Raster Analysis and Map Algebra

A raster is a grid of square cells, each holding one number: an elevation in metres, a temperature, a land-use code, a rainfall total. Because the whole layer is just numbers laid out in rows and columns, you can treat it like a giant spreadsheet and do arithmetic on it. Add two rasters and the GIS adds cell 1 of the first to cell 1 of the second, cell 2 to cell 2, and so on to the end. This is map algebra - a term coined by Dana Tomlin - and it is the beating heart of Module 5.

The golden rule is that the cells must line up. Two rasters can only be added, subtracted or compared if they share the same extent (they cover the same ground), the same resolution (the cells are the same size), and the same CRS (they are in the same coordinate system). If a 30 m CartoDEM and a 10 m Sentinel layer disagree on any of these, the maths is nonsense - you would be adding an elevation from one place to a value from another. In practice you resample and align first (Module 3's skills), then compute.

Raw rasters speak different languages. Slope is in degrees, distance is in metres, land use is a set of codes. You cannot meaningfully add 18 degrees of slope to 400 metres of distance. So before you combine layers you reclassify each one onto a shared, ranked scale - typically a small set of ordered classes such as 1 (good), 2 (fair), 3 (poor).

Reclassifying is a lookup: you write a rule - slope 0 to 5 degrees becomes class 1; 5 to 15 becomes 2; over 15 becomes 3 - and the GIS rewrites every cell. It is the single most useful raster operation for a designer, because it is how a continuous surface (a smooth DEM) turns into a decision surface (buildable / caution / avoid). Choose your class breaks honestly: they carry judgement, and a lazy break can quietly decide a whole analysis. Where a threshold matters - a legal flood level, a maximum ramp gradient - anchor the break to a real standard, not a round number that looked tidy.

Dana Tomlin's cartographic modelling organises every raster operation by one question: which input cells feed one output cell?

Local operations use only the cell in the same position - across one raster (reclassify) or several (add three suitability layers). Focal (neighbourhood) operations use a moving window around each cell - a 3x3 or larger kernel - to compute things like a smoothed average, or slope, which needs the neighbours to see the tilt. Zonal operations summarise cells grouped by a zone: mean elevation per ward, maximum flood depth per plot. Global operations use the whole grid at once - distance from every cell to the nearest road, or the cost of travelling across the surface.

Once you can name an operation as local, focal, zonal or global, you can find it in any software's menu and reason about what it needs. Slope? Focal. Average rainfall per district? Zonal. Nearest-hospital distance? Global.

Real analysis is rarely one sum. You reclassify slope, reclassify flood depth, reclassify distance-to-road, then add the three - a local operation on the results of three earlier ones. A sequence of raster operations like this is a cartographic model, and it is worth building it as a documented chain rather than a pile of throwaway clicks.

Both QGIS (the Graphical Modeler) and ArcGIS Pro (ModelBuilder) let you wire operations into a visual flowchart you can re-run, tweak and hand to a colleague. This matters professionally: an analysis you can reproduce and explain is evidence; a one-off map nobody can rebuild is just an assertion. In Module 5.4 the whole suitability method is exactly such a chain.

Three quiet traps catch beginners. First, NoData: cells with no value (outside the study area, or gaps in the source) are not zero - they are absent, and most tools propagate NoData through a calculation so one missing input can blank an output cell. Decide deliberately whether to fill, mask or ignore them. Second, integer versus float: dividing two integer rasters can truncate (7 / 2 becomes 3, not 3.5) unless you force floating-point output - a classic silent error in slope and index calculations. Third, edges: focal operations have no full window at the raster's border, so results there are weaker; clip your DEM generously beyond the site so the edge effects fall outside your area of interest.