Study on Recovering the Earth＇s Potential Field Based on GOCE Gradiometry

Given the second radial derivative Vrr（P） ｜δs of the Earth＇s gravitational potential V（P） on the surface δS corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVrr（P）^＊ and a fictitious second radial gradient field V：（P） in the domain outside an inner sphere Ki can be determined, which coincides with the real field V（P） in the domain outside the Earth. Vrr^＊（P）could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrV（P）^＊ could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain. In another aspect, the fictitious field V^＊（P） defined in the domain outside the inner sphere, which coincides with the real field V（P） in the domain outside the Earth, could be also expressed as a spherical harmonic expansion series. Then, the harmonic coefficients contained in the series expressing V^＊（P） can be determined, and consequently the real field V（P） is recovered. Preliminary simulation calculations show that the second radial gradient field Vrr（P） could be recovered based only on the second radial derivative V（P）｜δs given on the satellite boundary. Concerning the final recovery of the potential field V（P） based only on the boundary value Vrr （P）｜δs, the simulation tests are still in process.     

A Critical Analysis of a Recent Test of the Lense–Thirring Effect with the LAGEOS Satellites

In this paper, we quantitatively discuss the impact of the current uncertainties in the even zonal harmonic coefficients J _l of the Newtonian part of the terrestrial gravitational potential on the measurement of the general relativistic Lense–Thirring effect. We use a suitable linear combination of the nodes Ω of the laser-ranged LAGEOS and LAGEOS-II satellites. The one-sigma systematic error due to mismodelling of the J _l coefficients ranges from ~ 4% for the EIGEN−GRACE02S gravity field model to ~ 9% for the GGM02S model. Another important source of systematic error of gravitational origin is represented by the secular variations j _l of the even zonal harmonics. While the relativistic and J _l signals are linear in time, the shift due to j _l is quadratic. We quantitatively assess their impact on the measurement of the Lense–Thirring effect with numerical simulations obtaining a 10−20% one-sigma total error over 11 years for EIGEN-GRACE02S. Ciufolini and Pavlis (Nature 431:958–960, 2004) claim a total error of 5% at the one-sigma level.     

SIMPLE RESECTION

Abstract

The figure which follows shows the geometrical solution of Simple Resection by Cassini in 1669, two years before the Collins solution. It is clearly the geometrical illustration of the Delambre (1786) solution; for d_b = b cosec β, d_c = c cosec γ and the angle QAR is known, being BAC + β + γ ? 180°. Hence the Delambre solution-that in most common use to-day—reduces to a triangle in which two sides and the contained angle are given, as has been mentioned elsewhere.     

Construction of anisotropic covariance functions using Riesz-representers

A reproducing-kernel Hilbert space (RKHS) of functions harmonic in the set outside a sphere with radius R ₀, having a reproducing kernel K ₀(P,Q) is considered (P, Q, and later P _n being points in the set of harmonicity). The degree variances of this kernel will be denoted σ_{0 n} . The set of Riesz representers associated with the evaluation functionals (or gravity functionals) related to distinct points P _n ,n = 1,…,N, on a two-dimensional surface surrounding the bounding sphere, will be linearly independent. These functions are used to define a new N-dimensional RKHS with kernel (a _n >0)

Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration

 Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S _n and expressed in mm) is adequately approximated by the equation S _n =k _n /T ^0.5 with k _n =9.5 ± 2.1 mm · h^0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions are adequately approximated by the equations S _e =k _e /T ^0.5 and S _u =k _u /T ^0.5, respectively, with k _e =9.9 ± 3.1 mm · h^0.5 and k _u =36.5 ± 9.1 mm · h^0.5. Received: 5 February 2001 / Accepted: 14 May 2001     

