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**Biogeosciences**
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**Research article**
03 Sep 2018

**Research article** | 03 Sep 2018

Drivers of future seasonal cycle changes in oceanic *p*CO_{2}

^{1}Department of Oceanography, School of Ocean and Earth Sciences and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA^{2}International Pacific Research Center, School of Ocean and Earth Sciences and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA^{3}Center for Climate Physics, Institute for Basic Science (IBS), Busan, South Korea^{4}Pusan National University, Busan, South Korea

^{1}Department of Oceanography, School of Ocean and Earth Sciences and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA^{2}International Pacific Research Center, School of Ocean and Earth Sciences and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA^{3}Center for Climate Physics, Institute for Basic Science (IBS), Busan, South Korea^{4}Pusan National University, Busan, South Korea

**Correspondence**: M. Angeles Gallego (mdla@hawaii.edu)

**Correspondence**: M. Angeles Gallego (mdla@hawaii.edu)

Abstract

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Recent
observation-based results show that the seasonal amplitude of surface ocean
partial pressure of CO_{2} (*p*CO_{2}) has been increasing
on average at a rate of 2–3 µatm per decade
(Landschützer et al., 2018). Future increases in *p*CO_{2} seasonality
are expected, as marine CO_{2} concentration ([CO_{2}])
will increase in response to increasing anthropogenic carbon emissions
(McNeil and Sasse, 2016). Here we use seven different global coupled
atmosphere–ocean–carbon cycle–ecosystem model simulations conducted as
part of the Coupled Model Intercomparison Project Phase 5 (CMIP5) to study
future projections of the *p*CO_{2} annual cycle amplitude and to
elucidate the causes of its amplification. We find that for the RCP8.5
emission scenario the seasonal amplitude (climatological maximum minus
minimum) of upper ocean *p*CO_{2} will increase by a factor of
1.5 to 3 over the next 60–80 years. To understand the drivers and mechanisms
that control the *p*CO_{2} seasonal amplification we develop a
complete analytical Taylor expansion of *p*CO_{2} seasonality in
terms of its four drivers: dissolved inorganic carbon (DIC), total
alkalinity (TA), temperature (*T*), and salinity (*S*). Using this linear
approximation we show that the DIC and *T* terms are the dominant
contributors to the total change in *p*CO_{2} seasonality. To
first order, their future intensification can be traced back to a doubling of
the annual mean *p*CO_{2}, which enhances DIC and alters the
ocean carbonate chemistry. Regional differences in the projected seasonal
cycle amplitude are generated by spatially varying sensitivity terms. The
subtropical and equatorial regions (40^{∘} S–40^{∘} N) will
experience a ≈30–80 µatm increase in seasonal cycle
amplitude almost exclusively due to a larger background CO_{2}
concentration that amplifies the *T* seasonal effect on solubility. This
mechanism is further reinforced by an overall increase in the seasonal cycle
of *T* as a result of stronger ocean stratification and a projected shoaling
of mean mixed layer depths. The Southern Ocean will experience a seasonal
cycle amplification of ≈90–120 µatm in response to the
mean *p*CO_{2}-driven change in the mean DIC contribution and to
a lesser extent to the *T* contribution. However, a decrease in the DIC
seasonal cycle amplitude somewhat counteracts this regional amplification
mechanism.

How to cite

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top
How to cite.

Gallego, M. A., Timmermann, A., Friedrich, T., and Zeebe, R. E.: Drivers of future seasonal cycle changes in oceanic *p*CO_{2}, Biogeosciences, 15, 5315–5327, https://doi.org/10.5194/bg-15-5315-2018, 2018.

1 Introduction

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Owing to its large chemical capacity to resist changes
in [CO_{2}] (referred to as buffering capacity), the ocean has
absorbed nearly half of the anthropogenic CO_{2} produced by fossil fuel
burning and cement production since the industrial revolution
(Sabine et al., 2004). While the ocean's absorption of CO_{2} lowers the
atmospheric concentration, it also increases the ocean's [CO_{2}] and in turn
lowers its buffering capacity. This leads to a reduction in the oceanic
uptake of CO_{2} and an intensification of the *p*CO_{2} seasonal
cycle (from now on referred to as *δ**p*CO_{2}) (McNeil and Sasse, 2016; Völker et al., 2002). In a
recent key observational study by Landschützer et al. (2018), it
was demonstrated that the *δ**p*CO_{2} amplitude
increased at a rate of ≈2–3 µatm per
decade from 1982 to 2015.

