8.4 Digital elevation models and terrain analysis

Digital Elevation Models: Principles and Methods

Digital elevation models (DEMs) are grid-based representations of Earth's surface where each cell stores an elevation value, producing a continuous picture of terrain across a landscape. They're foundational to geophysics because they let you quantitatively analyze slopes, drainage, landforms, and even subsurface structures when combined with other datasets.

DEMs are built from a range of data sources, and the method you choose determines the resolution, coverage, and accuracy you'll get.

Generation of Digital Elevation Models

Ground surveys use traditional instruments like total stations or GPS receivers to collect elevation points. These produce high-resolution DEMs but only for relatively small areas, since someone has to physically visit each measurement location.

Aerial photogrammetry takes overlapping aerial photographs and extracts elevation through stereoscopic analysis. Two photos of the same area from slightly different angles let you calculate depth, much like how your two eyes perceive depth. This scales to larger areas than ground surveys.

LiDAR (Light Detection and Ranging) fires laser pulses toward the ground and measures the round-trip travel time to calculate elevation. Because light travels at a known speed, the return time gives a precise distance. LiDAR produces very high-resolution DEMs and can even penetrate vegetation canopy to map the bare-earth surface beneath.

InSAR (Interferometric Synthetic Aperture Radar) compares the phase differences between two or more SAR images acquired from slightly different positions or at different times. Those phase shifts encode elevation information, making InSAR especially useful for detecting surface elevation changes over time.

SRTM (Shuttle Radar Topography Mission) used a radar system aboard the Space Shuttle in 2000 to collect near-global elevation data. The resulting DEM covers latitudes from 60°N to 56°S at approximately 30-meter resolution (1 arc-second) for the most recent release, making it one of the most widely used global elevation datasets.

Accuracy and Uncertainties in Digital Elevation Models

DEM accuracy depends on three main factors: the acquisition method, the spatial resolution of the grid, and the post-processing applied to the raw data. Higher-resolution DEMs capture finer terrain detail but demand more storage and computational power.

Common sources of error include:

• Vertical and horizontal accuracy limitations inherent to the sensor or survey method
• Data gaps from shadowed areas, dense vegetation, or sensor geometry
• Artifacts such as striping, pits, or spikes introduced during processing

Quantifying these uncertainties matters. If you're using a DEM with ±10 m vertical accuracy to map subtle slope changes of a few degrees, your results may not be reliable. Always check the reported accuracy metrics (typically RMSE, or root mean square error) before applying a DEM to a geophysical problem.

Terrain Analysis for Geomorphological and Hydrological Insights

Terrain analysis extracts quantitative information about surface shape and water flow from DEMs. These derived attributes connect topography to physical processes like erosion, runoff, and sediment transport.

Quantitative Characterization of Topographic Attributes

Slope measures the steepness of the terrain at each grid cell, typically expressed in degrees or percent. Aspect indicates the compass direction that the steepest slope faces. Together, slope and aspect control surface processes: steep south-facing slopes in the Northern Hemisphere receive more solar radiation, affecting weathering rates and vegetation patterns.

Curvature describes how the surface bends, and it comes in two flavors:

• Profile curvature is the rate of change of slope along the direction of steepest descent. Positive profile curvature indicates a concave (decelerating) slope; negative indicates convex (accelerating).
• Plan curvature is the rate of change of aspect perpendicular to the slope direction. It tells you whether water flow converges (hollows) or diverges (ridges).

Curvature analysis helps distinguish landform types. Convex surfaces often mark ridgelines and hilltops, concave surfaces indicate valleys and hollows, and planar surfaces suggest uniform hillslopes.

Hydrological Analysis and Derived Terrain Attributes

Hydrological analysis uses DEMs to trace where water goes. The standard workflow follows these steps:

1. Fill sinks in the DEM to remove small depressions that would trap flow unrealistically.
2. Calculate flow direction using an algorithm like D8, which assigns flow from each cell to whichever of its eight neighbors has the steepest downhill gradient.
3. Calculate flow accumulation by counting how many upslope cells drain through each cell. High accumulation values trace out stream channels.
4. Delineate catchments by identifying the contributing area that drains to a specific outlet point. Every cell upslope of that outlet, as determined by flow direction, belongs to the catchment.

