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#### 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 [7-17] or [7-18] 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 [7-19] 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 sub-catchment, 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 under-estimate 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.

(c) Copyright 1984-2010 Alan A. Smith Inc.

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