BGBiogeosciencesBGBiogeosciences1726-4189Copernicus GmbHGöttingen, Germany10.5194/bg-12-5547-2015Can organic matter flux profiles be diagnosed using remineralisation rates derived from observed tracers and modelled ocean transport rates?WilsonJ. D.wilsonjd@cardiff.ac.ukhttps://orcid.org/0000-0001-7509-4791RidgwellA.BarkerS.https://orcid.org/0000-0001-7870-6431School of Earth and Ocean Sciences, Cardiff University, Cardiff, UKSchool of Geographical Sciences, University of Bristol, Bristol, UKDepartment of Earth Sciences, University of California, Riverside CA, USAJ. D. Wilson (wilsonjd@cardiff.ac.uk)30September20151218554755622March201519March201510September201515September2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://bg.copernicus.org/articles/12/5547/2015/bg-12-5547-2015.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/12/5547/2015/bg-12-5547-2015.pdf
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 CO2. Observed spatial patterns in sinking fluxes
and relationships between the fluxes of different particles in the modern
ocean have widely been used to invoke controlling mechanisms with important
implications for CO2 regulation. However, such analyses are limited by the
sparse spatial sampling of the available sediment trap data. Here we explore
whether model ocean circulation rates, in the form of a transport matrix, can
be used to derive remineralisation rates and infer sinking particle flux
curves from the much more highly resolved observations of dissolved nutrient
concentrations. Initially we show an example of the method using a transport
matrix from the MITgcm model and demonstrate that there are a number of
potential uncertainties associated with the method. We then use the Earth
system model GENIE to generate a synthetic tracer data set to explore the
method and its sensitivity to key sources of uncertainty arising from errors
in the tracer observations and in the model circulation. We use a 54-member
ensemble of different, but plausible, estimates of the modern circulation to
explore errors associated with model transport rates. We find that
reconstructed remineralisation rates are very sensitive to both errors in
observations and model circulation rates, such that a simple inversion cannot
provide a robust estimate of particulate flux profiles. Estimated
remineralisation rates are particularly sensitive to differences between the
“observed” and modelled circulation because remineralisation rates are 3–4
magnitudes smaller than transport rates. We highlight a potential method of
constraining the uncertainty associated with using modelled circulation
rates, although its success is limited by the observations currently
available. Finally, we show that there are additional uncertainties when
inferring particle flux curves from reliable estimates of remineralisation
rates due to processes that are not restricted to the vertical water column
transport, such as the cycling of dissolved organic matter.
Introduction
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”: ; see Fig. a) where POC
is rapidly remineralised in the upper water column (<1000m),
leaving a small fraction (5–10 %) of POC that sinks to greater
depths. The exponent of the Martin curve (b) reflects the distribution of
POC with depth and whether POC is remineralised higher or lower in the water
column. Recent studies using deep global sediment trap observations,
observations of 234Th and particle concentration data have suggested
a highly heterogeneous pattern of flux profiles and the existence of
a general latitudinal trend .
POC fluxes in high-latitude regions decrease faster with depth – i.e. flux
curves correspond to shallower remineralisation compared to those in
low-latitude regions, where a greater proportion of POC is remineralised at
deeper depths (Fig. a). However these patterns may be biased
by a focus on deep ocean fluxes due to sampling biases in shallower traps
. An analysis of neutrally buoyant sediment traps has
since suggested that shallower POC fluxes have a latitudinal pattern inverse
to that found in deep traps . Analysis of the POC fluxes
supports a number of mechanisms that explain these spatial patterns, including
increased sinking velocity of particles via a “ballast” effect from
minerals such as CaCO3;
aggregation of particles ; surface ecosystem dynamics, such
as the degree of nutrient recycling and blooms altering characteristics of
the particles being exported ; and
temperature-dependent remineralisation rates . However,
further progress has been hindered by the relatively low sampling density of
long-term sediment trap deployments, particularly in regions such as the
Southern Ocean e.g..
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 .
Atmospheric carbon dioxide (CO2) concentrations have been shown to
be sensitive to changes in flux profiles when modelled, primarily via the
effect of redistributing DIC in the modern ocean interior .
Atmospheric CO2 is also potentially sensitive to changes in the POC
flux to deep-sea sediments relative to fluxes of calcium carbonate
(CaCO3) over longer timescales
. The range of potential mechanisms
results in a range of potential feedbacks for the biological pump with
different magnitudes and directions that will respond to a range of different
environmental factors. An additional source of uncertainty in modelling
sensitivity studies is that only global changes in remineralisation depths,
not spatially variable changes, have been considered.
