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<br />Average Observed <br />" __ ;~-4 :lCUla:ed r ""i <br /> <br />800 1200 1600 2000 2400 <br />River Water Discharge Rate (cfs) <br /> <br /> <br />tv 1600 <br />0 <br />.... <br />~ <br /> 1200 <br /> ..; <br /> - 'I <br /> '" <br /> . <br /> " 800 \ <br /> '0 <br /> . \ <br /> '" <br /> '0 l <br /> " <br /> 0 <br /> ..; <br /> " <br /> u <br /> ~- <br /> 0 400 <br /> <br /> <br />Figure 1,3, Relation of chloride concentration to water discharge rate for the Saline River, <br />Kansas (taken from Durum 1953), <br /> <br />Ward (1958) developed the following <br />regression expression for the Arkansas River, <br />Oklahoma, and the Red River, Texas: <br /> <br />log Ci = s + b log Q + c (log Q)2 <br />in which <br /> <br />(1.2) <br /> <br />a, b, c <br />Ci <br /> <br />... Constants <br />... Specific ion <br />mg/l <br /> <br />concentration in <br /> <br />He tried other ions besides chlorides, <br />observed high vsrisbility in his data, and <br />achieved a low correlation coefficient. <br /> <br />Ledbetter and Gloyna (1964) proposed <br />three empirical equations for predicting the <br />salt load in southeastern streams. The <br />authors utilized an exponential loading <br />equation as the base function: <br /> <br />C = kQb . . . . . . . . . . . <br /> <br />(1.3) <br /> <br />in which <br /> <br />k and b = Constants <br />C ~ Salt concentration in mg/1 <br /> <br />Their second equation converted b to a <br />variable exponent; <br /> <br />b ~ pQn <br /> <br />. . . . . . . . . . <br /> <br />(1.4) <br /> <br />in which <br /> <br />p and n = Constants <br /> <br />Their third equation used a different func- <br />t ion for the variable exponent, namely; <br /> <br />b = f + g log / Aq + h Qn . . ., (1. 5) <br />in which <br /> <br />f, g, h, n <br />Aq <br /> <br />... Constants <br />= An antecedent <br />defined as: <br /> <br />flow index <br /> <br />A <br />qk <br /> <br />30 <br />E <br />i=l <br /> <br />Qi/i <br /> <br />(1. 6) <br /> <br />in which <br /> <br />The antecedent flow index on the <br />day of the event (day k) <br />Water flow rate in the stream on <br />dsy i in ds <br />= The number of days back from the <br />kth day <br />Hart et a1. (1964) observed that apply- <br />ing Ledbetter and Gloyna's (1964) equstions <br />requires excessive data and proposed, from <br />work done on the Russian River in California, <br />the function: <br />bl b2 <br />C ~ al Qg + a2 Qi + <br /> <br />Aqk <br />Qi <br /> <br />i <br /> <br />b3 <br />a3 Qs <br /> <br />(1. 7) <br /> <br />in which <br /> <br />Qg <br /> <br />Groundwater flow rate in the <br />river in cfs <br /> <br />Qi <br /> <br />Interflow flow rate in the <br />river in cfs <br /> <br />4 <br />