HORIZONTAL ANGLES IN TRIANGULATION: SOME PRACTICAL SUGGESTIONS REGARDING THEIR OBSERVATION AND ADJUSTMENT

Abstract

MR. RAINSFORD'S paper on Directions versus Angles in the Least Squares Adjustment of Triangulation in the October 1950 issue of the E.S.R. (x, 78, 353–366) has raised some interesting points and has prompted me to put on paper my own views and some of the results of my own experience.     

THE CLARKE FORMULÆ FOR LATITUDE,LONGITUDE AND REVERSE AZIMUTH,WITH CORRECTIVE TERMS FOR USE ON VERY LONG LINES

Abstract

This extremely simple and elegant method of computing geographical co-ordinates, given the initial azimuth and length of line from the standpoint, was published by Col. A. R. Clarke in 1880. There is no other known method giving the same degree of accuracy with the use of only three tabulated spheroidal factors. Clarke himself regarded this as an approximate formula (vide his remark in section 5, p. 109, “Geodesy”); but as this article demonstrates, it is capable of a high degree of precision in all occupied lati tudes when certain corrections are applied to the various terms. These corrections are comparatively easy to compute, require no further spheroidal factors, and some of them may be tabulated directly once and for all.     

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.     

GRID BEARINGS AND DISTANCES ON THE CONICAL ORTHOMORPHIC PROJECTION

Abstract

Scale Correction Factor at a Point in Terms of X and Y.—Let dσ be a small line element of the curve ACB on the plane and ds the corresponding line element on the spheroid.     

TWO PROBLEMS OF RESECTION

Abstract

That admirable annual, The Surveyor (Ceylon), was generously forwarded to us some months ago. In this issue, vol. 2, no. 4, p. 93, there is given the solution of a question on resection in an examination paper. Since the solution appears rather laboured and the problem is interesting in itself and by no means valueless, it seems not out of place to attempt a simpler and more obvious answer.     

CADASTRAL SURVEY AND LAND RECORDS

Abstract

We regret that, owing to illness and the pressure of other demands on them in the same field, it has been necessary to interrupt the publication of the papers on cadastral subjects which Sir Ernest Dowson and Mr. Sheppard are contributing to the Review. We hope, however, to resume this valuable and interesting series in the January 1947 issue.— ED., E.S.R.     

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.     

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.     

AN OLD FILE AND A NEW ARC

Abstract

In his article “Standards of Length in Question” published in the last number of this Review (Vol. i, pp. 277–-84) Captain G. T. McCawgave us most interesting and valuable history concerning the questionable past of the international metre. He has, it may be assumed, exhausted published evidence; but he states that he can find no reference to invitations from this country to France and Holland to send their fundamental standards for comparison with others at the Ordnance Survey in the eighteen sixties.     

'Be Map Aware: Cutting-edge…Not Close to the Edge'

Abstract

An assessment is made of the accuracy of the map and written survey, which is essentially a list of land-holders and the areas held by each, and of their mutual consistency. The geometry of the map is compared quantitatively with that of the first edition (1852) Ordnance Survey 6-inch (1 : 10 560) map. The Saxton map is found to have a scale of 1 : 5140, leading to the conclusion that the perch used in the scale bar represents 7¹/₉ yards or thereabouts. The areas quoted in the written survey are consistent with acres based on this value. The positional accuracy of points on the map is found to be ～20 m, and areas of typical plots determined from the map are uncertain by between about 4 and 12%. The relationship between these two facts can be understood through a detailed study of the statistics of the errors in separations of points on the map. The written survey is found to omit a substantial number of plots of land from its listings. The map thus appears to be more reliable overall than the written survey.     

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.     

LEAST SQUARES ADJUSTMENTS OF TRIANGULATION

Abstract

Mr. Rainsford's paper in E.S.R. No. 78 establishes as thoroughly as one can wish by computational example that there is little to choose in relative accuracy between direction adjustment and angle adjustment, and that the deciding factor is really ease and speed of computation.     

