Watershed Characteristics

January 28, 2000

Watershed: Definition and Delineation

The concept of a watershed is basic to all hydrologic designs. Since large watersheds are made up of many smaller watersheds, it is necessary to define the watershed in terms of a point. This point is usually the location at which the design is being made and is referred to as the watershed “outlet”. With respect to the outlet, the watershed consists of all land area that “sheds” water to the outlet during a rainstorm. Using the concept that “water runs downhill”, a watershed is defined by all points enclosed within an area from which rain falling at these points will contribute water to the outlet. Figure 1. depicts the delineation of a watershed boundary.

Figure 1. Delineation of a watershed boundary.

The Delineation Process:

Information Sources

USGS Topographic Maps

The fundamental source of data that we use for delineating and studying watersheds is the U.S. Geological Survey Quadrangle map. Each “Quad Sheet” map covers 7.5 minutes of longitude and latitude. These maps give a wealth of information including topographic contour lines, locations of cities, buildings, roads, road types, railroads, pipelines, water bodies, forested land, stream networks, and USGS stream gauging stations and benchmarks.

Quad sheet maps typically have a scale of 1:24,000 (i.e. 1 inch on the map = 24,000 inches in the real world). Depending on the age of the map, elevation data may be in English or Metric units. Typically, here in the Midwest, the contour intervals of the elevation data are 5 feet or 1.5 meter. For watershed delineation, quad sheet maps offer us the best starting point. More detailed analysis would require a detailed topographic survey of the area of interest. Topographic maps are generally available at all state and federal geological survey offices and can now be ordered over the internet. The cost of a 1:24,000 scale map is $4.00. For more information on USGS mapping products check out http://mapping.usgs.gov/.

Digital Elevation Models

In this age of computers, geographic data can now be stored electronically. Digital Elevation Models (DEM’s) store topographic data in the form of grid cells. Typically, these grid cells have a resolution of 30 meters and elevation intervals of 1 foot or 1 meter. Using a DEM within a Geographical Information System (GIS), we can perform digital terrain analysis (DTA) such as calculating slopes, flow lengths, and delineate watershed boundaries and stream networks. However, there are certain drawbacks to DTA because some algorithms are not very smart, especially in delineating watershed boundaries. To find DEM’s for the state of Michigan, check out http://edc.usgs.gov/doc/edchome/ndcdb/7_min_dem/states/MI.html

Delineation Steps

There are two basic steps to follow in watershed delineation.

Step 1:

Choose the point of the watershed outlet. This is generally our point of interest for designing a structure or monitoring location.

Step 2:

Delineate the watershed boundary by drawing perpendicular lines across the elevation contour lines for land that drains to the point of interest.

• Note - There are a few things to remember when you are working with topographic maps.

1. A watershed boundary always runs perpendicular to the contour lines.
2. “Arrows” that point upstream are valleys.
3. “Arrows” that point downstream are hills.

Important Watershed Characteristics

Drainage Area

The drainage area (A) is the probably the single most important watershed characteristic for hydrologic design. It reflects the volume of water that can be generated from rainfall. It is common in hydrologic design to assume a constant depth of rainfall occurring uniformly over the watershed. Under this assumption, the volume of water available for runoff would be the product of rainfall depth and the drainage area. Thus the drainage area is required as input to models ranging from simple linear prediction equations to complex computer models.

Watershed Length

The length (L) of a watershed is the second watershed characteristic of interest. While the length increases as the drainage increases, the length of a watershed is important in hydrologic computations. Watershed length is usually defined as the distance measured along the main channel from the watershed outlet to the basin divide. Since the channel does not extend to the basin divide, it is necessary to extend a line from the end of the channel to the basin divide following a path where the greatest volume of water would travel. The straight-line distance from the outlet point on the watershed divide is not usually used to compute L because the travel distance of floodwaters is conceptually the length of interest. Thus, the length is measured along the principal flow path. Since it will be used for hydrologic calculations, this length is more appropriately labeled the hydrologic length.

While the drainage area and length are both measures of watershed size, they may reflect different aspects of size. The drainage area is used to indicate the potential for rainfall to provide a volume of water. The length is usually used in computing a time parameter, which is a measure of the travel time of water through a watershed.

Watershed Slope

Flood magnitudes reflect the momentum of the runoff. Slope is an important factor in the momentum. Both watershed and channel slope may be of interest. Watershed slope reflects the rate of change of elevation with respect to distance along the principal flow path. Typically, the principal flow path is delineated, and the watershed slope (S) is computed as the difference in elevation (DE) between the end points of the principal flow path divided by the hydrologic length of the flow path (L):

S = DE/L

The elevation difference DE may not necessarily be the maximum elevation difference within the watershed since the point of highest elevation may occur along a side boundary of the watershed rather than at the end of the principal flow path.