The range of observed Martin curves and associated remineralisation
rate profiles. (a) The mean (b=-0.639) and global range (b=-1.18
to -0.24) of Martin curves found by calculated for
a unit flux and export depth (z0=100m) via Fz=1zz0b. (b) The first derivative of each
flux curve in panel (a), equivalent to a vertical profile of organic
matter remineralisation calculated as
dFzdz=Rz0zz0b-1,
where Rz0=1bz0; see for
a full derivation.
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 e.g.
(Fig. a and b). The global distribution of a biological
nutrient, such as phosphate (PO4), or dissolved inorganic carbon
(DIC), results from the net action of the biological pump (uptake during
photosynthesis at the ocean surface and subsequent remineralisation of
organic matter in the interior) in combination with physical processes (e.g.
air–sea gas exchange in the case of DIC) and other biological processes
(such as denitrification) that are integrated through time via ocean
circulation. In particular, apparent oxygen utilisation (AOU) has a long
history of use as a measure of net organic matter remineralisation in the
ocean interior. When combined with a tracer tracking the age of water masses,
AOU can be converted to apparent oxygen utilisation rates (AOUR) and related
to carbon remineralisation via stoichiometric ratios
e.g.. compiled AOUR-derived profiles
of organic carbon remineralisation rates for 10 regions in the Pacific, noting
higher rates in the North Pacific relative to the South Pacific and
similarities between regions with high rates and higher CaCO3
fluxes. However, the in situ AOUR of a water parcel reflects the history of
remineralisation over its whole trajectory (e.g. along an isopycnal),
producing an average AOUR that is biased towards shallower regions, where
remineralisation rates are higher. Therefore, when relating AOURs back to
flux profiles by integrating them vertically, estimates are representative of
large oceanic regions only – i.e. there is a high degree of spatial smoothing
.
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
e.g..
A recent development of this method, the total matrix intercomparison (TMI)
method described by , solves for up to six mass
fractions for each grid box in a 4∘×4∘
resolution with 33 vertical levels using temperature, salinity,
δ18O, and nutrients with an additional source term reflecting
organic matter remineralisation. The source term is related to the nutrients
using stoichiometric ratios. The TMI method therefore produces
a high-resolution field of remineralisation estimates. However, these terms
do not reflect a rate – i.e. TMI predicts mol PO4 remineralised in
a grid box rather than mol PO4yr-1. This is because the
TMI method reflects the pathways of ocean transport but not the rates of
transport , although have
shown that rates can be estimated when combining the TMI method with
radiocarbon data.
Spatial gradients in tracers have also been used to diagnose export fluxes of
calcium carbonate and opal
from the surface. The method is based on taking the ratio between the
vertical gradients of alkalinity and nitrate in the upper ocean, to reflect
the ratio of CaCO3 : organic carbon exported from the surface
assuming a dominance of vertical transport over horizontal transport
. The ratio is converted to a flux using estimates of
organic carbon export e.g.. However, a model-based
assessment of the method suggests that biases could occur due to the
remineralisation of dissolved organic matter (DOM) and strong meridional
transport that violate the assumption of processes occurring primarily in the
vertical dimension . This highlights an additional potential
issue of using remineralisation rates to infer flux curves that has not been
considered by previous studies.
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.
Estimating remineralisation rates using modelled ocean transport 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
. Remineralisation rates can then be used to estimate the
vertical particulate flux curve. A practical method for this is to apply
a transport matrix approach. A transport matrix, hereafter abbreviated to TM,
is a representation of steady-state transport rates in the form of a sparse
matrix that is derived empirically from an ocean circulation model
. Using a TM is akin to the fixed
transport rates implied in a box model (e.g. “LOSCAR”: )
but with the advantage that the rates are diagnosed from a dynamic ocean
model with a much higher spatial resolution.
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 for an illustrative example). Using the TM in
place of the model circulation, the evolution of a tracer in time is
cn+1=Acn+qn,
where A is the TM (unitless), c is a vector representation
of the gridded three-dimensional tracer field (e.g. mol kg-1) with
the superscript referring to the time-step index, and q is a vector
representation of any non-circulation-related sources and/or sinks for
a tracer during the time step (e.g. mol kg-1), for instance due
to remineralisation. Assuming steady state (where
c=cn+1=cn), the simplest approach to estimating
remineralisation rates using Eq. () is to solve for q
directly, given a TM and a steady-state tracer:
q=-(A-I)c,
where I is the identity matrix (see Table for
the differences between A and A-I). Applying
Eq. () with an observed tracer field is the same as
initialising an ocean circulation model with observed tracer concentrations
and then stepping the model forward for one time step. q will
therefore reflect the exact interior source/sink terms needed in one time
step to maintain the steady-state tracer concentrations given the model
transport rates. We refer to q as the interior source/sink (ISS)
although it is not necessarily representing a mechanistic process. q
reflects the amount of remineralisation predicted over the time step which we
convert to an amount per year by multiplying by the number of time steps
within a year.
