Runoff

Runoff

Learning Objectives

Define runoff and distinguish it from catchment yield.
Identify the core components of runoff: overland flow, interflow, and baseflow.
Understand the meteorological and physiographic factors that influence runoff.
Apply the Rational Method to estimate peak discharge for small catchments.
Calculate the Time of Concentration using Kirpich's and Kinematic Wave formulas.
Understand the SCS Curve Number method for estimating runoff volume.
Interpret flow duration curves and flow mass curves.

Exploring catchment characteristics, components of runoff, and estimating peak discharge using the Rational Method. This lesson explains the underlying principles of surface runoff, which is critical for flood design, reservoir sizing, and urban drainage planning.

Introduction to Runoff

The portion of precipitation that flows over the land surface and eventually reaches streams, rivers, or oceans. It is the output of the catchment system response to rainfall input.

Runoff vs. Catchment Yield

Runoff usually refers to the direct surface flow resulting from a specific storm event (short-term). Catchment Yield (or Basin Yield) refers to the total volume of water available from a stream over a long period (e.g., annual yield), combining both direct runoff and baseflow. It is critical for sizing reservoirs.

Components of Runoff

Overland Flow (Surface Runoff)

Water flowing over the land surface before reaching a defined channel. This occurs when rainfall rate exceeds infiltration capacity.

Interflow (Subsurface Stormflow)

Water entering the soil but moving laterally in the upper soil layers to a stream channel.

Baseflow (Groundwater Runoff)

Deep percolation that enters the groundwater table and slowly discharges into the stream.

Direct Runoff vs. Baseflow

Direct Runoff (DRO) consists of Surface Runoff + Rapid Interflow. It responds quickly to rainfall and causes flood peaks. Baseflow responds slowly and sustains river flow during dry periods (droughts).

Interactive Simulation: Hydrograph Components

Use the simulation below to explore how changes in rainfall intensity and duration affect surface runoff, interflow, and baseflow components of a hydrograph.

Hydrograph Components Simulator

Adjust the multipliers to see how Overland Flow, Interflow, and Baseflow contribute to the total stream discharge over time. Notice the different response times and durations for each component.

Overland Flow (Surface Runoff)1.0x

Interflow (Subsurface Stormflow)1.0x

Baseflow (Groundwater Runoff)1.0x

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Factors Affecting Runoff

Runoff is influenced by two main categories of factors: Meteorological and Physiographic (Catchment characteristics).

Meteorological Factors

These relate to the nature of the precipitation and weather conditions.

Rainfall Intensity and Duration

High intensity exceeds infiltration capacity, causing rapid runoff. Long duration saturates the soil, increasing the total runoff volume.

Distribution and Direction of Storm Movement

A storm moving downstream (towards the outlet) produces a higher, sharper peak than one moving upstream.

Physiographic Factors (Catchment Characteristics)

The physical properties of the catchment significantly influence runoff volume and timing.

Area ( $A$ ) and Slope

Area is the most important factor, as total runoff volume is directly proportional to it. Slope affects the flow: steeper slopes produce faster runoff velocities and higher peak discharges, with less time for infiltration.

Shape

Fan-shaped catchments cause runoff from different points to reach the outlet simultaneously, leading to a High Peak. Fern-shaped (Elongated) catchments cause runoff to reach the outlet at different times, leading to a Low Peak and Longer Duration.

Land Use

Urbanization (impervious surfaces like concrete and asphalt) drastically increases runoff volume and peak flow while reducing time to peak.

Rainfall-Runoff Relationships

The Rational Method

A simple empirical method widely used for estimating Peak Discharge ( $Q_p$ ) for small catchments ( $< 50$ km $^2$ ), primarily in urban drainage design (sewers, culverts).

Rational Method Formula

Estimates the peak discharge from a small catchment given the runoff coefficient, rainfall intensity, and catchment area.

