Anthropogenic emissions of greenhouse gases such as CO2
and N2O impinge on the Earth system, which in turn modulates
atmospheric greenhouse gas concentrations. The underlying feedback mechanisms
are complex and, at times, counterintuitive. So-called Earth system models
have recently matured to standard tools tailored to assess these feedback
mechanisms in a warming world. Applications for these models range from being
targeted at basic process understanding to the assessment of geo-engineering
options. A problem endemic to all these applications is the need to estimate
poorly known model parameters, specifically for the biogeochemical component,
based on observational data (e.g., nutrient fields). In the present study, we
illustrate with an Earth
system model that through such an approach biases and other model deficiencies in the physical ocean circulation model component can
reciprocally compensate for biases in the pelagic biogeochemical model
component (and vice versa). We present two model configurations that share a
remarkably similar steady state (based on ad hoc measures) when driven by
historical boundary conditions, even though they feature substantially
different configurations (parameter sets) of ocean mixing and biogeochemical
cycling. When projected into the future the similarity between the model
responses breaks. Metrics such as changes in total oceanic carbon content and
suboxic volume diverge between the model configurations as the Earth warms.
Our results reiterate that advancing the understanding of oceanic mixing
processes will reduce the uncertainty of future projections of oceanic
biogeochemical cycles. Related to the latter, we suggest that an advanced
understanding of oceanic biogeochemical cycles can be used for advancements
in ocean circulation modules.
Introduction
Challenges associated with climate change have triggered a discussion of
geo-engineering to combat negative effects of anthropogenic greenhouse gas
emissions on our planet. Among these options are ideas to purposely change
pelagic biogeochemical cycles in order to increase oceanic carbon
sequestration from the atmosphere e.g.,.
Currently, the effectiveness and potential side effects of such measures are
quantified with numerical Earth system models e.g., – tools known to be associated with substantial
uncertainty e.g.,. One source of
uncertainty in these models is related to unknowns in the mathematical representation
(typically a set of partial differential equations) of both the physical and
biogeochemical processes impacting the pelagic ocean.
As for the biogeochemical processes, considerable uncertainty is associated
with poorly known model parameters e.g.,,
such as growth rates or limitation thresholds, included in the
partial differential equations that underly the model. In an attempt to
reduce this uncertainty, several studies set out to estimate these parameters
by minimizing a cost function that measures the misfit between model
and observational data, such as climatological nutrient or phytoplankton
concentrations e.g.,. For typical model–data combinations (as
opposed to idealized special cases) it unfortunately turned out to be
impossible to determine an optimal parameter set . Among the suggested reasons for such failures are excessive
computational expenses along with sparse and noisy observational data
e.g.,. In addition, or as a consequence, the discussion of the problem entails suggestions that the optimization
problem is underdetermined and that the underlying
equations do not represent actual processes and conditions . In this study, we illustrate how deficiencies in the physical
model component impact the estimation of the biogeochemical parameters
e.g.,.
Typically, general ocean circulation models, designed to simulate the ocean's
physics such as the transport and mixing of water parcels (and therein
dissolved or dispersed substances of biogeochemical relevance), contain
various sources of uncertainties. Such uncertainties result, e.g., from
discretization issues or unresolved processes at the atmosphere–ocean
interface (that supply the energy for ocean currents and turbulence). In the
context of pelagic biogeochemical cycles, major uncertainty is associated
with energy dissipation and related diapycnal mixing. The reason is that
diapycnal (mixing) transport of nutrients to the sunlit surface ocean fuels
autotrophic growth of phytoplankton, and it thus counteracts the associated
vertical (sinking) export of organic carbon to depth, away from the
atmosphere. As such, diapycnal mixing is key to what is also referred to as
the biological carbon pump. However, even though diapycnal mixing is
also key in determining various physical properties, such as the simulated
thermocline depth e.g., and the simulated global
meridional overturning circulation e.g.,, it is not yet
well quantified by observations: large-scale tracer release experiments in
the thermocline of the oligotrophic subtropical North Atlantic suggest
diffusivities between 0.1 and 0.5 cm2 s-1, while
measurements that apply the Osborn–Cox relation between dissipation and
diffusion exceed these values locally over rough topography by an order of
magnitude.
It is somewhat disconcerting that effective diapycnal mixing is not even quantifiable
in ocean general circulation models, as the actual mixing results from a
combination of explicitly prescribed mixing rates and spurious mixing
associated with numerical advection and isopycnal diffusion algorithms
. Attempts to diagnose net effective mixing in
ocean general circulation models are a work in progress and, as suggested by ,
an increasing number of measurements of the saturation state of noble gases
in the world ocean may eventually provide guidance on the question of the realism of
simulated diapycnal mixing. For now, however, the values for diapycnal
(vertical) diffusivity, which are to be set explicitly in Earth system models,
are poorly known. Typical choices range roughly between 0.1 and 0.5 cm2 s-1.
Yet, changes from one value to another have been shown to profoundly change
simulated dynamics of biogeochemical processes, both for historical
atmospheric CO2 concentrations and for projections into a warming future
.
In general diapycnal mixing of a specific ocean model has a strong impact on
the respective biogeochemical component and its parameter settings because
the interplay between the biological pump and mixing is delicate. The latter
particularly holds as the development of Earth system models consists of
several modules. These are generally successively coupled together.
Generally, a pelagic biogeochemical module is added to an already coupled
ocean–atmosphere kernel. Thus, pelagic biogeochemistry modules are often
developed based on the presumption of a fixed
physical model component. This approach is equivalent to assuming that any
model–data misfit of biogeochemical cycles is attributable to a deficient
biogeochemical model formulation (i.e., an inapt set of partial differential
equations), an inapt choice of biogeochemical model parameters (such as
growth rates or limitation thresholds), or both while the biogeochemical
model is tuned. Here, tuning refers to tweaking equations and parameters
until “reasonable” agreement with climatological observations (such as
nutrients and surface chlorophyll a) is achieved e.g.,and many
more to follow.
To summarize: on the one hand, it is well known that the choice of diapycnal
diffusivity profoundly affects model solutions and that the prescribed value
of diapycnal diffusivity is highly uncertain. On the other hand, it is common
practice to tune biogeochemical modules to a fixed physical model component
(which is difficult to evaluate in terms of ocean mixing). We conclude that
this practice entails the danger of what we coin reciprocal bias compensation, whereby flaws of one model component (ocean mixing) are
compensated for by tuning–tweaking another model component (biogeochemical
cycling). The final result might be two flawed model components.