The *p*CO_{2} already experiences large seasonal fluctuations,
which in some regions can reach up to 60 % above and below the annual mean
*p*CO_{2} (Takahashi et al., 2002). An intensification of the
*δ**p*CO_{2} amplitude could produce seasonal hypercapnia
conditions (McNeil and Sasse, 2016), which together with increased [H^{+}]
seasonality (Hagens and Middelburg, 2016; Kwiatkowski and Orr, 2018) and aragonite undersaturation
events (Hauri et al., 2015; Sasse et al., 2015; Shaw et al., 2013) could expose marine life to harmful
seawater conditions earlier than expected if considering only annual mean
values. Moreover, a projected amplification of *δ**p*CO_{2} might
increase the net CO_{2} uptake in some regions, such as the Southern Ocean,
thereby further accelerating the decrease in the buffering capacity in that
region (Hauck and Völker, 2015).

The *p*CO_{2} seasonal amplitude is controlled mainly by seasonal changes in
temperature (*T*) and biological activity together with upwelling changes that alter DIC concentrations.
Usually, DIC and *T* changes work in opposite directions (Fay and McKinley, 2017; Sarmiento and Gruber, 2006; Takahashi et al., 2002).
In subtropical regions higher *p*CO_{2} values occur in summer when solubility decreases.
In subpolar regions, *p*CO_{2} increases in winter when waters upwell that are
rich in DIC and when respiration of organic matter takes place. Decreased subpolar
*p*CO_{2} occurs in summer when primary productivity is higher and upwelling diminishes.
Therefore, we find close relationships of *δ**p*CO_{2} with the
ocean's [CO_{2}], which controls chemical reactions, and with
mean *p*CO_{2}, which moderates exchange with the atmosphere.
Both factors are related by the solubility constant that depends on
temperature and salinity.

Furthermore, the regional differences in the influence of temperature and
biology on *δ**p*CO_{2} are modulated by the ocean's
buffering capacity. This is due to the ability of CO_{2} to react with
seawater to form bicarbonate $\left[{\mathrm{HCO}}_{\mathrm{3}}^{-}\right]$ and carbonate
$\left[{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}\right]$, leaving only a small portion of dissolved carbon
dioxide in the form of aqueous CO_{2} ([CO_{2}(aq)]). [CO_{2}(aq)] together
with carbonic acid ([H_{2}CO_{3}]) are defined as [CO_{2}].
Therefore, it is useful to define the total amount of carbon as DIC, which is
the sum of the three carbon species ($\left[{\mathrm{HCO}}_{\mathrm{3}}^{-}\right]$,
$\left[{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}\right]$, and [CO_{2}]). At current chemical conditions, most of
the DIC is in the form of ${\mathrm{HCO}}_{\mathrm{3}}^{-}$, and therefore the buffering capacity is
largely controlled by the ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ capable of transforming CO_{2}
into bicarbonate through the reaction
CO_{2}(aq) + ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ + H_{2}O = 2${\mathrm{HCO}}_{\mathrm{3}}^{-}$ (Zeebe and Wolf-Gladrow, 2001). The larger the buffering
capacity, the larger the *p*CO_{2} ability to resist changes in
DIC. To quantify this capacity, we can introduce the sensitivity factor
*γ*_{DIC}, which is inversely related to the buffering
capacity, defined as
${\mathit{\gamma}}_{\mathrm{DIC}}=\partial \mathrm{ln}\left(p{\mathrm{CO}}_{\mathrm{2}}\right)/\partial \mathrm{DIC}$, (Egleston et al., 2010).
Other sensitivity factors are related to the total alkalinity
(*γ*_{TA}), salinity (*γ*_{S}), and temperature
(*γ*_{T}) changes and are defined in a similar way as
$\partial \mathrm{ln}\left(p{\mathrm{CO}}_{\mathrm{2}}\right)/\partial \mathrm{TA}$,
$\partial \mathrm{ln}\left(p{\mathrm{CO}}_{\mathrm{2}}\right)/\partial S$, and
$\partial \mathrm{ln}\left(p{\mathrm{CO}}_{\mathrm{2}}\right)/\partial T$, respectively. It is important to
note that the *p*CO_{2} is highly sensitive to temperature due to
two factors: first through solubility changes that account for 2 ∕ 3 of the
present-day temperature impact, and second through the dissociation
constants that control the carbon system reactions (Sarmiento and Gruber, 2006).

