As organic matter from wastewater decomposes, it consumes oxygen, and an assessment of the effect of a wastewater discharge on the receiving water uses the saturation concentration of dissolved oxygen (DO) as a reference. This concentration decreases with temperature, salinity, and elevation. For freshwater at sea level, the saturation concentration o_sf in mg/L is given by (APHA 1992)
ln(o_sf) = -139.34411 + 1.575701 x 10^5/T_a - 6.642308x10^7/T_a^2 + 1.243800x10^10/T_a^3 - 8.621949x10^11/T_a^4
where T_a = T + 273.15 is the absolute temperature (K) and T is the temperature in deg C. For saltwater at seal level, the saturation concentration o_ss in mg/L is given by (APHA 1992)
ln(o_ss) = ln(o_sf) - S(1.7674x10^{-2} - 1.0754x10^1/T_a + 2.1407x10^3/T_a^2)
where S is the salinity in g/L or parts per thousand (ppt). Then if o_s0 is the saturation concentration at sea level (i.e., elevation 0), then the concentration o_sz at elevation z (in km) is (Zison et al. 1978)
o_sz = o_s0 (1 - 0.1148 z)
For T = 20 deg C, the saturation concentration of freshwater is 9.092 mg/L at sea level and 8.049 mg/L at an elevation of 1 km. For saltwater at sea level, a temperature of 20 deg C, and a salinity of 33 ppt, the saturation concentration is 7.484 mg/L.
Write a function to compute the saturation concentration of dissolved oxygen in water as a function of temperature, elevation, and salinity.
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Tim William George Berken Dyuman Joshi

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