In aquatic ecosystems, the single-station, single-stage

For two streams (one Chalk and one Greensand), the regression quotient
persistently underestimated the observed DO deficit. These two streams showed
similar timing patterns of oxygen dynamics with the point of minimum DO
occurring relatively quickly after sunset in spring and early summer,
although the two Chalk streams were more similar to one another in terms of
DO magnitudes. Comparisons between different streams using the single-station
model with constant

The dissolved oxygen (DO) signal has been used to quantify primary productivity and respiration in aquatic ecosystems since the pioneering work of Odum (1956). Recently, the increased capacity to deploy automatic data loggers coupled with the ability to automate the analysis of the DO signal (e.g. Grace et al., 2015) has enabled the processing of potentially large amounts of data across multiple aquatic systems. Estimates of primary production obtained from the DO signal can then be used through the photosynthetic quotient (e.g. Duarte et al., 2010; Westlake, 1963) to estimate the corresponding carbon uptake. Therefore, with growing awareness of the significance of river systems in global carbon cycling (Cole et al., 2007; Wohl et al., 2017) it becomes more relevant to ensure both that the models used are sound and that model limitations are apparent.

Ecosystem metabolism can be quantified by partitioning a single DO time series into its component fluxes, namely photosynthesis, ecosystem respiration and aeration. Although for parts of aquatic systems, oxygen consumption can be measured continuously, for example, through the use of benthic incubation chambers (e.g. Glud, 2008) or using eddy correlation techniques (e.g. Reimers et al., 2012), there is no method to measure oxygen consumption for the whole system. For aeration, although it is possible to measure the gas exchange constant using tracers such as sulfur hexafluoride (e.g. Beaulieu et al., 2013) or propane (e.g. Demars et al., 2011), from which the exchange constant for oxygen can be derived, only recently has a method been proposed (Pennington et al., 2018) to do this on a continuous basis. This means that time series estimates of oxygen consumption for a whole stream are coupled to estimates of the aeration flux and must be inferred, rather than measured, from DO time series, so that quantification of each depends on simultaneously quantifying the other.

There is experimental evidence that ecosystem respiration changes over a
single diurnal cycle (Staehr et al., 2010; Sadro et al., 2014; Alnoee et al.,
2014). However, for modelling purposes, both community respiration (

The open channel diel method requires the partitioning of the
stream-dissolved oxygen response into the dominant processes as described by
the following (single-stage

For nighttime, this relationship simplifies to the following:

Therefore, when

Therefore, if the model structure adequately captures DO dynamics,
at points of zero DO change in the nighttime DO time series the ratio of respiration to the volumetric aeration rate constant is equal to the observed oxygen saturation deficit. Thus, by identifying points in time of zero DO change, (DO

The questions addressed are as follows:

How does the observed oxygen saturation deficit at points of zero DO change (DOD

How do nighttime DOD

Does the time at which DOD

The study was conducted in the southern part of Britain in the Hampshire Avon
catchment. The catchment covers an area of 1706 km

Site location and catchment characteristics.

BFI: base flow index. Sources: Heppell et al. (2017) and for flow data, Heppell and Binley (2016). NA: not available.

Dissolved oxygen and temperature were logged continuously using miniDOT data
loggers (Precision Measurement Engineering, Inc.) at a resolution of
0.01 mg L

DO time series for 5 to 20 May 2015 for two Chalk streams

Figure

Distributions of DO values

Analysis of lagged differences in DO between normalised DO time
series.

In fact, the behaviour of the Ebble in terms of timing (i.e. phase) is much
closer to that of the Nadder than to the behaviour of the Wylye.
Figure

Time series for DO and

Time series for DO and

For the time series shown in Fig.

Identification of the point at which there is zero change in DO is not as
straightforward as at first it seems; the change in DO for any 1 min time
step may be very close to, but never equal to, zero because of short-term
stochastic variability in the DO signal.
Identification could be achieved by fitting a line to the points in
Fig.