While the mechanisms controlling the seasonal cycle of *p*CO_{2}
at present day are well documented, the future evolution of these drivers has
not been fully elucidated. Current literature suggests that seasonal
amplification is a consequence of an increase in the *T* and DIC contributions
to *δ**p*CO_{2} (Landschützer et al., 2018) and an
increased sensitivity of the ocean to these variables (Fassbender et al., 2017).

The aim of our paper is to provide an in-depth analysis of the mechanisms
controlling the future strength of *δ**p*CO_{2} and its
regional differences using seven CMIP5 global Earth system models. Our analysis
focuses on 21st century evolution using the Representative
Concentration Pathway 8.5 (RCP8.5) scenario. We give a comprehensive analysis
of the projected evolution of the DIC, TA, *T*, and *S* contributions to
*p*CO_{2} seasonality. To achieve this goal, we derive explicit
analytical expressions for *p*CO_{2} sensitivities in terms of
*γ*_{DIC}, *γ*_{TA}, *γ*_{T}, and
*γ*_{S}, thereby extending previous work done by Egleston et al. (2010).

2 Methodology

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For our analysis, *p*CO_{2}, DIC, TA, *T*, and *S* monthly mean
output variables covering the period from 2006–2100 were obtained from
future climate change simulations conducted with seven fully coupled Earth
system models that participated in the Coupled Model Intercomparison Project,
Phase 5 (CMIP5) (Taylor et al., 2012). The following models were selected based on data
availability: CanESM2, CESM1-BGC, GFDL-ESM2M, MPI-ESM-LR, MPI-ESM-MR,
HadGEM2-ES, and HadGEM2-CC (see the supplementary material of
Hauri et al., 2015). For the purpose of this paper, we used the Representative
Concentration Pathway 8.5 (RCP8.5) future climate change simulations
(IPCC, 2013). The ocean's surface data sets were regridded onto a
$\mathrm{1}{}^{\circ}\times \mathrm{1}{}^{\circ}$ grid using climate data operators (CDOs). The
Arctic Ocean and the region poleward of 70^{∘} S are removed from the
analyses because observational data for model validation are scarce.

To elucidate the underlying dynamical, thermodynamical, biological, and
chemical processes controlling *δ**p*CO_{2} we
calculated a first-order Taylor series expansion of
*δ**p*CO_{2} in terms of its four drivers, DIC, TA,
*T*, and *S*. While *T* and *S* are controlled only by physics, DIC and TA are
controlled by physical, chemical, and biological processes. Throughout this
paper we use salinity-normalized DIC and TA using a mean salinity of 35 psu.
This effectively removes the concentration–dilution freshwater effect,
following the procedure of Lovenduski et al. (2007). The salinity normalized
variables are referred to as DIC_{s} and TA_{s},
corresponding to DIC $\cdot {S}_{\mathrm{0}}/S$ and TA $\cdot {S}_{\mathrm{0}}/S$,
respectively. The freshwater effect on DIC and TA is now included in the *S* term, renamed as *S*_{fw}. For the Taylor series expansion, each
variable (*X*= DIC, TA, *T*, and *S*) is decomposed into $X=\stackrel{\mathrm{\u203e}}{X}+\mathit{\delta}X$. The term $\stackrel{\mathrm{\u203e}}{X}$ represents the 21-year mean and *δ**X* denotes the seasonal cycle (calculated
as the monthly mean deviation from the 21-year average). The Taylor
expansion is then computed for an initial (2006–2026) and final (2080–2100)
period. We use multi-decade means and eventually multi-model ensemble means
to remove the effects of interannual variability. The full first-order series
expansion is given by

$$\begin{array}{ll}{\displaystyle}\mathit{\delta}p{\mathrm{CO}}_{\mathrm{2}}\approx & {\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial \mathrm{DIC}}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}\mathit{\delta}{\mathrm{DIC}}_{\mathrm{s}}+{\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial \mathrm{TA}}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}\mathit{\delta}{\mathrm{TA}}_{\mathrm{s}}\\ \text{(1)}& {\displaystyle}& {\displaystyle}+{\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial T}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}\mathit{\delta}T+{\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial S}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}\mathit{\delta}{S}_{\mathrm{fw}}.\end{array}$$

