Rainfall runoff

The streamflow responses to rainfall and snowmelt produce identifiable differences in discharge hydrographs. Rainfall events produce streamflow dominated by surface runoff and or near-surface flow. These conditions can produce abrupt increases in streamflow, especially for small watersheds or urbanized watersheds. Land use and geology can delay runoff and produce less abrupt streamflow increases and more gradual decreases.

The climatic role in the runoff process is characterized by the path followed by water in arriving at the stream channel after it has been delivered to the surface by precipitation. This perspective provides a basis for distinguishing the climatic influence as distinct from the geomorphologic influence imposed by terrain characteristics related to the watershed's size, shape, and relief.

6.10.1 Similar basin area

Examining watersheds with similar size areas reduces some of the physical complexity, but does not eliminate all of the non-climatic influences. However, many watershed physical characteristics are recognized as being highly correlated with the size of the drainage basin, so comparing similar size watersheds reduces a good portion of the expected variability among watersheds. Three small streams emphasize watershed response differences in

K 15

30-Mar Date

26-Sep

Fig. 6.5. Daily mean streamflow (bold line) for Econfina Creek near Bennett, Florida (30° N, 90° W), and daily precipitation (gray line) for Apalachicola, Florida, for 1 October 1941 to 30 September 1942. (Streamflow data courtesy of the U.S. Geological Survey from their website at waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_daily.html.)

30-Mar Date

26-Sep

Fig. 6.5. Daily mean streamflow (bold line) for Econfina Creek near Bennett, Florida (30° N, 90° W), and daily precipitation (gray line) for Apalachicola, Florida, for 1 October 1941 to 30 September 1942. (Streamflow data courtesy of the U.S. Geological Survey from their website at waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_daily.html.)

selected areas of the United States. Daily streamflow for the period 1 October 1941 to 30 September 1942 is used to minimize human influences on runoff for all three watersheds. Precipitation for these months at a representative station near each watershed is used to define the moisture input. Runoff from small watersheds facilitates comparisons by maintaining daily values within ranges that focus on the outcome of the runoff process.

Econfina Creek (Fig. 6.5) in the south central Florida panhandle drains a 317 km2 watershed of relatively low relief underlain by limestone. Monthly precipitation for the period ranges from a low in April to a high in September, but 49% of the annual total is received from May to September. However, little evidence of this regime is seen in the streamflow response, which displays low flows from October to late December and the most consistent high flows in February and March. Most daily precipitation pulses are muted in the stream-flow response by the domination of the low relief and subsurface routes in limestone delivering water to the stream channel. Average daily streamflow is 15.6m3s_1, and the dominant role of base flow is apparent in the consistent flow exceeding 12 m3 s_1. Even during the summer months with a high energy demand for moisture, a major portion of precipitation appears to be allocated to subsurface routes that reduce evapotranspiration losses. Discharge peaks produced by storm events in all months are less than 3-times greater than the low flows during October to late December.

30-Mar Date

26-Sep

Fig. 6.6. Daily mean streamflow (bold line) for Cartecay River near Ellijay, Georgia (34° N, 85° W), and daily precipitation (gray line) for Rome, Georgia, for 1 October 1941 to 30 September 1942. Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/ epubs/ndp/ushcn/usa_daily.html.)

30-Mar Date

26-Sep

Fig. 6.6. Daily mean streamflow (bold line) for Cartecay River near Ellijay, Georgia (34° N, 85° W), and daily precipitation (gray line) for Rome, Georgia, for 1 October 1941 to 30 September 1942. Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/ epubs/ndp/ushcn/usa_daily.html.)

The Cartecay River (Fig. 6.6) drains 348 km2 of the southern tip of the Blue Ridge Mountains in northwestern Georgia. The watershed has relatively steep slopes, and the variable flow throughout the year indicates dominant surface runoff superimposed on a seasonally replenished variable base flow component. Monthly precipitation is greatest in March and least in April. The average daily streamflow is 6.5 m3 s_1. An increasing energy demand for moisture during the summer is evident in the gradually declining streamflow during the summer and fall even though precipitation is 48% of the annual total during these months. Although there is close agreement between daily precipitation pulses and streamflow peaks throughout the year, peak flows in the winter and early spring are especially concordant with precipitation. During this period, soil moisture is maximized, most precipitation is allocated to runoff, and surface runoff is a high proportion of total streamflow. The peak flow in late February is 29-times greater than the minimum flow in late October.

