USGS Home
Contact USGS
Search USGS

U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2008–5076

Back to Table of Contents

Appendix A. Calculation of the Rate of Change in Dissolved Oxygen Over 24 Hours from Light/Dark Bottle Incubations and the Extinction Coefficient

An estimate of the potential change in dissolved oxygen over a 24-hour period (ΔDO) was made from the measured oxygen production and consumption rates in the light and dark bottles at two levels in the water column and the measured extinction coefficient as follows. The gross production G in mg L^-1 hr^-1 was assumed to have the same exponential dependence with depth as light radiation. Then, in analogy with equation (21), the gross production at any depth in the water column G_z as a function of the gross production at the water surface G₀ is given by

    (A1)

Solving for G₀ in terms of the value obtained from 0.5 m depth yields

    (A2)

The gross production integrated over a water column of depth D is given by

    (A3)

where 10^-3 is a proportionality constant. The units of are mg m^-2 hr^-1.

Measured respiration rates (R) were very similar at both depths, and are therefore assumed to be constant throughout the water column for this calculation. Then the respiration integrated over the water column is given by

    (A4)

where 10^-3 is a proportionality constant and the units of are mg m^-2 hr^-1. The final simplification is to assume that the gross production rate is constant at for 12 hours of daylight in every 24 hours and zero for the remaining 12 hours, and the respiration rate is constant for a full 24 hours. Then the estimated change in dissolved oxygen over a 24-hour period, expressed in terms of a concentration (mg L^-1), is

    (A5)

Back to Table of Contents