1. Excess Rainfall and Direct Runoff
Excess (effective) rainfall is that rainfall which is neither retained on the land surface nor infiltrated into the soil.
After flowing across watershed it becomes direct runoff at the watershed outlet under the assumption of Hortonian Flow.
The graph of excess rainfall versus time is called excess rainfall hyetograph
The difference between total rainfall hyetograph and excess rainfall hyetograph is termed abstractions, or losses.
Two ways to compute ERH:
Streamflow data is available: Two commonly used ones are F-index method, runoff coefficients
Streamflow data is not available: Use any of the infiltration equations

2. F-Index Method
It is a constant rate of abstraction that will yield an ERH with a total depth equal to the depth of direct runoff over the watershed

3. F-Index: Example

4. Abstractions (Losses) Using Infiltration Equations
Problem: Given a rainfall hyetograph (pulse data) and infiltration parameters, we want to determine
ponding time
infiltration after ponding occurs and
effective hyetograph (ERH)
Principles: Three principles
In absence of ponding, cumulative infiltration is given by cumulative rainfall
Potential infiltration rate is calculated using cumulative infiltration
Ponding occurs when i > f

5. Determining Infiltration and Ponding Time under Variable Rainfall Intensity

7. SCS Method for Abstraction
Consider the following rainfall hyetograph
P: Cumulative depth of precipitation
Pe: Cumulative depth of excess precipitation
Ia: Initial abstraction before ponding
Fa: Continuing abstraction
S: Potential maximum continued abstraction.
Maximum potential runoff: (P-Ia)
SCS hypothesis: ratio of two actual and potential quantities are equal.

8. SCS Method for Abstraction
By study of results from many watersheds: l=0.2  Ia = 0.2S
P ≥ 0.2S
Normalized form of S is commonly used: (inches)
where S is in inches and CN: Curve Number (0 ≤ CN ≤ 100)
Curve number is function of hydrologic soil group, cover type, treatment, and hydrologic condition.
Theoretically, for impervious surfaces and water CN = 100; however in practice a value of 98 is used.
Tables are present for CN for normal antecedent moisture conditions (AMC II). USDA changed terminology to antecedent runoff condition (ARC), which is the central trend in all for all possible conditions

9. SCS Method for Abstraction
CN for wet and dry conditions are calculated by
How do we determine wet/dry AMC? (Application discouraged)
Total 5-day antecedent precipitation (inches)
AMC
Dormant Season
Growing Season I
< 0.5
< 1.4 II
0.5 to 1.1
1.4 to 2.1
III
> 1.1
> 2.1

11. Hydrologic Soil Groups
Soils are classified into HSG’s to indicate the minimum rate of infiltration obtained for bare soil after prolonged wetting.
Most soil survey reports provides HSG’s. (NRCS web soil survey)
A: High infiltration and low runoff potential when thoroughly wetted. Typically deep sand, deep loess, aggregated silts.
B: Moderate infiltration capacity. Shallow loess, sandy loam.
C: Low infiltration capacity. Clay loams, shallow sandy loam, soils low in organic content and soils high in clay content.
D: Very low infiltration capacity. Soils that swell significantly when wet, heavy plastic clays, soils with a permanent high water table.

12. HSG Based on Texture
HSG
Soil textures CN A
Sand, loamy sand, or sandy loam
25-77 B
Silt loam or loam
48-86 C
Sandy clay loam
65-91 D
Clay loam, silty clay loam, sandy clay, silty clay, or clay
73-94
Some soils are in group D because of a high water table that creates a drainage problem. Once these soils are effectively drained, they are placed in a different group.
For example, Ackerman soil is classified as A/D. This indicates that the drained Ackerman soil is in group A and the undrained soil is in group D.

13. Other Factors
Cover type such as vegetation, bare soil, and impervious surfaces. There are a number of methods for determining cover type. The most common are field reconnaissance, aerial photographs, and land use maps.
Treatment is a cover type modifier to describe the management of cultivated agricultural lands. It includes mechanical practices, such as contouring and terracing, and management practices, such as crop rotations and reduced or no tillage
Hydrologic condition indicates the effects of cover type and treatment on infiltration and runoff and is generally estimated from density of plant and residue cover on sample areas.
Good hydrologic condition indicates that the soil usually has a low runoff potential for that specific hydrologic soil group, cover type, and treatment.
Some factors to consider in estimating the effect of cover on infiltration and runoff are (a) canopy or density of lawns, crops, or other vegetative areas; (b) amount of year-round cover; (c) amount of grass or close-seeded legumes in rotations; (d) percent of residue cover; and (e) degree of surface roughness

14. Limitations
Curve numbers describe average conditions that are useful for design purposes. If the rainfall event used is a historical storm, the modeling accuracy decreases.
Runoff from snowmelt or rain on frozen ground cannot be estimated.
Ia, which consists of interception, initial infiltration, surface depression storage, evapotranspiration, and other factors, was generalized as 0.2S based on data from agricultural watersheds. To use a relationship other than Ia = 0.2S, one must redevelop CN equation by using the original rainfall-runoff data to establish new S or CN relationships for each cover and hydrologic soil group.
The CN procedure is less accurate when runoff is less than 0.5”.
The SCS runoff procedures apply only to direct surface runoff: do not overlook large sources of subsurface flow or high ground water levels that contribute to runoff. These conditions are often related to HSG A soils and forest areas that have been assigned relatively low CN’s.
When the weighted CN is less than 40, use another procedure

15. New Developments
Jiang (2001) using data from 307 watersheds and plots covering 28,301 events found l values varying from event to event and location to location.
90% of the events had values less than 0.2, l=0.05 was more representative.
With l=0.05 original equation becomes
S0.05=1.33S with S in inches
Substituting above into CN=1000/(10+S) leads to

16. Example

17. Example

18. Estimation of Peak Flow
Estimates of peak flow are required for design of culverts, drainage works, soil conservation works, spillways of farm ponds and small bridges
The most widely used and the simplest method in water resources applications is the Rational Method or Rational Equation
Qp = C i A
Qp: Peak flow in m3/s
i: rainfall intensity (mm/hr)
A: Drainage area (km2)
C: runoff coefficient [0-1]
This method assumes that rainfall continues at a uniform intensity with duration equal to the time of concentration (tc)
If i:in/hr and A:acres then Qp=CiA with Qp:cfs

19. Rational Method
Time of concentration is the time for runoff to travel from the hydraulically most distant point of the watershed to its outlet
At uniform rainfall intensity tc is equal to the time of equilibrium at which the rate of runoff is equal to the rate of rainfall supply.
Therefore the area of the watershed should be small (<10 km2) to have storm duration equal to tc.
If td < tc then water is not contributed from the entire watershed
Various formulas exists including Manning’s equation to estimate tc
Kirpich’s formula: tc = L0.77S (min)
L: distance from watershed divide to outlet (feet), S: average slope
In practice rainfall intensity is obtained from rainfall intensity-duration- frequency curves for the location with its frequency the same as the designed flood and duration equal to tc.

20. Intensity, Duration and Frequency (IDF) Curve
IDF curves are graphical representations of the probability that a given average rainfall intensity will occur. They are commonly used when determining the rainfall rate for the rational method
A standard IDF curve is plotted with duration on the horizontal axis and intensity on the vertical axis. Multiple curves are plotted on the same graph with each line representing the average frequency between occurrences for a given rainfall.

21. Rational Method
The runoff coefficient c is the least precise variable of the Rational Method
It should be function of
Imperviousness
Slope
Soil characteristics
Antecedent moisture condition
Proximity of water table
Vegetation
Etc.