Antelope Creek (Fig. 6.7) drains 320 km2 along the west slope of the southern Cascade Range in northern California. The watershed is characterized by relatively steep terrain and highly variable streamflow. Cool season precipitation is dominant, and January and February account for 49% of the annual total. Average daily streamflow is 6.5m3s_1. June through September receives little precipitation and this is evident in the absence of streamflow peaks in the hydrograph during this period. A summer and fall low-flow period without sharp runoff pulses contrasts markedly with the hydrographs for Econfina

1-Oct 30-Dec 30-Mar 28-Jun 26-Sep

Date

Fig. 6.7. Daily mean streamflow (bold line) for Antelope Creek near Red Bluff, California (40° N, 122° W), and daily precipitation (gray line) for Redding, California, for 1 October 1941 to 30 September 1942. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_daily.html.)

1-Oct 30-Dec 30-Mar 28-Jun 26-Sep

Date

Fig. 6.7. Daily mean streamflow (bold line) for Antelope Creek near Red Bluff, California (40° N, 122° W), and daily precipitation (gray line) for Redding, California, for 1 October 1941 to 30 September 1942. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_daily.html.)

Creek and the Cartecay River, which both display a streamflow response to storm events during these months. An additional contrasting feature is that the Antelope Creek peak flow in February is 2.8-times greater than the March peak flow for the Cartecay River. Antelope Creek received 178 mm of precipitation during a 3-day storm, and peak streamflow followed in one day. The 88 mm of precipitation for the Cartecay River was a single-day event and peak stream-flow occurred four days later. These differences indicate variations in the runoff process within each watershed that are not related to drainage area. Furthermore, a limited groundwater role in the Antelope Creek runoff process is indicated by the 10-times larger mean daily flows in October for Econfina Creek and the 1.6-times larger low flows for the Cartecay River.

6.10.2 Similar basin climate

Holding climate constant permits watershed physical characteristics responsible for water arriving at the stream channel to be emphasized in comparing stream hydrographs. A selection of streams in Northern California simplifies assessment of watershed conditions by maintaining a similar general climate setting in terms of precipitation seasonality. However, precipitation amounts, the energy-driven moisture demand, and watershed physical characteristics are different among the watersheds. The monthly data portrayed in Figure 6.8 are expressed as percentages of annual runoff, which has the advantage of facilitating comparisons among watersheds with different areas.

Month

Fig. 6.8. Monthly percentage of annual runoff for 1971-2000 for three California streams in a generally similar climate setting that emphasizes the influence of topography on the runoff process. (Data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/.)

Month

Fig. 6.8. Monthly percentage of annual runoff for 1971-2000 for three California streams in a generally similar climate setting that emphasizes the influence of topography on the runoff process. (Data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/.)

The Eel River basin (40° N) occupies 8094 km2 on the western slopes of the Coast Ranges in northwestern California. It receives average annual precipitation of 150 cm and produces 79 cm of average annual runoff (Rantz, 1972). Precipitation is concentrated in November to March which accounts for 79% of the annual total. Runoff during December to March dominates the streamflow regime for the Eel River. The coincidence of the precipitation and runoff implies that storm events are the major runoff producers for the watershed. The low runoff percentages during May to October and the abrupt increase in November runoff reflect the widespread occurrence of low permeability strata in the watershed that contributes to meager base flow.

The Orestimba Creek watershed (37° N) covers 348 km2 on the eastern slopes of the Coast Ranges in west-central California. This semiarid area receives about 25% of the precipitation amount occurring in the Eel River basin. The average annual precipitation for Orestimba Creek is 41 cm, and this produces 4 cm of average annual runoff (Rantz, 1972). The Orestimba Creek runoff regime is typical of a semiarid intermittent stream. Little or no runoff occurs during July through November, and runoff increases abruptly beginning in December to reach a peak in February. Over 80% of the annual runoff occurs from January through March. The high runoff during the rainy season and the absence of runoff during the summer indicate a stream system dominated by surface runoff.

Hat Creek (41° N) drains 421 km2 of the Modoc Plateau region of northeastern California. The watershed is dominated by layered basalts related to volcanic activity in the southern Cascade Range. The average annual precipitation for Hat Creek is 130 cm, and average annual runoff is 28 cm (Rantz, 1972). November through March accounts for 69% of annual precipitation. A slight runoff peak occurs in May and June, but this pulse of increased runoff is superimposed on a relatively steady base flow component indicated by the consistent flow in the other 10 months. Highly permeable basalts promote reduced surface runoff, and significant groundwater storage accounts for high base flow contributions all year in this watershed.

