[Runoff] [Questions] [Problems] [References] • [Top] [Precipitation] [Hydrologic Abstractions]
S
S
urface runoff in catchments occurs as a progression of the following forms, from small to large:1. Overland flow, 2. Rill flow, 3. Gully flow, 4. Streamflow, and 5. River flow.
Overland flow is runoff that occurs during or immediately after a storm, in the form of sheet flow over the land surface [Fig. 2-30 (a)]. Rill flow is runoff that occurs in the form of small rivulets, primarily by concentration of overland flow. Gully flow is runoff that has concentrated into depths large enough so that it has the erosive power to carve its own deep and narrow channel (b). Streamflow is concentrated runoff originating in overland flow, rill flow, or gully flow and is characterized by well defined channels or streams of sizable depth (c). Streams carry their flow into larger streams, which flow into rivers to constitute river flow (d).
Fig. 2-30 (a) Overland flow. Fig. 2-30 (b) Gully flow.
Fig. 2-30 (c) Streamflow. Fig. 2-30 (d) River flow.
A catchment can range from as little as 1 ha (or acre) to millions of square kilometers (or square miles). [The Amazon basin is 6.915 million km2]. Small catchments (small watersheds) are those where runoff is primarily controlled by overland flow processes. Large catchments (river basins) are those where runoff is controlled by storage processes in the river channels. Between small and large catchments, there is a wide range of catchment sizes with runoff characteristics falling somewhere between those of small and large catchments. In United States practice, midsize catchments are referred to as either watersheds or basins, depending on their drainage area.
Regardless of their size, catchments can drain either inwards, into lakes (or seasonally dry lakes in arid regions), or outwards, and head toward the ocean. Catchments draining inwards have endorheic
(or inland continental) drainages (Fig. 2-31). Catchments draining outwards have exorheic (or peripheral continental) drainages. Exorheic drainages have a catchment outlet or mouth at the point of delivery to the next largest stream, and ultimately, to the ocean.
Fig. 2-31 The Great Basin, the largest endorheic basin in the United States.
The hydrologic characteristics of a catchment are described in terms of the following properties:
(1) area, (2) shape, (3) relief, (4) linear measures, (5) topology, (6) density, and (7) drainage patterns.
Catchment Area
Area, or drainage area, is perhaps the most important catchment property. It determines the potential runoff volume, provided the storm covers the whole area. The catchment divide is the loci of points delimiting two adjacent catchments, i.e., the collection of high points (peaks and saddles) separating catchments draining into different outlets. Due to the effect of subsurface flow (groundwater flow), the hydrologic catchment divide may not strictly coincide with the topographic catchment divide (Fig. 2- 32). The hydrologic divide, however, is less tractable than the topographic divide; therefore, the latter is preferred for practical use.
Fig. 2-32 A river coming out of the ground (Huanuco, Peru).
The topographic divide is delineated on a quadrangle sheet or other suitable topographic map. The direction of surface runoff is perpendicular to the contour lines. All peaks and saddles are identified at the outset (Fig. 2-33). Runoff from a peak is in all directions; runoff from a saddle is in the two opposing directions perpendicular to the saddle axis. The catchment divide is delineated by joining peaks and saddles with a line which remains perpendicular to the topographic contour. The area enclosed within the topographic divide is measured to determine the catchment area.
Fig. 2-33 Delineation of watershed boundary in Campo Creek, Southeast San Diego County, California (peaks and saddles are shown as purple dots).
In general, the larger the catchment area, the greater the amount of surface runoff and, consequently, the greater the surface flows. Several formulas have been proposed to relate peak flow to catchment area (Chapter 7). A basic formula is:
Qp = c A n (2-49)
in which Qp = peak flow, A = catchment area, and c and n are parameters to be determined by regression analysis. Other peak flow methods base their calculations on peak flow per unit area, for instance, the TR-55 method (Chapter 5).
Catchment Shape
Catchment shape is the outline described by the horizontal projection of a catchment. Horton [28]
described the outline of a normal catchment as a pear-shaped ovoid. Large catchments, however, vary widely in shape. A quantitative description is provided by the following formula [26]:
A Kf = _______
L 2
(2-50)
in which Kf = form ratio, A = catchment area, and L = catchment length, measured along the longest watercourse. Area and length are given in consistent units such as square kilometers and kilometers, respectively.
