Coastal seas represent one of the most valuable and vulnerable habitats on
Earth. Understanding biological productivity in these dynamic regions is
vital to understanding how they may influence and be affected by climate
change. A key metric to this end is net community production (NCP), the net
effect of autotrophy and heterotrophy; however accurate estimation of NCP has
proved to be a difficult task. Presented here is a thorough exploration and
sensitivity analysis of an oxygen mass-balance-based NCP estimation technique
applied to the Warp Anchorage monitoring station, which is a permanently
well-mixed shallow area within the River Thames plume. We have developed an
open-source software package for calculating NCP estimates and air–sea gas flux.
Our study site is identified as a region of net heterotrophy with strong
seasonal variability. The annual cumulative net community oxygen production
is calculated as (

Marine areas play a fundamental role in the cycling of carbon

Understanding the mechanisms driving these processes is vital for predicting
how marine waters will respond to and influence climate change

The balance between dissolved inorganic carbon (DIC) fixation (i.e.
autotrophy) and production of DIC through heterotrophy over a specified
period is known as net community production (NCP;

NCP is a key metric for quantifying the cycling of biological carbon

Estimating net community production rates in the ocean is notoriously
difficult

The remote sensing of NCP via ocean colour is in its infancy and requires
calibration against reliable in situ measurements

Given that production is episodic rather than continuous

Oxygen mass-balance techniques utilise measured changes in oxygen saturation
and attempt to quantify the biological contribution to those changes in
saturation. The approach to teasing apart the physical and biological drivers
to these saturation changes can be subdivided into two groups: those which
use a biologically inert analogue to oxygen, typically argon

The gas transfer parameterisation approach can be applied to historic
data sets; given that the concentration of dissolved oxygen is the most
widely measured property of seawater after temperature and salinity

To date, the majority of oxygen-based NCP estimates have focused on oceanic
waters

The Cefas (Centre for Environment, Fisheries and Aquaculture Science)
SmartBuoy network consists of autonomous data collection moorings placed at
key locations in the UK shelf seas

In this paper we present new estimates of NCP from a long-term SmartBuoy mooring situated in the southern North Sea. We explore the uncertainty in these estimates and their sensitivity to uncertain input parameters. Lastly we make our algorithms available as open-source tools for readers to perform their own NCP calculations.

The SmartBuoy sensor package consists of a Cefas ESM2 data logger coupled with
Falmouth Scientific OEM conductivity and temperature sensors (Falmouth
Scientific, USA), an Aanderaa 3835 series optode (Aanderaa Data Instruments,
Norway), a chlorophyll fluorometer (Seapoint Inc., USA), and a quantum
photosynthetically active radiation meter (PAR; LiCor Inc., USA). The ESM2
includes a three-axis roll and pitch sensor with a internal pressure sensor
(PDR1828 – Druck Inc). The data logger was configured to sample for a
10 min burst every half hour. Salinity, temperature, chlorophyll, and PAR are
sampled at 1

The Warp Anchorage SmartBuoy site, shown in Fig.

Map of Warp Anchorage study site.

Study site characteristics for

SmartBuoy data undergo rigorous automated and manual quality assurance processes. Automated processes apply a quality flag to data which fall outside realistic value bounds. Manual processes assess the instrument performance and apply flags where the data quality is compromised, e.g. due to biofouling or sensor damage. The CT sensor salinity data are corrected using in situ bottle samples analysed using a Guildline Portsal 8410A (Guildline, Canada) standardised with IAPSO standard seawater.

Validation of ECMWF MACC reanalysis 10 m wind speed vs. height-corrected shipborne anemometer wind speed.

Water depth was calculated using a global tidal model forced with European
shelf area constituents (TPX08-atlas). Tidal waves have been shown to arrive
almost simultaneously at both the Sheerness and the Warp SmartBuoy site

Parameters and their uncertainty distributions used for LHS/PRCC and eFAST at the Warp site.

SE: the standard error of the mean.

Continuity of the 10-year Warp oxygen data set is hampered primarily by
biofouling of the instrumentation. To avoid extrapolation or interpolation of
the data, only periods of complete data were used in the analysis. Two
contrasting periods were selected, a spring–summer period of 150 days from
January to June 2008 and an autumn–winter period of 95 days from September to
December of the same year. The 10 min half-hourly burst data from the buoy
and the tidal model output were combined with the 6-hourly ECMWF data. These
burst means were further smoothed to 25 h averages to remove any structural
biases in the data caused by the tidal cycle

Aanderaa Instruments model 3830 and 3835 optodes (Aanderaa, Norway) have been
fitted to the Cefas SmartBuoys since 2005. Optodes drift due to foil
photobleaching in a predictable way

NCP is calculated here using a modified version of the zero-dimensional oxygen
mass-balance (box) model of

Given that the Warp site is permanently mixed, there is in effect direct connection
between the atmosphere and the benthos. It is thus an important distinction
from prior studies that our community productivity estimate considers both
the pelagic and benthic processes as one system. This method assumes that
other oxygen-consuming processes in the water column such as nitrification,
methanotrophy, and photooxidation are negligible relative to respiration

The model (Eq.