Q_p = 0.278 C I A

Variables

Symbol	Description	Unit
$Q_p$	Peak discharge	$m^3/s$
$C$	Runoff coefficient (dimensionless, 0 to 1). Represents the fraction of rain that becomes runoff.	-
$I$	Rainfall intensity for a duration equal to the Time of Concentration ( $t_c$ )	mm/hr
$A$	Catchment area	$km^2$

Unit Conversion Factor

The constant 0.278 is a unit conversion factor derived from $1 / 3.6$ . If using Area in hectares ( $\text{ha}$ ), the formula is often written as $Q = \frac{CIA}{360}$ .

Limitations of the Rational Method

It assumes rainfall intensity ( $I$ ) is constant over the entire catchment area and throughout the entire storm duration ( $t_c$ ). Because real storms are variable in both space and time, the method overestimates discharge for large catchments. Hence, it is restricted to small drainage areas (typically less than $50 \text{ km}^2$ , often much smaller for urban design).

Interactive Simulation: Rational Method

Use the simulation below to see how varying the area, runoff coefficient, and rainfall intensity affects the calculated peak discharge.

Rational Method Calculator

Q = 0.695 m³/s

Peak Discharge

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Runoff Coefficient (C)0.5

0.1 (Parks) to 0.9 (Pavements)

Intensity (I)50 mm/hr

Area (A)10 ha

Formula:

Q = 0.278 C I A

(Note: This simple version assumes A is converted to km² internally for the 0.278 constant)

t_c

The Time of Concentration is a fundamental parameter in runoff estimation, particularly for the Rational Method. It is assumed that the peak discharge occurs when the entire catchment is contributing to flow, which happens when the storm duration equals $t_c$ .

Time of Concentration ( $t_c$ )

The time required for water to flow from the most hydraulically remote point of the catchment to the outlet.

Several empirical formulas exist to estimate Time of Concentration based on the flow regime: overland flow (sheet flow), shallow concentrated flow, and open channel flow. The most common formulas are the Kinematic Wave equation for overland flow and Kirpich's Formula for channel flow in small catchments.

Overland Flow vs. Channel Flow

Overland Flow is slow and highly dependent on surface roughness (Manning's $n$ ) and rainfall intensity. Channel Flow is much faster and primarily depends on the length of the channel ( $L$ ) and its slope ( $S$ or $H/L$ ).

Kirpich's Formula (Channel Flow)

An empirical formula commonly used to estimate the time of concentration for small, steep agricultural catchments.

t_c = 0.0195 L^{0.77} S^{-0.385}

Variables

Symbol	Description	Unit
$t_c$	Time of concentration	minutes
$L$	Maximum length of travel or flow path	m
$S$	Average slope (equivalent to $H/L$ , where $H$ is elevation difference)	m/m

Kirpich's Formula (Alternative Form)

Kirpich's equation is also sometimes written using the elevation difference H.

t_c = 0.0195 \left( \frac{L^3}{H} \right)^{0.385}

Variables

Symbol	Description	Unit
$t_c$	Time of concentration	minutes
$L$	Maximum length of travel or flow path	m
$H$	Elevation difference	m

Kinematic Wave Formula (Overland Flow)

Estimates the time of concentration for shallow overland flow where surface roughness is a major factor.

t_c = \frac{6.92 (L \cdot n)^{0.6}}{I^{0.4} \cdot S^{0.3}}

Variables

Symbol	Description	Unit
$t_c$	Time of concentration	minutes
$L$	Length of flow path	m
$S$	Average slope	m/m
$n$	Manning's roughness coefficient	-
$I$	Rainfall intensity	mm/hr

Interactive Simulation: Time of Concentration

Use the simulation below to explore how the length of the flow path, slope, and surface roughness influence the Time of Concentration.

Time of Concentration ( $t_c$ ) Simulator

Kirpich's Formula (Channel Flow)Kinematic Wave (Overland Flow)

Flow Length (L): 1000 m

Slope (S): 0.010 m/m

Estimated Time of Concentration ( $t_c$ )

23.4 min

Formula:

t_c = 0.0195 \cdot L^{0.77} \cdot S^{-0.385}

Flow Duration Curve

A cumulative frequency curve that shows the percentage of time specified discharges were equaled or exceeded during a given period. It characterizes the variability of flow at a specific location.

Q50

Median flow.

Q90

Low flow (flow exceeded 90% of the time). Important for water supply reliability and environmental flow assessment.