6.10.3 Ungauged basins

For gauged watersheds, hydrographs provide a basis for assessing the relationship between the quantity and timing of rainfall and runoff, but procedures are required for estimating runoff using available information that simulates runoff production from a measured rainfall quantity. Rainfall-runoff assessments commonly involve determination of the peak runoff rates, the depth or volume of runoff, or a storm hydrograph. Each approach employs techniques designed to incorporate specific features of the runoff process.

Estimating peak flow

The simplest way to view the rainfall-runoff process responsible for watershed discharge is to use a system-based conceptual perspective that treats the watershed as a black box. In this approach, some function transforms a given time-varying input into a time-varying output without detailed consideration of the physical processes producing the response (Dingman, 1994). The black box provides little understanding of the processes involved in the transformation. In the United States, the widely used empirical rational method for estimating peak runoff in designing ditches, channels, and storm water control systems for small areas of up to 80 hectares with no significant flood storage illustrates this approach. The rational method is expressed as

where Qp is the peak flow in m3s_1, 0.28 is a unit conversion factor, Cs is a dimensionless empirical coefficient based on soil type, slope, vegetation cover, soil moisture content, and land use characteristics, Ip is the average rainfall intensity in mm hr_1 during the time of concentration, and A is the watershed area in km2. The time of concentration is the time required for water to move from the most distant point in a watershed to the outlet, and it is mainly a function of the watershed size and shape (Mansell, 2003). The empirical runoff coefficient Cs is the major source of uncertainty in applying the rational method. The coefficient incorporates all the factors influencing the relation of peak flow to average rainfall intensity in the watershed other than response time and watershed area. A common feature of these coefficients is they are based on judgments rather than experimental data (Pilgrim and Cordery, 1993). Typical

Table 6.3. Rational method runoff coefficients (Cs)for selected land use and soil groups and a 2-6% slope

Well-drained soil (Hydrologie Poorly drained soil Land use soil group A) (Hydrologie soil group D)

Industrial 0.68a, 0.85b 0.69,0.86

Commercial 0.71,0.88 0.72,0.89

Residential 0.23,0.32 0.32, 0.40

Cultivated 0.13,0.18 0.23,0.29

a Runoff coefficients for storm recurrence intervals less than 25 years. b Runoff coefficients for storm recurrence intervals of 25 years or more.

runoff coefficients for selected conditions are shown in Table 6.3. Larger values of Cs indicate increased runoff potential as is seen by comparing the values for forested areas, residential land, and commercial property. A comprehensive list of runoff coefficients is found in McCuen (2005).

The popularity of the rational method is due to its simplicity, but it is based on assumptions that are rarely realized under actual circumstances. The methodology assumes that rainfall is uniformly distributed over the entire drainage area, that the rainfall fraction that becomes runoff is independent of rainfall intensity and volume, and that the predicted peak discharge has the same probability of occurrence as the rainfall intensity (Ward, 1995). Choosing the correct rainfall duration is one of the major challenges of the rational method because the duration must be just long enough for maximum runoff to occur. Nevertheless, this methodology is widely used in urban settings for forecasting and predicting peak flow because of the difficulty in obtaining enough information to adequately characterize the spatial and temporal variability of hydro-logic processes (Mansell, 2003). A modification commonly employed in urban applications is to partition the watershed into subareas based on various surface characteristics and to sum the products of the runoff coefficient and area representing each surface type (Mays, 2005). In other applications, a storage coefficient is added to the rational method to account for a recession time longer than the time required by the hydrograph to rise.

Estimating runoff volume

The transparent box perspective provides a more process-oriented approach to understanding runoff. This approach emphasizes that streamflow is a spatially and temporally integrated response determined by varying input rates and the time required for water to travel from where it arrives on the watershed surface to the stream and then to the point of measurement. The essential aspects of this perspective are that water moves within the watershed in an infinite number of surface and subsurface flow paths. Each flow path in a watershed is an accumulation of lateral water inflows that vary in space and time.

