2 Statistical surface Concept of a statistical surface Mapping the statistical surface with point, line and area symbols Portraying the land-surface form
Surface Mapping3 Statistical surface The statistical surface is one of the most important concepts in cartography. The magnitudes of the attribute values, referenced to unit areas, lines or points, can be viewed as having a vertical dimension. The magnitudes can therefore be visualised as a 3-dimensional surface.
Surface Mapping4 Concepts of statistical surface Left: An array of attribute values for unit areas. The numbers are rural population densities for minor civil divisions in a part of Kansas. Right: Elevated points whose relative height above the datum for each unit area is proportional to the attribute value in that unit area shown on the left. From Robinson, et al., 1995
Surface Mapping5 Left: A perspective view of a smoothed statistical surface produced by assuming gradients among all the attribute values. Right: A perspective view of the statistical surface produced by erecting prisms over each unit area proportional in height to the attribute values. From Robinson, et al., 1995 Continuous and non- continuous surfaces
Surface Mapping6 2-D representations by isarithmic and choropleth maps Up: An isarithmic map of the statistical surface. Right: A choropleth representation of the same data set using 5 range- graded categories. From Robinson, et al., 1995
Surface Mapping7 Mapping the statistical surface with point symbols Dot map Unit value Size Location A well-rendered dot map in which each dot represents 16.2 hectares of land in potato production. From Robinson, et al., 1995
Surface Mapping8 Mapping the statistical surface with line symbols Hachures: short line symbols whose width or spacing depends upon the slope at a point on the statistical surface. Profiles: the lines of intersection between the series of parallel planes intersecting the datum at the right angle. Oblique traces: intersects between 0 to 90°. Isarithms: parallel to the datum.
Surface Mapping9 Hachures Line symbolisation of slopes or gradients by using hachures. In this diagram, hachures are equally spaced but vary in thickness depending on the value of the gradient being portrayed. Cited in Robinson, et al., 1995
Surface Mapping10 Hachures (cont.) Line symbolisation of slopes or gradients by using hachures. In this diagram, hachures are of equal thickness but vary in spacing depending on the value of the gradient being portrayed. Cited in Robinson, et al., 1995 BenoitBonneHossard
Surface Mapping11 Profiles A series of profiles situated at right angles to one another gives a clear picture of the surface and its underlying strata. Cited in Robinson, et al., 1995
Surface Mapping12 Construction of a profile The construction of a profile from an isarithmic map. Line AB is drawn on the map. Intersections of the isarithms with line AB are perpendicularly projected to the appropriate line of a set of parallel ruled lines below. The resulting points are connected by a smooth line resulting in a profile A’B’. From Robinson, et al., 1995
Surface Mapping13 Oblique traces A reduced portion of a planimetrically correct terrain drawing of the Isle of Yell (Shetland Group). Cited in Robinson, et al., 1995
Surface Mapping14 Perspective traces Perspective traces: (a) “fishnets” where traces are drawn in both the x and y directions, (b) traces drawn only parallel to the x direction, (c) traces drawn only parallel to the y direction. From Robinson, et al., 1995 a c b
Surface Mapping15 Two sets of perspective traces: (a) suing one-point perspective, and (b) using two-point perspective. From Robinson, et al., 1995 Perspective traces (cont.)
Surface Mapping16 Isarithmic mapping An isarithm is also called isoline or isogram. Emphasise on the geographical distribution outside surface enclosing the geographical volume. Focus is on the attribute values at points of a truly continuous distribution.
