Geog. 370 Lecture 10

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Isoline map

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isoline map (again): a thematic map in which interpolation is applied to points of known values to create lines of equal attribute values
appropriate for mapping continuous phenomena that change smoothly
particularly useful for phenomena that exist continuously, but only can be sampled discretely #Interpolation
most appropriate for mapping volumetric phenomenon (2.5D or 3D)
 isoline maps primarily use the visual variables location to represent attribute information

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2.5D phenomenon vs. 3D phenomenon

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2.5D phenomenon: attribute values can be observed at any X/Y coordinate, but only at the surface of the Z coordinate
 example: Science Hall Relief Models
3D phenomenon: attribute values can be observed at any position across the X, Y, and Z coordinates

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Isometric maps

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isometric maps: isolines are interpolated using attribute values at point observations
represent individual level information or true point information

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Isoplethic Maps

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2. isoplethic maps: isolines are interpolated using aggregated attribute values positioned at the centroids of enumeration units
o represent enumerated information or conceptual point information

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Hypsometric tints

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i.e., the term #HypsometricTints applies to elevation only #TerrainRepresentation

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Isoline/isarithm

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isoline/isarithm: a line of equal attribute value

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Contour line

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contour: lines of equal elevation

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Isobar

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isobar: lines of equal atmospheric pressure

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Isobath

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isobath: lines of equal water depth

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Isochrome

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isochrone: lines of equal time

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Isohyet

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isohyet: lines of equal precipitation

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Isorithm

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isorithm: lines of equal population density

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Isotherm

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isotherm: lines of equal temperature

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Manual interpolation

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continuous phenomenon exist everywhere, but can only be sampled discretely
too expensive to sample every location
can capture the character of variation with small sample of observations #Generalization

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Interpolation

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interpolation: estimating a value at a point using information from surrounding points

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Tobler's first law of Geography

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everything is related to everything else, but near things are more related than distant things

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Extrapolation

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extrapolation: estimating a value at a point using information from adjacent, but not surrounding points

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Steps for manual interpolation (5)

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1. begin with a sample of points dense enough to capture variation in geographic phenomenon
2. create a triangular irregular network (TIN), or a surface comprised of triangles using the sample points as vertices
3. determine the #IsolineInterval and add associated tick marks at that interval to the TIN edges
o use a rounded, meaningful interval value
4. thread isolines by connecting tick marks of equal values
5. smooth the isolines #SmoothOperator

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Automated interpolation

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 luckily, we now have GIS to process the interpolation for us
major area of research within GIScience due to the impact on spatial analysis

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Nearest neighbor

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1. nearest neighbor: determine an unknown value by using the value of the nearest observation
pro: computationally efficient (fast)
con: takes into account only one observation, producing an abrupt surface

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Triangulation

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2. triangulation: determine an unknown value by creating a continuous surface of triangular facets with the observations and then threading isolines through the facets #TriangularIrregularNetwork
con: takes into account only three observations, making contour spacing more even than exhibited by the phenomenon
con: interpolation is discontinuous at the edges of the triangles, leading to angular contours
 spline smoothing: applying a mathematical function to points defining a isoline
con: the isoline depiction varies based on how the triangles are drawn

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Inverse Distance Weighting

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3. inverse-distance weighting (IDW): determine an unknown value by generating an average of all proximate observations, weighted according to their distance from the unknown point
pro: takes into account a large number of observations
pro: interpolates to regularly spaced lattice or grid, allowing for a smoother surface
con: common to produce island effects, or circular artifacts, around high or low values
con: the isoline depiction varies according to the observations used in the weighted calculation

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Kriging

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4. kriging: a variation on inverse-distance weighting that takes into account spatial autocorrelation between the unknown locations and known observations
pro: interpolates to regularly spaced values, Gridding
pro: produces a local, "optimal" solution for each interpolation value
pro: provides a measurement of uncertainty for interpolated values
con: the resulting isolines often are very jagged
con: computationally intensive

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Sample points - design consideration

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sample points: the size and distribution of your sample points
too few: the map will not show true variation in the phenomenon
too many: the map will be overly detailed
although typically not #Normalized, may want to consider normalization for human phenomenon

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Isoline interval - design consideration

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3. isoline interval: the difference in attribute value between adjacent isolines
want to capture variation of phenomenon without providing superfluous detail
use rounded, meaningful intervals
index lines: use of a thicker line every n number of lines to organize lines visually

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Fulcrum value - design consideration

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4. fulcrum value: a #CriticalValue to which the interval is subtracted or added

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5. depicting extremities and meaningful variations between intervals - design consideration

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5. depicting extremities and meaningful variations between intervals - design consideration

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spot heights

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spot heights: marks indicating the highest or lowest observation

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depression lines

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depression lines: lines to indicate that an island is a valley, not a ridge

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supplementary lines

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supplementary lines: additional isolines added to capture important variation

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6. isoline simplification and smoothing #Generalization - design consideration

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6. isoline simplification and smoothing #Generalization

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Color tinting - design consideration

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7. color tinting: applying a color scheme to the area between isolines #EquivalentProjection
may be discrete or continuous (classed/unclassed)
when using color tinting, must use an #Equivalent projection to maintain the relative areas

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surface mapping

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surface mapping: application of color to the interpolated grid, not the area between isolines #IDW #Kriging

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isoline tinting

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o isoline tinting: applying a color ramp to the isolines, not the area between isolines

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Isoline labeling - design consideration

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8. isoline labeling
o label directly atop the isoline, using a line break
o try to label at most horizontal point
o try to align labels for easier reading
o repeat labels for long isolines

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Isoline legends

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9. isoline legends
o typically just a verbal indication of the isoline value #Location
 example: Happy Hollow Program Center
o use a contiguous legend for color tinting