A New Construction Method for Circle Cartograms

An area cartogram is a transformed map on which areas of regions are proportional to statistical data values; it is considered to be a powerful tool for the visual representation of statistical data. A circle cartogram is a type of area cartograms, on which regions are represented by circles. Its first construction algorithm is proposed by Dorling in 1996, based on the following requirements to construct visually elegant cartograms: 1) maintain the similarity of configurations between circles and regions, 2) express the contiguity of regions on cartograms if possible, and 3) avoid overlap of circles. The algorithm is widely used for its easiness to use and its ability to express a spatial distribution of data; however, the relative positions of circles on cartograms sometimes greatly differ from the geographical maps, since the algorithm does not consider the first requirements explicitly. In this paper, it is first pointed out that the construction problem of circle cartograms resembles that of distance cartograms, and the only difference is the existence of third requirement. Then a new construction method for circle cartograms is proposed based on the distance cartogram construction method; the proposed method is formulated as non-linear minimization with inequality constraint conditions. Finally its applicability is confirmed using dataset, including the comparison with the result of previous algorithm.     

Fast integration of low orbiter's trajectory perturbed by the earth's non-sphericity

A fast algorithm is proposed to integrate the trajectory of a low obiter perturbed by the earth's non-sphericity. The algorithm uses a separation degree to define the low-degree and the high-degree acceleration components, the former computed rigorously, and the latter interpolated from gridded accelerations. An FFT method is used to grid the accelerations. An optimal grid type for the algorithm depends on the trajectory's permissible error, speed, and memory capacity. Using the non-spherical accelerations computed from EGM96 to harmonic degree 360, orbit integrations were performed for a low orbiter at an altitude of 170 km. For a separation degree of 50, the new algorithm, together with the predict-pseudo correct method, speeds up the integration by 145 times compared to the conventional algorithm while keeping the errors in position and velocity below 10⁻⁴ m and 10⁻⁷ m/s for a 3-day arc. Received: 28 July 1997 / Accepted: 1 April 1998     

A perception-based color recommendation algorithm for hierarchical regions

The visualization of hierarchical and nested spatial regions remains a challenge to cartographers. Despite progress in computer algorithms for visualizing general hierarchical data, mapping spatial hierarchical regions, especially with static, noninteractive means, still requires considerable manual efforts. This paper proposes a two-step algorithm that can automatically recommend perception-based colors and help reveal the hierarchical structure embedded in nested regions. It first systematically sorts regions according to their contiguity and containment relations at multiple hierarchical levels. Then, perception-based colors are generated using the order of regions with the goal of maximizing differentiability between top-level regions while retaining the perceived uniformity of the bottom-level regions. With the coloring scheme recommended by this algorithm, the metric color differences among regions mathematically reflect their hierarchical positions and spatial relations. The resultant colors, therefore, can potentially help map-readers perceive the spatially constrained hierarchy structure built in nested regions.     

海洋激光雷达反演水体光学参数

研制了一套船载海洋激光雷达,用于探测海水光学参数垂直廓线。2017年8月,该系统在黄海海域进行了实验测量。在准单次散射模型中引入原位测量的光学参数,实现了理想激光雷达回波信号的模拟,并将该理想信号与系统响应函数卷积后精确复现了实验的激光雷达信号。采用Fernald后向迭代积分法(简称Fernald法),比较了不同水体悬浮物激光雷达比下反演的激光雷达衰减系数α与原位漫射衰减系数Kd的差别。基于停航时标定的水体悬浮物激光雷达比,采用Fernald法获得了走航时的激光雷达衰减系数。进一步地,提出一种基于米散射激光雷达数据和原位测量的后向散射数据的融合算法,模拟了高光谱分辨率激光雷达(HSRL)反演α的过程,并将其与Fernald法进行了比较。实验结果表明,自研的海洋激光雷达能够有效探测海水光学参数,基于合适的水体悬浮物激光雷达比的Fernald法可以有效应用于米散射激光雷达的反演,未来无需假设的HSRL在海水光学参数探测领域具有更大的优势。     