Example of using a transport matrix to calculate PO4
remineralisation (µmolkg-1yr-1) in one grid box from
PO4 concentrations (µmolkg-1) given in c. Grid
boxes, taken from a row of the TM, are arbitrarily numbered, where 1 is the
central grid box where the calculation is taking place. The example shows a
simplified situation where there are six neighbouring grid boxes with their
relation to the central grid box given by the directions in brackets. Each
coefficient in the six boxes represents the flux of PO4 into the
central box from that grid box. The coefficient in the central grid box for
A (see Eq. ) represents the amount of tracer left in
the central grid box after one time step, whilst the coefficient for
A-I (see Eq. ) is the flux out, equal to
0.9816–1. The sum of coefficients is shown underneath, with the estimated
remineralisation (q in Eq. ) in bold calculated as the
sum of the element-wise multiplications of A-I and
c.
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 . The
gradient of the function can be related to the flux profile exponent by
adding 1 (Fig. ).
Example of using a GCM transport matrix to estimate PO4
remineralisation rates. (a) The estimated PO4
remineralisation rates generated using the MITgcm transport matrix at 170
and (b) 2030 m. (c) Power-law flux curve exponents
(b) inferred from the estimated remineralisation rates by fitting a
linear function to the log-transformed data as in Fig. b.
Example using a general circulation model transport matrix
As an example of the approach, we use the annual average TM derived from
a 2.8∘ configuration of the MITgcm model (available online:
http://www.ldeo.columbia.edu/~spk/) to invert a field of regridded
annual climatological [PO4] observations (World Ocean Atlas 2009:
), using Eq. () (Fig. ). The
resulting ISS estimates at shallower depths of the ocean interior
(170 m) show some spatial patterns that are consistent with
expectations of general export patterns, such as higher rates in the
equatorial upwelling regions, and the subpolar regions of the Southern Ocean
(Fig. a). However, negative ISSs also exist,
indicating a sink of PO4, such as in regions of the subpolar Southern
Ocean and North Atlantic. At deeper depths (2030 m) the elevated
values in the Southern Ocean match the shallower pattern, but overall there
are fewer clear spatial features and a more random pattern of positive and
negative ISSs (Fig. b). The existence of so many negative values
gives rise to near-zero values when averaging over large spatial scales.
Linear functions were fitted to the log-transformed water column profiles of
estimated remineralisation rates to infer particulate flux curve exponents
(Fig. c). The reference depth (depth at which organic matter is
exported from the surface) is taken as the edge of the second shallowest
grid box (120 m). The significance of this choice is discussed later in
Sect. . Functions were only fitted where water columns
containing >3 grid boxes with positive rates. The global mean value for b
is -0.77 ± 1.76(±1 SD), close to the value found by
, the mean (b=-0.7) found in a reanalysis of globally
distributed sediment trap data and the global mean value
(b=-0.639) found by . The value is, however, smaller than
values around -1.0 found when optimising ocean biogeochemical models
. However, there is a wide range of values for b,
including positive values, indicating an increasing flux with depth. There is
also no clear pattern in the flux curves (Fig. ). The negative
ISSs and positive values for b suggest that the simple inversion of
[PO4] observations using this approach is susceptible to large errors
that warrant further analysis to characterise and quantify potential
uncertainties with this method when used with any modelled circulation.
Uncertainty analysisModel description
To explore the errors when using modelled transport rates, we first derive
a synthetic data set using the Earth system model “GENIE”
. GENIE features a 3-D ocean circulation model
coupled to a 2-D energy-moisture balance model of the atmosphere and
a dynamic–thermodynamic sea-ice model . In the
configuration used here, the ocean model is non-seasonally forced and solved
on a simplified 36×36 equal-area horizontal grid (10∘
longitude by 3–15∘ latitude) with eight vertical layers. The
biogeochemical model is that described in .
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 ensemble members are therefore different
realisations of the modern ocean circulation (see Supplement). The
availability of this ensemble enables us to explore errors associated with
uncertainty in model circulation states. The non-seasonal circulation,
coarse resolution and integration speed of GENIE also facilitate the relatively easy
and fast retrieval of TMs. This is the first time that transport matrices
have been constructed from an Earth system model. The relative simplicity of
GENIE also keeps a focus on the methodological concept. It is worth noting
that much of this could also be achieved by “coarse-graining” a TM derived
from a higher resolution model, described in , but
without the availability of alternative circulation states.
