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<br />based on the physical characteristics of the watershed and is simple to apply since it <br />requires only one parameter to be estimated, it has been increasingly used in <br />applications that its authors had not intended. <br /> <br />In development of the method, the basic assumption was that during a <br />storm event, there is a threshold which must be exceeded before runoff occurs which <br />satisfies interception, depression storage, and the infiltration quantity before the start <br />of runoff. This amount of rainfall is termed the initial abstraction, or la. After the <br />initial abstraction is satisfied, the total actual retention increases with increasing <br />rainfall up to the maximum retention. Since runoff also increases as the rainfall <br />increases, the SCS hypothesized that the ratio of actual retention to maximum <br />retention is assumed to be equal to the ratio of runoff to rainfall minus initial <br />abstraction. This assumed relationship is expressed mathematically as follows: <br /> <br />Q / ( P - la ) = F / S <br /> <br />(1) <br /> <br />where, <br /> <br />Q = Runoff in inches <br />P = Precipitation in inches <br />la = Initial abstraction in inches <br />F = Total retention in inches <br />S = Maximum retention in inches <br /> <br />A second equation, based on the water balance equation, was developed <br />and is presented as follows: <br /> <br />P = Q + la + F <br /> <br />(2) <br /> <br />When equation (1) and (2) are solved simultaneously for Q, they yield: <br /> <br />Q = ( P - la ) ** 2 / {( P - la) + S ) <br /> <br />(3) <br /> <br />Since equation (3) requires two parameters (Ia and S), the SCS further <br />simplified it by developing an empirical relationship between la and S based on field <br />data. <br /> <br />la = 0.2 * S <br /> <br />(4) <br /> <br />When equation (4) is substituted into equation (3), the result is the SCS <br />one parameter infiltration equation: - <br /> <br />Q = ( P - 0.2 * S) ** 2/( P + 0.8 * S) <br /> <br />(5) <br /> <br />7-4 <br />