15.3 Digital elevation models and terrain analysis

Digital Elevation Models for Geomorphology

Fundamentals and Applications of DEMs

A Digital Elevation Model (DEM) is a raster grid where each cell stores an elevation value, creating a continuous 3D representation of a terrain surface. DEMs give geomorphologists the ability to quantify landscape features and processes across areas far too large to survey on foot.

DEM resolution (the size of each grid cell) controls how much terrain detail you can capture. A 1-meter DEM reveals individual gullies and terrace scarps; a 30-meter DEM (like SRTM) is better suited for regional drainage patterns. Higher resolution means finer detail, but also larger file sizes and heavier processing demands.

From a single DEM, you can extract several topographic attributes that drive surface processes:

• Slope: steepness of the terrain surface, controlling flow velocity and erosion potential
• Aspect: compass direction a slope faces, which affects solar radiation receipt and moisture availability
• Curvature: whether the surface is convex (diverging flow) or concave (converging flow)

These attributes form the foundation for nearly every geomorphic analysis described below.

DEM Applications in Geomorphology

• Watershed delineation traces drainage basin boundaries and extracts stream networks directly from flow-routing algorithms
• Slope stability analysis identifies areas prone to landslides by combining slope, curvature, and material properties
• Flood modeling simulates inundation extents and depths for different discharge scenarios
• Landform classification automatically categorizes terrain into geomorphic units such as ridges, valleys, and plains
• Sediment transport modeling estimates spatially distributed erosion rates and sediment flux
• Tectonic geomorphology examines how landscapes respond to active faulting and differential uplift, using metrics like channel steepness and knickpoint distributions

Limitations and Considerations

DEMs are not perfect representations of the real surface. Several sources of error and limitation affect every analysis you run:

• Data collection errors stem from instrument accuracy and point density. Sparse survey points in rugged terrain produce less reliable elevations.
• Interpolation artifacts can smooth out real features (like narrow channels) or introduce false ones, depending on the algorithm used.
• Surface vs. subsurface: DEMs represent only the ground surface (or, in some cases, the canopy surface). They tell you nothing about bedrock depth or subsurface structure.
• Temporal resolution is limited. A DEM is a snapshot. Rapid changes from landslides or volcanic eruptions won't appear unless you acquire new data afterward.
• Vertical accuracy varies with terrain type and collection method. Steep, forested slopes typically have larger elevation errors than flat, open ground.
• Edge effects at dataset boundaries can introduce discontinuities, requiring careful mosaicking and blending when merging adjacent DEMs.

DEM Generation and Processing

Data Acquisition Methods

LiDAR (Light Detection and Ranging) fires laser pulses from an aircraft or drone and measures return times to calculate elevation. Because laser pulses can penetrate gaps in vegetation canopy, LiDAR is especially valuable for producing bare-earth models in forested areas. Under ideal conditions, vertical accuracy reaches sub-meter levels.

Photogrammetry constructs DEMs by matching features across overlapping images and triangulating their 3D positions.

• Structure from Motion (SfM) uses many overlapping photos from drones or handheld cameras to build detailed 3D models, often at centimeter-scale resolution for small study sites.
• Satellite stereo imagery enables global-scale DEM generation. Products like ASTER GDEM (~30 m) and SRTM (~30 m) are freely available and widely used.

Interferometric Synthetic Aperture Radar (InSAR) measures phase differences between radar signals to derive surface elevation. It works through cloud cover and at night, making it useful for large-scale mapping in persistently cloudy regions. InSAR also detects subtle surface deformation (millimeter-scale), which is valuable for monitoring volcanic inflation or fault creep.