Each term of the right-hand side of Eq. (1) represents the
contribution from one of the four drivers of *δ**p*CO_{2}.
The analytical expressions for the derivatives (without the salinity
normalization) are given by the following.

$$\begin{array}{ll}\text{(2)}& {\displaystyle}& {\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial \mathrm{TA}}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}=\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot {\displaystyle \frac{-{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}}{\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}\cdot \mathrm{\Theta}-{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}^{\mathrm{2}}}}{\displaystyle}& {\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial \mathrm{DIC}}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}=\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot {\displaystyle \frac{\mathrm{\Theta}}{\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}\cdot \mathrm{\Theta}-{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}^{\mathrm{2}}}}\\ {\displaystyle}& {\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial T}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}=\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot {\displaystyle \frac{\mathrm{1}}{\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}\cdot \mathrm{\Theta}-{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}^{\mathrm{2}}}}\\ {\displaystyle}& {\displaystyle}\left[{\stackrel{\mathrm{\u203e}}{\mathrm{TA}}}_{\mathrm{c}}\cdot ({\displaystyle \frac{\partial {\mathrm{Alk}}_{\mathrm{c}}}{\partial T}}+{\displaystyle \frac{\partial \left[\mathrm{B}(\mathrm{OH}{)}_{\mathrm{4}}^{-}\right]}{\partial T}}+{\displaystyle \frac{\partial \left[{\mathrm{OH}}^{-}\right]}{\partial T}})\right.\\ \text{(3)}& {\displaystyle}& {\displaystyle}\left.-\mathrm{\Theta}\cdot {\displaystyle \frac{\partial (\mathrm{DIC}-[{\mathrm{CO}}_{\mathrm{2}}\left]\right)}{\partial T}}\right]-{\displaystyle \frac{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot}{\stackrel{\mathrm{\u203e}}{{K}_{\mathrm{0}}}(T,S)}}{\displaystyle \frac{\partial {K}_{\mathrm{0}}(T,S)}{\partial T}}{\displaystyle}& {\displaystyle \frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial S}}{\mathrm{|}}_{\stackrel{\stackrel{\mathrm{\u203e}}{\mathrm{TA}},\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}}{\stackrel{\mathrm{\u203e}}{T},\stackrel{\mathrm{\u203e}}{S}}}=\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot {\displaystyle \frac{\mathrm{1}}{\stackrel{\mathrm{\u203e}}{\mathrm{DIC}}\cdot \mathrm{\Theta}-{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}^{\mathrm{2}}}}\\ {\displaystyle}& {\displaystyle}\left[{\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}\cdot ({\displaystyle \frac{\partial {\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}}{\partial S}}+{\displaystyle \frac{\partial \left[\mathrm{B}(\mathrm{OH}{)}_{\mathrm{4}}^{-}\right]}{\partial S}}+{\displaystyle \frac{\partial \left[{\mathrm{OH}}^{-}\right]}{\partial S}})\right.\\ \text{(4)}& {\displaystyle}& {\displaystyle}\left.-\mathrm{\Theta}\cdot {\displaystyle \frac{\partial (\mathrm{DIC}-[{\mathrm{CO}}_{\mathrm{2}}\left]\right)}{\partial S}}\right]-{\displaystyle \frac{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot}{\stackrel{\mathrm{\u203e}}{{K}_{\mathrm{0}}}(T,S)}}{\displaystyle \frac{\partial {K}_{\mathrm{0}}(T,S)}{\partial S}}{\displaystyle}\end{array}$$