Surface Mapping17 Isarithmic mapping (cont.) In the upper diagram, horizontal levels of given z values are seen passing partway through a hypothetical island. Traces of intersections of the planes with the island surface are indicated by dotted lines. In the lower drawing, the traces have been mapped orthogonally on the map datum and represent the island by means of isarithms. From Robinson, et al., 1995
Surface Mapping18 Kinds of isarithmic mapping Attribute values that can occur at points Isometric lines Attribute values that cannot occur at a point Isopleths
Surface Mapping19 Mapping the statistical surface with area symbols Choroplethic mapping Simple choropleth mapping Classless choropleth mapping Elements of choroplethic mapping Size and shapes of unit areas Number of classes Class limit determination Dasymetric mapping
Surface Mapping20 Choroplethic mapping Examples of three ways we can map a set of z values that refer to enumeration districts or unit areas: (a) a simple choropleth map, (b) a dasymetric map, and (c) an isoplethic map. From Robinson, et al., 1995
Surface Mapping21 Size and shape of unit areas The same distribution mapped with three different sets of unit areas, using the same class interval scheme: (a) uses large units of equal area, (b) uses small units of equal area, and (c) uses irregularly size unit areas. From Robinson, et al., 1995 > 40 25 - 40 10 - 25 < 10 AB C
Surface Mapping22 Number of classes Both (a) and (b) show five classes. Because of the simple distribution pattern on (a), we could increase the number of classes used. The lack of pattern in the distribution of (b) would make it even more confusing to the map reader if more classes were used. Cited in Robinson, et al., 1995 AB
Surface Mapping23 Class interval series (cont.) Left: An unclassed perspective view of a statistical distribution. Each unit area is shown as a prism whose height is proportional to the value of the mapped distribution, and whose base is a scaled representation of the unit area. Right: A five-classed, perspective view of the same statistical distribution. Cited in Robinson, et al., 1995
Surface Mapping25 Portraying the land- surface form Historical background Visualisation methods Terrain unit maps and hachures Morphometric maps Contouring Hill shading Perspective pictorial maps Oblique regional views Schematic maps
Surface Mapping26 Early maps Examples of portraying hills and mountains in stylised form on early maps. From Robinson, et al., 1995
Surface Mapping27 Landform portrayal “From the 15 th to 18 th centuries, landform portrayal developed along with landscape painting of the period. Thus, perspective-like, oblique, or bird’s-eye views for limited areas became popular”. Cited in Robinson, et al., 1995
Surface Mapping28 Landform portraying Chinese ancient maps also shows excellent art works in landscape portraying.
Surface Mapping29 A section of topographic map that portrays the land-surface form with vertically illuminated hachuring. Cited in Robinson, et al., 1995 Terrain unit maps
Surface Mapping30 Terrain unit maps and hachures A section of topographic map that portrays the land-surface form with obliquely illuminated hachuring. Cited in Robinson, et al., 1995
Surface Mapping31 Morphometric maps On the left is a relatively realistic portrayal of the region. On the right is the same area, which employs a schematic treatment to emphasise the geomorphic characteristics Cited in Robinson, et al., 1995
Surface Mapping36 Hill shading Courtesy www.hear.org/starr/maps/stock/index.html
Surface Mapping37 Hill-shaded topographic map “Recent printed topographic maps which combine hill shading with contours are the most effective ever produced by manual methods”. Cited in Robinson, et al., 1995
Surface Mapping38 To see to believe? Left: hill-shaded topography with the illumination source located in the South – the real-world simulation for the North Hemisphere. On this image, the landform appears inversed. Right: the upside-down view of the same image.
Surface Mapping40 Layer tinting with contours Courtesy geology.csustan.edu
Surface Mapping41 Block diagrams “Even the simplest block diagram is easily accepted as a reduced replica of reality and is remarkably graphic”. From Robinson, et al., 1995
Surface Mapping42 Oblique regional views A reduced preliminary “worksheet” of an oblique regional view of Europe as seen from the southwest, to illustrate a strategic viewpoint during the World War II. Cited in Robinson, et al., 1995
Surface Mapping43 Perspective view with hill shade Shaded 3-dimensional landscape (courtesy http://hirise.lpl.arizona.edu/HiBlog/tag/dtm/).
Surface Mapping44 Perspective view with hill shade and shadow
Surface Mapping45 Perspective pictorial maps 3-dimensional surface draped with airphoto to show the 3- dimensional landscape – Ap Lei Chau, Hong Kong.
Surface Mapping46 Visual effects can also be added for visualising the 3- dimensional surface more realistically (sky colours, clouds, etc.) – Ap Lei Chau, Hong Kong. Visual effects