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<br />If <br />II <br />II <br />Ii <br />I. <br />II <br />II <br />II <br />II <br />II <br />II <br />I. <br />II <br />II <br />II <br />II <br />II <br />II <br />II <br /> <br />Hydrologic Design Manual <br />for Maricopa County <br /> <br />Rainfall Losses <br /> <br />parameters, or for other valid reasons. It should be realized, as explained later, that <br />the use of the Green and Ampt equation and parameters, as defined herein, will <br />probably result in lower peak discharges and runoff volumes than the use of the <br />IL+ULR. <br /> <br />Other methods should be used only if there is technical justification for a variance <br />from this recommendation and if adequate information is available to estimate the <br />necessary parameters. Use of rainfall loss methods other than those recommended <br />should not be undertaken unless previously approved by the Flood Control District <br />and the local regulatory agency. <br /> <br />4.4.1 Green and Ampt Infiltration Equation <br /> <br />This model, first developed in 1911 by W.H. Green and G.A. Ampt, has since the <br />early 19705, received increased interest for estimating rainfall infiltration losses. <br />The model has the form: <br /> <br />f=Ks(1+~) <br />F <br /> <br />for f <i <br /> <br />(1) <br /> <br />f=i <br /> <br />for f~ i <br /> <br />where <br /> <br />f = infiltration rate (LIT), <br />i = rainfall intensity (LIT), <br /> <br />Ks = hydraulic conductivity, wetted zone, steady-state rate (LIT) <br />'I' = average capillary suction in the wetted zone (L), <br /> <br />o = soil moisture deficit (dimensionless), equal to effective soil <br />RQ!osity time~ . <br />'the difference in final and initial volumetric soil saturations, and <br /> <br />F = depth of rainfall that has infiltrated into the soil since the beginning of <br />rainfall (L). <br /> <br />A sound and concise explanation of the Green and Ampt equation is provided by <br />Bedient and Huber (1988), <br /> <br />It is Important to note that as rain continues, F increases and f approaches Ks, and <br />therefore, f is inversely related to time. Equation 1 is implicit with respect to f which <br />causes computational difficulties. Eggert (1976) simplified Equation 1 by expand- <br />ing the equation in a power series and truncating all but the first two terms of the <br />expansion. The simplified solution (Li and others, 1976) is: <br /> <br />F=-o.5 (2F -Ks At) + 0.5 [(2F -Ks M)2 + 8I<'sAt (O'l'+F))1,,2 <br /> <br />(2) <br /> <br />o(-~:.:~<<>:.~:~~,:*:.:~.:.;.;.:r..;.,:-,:.;.;~.x.:>,,:;,;.:'''';m-.wM~''''';<<~':<<->>:-:-;';';(-;';'~(-;.;-:...~(.-.;~.;.;.:-;.;: ;';':';:':-:-;(:-"'-:':~-;':'~:-:-;';>>>?":'XNl:{~;-: ;.::.;.:.;.:.;.; ;';';":-X:';':N}:'; ':',Y":'Y":1-:"":O}:-:;:'}:>'~,;,;,; :};,;,;',;.;.>>x-:.o::*>;i,;':-}}:';'W.'~}:{';='};':';:;';' <br />4S <br />