Here, $\mathrm{\Theta}=\left[{\mathrm{HCO}}_{\mathrm{3}}^{-}\right]+\mathrm{4}\left[{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}\right]+\frac{\left[\mathrm{B}\right(\mathrm{OH}{)}_{\mathrm{4}}^{-}]\left[{\mathrm{H}}^{+}\right]}{({k}_{\mathrm{b}}+[{\mathrm{H}}^{+}\left]\right)}+\left[{\mathrm{H}}^{+}\right]+\left[{\mathrm{OH}}^{-}\right]$ and
${\stackrel{\mathrm{\u203e}}{\mathrm{Alk}}}_{\mathrm{c}}=\left[{\mathrm{HCO}}_{\mathrm{3}}^{-}\right]+\mathrm{2}\left[{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}\right]$. The explicit *T* and *S* partial derivatives are given in the Supplement (Text S1).
The first two derivatives coincide with the results of Egleston et al. (2010) and Hagens and Middelburg (2016),
with the exception of the sign of [OH^{−}] in the Egleston et al. (2010) term *S*.
To verify this approach we compared the sum of the Taylor expansion terms with the full simulated
range of *δ**p*CO_{2}
from the model's output. The Taylor expansion reproduces the full seasonal cycle amplitude of the original
climate model simulations well (Fig. S1 in the Supplement). The analytical expressions for temperature and
salinity presented here
are – to our knowledge – the first ones of their kind. Previously the calculation of these terms was based on the
approximation given by Takahashi et al. (1993) or on numerical calculations.

To gain more insight into the processes causing the amplification of
*δ**p*CO_{2} we introduce a method based on a
second Taylor series expansion described below. Equation (1) can be
rewritten using the expressions for the sensitivities *γ*
determined by the relation $\frac{\mathrm{1}}{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}}\frac{\partial p{\mathrm{CO}}_{\mathrm{2}}}{\partial \mathrm{X}}={\mathit{\gamma}}_{\mathrm{X}}$. These sensitivities have been historically
used to represent the percentage of change in *p*CO_{2} per unit
of DIC, TA, *T*, or *S*. With this notation, Eq. (1) can be
expressed in the following way.

$$\begin{array}{ll}{\displaystyle}\mathit{\delta}p{\mathrm{CO}}_{\mathrm{2}}\approx & {\displaystyle}\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot \left({\mathit{\gamma}}_{\mathrm{DIC}}\cdot \mathit{\delta}{\mathrm{DIC}}_{\mathrm{s}}+{\mathit{\gamma}}_{\mathrm{TA}}\cdot \mathit{\delta}{\mathrm{TA}}_{\mathrm{s}}+{\mathit{\gamma}}_{\mathrm{T}}\right.\\ \text{(5)}& {\displaystyle}& {\displaystyle}\left.\cdot \phantom{\rule{0.125em}{0ex}}\mathit{\delta}T+{\mathit{\gamma}}_{{S}_{\mathrm{fw}}}\cdot \mathit{\delta}{S}_{\mathrm{fw}}\right)\end{array}$$

Each term in Eq. (5) consists of three parts:
$\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$, the sensitivity *γ*_{X}, and the
corresponding seasonal cycle *δ**X*. To understand which
component is the main driver for *δ**p*CO_{2} changes, we
perform a second Taylor expansion of the end of the century's *δ**p*CO_{2} around the initial state of the system in 2006–2026.

To maximize mathematical clarity we will introduce some definitions: first,
we introduce the symbol Δ to indicate the difference between
the period 2080–2100 and 2006–2026. Therefore, the total future change in
*δ**p*CO_{2} is now referred to as
Δ*δ**p*CO_{2}. In the same manner, the total changes in
sensitivities and seasonal cycles are written as
$\mathrm{\Delta}{\mathit{\gamma}}_{\mathrm{DIC}{}_{\mathrm{s}},\mathrm{\Delta}{\mathit{\gamma}}_{\mathrm{TA}{}_{\mathrm{s}}},\mathrm{\Delta}{\mathit{\gamma}}_{\mathrm{T}},\mathrm{\Delta}{\mathit{\gamma}}_{\mathrm{S}{}_{\mathrm{fw}}}}$ and $\mathrm{\Delta}\mathit{\delta}{\mathrm{DIC}}_{\mathrm{s}},\mathrm{\Delta}\mathit{\delta}{\mathrm{TA}}_{\mathrm{s}},\mathrm{\Delta}\mathit{\delta}T,\mathrm{\Delta}\mathit{\delta}{S}_{\mathrm{fw}}$, respectively. Finally, we
introduce the vector ** X** formed by the four variables
DIC