Diagnosing transport matrices in GENIE
The method of is adapted to diagnose a steady-state
ocean circulation simulation in GENIE (see Supplement). The nth
ocean grid box in GENIE is dyed with 1 molkg-1 of an inert
“colour” tracer. After the model is integrated for one time step, the
resulting pattern of tracer is recovered, vectorised, and forms the
nth column of a 6210×6210 sparse matrix. This is repeated
for all 6210 ocean grid boxes in GENIE. Our method of diagnosing the
TM in GENIE differs from that detailed by in two ways.
First, we do not use smoother basis vectors and instead use the simpler
method of dyeing a single grid box. Secondly, each grid box is initialised
only once and there is no averaging because the circulation in the
eight-level version of GENIE is non-seasonally forced. The circulation can
therefore be diagnosed during a single continuous simulation. The length of
the time step at which the TM is diagnosed in GENIE is 0.01 year. The
TM diagnosed here includes the effects of virtual salinity fluxes applied in
the ocean model to account for changes in volume
. To account for this, all tracer
concentrations multiplied by the TM are first normalised by the corresponding
salinity field and then converted back to concentration units afterwards
.
Synthetic data sets
We use the biogeochemical model described in with
the biogeochemical parameter values described in
to produce a synthetic data set of tracers. In
this, nutrients in the surface grid boxes are utilised by biological activity
limited by [PO4] according to a Michaelis–Menten-type limitation (a
maximum rate of 1.96 µmol kg-1 year-1 and half-saturation constant of 0.22 µmol kg-1) and the ambient light
levels (a linear limitation term). A fixed fraction of the uptake
(66 %) is immediately transformed to DOM which can be transported by
circulation and remineralised with a time constant of 1/0.5year. The remaining fraction is exported (34 %) as
particulate organic matter (POM), which remineralises instantaneously at depth
according to the Martin curve with a global b value of -0.858. The use of
a Martin curve keeps the discussion relevant to its use with sediment trap
data and is the only difference between our model setup and that of
. POM remaining in the
deepest grid box is completely remineralised to maintain a closed system –
i.e. there are no interactions with a (hypothetical) sediment.
[PO4] is used as the tracer for inversion by the TM. An alternative
tracer for this could be AOU (related to PO4 via stoichiometric
ratios), as this tracks only organic matter remineralisation (regenerated
PO4), whilst total phosphate also includes phosphate that has been
advected from the surface (preformed PO4). However, AOU is subject to
assumptions about oxygen saturation and may also
reflect non-biological processes . To focus on
errors deriving only from the method of inverting tracers, we choose to use
[PO4] over AOU. We compare our TM-derived estimates of PO4
remineralisation with the actual model remineralisation of PO4 in each
grid box as diagnosed within the experiment run as mol PO4kg-1year-1. The
[PO4] field is the annual average taken from the last year of
a 10 000-year spin-up. A corresponding TM is diagnosed at the end of
the 10 000-year run. This synthetic data set is referred to as SYN. A second synthetic data set (SYN-NODOM) is also
produced in the same way as the SYN data set except no DOM is produced to
explore the effect of DOM when inferring flux curves from remineralisation
rates.
Experiments
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
[PO4] field as a proof of concept of the method (a twin test), i.e. to test that the modelled remineralisation rates can be recovered by
applying the TM to the modelled [PO4] field.
(ERR-OBS) The effect of errors from the tracer observations themselves is simulated by calculating 100 random perturbations to the synthetic PO4
concentrations (SYN) within one SE. For each grid box, the mean is taken as the synthetic PO4 concentration (SYN), and one SE from the SE of World Ocean
Atlas (WOA) [PO4] observations regridded to the GENIE grid ().
(ERR-CIRC) To explore the effect of circulation uncertainty, we diagnose 54 individual TMs from an existing perturbed physics ensemble .
The ensemble is the result of tuning circulation parameters to fit modern temperature and salinity fields using an ensemble Kalman filter. Each ensemble member
is spun up for 10 000 years, after which the TM is diagnosed and used to invert the synthetic [PO4] field (SYN). The circulation parameters in
are an average of the ensemble parameters, such that the 54 TMs offer a range of different ocean circulation states.
Details of the ensemble parameters and comparisons against the standard configuration can be found in the Supplement.
(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 PO4 is exported as particulate organic matter.
The synthetic tracer data set used for transport matrix inversions.
(a) [PO4] (µmolkg-1) at 290 and (b)
2106 m. (c) The total annual remineralisation flux of
PO4 (nmol kg-1yr-1) at 290 and (d)
2106 m. (e) The water-column-integrated inventory of
phosphorus in dissolved organic matter in the ocean interior (mol P).