This study sets out to illustrate the consequences of reciprocal bias
compensation by replicating the typical workflow of Earth system model
development with twin experiments based on the University of Victoria
Earth System Climate Model UVic: we define the model
configuration described by as the Genuine Truth.
Further, we define a twin that has a biased physical ocean component relative
to the Genuine Truth in that the vertical diffusion is increased severalfold
(configuration MIX+). Finally, we optimize the biogeochemical parameters of
the biased twin such that it resembles the Genuine Truth as closely as
possible (configuration TUNE). Such an approach gives us full control over
the abundance of data (model output) in space and time and the underlying
equations (which is not the case for real-world observations). In a nutshell,
our study discusses three model configurations applied to both historical
CO2 concentrations and anticipated future CO2 emissions (RCP8.5
scenario). The model setups comprise a Genuine Truth, a biased version of the
Genuine Truth, and a reciprocally bias-compensated version of the latter
(see Table 2).
We describe the design of the numerical experiments in detail in the
following section. Section 3 compares model results under preindustrial and
anticipated future conditions. Section 4 discusses the results, and Sect. 5
closes with a summary and conclusions.
Methods
This study is based on a suite of numerical experiments performed with the
UVic 2.9 Earth System Climate Model, a model of intermediate complexity with
relatively low computational cost. The model has recently been applied to
explore geo-engineering options in a number of studies
e.g.,. In Sect. and we present the three
configurations of the model used in this study. Two configurations are very
similar and one configuration is identical to the configuration that has been
comprehensively documented and assessed in the model description paper by
.
Earth system model
Common to all of our three UVic configurations is a horizontal resolution of
1.8∘ in latitude and 3.6∘ in longitude in all submodules
land with active terrestrial vegetation component, ocean, atmosphere,
dynamic–thermodynamic sea ice, simple land ice;. The
atmospheric component comprises a single-level atmospheric energy–moisture
balance model. Surface winds are prescribed from the NCAR/NCEP monthly
climatology. The prescribed winds are used to calculate the momentum transfer
to the ocean, the momentum transfer to a dynamic–thermodynamic sea ice model,
the surface heat and water fluxes, and the advection of water vapor in the
atmosphere.
The ocean submodule is based on a three-dimensional primitive-equation model
. The vertical discretization of the ocean comprises 19
levels. The vertical resolution increases gradually from 50 m at the
surface to 500 m at depth. The vertical background mixing parameter,
κh, is constant (0.15 cm2 s-1 in the reference version – Genuine Truth) – apart from the Southern Ocean (south of 40∘ S) where the
background value is increased by 1.0 cm2 s-1. An anisotropic
viscosity scheme from is implemented, as in
, to improve the equatorial circulation. Further, the ocean
component of UVic applies convective adjustment and uses a tidal mixing
parameterization according to .
A marine pelagic biogeochemical model is coupled to the ocean circulation
component. Its prognostic variables are phytoplankton (Po), diazotrophic
phytoplankton (PD), zooplankton (Z), detritus (D), nitrate (NO3),
phosphate (PO4), dissolved oxygen (O2), dissolved inorganic carbon
(DIC), and alkalinity (ALK). The original configuration of
has been tuned to match the annual mean nutrient fields provided by the
World Ocean Atlas .
The temporal evolution of each prognostic variable is given by
∂C∂t=DTR+SRC,
where DTR denotes the convergence (or divergence) of physical transports
(sum of advection and isopycnal and diapycnal diffusion), and SRC denotes the
source minus sink terms (such as differences between growth and mortality,
air–sea fluxes, sinking). The biogeochemical module is described in detail in
and . Here, we present a choice of
details relevant to those processes that we change (in the configuration
TUNE, as described in Sect. ). These processes are the sinking
of detritus, the remineralization of detritus, and grazing by zooplankton.
More specifically we apply changes to the following model parameters (see
also Table ): (1) the maximum grazing rate μZ, (2) the sinking speed
of detritus wD0, and (3) the remineralization rate of detritus
μD0. In the following we present the equations in which these model
parameters are applied.
Phytoplankton growth is controlled by the availability of light and nutrients
(here, nitrate, phosphate, and iron; the latter is parameterized by an
iron mask based on monthly mean dissolved iron concentration outputs from
the BLING model rather than explicitly resolved). The
simulated phytoplankton concentrations have a weak impact on sea surface
temperatures as it is assumed that in the presence of phytoplankton more
sunlight is absorption in the upper layer of the ocean model. Phytoplankton
blooms are terminated by zooplankton grazing once essential nutrients are
depleted. Zooplankton grazes on phytoplankton, diazotrophs, detritus, and
other zooplankton (self-predation). Zooplankton growth is limited by a
maximum zooplankton growth rate. This rate, μZmax, is dependent on
temperature (T in units ∘C) and oxygen concentrations (O2 in
units mmol m-3). In our parameter tuning experiment we change the
value of the model parameter μZ in the equation
μZmax=μZmax0,0.5(tan(O2-8)+1)1.066min(20,T).
Both phytoplankton and zooplankton produce detritus that sinks to depth. This
sinking speed, in combination with the remineralization rate, determines
the depth range at which detritus is converted back into dissolved species
(such as nitrate, phosphate, DIC) and stops sinking to the seafloor. The
sinking speed of detritus, wD, increases linearly with depth:
wD=wD0+mWz,
where wD0 denotes the sinking speed at the surface and mW the
derivative with respect to depth, and z is the effective vertical
coordinate (positive downward). In our configuration TUNE we change the value
of the model parameter wD0.
Remineralization of detritus returns the nitrogen (N) and phosphorus (P)
content of detritus back to nitrate (NO3) and phosphate (PO4),
consumes oxygen, and releases inorganic carbon. The rate of remineralization
μD is both temperature dependent (T) and a function of ambient oxygen
concentrations (it decreases by a factor of 5 in suboxic waters):
μD=μD0expTTb(0.65+0.35tanh(O2-6)).Tb is the e-folding temperature of biological rates notation
after, and T and O2 are ambient temperature (∘C)
and oxygen concentration (mmol O2 m-3), respectively. In one of our
configurations we change the remineralization rate μD0, which sets the
rate at 0 ∘C under oxygen-replete conditions.
Numerical experiments
We present results from numerical experiments with three different
configurations of the numerical Earth system model UVic (see Table 2). For
all three different configurations we apply both constant preindustrial
atmospheric CO2 concentrations and increasing atmospheric CO2
emissions over time.
