DO Saturation and Sensor Check

A DO analyzer is calibrated against the oxygen that water can hold at saturation, which falls with temperature and elevation. This finds the saturation value for your conditions, shows a reading as percent saturation, and compares an online analyzer with a Winkler or calibrated handheld reading.

DO Saturation and Sensor Check

Formula

DO (fresh water, 1 atm), mg/L = exp[-139.34411 + 1.575701e5/T - 6.642308e7/T² + 1.2438e10/T³ - 8.621949e11/T⁴]
   T = °C + 273.15 (Benson and Krause; Standard Methods 4500-O; USGS)
Salinity factor = exp[-S x (0.017674 - 10.754/T + 2140.7/T²)]
Pressure factor = (P - u)(1 - θP) / [(1 - u)(1 - θ)], P in atm
   u = exp(11.8571 - 3840.70/T - 216961/T²),  θ = 0.000975 - 1.426e-5 t + 6.436e-8 t²
P from elevation: mm Hg = 760 x (1 - 6.8756e-6 x ft)^5.2559

Inputs used

Water temperature (°C)
Elevation above sea level (ft)
Barometric pressure, true (not sea-level corrected) (optional) (mm Hg)
Salinity (optional) (ppt (g/kg))
Analyzer reading (optional) (mg/L)
Reference reading: Winkler or calibrated handheld (optional) (mg/L)
Allowed difference (optional) (mg/L)

Worked example (fictional plant data)

Aeration basin at 20 °C, plant elevation 1,000 ft, fresh water
Pressure = 760 x (1 - 6.8756e-6 x 1,000)^5.2559 = 732.9 mm Hg
Saturation at sea level, 20 °C = 9.09 mg/L; corrected for pressure = 8.76 mg/L
Analyzer reads 7.9 mg/L = 90.2% saturation
Winkler reads 8.2 mg/L: difference = -0.30 mg/L, more than the 0.2 mg/L allowed, so recheck the sensor

Cautions

Use true (station) barometric pressure for calibration. Weather reports give sea-level corrected pressure, which is wrong for this.
Compare readings at the same spot, depth and time. DO changes quickly across an aeration basin.
Optical (luminescent) sensors drift less than membrane sensors but still need cap replacement and cleaning.
If the analyzer and reference disagree, clean and verify before you recalibrate. Do not calibrate a dirty sensor.

References

Standard Methods for the Examination of Water and Wastewater, 4500-O (oxygen solubility table and equations).
U.S. Geological Survey, Office of Water Quality Technical Memorandum 2011.03, and the USGS DOTABLES program.
Benson, B.B., and Krause, D., 1984, Limnology and Oceanography, v. 29, no. 3, p. 620 to 632.

Results are estimates for operator and technician use. Equations follow the references above; always check against the instrument manual, your calibration procedure and plant data.