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Raster Processing and Map Algebra

Rasters represent continuous geographic surfaces (such as elevation, temperature, or spectral indices) using a grid of cells (pixels). Unlike vector shapes, raster processing is performed on a cell-by-cell basis across grid rows and columns. This section covers map algebra, raster warping/resampling, reclassification, and raster-vector conversions.

We will use the localized Digital Elevation Model (DEM) dataset:

1. Raster Structure and Cell Concepts

A raster grid consists of columns and rows defined by spatial coordinate parameters:

    RASTER CELL LAYOUT (DEM EXAMPLE)
    +-------+-------+-------+
    | 650.5 | 682.2 | 710.8 |  <-- Cells containing elevation values (meters)
    +-------+-------+-------+
    | 640.1 | 674.9 | 705.2 |  
    +-------+-------+-------+
    | 632.0 | -9999 | 698.8 |  <-- -9999 represents NoData (null) cells
    +-------+-------+-------+
    [Cell Size: 30m x 30m]
  • Cell Size (Resolution): The geographic width and height of a single pixel (e.g., \(30\text{ m}\) for the ALOS PALSAR / SRTM grids). All calculations inside a cell are averaged across this area.
  • NoData Value: A designated placeholder number (e.g., -9999 or -3.402823e+38) indicating the absence of data. Operations on a NoData cell always output NoData.
  • Bands: A single raster file can contain multiple stacked layers (bands). For example, satellite scenes contain separate spectral bands (Red, Green, Blue, Near-Infrared), whereas elevation DEMs are singleband rasters.

2. Map Algebra and the Raster Calculator

The Raster Calculator (Raster > Raster Calculator) evaluates mathematical or logical expressions on one or more raster grids on a cell-by-cell basis:

\[\text{Output Cell} = f(\text{Input Cell}_A, \text{Input Cell}_B)\]

Exercise 1: Extract High-Altitude Zones (Binary Masking)

Isolate all mountainous terrain higher than \(4000\text{ meters}\) in output_hh.tif.

  1. Open Raster > Raster Calculator.
  2. Under Raster Bands, double-click "output_hh@1" to add it to the expression box.
  3. Complete the expression to check for values greater than 4000: 
    "output_hh@1" > 4000
  4. Set the Output layer to save inside your project output folder as high_altitude_mask.tif.
  5. Ensure the Spatial Reference System matches output_hh.tif. Click OK.
  6. The output is a binary grid where pixels are assigned \(1\) (elevations \(> 4000\text{ m}\)) or \(0\) (elevations \(\le 4000\text{ m}\)).

Exercise 2: Extract Altitudinal Valleys (Multi-Criteria Masking)

Extract middle-altitude valleys and hills ranging strictly between \(1500\) and \(3500\text{ meters}\).

  1. Open the Raster Calculator.
  2. Enter the following logical combination expression: 
    ("output_hh@1" >= 1500) * ("output_hh@1" <= 3500)
    (Multiplying these boolean statements acts as a logical AND operation—only cells where both conditions are true (\(1 \times 1\)) will output \(1\).)
  3. Save the output as valley_hills_mask.tif and click OK.

3. Raster Warping and Resampling Algorithms

When running analysis combining multiple rasters, they must share the exact same cell sizes, extents, and spatial alignments.

  • Raster Warping (Reprojection): Changes the Coordinate Reference System (CRS) of a raster grid. Access via Raster > Projections > Warp (Reproject).
  • Resampling: Injected during reprojection or cell resizing to calculate new pixel values from the old grid layout. Selecting the wrong resampling algorithm will corrupt your data:
Resampling Method Ideal Data Type Calculation Logic Hydrological Impact
Nearest Neighbor Categorical / Discrete Copies the value of the nearest cell. Preserves class values (e.g., landuse codes \(1, 2, 3\)). Using it on continuous elevation data creates blocky steps.
Bilinear Continuous Calculates a linear average of the 4 nearest pixels. Smooths values. Ideal for continuous rasters like elevation grids (DEMs) or temperature surfaces.
Cubic Convolution Continuous Fits a smooth curve across the 16 nearest pixels. High precision, but computationally heavy. Best for high-resolution imagery and ortho-rectification.