From these basics, you can derive more advanced terrain attributes:

• Topographic Wetness Index (TWI) combines slope and upstream contributing area: $TWI = \ln\left(\frac{a}{\tan \beta}\right)$ where $a$ is the specific upslope contributing area (area per unit contour length) and $\beta$ is the local slope angle. High TWI values flag areas prone to soil saturation, making it useful for mapping potential wetlands, recharge zones, and flood-susceptible areas.
• Geomorphometric classification algorithms analyze local geometry to automatically identify landforms like ridges, valleys, peaks, and depressions. These rely on combinations of slope, curvature, and relative position within the landscape.

DEM Integration for Geophysical Interpretation

A DEM on its own shows you surface shape. Combining it with other datasets is where the real analytical power emerges.

Enhancing Understanding through Data Integration

Geological maps and structural data overlaid on DEMs reveal how subsurface geology shapes the landscape. Faults often produce linear scarps or offset drainage patterns visible in the topography. Folds can create systematic asymmetries in ridge profiles. Draping structural data onto a 3D DEM visualization makes these relationships much easier to interpret.

Remote sensing imagery (multispectral, hyperspectral) combined with DEMs enables mapping of surface materials, vegetation, and land use in a topographic context. For example, you can distinguish erosion-prone bare soil on steep slopes from vegetated stable areas, or track how land cover change correlates with terrain position.

Integrating Geophysical and Deformation Data

Gravity, magnetic, and seismic data gain context when viewed alongside surface topography. A gravity anomaly that aligns with a topographic depression might indicate a sedimentary basin, while a magnetic anomaly along a ridge could reflect an exposed igneous intrusion. The DEM helps constrain where subsurface features connect to surface expressions.

Surface deformation monitoring using GPS and InSAR data integrated with DEMs allows you to track ground movements from earthquakes, volcanic inflation, and landslides. The DEM provides the baseline topography against which deformation is measured and helps interpret whether observed movements correlate with specific terrain features like fault scarps or steep slopes.

Hydrological modeling benefits from combining DEMs with soil property maps, land cover data, and climate variables (precipitation, evapotranspiration). This integration enables simulation of surface runoff, subsurface flow, soil moisture dynamics, and flood hazard assessment.

When integrating datasets, pay attention to:

• Resolution mismatches between datasets (a 90 m DEM paired with 10 m land cover data requires resampling decisions)
• Coordinate system differences that need reprojection
• Error propagation, since uncertainties in each dataset compound in the integrated analysis

DEM Applications in Landslide Susceptibility and Groundwater Exploration

Landslide Susceptibility Mapping

Landslide susceptibility mapping estimates the spatial likelihood of landslide occurrence by combining topographic, geological, and environmental factors. DEMs are central to this because they provide the topographic predictors that most strongly control slope failure.

Key DEM-derived inputs for landslide models include:

• Slope gradient: Steeper slopes experience greater gravitational shear stress. Most landslide inventories show a strong correlation between failure locations and slopes above a critical threshold (often 25°–35°, depending on material).
• Aspect: Controls moisture and vegetation patterns that affect slope stability.
• Curvature: Concave slopes concentrate water, increasing pore pressure and failure risk.
• TWI and stream power index (SPI): Indicate where soil saturation and erosive energy are highest, both of which are landslide triggering factors. SPI is calculated as $SPI = a \times \tan \beta$, where $a$ is the specific catchment area and $\beta$ is slope.

Combining these topographic attributes with geotechnical data (soil shear strength, cohesion, groundwater table depth) and rainfall patterns produces susceptibility models that account for both surface and subsurface controls on stability. Statistical approaches like logistic regression or machine learning classifiers are commonly used to weight these factors against known landslide inventories.

Groundwater Exploration

DEMs help identify where groundwater accumulates, recharges, and discharges by revealing the topographic controls on subsurface water flow.

Drainage network delineation and catchment analysis highlight recharge zones (typically topographic highs with permeable soils) and discharge zones (topographic lows, springs, and gaining streams). Flow accumulation patterns point to areas where surface water concentrates and potentially infiltrates.

Integrating DEMs with geological and hydrogeological data strengthens the analysis:

• Lithology maps identify permeable vs. impermeable formations
• Fracture network data reveal preferential flow paths through bedrock
• Aquifer property data constrain where productive wells are most likely

The TWI, introduced earlier, also serves as a proxy for groundwater potential. Areas with high TWI values tend to have shallow water tables and higher soil moisture, making them priority targets for exploration.

Combining DEMs with geophysical survey data (electrical resistivity tomography, seismic refraction) further refines the picture. Resistivity data can delineate aquifer boundaries and estimate saturated thickness, while the DEM provides the surface topographic framework that controls recharge distribution. Together, these datasets guide well placement decisions and aquifer characterization far more effectively than any single data source alone.