Catchment Area

• Drainage area determines the potential runoff volume, provided the storm covers the whole area.

• The larger the catchment, the less likely that the storm will cover all the area.

• The collection of peaks and saddles determine the location (loci) of the catchment divide.

• The topographic divide may not coincide with the hydrologic divide (subsurface flow)

• Unless there is a detailed groundwater flow evaluation, the topographic divide is used as a hydrologic divide.

• Runoff originates at high points and moves toward lower points in a direction perpendicular to the terrain's contour lines.

• Several formulas have been proposed to relate peak flow to catchment area.

• A basic formula is:

  Qp = C Am

  in which:

  Q_p = peak flow

  A = catchment area

  c and m = constants.

Catchment Shape

• Horton described the outline of a normal catchment as a pear-shaped ovoid.

• A form ratio is defined as:

  Kf = A / L2

  in which:

  K_f = form ratio

  A = catchment area

  L = catchment length, measured along the longest watercourse.

• An alternate description is based on catchment perimeter rather than area.

• For this purpose, an equivalent circle is defined as a circle of area equal to that of the catchment.

• The compactness ratio is the ratio of the catchment perimeter to that of the equivalent circle.

  Kc = Pc / Pe

  Pe = π Dc

  Ac = (π/4) (Dc)2

  Pe = π (4Ac/π)1/2

  Kc = Pc / [2 (π)1/2 Ac1/2]

  Kc = 0.282 Pc / Ac1/2

  in which:

  K_c = compactness ratio

  P_c = catchment perimeter

  P_e = perimeter pf the equivalent circle

  A_c = catchment area.

   

• Catchment response refers to the relative concentration and timing of runoff.

• A high form ratio or a compactness ratio close to 1 describes a catchment having a fast and peaked catchment response.

• Other factors such as relief, vegetative cover, and drainage density are usually more important than shape in determining catchment response.

Catchment relief

• Maximum catchment relief is the elevation difference between the highest point in the catchment divide and the lowest point, located at the catchment outlet.

• The principal watercourse is the largest watercourse, and the one conveying the flow to the outlet.

• Relief ratio is the ratio of maximum catchment relief and the longest horizontal distance, measured along the principal watercourse.

• The relief ratio is a measure of the intensity of erosional processes, or geodynamics.

• Relief is quantitatively described with a hypsometric curve.

• This is a dimensionless plot of the variation of surface area with elevation.

• To develop a hypsometric plot, several elevations are selected, and each elevation is associated with a partial area above that elevation.

• Elevations and partial areas are expressed in percentage of the maximum height and area, respectively.

Fig. 2-17

• The longitudinal profile of a channel is a plot of elevation vs horizontal distance.

• Channel slope or channel gradient is the ratio of vertical to horizontal distance.

• In the absence of geologic controls, longitudinal profiles are usually concave when viewed from above.

• Channel gradients are directly related to bottom friction and inversely related to flow depth.

• Typically, friction decreases and flow depth increases in the downstream direction.

• If the profile is convex, there are geologic controls (rock outcroppings) acting to invalidate the geomorphological principle.

Fig. 2-18

• Channel gradients vary widely, from steeper than 0.1 to as mild as 0.000006.

• The channel gradient obtained from the maximum and minimum elevations is referred to as S₁ slope.

• The S₂ slope is the constant slope that makes the shaded area above it equal to the shaded area below it.

• An expedient way to calculate the S₂ slope is to equate the total area below it to the total area below the longitudinal profile.

Fig. 2-19

• S₃ equivalent slope takes into account the basin response time.

• The channel is divided into n subreaches, and a slope calculated for each subreach.

• The time of travel through each subreach is directly proportional to its length and inversely proportional to its velocity, i.e., to the square root of its slope (the Manning equation).

• The time of travel through the whole channel is assumed to be directly proportional to its length and inversely proportional to the square root of S₃.

Eq. 2-55

• The USGS State Equations compute channel slope S between two points located at 10% and 85% of the channel, measured in the upstream direction.

• The NRCS (ex SCS) determines average surface slope by overlying a square grid pattern over a topographic map of the watershed.

• The maximum slope at each intersection is evaluated, and the average of all values calculated.

  Fig. 2-20

Linear Measures

• The catchment length (or hydraulic length) is the length measured along a principal watercourse.

• The length to catchment centroid is the length measured along the principal watercourse, from the catchment outlet to a point located closest to the catchment centroid.

• Stream order is essential to the hierarchical description of streams.

• Overland flow is of hypothetical zero order.

• A first-order stream receives flows from zero-order streams.

• Two first-order streams combine to form a second-order stream.

• The catchment's stream order is the order of the main stream at the mouth.

Figs. 2-22 and 2-23

Drainage density

• The catchment's drainage density is the ratio of total stream length to catchment area.

• D = ΣL / (2 L_o ΣL) = 1 / (2 L_o)

• L_o = mean overland flow length

• A high drainage density reflects a fast and peaked runoff response.

• A low drainage density is characteristic of a delayed response.

• The mean overland flow length is approximately equal to half the mean distance between stream channels.

• It can be estimated as one-half of the reciprocal of the drainage density.

Lo = 1 / (2D)

• This approximation neglects the effect of channel and surface (ground) slope, which increases the value of L_o.

• Use the following equation to include channel and surface slope into overland flow length calculation:

Lo = 1 / {(2D) [1 - (Sc / Ss)]}

Drainage patterns

• Drainage patterns vary widely.

• Types of drainage patterns that are recognizable on aerial photos are shown in Fig. 2-24.

• There patterns reflect geologic, soil, and vegetation effects, and are related to hydrologic properties such as runoff response or annual water yield.

Fig. 2-24

Go to Chapter 2D.