COMPENSATION AS A CONSEQUENCE OF TWO KINDS OF ROCK STRUCTURE

Abstract

The following points occurred to me when reading the interesting paper on crustal equilibrium in E.S.R. No. 23. The principle of compensation or isostasy necessarily involves the idea of two different kinds of rock structure—one strong, the other weak or in extreme cases fluid; for example, there is the familiar case of the strong iceberg resisting change of shape in the liquid sea. In dealing with crustal problems of the earth then, we should make up our minds which part is to be considered as strong, e.g. the granite crust, and which part as weak or fluid, e.g. material at a depth x km. (say roo km.); by weak or fluid I mean that a possibility exists of horizontal movement.     

A NOVEL METHOD OF MEASURING THE COEFFICIENT OF THERMAL EXPANSION OF INVAR

Abstract

In a letter published in a recent issue of Nature, Prof. L. F. Bates and Mr J. C. Wilson, of University College, Nottingham, have described a new and novel method of determining the coefficient of thermal expansion of invar. Although this method is hardly likely to be applied to the measurement of the coefficient of expansion of long invar tapes, such as are used by surveyors, yet it is so novel and ingenious in itself that a short reference to it may not be out of place in this Review. One extremely interesting thing about it is that no measurements of a length, or of changes of length, are involved.     

THE FIXATION OF MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

The fixation of Minor Triangulation in a Primary system does not, in general, warrant rigorous adjustments of figures; less laborious methods are desirable. For Secondary work a least square adjustment to approximate coordinates is quite sufficient, while, for Tertiary, graphical solutions are amply accurate. Apart from that, cases may arise to which a figure adjustment is not applicable, as in the small net shown in Fig. 2, p. 464. The line BC cannot be equated to the line AB in the ordinary way since it is not the side of a triangle. In this case an adjustment to approxima te coordina tes will overcome the difficulty.     

SURVEY IN THE GREAT WAR

Abstract

Artillery Survey.—Included in the term “Artillery Survey are two distinct problems, the first that of determining the “line” and “range” at which fire should be opened, and the second that of laying the gun in the required line. To appreciate these problems it. is necessary to know a little about the technique of gunnery, and for the benefit of those who have no acquaintance with the subject the following brief résumé may be given.     

LENGTH AND AZIMUTH OF LONG LINES ON THE EARTH

Abstract

In the E.S.R., viii, 59, 191–194 (January 1946), J.H. Cole gives a very simple formula for finding the length of long lines on the spheroid (normal section arcs), given the coordinates of the end points. In the course of the computation the approximate azimuth of one end of the line is found, the error over a 500-mile line being of the order of 3″ or 4″. If the formula is amended so that the azimuth at the other end of the line is used in computing the length of the arc, the error is then less than 0″·1 over such a distance. An extra term is now given which makes this azimuth virtually correct over any distance. Numerical tests show that Cole's formula for length and the new one for azimuth are very accurate and convenient in all azimuths and latitudes.     

Individual tree crown segmentation in tropical peat swamp forest using airborne hyperspectral data

Abstract

Individual tree crown segmentation is important step for deriving various information for fine-scale analysis of ecological process. However, only several studies have applied tree crown segmentation in tropical forest ecosystems, especially in mixed peat swamp forests. In this study, hyperspectral data were used to detect changes in the biochemical and biophysical characteristics, which are important factors for tree crown segmentation. Principal Component Analysis method was performed to investigate its influence on crown segmentation. Visually Selected PCs, 160 PCs and 160 Spectral Bands image were used and two segmentation techniques; Watershed Transformation and Region Growing segmentation were applied on those images. The highest accuracy was achieved for the crown segmentation is using Region Growing segmentation, based on 1:1 measurement, D value and RMSE value. The results obtained from 160 PCs image using region growing algorithm shows better accuracy with D value of 0.2 (80% accuracy, 20% error) and RMSE of 9.9 m².