A new approach for airborne vector gravimetry using GPS/INS

A new method for airborne vector gravimetry using GPS/INS has been developed and the results are presented. The new algorithm uses kinematic accelerations as updates instead of positions or velocities, and all calculations are performed in the inertial frame. Therefore, it is conceptually simpler, easier, more straightforward and computationally less expensive compared to the traditional approach in which the complex navigation equations should be integrated. Moreover, it is a unified approach for determining all three vector components, and no stochastic gravity modeling is required. This approach is based on analyzing the residuals from the Kalman filter of sensor errors, and further processing with wavenumber coefficient filterings is applied in case closely parallel tracks of data are available. An application to actual test-flight data is performed to test the validity of the new algorithm. The results yield an accuracy in the down component of about 3–4 mGal. Also, comparable results are obtained for the horizontal components with accuracies of about 6 mGal. The gravity modeling issue is discussed and alternative methods are presented, none of which improves on the original approach. Received: 18 April 2000 / Accepted: 14 August 2000     

Computing components of the gravity field induced by distant topographic masses and condensed masses over the entire Earth using the 1-D FFT approach

 A new method for computing gravitational potential and attraction induced by distant, global masses on a global scale has been developed. The method uses series expansions and the well known one-dimensional fast Fourier transform (1-D FFT) method. It has been proven to be significantly faster than quadrature while being equally accurate. Various quantities were studied to cover the two primary applications of the Stokes–Helmert scheme of modeling effects. These two applications (or paths), given the names R/r/D and R/D/r, are briefly discussed, although the primary objective of the paper is to provide computational information to either path, rather than choosing one path as preferable to the other. It is further shown that the impact of masses outside a 4-degree cap can impact the absolute computation of the geoid at more than 1 cm, and should therefore be included in all local geoid computations seeking that accuracy. Received: 13 December 2000 / Accepted: 3 September 2001     

Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data

At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.̋1 and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds to a relative accuracy of about 0.05−0.1 ppm. Application examples are given, such as the local and regional validation of gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered regions.     

A new estimator for VLBI baseline length repeatability

The goal of this paper is to introduce a more effective technique to approximate for the “repeatability–baseline length” relationship that is used to evaluate the quality of geodetic VLBI results. Traditionally, this relationship is approximated by a quadratic function of baseline length over all baselines. The new model incorporates the mean number of observed group delays of the reference radio sources (i.e. estimated as global parameters) used in the estimation of each baseline. It is shown that the new method provides a better approximation of the “repeatability–baseline length” relationship than the traditional model. Further development of the new approach comes down to modeling the repeatability as a function of two parameters: baseline length and baseline slewing rate. Within the framework of this new approach the station vertical and horizontal uncertainties can be treated as a function of baseline length. While the previous relationship indicated that the station vertical uncertainties are generally 4–5 times larger than the horizontal uncertainties, the vertical uncertainties as determined by the new method are only larger by a factor of 1.44 over all baseline lengths.     

Influence of resonances on the phase and the group refractive indices of air

The Barrell and Sears and Edlen formulae use the Sellmeier form away from resonances, which gives a “smooth” dependence within the visible and near-infrared spectra. All known atlases indicate numerous resonances in these regions, which cause local disturbance of the dispersion curve. Anomalous dispersion may be estimated from an absorption by the Kramer-Kronig ratios. It gives a change of phase refractive index of air in a range from several ppt to 1 ppb within narrow optical regions, causing large local dispersions. Computation of the group refractive index with the use of Rayleigh's ratio shows that the influence of resonance effects may be more than several ppm. For example, the error of the group refractive index for high-precision EDM using HeNe lasers (633 nm) varies between 0.2 and 0.7 ppm, depending on the laser stability. Received: 17 July 1996 / Accepted: 27 March 1997     

A new approach to GPS ambiguity decorrelation

Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests. Received: 9 March 1998 / Accepted: 1 June 1999     

GPS vector configuration design for monitoring deformation networks

 The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring networks, a common practice worldwide. Received: 30 July 2001 / Accepted: 3 June 2002 Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks.     

Solution and econometric estimation of spatial dynamic models in continuous space and continuous time

 This paper presents and demonstrates a general approach to solving spatial dynamic models in continuous space and continuous time that characterize the behaviour of intertemporally and interspatially optimizing agents and estimating from discrete data the parameters of such models. The approach involves the use of a projection method to solve the models and a quasi-Newton algorithm to update quasi-FIML parameter estimates. Received: 26 July 2000 / Accepted: 31 January 2001     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

基于地理加权中心节点距离的网络社区发现算法

提出一种基于地理加权中心节点距离的网络社区发现算法（geographical weighted central node distance based Louvain method,GND-Louvain）。该算法扩展了传统复杂网络领域的经典社区发现方法Louvain,利用地理加权中心节点来度量社区发现过程中的空间距离关系,并将此距离衰减效应加入到距离模块度模型中,以此来计算和评估空间网络社区划分结果的质量,并探究了空间社区发现结果不稳定的原因。通过定义节点计算顺序,保证了社区发现结果的质量和稳定性。利用中国铁路网线路数据,设计了5种不同空间约束的空间社区发现对比性实验。结果证明,GND-Louvain算法的准确性最高,并且算法结果最稳定。     