Model parameters explored for the three model
configurations used in this study (see also Table 2). The Genuine Truth
configuration is identical to the one introduced by . MIX+
and TUNE are identical to the Genuine Truth except for the differences in
parameter values listed here.
ParameterDescriptionGenuine TruthMIX+TUNEUnitκhVertical diffusion0.150.40.4cm2 s-1wD0Detritus sinking speed at the surface12.512.540m d-1μD0Remineralization rate at 0∘0.0420.0420.09d-1μZMaximum zooplankton growth rate at 0∘0.40.40.45d-1Model configurations
Table lists the model configurations. The Genuine Truth
configuration is identical to the reference simulation in
and has been developed and introduced by
. Note that this Genuine Truth model version by
was modified (or tuned) such that the misfit to
climatological observations of biogeochemical relevance, such as dissolved
phosphate concentrations and phytoplankton , is reduced
relative to the original biogeochemical module from .
We compare this Genuine Truth to the model configurations with
increased mixing, MIX+ and TUNE.
The first model modification, referred to as MIX+, is identical to the model
version underlying the Genuine Truth, except for an increase in the vertical
background diffusion from κh=0.15 up to 0.4 cm2 s-1 (see
Tables and ). This choice is motivated by , who increased
κh from 0.15 to 0.43 cm2 s-1 (in the same model) in order
to compensate for a collapsed meridional overturning circulation when
switching from one numerical advection scheme to another (to facilitate the
design of an offline model version). Also, the regarded value is well within
the range explored by with the same model.
Configurations of the numerical Earth system model UVic
used in this study.
ConfigurationDescriptionExperimentsGenuine Truthintroduced by , identical to the reference simulation historical (+ transition phase) + RCP8.5 scenarioMIX+identical to the Genuine Truth configuration, except for an increase in background diffusivity κhhistorical (+ transition phase) + RCP8.5 scenarioTUNEidentical to MIX+ except for changes to the biogeochemical parameters wD0, μZ, μD0historical (+ transition phase) + RCP8.5 scenario
TUNE is another twin to the Genuine Truth and identical to MIX+, except for
changes to three biogeochemical model parameters: wD0,
μD0, and μZ (see Table ). The leading
thought behind our changes relative to MIX+ is to mimic the behavior of the
Genuine Truth configuration even though the vertical background diffusion is
substantially different from the Genuine Truth. Or, in other words, changes
to biogeochemical model parameters in TUNE are chosen such that the root mean
square error (and with it the bias) in the simulated three-dimensional
distribution of phosphate and phytoplankton concentrations between the
Genuine Truth and MIX+ is compensated for. The procedure to achieve such a
bias compensation is as follows. (1) We chose the three parameters somewhat
arbitrarily, guessing that they are capable of reciprocally compensating for
the effect of an increased vertical diffusivity. (2) We performed 48 spin-ups
(see Sect. ) with increased diffusivity and differing sets of
values for the aforementioned biogeochemical model parameters. In these runs
wD0 is spaced uniformly from 20 to 45 m d-1,
μD0 from 0.07 to 0.09, and μZ from 0.4 to 0.45 (grid
design; 6×4×2). The idea behind this approach is to counteract the enhanced upwelling of
nutrients by enhanced detritus export. Additionally, μD0 was
increased to keep detritus concentrations on a reasonably low level. Note
that prior to applying this concept to a 3-D model, it was tested in a
simplified water column setup. (3) From this set of 48 we chose the
configuration TUNE, which was “most similar” to the Genuine Truth (see
Table 3). Following the rather generic workflow of biogeochemical model
development we defined “similar to the Genuine Truth” as yielding a low
volume-weighted root mean square error (RMSE) with respect to surface phytoplankton and global (3-D) oceanic
phosphate concentrations (both values were averaged after unit conversion
via a fixed Redfield ratio). This comparison between TUNE and the Genuine
Truth was performed under preindustrial atmospheric CO2
concentrations note that there is an ongoing discussion on misfit
metrics that is beyond the scope of this paper; e.g.,. Please note that the parameter choice for TUNE that yields an
even better bias compensation than the one we present in
Table may well exist and be found by using automated
parameter optimization approaches such as suggested by .
Also, the bias might potentially be lowered when considering more
biogeochemical model parameters. However, given the already remarkable
similarity between TUNE and the Genuine Truth (as will be put forward in
Sect. ), we decided against the associated computational cost for
the rather illustrative purpose of this study.
Spin-up procedure, historical model solution, and projections into the future
All numerical experiments presented in this study start from observed tracer
distributions . Each of the three model configurations
(Genuine Truth, MIX+, and TUNE; Sect. ) is then integrated
under preindustrial atmospheric CO2 concentrations for 3000 years in
order to reach quasi-equilibrated spun-up model states
e.g., for all three configurations. The results (more
specifically, the average of the last 10 years of the respective 3000-year
spin-ups) of these three numerical experiments are dubbed historical
model solutions because they are representative of the preindustrial
world.
Subsequently, starting from the respective spun-up states of the three model
configurations, so-called 1000-year-long drift runs are performed, wherein
only the CO2 emissions (instead of concentrations) are prescribed, while
the atmospheric CO2 content is allowed to vary in response to
preindustrial emissions. After this drift phase virtual air–sea fluxes
of biogeochemical species are also turned on (i.e., changes in DIC due to
evaporation, precipitation, and runoff; ). This procedure
has proven to be efficient in switching from a prescribed atmospheric CO2
setup to an atmospheric emission-driven setup while keeping the spin-up times
within reasonable bounds also used in, e.g.,. Finally, we
annex projections into the future by considering the years 1850–2100. From
2005 to 2100 we apply the emission scenario RCP8.5 . Please
note that differences among the three setups emerge during the transition
phases. This model behavior is a reminder that, on the one hand, the
state at which models are assessed matters, while on the other hand, there is
no consensus on which state should be used for model assessment. In this study
we follow the typical procedure as applied by, e.g., .
In summary, we present six numerical experiments: a historical model solution
and an RCP8.5 scenario for each of the three model configurations – Genuine Truth, MIX+, and TUNE.
Results
In Sect. , we focus on the three historical
model simulations (Genuine Truth, MIX+, and TUNE). This subsection
illustrates reciprocal bias compensation. In Sect. ,
we present the results from the RCP8.5 scenario simulations. The aim of the
latter is to explore the robustness of the reciprocal bias compensation
under a typical global warming scenario.