(f) A measure of the convection occurring in a water column in one
model year (unitless). Higher values indicate the number of vertical levels
involved in convection in the model, i.e. stronger convection.
Results from inverting the synthetic data set with its corresponding
transport matrix. (a) The interior source/sink estimate for
PO4 when inverting the synthetic [PO4] field with the
corresponding transport matrix vs. the synthetic PO4 remineralisation
with a 1:1 ratio line. (b) The distribution of errors for the
PO4 interior source/sink estimates (50 bins sized 0.15×10-5). (c) The interior source/sink estimate for PO4 at
290 and (d) 2106 m. (e) Difference between inverse
interior source/sink estimates and the synthetic remineralisation field at
290 and (f) 2106 m.
Uncertainty analysis resultsAssessment of the transport matrix inversion method
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 a and b show the [PO4]
field in GENIE at two depths, directly below the surface (290 m) and
in the deep ocean (2106 m), with the corresponding annual average
input of PO4 from the continual remineralisation of sinking particles
and dissolved organic matter at the same depths (Fig. c and
d). The higher remineralisation values calculated for single grid boxes occur
where the remaining particulate flux is remineralised at the seafloor to
maintain a closed system, i.e. to ensure there are no losses to sediments
(Fig. d). We also show the inventory of phosphorus in DOM
integrated over the ocean interior below 175 m
(Fig. e). DOM has a visually similar pattern to shallow
PO4 remineralisation, because they are both linked by export
production. The close resemblance and magnitude of the DOM at shallow depths
may have implications for using remineralisation rates to infer
remineralisation fluxes; these will be discussed in
Sect. . Finally, we note a correspondence between
areas in the Southern Ocean with a large magnitude of remineralisation at
shallow depths and locations where convection occurs in the model
(Fig. f). This is consistent with high productivity driven
by nutrients delivered to the surface via strong vertical mixing.
To demonstrate and test the method described in Sect. , we
first invert the model-generated synthetic [PO4] field using the
corresponding TM as per Eq. () (Fig. a). The
interior source/sink term (ISS) calculated by inverting the synthetic
[PO4] field is consistent with the model-calculated remineralisation
with minor deviations from the 1:1 ratio line (Fig. a).
This demonstrates the success of the approach as the errors in the synthetic
tracer field and circulation scheme are effectively reduced to near zero in
this example. The errors between estimated and modelled remineralisation
rates cluster around zero with a median proportion of error of 6.3×10-5 (Fig. b). Minor errors likely represent small
differences in the circulation at individual time steps that have been
sampled by our method of sequentially dyeing grid boxes during a single run.
Overall, however, the TM inversion of the synthetic [PO4] estimates the
PO4 remineralisation rates very well (compare Fig. c and d
with Fig. c and d) with minor errors. This demonstrates
that, in theory at least, modelled circulation rates in the form of
a transport matrix can be used to successfully estimate remineralisation
rates from a tracer field.
Sensitivity of inversions to sources of errors
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
[PO4] observations. (a) The SE of [PO4] from the
World Ocean Atlas 2009 () 1∘ climatology
regridded to the GENIE grid at 290 and (b) 2106 m.
(c) SD of all PO4 interior source/sink estimates when the
synthetic [PO4] field is randomly perturbed within a normal
distribution given by the SE of observations. The colour scale indicates the
size of the “flux-out” term, where a larger value indicates relatively
larger circulation fluxes in that grid box. (d) The SD of
[PO4] ISSs at 290 m.
Assessment of error arising from using circulation estimates.
(a) Comparison of ISS estimates for each grid box from the 54
ensemble members against the synthetic data set remineralisation. Error bars
are 1 SD around the mean. Red values indicate regions with convection.
(b) As panel (a) but with the red values removed. Note the
difference in scale. (c) The SD of PO4 ISS errors (ISS –
model) in µmolkg-1yr-1 for 290 m. Values are
shown on a log scale. (d) As panel (c) but at
2106 m.
Error from observations
Error related to the 1∘ World Ocean Atlas annual mean
climatology will introduce some uncertainty in the TM
inversion due to measurement errors and biases in the climatology itself. As
a measure of how sensitive the TM inversion method is to these errors, we
regrid the SE of annual [PO4] observations onto the GENIE grid
(Fig. ). We do not consider any additional uncertainty here
that may arise through the re-gridding process e.g..
The SEs in each grid box are used to produce an illustrative estimate of the
uncertainty inherent in the observations. The SEs are highest in the coastal
regions and high latitudes, and at shallower depths
(compare Fig. a and b). We note that errors in the observations may
be spatially correlated, which will warrant consideration in future work.
