Temperature dependence of stream aeration coefficients and the effect of water turbulence: a critical review

Abstract

The gas transfer velocity (K(L)) and related gas transfer coefficient (k(2) = K(L)A/V, with A, area and V, volume) at the air-water interface are critical parameters in all gas flux studies such as green house gas emission, whole stream metabolism or industrial processes. So far, there is no theoretical model able to provide accurate estimation of gas transfer in streams. Hence, reaeration is often estimated with empirical equations. The gas transfer velocity need then to be corrected with a temperature coefficient θ = 1.0241. Yet several studies have long reported variation in θ with temperature and 'turbulence' of water (i.e. θ is not a constant). Here we re-investigate thoroughly a key theoretical model (Dobbins model) in detail after discovering important discrepancies. We then compare it with other theoretical models derived from a wide range of hydraulic behaviours (rigid to free continuous surface water, wave and waterfalls with bubbles). The results of the Dobbins model were found to hold, at least theoretically in the light of recent advances in hydraulics, although the more comprehensive results in this study highlighted a higher degree of complexity in θ's behaviour. According to the Dobbins model, the temperature coefficient θ, could vary from 1.005 to 1.042 within a temperature range of 0-35 °C and wide range of gas transfer velocities, i.e. 'turbulence' condition (0.005 < K(L) < 1.28 cm min(-1)). No other theoretical models showed any significant variability in θ with change in 'turbulence', and only modest variability in θ with change in temperature. However, the other theoretical models did not have the same temperature coefficient θ (with 1.000 < θ < 1.056 within 0-35 °C). A model integrating turbulence and bubble mediated gas transfer velocities suggested a lower temperature dependence for bubble (1.013<θ < 1.017) than turbulence (1.023<θ < 1.031) mediated processes. As it stands, the effect of turbulence on the temperature dependence of gas transfer at the air-water interface has still to be clarified, although many models simulate different flow conditions which may explain some of the observed discrepancies. We suggest that the temperature dependence curves produced by the Dobbins model may be used tentatively as a simple theoretical guide for streams with free surface water but not self-aerated flows encountered in whitewater rapids, cascades or weirs. Greater awareness of the different models and conditions of applications should help choosing an appropriate correction. Three case studies investigated the effect of the temperature coefficient on reaeration and stream metabolism (photosynthesis and respiration). In practice, the temperature correction may be an important parameter under constant turbulence conditions, but as the range in turbulence increases, the role of temperature may become negligible in determining K(L), whatever the temperature correction. The theoretical models reviewed here are also useful references to correct K(L) values determined using a reference tracer gas to a second species of interest.