Harmonic analysis of total electron contents time series: methodology and results

In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of ω _i  = 2πi are modulated with the annual signal harmonics of ω _j  = 2πj/365.25 as ω _ijM  = 2πi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.     

On Definition of Geograghic Variable Scaling

IntroductionThe map is a basic form of geographic informationvisualization[1]. To provide space attributes or geo-graphic orders is the basic function of a map. Incartography, according to the different measure ofphenomenal quantitative attribute, four fo…     

Le projet gradio et la determination a haute resolution du geopotentiel

Résumé Une des techniques de détermination fine et globale du champ de gravitation terrestre U est la gradiométrie spatiale, dans laquelle on mesure à bord d'un satellite sur orbite basse certaines combinations linéaires des composantes du tenseur ∂² U/∂x_i ∂x_j dans des axes {x _i } liés au satellite. Un tel projet, appelé GRADIO, est actuellement à l'étude en France et pourrait aboutir à partir de 1990. Après avoir rappelé les objectifs scientifiques d'une telle mission, nous en donnons les spécifications—étayées par une série d'études analytiques; nous définissons ensuite le satellite porteur et ses caractères techniques, en insistant sur les points délicats de la faisabilité (facteurs d'échelle des micro-accéléromètres constituant l'appareil, connaissance de l'attitude...) et en présentant des idées de solution en cours d'approfondissement.

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Summary Satellite gradiometry arises as one of the methods for improving our knowledge of the global Earth gravity field at high resolution: by means of micro-accelerometers on board a low orbiting spacecraft, linear combination of the gravity tensor components ∂² U/∂x_i ∂x_j are measured in a satellite-fixed reference frame {x _i }. Based on this technique, a project named GRADIO is presently under study in France and could fly in 1990 at the earliest. After the scientific objectives of that experiment have been reviewed, the measurement specifications are given as coming from various analytical studies. The platform and its characteristics are then defined: the critical realization problems (scale factors of the micro-accelerometers, spacecraft attitude control and restitution) are pointed out together with some ideas for their solution which are under analysis and require further study.

     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

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.     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

In the course of his stimulating and suggestive paper in your recent issue, No. ro, pp. 226–38, Mr. A. J. Potter writes on p. 233 “but there is no simple construction by which X can then be found”, and again on p. 237 “a direct construction, if there be such”. This cheerful challenge invites the construction of a circle centred on a given line, passing through a given point thereon, and touching a given circle, and I have found the lure of Mr. Potter's gauntlet as irresistible as its recovery has proved delicate. In order to shoulder responsibility and by no means to claim highly improbable originality, let me confess that the problem is new to me and the two constructions I offer are my own; I venture to hope that Mr. Potter may consider one or other of them not unworthy of his epithet “simple”, though I freely admit the aptitude of his empiric procedure to its purpose. The proofs are not long, but for fear of overshooting my welcome I offer them to anyone for the asking; and for the same reason my diagrams are small and therefore mere.     

CONNECTION OF INDIA,SIAM AND MALAYA TRIANGULATIONS

Abstract

In an article in the Review of October 1938, iv, 30,450-457, under the heading “Geographical Positions in Malaya and Siam”, Mr. A. G. Bazley gives a comparison of the Indian and Siamese, and Siamese and Malaya, triangulations at common points and discusses the possibility of an error in the longitude of the datum of the Malayan system. In the Review of April, 1939, v, 32, 112-113, he has elaborated certain points, and remarks in connection with the doubt in the longitude of the Malayan datum that connection of the F.M.S. network with that of Siam and India, and some more latitude and longitude observations by the F.M.S. Survey, are essential to a satisfactory solution of this rather involved problem. Since the above article was written, a lot more infornlation has become available about the Indo-Siamese triangulation connections and a firm connection between the triangulations of Sianl and Malaya has been established in 1946. It is hoped that a review of the present position would be of interest, especially as the various links effected open up a definite possibility of a continuous chain of triangulation from India to Australia.     

NORMAL EQUATIONS RESOLVED BY APPROXIMATION

Abstract

We are indebted to Professor R. V. Southwell for the approximate method of computation known as the systematic relaxation of constraints. In an article to the Empire Survey Review, 1938, Mr A. N. Black showed how Southwell's ideas could be applied to the adjustment of the co-ordinates of a point.     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

At the suggestion of Mr. T. H. Corfield, who has himself given two solutions (E.S.R., No. 12, pp. 345–6) of Mr. A. J. Potter's problem, I venture to submit a third solution, which has at least the merit of simplicity.     

