American Society of Civil Engineers

Delta Method for Estimating Primary Production, Respiration, and Reaeration in Streams

by Steven C. Chapra, A.M.ASCE, (Prof., Ctr. for Advanced Decision Support for Water and Envir. Systems, Civ., Envir. and Arch. Engrg., Univ. of Colorado, Boulder, CO 80309-0428) and Dominic M. Di Toro, M.ASCE, (Res. Prof., Envir. Engrg. and Sci., Manhattan Coll., Bronx, NY 10471)

Journal of Environmental Engineering, Vol. 117, No. 5, September/October 1991, pp. 640-655, (doi:

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Document type: Journal Paper
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Discussion: by Ronald R. H. Cohen    (See full record)
Discussion: by John B. Erdmann    (See full record)
Discussion: by Michael G. Waldon    (See full record)
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Abstract: A simple approach, the delta method, is derived to estimate stream reaeration, primary production, and respiration rates on the basis of diurnal dissolved oxygen measurements. The method uses three features of the diurnal curve to determine these quantities. The time of minimum deficit (relative to solar noon) is used to estimate the reaeration rate. Given the reaeration rate, the deficit range Δ is employed to predict photosynthetic production. Finally, the average deficit can be used in conjunction with the reaeration and production rates to compute respiration. A graphical procedure is presented to implement the method. The approach is demonstrated by applying it to the Grand River in Michigan. Although the method has general applicability, a sensitivity analysis indicates that it is particularly effective for streams with lower reaeration rates (i.e., < 1.0 d-¹). An efficient piecewise solution of the diurnal oxygen deficit balance is derived as an alternative to a Fourier series and numerical solutions. Finally, we develop some simplified analytical solutions that make the delta method easier to implement.

ASCE Subject Headings:
Dissolved oxygen
Rivers and streams
Water quality