Historical model solutions
The massive, severalfold increase in background diffusivity introduces
surprisingly few differences in common ad hoc measures of the simulated ocean physics: the differences in sea surface temperature are
very small in Fig. , and the relatively largest differences
occur in the high latitudes, especially close to the ice edge. A similar
picture evolves for sea surface salinity (Fig. 2): generally, differences in
response to increased vertical mixing rates are small (Fig. 2c) with an
exception in the Arctic where surface salinity increases by up to 1 PSU in
response to increased vertical mixing rates. This is consistent with an
increase in the meridional overturning circulation from 19 Sv in the Genuine
Truth to 22 Sv in MIX+, which compensates for some of the net air–sea
freshwater fluxes in the high latitudes (and thus increases sea surface
salinities in these latitudes). Expressed in terms of a global mean
difference, the Genuine Truth and MIX+ historical simulations differ by
0.03 K and 0.13 PSU only. Figure supports the impression of
similarity by showing that differences in the simulated zonally averaged net
air–sea heat fluxes are within the range of measurement uncertainty in the
field e.g.,. High values are restricted to very limited
regions impacted by sea ice or deepwater formation.
Simulated sea surface temperature in degrees Celsius for the historical
simulations (see Sect. ). Panels (a) and (b) refer to
results from the model configurations Genuine Truth and MIX+, respectively.
MIX+ features an increased vertical background diffusivity relative to the
Genuine Truth (see also Table ). Panel (c) shows the difference between MIX+
and the Genuine Truth.
In contrast to the barely detectable changes in
the physical ocean dynamics described
above, conventional proxies for biogeochemical cycling turn out to be very
sensitive to the change in vertical background diffusivity. The surface
phosphate concentrations (compare panels (a) and (c) of Fig. ) and
surface phytoplankton concentrations (compare panels (a) and (c) of
Fig. ) showcase this amplified sensitivity of biogeochemical
variables to changes in governing physics in a drastic way: while the
increased vertical diffusion of cold abyssal waters from depth to the surface
effects only minor changes to sea surface temperature and air–sea heat
fluxes (as discussed above), it brings substantially more phosphate to the
nutrient-depleted sunlit surface layer in which it drives a substantial
increase in autotrophic production and the standing stock of phytoplankton.
As a consequence, the cycling of phosphate in the upper thermocline
accelerates. The export of particulate organic matter increases and the
subsequent remineralization sharpens the vertical nutrient gradient at the
base of the euphotic zone, which in turn increases diffusive nutrient fluxes
to the sunlit surface layer. Among the overall net effects is the increased
phosphate pool in the upper thermocline shown in Fig. (except in
the Southern Ocean where the combination of iron limitation, seasonal light
limitation, and unique ventilation patterns overcomes the aforementioned
effect). As concerns dissolved oxygen, the increase in vertical diffusivity
has two opposing effects: on the one hand, the increased mixing ventilates
the abyssal ocean by mixing oxygenated surface waters downward. On the other
hand, the increased mixing accelerates biogeochemical cycling of organic
matter (as described above) and thus, as a consequence of the associated
accelerated remineralization of organic matter, increases the oxygen demand.
Figure c reveals that the ventilating effect prevails in MIX+; i.e.,
the oceanic oxygen inventory rises in response to the higher diffusivity.
Simulated sea surface salinity in practical salinity units (PSUs) for the historical simulations
(see Sect. ). Panels (a) and (b) refer to results from the
model configurations Genuine Truth and MIX+, respectively. MIX+ features an
increased vertical background diffusivity relative to the Genuine Truth (see
Table ). Panel (c) shows the difference between MIX+ and the Genuine Truth.
Simulated zonally averaged net air–sea heat fluxes in watts per
square meter (W m-2) for the historical simulations (see
Sect. ). Positive numbers denote ocean warming. The black and
red lines refer to results from the model configurations Genuine Truth and
MIX+, respectively.
The above results are in line with the intended model design (which mimics
the typical workflow of Earth system model development): the Genuine Truth
simulation represents a global set of (synthetic) observations. MIX+ is a
physically biased model version of the Genuine Truth with, as illustrated
above, drastic consequences for the simulated biogeochemical tracer
distributions. The setup TUNE is an attempt to
tweak (tune) the biogeochemistry in
the deficient model MIX+ such that it
resembles the Genuine Truth under historical conditions. Thus, in TUNE we
compensate for the bias imposed by
the physics via tuning the
biogeochemistry. Under historical forcing, the physical ocean circulation is
almost identical in TUNE and MIX+ (not shown). This low sensitivity might
partly be due to the prescribed atmospheric CO2 concentrations in the
historical simulations, since the feedback from changed biogeochemistry via
oceanic carbon uptake to atmospheric CO2 and associated changes in
air–sea heat fluxes is damped.
Misfits of historical model solutions relative to the Genuine Truth
calculated as the volume-weighted root mean square error (RMSE)
between respective numerical experiments. Note that only phosphate
and phytoplankton concentrations were used to tune the model.
ConfigurationPhosphatePhytoplanktonSurf. phosphateOxygenTotal carbonSSTMIX+0.21 mmol P m-30.1 mmol N m-30.37 mmol P m-340.74 mmol O2 m-30.48 g C m-30.46 KTUNE0.14 mmol P m-30.06 mmol N m-30.16 mmol P m-321.34 mmol O2 m-30.39 g C m-30.46 K
In terms of biogeochemistry, however, TUNE and MIX+ do differ considerably.
Figures b and b show that the surface phosphate and
phytoplankton concentrations simulated with TUNE are much more like the
Genuine Truth than MIX+. Accordingly, the mean bias in surface phosphate
decreases to 0.05 mmol P m-3 for the experiment TUNE relative to
0.27 mmol P m-3 in the simulation MIX+. Similarly, the bias in
surface phytoplankton is reduced from 0.12 to -0.05 mmol N m-3 in
TUNE. The similarity between the Genuine Truth and TUNE (in contrast to the
difference between the Genuine Truth and MIX+) is not restricted to surface
properties but extends to depth. For example, Fig. shows that the
zonally averaged phosphate concentrations of TUNE are much more similar to
the Genuine Truth than is the case with MIX+. Further, Fig. b shows
a similar behavior of the oceanic oxygen inventory. Expressed in numbers, the
respective mean bias in TUNE is 12.99 mmol O2 m-3 relative to
30.08 mmol O2 m-3 in MIX+. A similar bias reduction in TUNE
holds as well for the global extent of the simulated suboxic volume (not
shown). The latter is remarkable since oxygen was not included in our metrics
applied for the tuning process. Table additionally contains a list
of RMSEs relative to the Genuine Truth: e.g., the RMSE between global
distributions of phosphate (phytoplankton) concentrations simulated with the
Genuine Truth and MIX+ is 0.21 mmol P m-3 (0.1 mmol N m-3).