SCS Curve Number (CN) Method

Developed by the Soil Conservation Service (now NRCS), this method estimates total runoff volume from rainfall depth based on land use, soil type, and antecedent moisture condition.

Curve Number (CN)

A dimensionless number from 0 to 100 representing runoff potential. A higher CN (e.g., 98 for pavement) means high runoff and low infiltration. A lower CN (e.g., 30 for forested land with permeable soil) means low runoff and high infiltration.

SCS Runoff Equation

Calculates total runoff depth given total rainfall and the potential maximum retention of the soil.

Q = \frac{(P - 0.2S)^2}{P + 0.8S}

Variables

Symbol	Description	Unit
$Q$	Total runoff depth	inches or mm
$P$	Total rainfall depth	inches or mm
$S$	Potential maximum retention after runoff begins	inches or mm

Potential Maximum Retention Calculation

Calculates the potential maximum retention after runoff begins using the Curve Number (for inches).

S = \frac{1000}{CN} - 10

Variables

Symbol	Description	Unit
$S$	Potential maximum retention after runoff begins	inches
$CN$	Curve Number	-

Note: Runoff $Q = 0$ if rainfall $P \le 0.2S$ (Initial abstraction).

Initial Abstraction (Ia)

The amount of rainfall lost before runoff begins, consisting of interception, depression storage, and initial infiltration.

Initial Abstraction Empirical Relation

The SCS method empirically relates initial abstraction to the potential maximum retention.

I_a = 0.2S

Variables

Symbol	Description	Unit
$I_a$	Initial abstraction	inches or mm
$S$	Potential maximum retention	inches or mm

Interactive Simulation: SCS Curve Number

Explore how altering the Curve Number and rainfall depth impacts the total runoff depth using the simulation below.

SCS Curve Number (CN) Method Simulator

Rainfall (P): 50.0 mm

Curve Number (CN): 75

Lower CN = Permeable (e.g., woods, sandy soil)
Higher CN = Impermeable (e.g., pavement, clay)

Potential Maximum Retention (S)

84.67 mm

Initial Abstraction (Ia = 0.2S)

16.93 mm

Direct Runoff (Q)

9.29 mm

Water Balance Visualization

Runoff

Initial Abstr.

Retention

Runoff (Q) Initial Abstraction (Ia) Actual Retention

Antecedent Moisture Condition (AMC)

The initial wetness of the soil significantly affects the Curve Number and resulting runoff. The SCS method defines three AMCs based on total rainfall in the preceding 5 days:

AMC I (Dry)

Lowest runoff potential. Soils are dry (e.g., after a drought). CN is adjusted downward from the standard value.

AMC II (Average)

Normal conditions. This is the baseline CN value found in standard published tables.

AMC III (Wet)

Highest runoff potential. Soils are saturated (e.g., after consecutive rainy days). CN is adjusted upward.

Flow Mass Curve and Safe Yield

Flow Mass Curve

A Flow Mass Curve is a plot of cumulative runoff volume against time. The slope of the curve at any point represents the rate of flow (discharge). It is primarily used to determine the storage capacity required for a reservoir to meet a specific continuous demand.

Safe Yield

The maximum quantity of water that can be guaranteed continuously from a source (like a reservoir or aquifer) over a specified period, typically determined from the most critical dry period in the historical flow record.

Advanced Runoff Models

While the Rational Method estimates only peak discharge, advanced modeling techniques are required to generate entire runoff hydrographs for complex or urbanizing catchments.

Time-Area Histogram Method

This method relies on the concept of isochrones—contours of equal travel time to the catchment outlet. The catchment is divided into zones by these isochrones (e.g., 1-hour, 2-hour travel time zones). The area between isochrones is the "time-area." By applying effective rainfall to this time-area histogram and lagging the flows appropriately, a complete surface runoff hydrograph can be constructed without assuming constant rainfall intensity.

Storm Water Management Model (SWMM) Basics

SWMM is a dynamic rainfall-runoff simulation model used extensively for single-event or long-term simulation of runoff quantity and quality.

