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<br />20 <br /> <br />PROBAIlILlTY DISTRlBUTIO:-: OF BASE FLO\\" <br /> <br />The areal variation of the available supply of base flow and its distri- <br />bution by seasons was hdefly presented in the pl"evious chapter. A major <br />purpose of this repan is to show how available base-fio\v supply is dis- <br />tributed within the year' and to relate its distribution to the pl'obability of <br />attaining cet'tain magnitudes of base now in each month. These data ",ill <br />be discussed in this chapter for 105 streamflow sites. In the follov.ing <br />chapter, the cau~es for the differences in base flow \vi11 be investigated to <br />develop methods for estimating base flow at ungaged sHes. <br /> <br />A convenient way of expressing the probability of base flow equalling <br />or' exceeding certain amounts is by means of a flow-duration curve. Such <br />a curve is developed by alTaying in ()I'der of magnitude all of the daily, or <br />monthly. hase-flow values at a selected site, computing the percent of time <br />that the \'al'ious rates of flow are equalled or exceeded, and then plotting <br />the flow rates against the corresponding percentages of time. .:\ curve <br />through these points defines the fl'cquency of equalling 01' exceeding val'ious <br />rates of base flow, The details of this procedul'c are the same as those <br />described in Technical !'cport 1 (p. 13-21) where computations are described <br />for developing flow-duration cUI'ves of the total daily flow of streams in- <br />stead of the base-flow portion of total flow. <br /> <br />Because of the work involved in computing base flow and arraying the <br />data in order of magnitude. some investigators have used existing duration <br />curves of total flow to estimate base-flow values or base-flow dut'atioll <br />cllrves. Walton (I~()5, p. 37-39) detennined base flow fl'om hydl'ographs of <br />a sample of Illinois stations and found "normal" base flow equal to the <br />value of total flow that has an expected duration 32 to 58 pel'cent of the <br />time. He establi~hed a relation with degrees of latitude to compute hase <br />flow at other sites. C 1.05S (lfl4f}) mapped the values of total daily stream- <br />flow expected gO pe rcent 01 the time for gaged I'i vc [' basins in Ohio to de- <br />fine an index of dr',v weather flow which was considered essentially con- <br />trihuted fl'om ground-watel' sourceso However'. this simplified method <br />does not work in Kansas, because the a\Oel'age daily base flo\o,' cOITesponds <br />to values of total daily flov..' that may be expected anywhere in the wide <br />range between 10 and 63 pel'cent of the time. <br /> <br />lorns and othel's (l!J65. p, 48-53) estimated base-flow dUl'ation curves <br />by constructing a tangent at the steepest part of the total !10w-dul'ation line <br />to separate direct runoff f1'om total flow. The difference between the two <br />lines represented base flow. Figure 9 shO'\\"s a comparison of hase-flow <br />and total t1ow-dul'ation curves fOl' four t)-pical Kansas streams, The pail'S <br />