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}\mathrm{\Delta}\mathit{\delta}p{\mathrm{CO}}_{\mathrm{2}}=\phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\sum _{k=\mathrm{0}}^{\mathrm{3}}{{\mathit{\gamma}}_{{X}_{k}}}^{i}\cdot \mathit{\delta}{{X}_{k}}^{i}\\ {\displaystyle}& {\displaystyle}+{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}}^{i}\sum _{k=\mathrm{0}}^{\mathrm{3}}\mathrm{\Delta}{\mathit{\gamma}}_{{X}_{k}}\cdot \mathit{\delta}{{X}_{k}}^{i}\\ {\displaystyle}& {\displaystyle}+{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}}^{i}\sum _{k=\mathrm{0}}^{\mathrm{3}}{{\mathit{\gamma}}_{{X}_{k}}}^{i}\cdot \mathrm{\Delta}\mathit{\delta}{X}_{k}\\ {\displaystyle}& {\displaystyle}+\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\sum _{k=\mathrm{0}}^{\mathrm{3}}\mathrm{\Delta}{\mathit{\gamma}}_{{X}_{k}}\cdot \mathit{\delta}{{X}_{k}}^{i}\text{(second-order\hspace{0.17em}\hspace{0.17em}terms)}\\ {\displaystyle}& {\displaystyle}+\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\sum _{k=\mathrm{0}}^{\mathrm{3}}{{\mathit{\gamma}}_{{X}_{k}}}^{i}\cdot \mathrm{\Delta}\mathit{\delta}{X}_{k}\\ \text{(6)}& {\displaystyle}& {\displaystyle}+{\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}}^{i}\sum _{k=\mathrm{0}}^{\mathrm{3}}\mathrm{\Delta}{\mathit{\gamma}}_{{X}_{k}}\cdot \mathrm{\Delta}\mathit{\delta}{X}_{k},\end{array}$$

where the first, second, and third terms represent the contributions to
Δ*δ**p*CO_{2} due to changes in the mean
*p*CO_{2} ($\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$), the
*p*CO_{2} sensitivities ($\mathrm{\Delta}{\mathit{\gamma}}_{X{}_{k}}$), and the
seasonal cycles (Δ*δ**X*_{k}), respectively; the fourth to
sixth rows are the second-order terms. This method is similar to the one used
by Landschützer et al. (2018).

3 Results and discussion

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Figure 1a shows the ensemble mean
*δ**p*CO_{2} amplitude (calculated as climatological
maximum minus minimum) for the initial period 2006–2026. The values range
from ≈98 µatm for the high latitudes
(40–70^{∘} S, 40–60^{∘} N) to
≈60 µatm between 40^{∘} S and 40^{∘} N. The
ensemble mean initial seasonal amplitude range is in good agreement with
observational estimates calculated for the reference year 2005
(Takahashi et al., 2014b) and for the 1982–2015 period (Landschützer et al., 2017).
The agreement between models and observations is remarkably good in the
equatorial regions, but the initial amplitude is slightly overestimated in
the middle and high latitudes (see Fig. S3 in the Supplement). The higher amplitude
in models than observations is expected, as the initial period 2006–2026
already experienced an amplification compared to previous years. Moreover,
Tjiputra et al. (2014) found that the ocean's *p*CO_{2} historical
trend is larger in models than observations when it is estimated in large-scale areas of the ocean. However,
they found that model
*p*CO_{2} trends agree with observations when the trends are
subsampled to the locations where the observations were taken, and therefore
they do a good job of reproducing well-known time series. Moreover, differences
are expected as Pilcher et al. (2015) suggested that CMIP5 models perform well in
reproducing the seasonal cycle timing, but still show considerable errors in
reproducing the seasonal amplitude of *p*CO_{2} due to
differences in the mechanisms represented in each model, especially in
subpolar biomes.