COMPILATION OF THE LAND REGISTER OF ENGLAND AND WALES

Abstract

Skillfully as those charged with the shaping and conduct of the crowded time-table of the Conference of Commonwealth Surveyors in 1947 managed their difficult task, physical inability to squeeze many good gallons’ measure into a pint pot relentlessly closured discussions and allowed no opportunity to collect and appraise the yield in any vat on the spot. We were very sensible of these effects in relation to our own and other papers on Land Registration. Our own paper too—owing to transient circumstances which overlapped the Conference—had to be presented in the stodgy form of a synopsis and—through accidents of travel—only reached some delegates, whose comments were particularly desired, on the eve of its presentation. Nevertheless the generous reception accorded to this and other ‘papers on the subject and the many stimulating points that were raised in their discussion, limited though this was, call’ for further consideration and digestion if the resultant lessons are to be elicited and put to practical use. We have, therefore, sought the approval of the Editor of this Review to pursue this purpose, so far as space permits, in this and later numbers. Our remarks should be read in conjunction with the relevant portions of the Proceedings of the Conference which are in the press but are not expected to be available for some months yet. We have especially in mind the observations of the following speakers: Mr. G. H. Curtis, Chief Land Registrar, H.M. Land Registry, London; Mr. John Dewar, previously Surveyor-General of Malaya; Mr. R. G. Dick, -Surveyor-General of New Zealand; Lt.-Col. Elkington, Divisional Officer, Ordnance Survey Office, London; Mr. F. M. Johnstone, Surveyor-General of the Commonwealth of Australia; Mr. E. A. Malby, Chief Superintendent Mapping Branch, H.～. Land Registry; and Major-General M. N. MacLeod, previously Director- General of the Ordnance Survey.     

ROAD LOCATION IN FOREST COUNTRY

Abstract

THE very interesting article on “Road-surveying in the East” by J. N. List appearing in NO. 6 of the Review suggests that the following notes on the methods of road location used in the Gold Coast may be of interest. These methods enter into considerably more detail than those described by Mr. List and are of proved economic value.     

A TEST OF AUTO-COLLIMATION

Abstract

In the July 1940 issue of the Empire Survey Review Mr A. V. Lawes contributes a valuable article, “The Application of the Gauss Method of Collimation to the Adjustment of Survey Instruments”. One section of the article describes four methods of adjusting collimators at solar focus, in other words of assuring that the emitted rays are parallel or that the target appears at an infinite distance. Mr Lawes rightly claims that auto-collimation is the most accurate of the four methods, and he warns readers that “the reflector used in this method must be as perfect optically as the objective”. However, he fails to give any method of testing the result obtained by following his directions, and experience suggests that auto-collimation may give a result considerably in error even though the reflector may with some justification be presumed to be good.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour.     

TRAVERSE ADJUSTMENT: WHY NOT LEAST SQUARES?

Abstract

In the above article by Mr H. L. P. Jolly published in a previous issue (E.S.R., vol. iv, no. 28) the author, after referring to the precision of the Nigerian traverses, makes the statement that measurements of the highest accuracy are worthy of the best possible methods of adjustment. But this argument cuts both ways. For in general the greater the accuracy of measurement the smaller will be the ultimate misclosure to be eliminated; so that different methods of adjustment will produce smaller and smaller variations in the corrections, until in the limit when there is no error we should obtain the same result however much latitude we permitted in the adjustment.     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

GEOGRAPHICAL POSITIONS IN MALAYA AND SIAM

Abstract

Malaya.—The geographical positions of points in the “Primary Triangulation of Malaya”, published in 1917, depend upon latitude and azimuth determinations at Bukit Asa and on the longitude of Fort Cornwallis Flagstaff, Penang, the latter being supposed to be 100° 20′ 44″.4 E. This value was obtained by Commander (later Admiral) Mostyn Field in H.M.S. Egeria 1893, by the exchange of telegraphic signals with Mr Angus Sutherland at Singapore, Old Transit Circle. The longitude, 103° 51′ 15″.75 E., accepted for Singa- pore in order to arrive at this determination of Fort Cornwallis Flagstaff, was based upon that of an Observation Spot, 103° 51′ 15″.00 E., fixed in 1881 by Lieutenant Commander Green, United States Navy, by meridian distance from the transit circle ofMadras Observatory, the corresponding longitude of the latter being taken as 80° 14′ 51″.51 E.     

DIRECTIONS AND ANGLES IN A SIMPLE CHAIN

Abstract

Mr. Rainsford's article on “Least Square Adjustments of Triangulation: Directions versus Angles” in the Empire Survey Review No. 78, Vol. x, October 1950, leads to many speculations and interesting results. I try to show here, how, by assuming artifices to simplify the results, weights may be assigned to angles derived from directions so that the results of adjustment by angles, with these weights, will be the same as the adjustment by directions, all of equal weight.     

INTERPOLATING FROM TRAVERSE TABLES TO SECONDS

Abstract

In the Empire Survey Review, no. 4, 1932, Mr. Clendinning has described a method of interpolating from traverse tables to seconds. Below is another method, due to Prof. Nekrassov, for use with traverse tables published by him. The method is described in The Geodezist, Moscow, 1936, no. I, pp. 47–52.