The average depth in the ocean at which the majority of sinking organic
matter particles remineralise is a fundamental parameter in the ocean's role
in regulating atmospheric CO

Sediment trap studies show that the vertical flux of particulate organic
carbon (POC) can be described empirically by a power-law curve (e.g. the
“Martin curve”:

Understanding the underlying reasons for the spatial patterns in
remineralisation is a valuable step in understanding mechanisms driving the
biological pump. This is key to understanding how the biological pump will
respond to both past and current changes in climate

The range of observed Martin curves and associated remineralisation
rate profiles.

A potential approach to increasing and enhancing the resolution of POC
observations is to use climatological fields of dissolved nutrients to
estimate POC remineralisation rates. The water column profile of
remineralisation rates can be related to flux curves by the fact that the
vertical profile of remineralisation rates is the first derivative of the
vertical profile of fluxes

An alternative to combining AOU and age tracers is to use the spatial
gradients in tracers to separate out and quantify the change in
a concentration of a tracer at any point from circulation only. Spatial
gradients of a tracer along the trajectory of a water mass in the ocean
interior reflect mixing with other water masses and processes such as the
remineralisation of organic matter. Gradient-based approaches aim to solve
for the effect of mixing by defining a water mass as the sum of mass
fractions from different sources

Spatial gradients in tracers have also been used to diagnose export fluxes of
calcium carbonate

Ocean circulation models offer the opportunity to estimate remineralisation rates of organic matter from tracer data by exploiting the calculated modelled transport rates to account for the effects of ocean circulation on tracers. The aim of this paper is to explore the feasibility of inferring flux profiles of particulate organic matter from remineralisation rates that have been derived from observed tracers using this method. A method and example of estimating remineralisation rates using transport matrices is first introduced. We identify potential sources of error for this method. We then derive a set of model experiments that are used as a synthetic data set with which to test the sensitivity of the approaches to various sources of error and explore potential constraints on estimates. Finally, we explore the uncertainties associated with the broader concept of inferring flux curves from remineralisation rates.

Remineralisation rates can be calculated as the amount of tracer supply
needed to maintain tracer observations at steady state once the effects of
model ocean transport have been accounted for, i.e. transport divergence

For every grid box in the model the TM defines a set of coefficients for
neighbouring grid boxes that represent the change in any tracer due to ocean
circulation during a single time step of the model (see
Table

Example of using a transport matrix to calculate

To infer particulate flux curves from estimates of the remineralisation
rates, we fit a linear function to the log-transformed profiles of rates in
the ocean interior vs. depth

Example of using a GCM transport matrix to estimate

As an example of the approach, we use the annual average TM derived from
a 2.8

Linear functions were fitted to the log-transformed water column profiles of
estimated remineralisation rates to infer particulate flux curve exponents
(Fig.

To explore the errors when using modelled transport rates, we first derive
a synthetic data set using the Earth system model “GENIE”

Our choice of GENIE over other possible models and available transport
matrices reflects a number of considerations. The configuration of GENIE used
here was derived using a set of ensemble parameters relevant to the physical
circulation that were sampled from ranges to test the sensitivity of the
model to assumptions about ocean circulation and find an optimal set of
parameters

The method of

We use the biogeochemical model described in

[

We design a number of experiments to explore the sensitivity of the approach
to various sources of error (experiment names are indicated in brackets):

(TWIN) We first use the TM corresponding to the synthetic data set (SYN) to estimate remineralisation rates from the corresponding
[

(ERR-OBS) The effect of errors from the tracer observations themselves is simulated by calculating 100 random perturbations to the synthetic

(ERR-CIRC) To explore the effect of circulation uncertainty, we diagnose 54 individual TMs from an existing perturbed physics ensemble

(ERR-DOM) We explore the effect of DOM when inferring particulate flux curves from remineralisation rates. As a comparison to the synthetic data set, we run an
identical experiment but with no DOM created (SYN-NODOM) – i.e. all

The synthetic tracer data set used for transport matrix inversions.

Results from inverting the synthetic data set with its corresponding
transport matrix.

We use the output from GENIE as a synthetic data set from which to assess the
transport matrix inversion method and identify the sources and nature of the
errors involved. Figure

To demonstrate and test the method described in Sect.

Although remineralisation rates can be estimated by applying transport rates to a tracer field as shown above, there are several assumptions that will introduce error when this is applied to observations. In the following sections, we detail the results of experiments designed to explore these sources of error.

Assessment of the errors arising from the uncertainty in
[

Assessment of error arising from using circulation estimates.