Traditional field surveying provides high-accuracy point data for smaller study areas:

• Total station measurements
• Differential GPS surveys
• Terrestrial laser scanning (TLS) for high-resolution local DEMs

DEM Creation Process

Raw elevation data requires several processing steps before it becomes a usable DEM:

1. Noise removal: Filter out erroneous points and outliers caused by sensor errors, birds, or other non-ground returns.
2. Georeferencing: Align all data to a common coordinate system and datum so that points from different sources register correctly.
3. Point classification (for LiDAR): Separate ground returns from vegetation, buildings, and other above-ground objects. This step is what makes bare-earth DEMs possible.

Once you have clean, classified ground points, interpolation creates a continuous surface from those discrete measurements:

• Inverse Distance Weighting (IDW) estimates unknown elevations by averaging nearby known points, weighted by their distance. Closer points have more influence.
• Kriging uses geostatistical models of spatial autocorrelation to produce statistically optimal estimates, along with uncertainty maps.
• Triangulated Irregular Network (TIN) connects input points into a mesh of non-overlapping triangles. TINs preserve original data values and adapt triangle density to terrain complexity.

Finally, resampling adjusts the DEM to a target resolution. Bilinear interpolation produces smoother transitions between cells, while nearest-neighbor resampling preserves original cell values (useful when you need to avoid altering the data).

Quality Assessment and Error Correction

Before running any analysis, assess DEM quality:

• Visual inspection using hillshade and contour overlays reveals obvious artifacts like striping, pits, or flat areas that shouldn't be flat.
• Statistical analysis of elevation distributions and derivatives (slope histograms, for example) can flag systematic biases.
• Comparison with reference data, such as GPS checkpoints or higher-accuracy DEMs, quantifies absolute vertical error.

Common corrections include:

• Stripe removal for sensor-related banding artifacts
• Void filling using interpolation or auxiliary datasets (e.g., filling SRTM voids with ASTER data)
• Hydrological conditioning ensures water flows correctly across the DEM by filling spurious sinks and enforcing drainage through flat areas

Uncertainty assessment is critical for any derived product. Error propagation analysis tracks how DEM errors affect calculated slopes, volumes, or flow paths. Monte Carlo simulations repeatedly perturb the DEM within its error bounds to quantify how sensitive your results are to elevation uncertainty.

Terrain Analysis with DEMs

Topographic Attribute Extraction

Slope quantifies terrain steepness, typically calculated using finite difference methods that compare a cell's elevation to its neighbors. It's expressed in degrees or as percent rise. Slope is fundamental to understanding erosion potential, mass wasting susceptibility, and overland flow velocity.

Aspect identifies the compass direction each slope faces. South-facing slopes in the Northern Hemisphere receive more solar radiation, affecting soil moisture, vegetation patterns, and weathering rates. Aspect is usually represented as an azimuth (0°–360°) or grouped into cardinal/intercardinal directions.

Curvature describes how the surface bends:

• Profile curvature measures curvature in the downslope direction (parallel to flow). Positive profile curvature indicates a convexity where flow accelerates; negative indicates a concavity where flow decelerates.
• Plan curvature measures curvature perpendicular to the slope. It controls whether flow converges (hollows) or diverges (noses/spurs).

Together, these curvature types help delineate ridges, valleys, and zones of erosion versus deposition.

Hydrological Modeling

Flow direction algorithms determine where water moves from each cell. The simplest is the D8 algorithm, which routes all flow from a cell to whichever of its eight neighbors has the steepest descent. This works well for channelized flow but forces all water into a single path. Multiple flow direction (MFD) algorithms distribute flow proportionally among downslope neighbors, better representing diffuse hillslope runoff.

Flow accumulation counts how many upstream cells drain through each cell. Cells with high accumulation values correspond to stream channels. You define channel initiation by setting a contributing-area threshold (e.g., all cells with accumulation > 1000 cells become part of the stream network).

The Topographic Wetness Index (TWI) predicts where soil moisture accumulates:

$TWI = \ln\left(\frac{a}{\tan \beta}\right)$

where $a$ is the specific upslope contributing area (area per unit contour length) and $\beta$ is the local slope angle. High TWI values occur where large contributing areas drain onto gentle slopes, indicating saturation-prone zones. TWI is widely used in soil mapping and hydrological modeling.