The generalized Mollweide projection of the biaxial ellipsoid

Summary The standard Mollweide projection of the sphere S _R ² which is of type pseudocylindrical — equiareal is generalized to the biaxial ellipsoid E _A,B ² .Within the class of pseudocylindrical mapping equations (1.8) of E _A,B ² (semimajor axis A, semiminor axis B) it is shown by solving the general eigenvalue problem (Tissot analysis) that only equiareal mappings, no conformal mappings exist. The mapping equations (2.1) which generalize those from S _R ² to E _A,B ² lead under the equiareal postulate to a generalized Kepler equation (2.21) which is solved by Newton iteration, for instance (Table 1). Two variants of the ellipsoidal Mollweide projection in particular (2.16), (2.17) versus (2.19), (2.20) are presented which guarantee that parallel circles (coordinate lines of constant ellipsoidal latitude) are mapped onto straight lines in the plane while meridians (coordinate lines of constant ellipsoidal longitude) are mapped onto ellipses of variable axes. The theorem collects the basic results. Six computer graphical examples illustrate the first pseudocylindrical map projection of E _A,B ² of generalized Mollweide type.     

CONDITION FOR THE CONSTRUCTION OF A CONFORMAL PROJECTION

Abstract

In the Empire Survey Review for October 1938 (iv, 30, 480) a simple demonstration of the condition to be satisfied for conformal representation was given. This condition may be expressed by the equation w = f(z), where w and z are complex variables representing corresponding points in the w-plane and z-plane respectively, and f(z) is an analytic function of z.     

Light mode and dark mode: Which one is suitable when using public-facing web maps? An experimental evaluation using eye-tracking

Dark maps, which are also called dark modes or dark themes, have gained popularity, but their usability has not been experimentally evaluated. This article presents a user experiment that uses eye-tracking to assess the usability of dark and light maps. Here, two widely used web maps, Google Maps and Gaode Maps, are selected at the street and city scales. Eight map-use tasks are designed and cover four operations (identify, compare, rank, and associate) with space-alone and attributes-in-space distinctions. Four pairs of map-use tasks (light-during-the-day, dark-during-the-day, dark-at-night, and light-at-night) are examined from three aspects: effectiveness, efficiency, and cognitive load. The results provide preliminary evidence that the light-during-the-day performance is generally the best in most cases, followed by the dark-at-night performance; the dark-during-the-day performance is the worst in all cases, followed by the light-at-night performance, which suggests that aligning the map design with the environment (i.e., lighting environment) is critical for better communication. The light-during-the-day performance is the best for space-alone tasks, and the dark-at-night performance is the best for attributes-in-space tasks. Our investigation also indicates that dark maps are far less favored in practice, which suggests that users' preference for using the dark mode of public-facing web maps needs to be shaped. Since light and dark maps are associated with photopic and scotopic vision, respectively, the results indicate the need for future studies on how to leverage scotopic vision to design better dark maps.     

Digitizing the thermal and hydrological parameters of land surface in subtropical China using AMSR-E brightness temperatures

ABSTRACT

Digitizing the land surface temperature (T_s) and surface soil moisture (m_v) is essential for developing the intelligent Digital Earth. Here, we developed a two parameter physical-based passive microwave remote sensing model for jointly retrieving T_s and m_v using the dual-polarized T_b of Aqua satellite advanced microwave scanning radiometer (AMSR-E) C-band (6.9 GHz) based on the simplified radiative transfer equation. Validation using in situ T_s and m_v in southern China showed the average root mean square errors (RMSE) of T_s and m_v retrievals reach 2.42 K (R² = 0.61, n = 351) and 0.025 g cm^?3 (R² = 0.68, n = 663), respectively. The results were also validated using global in situ T_s (n = 2362) and m_v (n = 1657) of International Soil Moisture Network. The corresponding RMSE are 3.44 k (R² = 0.86) and 0.039 g cm^?3 (R² = 0.83), respectively. The monthly variations of model-derived Ts and mv are highly consistent with those of the Moderate Resolution Imaging Spectroradiometer T_s (R² = 0.57; RMSE = 2.91 k) and ECV_SM m_v (R² = 0.51; RMSE = 0.045 g cm^?3), respectively. Overall, this paper indicates an effective way to jointly modeling T_s and m_v using passive microwave remote sensing.     