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. This leads to:
0.282 P Kc = ____________
A 1/2
(2-51)
in which Kc = compactness ratio, P = catchment perimeter, and A = catchment area, with P and A given in any consistent set of units.
Hydrologic response refers to the relative concentration and timing of runoff (Fig. 2-34). The role of catchment shape in hydrologic response has not been clearly established. Other things being equal, a high form ratio (Eq. 2-50) or a compactness ratio close to 1 (Eq. 2-51) describes a catchment having a fast and peaked catchment response. Conversely a low form ratio or a compactness ratio much larger than 1 describes a catchment with a delayed runoff response. However, many other factors, including catchment relief, vegetative cover, and drainage density are usually more important than catchment shape, with their combined effect not readily discernible.
Fig. 2-34 Hydrologic response of La Leche river basin, Lambayeque, Peru.
Catchment Relief
Relief is the elevation difference between two reference points. Maximum catchment relief is the elevation difference between the highest point in the catchment divide (Fig. 2-35) and the catchment outlet. The principal watercourse (or main stream) is the central and largest watercourse of the catchment and the one conveying the runoff to the outlet. Relief ratio is the ratio of maximum catchment relief to the catchment's longest horizontal straight distance measured in a direction parallel to that of the principal watercourse. The relief ratio is a measure of the intensity of the erosional processes active in the catchment.
Fig. 2-35 Highest point in the Missouri river basin, along the border between Montana and Idaho (click -here- to display).
The overall relief of a catchment is described by hypsometric analysis [52]. This refers to a dimensionless curve showing the variation with elevation of the catchment subarea above that elevation (Fig. 2-36). To develop this curve, the elevation of the highest or maximum point in the catchment divide, corresponding to 0 percent area, is identified. Also, the elevation of the lowest or minimum point of the catchment, corresponding to 100 percent area, is identified. Subsequently, several elevations located between maximum and minimum are selected, and the subareas above each one of these elevations determined by measuring along the respective topographic contour lines. The elevations are converted to height above minimum elevation and expressed in percentage of the maximum height. Likewise, the subareas above each one of the elevations are expressed as percentages of total catchment area. The hypsometric curve shows percent area in the abscissas and percent height in the ordinates (Fig. 2-36). The median elevation of the catchment is obtained from the percent height corresponding to 50 percent area.
Fig. 2-36 A hypsometric curve.
The hypsometric curve is used when a hydrologic variable such as precipitation, vegetative cover, or snowfall shows a marked tendency to vary with altitude. In such cases, the hypsometric curve provides the quantitative means to evaluate the effect of altitude.
Other measures of catchment relief are based on stream and channel characteristics. The longitudinal profile of a channel is a plot of elevation versus horizontal distance (Fig. 2-37). At a given point in the profile, the elevation is usually a mean value of the channel bed. Between any two points, the channel gradient (or channel slope) is the ratio of elevation difference to horizontal distance separating them.
Fig. 2-37 Typical shape of the longitudinal profile of streams and rivers.
In the absence of geologic controls, longitudinal profiles of streams and rivers are usually concave upward, i.e. , they show a persistent decrease in channel gradient in the downstream direction as the
flow moves from mountain streams to river valleys and into the ocean (Fig. 2-37). The reason for this downstream decrease in channel gradient requires careful analysis. It is known that channel gradients are directly related to bottom friction and inversely related to flow depth. Typically, small mountain streams have high values of bottom friction (due to the presence of cobbles and boulders in the stream bed) and small depths [[Fig. 2-38 (a)]. Conversely, large rivers have comparatively lower values of bottom friction and larger depths [Fig. 2-38 (b)]. This interaction of channel gradient and bottom friction helps explain the typical decrease in channel gradient in the downstream direction.
Fig. 2-38 (a) Rachichuela Creek, Lambayeque, Peru.
Fig. 2-38 (b) Mouth of the Amazon river, Amapa, Brazil.
Convex channel bed profiles (Fig. 2-39) are caused by tectonism, uplift, geologic controls, or rock outcrops predominating over an otherwise alluvial channel morphology in equilibrium. These convex stream profiles usually lead to sediment deposition upstream of the outcrop, and to channel erosion immediately downstream.
