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1.
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.  相似文献   

2.
SIMPLE RESECTION     
《测量评论》2013,45(1):31-33
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 db = b cosec β, dc = 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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
Construction of anisotropic covariance functions using Riesz-representers   总被引：1，自引：1，他引：0  
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 σ0 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)
If the points all are located on a concentric sphere with radius R 1>R 0, and form an ε-net covering the sphere, and a n are suitable area elements (depending on N), then this kernel will converge towards an isotropic kernel with degree variances
Consequently, if K N (P,Q) is required to represent an isotropic covariance function of the Earth's gravity potential, COV(P,Q), σ0 n can be selected so that σ n becomes equal to the empirical degree variances. If the points are chosen at varying radial distances R n >R 0, then an anisotropic kernel, or equivalent covariance function representation, can be constructed. If the points are located in a bounded region, the kernel may be used to modify the original kernel
Values of anisotropic covariance functions constructed based on these ideas are calculated, and some initial ideas are presented on how to select the points P n . Received: 24 September 1998 / Accepted: 10 March 1999  相似文献   

7.
 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 · h0.5 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 · h0.5 and k u =36.5 ± 9.1 mm · h0.5. Received: 5 February 2001 / Accepted: 14 May 2001  相似文献   

8.
《测量评论》2013,45(47):30-35
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.  相似文献   

9.
The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W 0. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W 0 have been investigated. The rounded value W 0 = 62636856.0 ± 0.5) m 2 s −2 has already been adopted by the International Astronomical Union for the definition of the constant L G = W 0/c 2 = 6.969290134 × 10−10 (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L G , based on the above value of W 0, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W 0 is used to specify a global vertical reference system (GVRS). W 0 ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W 0, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J 2) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W 0 to be consistent with the geocentric coordinate time. As an example of using W 0 for a GVRS realization, the geopotential difference between the adopted W 0 and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.  相似文献   

10.
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 (GPPEC) 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 GPPEC 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.  相似文献   

11.
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...  相似文献   

12.
G. T. M. 《测量评论》2013,45(21):427-428
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.  相似文献   

13.
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(LSTnight)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LSTnight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。  相似文献   

14.
The spectral analysis of the Earth’s gravitational potential, its first and second derivatives is performed in spherical/ellipsoidal harmonics relative to the International Reference Sphere/International Reference Ellipsoid. The highlights of the diagrammatic approach are: (1) Up- and downward continuation of incremental gravity gradients, (2) Downward continuation of incremental gravity gradients (four tensor-valued harmonic functions) to the incremental gravity potential on the International Reference Figure, (3) Direct conversion of external incremental gravity gradients to geoidal undulation by means of the spherical/ellipsoidal Bruns Formula. The International Reference Ellipsoid was chosen as an equipotential surface in the Somigliana-Pizzetti reference potential field.  相似文献   

15.
 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  相似文献   

16.
Ross-Li核驱动模型热点参数化及其校正—以POLDER数据为例   总被引：1，自引：1，他引：0  
半经验、核驱动二向性反射分布函数(BRDF)模型是多角度遥感领域的一个重要模型,其热点效应在应用BRDF反演其它地表参数时有重要作用。本研究针对树冠内部叶片的间隙对热点的影响,对几何光学核的重叠函数进行热点效应的改进,并利用POLDER多角度观测数据集,对改进热点效应后的不同核函数组合模型的最优热点参数进行了确定。通过最小均方根误差(RMSE)筛选出最优热点参数,进一步分析不同模型对热点参数的敏感性和RMSE随热点参数的变化情况。结果表明:(1)该热点参数化方法可用于Ross-Li核驱动模型不同核函数组合的情况,热点校正后的模型相对于原模型很好地改善了对热点反射率的拟合能力;(2)热点参数最优值在几何光学核为LSRC (LiSparseRChen)与LDRC (LiDenseRChen)组成的模型中出现明显差别,C1在LDRC模型中的值远小于LSRC模型,主要是因为LDRC核函数自身较好考虑了树冠尺度下的热点效应,所以该热点参数改进方法起到的补偿作用较小;(3)总体上,同一模型的C1参数比C2参数对热点的变化更敏感。本研究为Ross-Li核驱动模型的热点效应进一步校正及热点参数的取值范围提供了依据,对Ross-Li模型的推广有重要意义,改进热点效应后的模型可用于未来国产多角度卫星的数据处理流程中,以获取加精确的地物热点反射率信息。  相似文献   

17.
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.  相似文献   

18.
Applying remote sensing techniques to develop the retrieval models and further to obtain the spatiotemporal information of water quality parameters is necessary for understanding, managing, and protecting lake ecosystems. This study aimed to calibrate and validate the retrieval models for estimating the concentrations of chlorophyll a (CCHL), suspended particulate matter (CSPM), and dissolved organic carbon (CDOC) with the in situ hyperspectral measurements in Poyang Lake, China in 2010 and 2011. The model calibration and validation results indicated that: (1) for CCHL retrieval, significantly strong and moderate correlations existed between the measured and estimated values (with the correlation coefficient r = 0.92 and r = 0.76) using the exponential model and the three-band model, respectively, with biased estimation observed for the exponential model; (2) for retrieving CSPM, there was a strong correlation between the measured and estimated values (r = 0.95) using the exponential model; and (3) no significant correlation between measured and estimated CDOC values was found with our developed models. More work is needed to allow the water quality of Poyang Lake to be accurately and steadily estimated, especially for CCHL and CDOC.  相似文献   

19.
Based on the estimating rule of the normal vector angles between two adjacent terrain units, we use the concept of terrain complexity factor to quantify the terrain complexity of DEM, and then the formula of terrain complexity factor in Raster DEM and TIN DEM is deduced theoretically. In order to make clear how the terrain complexity factor E CF and the average elevation h affect the accuracy of DEM terrain representation RMSE Et , the formula of Gauss synthetical surface is applied to simulate several real terrain surfaces, each of which has different terrain complexity. Through the statistical analysis of linear regression in simulation data, the linear equation between accuracy of DEM terrain representation RMSE Et , terrain complexity factor E CF and the average elevation h is achieved. A new method is provided to estimate the accuracy of DEM terrain representation RMSE Et with a certain terrain complexity and it gives convincing theoretical evidence for DEM production and the corresponding error research in the future.  相似文献   

20.
 This paper generalizes the Stokes formula from the spherical boundary surface to the ellipsoidal boundary surface. The resulting solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal height N 0 evaluated from Stokes's formula and the ellipsoidal correction N 1, makes the relative geoidal height error decrease from O(e 2) to O(e 4), which can be neglected for most practical purposes. The ellipsoidal correction N 1 is expressed as a sum of an integral about the spherical geoidal height N 0 and a simple analytical function of N 0 and the first three geopotential coefficients. The kernel function in the integral has the same degree of singularity at the origin as the original Stokes function. A brief comparison among this and other solutions shows that this solution is more effective than the solutions of Molodensky et al. and Moritz and, when the evaluation of the ellipsoidal correction N 1 is done in an area where the spherical geoidal height N 0 has already been evaluated, it is also more effective than the solution of Martinec and Grafarend. Received: 27 January 1999 / Accepted: 4 October 1999  相似文献   

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