By tweaking biogeochemical model parameters in simulation TUNE the RMSE is
reduced by ≈40% (down to 0.14 mmol P m-3 and
0.05 mmol N m-3; Table ).
Simulated surface phosphate concentrations in millimoles of phosphate per cubic meter
(mmol P m-3) for the
historical simulations (see Sect. ). Panel (a) refers
to results from the model configuration Genuine Truth. Panels
(b) and (c) show the difference between the results from
the model configurations TUNE and MIX+ and the Genuine Truth, respectively.
MIX+ and TUNE feature increased vertical background diffusivity relative to
the Genuine Truth. In addition, TUNE features retuned biogeochemical model
parameters (see Table ).
Simulated phytoplankton concentrations in millimoles of nitrogen per cubic meter
(mmol N m-3) for the
historical simulations (see Sect. ). Panel (a) refers
to results from the model configuration Genuine Truth. Panels
(b) and (c) show the difference between the results from
the model configurations TUNE and MIX+ and the Genuine Truth, respectively.
MIX+ and TUNE feature increased vertical background diffusivity relative to
the Genuine Truth. In addition, TUNE features retuned biogeochemical model
parameters (see Table ).
Model projections into a warming future
All of our numerical configurations agree in that they feature a considerable
sea surface temperature increase by the year 2100 when driven by the RCP8.5
greenhouse gas emission scenario . The associated increase in
radiative forcing warms the surface ocean and increases the stability of the
water column (because relatively warmer and more buoyant water sits on top of
cold abyssal water).
Expressed in terms of a global mean sea surface temperatures, the projected
increase differs by up to 12 % depending on the underlying model
configuration: the projected global mean temperature rise is 2.5,
2.2, and 2.3 K for the configurations Genuine Truth, TUNE, and MIX+,
respectively. These differences among the experiments are consistent with the
fact that (by construction) the simulations based on MIX+ and TUNE distribute
heat over greater depth. Thus, their increased background diffusivity
cools the surface (and warms the deep ocean) relative to the Genuine Truth.
Consequentially, TUNE and MIX+ feature a stronger warming in the deep ocean
than the Genuine Truth (the respective temperature increase is doubled below
1500 m of depth). This effect is somewhat offset in MIX+, which shows more
temperature increase at the surface than TUNE, even though MIX+ and TUNE
share the same physical model parameters. This is consistent with MIX+
featuring a phytoplankton standing stock that exceeds the standing stocks of
both TUNE and the Genuine Truth by 150 %. This increased phytoplankton
concentration absorbs more light at the surface and intensifies the surface
warming.
Differences between simulated meridionally averaged phosphate
concentrations in millimoles of phosphate per cubic meter (mmol P m-3) for the historical simulations (see Sect. ). Panels
(a) and (b) refer to TUNE minus Genuine Truth and MIX+
minus Genuine Truth, respectively.
(a) Simulated depth-averaged oxygen concentrations in millimoles of oxygen per cubic meter
(mmol O2 m-3) for the
historical simulation of the Genuine Truth. Panel (b) refers to the
differences between TUNE and the Genuine Truth of simulated depth-averaged
oxygen concentrations in units mmol O2 m-3 for the historical
simulations (see Sect. ). Panel (c) is identical
to (b) but shows the difference to MIX+ instead of TUNE.
Regionally, the differences in projected sea surface temperatures (SSTs)
can be much larger than in the global mean: Fig. shows a
comparison of sea surface temperature warming between TUNE and MIX+ relative
to the Genuine Truth configuration in response to the RCP8.5 emission
scenario. As expected, the comparisons to TUNE and MIX+ are very similar, but
anomalies are somewhat more pronounced in TUNE. The differences between the
TUNE and the Genuine Truth configuration exceed at maximum 1.8 K. The
overall pattern is 0.2 to 0.5 K less warming in the Northern Hemisphere and
0.1 to 0.5 K more warming in the Southern Ocean in TUNE compared to the
Genuine Truth. Hence, Southern Ocean SST warming in TUNE, in response to the
increased greenhouse gas emissions, is stronger than in the Genuine Truth,
even though the Genuine Truth overall warms more quickly than TUNE. We
speculate that the increased background diffusivity in TUNE reduces the
cooling effect of deep convection in the Southern Ocean by 2100 (relative to
the Genuine Truth) because the abyssal waters (which the deep convection
taps into) in TUNE have received more heat (relative to the Genuine Truth)
prior to the year 1850. Also, the maximum overturning shows a stronger
projected decline with increased vertical diffusivity.
Comparison of sea surface temperature warming in response to RCP8.5
emissions. (a) The contours (both colored and labeled) denote the
differences in simulated sea surface temperature anomalies between the years 2100
and 1850 in the projection based on the Genuine Truth setup in units of Kelvin.
Panels (b) and (c) show the same differences for the projections based on
TUNE and MIX+ relative to the Genuine Truth, respectively. Negative numbers
indicate regions where the Genuine Truth warmed more than TUNE in the year
2100.
In terms of biogeochemistry, the similarity of model projections depends on
the considered metric. For some biogeochemical tracers the reciprocal bias
compensation (whereby an increase in diapycnal mixing is compensated for by changes to
biogeochemical model parameters) is robust under global warming, while the
historical similarities break for others. In
Sect. to we illustrate the respective range.
We start with a metric that is most robust and end with a metric with which the
bias compensation breaks under the emission scenario.
Surface phytoplankton concentrations
Projections of phytoplankton are of interest because phytoplankton forms
the base of the food chain and thereby exerts control on fisheries. The
Genuine Truth simulation projects globally decreasing surface phytoplankton
concentrations (see Fig. , left panel), corresponding to a global
mean decrease of 7 % by 2100. This is consistent with the increased stability
of the water column (effected by global warming), reducing the turbulent
vertical mixing of nutrient-replete waters from depth to the
nutrient-depleted sunlit surface ocean. In limited regions the projected
changes can be opposed to the overall trend. These differences are most
likely attributed to circulation changes (see Fig. 8). Examples of such
regions are the Arctic, the equatorial Pacific, and the Southern Ocean.
