Surveying & Prospection for Archaeology & Environmental Science Topographic Surveying & Feature Mapping Phil Buckland

Contents Topographic survey & feature mapping Equipment - introduction Coordinates & Trigonometry - the basic maths of triangles Surveying in practice Alternative data acquisition (briefly)

Topographic survey & feature mapping Topographic survey - create a cartographic representation of landscape features - coordinate data (x,y,z - or variants of) - detail (scale/resolution) defined by project aims - end product usually a 2D contour map (but 3D models becoming more common) - field techniques improve realism/accuracy

Topographic survey & feature mapping Feature mapping (objects) - site specific, many variations - locate & relate objects/areas spatially - includes attribute data on objects (object type, name etc.) as well as coordinates. This is a key feature of GIS - end product often a 2D map or 3D model - can overlay on topographic maps

Equipment - introduction Three groups used (in this course): - Levels (dumpy level, theodolite) - Total Stations (EDM - Electronic Distance Measurers) - GPS (Global Positioning System)

Equipment - introduction

Coordinates Relate points/objects together in space - in a plane (horizontal) - vertically (height) Using coordinates (e.g. x,y,z) with the help of angles and distances Bearing = angle relative to reference direction (e.g. North, grid North...)

Coordinates in a plane Cartesian coordinates Perpendicular axes Origin at (0,0) Coordinates increase right & up of origin Coordinates decrease down & left of origin Descarte (1637) (0,0) x

Coordinates in a plane Cartesian coordinates Coordinates of point given by bracketed pairs of numbers: (right,up) (0,0) x (3,4) x (-3,-2) x (x,y) (Easting,Northing) -depending on coordinate system used

Coordinates in a plane Often easier to avoid negative values by increasing origin coordinates + + (1000,1000) x (1004,1006) x (1001,1002) x (998,999) x NOTE: Some countries (incl. Sweden) use on maps: y=East x=North Others use opposite (e.g. (England, USA) We’ll use (Easting,Northing)

Finding Coordinates p0 x p1 x Find coordinates of p1 in relation to p0 Easting Northing

p0 x p1 x Reference bearing (N) Measuring in a plane Instrument p0 (instrument) has known coordinates (0,0) for the moment reference bearing is known (N) p1 has a unknown coordinates

Finding Coordinates ө Northing = d cos(ө) Easting = d sin(ө) Use instrument to measure: d - (horizontal) distance p0-p1 ө - angle between North & bearing of p1 from p0 p0 p1 x Reference bearing (N) ө = bearing from reference d = distance from p0 to p1 Theta d with trigonometry... Polar Coordinates

Finding Coordinates ө Northing = d cos(ө) Easting = d sin(ө) p0 x p1 x Reference bearing (N) d 10m 36.87° Easting = d sin(ө) = 10 sin(36.87) = 10*0.6 = 6m Northing = d cos(ө) = 10 cos(36.87) = 10*0.8 = 8m ө also called the azimuth

Finding Coordinates ө Northing = d cos(ө) Easting = d sin(ө) p0 x p1 x Reference bearing (N) d 10m 36.87° (6,8) p1(Easting) = p0(Easting) + (d sin(ө)) p1(Northing) = p0(Northing) + (d cos(ө)) So if p0=(1000,1000) then p1(Easting,Northing) = (1006,1008)

Trigonometry ө distance (d) Hypotenuse Abscissa Opposite Tip: abscissa = ‘adjacent’

Trigonometry ө distance (d) Hypotenuse Abscissa Opposite Tip: abscissa = ‘adjacent’ SOHCAHTOA

Trigonometry - checking ө distance (d) Hypotenuse Abscissa Opposite Use Pythagoras theorem: a 2 +b 2 =c 2 Opposite 2 +Abscissa 2 =Hypotenuse 2

Trigonometry - checking ө distance (d) Hypotenuse = 10 Abscissa = 8 Opposite = 6 Use Pythagoras theorem: a 2 +b 2 =c 2 Abscissa 2 +Opposite 2 =Hypotenuse = =100

Measuring height (Level) Objekt Instrument height ( I h) Signal height (Sh) Object height (Z) = Instrument height - Signal height + Known height Object height (Z) relative known height Known height (benchmark) = Ih - Sh + p0 height p0 p1 horizontal distance (d) Remember: Instrument must be able to see base of signal staff.

