title: "Chapter 2 — Watershed Delineation" chapter: 2

Chapter 2 — Watershed Delineation

Every raindrop that falls on land belongs to exactly one drainage basin. The invisible line separating basins — the watershed divide — can be drawn automatically from any DEM using the flow-direction grid we built in Chapter 1.

2.1 — What Is a Watershed?

A watershed (or catchment) is the set of all cells whose water eventually reaches a given pour point — the outlet where flow leaves the area of interest. The contributing area $A$ at a pour point $(i,j)$ satisfies:

Every cell upstream of $(i,j)$ is part of its watershed; every cell that drains elsewhere is not.

Click any cell to trace its path downstream ("Trace Down"), or to light up every cell that drains through it ("Show Watershed"). Left-click a cell in the watershed mode to relocate the pour point; check "✏️ Edit Terrain" to modify elevations.

Notice how clicking the outlet corner (3,3) highlights all 16 cells — the entire grid is one watershed when there is a single outlet. Move the pour point inland to select only the contributing sub-area.

2.2 — The Upstream Tracing Algorithm

D8 arrows point downstream. To find a watershed we must follow them backwards — a Breadth-First Search (BFS) upstream.

watershed ← {pour_point}
queue     ← [pour_point]

while queue not empty:
    (r, c) ← queue.dequeue()
    for each neighbour (nr, nc) of (r, c):
        if flow[nr][nc] points INTO (r, c):   # arrow tip lands on (r,c)
            watershed.add(nr, nc)
            queue.enqueue(nr, nc)

The key test: does flow[nr][nc] point into (r,c)? In D8 terms, nr + Δr = r and nc + Δc = c.

Click any cell to place the pour point, then press "▶ Delineate" to watch BFS expand step by step. The queue panel on the right shows pending cells (amber = currently examined); the step log records every neighbour check.

BFS visits every cell at most once, so delineation runs in $O(MN)$ — a full continental DEM with 10⁸ cells takes only seconds.

2.3 — Divides, Multiple Catchments & Stream Order

Real landscapes contain many basins separated by divides — ridgelines where adjacent cells flow in opposite directions.

Tab 1 colours the two basins and marks divide cells in orange. Tab 2 animates two raindrops released on either side of the ridge — they flow to opposite outlets. Tab 3 shows the Strahler stream order: order 1 at headwaters, order increases only when two streams of the same order merge.

The ridge terrain splits cleanly into two 8-cell basins. Drag the FA threshold slider in Tab 3 to see how the stream network grows as you lower the minimum contributing area.

2.4 — Explore Full Terrain

Switch between five 8×8 presets — valley, mountain, ridge, slope, basin — and explore how terrain shape controls basin geometry and stream structure.

• ✏️ Edit: raise / lower any cell; watershed and streams update instantly.
• 📍 Pour Point: click any cell to delineate its watershed in one step.
• 🌊 Stream Network: view the channel network without a pour point; adjust FA threshold $\tau$.

Toggle Strahler Colors to see stream order superimposed on the watershed shading.

2.5 — For Grad Students

Pfafstetter coding (1997) — hierarchical basin numbering 1–9; odd digits = tributary basins, even digits = mainstem inter-basin segments. Up to 9 nesting levels encode every sub-basin globally without overlap:

Hypsometric curve — cumulative fraction of area above elevation $h$:

HI > 0.6 → young, actively dissected landscape; HI < 0.35 → peneplain (monadnock stage).

Flat-area routing — Wang & Liu fill creates artificial flats where D8 is ambiguous. Solutions: (1) Priority-Flood + $\varepsilon$-gradient (Barnes 2014); (2) least-cost-distance routing (LDD); (3) D∞ on the original unfilled DEM.

Algorithmic complexity:

Summary

Chapter 3 → Rainfall–runoff processes — how precipitation becomes streamflow through Hortonian overland flow, saturation-excess, and infiltration.