Box plot time series of DO deficits at points of steady-state DO for the nights of 9/10 and 16/17 May 2015 for Ebble and Nadder

For the same two nights, the sets of DOD

For the Wylye (panel b), the regression quotient overestimates on 9/10 and
underestimates on 16/17. Thus, on the night when the DO minimum comes early
after sunset and the Wylye behaves more like the Ebble and the Nadder in
terms of timings of DO dynamics, the regression quotient underestimates the
median DOD

For data covering the entire study period (August 2014 to August 2015), the
distribution of the ratio of median DOD

A time series of median DOD

Also shown (Fig.

Nighttime simulations for 16/17 May for Ebble and Avon. For Ebble, median DOD

Distributions of the ratio of DO deficit at points of zero DO change to the regression quotient.

Figure

Time series (2014–2015) of the DO deficit at points of zero DO change (black circles) and comparison with corresponding ratio derived from nighttime regression (grey crosses). Trend lines are shown for both time series. For grey dashed line (Nadder), see text.

The regression quotient up to this point was computed using all data points
for any given night. An alternative would be to calculate the regression
quotient using only a subset of nighttime points. One possibility would be to
do so using only those data points clustered around the time after sunset at
which

For four sites on four separate rivers, two Chalk (Wylye and Ebble) and two
Greensand (Avon and Nadder), DO data were analysed for the period August 2014
to August 2015 with particular focus on a 2-week period in May 2015. For each
night in the year, the nighttime dissolved oxygen deficit at points of zero
DO change (DOD

Typically, single-station DO models assume constant

A plot of

At the point where

If Eq. (1) adequately describes the nighttime DO dynamics, then ratio 1 will
be equal to ratio 2. If, however, they diverge significantly, then the
assumptions are not satisfied. For 16 May, for example, for the Ebble,
ratio 1 is 1.6 and ratio 2 is 1.7, but for the Avon, they are equal (3.05),
and the corresponding simulations (Fig.

In itself, this divergence does not demonstrate that

On the other hand, ecosystem respiration is known to change over a single
diurnal cycle (Staehr et al., 2010; Sadro et al., 2014; Alnoee et al., 2014).
Schindler et al. (2017) suggest that increases in nighttime oxygen
concentrations, as is the case for both the Ebble and the Nadder in May
(Figs.

Relationship between time after sunset until the point of zero DO
change and the ratio DOD

Time after sunset at which

Scatter plots for regression quotient against median DO deficit at points of zero DO change for the Nadder.

No part of the analysis presented above demonstrates, however, that

Behaviour of DO dynamics were also examined with regard to hours after sunset at which

The regression quotient was calculated for the night as a whole and also by
restricting the data points included to those

This paper began with a comment on the proliferation of automatic logging devices which vastly increases the potential for analysis of river oxygen and therefore river carbon dynamics. Oxygen dynamics are often analysed using models that make simplifying assumptions about the underlying processes, specifically about the constant values of both community aerobic respiration and the reaeration rate constant over the course of a single day. However, there is a debate about the extent to which respiration in particular can be represented by a single daily value. Through analysis of the dissolved oxygen deficit at points of zero DO change for four sites on four rivers, it was shown here that the assumption of constant values for either respiration or the aeration rate constant was violated perennially for two of those sites. It was suggested that this is likely to be because of two-stage rather than one-stage respiration, although it should be noted that variability in the volumetric aeration rate or even unidentified factors could account for the findings. In any case, this means that the use of single station, single-stage respiration diel oxygen models might not be optimal in such cases. This is not to decry the use of such models, as the purpose of a model is to abstract from reality. However, if analysis of DO time series were to become routine with results impacting environmental policy decisions, then it would be important to understand when these models are failing rather than presume that they are fit for purpose.

Natural Environment Research Council (NERC) data at

The author declares that there is no conflict of interest.

Foundation work was carried out as part of post-doctoral research at Imperial College London. Thanks to Adrian Butler for support.

This research has been supported by the Natural Environment Research Council (grant nos. NE/J01219X/1 and NE/J012106/1).

This paper was edited by Perran Cook and reviewed by two anonymous referees.