Watershed Shape

Basin shape is not usually used directly in hydrologic design methods; however, parameters that reflect basin shape are used occasionally and have a conceptual basis. Watersheds have an infinite variety of shapes, and the shape supposedly reflects the way that runoff will “bunch up” at the outlet. A circular watershed would result in runoff from various parts of the watershed reaching the outlet at the same time. An elliptical watershed having the outlet at one end of the major axis and having the same area as the circular watershed would cause the runoff to be spread out over time, thus producing a smaller flood peak than that of the circular watershed.

A number of watershed parameters have been developed to reflect basin shape. The following are a few typical parameters:

1. Length to the center of area (L_ca): the distance in miles measured along the main channel from the basin outlet to the point on the main channel opposite the center of area.

2. Shape Factor (L_l)

L_l = (LL_ca)^0.3

Where L is the length of the watershed in miles

3. Circularity ratio (F_c):

F_c = P/(4pA)^0.5

Where P and A are the perimeter (ft) and area (ft²) of the watershed, respectively.

4. Circularity ration (R_c):

R_c = A/A_o

Where A₀ is the area of a circle having a perimeter equal to the perimeter of the basin.

5. Elongation Ration (R_e):

R_e = 2/L_m(A/p)^0.5

Where L_m is the maximum length (ft) of the basin parallel to the principal drainage lines.

Generally, the shape factor (L_l) is the best descriptor of peak discharge. It is negatively correlated with peak discharge (i.e. as the L_l decreases, peak discharge increases).

Other Important Watershed Factors

Land Cover and Use

Surface Roughness

Soil Characteristics

Texture

Soil Structure

Soil Moisture

Hydrologic Soil Groups

Channel Geomorphology

Channel Length

In addition to the drainage area and the watershed length, the channel length is used frequently in hydrologic computation. Two computational schemes are used to computer the channel length:

1. The distance measured along the main channel from the watershed outlet to the end of the channel as indicated on the figure below, which is denoted as L_c.

2. The distance measured along the main channel between two points located 10 and 85% of the distance along the channel from the outlet, which is denoted at L_10-85.

These definitions along with the watershed length are illustrated below. The watershed length is defined by extending a line on the map from the end of the main channel to the divide. This requires some subjective assessment and is often a source of inaccuracy. The definitions for channel length also involve a measure of subjectivity because the endpoint of the channel is dependent on the way the map was drawn.

Channel

Definition 1: L

Definition 2: L_c

Definition 3: L_10-85

Channel Slope

The channel slope can be described with any one of a number of computation schemes. The most common is

S_c = DE_c/L_c

In which DE_c is the difference in elevation between the points defining the upper and lower ends of the channel and L_c is the length of the channel between the same to points. The 10-85 slope can also be used:

S_10-85 = DE_10-85/L_10-85

For cases where the channel slope is not uniform, a weighted slope may provide an index that better reflects the effect of slope on the hydrologic response of the watershed.

Drainage Density

The drainage density (D0 is the ratio of the total length of streams within a watershed to the total area of the watershed; thus D has units of the reciprocal of length (1/L). A high value of the drainage density would indicate a relatively high density of streams and thus a rapid storm response. Values typically ranges from 1.5 to 6 mi/mi².

D = L_t/A

Horton’s Laws

Our old pal Horton (from Horton’s infiltration equation fame) developed a set of “laws” that are indicators of the geomorphological characteristics of watershed. The stream order is a measure of the degree of stream branching within a watershed. Each length of stream is indicated by its order (for example, first-order, second-order, etc.). A first-order stream is an unbranched tributary, a second-order stream is a tributary formed by two or more first-order streams. A third-order stream is a tributary formed by two or more second-order streams and so on. In general, an n^th order stream is a tributary formed by two or more streams of order (n-1) and streams of lower order. For a watershed, the principal order is defined as the order of the principal channel. The figure below gives an example of stream ordering.

The concept of stream order is used to computer other indicators of drainage character. The bifurcation ratio (R_b) is defined as the ratio of the number of streams of any order to the number of streams of the next highest order. Values of R_b typically range from the theoretical minimum of 2 to around 6. Typically, the values range from 3 to 5. The bifurcation ratio is calculated as

R_b = N_i/N_i+!

From this, Horton developed the Law of Stream Numbers which relates the number of streams of order I (N_i) to the bifurcation ratio and the principal stream order (k)

N_i = R_b^k-1

Example:

The bifurcation ratio of a watershed is the average of the bifurcation ratios of each stream order

For a watershed with a bifurcation ratio of 2.6 and a fourth-order principal stream,

N_i = 2.6^4-I

This would predict 18, 7, and 3 streams of order 1, 2, and 3, respectively.

In addition to this Horton proposed a Law of Stream Lengths, in which the average lengths of the streams of successive orders are related by a length ratio R_L:

R_L = L_i+1/L_i

L_i = L₁r_L^i-1

By similar reasoning, Schumm (1956) proposed a Law of Stream Areas to relate the average areas A_i drained by streams of successive order

R_A= A_i+1/A_i

Example