VLBI networks. Thus, performing correct EOP comparison allows us to investigate accurately finer factors affecting the EOP errors. In particular, it was found that the dependence of the EOP precision and accuracy on the recording data rate can also be described by a power law. One important conclusion is that the EOP accuracy depends primarily on the network geometry and to lesser extent on other factors, such as recording mode and data rate and scheduling parameters, whereas these factors have a stronger impact on the EOP precision.     

Digital Earth: a new challenge and new vision

ABSTRACT

Digital Earth has seen great progress during the last 19 years. When it entered into the era of big data, Digital Earth developed into a new stage, namely one characterized by ‘Big Earth Data’, confronting new challenges and opportunities. In this paper we give an overview of the development of Digital Earth by summarizing research achievements and marking the milestones of Digital Earth’s development. Then, the opportunities and challenges that Big Earth Data faces are discussed. As a data-intensive scientific research approach, Big Earth Data provides a new vision and methodology to Earth sciences, and the paper identifies the advantages of Big Earth Data to scientific research, especially in knowledge discovery and global change research. We believe that Big Earth Data will advance and promote the development of Digital Earth.     

Multitemporal settlement and population mapping from Landsat using Google Earth Engine

As countries become increasingly urbanized, understanding how urban areas are changing within the landscape becomes increasingly important. Urbanized areas are often the strongest indicators of human interaction with the environment, and understanding how urban areas develop through remotely sensed data allows for more sustainable practices. The Google Earth Engine (GEE) leverages cloud computing services to provide analysis capabilities on over 40 years of Landsat data. As a remote sensing platform, its ability to analyze global data rapidly lends itself to being an invaluable tool for studying the growth of urban areas. Here we present (i) An approach for the automated extraction of urban areas from Landsat imagery using GEE, validated using higher resolution images, (ii) a novel method of validation of the extracted urban extents using changes in the statistical performance of a high resolution population mapping method. Temporally distinct urban extractions were classified from the GEE catalog of Landsat 5 and 7 data over the Indonesian island of Java by using a Normalized Difference Spectral Vector (NDSV) method. Statistical evaluation of all of the tests was performed, and the value of population mapping methods in validating these urban extents was also examined. Results showed that the automated classification from GEE produced accurate urban extent maps, and that the integration of GEE-derived urban extents also improved the quality of the population mapping outputs.     

Modeling the length of day and extrapolating the rotation of the Earth

The stochastic behavior of the length of day (LOD) process is analyzed and is modeled within statistical accuracy on a time-scale ranging from weeks to millennia by a three-component model comprising a global Brownian motion process, decadal fluctuations, and a 50-day Madden–Julian oscillation. While the model is intended to be phenomenological, some possible physical models underlying the three components are speculated upon. The model is applied to estimate long-range extrapolation errors. For example, it predicts a standard error of 1 h in the clock-time correction ΔT for extrapolation by 1,500 years from 500 to 2000 BC.     

Global geospatial data from Earth observation: status and issues

ABSTRACT

Data covering the whole of the surface of the Earth in a homogeneous and reliable manner has been accumulating over many years. This type of data became available from meteorological satellites from the 1960s and from Earth-observing satellites at a small scale from the early 1970s but has gradually accumulated at larger scales up to the present day when we now have data covering many environmental themes at large scales. These data have been used to generate information which is presented in the form of global data sets. This paper will give a brief introduction to the development of Earth observation and to the organisations and sensors which collect data and produce global geospatial data sets. Means of accessing global data sets will set out the types of data available that will be covered. Digital elevation models are discussed in a separate section because of their importance in georeferencing image data as well as their application to analysis of thematic data. The paper will also examine issues of availability, accuracy, validation and reliability and will look at future challenges.     

Blue Earth River quality monitoring using ARCHER hyperspectral data and field measurements

In past decades, remote sensing studies on water quality mapping mainly focused on lakes using medium resolution imagery. Little research utilizes hyperspectral images to assess river water quality. This study aims to assess the capability of using Airborne Real-time Cueing Hyperspectral Enhanced Reconnaissance (ARCHER) for river water quality mapping and to characterize spatial patterns of turbidity and chlorophyll in the Blue Earth River (BER) system of Minnesota. The BER was characterized by both hyperspectral imagery (HSI) and laboratory analysis of synchronously collected water quality data. The optimal bands for water quality mapping were determined using a method based on hyperspectral profiles and derivative analysis. Finally, based on the regression analysis and modelling, we mapped continuous surface water turbidity. The results revealed that the ratio of HSI band 17 to band 9 effectively determined turbidity and chlorophyll concentrations. The study also found that turbidity and chlorophyll in the river generally increases downstream.     

Effect of post-seismic deformation on earth orientation parameter estimates from VLBI observations: a case study at Gilcreek, Alaska

Earth orientation parameters (EOPs) provide a link between the International Celestial Reference Frame (ICRF) and the International Terrestrial Reference Frame (ITRF). Natural geodynamic processes, such as earthquakes, can cause the motion of stations to become discontinuous and/or non-linear, thereby corrupting the EOP estimates if the sites are assumed to move linearly. The VLBI antenna at the Gilcreek Geophysical Observatory has undergone non-linear, post-seismic motion as a result of the M_w=7.9 Denali earthquake in November 2002, yet some VLBI analysts have adopted co-seismic offsets and a linear velocity model to represent the motion of the site after the earthquake. Ignoring the effects of the Denali earthquake leads to error on the order of 300–600 μas for the EOP, while modelling the post-seismic motion of Gilcreek with a linear velocity generates errors of 20–50 μas. Only by modelling the site motion with a non-linear function is the same level of accuracy of EOP estimates maintained. The effect of post-seismic motion on EOP estimates derived from the International VLBI Service IVS-R1 and IVS-R4 networks are not the same, although changes in network geometries and equipment improvements have probably affected the estimates more significantly than the earthquake-induced deformation at Gilcreek.     

Monitoring and modelling of urban sprawl using remote sensing and GIS techniques

The concentration of people in densely populated urban areas, especially in developing countries, calls for the use of monitoring systems like remote sensing. Such systems along with spatial analysis techniques like digital image processing and geographical information system (GIS) can be used for the monitoring and planning purposes as these enable the reporting of overall sprawl at a detailed level.     

Atmospheric Angular Momentum Time-Series: Characterization of their Internal Noise and Creation of a Combined Series

The atmosphere induces variations in Earth rotation. These effects are classically computed using the “angular momentum approach”. In this method, the variations in Earth rotation are estimated from the variations in the atmospheric angular momentum (AAM). Several AAM time-series are available from different meteorological centers. However, the estimation of atmospheric effects on Earth rotation differs when using one atmospheric model or the other. The purpose of this work is to build an objective criterion that justifies the use of one series in particular. Because the atmosphere is not the only cause of Earth rotation variations, this criterion cannot rely only on a comparison of AAM series with geodetic data. Instead, we determine the quality of each series by making an estimation of their noise level, using a generalized formulation of the “three-cornered hat method”. We show the existence of a link between the noise of the AAM series and their correlation with geodetic data: a noisy series is usually less correlated with Earth orientation data. As the quality of the series varies in time, we construct a combined AAM series, using time-dependent weights chosen so that the noise level of the combined series is minimal. To determine the influence of a minimal noise level on the correlation with geodetic data, we compute the correlation between the combined series and Earth orientation data. We note that the combined series is always amongst the best correlated series, which confirms the link established before. The quality criterion, while totally independent of Earth orientation observations, appears to be physically convincing when atmospheric and geodetic data are compared