The SEs are used to produce 100 versions of the synthetic [PO4] field
that have been perturbed within the observation uncertainty which are then
inverted using the TM. The resulting variability in the PO4 ISSs, as
characterised by the SD, is relatively large compared to the ISS values
themselves, around 1–3 orders of magnitude larger than the ISS values (see
also Fig. ). There are positive linear trends between the
SD of the 100 perturbed observations in each grid box and the SD of the 100
corresponding ISS estimates in each grid box (Fig. c). Having grid
boxes with higher uncertainty in the observation results in greater uncertainty in the ISS estimates. However, two clusters
can be broadly defined in Fig. c, both with separate linear
trends that correspond well with the size of the “flux-out” term of the TM
(i.e. the flux of tracer associated only with ocean transport; see
Table ). The colour scale gives an indication of the
relative size of the flux out for each grid box due to circulation. Where the
central grid-box coefficient is larger, the uncertainty in ISS arising from
the uncertainty in the observations is much more sensitive. This suggests
that the ISS uncertainty is partly a function of the circulation diagnosed in
the TM – i.e. if the observation uncertainty were fixed to a constant across
all grid boxes, ISSs in some grid boxes will have greater uncertainty than
others due to this effect. The flux-out term is largest in areas in our TM
where convection occurs, i.e. the Southern Ocean and North Atlantic
(Fig. f), because this is where the largest transport
fluxes are in the model (Fig. d).
Error from circulation estimates
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 a shows the mean and 1 SD of the ISS
estimates generated when inverting the synthetic [PO4] field with all
54 ensemble TMs. The values furthest from the 1:1 ratio line and those with
the largest error bars are located in regions where convection occurs in the
model (Fig. a and c). The strength of overturning varies
within the ensemble (see Supplement), suggesting that this structural
uncertainty in the model is a likely cause for the wide range of
remineralisation estimates. An additional issue is that, unlike most
grid boxes in our TM, where the spread of a tracer over one time step is
limited to neighbouring grid boxes, convection increases the number of
grid-box connections in the vertical. This could have the effect of
increasing the range of remineralisation estimates because there are more
grid boxes. Figure b shows the same as
Fig. a but with the convection-related values removed. Even
in areas where there is no convection in the model, the range of ISS
estimates from circulation uncertainty is larger relative to the range of
remineralisation values. The range of errors arising from using different
circulations are also larger at shallower depths compared to deeper depths in
the water column (Fig. c and d).
To understand why different circulation estimates can have a large impact on
ISSs, we explore the size of the PO4 remineralisation flux in
a grid box relative to the size of PO4 flux from the modelled
circulation. To illustrate this, we compare the steady-state circulation flux
of PO4 into a grid box with the remineralisation flux of PO4
into each grid box from the synthetic run (the sum of these at steady state
will equal the flux of PO4 out of the box). Across the whole model
ocean interior, the mean proportion of remineralisation flux to the total
flux into each grid box is 0.005±0.025 (±1 SD). The proportion is
generally 2 orders of magnitude higher at shallower depths (290 m)
than at depth (2106 m) (compare Fig. a and b), reflecting
the decrease in remineralisation fluxes with depth, whilst circulation fluxes
vary much less in magnitude in GENIE (Fig. c and d). Even
relatively small errors in the circulation fluxes are therefore likely to
dominate over the remineralisation fluxes, leading to large errors when using
modelled circulation rates.
Comparison of inputs of PO4 from remineralisation and
circulation at steady state. (a)PO4 remineralisation as
a proportion of the total PO4 flux into each grid box calculated
using the synthetic tracer field at 290 m and (b)
2106 m. (c) The flux of PO4 into each grid box from
circulation only (µmolkg-1yr-1) from the synthetic tracer
fields at 290 and (d) 2106 m.
Comparison of error magnitudes when estimating remineralisation
rates. The global mean PO4 remineralisation profile from the
synthetic data set is shown with the plus and minus the mean and median SDs
from the ERR-OBS and ERR-CIRC experiments.
Error comparison
To compare the magnitude of the various possible errors, we show the global
mean synthetic PO4 remineralisation profile with the global mean and
median SDs of the ISSs calculated for each of the ERR-OBS and ERR-CIRC
experiments – i.e. a SD is calculated for the experiments in each grid box,
which are then averaged (Fig. ). We use both the mean and
median SD in this figure because the mean SDs of the ERR-CIRC experiments are
skewed by the large variability in high-latitude regions
(Fig. a; see also Supplement). Both sources of error are
larger at shallower depth and mostly decrease in magnitude with depth
although the mean circulation uncertainty increases below 2000 m. The
magnitude of median uncertainty from the observations is much larger than
from our circulation estimates although the two are similar magnitudes when
the mean SD is used.