Subcatchments: It models the catchment as a collection of subcatchments that receive precipitation and generate runoff and pollutant loads.
Nodes & Links: The generated runoff is then routed through a network of pipes, channels, storage/treatment devices, pumps, and regulators using hydraulic routing (St. Venant equations).

Key Takeaways

Runoff is the primary output variable in surface hydrology, representing precipitation that hasn't evaporated or infiltrated deep into the ground.
It is the critical parameter for flood design, water supply planning, and environmental management.
Direct Runoff (DRO) is the immediate response to rainfall, primarily composed of overland surface flow.
Baseflow is the delayed, slow release of groundwater into the stream, sustaining flow between storms.
Total streamflow is the sum of direct runoff and baseflow.
Catchment Yield is the long-term total water volume available, whereas runoff is typically event-based.
Area and Slope are the dominant physical factors governing runoff volume and velocity.
Catchment Shape dictates how quickly water from different areas converges at the outlet.
Urbanization significantly increases both the volume and peak intensity of runoff due to the addition of impervious surfaces.
The Rational Method ( $Q_p = CIA$ ) is the standard empirical equation for estimating peak discharge in small catchments ( $< 50 \text{ km}^2$ ).
The critical design storm duration is set equal to the Time of Concentration ( $t_c$ ), ensuring the entire basin is contributing to flow.
Kirpich's Formula is a common empirical method to estimate $t_c$ based on channel length and slope.
A Flow Duration Curve illustrates the historical frequency of various discharge levels.
It is an essential tool for assessing long-term water supply reliability and determining environmental baseflow requirements (like $Q_{90}$ ).
The SCS Curve Number Method estimates total runoff volume (depth) rather than just peak discharge.
The baseline Curve Number (CN) is derived for average conditions (AMC II).
The CN must be adjusted for Antecedent Moisture Conditions (AMC): lowered for dry soils (AMC I) or raised for saturated soils (AMC III).

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Runoff

Learning Objectives

Introduction to Runoff

Runoff

Runoff vs. Catchment Yield

Components of Runoff

Overland Flow (Surface Runoff)

Interflow (Subsurface Stormflow)

Baseflow (Groundwater Runoff)

Direct Runoff vs. Baseflow

Interactive Simulation: Hydrograph Components

Hydrograph Components Simulator

Factors Affecting Runoff

Meteorological Factors

Rainfall Intensity and Duration

Distribution and Direction of Storm Movement

Physiographic Factors (Catchment Characteristics)

Area (AAA) and Slope

Shape

Land Use

Rainfall-Runoff Relationships

The Rational Method

Rational Method Formula

Unit Conversion Factor

Limitations of the Rational Method

Interactive Simulation: Rational Method

Rational Method Calculator

Time of Concentration (tct_ctc​)

Time of Concentration (tct_ctc​)

Overland Flow vs. Channel Flow

Kirpich's Formula (Channel Flow)

Kirpich's Formula (Alternative Form)

Kinematic Wave Formula (Overland Flow)

Interactive Simulation: Time of Concentration

Time of Concentration (tct_ctc​) Simulator

Estimated Time of Concentration (tct_ctc​)

Flow Duration Curve

Q50

Q90

SCS Curve Number (CN) Method

Curve Number (CN)

SCS Runoff Equation

Potential Maximum Retention Calculation

Initial Abstraction (Ia)

Initial Abstraction Empirical Relation

Interactive Simulation: SCS Curve Number

SCS Curve Number (CN) Method Simulator

Potential Maximum Retention (S)

Initial Abstraction (Ia = 0.2S)

Direct Runoff (Q)

Water Balance Visualization

Antecedent Moisture Condition (AMC)

AMC I (Dry)

AMC II (Average)

AMC III (Wet)

Flow Mass Curve and Safe Yield

Flow Mass Curve

Safe Yield

Advanced Runoff Models

Time-Area Histogram Method

Storm Water Management Model (SWMM) Basics

Area ( $A$ ) and Slope

Time of Concentration ( $t_c$ )

Time of Concentration ( $t_c$ )

Time of Concentration ( $t_c$ ) Simulator

Estimated Time of Concentration ( $t_c$ )