遥感影像并行分割的无缝拼接算法

针对影像数据分块并行处理造成的接边问题,该文基于构建缓冲区的方法提出了一种新的拼接算法。该算法只在每一个数据分块的右侧和下侧构建缓冲区,消除拼接线的原则是保证分割边界的准确性和拓扑关系的正确性。数据分块完成后采用并行的策略对第一个块进行分割,然后将每一块的分割结果与相邻的块进行拼接,在缓冲区内按一定规则判断各块分割对象是否保留并对拓扑关系进行检查,拼接完各块后并行输出对象矢量化后的结果。通过实验验证,该算法不仅保证了分割边界的准确性,而且能够处理大影像,提高了工作效率。     

A non-iterative and non-singular perturbation solution for transforming Cartesian to geodetic coordinates

The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km the second-order expansions yields ~mm satellite geodetic height errors and ~10⁻¹² rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate the effectiveness of the new algorithm.     

基于葵花-8卫星大气产品的地表下行短波辐射计算

地表下行短波辐射DSSR(Downward Surface Shortwave Radiation)的准确估算在气候变化研究和地表太阳能估算等领域具有重要作用。新一代静止气象卫星葵花-8(Himawari-8)具有高达10 min的对地观测能力,为DSSR近实时估算提供了新机遇。然而,日本宇宙航空研究开发机构(JAXA)对外公开的葵花-8辐射产品中,没有将其反演的云、气溶胶产品作为DSSR的输入参数,从而没有形成一整套的DSSR估算算法流程,缺乏产品输出的一致性。大气中的云、气溶胶是DSSR的重要影响因子,本文重点考虑云、气溶胶对太阳辐射的影响,基于大气辐射传输模式RSTAR构建了DSSR查找表,开发了DSSR的快速计算方法,进而将JAXA葵花-8二级云、气溶胶产品(光学厚度,粒子有效半径等)作为快速化计算方法的输入参量,计算得到了DSSR。通过与JAXA葵花-8二级DSSR产品(JAXA DSSR)对比,发现两者具有很好的空间一致性。为了进一步评价本文的DSSR计算精度,分别选取了陆地(Yonsei)和海洋(0n_165e)的观测数据验证了2016年4、7、10和12月本文计算的DSSR和同时期的JAXA DSSR产品,验证结果显示两者的DSSR在两个观测站点均具有非常高的相关性(全天空、晴空和云天条件下的相关系数R均大于0.88)。在两个站点云天条件下的验证结果中,考虑了云相态并在冰云模型中使用了非球形冰晶粒子(六棱柱)来计算DSSR,获得了比JAXA DSSR更小的偏差。本文提出的快速化计算方法能快速准确地计算DSSR,可为计算地表辐射收支等研究提供重要数据支撑。     

Preliminary geoid over Zambia

In the determination of the preliminary geoid over Zambia, we compare three methods of the modified Stokes formula: that of Vincent and Marsh, a modified Wong and Gore method, and a modified spectral weighting method, with the final solution being estimated by the modified Wong and Gore procedure. The geoid over Zambia (based on GRS80) is rising from north-east to south-west. It coincides with the reference ellipsoid in the north-western and southern regions of Zambia. The preliminary estimate indicates maximum and minimum values of about 13.7 and −16.8m, respectively. The mean geoid over the area is −2.8m. Formal analysis of global root mean square errors for the three models leads us to conclude that for an integration cap radius of about 3 or less, the modified formula using optimal spectral weighting is superior to the Vincent and Marsh method, and to the modified and unmodified Wong and Gore. Received: 8 October 1996 / Accepted: 25 June 1997     

Alonso's Theory of Movements: Developments in Spatial Interaction Modeling

 The Spatial Interaction Model proposed by Alonso as “Theory of Movements” offers an innovative specification of spatial origin-destination flow models. Equations for flows between regions, total outflow from and total inflow to a region are linked by balancing factors. This paper presents a consistent formulation of Spatial Interaction Models in the Wilson tradition and Alonso's Theory of Movements. The paper is intended as an introduction to the model and a review of␣the state of the art. Besides it is argued that simultaneous equation techniques are required to estimate the so-called systemic parameters. Received: 21 May 2000 / Accepted: 18 January 2001     

Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference

 This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions. Received: 6 May 1996; Accepted: 30 October 1996