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Surface Analysis

Key ideas in surface analysis

tea fields in Cameron Highlands, Malaysia
image source commons.wikimedia.org by Will Ellis

More than elevation

A mathematical representation that assumes some phenomenon can be measured or recorded everywhere

DEM of Cotopaxi volcano
image source commons.wikimedia.org
source NASA Earth Observatory

Scalar fields

Numeric value at each location

Most often physical data

Density surfaces an exception

source Alasdair Rae (formerly) at
the University of Sheffield

London population density visualised as a density surface in Wood JD, PF Fisher, JA Dykes, DJ Unwin and K Stynes. 1999. The Use of the Landscape Metaphor in Understanding Population Data Environment and Planning B: Planning and Design 26(2) 281–295.

from Stewart JQ. 1947. Empirical mathematical rules concerning the distribution and equilibrium of population. Geographical Review 37(3), 461-485.

source earth.nullschool.net

Vector fields

Not strictly a surface

from Tobler WR. 1987. Experiments In Migration Mapping By Computer. The American Cartographer 14(2), 155-163.

# Defining surfaces ## In geospatial, a surface is effectively, some ‘third value’, $z$, defined at every $(x,y)$ location ## $z=f(x,y)$

Segway polo image source
commons.wikimedia.org
by Braden Kowitz

So...

A nice idea

But...

©Stan Openshaw

Conceptual ideal gets captured many different ways...

Figure 9.1 from O’Sullivan & Unwin

image source commons.wikimedia.org

Triangulated irregular networks (TIN)

Effectively a kind of interpolation

Efficient way to store surfaces

Popular for visualization purposes

A digital elevation model (59.8MB)

TIN edges extracted

TIN edges on their own

TIN faces colored by elevation (10.7MB)

Mt Ruapehu hillshade made
using terra::shade function

Some key methods

Most of these are most easily performed on a raster grid of values

So before all other methods, comes interpolation to create a surface

Assuming we have such a surface, many methods are available...

Relative relief or ruggedness

Aspect and slope

Hillshade

Focal operations

Applied in a moving window centred at each grid cell

Figure 9.13 from O’Sullivan & Unwin

More complex operations

These demand iteration, and often storage of intermediate results for further processing

Direction

Accumulation

Streams

# Summary ## Surface representations are an idealisation ## Important to note they may be used in social geography contexts too ## Often require a lot of work, particularly _interpolation_ to create ## Once built many analytical options are available ## Tools: `raster` or `terra` package, Whitebox Tools, Spatial Analyst in Arc, various geoprocessing tools in QGIS