Simulated changes in surface phytoplankton concentrations as a
consequence of rising CO2 concentrations (emission scenario RCP8.5)
calculated as the annual mean concentration difference between the years 2100
and 1850 (mmol N m-3).
The projection based on MIX+ differs substantially from the Genuine Truth in
that it projects an overall increasing surface phytoplankton concentration
(see Fig. ). Most of this difference to the Genuine Truth is
agglomerated in the Pacific Ocean, a region infamous for its nonlinear
behavior in our model; see also Sect. 3.2. in. The
projected phytoplankton change based on TUNE is very similar to the Genuine Truth (see Fig. , middle panel), corresponding to a
globally averaged decrease of 8 % by 2100 – even though it shares the same
biased physics with MIX+. This illustrates that for projected surface
phytoplankton patterns the reciprocal bias compensation is (in our model)
robust under the RCP8.5 scenario.
Surface phosphate concentrations
Projections of phosphate are of interest because phosphate is an essential
nutrient that limits the growth of phytoplankton and the associated biotic
export of organic matter to depth. In most state-of-the-art, global, coupled
ocean circulation biogeochemical models, phosphate is the “base
currency”;
i.e., its cycling is directly (often linearly) related to the cycling of
plankton and gases such as oxygen and CO2. The Genuine Truth simulation
projects globally decreasing surface phosphate concentrations (see
Fig. , left panel), corresponding to a global mean decrease of
17 % by 2100. As described above, this result is consistent with the
increased stability of the water column that is effected by net air–sea heat
fluxes (and associated buoyancy because warmer water is lighter than colder)
caused by global warming. In the Southern Ocean, the processes at work are more
complex. Here, the projected sea surface temperatures in the Genuine Truth
simulation show alternating patterns of increasing and decreasing sea surface
temperatures until the year 2100 (see Fig. 8). Downstream of regions where
sea surface temperatures are reduced, more nutrients are mixed up to the
surface in convective events and, simultaneously, surface mixed layers are
increased. The latter leads to opposite effects compared to the above
considerations on a global scale.
Simulated changes in surface phosphate concentrations as a
consequence of rising CO2 concentrations (emission scenario RCP8.5)
calculated as the annual mean concentration difference between the years 2100
and 1850 (mmol P m-3).
The MIX+ projection is similar to the Genuine Truth as it projects that
decreasing surface phosphate concentrations prevail globally (see
Fig. , right panel). This decrease averages to 17 % globally by
the year 2100. In the Southern Ocean, however, MIX+ differs substantially in
that the alternating patches of increasing and decreasing surface phosphate
concentrations apparent in the Genuine Truth are smoothed out
(Fig. , compare left and right panel). We speculate that the
absence of patches with strongly increasing surface phosphate indicates
less-deep convection events. The latter is in line with the projected SSTs
(Fig. 8).
The projection based on TUNE is generally very similar to the MIX+
projection: in this simulation decreasing surface phosphate
concentrations also prevail globally (see Fig. , middle panel),
corresponding to a globally averaged decrease of 17 % by 2100. In
the Southern Ocean, however, TUNE is much more similar to MIX+ than the
Genuine Truth. This illustrates that for projected surface phosphate patterns
the reciprocal bias compensation is not very robust (especially locally,
where circulation effects kick in) and some of the similarities apparent
under historical conditions break under the RCP8.5 emission scenario.
Total oceanic carbon content
Projections of oceanic carbon content are of interest because the
oceans currently take up a significant fraction of anthropogenic carbon
emissions of the order of 25 %; e.g.,. Therefore,
changes in the capability of the ocean to sequester carbon away from the
atmosphere in a warming future will directly affect the rate of global
warming itself. This strong feedback is among the main drivers behind the
development–inclusion of biochemical carbon modules in Earth system models
that are used to assess the effects of climate change (and to develop
mitigation strategies).
(a) Differences in projected anomalous total carbon content of the ocean in
response to rising CO2 concentrations (emission scenario RCP8.5; in
units of gigatons of carbon). (b) Simulated temporal evolution of the volume of global
suboxic waters (emission scenario RCP8.5).
Figure a shows that the reciprocal bias compensation is not
robust when regarding the projected oceanic carbon content. In the historical
model solutions, the simulated carbon content of the ocean varies by less
than 0.6 % between the simulations. In the future projections, both MIX+
and TUNE propose to take up 200 Gt C more than the Genuine Truth by the
year 2100. This difference refers to 32 % of the maximum projected change. In line with
earlier studies, we presume that these strong differences must be attributed
to differences in the solubility pump. Our results indicate that for oceanic
carbon content, the reciprocal bias compensation is not robust once the
boundary conditions strongly change.
Suboxic volume
Projections of suboxic volume are of interest because suboxia triggers
denitrification and thus reduces the global availability of fixed nitrogen,
an essential nutrient for all phytoplankton other than diazotrophs.
Figure b shows that the suboxic volume, according to the Genuine
Truth projection, decreases with global warming. A similar surprising
behavior has been reported from other Earth system models
e.g.,, which is surprising since it is counter to
intuition because (1) warming reduces the solubility of oxygen, and (2) the
increased stratification of the water column comes along with reduced
ventilation; i.e., both of these processes directly associated with warming
tend to reduce oceanic oxygen levels and thus promote suboxia.
MIX+ shows that an increased background diffusion can reverse the projected
trend in suboxic volume. This is consistent with results from
and , highlighting the sensitivity
of suboxic waters to the resolved and parameterized ocean physics.
The projection based on TUNE behaves like MIX+ in that it also shows a trend
opposing the Genuine Truth. Remarkably, its trend is even more off relative to
the Genuine Truth than the trend of MIX+. This illustrates that for suboxic
volume the reciprocal bias compensation is not at all robust when the models
are projected into the future.
Discussion
We set out to explore reciprocal bias compensation in Earth system models
in which deficiencies in the ocean circulation module are deliberately
outweighed by tweaking the biogeochemical module. In the following, we will
discuss the choice of our Earth system model (Sect. ), the changes
applied to the physical module (Sect. ), and the changes applied to
the biogeochemical module (Sect. ). In Sect. we will
discuss the similarity between TUNE and Genuine Truth under historical
forcing (and argue that we cannot decide based on ad hoc measures of typical
present-day observations which setup is better suited to make reliable
projections into a warming future). Section closes this discussion
by highlighting the differences between projections based on the model
configurations TUNE and the Genuine Truth.