Fig. 2-39 Bed profile of El Barbon-Guadalupe Creek, Baja California, Mexico.
Channels gradients are usually expressed in dimensionless units. For convenience, they can be also expressed in m km-1, cm km-1, or ft mi-1. In nature, channel gradients vary widely, from higher than 0.1 in very steep mountain streams [see, for instance, Fig. 2-38 (a)], to less than 0.000006 in large tidal rivers [19].
In certain unusual geomorphological settings, inland rivers may feature very small channel gradients;
for instance, the Upper Paraguay river near Porto Murtinho, Brazil, which has an average channel
slope of 2 cm km-1 (S = 0.00002) (Fig. 2-40).
Fig. 2-40 Upper Paraguay river near Porto Murtinho, Brazil.
The channel gradient of a principal watercourse is a convenient indicator of catchment relief. A longitudinal profile is defined by its maximum (upstream) and minimum (downstream) elevations, and by the horizontal distance between them (Fig. 2-41). The channel gradient obtained directly from the upstream and downstream elevations is referred to as the S1 slope.
A somewhat more representative measure of channel gradient is the S2 slope, defined as the constant slope that makes the shaded area above it equal to the shaded area below it (Fig. 2-41). 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. 2-41 Sketch of S1 and S2 channel gradients.
A measure of channel gradient which takes into account the basin response time is the equivalent slope, or S3. To calculate this slope the channel is divided into n subreaches, and a slope is calculated for each subreach. Based on Manning's equation (Section 2.4), the time of flow travel through each subreach is assumed to be inversely proportional to the square root of its slope.
Likewise, the time of travel through the whole channel is assumed to be inversely proportional to the square root of the equivalent slope. This leads to the following equation:
n
Σ
Li i = 1S3 =
[
_______________]
2n
Σ
( Li / Si 1/2 ) i = 1(2-52)
in which S3 = equivalent slope, Li = each i of n subreach lengths, and Si = each i of n subreach slopes.
Grid methods are often used to obtain measures of land surface slope for runoff evaluations in small and midsize catchments. For instance, the USDA Natural Resources Conservation Service (NRCS) determines average surface slope by overlaying a square grid pattern over the topographic map of the watershed [79]. The maximum surface slope at each grid intersection is evaluated, and the average of all values calculated. This average is taken as the representative value of land surface slope (Fig. 2-42).
Fig. 2-42 Grid overlay to determine land surface slope.
Example 2-9.
Given a longitudinal profile with the following distances and elevations, calculate the slopes S1, S2, and S3.
Distance (m) 0 5,000 10,000 15,000 20,000
Elevation (m) 900 910 930 960 1000
The maximum and minimum elevations are 1000 and 900 m, respectively. The horizontal distance between them is 20,000 m. Therefore, S1 = 100 / 20,000 = 0.005. With reference to Fig. 2-41, S2 = Y / 20,000. The area under the longitudinal profile is 750,000 m2. The area under S2 is: 20,000 Y / 2 = 10,000 Y. Therefore, Y = 75 m, and S2 = 75 / 20,000 = 0.00375. The individual reaches are all 5000 m long, and the individual slopes are 0.002, 0.004, 0.006, and 0.008 respectively. The application of Eq. 2-52 leads to S3 = 0.0041.
The results are shown in Fig. 2-43.
Fig. 2-43 S1, S2, and S3 channel gradients.
Linear Measures
Linear measures are used to describe the one-dimensional features of a catchment. For instance, for small catchments, the overland flow length Lo is the distance of surface runoff that is not confined to any clearly defined channel.
The catchment length (or hydraulic length) L is the length measured along the principal watercourse (Fig. 2-44). The principal watercourse (or main stream) is the central and largest watercourse of the catchment and the one conveying the flow to the outlet.
Fig. 2-44 Linear measures of a catchment.
The length to catchment centroid Lc is the length measured along the principal watercourse, from the catchment outlet to a point located closest to the catchment centroid (point G in Fig. 2-44). In practice, the catchment centroid is estimated as the intersecting point of two or more straight lines that bisect the catchment area in approximately equal subareas.
Basin Topology
Basin topology refers to the regional anatomy of the stream network. Distributed rainfall-runoff modeling (Chapter 10) requires the hierarchical description of stream connectivity, i.e., of its topology.
