GPS radio occultation measurements on ionospheric electron density from low Earth orbit

Since the proof-of-concept GPS/Meteorology (GPS/MET) experiment successfully demonstrated active limb sounding of the Earth’s neutral atmosphere and ionosphere via GPS radio occultation (RO) from low Earth orbit, the developments of electron density (n _e) retrieval techniques and powerful processing systems have made a significant progress in recent years. In this study, the researches of n _e profiling from space-based GPS RO observations are briefly reviewed. Applying to the Formosat-3/Constellation Observing System for Meteorology, Ionosphere and Climate (FS3/COSMIC) data, we also present a compensatory Abel inversion technique including the effects of large-scale horizontal gradients and/or inhomogeneous ionospheric n _e obtained from an improved near real-time phenomenological model of the TaiWan Ionospheric Model. The results were evaluated by the ionosonde foF2 and foE data and showed improvements of rms foF2 difference from 29.2 to 16.5% in relative percentage and rms foE difference from 54.2 to 32.7% over the standard Abel inversion.     

非球形冰晶的毫米波k-Ze关系研究

针对毫米波雷达处理数据的实际需要,应用离散偶极子近似法DDA,获得了非球形冰晶的后向散射及衰减截面并进行了参数化,并主要基于细化的冰云模型,假设冰晶粒子谱为Γ分布,通过模拟取样各1330次（代表1330种粒子分布）,分别计算得到了W波段（94 GHz）与Ka波段（35 GHz）毫米波雷达探测的冰云衰减系数k及雷达反射率因子Z_e,而且利用数值模拟的方法,建立了k-Z_e关系的具体表达式。计算表明,非球形和非瑞利散射对W波段毫米波雷达衰减的影响较大,而且在同样滴谱分布条件下,W波段毫米波雷达的衰减比Ka波段毫米波雷达的大几倍,此外细化的冰云模型对k-Z_e关系具有影响。本研究对中纬度非降水性冰云的毫米波雷达的衰减订正具有参考价值,并对中国的毫米波雷达应用具有借鉴作用。     

On the approximation of external gravitational potential with closed systems of (trial) functions

Summary Let S be the (regular) boundary-surface of an exterior regionE _e in Euclidean space ℜ³ (for instance: sphere, ellipsoid, geoid, earth's surface). Denote by {φ_n} a countable, linearly independent system of trial functions (e.g., solid spherical harmonics or certain singularity functions) which are harmonic in some domain containingE _e ∪ S. It is the purpose of this paper to show that the restrictions {ϕ_n} of the functions {φ_n} onS form a closed system in the spaceC (S), i.e. any functionf, defined and continuous onS, can be approximated uniformly by a linear combination of the functions ϕ_n. Consequences of this result are versions of Runge and Keldysh-Lavrentiev theorems adapted to the chosen system {φ_n} and the mathematical justification of the use of trial functions in numerical (especially: collocational) procedures.     

INTERVISIBLE FEATURES

Abstract

It is frequently required to find whether a feature A of height h ₀ will interrupt the view between two other features A₁ and A₂, of heights h ₁ and h ₂ respectively. Suppose that the right line from A₁ to A₂, whose zenith distance is ζ at A₁, has a height h at A; it is then obvious that no more is necessary than to compute h and compare it with the known height h ₀ of the feature A.     

机载激光雷达数据分析与反演青海云杉林结构信息

利用机载激光雷达点云数据,计算了9种度量指标,并将其分为冠层的高度指标、结构复杂度指标和覆盖度指标。利用高度指标和结构复杂度指标,结合大量实测单木结构与年龄估测数据,从样点和区域尺度分别分析了青海云杉林冠层垂直结构分布,分析得知实验区内主要以中龄林和成熟林为主,冠层垂直分布复杂程度偏低,高度分化程度一般。通过回归分析发现首次回波覆盖度指标FCI与实测的有效植被面积指数PAI_e有良好的相关性（R²=0.66）,在此基础上基于辐射传输模型反演了实验区内PAI_e的水平分布,且用实测数据验证发现反演的PAI_e略高于实测值（R²=0.67）,绝对平均误差为0.65。分析结果很好地反映了激光雷达在森林空间结构信息提取方面的应用潜力。     