Exercise: Reproject and Resample the DEM

Reproject the elevation grid from a geographic coordinate system to a metric coordinate system for accurate slope calculations.

  1. Go to Raster > Projections > Warp (Reproject).
  2. Set the parameters:
  3. Input Layer: output_hh.tif (EPSG:4326).
  4. Target CRS: Select WGS 84 / UTM Zone 45N (EPSG:32645) (metric UTM projection).
  5. Resampling method to use: Select Bilinear (vital for continuous elevation data to prevent stepping artifacts).
  6. Output file resolution: Enter 30 (forces the output pixels to be exactly \(30\text{ m} \times 30\text{ m}\)).
  7. Reprojected: Save the file as output_hh_utm_30m.tif.
  8. Click Run. The output raster is now projected in meters, ready for catchment slope derivations.

4. Raster Reclassification

Reclassification groups continuous cell values into simplified, discrete categories (converting continuous rasters to categorical rasters).

  • Accessing: Open the Processing Toolbox and select Raster Analysis > Reclassify by Table.

Exercise: Reclassify DEM into Altitudinal Zones

Classify the continuous elevation raster output_hh.tif into three simple ecological zones: Lowland, Mid-hills, and Highland.

  1. Search for Reclassify by Table in the Processing Toolbox.
  2. Set the Input raster to output_hh.tif.
  3. Under Reclassification table, click ... to open the table editor. Add three rows:
Minimum Maximum Value
600 2000 1
2000 4500 2
4500 7000 3
  1. Check Use no data when no range matches.
  2. Save the output raster as elevation_ecological_zones.tif and click Run.
  3. The output will contain only three pixel values (\(1\), \(2\), and \(3\)), representing the three zones.

5. Raster-Vector Conversions

In spatial analysis workflows, you often need to transfer data between vector formats and raster structures:

Raster to Vector (Polygonize)

Converts a raster grid into vector polygons. Adjacent pixels with identical integer values are merged into single polygon boundaries.

  • Accessing: Go to Raster > Conversion > Polygonize (Raster to Vector).
  • Exercise: Convert the binary high-altitude raster mask created in Section 2 into vector polygons.
  • Open Raster > Conversion > Polygonize.
  • Input Layer: Select high_altitude_mask.tif (the binary mask).
  • Name of the field to create: Enter altitude_class (stores values \(1\) or \(0\)).
  • Vectorized: Save as a GeoPackage table named high_altitude_peaks.
  • Click Run. Select the polygons where altitude_class = 1 to isolate the peaks.

Vector to Raster (Rasterize)

Converts vector geometries (points, lines, or polygons) into a grid of raster cells.

  • Accessing: Go to Raster > Conversion > Rasterize (Vector to Raster).
  • Exercise: Rasterize country boundaries to create a spatial analysis mask aligning with the DEM grid.
  • Load ne_10m_admin_0_countries and select Nepal.
  • Open Raster > Conversion > Rasterize (Vector to Raster).
  • Set the parameters:
    • Input Layer: ne_10m_admin_0_countries (check Selected features only).
    • Field to use for burn-in value: Select MAPCOLOR7 (or enter a fixed value of 1 under A fixed value to write).
    • Output raster size units: Select Pixels.
    • Width/Horizontal resolution: Match the width of output_hh.tif (e.g. use the output_hh.tif layer's properties to check pixel dimensions, or set resolution to match).
    • Output bounds: Click ... > Use Extent from > Select output_hh.tif (forces the grid extent to match the DEM).
    • Rasterized: Save as nepal_raster_mask.tif.
  • Click Run. This generates a grid matching the DEM cell structure, containing \(1\) over Nepal and \(0\) (or NoData) elsewhere.