Advanced Terrain Analysis

Roughness indices quantify terrain complexity at various scales:

• Terrain Ruggedness Index (TRI) calculates the mean absolute elevation difference between a cell and its neighbors. Simple to compute and interpret.
• Vector Ruggedness Measure (VRM) uses the dispersion of 3D surface normal vectors. It captures both slope and aspect variability, making it more sensitive to complex terrain than TRI alone.

Roughness metrics are useful for distinguishing geomorphic surfaces (e.g., smooth alluvial fans vs. rough lava flows) and for ecological habitat modeling.

Geomorphon classification identifies landform elements using pattern recognition based on local ternary patterns. The algorithm compares each cell's elevation to points at a specified search distance in eight directions, classifying terrain into 10 common landform types: flat, peak, ridge, shoulder, spur, slope, hollow, footslope, valley, and pit.

The Topographic Position Index (TPI) compares each cell's elevation to the mean elevation of a surrounding neighborhood. Positive TPI values indicate ridges or hilltops; negative values indicate valleys or depressions; values near zero indicate flat areas or mid-slopes. Varying the neighborhood radius lets you detect landforms at different scales.

Interpreting DEM-Derived Products

Visualization Techniques

Hillshade rendering simulates how sunlight would illuminate the terrain from a specified angle and elevation. The resulting shaded relief map makes subtle landforms (fault scarps, fluvial terraces, levees) visually obvious. Adjusting the light source direction can highlight features with different orientations.

Contour maps remain useful for identifying elevation gradients and landform boundaries. Choosing the right contour interval matters: too fine and the map becomes cluttered, too coarse and you lose important detail.

3D visualization techniques include draping satellite imagery or thematic layers over a DEM surface, creating virtual fly-throughs, and using augmented reality in the field. These approaches are especially helpful for communicating results to non-specialist audiences.

Quantitative Landscape Analysis

Hypsometric analysis examines the distribution of elevation within a drainage basin. The hypsometric curve plots the proportion of total basin area at or above each relative elevation. The hypsometric integral (HI) summarizes the curve as a single value between 0 and 1. High HI values (~0.6+) suggest a youthful, tectonically active landscape with much of its mass intact. Low values (~0.3 or below) indicate a more eroded, mature landscape.

Cross-sectional profiles extract elevation along a transect, revealing valley shapes, terrace levels, and knickpoints. Stacking multiple parallel profiles creates a swath profile, which shows the range of elevations across a corridor and is useful for detecting broad tectonic tilting or regional erosion patterns.

Slope-area analysis plots local channel slope against upstream drainage area on log-log axes. In bedrock rivers, this relationship follows a power law: $S = k_s A^{-\theta}$, where $k_s$ is the steepness index and $\theta$ is the concavity index. Breaks in this scaling relationship help identify transitions between hillslope and fluvial process domains, or the locations of knickpoints related to base-level change.

Multi-temporal and Integrated Analysis

Change detection compares DEMs from different time periods to quantify surface changes. This requires that both DEMs have consistent resolution, coordinate systems, and comparable accuracy. Applications include estimating landslide volumes, tracking glacier mass balance, and monitoring coastal retreat rates.

DEM differencing subtracts one DEM from another to produce a map of elevation change. Positive values indicate deposition or uplift; negative values indicate erosion or subsidence. Careful error propagation is essential here: if your DEM uncertainty is ±0.5 m, you can't confidently interpret a 0.3 m elevation change as real. Significance testing helps distinguish genuine surface change from noise.

GIS integration combines DEM-derived products with other spatial datasets to address complex geomorphic questions:

• Overlaying slope and geology maps to assess landslide susceptibility
• Combining TWI with land cover data to model habitat suitability or runoff generation
• Merging terrain attributes with climate data (rainfall intensity, temperature) for spatially distributed soil erosion modeling (e.g., RUSLE)