地球引力位球谐级数展开的收敛性研究(英文)

Given a continuous boundary value on the boundary of a "simply closed surface"S that encloses the whole Earth, a regular harmonic fictitious field V*(P) in the domain outside an inner sphere K i that lies inside the Earth could be determined, and it is proved that V*(P) coincides with the Earth’s real field V(P) in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V*(P) could be expressed as a uniformly convergent spherical harm...     

GOCE gravitational gradients along the orbit

GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is, the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V _XX , V _YY , V _ZZ and V _XZ are much more accurate than V _XY and V _YZ , and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed. We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10⁻³ level. Furthermore, we found that the error of V _XX and V _YY is approximately at the level of the requirement on the gravitational gradient trace, whereas the V _ZZ error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients is good and that with this type of data valuable new gravity field information is obtained.     

Advanced vegetation indices for sensing paddy growth via hyperspectral measurements

In this study, field-based spectroradiometer measurements were carried out in 72 plots with eight rice varieties along with three nitrogen applications. The critical wavelengths for the studied rice varieties at which the effects of nitrogen applications on spectral reflectance response were found significant, are ρ₅₅₀, ρ₅₆₀, ρ₆₅₅, ρ₇₅₀, ρ₇₅₅, ρ₇₈₀, ρ₈₁₀, ρ₈₄₀, ρ₉₀₀, ρ₉₂₀, ρ₁₀₀₀, ρ₁₀₁₀, ρ₁₀₂₀. Using the critical wavelengths, three derived vegetation indices were compared with established indices (VI and GRI) sensitive to nitrogen. VI₁ and VI₂ were efficiently able to discriminate the level of nitrogen treatments for most of the rice genotypes whereas VI and GRI were unable to find significant difference in nitrogen treatments for rice genotypes except two. Furthermore, nitrogen difference plots exhibited that the paddy crop growth has started earlier with N₃ (150 kg/ha) than N₂ (100 kg/ha) application. Quantitative analysis of rice genotypes revealed that VI₂ can be applied functionally for the assessment of nitrogen stress in rice agriculture system.     

EXPANSION OF PAPER AS AFFECTING AREA

Abstract

For the sake of the junior reader we may repeat an old and simple investigation. Let us suppose that the paper on which a map is printed undergoes a regular expansion p in one direction, say the X direction, and another regular expansion q in the Y direction, perpendicular to the former; it is required to know the effect of these expansions on the area of any parcel on the map. Note that, so far as the mathematics are affected, X and Y are not necessarily parallel to the margins of the sheet; we shall take them here as axes of any rectangular coordinate system. The symbols p and q are regarded as ratios, so that 100p and 100p represent the percentage expansions; if the paper contracts instead of expanding, no more is necessary than to change the sign.     

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.     

1979年—2014年三峡库区月平均气温的时空变化分析

三峡区域气温变化长期以来受到科研人员和公众的关注。受三峡复杂地形的影响,仅仅基于气象站点观测数据很难准确获取区域气温变化的空间格局,遥感技术则可以通过提供空间连续的地表观测数据来辅助气温变化分析。以广义加性模型GAM (General Additive Model)为插值算法,以高程和夜间地表温度(LST_night)遥感产品为辅助变量,估算三峡库区1979年—2014年1 km空间分辨率的月气温数据,在此基础上分析了气温变化趋势的时空特征及其与高程和森林覆盖率的关系。研究表明,(1)在插值算法中引入遥感产品LST_night作为辅助变量可以明显改善气温估算精度,冬春季的改善幅度高于夏秋季;(2)三峡库区年平均气温在1997年后明显上升,但在2003年库区蓄水后无明显变化趋势,几乎所有月(除12月以外)的气温都呈现上升趋势,增温趋势最显著是3月和9月,3月增温主要来自于库区东部山区的贡献,而9月增温主要来自于库区西部平原的贡献;(3)多数月份(除7月、8月、9月以外)的低温上升速度超过高温上升速度,导致区域气温的动态变化范围缩小;(4)三峡库区年平均气温上升速度与高程呈正相关,即海拔越高,升温越快,但在同一海拔高度处,森林覆盖率越高,年均气温上升速度越慢,暗示森林具有抑制增温的作用。     