Stream Order. The concept of stream order classifies streams in a network following a hierarchical numbering system. Overland flow can be considered as a hypothetical stream of zero order. A first- order stream is that receiving flow from zero-order streams, i.e., overland flow. Two first-order streams combine to form a second-order stream. In general, two m-order streams combine to form a stream of order m + 1. The catchment's stream order is the order of the most-downstream main stem (Fig. 2-45).
Fig. 2-45 Concept of stream order. / Concepto de orden arroyo.
A catchment's stream order is directly related to its size. Large catchments may have stream orders of 10 or more. The evaluation of stream order is highly sensitive to map scale. Therefore, considerable care is needed when using stream order analysis in comparative studies of catchment behavior.
Pfasfstetter Coding System. The Pfafstetter coding system is a widely accepted methodology for the description of watershed/basin topology. The system describes the regional anatomy of a stream network using a hierarchical arrangement of decimal digits.
A Level 0 catchment corresponds to a continental-scale size or, alternatively, one that drains into the ocean. Higher levels represent progressively finer subdivisions of the Level 0 catchment.
Theoretically, the system is not limited in the number n of levels. In practice, however, n = 6 to 8 levels are usually sufficient. At each level, each watershed is assigned a specific integer m, varying from m = 0 to 9, based on its location and function within the drainage network.
At each level, watersheds are assigned into three types: (1) basin, (2) interbasin, and (3) internal basin (Table 2-9). A basin is a watershed that does not have upstream inflow. An interbasin is a watershed that has upstream inflow from other watersheds, either basins or interbasins. An internal basin is a watershed that does not have outflow, i.e., it refers to an endorheic or closed basin.
Table 2-9 Subdivision in Pfafstetter Coding System.
No. Type Inflow Outflow
1 Basin NO YES
2 Interbasin YES YES
3 Internal basin YES NO
For each level, from 1 to n, the assignment of Pfafstetter codes is performed as follows:
1. From the catchment outlet, trace upstream along the main stem, and identify the four (4) tributaries with the largest drainage areas. The watersheds containing these four tributaries are classified as basins and assigned even digits (m = 2, 4, 6, and 8) from downstream to upstream.
2. The intervening watersheds, i.e., those contributing lateral inflow to the main stem, are classified as interbasins and assigned odd digits (m = 1, 3, 5, and 7) from downstream to upstream.
3. The last odd digit m = 9 is reserved for the headwater watershed, i.e., that tributary to interbasin 7.
4. The largest internal basin, if present, is assigned the number m = 0. Other internal basins, if present, are incorporated into neighboring basins or interbasins.
Figure 2-46 shows a 3-level example of the Pfasfstetter coding system. For each level, say Level 3, the assigned digits (XYm) are appended on to the Level 2 code (XY). For instance, watershed 849 is watershed 8 of Level 1 (coarser), watershed 4 of Level 2 (intermediate), and watershed 9 of Level 3 (finer).
Fig. 2-46 The Pfafstetter coding system for watershed identification (Click -here- to display).
Drainage Density
The catchment's drainage density is the ratio of total stream length (the sum of the lengths of all streams) to catchment area. A high drainage density reflects a fast and peaked runoff response, whereas a low drainage density is characteristic of a delayed runoff response.
The mean overland flow length is approximately equal to half the mean distance between stream channels. Therefore, it can be approximated as one-half of the reciprocal of drainage density:
1 Lo = _______
2D
(2-53)
in which Lo = mean overland flow length, and D = drainage density. This approximation neglects the effect of ground and channel slope, which makes the actual mean overland flow length longer than that estimated by Eq. 2-53. The following equation can be used to estimate overland flow length more precisely:
1
Lo = _________________________
2D [ 1 - (Sc /Ss) ] 1/2
(2-54)
in which Sc = mean channel slope, and Ss = mean surface slope.
Drainage Patterns
Drainage patterns in catchments vary widely. The more intricate patterns are an indication of high drainage density. Drainage patterns reflect geologic, soil, and vegetation effects (Fig. 2-47) and are often related to hydrologic properties such as runoff response or annual water yield. Types of drainage patterns that are recognizable on aerial photographs are shown in Fig. 2-48 [30].
Fig. 2-47 Drainage patterns as affected by local geology.
Fig. 2-48 Drainage patterns recognizable on aerial photographs.