3.2 Topographic Mapping, Contours, and Digital Terrain Models

Contours and Contour Interval

A contour line connects points of equal elevation referenced to a vertical datum (usually NAVD 88). Contours are interpreted, not directly observed: they are drawn by interpolating between surveyed spot elevations or a terrain model. Several rules govern their behavior and appear directly on the FS exam:

• Contours are closed loops (they may close beyond the map edge).
• Contours never cross or merge, except at a vertical cliff (touch) or an overhang (briefly cross).
• Closely spaced contours indicate steep slopes; widely spaced indicate gentle slopes.
• Contours point upstream (V's point uphill) when crossing a stream or valley and point downhill across a ridge.
• Evenly spaced parallel contours indicate a uniform slope.

The contour interval (CI) is the constant vertical distance between adjacent contours. It is selected from terrain relief and map scale: flat terrain and large-scale mapping use small intervals (0.5-2 ft); rugged terrain or small scale uses larger intervals (5-20 ft). Every fifth contour is usually an index contour, drawn heavier and labeled.

Spot Elevations, Breaklines, and Surface Structure

A topographic survey samples the ground with spot elevations at points and along features. The mapped surface is only as good as where it was sampled. Two structural elements control quality:

• Breaklines are linear features where the slope changes abruptly: ridges, valleys (drainage), curb lines, ditch flowlines, edges of pavement, and walls. A surface built without breaklines will round off these edges, flattening a ditch or rounding a curb and corrupting drainage and volume results.
• Mass points are general ground shots that fill in between breaklines.

A terrain model can be accurate at every surveyed point yet wrong between points if structure (breaklines, adequate density) is missing. FS scenarios frequently exploit this: dense shots on open ground but none along a critical drainage swale yield contours that miss the swale entirely.

Digital Terrain Models: TIN vs. Grid

A digital terrain model (DTM) or digital elevation model (DEM) represents the bare-earth surface. Two structures dominate:

1. A TIN (triangulated irregular network) connects mass points and breakline vertices into non-overlapping triangles (Delaunay triangulation). TINs honor breaklines exactly and adapt density to terrain.
2. A grid/raster DEM stores elevations on a regular cell spacing; it is simple and fast but can miss features smaller than a cell.

Distinguish the surfaces by what they include: a DTM/DEM is bare earth (ground only), a DSM (digital surface model) is the top of everything (tree canopy, rooftops, the first reflective surface). The difference DSM minus DTM gives feature heights (canopy height, building height).

Using Terrain Models: Slope, Volume, and Routes

From a DTM the engineer derives slope and aspect, watershed and drainage paths, earthwork volumes, and route profiles. Earthwork is commonly computed by comparing existing and proposed surfaces using the average-end-area method between cross sections, V = (A1 + A2)/2 x L, or by prismoidal and grid (borrow-pit) methods.

Because contours and volumes are derived from the model, surveyors validate the model against independent check shots rather than trusting the contours themselves. The right surface depends on the task: clearance and canopy studies need a DSM; grading, drainage, and earthwork need a bare-earth DTM. Choosing the wrong surface (e.g., a DSM where a bare-earth model is required) is a classic FS error scenario.

Interpolating Elevations and Reading Slopes

A frequent FS calculation is linear interpolation of a point's elevation between two contours or two spot shots. If point P lies on a uniform slope between elevation A and elevation B, its elevation is E_P = A + (d_A / D) x (B - A), where d_A is the horizontal distance from the A contour and D is the total horizontal distance between the two contours. The same proportion locates where a target contour crosses a survey line.

Slope is the ratio of vertical change to horizontal change, reported as a percent (rise/run x 100), as a ratio (H:V, e.g., 3:1 = three horizontal to one vertical), or as an angle. On a contour map, slope between two contours is the contour interval divided by their horizontal separation at map scale. Steep grades therefore crowd contours together; flat ground spreads them apart. A surveyor reads drainage from this: water flows perpendicular to the contours, toward lower elevation.

Sources of Terrain Data and Their Limits

Terrain models are built from several sources, each with characteristic density and accuracy: conventional total-station/GNSS shots (sparse but very accurate at each point), photogrammetry (dense, surface-only), and LiDAR (dense, can reach bare earth under vegetation). The model's reliability is governed by point density, the presence of breaklines, and how the surface was triangulated or gridded, not merely by the accuracy of individual shots.

A model can therefore meet a vertical accuracy spec at check points yet still misrepresent a feature it never sampled — which is why breaklines and adequate density, not just point accuracy, decide whether contours and volumes can be trusted.