11. Channel form: river cross- sections and long profiles Cross-section size and shape –The role of discharge and drainage area –Local variation –The role of perimeter sediment Longitudinal profiles –Equations characterizing long profiles –Degrees of concavity

Cross-section characteristics Cross-section size and shape essentially a function of drainage area and bed/bank material characteristics Variables used to define cross-section size and shape: - width (w) - average depth (d) - cross-section area (product w. d) - w/d Empirical relations established between drainage area (A d ) and variables defining cross-section size and shape; e.g. w = k A d a

Channel form and hydraulic geometry As a surrogate for drainage area, discharge (e.g. mean annual discharge) is usually used in empirical relations (in temperate climates, mean annual discharge is roughly proportional to drainage area) The most commonly used hydraulic geometry relations used are: w = a Q b d = c Q f U = kQ m where w is channel width, d is average depth, U is average velocity and Q is discharge

Hydraulic geometry relations The exponents b, f, and m represent the rate of change of width, depth, and velocity with increasing discharge downstream (note that b + f + m =1). Characteristic exponents of hydraulic geometry relations: b = 0.5 in w = a Q b f = 0.4 in d = c Q f m = 0.1 in U = kQ m Implications: –Slight increase in average velocity (U) with increasing distance downstream –Width increases faster than depth in most rivers – with distance downstream

The role of perimeter sediment on channel form Difficult to quantify because: –Bank material size may vary rapidly longitudinally and vertically within a bank –“Erodibility” depends also on antecedent moisture conditions Ratio of width to depth decreases as % of silt and clay on banks increases Examples of empirical relations involving discharge and bank or bed material size: d = 0.4 Q 0.4 D w = 25 Q 0.6 B -0.6 where D 90 : bed material size and B: % of silt-clay bank material

The role of vegetation Vegetation has a clear and direct influence on channel shape (ratio of width to depth as well as degree of asymmetry) Presence of vegetation increases degree of cohesion of banks (restrain bank erosion) Both type of vegetation and density are significant –from grass to shrub to trees: gradual increase in degree of cohesion –Bank cohesion (and resistance to erosion) also increases with an increase in the density of vegetation

…the role of vegetation So, banks with dense population of tress will tend to be narrower and deeper than grass and shrubs….

Local variations… There are many additional factors which, locally, affect size and shape of a given cross-section (in addition to drainage area) –Changes in boundary conditions (perimeter sediment) –Changes in bank vegetation characteristics –Meander planform characteristics These local variations can be used to explain the “scatter” observed in empirical hydraulic geometry relations

Long profile characteristics

Long profiles…. (i)Description A long profile is a graph of elevation (E) against distance downstream (D d ) E = f (D d ) –Elevation is actually decreasing exponentially downstream –Long profiles can be characterized by: E = a – b log D d

…long profile (ii) Controls on channel gradient Channel gradient therefore decreases downstream and: S = k D a A d -b S: channel slope D: bed material size A d : drainage area

Long profile characteristics… Slope at any point is related to bed material size and discharge (or drainage area) Variations in profile concavity (or downstream rate of change of channel slope) can be explained in terms of downstream change in grain size and discharge –Profiles more concave when bed material size decreases more rapidly –Greater rate of change in channel slope when discharge increases rapidly –This, in turn, implies an ability to transport the same bed material load over progressively lower slopes

It is important to mention that the size and sorting of the bed material at any point are determined by: –The initial conditions of supply (over which type of bed material the river is flowing) –The subsequent action of sorting and abrasion processes during downstream transport

Bedrock influences on long profiles… Bedrock type influences initial size and its downstream rate of reduction Different lithologies do present profiles with different concavities: e.g. S = 0.05 D d shale S = D d limestone S = D d sandstone