1. Stream Networks & Geomorphology
In running from the land to the sea water organizes itself into drainage networks which reflect original geological structures and are bounded by topographic or subsurface water divides to form basins.
Over geologic time channel networks evolved so as to dispose of water’s potential and kinetic energy in the most efficient manner.
Geomorphology is the quantitative study of the surface landform and is used to arrive at measures of geometric similarity among watersheds, especially among their stream networks.
The line that separates adjacent basins, passing through the highest points between them and leaving all the branches of the rivers at opposite sides is called water divide or boundary of basin.
The area in this boundary is the drainage area. The length of the boundary is called perimeter.

2. Surface and Subsurface Divides
Surface and subsurface divides may change according to the geologic formation below the surface.

3. Basins Gradient
Gradient of the basin is best defined by and area-elevation (hypsometric) curve of the basin.
Relief is the elevation difference between two points. Maximum basins relief is the elevation difference between the highest point on the boundary and the lowest point (outlet)

4. Horton’s (Strahler) Stream Ordering
Stream that takes no branch but only overland flow is called a first order stream.
When two first order streams join, they form a 2nd order stream
3rd order streams are formed when two 2nd order streams join
When a lower order stream joins a higher order the stream order does not change
When nth and mth order streams merge, the resultant stream order is
max(n,m) if n m
(n+1) or (m+1) if n = m

5. Horton’s (Strahler) Stream Ordering
Very sensitive to map scale
A 1:50,000 scale map will show a few orders more than a map with 1:100,000 scale
At 1:25,000 Mississippi River is a 12th order stream at its mouth
The order of the basin is the highest stream order
In this example this is a 4 order basin

6. Law of Stream Number
Horton (1945) found empirically that the bifurcation ratio RB, or the ratio of the number Ni, of channels of order i to the number Ni+1 of channels of order i+1 is relatively constant from one order to another.
For the basin previous slide: N1=23, N2=11, N3=3, N4=1.
Plot stream order, i versus logarithm of number of streams with order i (Ni).
RB = e-slope  RB = 2.9

7. Law of Stream Number
RB gives information about the shape of the basin, consequently shape of the outflow hydrograph

8. Some other Concepts
Drainage Density (Dd ): Total length of all the branches of a river per unit drainage area.
Dd from USGS topo maps at 1:24,000 are close to observed field values (Sellman and Dingman, 1970)
Drainage Frequency (Df ): Same with drainage density but use number of branches instead of total length of branches
Low of Stream Lengths and Areas:
If streams are fed by Hortonian overland flow, then he average length of overland flow, L0 is approximated by L0 = 1/2Dd
Fraction of a watershed draining directly to first-order streams:
where RB is bifurcation ratio, RA is drainage area ratio, and W is the order of the largest stream.