The square root of the squared mean was used for wind speed to fit with the
quadratic

The injection of bubbles into the mixed layer through wave action can
supersaturate the surface waters even if net gas exchange is zero

We solve Eq. (

Accurately assessing the sensitivity of a model output to uncertain input
variables has many uses. Primarily it is to determine the precision of the
model output and the sources of output uncertainty, knowledge of which
informs future research in targeting the main sources of uncertainty if
robustness is to be increased

Local sensitivity analysis methods, such as the so-called one-at-a-time
techniques, are limited to providing information only in a very specific
location of the parameter space. These methods rely on the selection of an
applicable baseline and varying a single input parameter, which ignores the
effects of covariant parameter uncertainty

Global methods such as Latin hypercube sampling with partial rank correlation coefficients (LHS/PRCCs) and the extended Fourier amplitude sensitivity test (eFAST) are capable of assessing multiple locations across the entire parameter space; thus covariant parameter uncertainty is captured.

LHS/PRCC and eFAST have proven to be two of the most efficient and reliable
methods in each of their classes, sampling-based and variance
decomposition-based respectively

LHS is performed by assigning a error probability density function (PDF) to
each of the parameters. Each PDF is split into

While there is no a priori exact rule for determining sensible sample size
for these methods, minimum values are known to be

LHS/PRCC and eFAST analyses were run 500 times for each 25 h step of the
time series, and the results were aggregated. For cumulative calculations

Critical to the value of any sensitivity or uncertainty analysis is the
selection of adequate probability distribution functions for each input
parameter

The two oxygen terms (

The calculation of

At the Warp site, given the assertion that it is always fully mixed, the uncertainty in

Regressions between the predicted height from the model and the Sheerness tide gauge results in a RMSE of approximately 0.4 %. These estimates of parameter measurement uncertainty were combined, using the square root of the sum of squares, with the standard error of each mean observed value. The uniform bias was found to be relatively small compared to the observed standard errors, and thus the overall parameter error is considered to be normally distributed.

Uncertainty distributions for

Spring 2008 Warp Anchorage time series.

The 25 h mean chlorophyll time series for the Warp site is shown in
Fig.

All NCP values are given as oxygen equivalents unless otherwise stated. NCP is
characterised by small, mostly negative fluxes for the first 3 months. This is
followed by a marked phytoplankton bloom (Fig.

The maximum rate of net community oxygen production was calculated as
(485

Spring 2008 Warp Anchorage time series.

Warp 2008 winter cumulative NCP. Mean value shown in blue. Red lines indicate 95 % confidence limits. Black lines correspond to each simulation run.

The maximum rate of

Warp June–October NCP estimates from other years demonstrating no significant periods of net production.

Warp sensitivity analysis indices.

Mean gas residence time for oxygen was calculated to be 5 days. Calculating
the seasonal net balance (Fig.

We estimate the cumulative NCP for the missing 4-month period of 2010
(July–October) using the mean rate for this period across other years of the
10-year Warp data set, a subset of which is shown in
Fig.

We thus determine that the Warp site is net heterotrophic with an annual
oxygen NCP of (

Figure

The squared PRCC values from spring 2008 are shown in Fig.

Both techniques indicate the determination of the change in oxygen
concentration (

Warp eFAST total-order Sobol indices over time, indicating changing fractional contributions to uncertainty from each of the main parameters.

The large confidence limits shown for

LHS/PRCC is not suitable for assessing the effects of measurement and
parameterisation bias on the cumulative NCP estimate. Uncertainty in some of
the parameters, principally

As the water column at the Warp site is fully mixed, processes occurring at or in
the seabed are incorporated into the mixed-layer mass balance and thus the
NCP estimate. This includes non-respiration oxygen-consuming processes such
as nitrification and the oxidation of reduced compounds other than ammonia
and nitrite. A previous study at the Warp site using incubated sediment cores
provides estimated rates of sedimentary oxygen uptake of 55 in July and
26

It is important to consider that chemoautotrophic processes, such as
nitrification, contribute positively to the metabolic balance but negatively
to the oxygen inventory. This is true not just for benthically coupled sites
like Warp but for any system where these processes occur. These
processes, while assumed small relative to respiration and photoautotrophy by

Warp eFAST first-order (red) and total-order (Cyan) Sobol indices for cumulative NCP, indicating relative contributions from parameter bias uncertainty to cumulative NCP uncertainty.

Raw (30 min) Warp SmartBuoy time series showing significant variability in oxygen anomaly (red) and salinity (blue) within each tidal cycle. Here the oxygen anomaly neglects the supersaturating effects of bubbles.