Global and local methods for tracking the intersection curve between two surfaces

At present, the modelling of terrain edges from discrete data clouds {x,y,z} is one of the ‘hot topics’ in the processing of laser scanning data. This paper proposes two different methods for the three-dimensional modelling of terrain edges. Common to both methods is the idea to describe the terrain edge as the intersection line of two surface patches z_i=z(x,y), i=1,2. The first method is based on numerical integration of a differential equation describing the intersection line. The second method uses the snakes algorithm for the identification of the terrain edge. Both methods are tested for synthetic and real-world data examples, which shows that they are suitable for the practical extraction of edges from laser scanning data.     

A SIMPLE PROPOSITION lN,TRIGONOMETRICAL SURVEY AND ITS USES

Abstract

1. The proposition which expresses in terms of the three sides the rate of change of the angle at the vertex of a triangle whose base is stationary and whose vertex is given a small displacement is an important one in plane survey. It must have beeJ1.known to some surveyors for a century or more but there is no doubt that even to-day it is not widely known. This, too, in spite of its extreme simplicity, which makes it, once known, impossible to forget. It's discoverer is unknown to the writer, who was somewhat intrigued to discover it for himself about 25 years ago in the course of field operations of the kind described in § V hereafter. The probability is that many people have discovered it independently.     

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     

A new method for computing the ellipsoidal correction for Stokes's formula

 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     

MACHINE METHOD OF INTERSECTION

Abstract

The following method will be found better and quicker than the usual logarithmic process in computing the co-ordinates of intersected points in minor triangulation and traverse work. Let A and B be two stations whose co-ordinates (x ₁ y ₁), (x ₂ y ₂) are known. Let P be an intersected point whose co-ordinates (x, y) we wish to determine. Let α and β be the observed angles at A and B respectively.     

Equatorial radius of the Earth: A dynamical determination

An intrresting variation on the familiar method of determining the earth's equatorial radius a_e, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142±5 meters. The associated parameters are GM=3.986005±.000004 × 10²⁰ cm³ sec-⁻² which excludes the relative mass of atmosphere ≅10⁻⁶ ξ GM, the equatorial gravity γ_e 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction is more directly, orless indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f=1/298.255.     

Assessing soil salinity using WorldView-2 multispectral images in Timpaki,Crete, Greece

Salinization is one of the major soil degradation threats occurring worldwide. This study evaluates the feasibility of operational surface soil salinity mapping based on state-of-the-art Earth Observation (EO) products captured by sensors on-board WorldView-2 (WV2) and Landsat 8 satellites. The proposed methods are tested in Timpaki, south-central Crete,Greece, where brackish water irrigation puts soil health at risk of soil salinization. In all cases, EO products are calibrated against soil samples collected from bare soil locations. Results indicate a moderate correlation of observed EC_e values with the investigated remote sensing parameters. Regarding sensitivity to saline soil, the yellow band displays higher values. Comparison between methods used in the literature shows that those developed specifically for soil salinity, and especially index S5, perform better. The proposed ‘detection index’ and 3D PCA transformation methodology perform reasonably well in detecting areas with high EC_e values and provide a simple and effective operational alternative for saline topsoil detection and mapping.     

LONG LINES ON THE EARTH

Abstract

The Arc of the Geodesic.—In the first part of this paper a method was given for computing the azimuth of a geodesic. The method gives the convergence of the geodesic correctly up to the second power of e the eccentricity. The formula (9), however, also depends on the assumption that σ, the arc-length of the geodesic, can be obtained with sufficient accuracy from the Supplemental Dalby Theorem, that is to say, by a purely spherical computation. It is, therefore, needful to show that this supposition is justifiable; a means must in fact be indicated for verifying the assumption.     

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.     