Error related to the 1

The SEs are used to produce 100 versions of the synthetic [

Another potential source of error when inverting nutrient observations arises
from the use of a modelled circulation field that will inevitably have
a somewhat poorly quantified relationship to the circulation of the real
ocean. Using TMs representing plausible but different realisations of the
modern ocean circulation from an ensemble to invert our synthetic data set, we
can explore the effect of errors arising from uncertainties in circulation
rates only. Figure

To understand why different circulation estimates can have a large impact on
ISSs, we explore the size of the

Comparison of inputs of

Comparison of error magnitudes when estimating remineralisation
rates. The global mean

To compare the magnitude of the various possible errors, we show the global
mean synthetic

Despite similar magnitudes of uncertainty arising from both potential errors
in the observations and from the model circulation field, the nature of the
uncertainty is different. Uncertainty from the observations is higher in
regions where observations are more uncertain, e.g. coastal areas in
Fig.

We have presented a straightforward method of using a steady-state model
circulation, as represented by a transport matrix, to estimate organic matter
remineralisation rates from a tracer climatology. Our main goal is to explore
the feasibility of using this method to infer spatially explicit organic
matter flux curves, aiding additional understanding of the biological pump in
the modern ocean. Our results show that this method is associated with
a number of significant sources of error that give rise to the spatial
patterns and negative values seen in an example inversion using a circulation
field from a coarse-resolution ocean model (Fig.

The sensitivity to errors in the observations is a result of the way that the
transport matrix (TM) is constructed. A change in a tracer due to circulation
in a model time step is relatively localised due to the finite speed of
advection and diffusion in the model

Inversion of salinity as a possible constraint on the uncertainty
from using a modelled circulation.

Assessment of the uncertainty associated with dissolved organic
matter when inferring flux profiles. Value of the exponent when fitting
a power law to the water column remineralisation rates from

The flipside of the magnitude and nature of the circulation control on the
diagnosed remineralisation rates is that tracers with a steady-state
constraint, where it is expected that there should be no significant sources
or sinks at depth, could be used to estimate the magnitude of the
circulation-based error. As an example, we show an ISS field generated when
inverting the salinity field from our synthetic data set with the synthetic
transport matrix (Fig.

Redefining the modelled circulation terms to reflect that the modelled
circulation is a function of a “true” circulation term and an error term
(

For a conservative tracer at steady state, it is expected that

In the previous sections, we have shown that a simple approach to estimating
remineralisation rates using modelled transport rates is sensitive to
different sources of errors. Taking the next step, in the case that
remineralisation rates could be estimated with some reliability, we explore
the sensitivity of inferring flux curves by vertically integrating
remineralisation rates in the presence of DOM. The remineralisation of DOM
can occur away from where it was exported, affecting the assumption that the
remineralisation rates reflect only vertical processes. To explore this, we
infer flux curves using remineralisation rates from the synthetic data set
(SYN) and a second run where no DOM is created (SYN-NODOM). To infer a power-law curve, a linear trend is fitted to the log-transformed remineralisation
rates following previous studies

The exponents from power-law curves, fitted to vertical

A range of issues relevant to fitting flux curves are also relevant to the
retrieval of reliable estimates of flux curves from modelled remineralisation
rates. Previous studies have noted that fitted values of

Any method of inferring particulate organic matter flux curves from estimated
remineralisation rates, whether using model transport rates or using
observations

Profiles of remineralisation rates derived from ocean tracers offer
a potential method to estimate high-resolution fields of flux curves that
could supplement existing global sediment trap studies. The use of model
transport rates offers one way of estimating remineralisation rates that
could avoid the spatial averaging issues of combining AOU with age
tracers. Using the transport rates in the form of a transport matrix is a
first step towards this, but the simple application to a tracer such as
[PO

The spatial variability in POC fluxes observed in the modern ocean has important implications for our understanding of how the biological pump may have changed in the past and in the future. New approaches to estimating POC fluxes will help provide estimates in regions, such as the Southern Ocean, that are currently undersampled by sediment traps and key to testing existing mechanistic hypotheses. Exploring the spatial variability of POC fluxes in ocean biogeochemical models by finding a set of POC flux profiles that best fits observed tracers will help approach the uncertainties highlighted in this paper but also provide a quantitative analysis of the significance of spatially varying POC fluxes.

This work was conducted as part of a project studentship (J. D. Wilson) associated with the UK Ocean Acidification Research Programme (UKOARP, grant NE/H017240/1) to A. Ridgwell and S. Barker. J. D. Wilson and A. Ridgwell acknowledge support via EU grant ERC-2013-CoG-617313. A. Ridgwell also acknowledges support through a Leverhulme award (RPG-2013-106). We thank Samar Khatiwala for making code and matrices available online, Julia Hargreaves for providing the ensemble data, and the two anonymous reviewers and the editor for their comments and feedback. Edited by: J. Middelburg