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Effects of temperature variation on critical stream dissolved oxygen
Author(s) -
Eheart J. Wayland,
Park Heekyung
Publication year - 1989
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr025i002p00145
Subject(s) - saturation (graph theory) , monotonic function , derivative (finance) , oxygen , temperature coefficient , streams , thermodynamics , second derivative , chemistry , analytical chemistry (journal) , materials science , mathematics , physics , chromatography , mathematical analysis , computer network , organic chemistry , combinatorics , computer science , financial economics , economics , composite material
The classical assumption that the lowest dissolved oxygen (DO) occurs at the highest temperature may not always hold. The DO saturation concentration decreases monotonically with increasing temperature, lowering the DO, but the reaeration coefficient increases monotonically with increasing temperature, tending to raise it. The decay coefficient monotonically increases with increasing temperature, lowering the DO for single discharges but not necessarily for multiple discharges. (Lower decay rates attending lower temperatures could result in low DO at the point where the impact from one discharge meets that of another.) This paper addresses the question of whether DO might under some circumstances worsen with decreasing temperature. Using a linear programing model it is shown that for a uniform stream at constant streamflow, the pattern of discharge that maximizes the derivative of critical dissolved oxygen with respect to temperature is an infinite uniformly distributed load. This suggests that streams receiving a large number of discharges may be more susceptible to DO increasing with decreasing temperature than streams receiving a small number of discharges. The corresponding maximum value of the derivative is shown to be dC S / dT + ( C S ‐ C * ) ln Φ mg/L ‐1 °C −1 , where T is the temperature in °C, C * is the dissolved oxygen standard, C S is the DO saturation concentration (both in milligrams per liter), and Φ is the temperature adjustment factor for the reaeration coefficient. The maximum derivative value does not depend on the decay coefficient or its temperature adjustment factor. For the maximum reported value of Φ of 1.047, the maximum derivative value is 0.26273 ‐ 0.0028610 T + 0.00013371 T 2 ‐ 0.35718 T 3 ‐ 0.045929 C * , for which the assumption that DO decreases monotonically with increasing temperature is valid for C * greater than about 6 mg/L. However, this assumption breaks down for values of Φ just above the range reported in the literature and values of C * just below the normally chosen range of 5–6 mg/L.