There are two events – one at the start of February, another in the second
week of March – where high winds appear to coincide with increased negative NCP
(Fig.

While its use in improving our knowledge of carbon cycling is well known, NCP also represents a potential next-generation indicator of ecosystem health. The short duration of the bloom and the large impact that a 2-week period has on the annual budget could indicate that annual estimates, while vital for carbon cycling studies, are a less useful indicator for ecosystem health. A carefully resolved bloom period NCP may be more useful.

The commonly used “Redfield” stoichiometric ratio for O : C of 1.45

Literature values for NCP estimates from regions similar to the Warp site are
scarce.

The rates of net production seen at the Warp site when expressed in units of carbon
are of comparable magnitude to other estimates, with a maximal carbon NCP
rate of (346

Prior oxygen NCP studies have neglected to include the production of oxygen within the time step; that is to say they assume an instantaneous production of NCP at the end of their time step when the measured oxygen concentration and abiotically predicted concentration are compared. This results in the underestimation of the magnitude of NCP. For example, oxygen produced at the start of the time step will out-gas quicker due to the increased air–sea concentration gradient, and when the degree of supersaturation is later measured at the end of the time step the true magnitude of the supersaturation will be masked.

The effect of neglecting the within-time-step NCP is negligible when
conditions are near equilibrium saturation. However, during the bloom,
neglecting the within-time-step NCP would result in a
45

The results from both LHS/PRCC and eFAST techniques support the conclusion
that the bulk of the uncertainty in the NCP calculation is dependent on the
determination of changing oxygen in the mixed layer. This is in keeping with
the observations of the

The mean and median value for

Thus we believe improvements in identifying homogeneous water masses over the tidal cycle, rather than integrating it entirely, is the best approach to reducing uncertainty with this scheme.

Shipboard transect studies (typically utilising O

For the investigation of cumulative uncertainty we consider only the bias in
each parameter. The bubble supersaturation term (

Optodes tend to drift towards underestimating oxygen concentrations

Future studies are likely to benefit from newer optode designs than those
used here. Together with the improved multi-point calibration equation
(Stern–Volmer) of

Previous studies in open-ocean environments have ignored horizontal advection

The box model presented here relies on the assumption that the instruments are measuring the same body of water twice; i.e. the comparison of two consecutive 25 h averages represents the same mass of water evolved over time.

If we assume that conditions along the path length are homogeneous on 25 h
time scales, in effect the NCP estimates presented here can be thought of as
integrating over a length scale proportional to the residual flow. Historic
in situ acoustic Doppler current profiler data gathered over 3 months at the
Warp site (see Appendix A) show a residual mean current flow estimated at
1.9–2.2

While our 25 h averages and d

Residual currents will also affect the NCP estimates by the addition and loss
of water from outside of our observational window.

We have attempted to estimate the oxygen concentration gradient from the
tidally driven oxygen variability, that is, the difference between the oxygen
concentration at low and high tide. We calculate this for our January period
to be approximately 2

This is not an insignificant flux relative to our calculated winter heterotrophy and would indicate that our site could actually be autotrophic with the heterotrophic processes occurring upstream. It is clear that consideration of advection is required to accurately estimate the annual metabolic state at this site.

There are several other known contributors to NCP uncertainty which are
outside the scope of this study.

Similarly while sea spray may also enhance gas transfer, we believe this to
also already be accounted for in the parametrisation. Further uncertainties
relating to the parametrisation of

Our work identifies the Warp SmartBuoy site as an annually net heterotrophic location with strong seasonal variability and autotrophy during the growth phase of the bloom. However, this assertion is brought into question due to significant unconstrained uncertainties from horizontal advection, the determination of which is outside the scope of this study.

We have demonstrated that the largest constrained source of uncertainty in our NCP estimates comes not from the selection of gas exchange parametrisation, or the quality of remote-sensed and modelled parameters, but from the measurement of the changing oxygen concentration. For cumulative annual estimates, the strongly biasing uncertainty of bubble-induced supersaturation is the dominant source of uncertainty.

Constraining the degree of horizontal advection is vital to improving long-term NCP estimates and to determining the overall metabolic balance. Further work should also focus on understanding the nature of the short-term variability associated with changing oxygen concentration to enable better NCP estimates in dynamic areas such as the Warp site.

Shipborne anemometers data were adjusted to 10 m height using the scheme of

Acoustic Doppler current profilers were deployed at the Warp SmartBuoy site
between November 2001 and April 2002. Three deployments were made using
1

Thanks are owed to the Cefas MOS team, in particular David Sivyer and
David Pearce. We thank Tiago Silva for providing the modelled tidal data,
Jonathan Fellows for his mathematical insights, and Tim Jickells and Clare Ostle
for fruitful discussions. The officers and crew of the RV