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. a and b, and in regions of the model where convection
occurs (Fig. c). In contrast, the uncertainty arising from
the model circulation field used will be systematic and dependent on where
the model circulation is most different to the real ocean, e.g.
Fig. . Although the patterns in the surface PO4 ISSs
from the MITgcm inversion are systematic (patches of positive and negative
ISSs in the Southern Ocean: Fig. a), it is difficult to tell
whether this reflects a systematic difference between observed and simulated
circulation rates or a caveat associated with convection in the model and
larger circulation fluxes in these areas. The relative smoothness of the ISS
estimates may reflect the use of the climatology which has already been
smoothed .
Discussion
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. ). In the
following sections we discuss potential directions for estimating
remineralisation rates from tracer data using model circulation and
additional considerations needed when using these to infer particle flux
curves.
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 . Therefore, the
ISS estimates are sensitive to the resulting large coefficient in the central
grid box (see Table ). This will be a feature of all TMs
constructed using the method of regardless of the
resolution or model used. Our results also illustrate the sensitivity of
remineralisation estimates to differences between the model transport rates
and actual transport rates in the ocean. Remineralisation fluxes of
PO4 in the synthetic tracer experiments are orders of magnitude
smaller than fluxes of PO4 from circulation. Model transport rates
would therefore need to attain a high level of accuracy to minimise the
effect of error on the solutions .
Even a data assimilated model, such as that produced by the ECCO
(“Estimating the Circulation and Climate of the Ocean”;
) consortium, designed to be a dynamically consistent estimate of
ocean circulation over recent decades may still lead to large diagnosed flux
errors. An additional consideration may also be the representation of a
steady state in the TM, either because a model is not spun up fully or
because there is seasonality.
Inversion of salinity as a possible constraint on the uncertainty
from using a modelled circulation. (a) Inversion of the salinity
field from the synthetic data set using the corresponding transport matrix at
290 m (PSU yr-1) and at (b) 2106 m.
(c) Inversion of the salinity field using a alternative transport
matrix from the perturbed-physics ensemble (PSU yr-1) at 290 and
(d) 2106 m. (e) The error of the synthetic
PO4 ISS (µmolkg-1yr-1) (ISS – synthetic) using the
same transport matrix in panels (c, d) at 290 and (f)
2106 m.
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 (a)
a model with remineralisation from only sinking particulate and (b)
a model with particulate and dissolved organic matter. A value of -0.858
for the Martin curve was used in both models. All curves were fitted with an
R2>0.9. The exponent for the remineralisation curve is equivalent to
-0.858-1. More negative values indicate a Martin curve that predicts
shallower remineralisation in the water column. Hatched areas indicate where
the water column contained too few boxes to fit a remineralisation curve
(n<3).
Are there constraints on the circulation uncertainty?
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. a and b). Salinity ISSs are
randomly distributed around zero, consistent with the concept that there are
no significant local sources or sinks in the ocean interior. In comparison,
applying a different transport matrix, arbitrarily chosen from the ensemble
of alternative modern circulations, results in distinct spatial patterns in
the ISSs (Fig. c and d). Comparing the errors from the
inversion of the synthetic [PO4] field using the same TM shows that
the two have some visible similarities (Fig. e and f).
For example, there are correspondences in the deep South Atlantic
(Fig. d and e) and the subtropical regions of the
Pacific at 290 m (Fig. c and e). We do not expect an
exact correspondence, but the visual similarities support the idea that they
are related via errors in the model circulation. This suggests that
conservative tracers, i.e. tracers that do not have sources or sinks in the
ocean interior, could provide a constraint on the magnitude of error. For
example, considering Eq. () but focussing on an individual
grid box, the ISS (qi=1) is a function of the TM coefficients
(Mi) and the tracer concentrations (Ci) as per the example in
Table :
qi=1=∑i=1NMiCi.
Redefining the modelled circulation terms to reflect that the modelled
circulation is a function of a “true” circulation term and an error term
(Mi=Fi+ϵi) and substituting into
Eq. () and expanding,
qi=1=∑i=1NFiCi+∑i=1NϵiCi.
For a conservative tracer at steady state, it is expected that
∑i=1NFiCi=0. A significant departure from zero in
qi=1 is likely to result from the error terms. This may provide
a way forward to constrain the ISSs produced by the TM method described here.
Such a method would be conceptually similar to the TMI method
. There are, however, a limited number of tracers
available (e.g. temperature, salinity, δ18O, Δ14C, CFCs)
that could realistically be used to constrain model circulation errors. Of
these tracers, CFCs are not yet present in the deep ocean and thus are not in
steady state. In our TM, there are typically 15 grid-box connections (6
neighbouring grid boxes plus extra connections due to the Gent–McWilliams
parameterisation) used for each calculation which would lead to an
underdetermined solution, i.e. where the unknowns outnumber the constraints.
