Geog258: Maps and GIS
Midterm Review
February 1ST WED,
2006
Exam here on February 6th Monday
50 minutes
20 multiple choice and 2 short essay questions of your choice (test whether you understand broad concept)
Bring bubble sheet, blue book, pencil and eraser
Bring calculator if you want to; questions can be answered without calculator (simple multiplication and division is involved in one or two questions)
1. Introduction
to the Map
Definition of maps
Graphic representation of surroundings
Three defining characteristics of maps
(1) map scale (2)
map (cartographic) abstraction (3) map projection
A map is a model of reality: reduced, abstracted, and flattened version of reality
Ø Map scale: how much the ground is reduced into the map
Ø Map abstraction: selecting relevant details (selection), simplifying its appearance (simplification), classifying its value (classification), and portraying the reality with proper symbol (symbolization)
Ø Map projection: round earth is transformed into flat map
Mapness continuum
Maps showing the same area can lie along mapness continuum based on defining characteristics of maps. For example,
aerial photo: none of the three
orthophoto: map scale, map projection
topographic map: map scale, map projection, map abstraction
Kinds of maps
Ø Mental map: maps in mind, internal (egocentric) representation of space, human perception of surroundings, highly subjective, combination of direct and indirect experience forms mental map, base of environmental perception, and related decision making, distinct from cartographic map, in this class we confine the map into cartographic map
Ø Reference map: account of location of features (e.g. Atlas)
Ø Thematic map: portrayal of a specific theme (e.g. world climate map)
Ø Navigation map: map helping navigation (e.g. nautical charts)
Ø Persuasive map: propaganda tools taking advantage of power of visual
2.
Geographic Data
Nature of environments
Human concepts lie between environment and its representation on the map
Building blocks of human conceptualization of environment include
Ø Continuous field vs. discrete object: some phenomena is continuous (hard to measure its spatial dimension e.g. temperature) while some phenomena is discrete (easy to measure its spatial dimension e.g. land parcel). It needs different handling for representation
Ø Dimensionality of discrete object: if the geographic phenomenon is discrete, spatial dimension is easily identified; categorized into zero-dimension (point), one-dimension (line), and two-dimension (area). Zero-dimension has only location, one-dimension has location, length, and direction, and three-dimension has location, length (perimeter), area, shape, compactness and so on.
Ø Three components of geographic data: we can identify space, time, and attribute of every geographic phenomenon portrayed on the map; data is collected at some point of time, the map has its study area, and it portrays some attribute. The attribute can be measured in different measurement scales (see Level of Measurement)
Level of measurement
Attribute can be measured in varying levels of details, in the order of nominal, ordinal, interval, and ratio.
Ø Nominal: can’t order values, values are most likely to be category or type
Ø Ordinal: can order values
Ø Interval: know the difference between two values, but no original point revealed
Ø Ratio: original point is known
For example, cancer mortality rate can be measured in nominal scale if the map only shows critical versus non-critical, can be measured in ordinal scale if the map shows the rank of values only, and can be measured in ratio if the map shows mortality rate values
3.
Cartographic Abstraction
Classification
If attribute values are measured in numeric scale (interval and ratio), a range of values will be very large. Assigning different symbols to a complete range of values may be too much detail to map readers. Classification allows map makers to reduce details while gaining an interpretative power given that map readers are more interested in general impression of geographic distribution of values. Different classification schemes can be used. However, using different classification schemes lead to totally different impression of geographic distribution of values mapped. The classification schemes include
Ø Equal intervals: break values into groups divided in equal interval; division of class has nothing to do with data distribution since it’s simply arbitrary
Ø Natural breaks: break values into most natural subgroups; it’s most intuitive and desirable in that it takes into account data distribution
Ø Quantiles: put the equal number of observations into classes; it usually flattens values around mean
Ø Standard deviation: obtain mean and standard deviation from attribute values, and break values into groups based on adding or subtracting the deviation from the mean
Symbolization
Maps use different kinds of map symbols based on the level of measurement of attribute mapped.
Ø Different kinds of map symbols include shape, size, color {hue, value, saturation}, and pattern {arrangement, orientation, texture}: please see lecture note for graphics
Ø If the level of measurement is qualitative (nominal), distinguishing types of map symbols should be used
Ø If the level of measurement is quantitative (ordinal, interval, ratio), ordering types of map symbols should be used
Ø Distinguishing type of map symbols include shape, color-hue, pattern-arrangement, pattern-orientation
Ø Ordering type of map symbols include size, color-value, color-saturation, pattern-texture
Ø If the dimensionality of symbol is area (2-dimension), size and shape can’t be used as it distorts geometry
4. Map Scale
Map scale is the ratio of map distance to earth distance; it tells you how much the map reduces the ground. For example, 1:63,360 means that 1 inch on the map corresponds to 63,360 inch on the ground. As 63,360 inch equals 1 mile, you can say that 1 inch on the map represents 1 mile on the ground. With scale bar and ruler, you can derive map scale. For example, if you want to know distance between two points, measure the distance by a ruler between point A and point B, and place the measurement marked on your ruler (A) over graphic bar. The corresponding distance on the graphic bar (B) is the real distance. A: B in the same measurement unit will give you map scale.