Quantifying water stress effect on daily light use efficiency in Mediterranean ecosystems using satellite data

ABSTRACT

The capacity of six water stress factors (ε′_i) to track daily light use efficiency (ε) of water-limited ecosystems was evaluated. These factors are computed with remote sensing operational products and a limited amount of ground data: ε′₁ uses ground precipitation and air temperature, and satellite incoming global solar radiation; ε′₂ uses ground air temperature, and satellite actual evapotranspiration and incoming global solar radiation; ε′₃ uses satellite actual and potential evapotranspiration; ε′₄ uses satellite soil moisture; ε′₅ uses satellite-derived photochemical reflectance index; and ε′₆ uses ground vapor pressure deficit. These factors were implemented in a production efficiency model based on Monteith’s approach in order to assess their performance for modeling gross primary production (GPP). Estimated GPP was compared to reference GPP from eddy covariance (EC) measurements (GPP_EC) in three sites placed in the Iberian Peninsula (two open shrublands and one savanna). ε′_i were correlated to ε, which was calculated by dividing GPP_EC by ground measured photosynthetically active radiation (PAR) and satellite-derived fraction of absorbed PAR. Best results were achieved by ε′₁, ε′₂, ε′₃ and ε′₄ explaining around 40% and 50% of ε variance in open shurblands and savanna, respectively. In terms of GPP, R²?≈?0.70 were obtained in these cases.     

Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution

 Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative (the standardized harmonic coefficients) characteristics of the behavior of the potential V ₂(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients are estimated in addition to ˙Cˉ ₂₀, ˙Cˉ ₂₁, and ˙Sˉ ₂₁ of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ _2m (t), Sˉ _2m (t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V ₂(ψ) instead of V ₂(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V ₂(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval. Received: 25 September 1998 / Accepted: 28 June 2000     

Topological relations between spherical spatial regions with holes

ABSTRACT

There is growing interest in globally modelling the entire planet. Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated, few studies have focused on the topological relations between spherical spatial regions with holes. The 16-intersection model (16IM) is proposed to describe the topological relations between spatial regions with holes. A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes. The results show that (1) 3 disjoint relations, 3 meet relations, 66 overlap relations, 7 cover relations, 3 contain relations, 1 equal relation, 7 coveredBy relations, 3 inside relations, 1 attach relation, 52 entwined relations, and 28 embrace relations can be distinguished by the 16IM and that (2) the formalisms of attach, entwined, and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different, whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.     

Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

A cross-analysis framework for multi-source volunteered,crowdsourced, and authoritative geographic information: The case study of volunteered personal traces analysis against transport network data

Abstract

The paper discusses the need of a high-level query language to allow analysts, geographers and, in general, non-programmers to easily cross-analyze multi-source VGI created by means of apps, crowd-sourced data from social networks and authoritative geo-referenced data, usually represented as JSON data sets (nowadays, the de facto standard for data exported by social networks). Since an easy to use high-level language for querying and manipulating collections of possibly geo-tagged JSON objects is still unavailable, we propose a truly declarative language, named J-CO-QL, that is based on a well-defined execution model. A plug-in for a GIS permits to visualize geo-tagged data sets stored in a NoSQL database such as MongoDB; furthermore, the same plug-in can be used to write and execute J-CO-QL queries on those databases. The paper introduces the language by exemplifying its operators within a real study case, the aim of which is to understand the mobility of people in the neighborhood of Bergamo city. Cross-analysis of data about transportation networks and VGI from travelers is performed, by means of J-CO-QL language, capable to manipulate and transform, combine and join possibly geo-tagged JSON objects, in order to produce new possibly geo-tagged JSON objects satisfying users’ needs.