Choice of model framework
Our results are based on integrations of the UVic Earth system model
. The model is relatively simple (i.e., it is an Earth
system model of intermediate complexity – EMIC) and rather coarsely resolved
(≈200 km) compared to the cutting-edge generation of IPPC-type
atmosphere–ocean general circulation models (AOGCMs). Since EMICs and AOGCMs
share very similar (or sometimes even identical) ocean circulation and
pelagic biogeochemistry kernels, we speculate that our EMIC-based
results are also applicable to IPCC-type AOGCMs. Accordingly, earlier
findings from model intercomparison studies (e.g., ) are
consistent with our results. Even so, we wish to stress that our mixing
parameter settings in MIX+ and TUNE are at the upper limit of proposed
values and are chosen to cover the whole range.
We compare three configurations of UVic dubbed the Genuine Truth, MIX+,
and TUNE. All setups are very similar (for the Genuine Truth even
identical; see Sect. ) to the
configuration. This choice is motivated by the fact that this configuration
is extensively used to assess the impact of geo-engineering options. Among
recent studies are , who explored the impacts of sea spray
geo-engineering, , who explored the effects of carbon
sequestration by direct injection into the ocean, and , who
assessed the effects of ocean albedo modification in the Arctic.
Choice of modification to background diffusivity
Two of our configurations (MIX+ and TUNE) feature an increased
vertical diffusivity as the only change relative to the physical component of
the original configuration (which we dubbed the Genuine Truth).
The choice of changing the vertical background diffusivity is motivated by
the fact that vertical diapycnal mixing is not well quantified in
models or in the real ocean. What is known, though, is that diapycnal mixing
is highly heterogenic both in time and space. Enhanced diffusivities up to
10 cm2 s-1 near the bottom have been observed over rough topography
, while large-scale estimates derived from purposeful
tracer release experiments in the subtropical North Atlantic yield values of
0.17±0.02 cm2 s-1 when considering a 2-year average
. Even if the temporal and spacial variability were
mapped out (which is not yet the case), the challenge is to transfer these
numbers into a model parameterization that ensures realistic diffusive
transports (of heat, salt, nutrients, etc.), which are defined as the product
of the respective spacial (vertical) property gradient and diffusivity. Thus,
using a vertical diffusivity that is averaged over time and space (as is
inevitable in the current generation of models that apply a
finite-difference discretization) is fraught with uncertainties. An
additional source of uncertainty is implicit diffusion, a spurious and
hard-to-quantify artifact (see ) of the underlying
numerical advection algorithm. To summarize: the uncertainty of the value of
the vertical diffusion parameter of our physical model component is
substantial and it cannot currently be well constrained by
observations or experiments. Hence, we use the original diffusivity proposed
for UVic and compare it to a value that was applied in the same model that
uses a slightly different advection scheme but is otherwise identical. This
model version with a changed advection scheme and increased diffusivity is used
as the basis for the offline approach described by .
Using ad hoc measures, based on temperature and salinity, our change in
diffusivity has a rather weak impact on physical tracers: only 0.03 K in terms
of global sea surface temperature differences; in terms of meridional
averaged heat fluxes, the differences are below 5 W m-2 from 50∘ S
to 50∘ N, reaching 25 W m-2 at high latitudes.
The maximum meridional overturning circulation increases (as expected) with
increased vertical diffusion and is 22 Sv in the reference simulation of
MIX+ versus 19 Sv in the Genuine Truth. These numbers are broadly
consistent with IPCC models: show values in the range 22–24 Sv for the Australian Community Climate and Earth System Simulator
coupled CMIP5 model under preindustrial conditions. For the late twentieth
century, report an ensemble mean of a maximum overturning of
19 Sv in CMIP5 and 16 Sv in CMIP3 models. The spread among models in the
late twentieth century has a range of 6.6–27.4 Sv in CMIP3 and 12.1–29.7 Sv in CMIP5 models, which is huge. Thus, the difference between the lowest and highest
projected maximum overturning in CMIP5 models is almost as high as the present-day
observational estimate (17.5 Sv based on the RAPID array at 26∘ N;
).
Choice of changes to biogeochemical model parameters
One of our model configurations, TUNE, has both changed physics like MIX+
(described above) and changed biogeochemical parameter values chosen to
reduce the misfit between this model and data (generated by Genuine Truth).
To this end, μZ, μD, and wD0 have been changed by 12.5 %,
≈200 %, and 115 %, respectively. These changes are well within today's
uncertainties, i.e., within the range of what is applied in other studies.
For example, assume that zooplankton mortality is
uncertain within 4000 %, and the sinking speed at the surface in the Genuine Truth setup exceeds the value used by by 180 %. All
parameter values considered in this study are well within the range used by
in an automated parameter optimization study.
Similarity between the reciprocally bias-compensated couple
For the historical runs we showed in Sect. 3.1 that the simulations TUNE and
the Genuine Truth are very similar to one another; i.e., the reciprocal bias
compensation was effective.
Given the close resemblance of temperature, salinity, air–sea heat fluxes,
phosphate, phytoplankton, and oxygen in Figs. 1 to 7, we argue that both
simulations, TUNE and the Genuine Truth, feature comparable misfits to
observations for common model evaluation metrics. Since the Genuine Truth
configuration is rated applicable to carry out geo-engineering studies (as
outlined above), we conclude in turn that the configuration TUNE would be
equally applicable to address today's pressing climate-related problems.
Ensuing uncertainties in response to RCP8.5
As outlined above, it is hard to argue based on a priori knowledge of the
differences among their underlying model parameters which model
configuration, the Genuine Truth or TUNE, is more realistic. Also, choosing
the better model based on its performance in reproducing historical
observations is difficult: the differences are rather small and the best
choice will depend on
the applied metric (or cost) to measure the misfit to the observations.
It is disconcerting that the two
configurations differ in what they project to come in response to the RCP8.5
emission scenario. The uncertainties in projected sea surface temperatures
imposed by ocean mixing are locally substantial: for the Northern Hemisphere,
we found differences of on average 0.5 K between the Genuine Truth and the
simulation TUNE – a large value, particularly given that consensus has been
reached on trying to keep global warming below 2 K. This finding, that
vertical diffusion matters, is in line with earlier studies that stress the
importance of the vertical diffusion coefficient for several physical
properties of the ocean: e.g., pointed out that this
parameter strongly impacts sensitivity towards wind forcing and thus the
simulated large-scale meridional overturning.