5. Remote
Sensing
Remotely sensing allows us to collect the image of geographic features without direct contact. It can be taken by camera mounted on aircraft (aerial photographs), and by scanners mounted on satellite (satellite image). Its output is called remotely sensed image. Interpreting the image is equivalent to understanding the principle of how things are seen by sensors (like human eyes). What you see is actually electromagnetic energy that interacts with objects.
Spectral signature and image interpretation
Different features (vegetation, soil, water, snow) interact with electromagnetic energy differently. Moreover, the way in which features interact with electromagnetic energy differs as a function of wavelength. Therefore, images taken by different spectral bands will have different appearances. For instance, pancromatic image obtained from green band (such as TM band 2 of Landsat 7) will have darkish look for vegetation. Panchromatic image taken from near infrared band will record high intensity in the area where vegetation is lush because it has high reflectance in that band.
True-color vs. false-color image
You can obtain color image by combining images taken from different bands in the same way human eyes recognize color by combining energy reflected differently across a range of wavelengths in visible bands. If RGB colors are assigned to images from RGB bands respectively, it becomes true-color image, emulating the image perceived by human eyes. Otherwise (RGB colors are arbitrarily assigned to images from any three bands), the image would not look like the one seen from eye, yielding false-color image.
Passive vs. active remote sensing system
Remote sensing can be divided into two systems – active and passive – depending on whether sensors are reliant on external energy sources. Passive remote sensing is reliant on external energy sources (most commonly solar energy), thus it can record the image at night. On the other hand, active remote sensing system can collect data even at night because it sends out its own energy source (most commonly microwave) and it receives the energy reflected by terrestrial objects. A collection of remote sensing system that uses microwave as an energy source is called Radar imaging. One other advantage of Radar imaging is that it can record the image regardless of weather condition because microwave can pass through the atmosphere very well. Thus, Radar sensor can collect information all night and all weather.
Resolutions of remotely sensed image and its use
Remotely sensed image has different uses depending on its resolutions (spatial, temporal and spectral). For example, the image that shows the same area with high temporal resolution (i.e. updated very often) will be useful for weather broadcasting. Image with low spatial resolution is suitable for vegetation mapping and land cover mapping whereas image with high spatial resolution is useful in detecting cultural features. Thermal infrared image (because it detects heat) is useful in detecting temperature of the earth, which can be of practical use in climate change research. False-color image that require spectral bands beyond visible light will be useful in detecting urban growth since fresh vegetation looks red.
6. Landform
Landform portrayal methods
Ø Absolute methods: precise measurement of elevation and water depth; include contours, isobath, and hypsometric tint. You should know how each method works
Ø Relative methods: overall impression of relative height; focused on creating 3D effect; include physical model, perspective view, and relief shading. You should know how each method works
Ø These methods are commonly combined
Ø Dynamic methods: temporal elements are introduced; change detection, a sort of virtual reality in the case of interactive methods in the sense you can choose options – it’s like you experience something with the help of computer without being there.
