Hydrological Theory
Calculating Effective Rainfall
The SCS Method 

From the MIDUSS Version 2
Reference Manual  Chapter 7
(c) Copyright Alan A. Smith Inc. 
In 1972 the U.S. Soil
Conservation Service suggested an empirical model for rainfall
abstractions which is based on the potential for the soil to absorb a
certain amount of moisture. On the basis of field observations, this
potential storage S (millimetres or
inches) was related to a 'curve number'
CN
which is a characteristic of the soil type, land use and the initial
degree of saturation known as the antecedent moisture condition.
The value of S is
defined by the empirical expression [717] or [718] depending on the
units being used.
(inches)
(millimetres)
Typical values for the
SCS Curve Number
CN
as a function of soil type, land use and degree of saturation can be
found in most texts on hydrology (e.g. See references such as
Viessman, 1977 or
Kibler, 1982) or from the section on Pervious Data
requirements. in Chapter 3 Hydrology Used in MIDUSS.
In some texts you may
see values of CN
quoted as a function of the percentage of impervious area. These are
usually calculated as a weighted average assuming
CNimpervious = 98 and
CNpervious
equal to the value for ‘Pasture in good condition’ for the various
soil types A, B, C or D. See Chapter 3 Hydrology used in MIDUSS,
eq. [3.10].
Values of
CN
estimated in this way are intended to be applied to the total
catchment assuming other parameters to be the same for both pervious
and impervious areas. Many programs (including MIDUSS) compute the
runoff from the pervious and impervious fractions separately and then
add the two hydrographs. In such cases, it is most important that you
do not use a composite value of
CN
since this would ‘double count’ the impervious fraction and greatly
exaggerate the runoff prediction.
The effective rainfall
is computed by the equation:
where
Q(t) =
accumulated depth of effective rainfall to time t
(t) =
accumulated depth of rainfall to time t
Ia
= initial abstraction
S
= potential storage in the soil
All of the terms in
equation [719] are in units of millimetres
or inches. Note that the effective rainfall depth or runoff will be
zero until the accumulated precipitation depth P(t) exceeds the
initial abstraction
Ia.
The original SCS
method assumed the value of the initial abstraction
Ia
to be equal to 20% of the storage potential S, but many engineers now
regard this as unacceptably high for most stormwater management
situations. MIDUSS uses an initial default value of 10% but allows
you to specify the ratio of
fa
= Ia /S
when you are entering the data for rainfall losses.
Alternatively, MIDUSS
lets you define the initial abstraction
Ia
explicitly as a depth. For suggested values, see the section on
Pervious Data requirements in Chapter 3 Hydrology Used in MIDUSS..
When you enter a value
for the SCS Curve Number, MIDUSS calculates the equivalent volumetric
runoff coefficient (C)
and displays this for information. You can also enter a value for the
runoff coefficient and MIDUSS will compute and display the
corresponding value of
CN.
The SCS CN
value is a function of runoff coefficient
C,
the total rainfall depth and the initial abstraction ratio
fa
= Ia./S.
The relationship used is as follows.
Sometime this is a
useful way to 'guesstimate' a value for
CN
in the absence of other information.
It is worth digressing
a little at this point to explain a feature of MIDUSS which you may
notice when you are reviewing an output file. If you specify a runoff
coefficient C
for a particular subcatchment, both the values of
C
and CN
are copied to the output file. However, if you run the program in
Automatic mode MIDUSS uses the
CN
value as the basis for estimating rainfall losses. The reason for
this is as follows. Typically, in designing a minor drainage system
the engineer will use a relatively modest storm (say 5 year return
interval) for which a reasonable estimate of
C
might be made based on records or previous experience with the
rational method.
When the design is
completed it is usual to subject the system to a more severe storm
with a much larger depth of precipitation
Ptot.
For the same ground conditions, the severe storm will produce a much
higher runoff coefficient than the 5‑ year storm. Now since the
CN
value is a measure of ground conditions it is preferable to use the
CN
value rather than the runoff coefficient C, which, if used with the
severe storm, would greatly underestimate the runoff. Of course, if
the output file is used as input for a subsequent run in which the 5‑
year storm is used again, the result will be identical to that which
would have been obtained using the runoff coefficient. After
specifying values for Manning's 'n' and the SCS curve number
CN
(or runoff coefficient
C)
MIDUSS displays the current value of the ratio
fa
= Ia /S
as well as the initial abstraction depth
Ia
in inches or millimetres. You have the
option to accept the current values or alter the ratio
Ia
/S or the initial abstraction
Ia
by entering values in the appropriate text boxes.
If either the ratio
fa
= Ia /S
or the initial abstraction depth
Ia
is altered, the displayed values of both
Ia
/S and
Ia
are updated. These values become the default for future uses of the
Catchment command but these are not retained for future design
sessions with MIDUSS.. However, if the output file is later used as
an input data file in Automatic mode the correct values will be used.
In both the Pervious
and Impervious forms, pressing the [Display] button causes a tabular
display of the effective rainfall to be displayed together with a
graph showing the storm rainfall and one or both of the two effective
rainfall hyetographs.