In line with results from, e.g., and ,
we find that the uncertainty in background diffusivity also maps onto uncertainties in
projected biogeochemical tracers. Striking examples, put forward in
Sect. , are phytoplankton concentrations in the equatorial
Pacific and suboxic volume (on which projections based on TUNE and the
Genuine Truth do not agree, even on the sign of projected changes). The
results for suboxic volume are consistent with findings by ,
who illustrate (in their Fig. 9) that the current generation of CMIP5 models
does not agree on the sign of change either.
In terms of oceanic carbon content, the differences between TUNE and the
Genuine Truth in projected future changes accumulate to 200 Gt of carbon in
the year 2100. Again, this difference is substantial: expressed in terms of
today's anthropogenic carbon emissions, the difference corresponds to 20 year's worth of anthropogenic emissions, which covers more than 40 % of the
respective differences among CMIP5 models .
Model evaluation metrics
Our study stresses the urgent need to evaluate the mixing in ocean models
carefully before projecting into the future. Our results are consistent with
earlier findings within the Ocean Carbon-cycle Model Intercomparison Projects
(OCIMIPs), which highlighted early on the importance of a realistic
representation of physical ocean processes for modeling pelagic
biogeochemistry (e.g., ). A definition of a suitable
evaluation metric, apart from assessing relatively simple common measures
such as temperature, salinity, and strength of the meridional overturning, is
still not straightforward and today there is no consensus how to assess ocean
models. It was suggested to also consider ventilation times (e.g.,
). Accordingly, additional inert chemical tracers
(e.g., chlorofluorocarbons (CFC11, CFC12), SF6), allow for an extended
model evaluation and are now required as standard output within CMIP6
(). Still, many open questions and problems remain with such
approaches. For example, the parameterized air–sea gas exchange induces
large uncertainties (e.g., ). Furthermore, dating ranges
of CFCs are not suitable to resolve the dynamics of the deep ocean, which
recently led to an investigation of the use of 39Ar as an
additional tracer . The latter promising approach is
currently under investigation. In summary, however, it still remains a
pressing open question which misfit metrics ensure reliable projections. One
major aim of the presented study is to remind us of these perpetual, often
disregarded problems and to trigger related work. As a measure for diapycnal
mixing in models we propose using the saturation state of noble gases, such
as argon. Although noble gas concentrations are conservative tracers, their
saturation states are not due to a nonlinear temperature and salinity
dependence on their solubility . In general, mixing of
saturated water parcels affects temperature, salinity, and noble gas
concentrations linearly and thus results in supersaturated argon
concentrations.
Conclusions
We present results from two configurations of an Earth system model that
feature a very similar behavior when driven with historical forcing but
diverge drastically when used to project into our warming future based on the
anthropogenic greenhouse gas emission scenario RCP8.5. The differences
between the two configurations (dubbed the Genuine Truth and TUNE) are a
modified vertical background diffusivity and changes applied to
biogeochemical model parameters. The values of the biogeochemical model
parameters were chosen to counteract the effects of the modified diffusivity.
Note that the respective modification of the vertical diffusivity is within
the range of what has recently been applied see settings
in. Likewise, the changes in biogeochemical model
parameters are within the range of state-of-the-art model configurations .
In terms of typical physical model assessment metrics (such as historical sea
surface temperatures and meridional overturning estimates referring to
currently applied assessment metrics such as in) and
biogeochemical metrics (such as historical observations of phytoplankton and
phosphate concentrations) neither of our two model configurations can be favored
or discarded. The reason is that, first, our increase in vertical
diffusivity has few effects on ad hoc measures of the ocean
component in our model framework. Second, while the effect of our increased
diffusivity substantially offsets generic biogeochemical assessment metrics
(see configuration MIX+), we were able to compensate for a large part of the
respective bias by changing biogeochemical model parameters. When driven with
an RCP8.5 scenario, however, the similarity between our model configurations
breaks for projections of societal relevance, such as the oceanic uptake of
carbon or the dynamics of oxygen minimum zones. For carbon the projections
accumulate a difference of 20 year's worth of today's anthropogenic emissions
by the end of 2100. For the suboxic volume, not even the sign of forecasted
changes coincides.
We conclude that an improved understanding of vertical diapycnal mixing in
Earth system models alleviates the risk of reciprocal bias compensation by
(wrongly) tweaking biogeochemical modules to a deficient physics,
particularly when using ad hoc measures to assess the quality of the
underlying ocean model. These results are consistent with earlier findings
within the Ocean Carbon-cycle Model Intercomparison Projects (OCIMIPs) that
highlighted the importance of a realistic representation of physical
ocean processes for modeling pelagic biogeochemistry (e.g.,
). Thus, an improved understanding of vertical diapycnal mixing
can be expected to reduce ensuing uncertainties in climate projections
considerably. Reverse reasoning suggests that an improved understanding of
biogeochemistry can help to assess the realism of diapycnal mixing in Earth
system models because (1) we found that some biogeochemical metrics are more
sensitive to changes in mixing parameterization than typical physical metrics
(such as overturning and temperature distributions), and (2) if the
biogeochemical model formulations could be sufficiently constrained, then
misfits between (more sensitive) biogeochemical metrics can be related back
to deficiencies in the physical component of coupled ocean circulation
biogeochemical models. With these findings, our study emphasizes the need to
develop and routinely apply misfit metrics that take diapycnal mixing into
account to obtain more reliable future projections.
Code availability
The model code is archived at
https://data.geomar.de/thredds/catalog/open_access/loeptien_dietze_2018_bg/catalog.html
(last access: 1 May 2019). Since the use of the source code requires
registration with the UVic model community
(http://climate.uvic.ca/model/, last access: 14 February 2018,
), the respective file is password protected and available
upon request. All required input files are downloadable under the above
link.
Data availability
The model output is archived at
https://data.geomar.de/thredds/catalog/open_access/loeptien_dietze_2018_bg/catalog.html
(last access: 1 May 2019).
Author contributions
Both authors were involved in the design of the work,
in data analysis, in data interpretation, and in drafting the
article.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work is a contribution of the project “Reduced Complexity Models”
(supported by the Helmholtz Association of German Research Centres (HGF) –
grant no. ZT-I-0010) and was additionally supported by the Deutsche
Forschungsgemeinschaft (DFG) in the framework of the priority program
“Antarctic Research with comparative investigations in Arctic ice areas”
SPP 1158 by grant no. SCHN 762/5-1. We thank Anne Willem Omta and an
anonymous reviewer for extremely detailed and helpful comments.
Review statement
This paper was edited by Katja Fennel and reviewed by Anne
Willem Omta and one anonymous referee.
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