Landform interpretation
Slope: vertical change between two points
Measurements of slope: slope ratio, percentage and angle
Slope ratio = rise/run where rise is the vertical change in elevation, and run is the ground distance between points; you should know how to measure slope between two points from contour maps
Slope percentage = slope ratio * 100
Slope angle = tan-1 (rise/run)
Gradient: maximum slope at any point; include two components - magnitude and azimuth
Gradient magnitude measures how steep the terrain at a given point is
Gradient azimuth measures in which direction the terrain at a given point is facing Gradient magnitude: sqrt [(x-slope)^2 + (y-slope)^2]
Gradient azimuth:
tan-1(x-slope/y-slope)
Formula will be given for the exam (you don’t need to memorize them)
Use of landform measurement in real world applications
Slope: whether it’s measured between two points or at any point (i.e. gradient magnitude) the slope for construction site should be less than some threshold, logging would not be permitted in steep terrain, the slope for potential route between two points should not be too steep
Aspect (i.e. gradient azimuth): terrain is facing in which direction? direction of water flow (run-off modeling) – which area is more likely to be affected by water pollution? house in south aspect would be warmer than one in north aspect, ski resort design should take into account aspect since more snow is expected in the area looking toward the north
7. The Earth
and Earth Coordinates
We measure the location of geographic features. The location is measured relative to what? Some kind of earth model needs to be defined such that the location can be determined precisely on the basis of the model; we can conceive
Ø Earth as a sphere: horizontal datum; basis for determining x, y value, assumes the earth to be a perfect sphere
Ø Earth as an oblate ellipsoid: horizontal datum; basis for determining x, y value, assumes the earth to be an ellipsoid (equatorial axis > polar axis)
Ø Earth as a geoid: vertical dataum; basis for determining z value
Earth as a sphere
Parallel: line parallel to the equator
Latitude: north-south angular distance from the earth’s center to a point of interest; measures offset from the equator
Longitude: east-west angular distance from the earth’s center to a point of interest; measures offset from the prime meridian
Graticule: arrangement of parallels and meridians
Geometric properties of spherical graticule:
The length of one degree of north-south latitude along the meridian is almost constant
The length of one degree of east-west longitude along the parallel is not constant because of converging meridian
The length of one degree longitude at latitude θ is r*cos θ where r is the length of one degree longitude in the equator, which is earth’s circumference / 360 = 24,907 /360 ≈ 69.2 miles
Great circle: any line that cuts across the earth in half (i.e. cut through the center of the earth); gives the shortest path
Earth as an oblate ellipsoid
The earth is not a perfect sphere, but rather close to ellipsoid. It is necessary to measure location based on the model of the earth seen as an oblate ellipsoid especially in the map that requires high positional accuracy. Coordinates based on ellipsoid is called geodetic coordinates. It is more accurate measurement of location. Geographic coordinates are widely used for small-scale mapping while geographic coordinates are widely used for large-scale mapping. Coordinate values reported in benchmark (highly accurate surveying point) are measured on the basis of an ellipsoid rather than spherical earth.
Topographic maps produced by USGS had used NAD27 (North American Datum 1927) which is the horizontal datum based on Clarke 1866 until 20 years ago. Now it has been migrated into NAD83 based on GRS80. (No need to memorize the name of ellipsoid).
Earth as a geoid
Z-value is measured relative to a geoid. Geoid is the surface of the same gravity, which is extended from mean sea level.
8. Map
Projections
Flattening the round earth onto the flat map is called map projections. Map projections can be classified on the basis of (1) which geometric properties are preserved (2) which developable surface are used
Geometric properties preserved in map projections
Ø Conformal: shape
Ø Equidistant: distance
Ø Equal-area: area
Ø Azimuthal: azimuth
The shape of developable surface in map projections
Ø Cylindrical: the generating globe is wrapped up by cylinder; good for portraying the world
Ø Conic: the generating globe is wrapped by cone; good for portraying mid-latitude
Ø Planar: the generating globe is wrapped by plane; good for portraying the hemisphere
To understand why map projections preserve one geometric property relative to others, you should look at how maps are used. Different map projections serve different purposes. For example, navigation maps require accurate or convenient portrayal of direction (→ conformal map such as Mercator) Pilot may be more interested in interpreting distance better to find the shortest route (→ equidistance map). Choropleth maps (where attributes are portrayed by graduated tones per enumeration units such as county) should be based on equal-area projection because areal size affects map interpretation.
Maps show different
areas of interest. If maps should show the continent, it may be useful to
have a map projection that will show large areas with necessarily much distortion
on average (→ cylindrical projection). If maps are used to show
mid-latitude, it may be better to have the point of tangency around
mid-latitude (→ conic projection). For example,
Pattern of distortion
Map projections cause distortion. If you imagine how maps are constructed with light bulb, developable surface, and generating globe, you can examine how distortion is distributed. No distortion occurs in the area where developable surface is tangent to generating globe. Distortion increases as the area is farther from this point (line) of tangency (point of tangency for planar projection). Scale factor is 1 at a point (line) of tangency. Scale factor is larger than 1 if features seen on the map appear larger than the actual size.
To minimize overall distortion, maps commonly adopt secant
case. Secant case is constructed in
a way that developable surface cuts through the generating globe slightly
instead of being tangent to it. The area within lines of tangency now has scale
factor less than 1. Scale factor outward from lines of tangency is larger than
1. Combined together, overall distortion is minimized. Albers equal-area conic
(commonly used for portraying the
Commonly used map projections
Ø Mercator: constant azimuth, necessarily distort the area in high latitude
Ø Gnomonic: any straight line becomes the shortest path
Ø Azimuthal equidistant: preserves distance true to the scale, shortest distance when drawn through the center of the map
Ø Transverse Mercator: developable surface is tangent to meridian rather than equator; good for portraying the area with greater north-south extent
9. Grid
Coordinate Systems
|
|
UTM |
SPC |
|
Boundary |
Latitude & Longitude |
Administrative boundary |
|
Projection |
Transverse Mercator |
Lambert
Conformal Conic Transverse
Mercator |
|
Geographic
scope |
International |
U.S. only |
|
Measurement
unit |
Meter |
Feet (SPC 27) Meter (SPC 83) |