Application of 3D triangulations of airborne laser scanning data to estimate boreal forest leaf area index

We propose 3D triangulations of airborne Laser Scanning (ALS) point clouds as a new approach to derive 3D canopy structures and to estimate forest canopy effective LAI (LAI_e). Computational geometry and topological connectivity were employed to filter the triangulations to yield a quasi-optimal relationship with the field measured LAI_e. The optimal filtering parameters were predicted based on ALS height metrics, emulating the production of maps of LAI_e and canopy volume for large areas. The LAI_e from triangulations was validated with field measured LAI_e and compared with a reference LAI_e calculated from ALS data using logarithmic model based on Beer’s law. Canopy transmittance was estimated using All Echo Cover Index (ACI), and the mean projection of unit foliage area (β) was obtained using no-intercept regression with field measured LAI_e. We investigated the influence species and season on the triangulated LAI_e and demonstrated the relationship between triangulated LAI_e and canopy volume. Our data is from 115 forest plots located at the southern boreal forest area in Finland and for each plot three different ALS datasets were available to apply the triangulations. The triangulation approach was found applicable for both leaf-on and leaf-off datasets after initial calibration. Results showed the Root Mean Square Errors (RMSEs) between LAI_e from triangulations and field measured values agreed the most using the highest pulse density data (RMSE = 0.63, the coefficient of determination (R²) = 0.53). Yet, the LAI_e calculated using ACI-index agreed better with the field measured LAI_e (RMSE = 0.53 and R² = 0.70). The best models to predict the optimal alpha value contained the ACI-index, which indicates that within-crown transmittance is accounted by the triangulation approach. The cover indices may be recommended for retrieving LAI_e only, but for applications which require more sophisticated information on canopy shape and volume, such as radiative transfer models, the triangulation approach may be preferred.     

THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

Impact of land-cover layout on particulate matter 2.5 in urban areas of China

ABSTRACT

Urbanization in China is closely connected with ambient particulate matter 2.5 (PM_2.5). However, the potential for altering PM_2.5 through the urban landscape characteristics is uncertain. In this study, we analyzed the urban PM_2.5 pollution situation for 2014–2016 and investigated the impact of landscape factors on urban PM_2.5 in China at the city level. All the prefecture-level cities were stratified by urban population size into small (<500,000), medium (500,000–1,000,000), and large (>1,000,000), and the other second-level administrative cities were assigned as ‘other’ cities. The multivariate regression model including both urban landscape factors and social-economic variables explained 70.0%, 32.8%, 19.2%, and 12.4% of the arithmetic mean PM_2.5 concentration (AMC-PM_2.5) for the other, small, medium, and large cities, respectively. With regard to the configuration of land cover, agricultural activity is a major contributor of PM_2.5 pollution, for which the explanatory power ranged from 7.6% (for the large cities) to 64% (for the other cities). In addition, grassland aggregation also has a limited but negative effect on urban PM_2.5 pollution, despite the negligible effect on dry deposition. Overall, these findings likely reflect the interaction between urban air quality and urbanization, and will have implications for air quality control strategies.     

CORRECTION TO BEARING FOR HEIGHT OF SIGNAL

Abstract

When a beacon B _h stands on a mountain of height h, the bearing of B _h as seen from another station A is in general affected by its elevation. The correction never exceeds one second of arc, but in primary triangulation it is not always negligible.     

THE ORTHOMORPHIC PROJECTION OF THE SPHEROID

Abstract

Chesterton did not, of course, intend this gibe to be taken literally. But the more we consider what he would doubtless have called the “Higher Geodetics”, the more we must conclude that there is some literal justification for it. Not only are straight lines straight. A sufficiently short part of a curved line may also be considered straight, provided that it is continuous (i.e. does not contain a sudden break or sharp corner), and provided we are not concerned with a measure of its curvature. Similarly a square mile or so on the curved surface of the conventionally spheroidal earth is to all intents and purposes flat. We shall achieve a considerable simplification, without any approximation, in the treatment of the present subject by getting back to these fundamental glimpses of the obvious, whether the formalists and conformalists accept them or not.     

Determination of complexity factor and its relationship with accuracy of representation for DEM terrain

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.