Measuring height (Total Station) Instrument height ( I h) Signal height (Sh) Object height (Z) relative known height Station height (Stn Z) p0 p1 horizontal distance (Hd) angled distance (Ad) vertical angle ( ө )

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography Survey points define resolution/accuracy of final map...

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography Survey points define resolution/accuracy of final map... Can interpolate - i.e. smooth between the points And extrapolate - i.e. extend beyond the points

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography Survey points define resolution/accuracy of final map... Can interpolate - i.e. smooth between the points And extrapolate - i.e. extend beyond the points

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography Can interpolate - i.e. smooth between the points And extrapolate - i.e. extend beyond the points But can never compensate for bad choice of survey points! GIGO: Garbage In - Garbage Out

Surveying in practice Using levels Radial method: position instrument centrally to survey points N object topography

Surveying in practice Using levels Traverse: a continuous series of lines of measured distance. angles & distances allow points to be located p0 N angles measured relative to previous bearings angles always clockwise p1 p2 p3 p4 p5

Surveying in practice Using levels Traverse: a continuous series of lines of measured distance. Use closed traverse for extra accuracy - errors check by trigonometry p0 N p1 p2 p3 p4 p5 p6

Surveying in practice Using levels Combining methods: Large areas of topography & features can be surveyed using radial, differential levelling & traverse methods together p1 p3 p4 p5 p6 p3 p0

Surveying in practice Using levels Differential Levelling: determining the difference in elevation between points on a transect. p0 p1 backsight foresight backsight foresight backsight foresight backsight foresight pA pB pC p0 = known point (benchmark)

Surveying in practice Using levels Differential Levelling: can be used to survey topography (or other) transects p0 p1 p0 = known point (benchmark)

Surveying in practice Using levels Differential Levelling: can be used to survey topography (or other) transects More efficiently with use of intermediate sights p0 p1 p0 = known point (benchmark) BSIS FS

Useful concepts Break of slope (break in slope; slope break) - dramatic change in angle (or tangent of curve) - usually best place to put staff 123

Useful concepts Break of slope (break in slope; slope break) - dramatic change in angle (or tangent of curve) - usually best place to put staff Think in triangles (preferably in 3D)

Useful concepts Break of slope (break in slope; slope break) - dramatic change in angle (or tangent of curve) - usually best place to put staff Think in triangles (preferably in 3D)

Useful concepts Break of slope (break in slope; slope break) - dramatic change in angle (or tangent of curve) - usually best place to put staff Think in triangles (preferably in 3D) AND Practicalities!

Useful concepts Different angle measurements degrees: trigonometry, common usage full circle = 360° gradians: surveying, engineering full circle = 400 gon (or grad) radians: mathematics, physics, Excel full circle = 2π rad

Useful concepts degrees: full circle = 360° 0° 45° 90° 135° 180° 225° 270° 315° gradians: full circle = 400 gon (also called ‘grad’) 0grad 50gon 100gon 150gon 200gon 250gon 300gon 350gon radians: full circle = 2π rad 0 rad 1.75π rad π rad 0.5π rad 0.25π rad 0.75π rad 1.5π rad 1.25π rad

Useful concepts Conversion between angle measures: gon to degrees: use DRG► (or DEG etc) button on calculator gon to radians:

Useful concepts Conversion between angle measures: In Excel: Excel uses radians in formulae (e.g. =sin(), =cos(), =tan()) =RADIANS(angle_in_degrees) degrees to radians: =RADIANS(angle_in_gon/400*360) gon to radians:

Alternative data acquisition Orthophotos - geometrically corrected aerial photographs GPS surveying - varying degrees of accuracy Satellite data - elevation; infra-red etc.; with image analysis can be used to differentiate land use & more Existing maps - ordinance survey; historical All have their uses - can be combined with survey data using GIS software (e.g. ArcGIS) (although corrections may be needed) Aerial photographs

Alternative data acquisition Prospection data - spatial sample data