Hydrological runoff is the portion of precipitation, such as rain or snowmelt, that flows across the land surface without being absorbed into the soil. This movement occurs when the rate of rainfall exceeds the soil’s capacity to infiltrate, or when surfaces are impervious. Calculating the volume and rate of runoff is necessary for managing water resources, designing infrastructure like storm drains and culverts, and assessing potential flood risks. Two widely used methods, the Rational Method and the Curve Number Method, offer different approaches to estimating runoff based on the size and nature of the drainage area.
Defining the Core Data Inputs
Determining runoff requires gathering specific data inputs that define the characteristics of a storm and the physical properties of the area being studied. The first input is the Area (A), which refers to the total surface area contributing flow to a specific point, often measured in acres or hectares. This area is typically delineated using topographic maps or modern Geographic Information Systems (GIS).
The second input is the Rainfall Intensity (I), which represents the rate of precipitation over a specific time period, usually expressed in inches or millimeters per hour. This value is derived from historical weather records and presented on Intensity-Duration-Frequency (IDF) curves. An IDF curve provides the intensity associated with a given storm duration and a chosen recurrence interval, such as a “10-year storm,” which is an event with a 10% chance of occurring in any given year.
The third component accounts for the Surface Characteristics of the drainage area, which dictate how much water soaks into the ground versus how much flows over it. These characteristics are quantified using specialized coefficients that are unique to each calculation method, serving as the link between rainfall and the resulting runoff.
Calculating Runoff for Small Areas: The Rational Method
The Rational Method is the simplest and most frequently applied approach for calculating the peak rate of runoff, \(Q\), from small, typically urban drainage areas, often limited to less than 200 acres. The method is represented by the formula \(Q = CiA\), where \(Q\) is the maximum rate of runoff in cubic feet per second (cfs).
The key variable in this formula is the Runoff Coefficient (\(C\)), a dimensionless number representing the ratio of peak runoff to rainfall. This coefficient is determined by the surface type, with highly impervious areas having a value near 1.0, and permeable surfaces having a value closer to zero. For instance, a concrete roof may have a high \(C\) value, while a flat lawn with sandy soil might be low. When the drainage area includes multiple surface types, a weighted average \(C\) value is calculated based on the proportion of each surface.
The correct rainfall intensity (\(i\)) for the formula is specifically tied to the area’s time of concentration (\(T_c\)). \(T_c\) is the time it takes for water to flow from the hydraulically most distant point of the drainage area to the point of calculation. The Rational Method assumes that the highest peak flow occurs when the storm duration is exactly equal to this \(T_c\), ensuring all parts of the area are contributing runoff simultaneously. Engineers use the calculated \(T_c\) to look up the corresponding rainfall intensity on the local IDF curve.
Estimating Runoff for Watersheds: The Curve Number Method
For larger areas, especially non-urban or agricultural watersheds, the Curve Number (CN) Method is the standard approach used to estimate the total volume of runoff. This method was developed by the U.S. Department of Agriculture’s Natural Resources Conservation Service (NRCS).
The Curve Number (\(CN\)) is the central parameter, a value between 1 and 100 that represents the composite runoff potential of a watershed. A high \(CN\) (near 100, like for concrete) indicates high runoff and low infiltration, while a low \(CN\) (near 30, like for a deep forest) indicates the opposite.
The \(CN\) is determined by combining the area’s land use, such as row crops or residential housing, with its Hydrologic Soil Group (HSG). Soils are categorized into four HSGs, labeled A, B, C, and D, based on their minimum infiltration rate when thoroughly saturated.
Group A soils, like deep, well-drained sands, have the highest infiltration rates and therefore the lowest runoff potential. Conversely, Group D soils, which are high in clay content or have a shallow layer over impervious material, have the lowest infiltration rates and the highest runoff potential.
By cross-referencing the land cover type with the HSG, a specific \(CN\) is selected from reference tables, which is then used in the underlying equation to estimate the total runoff volume.