Estimating the depth or runoff volume requires more information about the watershed than is needed for estimating the peak runoff rate. The U.S. Soil Conservation Service (SCS), now the Natural Resources Conservation Service (NRCS), curve number (CN) procedure is used globally for determining the depth of runoff (Michel et al., 2005). This approach is an empirical method derived from infiltrometer tests and measured rainfall and runoff on small plots and basins (Pilgrim and Cordery, 1993). It is best used as a means to transform a rainfall frequency distribution into a runoff frequency distribution (Jacobs et al.,

2003), but it has been applied successfully at a range of watershed scales (Rose,

2004). The CN method combines infiltration losses, surface storage, and short-duration high-intensity rainfall events nested within larger events to estimate accumulated runoff using the relationship

where Qis runoff in mm, P is the rainfall depth in mm, Ia is the initial abstractions due to surface storage, interception, and infiltration prior to runoff and is commonly approximated as 0.2S in mm. S is a parameter given in metric units by

where CN is the SCS curve number designed with a range of 0 to 100 and determined empirically to be a function of the ability of soils to infiltrate water, land use, and the antecedent soil moisture condition (AMC). In a watershed encompassing varying characteristics, an area-averaged composite CN can be computed for the entire watershed (Mays, 2005). The general form of Equation 6.4 is well established by both theory and observation, but the AMC is one of the greatest uncertainties of the CN methodology.

The SCS recognizes three AMC categories based on dormant season and growing season antecedent soil moisture amounts. AMC II is the average moisture condition and is often used as the representative value. AMC I applies to dry soil conditions, and AMC III applies to wet soil conditions. The infiltration characteristics of soils are used by the SCS to define four hydrologic soil groups. These groups range from Group A, which has low runoff potential and high infiltration rates, to Group D,

Table 6.4. U.S. Soil Conservation Service runoff curve numbers (CN) for antecedent soil moisture condition II and selected hydrologic soil groups and land uses

Hydrologie soil group A Hydrologie soil group D

Land use

Industrial

Commercial

Residential

Cultivated

Pasture

Forest

81 80 61 65 39 25

93 95 87 86 80 77

Data from U.S. Soil Conservation Service, 1986.

which has high runoff potential and low infiltration rates. Remotely sensed microwave soil moisture measurements and other new methods are helping to define spatial soil variations at higher resolution scales. Curve numbers represent the averages of median site values combining the AMC, hydrologic soil group, and numerous land use conditions, and CN tables developed by the SCS are presented in the original documentation (U.S. SCS, 1964) and in later editions. An example of CN values is shown in Table 6.4. Michel et al. (2005) revised the original CN formula to comply more explicitly with accepted soil moisture accounting procedures while maintaining the efficiency of the original methodology.

Storm hydrographs

Storm hydrographs require the most complex information and provide the most comprehensive runoff estimates. The unit hydrograph is probably the most widely applied method. It derives its name from the characteristic that the area under the hydrograph is equal to 1 mm. The unit hydrograph assumptions are that a rainfall excess is uniformly distributed over the watershed, the rainfall excess rate is uniform, and the runoff rate is proportional to the runoff volume for a rainfall excess of a given duration (Ward, 1995). The central hypothesis emerging from these assumptions is that the watershed response to the rainfall excess is linear and a single rainfall hyetograph defines the input. In this way, the unit hydrograph is the watershed response to a standard input for a specified time. Consequently the duration must be included in the name of the unit hydrograph (Pilgrim and Cordery, 1993). For example, a 1-h unit hydrograph is produced by 1 mm of rainfall excess occurring over a watershed in 1 h at a rate of 1 mmh-1.

Standard hydrograph separation techniques are used to determine direct runoff, which is taken as equal to rainfall excess. The average depth and intensity of basin rainfall in each time increment of the storm are estimated. The rainfall excess for each period of the storm is calculated using a loss model. For a single-period storm, a unit hydrograph is derived by dividing the ordinates of the surface runoff hydrograph by the depth of surface runoff in mm. The duration of the rainfall excess determines the time period of the unit hydrograph. Several analytical techniques are available to derive unit hydrographs for multiperiod storms (Pilgrim and Cordery, 1993).

The time-area method is a process-based procedure to determine the runoff volume and peak runoff rate from small watersheds. The approach does not consider interflow and assumes that surface and channel flow velocities do not change with time. The physically based kinematics approach is theoretically the most complete. The method is based on the solution of the continuity and momentum equations and the relationship between the watershed geometric characteristics and the drainage system (Ward, 1995). The antecedent precipitation index and normalized antecedent precipitation index methods estimate runoff where the initial watershed moisture condition is probabilistic. These methods are data intensive and most applications are solved using computers.

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