It would be interesting to see whether a simplified TM with fewer coefficients,
such as matching the method of by adopting a
seven-point stencil (six neighbouring grid boxes), could use this approach. Even
so, with a seven-point stencil, the solution may still be underdetermined.
Inferring flux curves from remineralisation rates
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 gradient of the linear trend gives the value of the exponent for the
remineralisation curve, which is converted to a flux curve by adding 1
(; see also Fig. ).
The exponents from power-law curves, fitted to vertical PO4
remineralisation profiles, when PO4 is only exported as particulate
organic matter, are all close to -1.9 (Fig. a). This
corresponds to a flux curve exponent of -0.9, in good correspondence with
the -0.858 used for the run. The presence of remineralisation from DOM (see
Fig. e) lowers the value of the fitted exponent reflecting
a shallower Martin curve (Fig. b). In our experiments, the
remineralisation of DOM lowers the fitted exponent by as much as 0.6. This
occurs because the remineralisation of DOM inflates the remineralisation rate
in the shallower grid boxes relative to those in the water column below. In a
few grid boxes in the North Atlantic the estimate of the flux curve exponent
increases. This has a strong correspondence with the deepest convection
(Fig. f) where DOM is transported deeper into the water
column before being remineralised. This highlights that an additional source
of remineralisation not restricted to vertical processes, such as the
remineralisation of DOM, can alter the flux curve in an unpredictable way.
The DOM bias in GENIE occurs predominantly in the high latitudes, where DOM is
efficiently advected into the ocean interior. The range of exponents purely
from this bias is of a similar magnitude and spatial distribution to the
Martin curve exponents found in .
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 b can be sensitive
to the estimate of the export depth (z0 in Fig. )
. Both and
consider that the export depth of particles may be deeper
than the euphotic zone when particles are physically mixed deeper in the
water column, as measured by the mixed layer depth (MLD). The model grids
used here impose a fixed export depth on flux curve estimates which could be
shallower than expected in the real ocean, such as in the high latitudes,
where MLDs are deeper. For example, if the uppermost grid box is considered
as the export depth when fitting Martin curves to the MITgcm example in
Sect. , rather than the two uppermost grid boxes
(Fig. c), the global mean Martin curve exponent is -0.90,
equivalent to shallower remineralisation. Developments in understanding the
uncertainty in fitting Martin curves to data are therefore equally important
to consider when fitting to estimated remineralisation rates
.
The way forward
Any method of inferring particulate organic matter flux curves from estimated
remineralisation rates, whether using model transport rates or using
observations e.g., will therefore need to take the
remineralisation of DOM (as well as other processes not constrained to the
vertical water column such as denitrification) into account, particularly in
regions where DOM is advected to deeper depths .
Ultimately, this additional source of uncertainty when inferring flux curves
combined with the uncertainties associated with estimating remineralisation
rates suggests this is a difficult task. An alternative approach that
explicitly includes the effects of DOM remineralisation is the optimisation
of ocean biogeochemical models. In this approach, a biogeochemical model is
set up and optimal values of the parameters found, such as the depth of
remineralisation, export production and the rate of DOM remineralisation,
that result in the best fit between modelled and observed nutrient fields
e.g..
For example, remineralisation depths could be varied in space and a solution
found that best fits tracer observations. A first step towards this has been
taken by . Such an approach allows additional
constraints such as export production magnitude to be taken into account as
well as providing further evaluation on circulation models via biogeochemical
tracers . Transport matrices are a useful tool in this
approach to help reduce lengthy multiple-thousand-year integration times for
model fields to reach equilibrium as well as providing alternative methods to
efficiently reach steady-state solutions . Ultimately,
the approach of optimising biogeochemical models is complimentary to the
approach described in this paper as they both rely on the combination between
observations and models but in different ways, which could help facilitate a
better understanding of biogeochemistry as well as of the models used to
study it.
Conclusions
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
[PO4], to estimate steady-state remineralisation rates, is subject to
potentially large uncertainties related to both uncertainties in the
observations and the modelled transport rates. There are potential methods to
constrain the uncertainty in the modelled transport rates, but these are
currently limited by the number of tracers available. We also highlight that
there significant uncertainties when integrating remineralisation rates
vertically, a step necessary to estimate particle flux curves, associated
with processes such as the remineralisation of dissolved organic matter. This
last uncertainty has implications for deriving flux curves from data-based
estimates of remineralisation rates as well as model-based ones.
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.
The Supplement related to this article is available online at doi:10.5194/bg-12-5547-2015-supplement.
Acknowledgements
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
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