GEOG 586
Geographic Information Analysis

Derived Measures on Surfaces

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Required Reading:

 

Before we go any further, you need to read the following text, which is available through the Library Resources tab in Canvas:

  • Chapter 11: GIS - Fundamentals: A First Text On Geographic Information Systems by Paul Bolstad, 2005

The measures discussed in this section are just a small sample of the types of surface analysis measures that can be devised. Map algebra operations can vary in complexity from simple to advanced.

In doing so, they may integrate single mathematical functions or increase in complexity by integrating multi-step mathematical functions/operations that may be evaluative (e.g., nested functions) and/or dynamical in nature (e.g., spatio-temporal models, agent-based models, process-based models, overlay models (more on this in Lesson 8), depending on what is being analyzed.

Agent-based models are spatio-temporal models that are often applied in cell-based environments and contain agents that move across the landscape reacting to the environment based on a set of pre-defined rules.

Process-based models might be used to predict the temporal fluctuations in soil moisture, water levels and hydrologic networks or for disease prediction where temporal fluctuations in temperature and rainfall might affect the host-pathogen interaction and disease outcome in the environment (e.g. Blanford, et al. 2013 Scientific Reports).

The examples below should give you a feel for the flexibility of the map algebra framework and how it can be used to capture simple processes as well as more complex processes.

In this week's project, you will have an opportunity to explore map algebra more thoroughly in a practical setting.

Table 7.1
Relative relief Relative relief, from the definition in the text, is readily expressed as a map algebra function:

rel_relief = focal_max( [elevation] ) – focal min( [elevation] )

where the focal region is defined accordingly.
Surface gradient and aspect Surface gradient is more complex to model, requiring a number of steps.

First, two focal functions must be defined to calculate the slope in two orthogonal directions. These will be similar functions but must have specially defined focal areas that pick out the immediately adjacent grid cells on either side of the focal cell in each of the two cardinal directions.

If these resulting slopes are called ew-gradient (for east-west) and ns-gradient (for north-south), then the overall gradient can be calculated in the second step by:

gradient = square-root( ( arctan( ew-gradient ) )2 + ( arctan( ns-gradient ) )2 )

and the overall aspect is given by

aspect = arctan( ( ew-gradient ) / ( ns-gradient ) )
Nested Functions A conditional statement works in much the same way as an if-then-else statement and can be used to nest functions.

Output = Con (Test statement, if true do something, if false do something)

For example, to identify roads that are in areas with low avalanche risk, the following statement will create a new output that only contains roads that are in low risk areas.

SuitableRoads = Con (AvalancheRisk < 1, Roads)