By 2080–2100 the annual cycle amplitude attains values of ≈197 and ≈101 µatm in the high and middle to low
latitudes, respectively (Fig. 1b). These seasonal variations
correspond to 20 % and 18 % of annual $\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ for the
initial and final periods, respectively. Figure 1c shows
that the global ocean *δ**p*CO_{2} will intensify by a
factor of 1.5 to 3 for the 2080–2100 period relative to the 2006–2026
reference period. Figure 1d shows the difference in
amplitude (Δ*δ**p*CO_{2}); this pattern differs from the
ratio because the ratio overestimates the amplification in areas where the
initial amplitude is lower than ≈10 µatm.
McNeil and Sasse (2016) used observations and a neural-network clustering algorithm
to project that by the year 2100, the *δ**p*CO_{2} amplitude in
some regions could be up to 10 times larger than it was in the year 2000. Our
mean amplification factor estimation agrees with the mean threefold
amplification found for most of the ocean by McNeil and Sasse (2016). However, the
high values in this previous study cannot be reproduced here, mainly
because we consider 21-year average ratios instead of single-year ratios,
which are strongly affected by interannual variability. Using observations,
Landschützer et al. (2018) found an increase of 2.2 µatm per decade, which is
smaller than our findings of a total 42 µatm increase by the end of the
century between 40^{∘} S and 40^{∘} N and a global mean change
of 81 µatm on the high latitudes. This difference is again possibly due
to the higher mean *p*CO_{2} values in models than observations.

The global ocean mean amplification factor of *δ**p*CO_{2}
roughly coincides with a doubling of $\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ (Fig. 2). The direct relationship between these two is explained in
Sect. 3.5. Figure 1e–h show the zonal mean
of Fig. 1a–d; in general, towards the end of the century the
*p*CO_{2} amplifies more in high latitudes, but so does the
standard deviation uncertainty among models. This regional pattern agrees
with the observation-based findings of Landschützer et al. (2018), which show that
high latitudes have already experienced a larger amplification than middle to low
latitudes from 1982 to 2015. Furthermore, the same pattern is projected by
CMIP5 models for the seasonal amplification of [H^{+}] by the end of the
century (Kwiatkowski and Orr, 2018). This is expected from the near-linear relation
between *p*CO_{2} and [H^{+}]. These regional differences in
amplification for *p*CO_{2} can be explained in terms of the
relative magnitudes and the phases between the DIC, TA, *T*, and *S* contributions, which are explained in subsequent sections.

To understand the driving factors of *δ**p*CO_{2} and its
spatiotemporal differences, we split *δ**p*CO_{2} into the
four different contributions from DIC_{s}, TA_{s}, *T*, and
*S*_{fw} for the initial and final periods, following Eq. (1). The results are shown in Fig. 3. For most of
the ocean, the ensemble mean estimated contributions from DIC_{s}
and *T* to the present-day *δ**p*CO_{2} are in good agreement
with the data-based estimates of Takahashi et al. (2014b) and
Landschützer et al. (2017), particularly in the equatorial regions (see
Fig. S3 in the Supplement). However, our *T* and DIC contributions are slightly
larger in middle and high latitudes for the same reasons the
*p*CO_{2} seasonal amplitude is overestimated (see Sect. 3.1).
Also, differences arise between our DIC_{s} contribution and the
observation-based so-called “nonthermal” contribution because the
nonthermal contribution also includes the total alkalinity and salinity
effects. Nonetheless, between 40^{∘} S and 40^{∘} N our ensemble
mean shows that *δ**p*CO_{2} is dominated by changes in
temperature that control CO_{2} solubility, which decreases in summer,
enhancing *p*CO_{2}; this is in agreement with observations. The Southern
Ocean is controlled by DIC, which responds to changes in upwelling and
phytoplankton blooms. Both mechanisms act together to decrease (increase) DIC
in summer (winter) (Sarmiento and Gruber, 2006).

The models show that the *δ**p*CO_{2} in the
40^{∘} N to 60^{∘} N band is controlled by *T*, which disagrees
with the abovementioned observations that show a non-temperature dominance
in this band. The difference between models and observations arises from two
regions: the North Atlantic basin and the northwestern Pacific, specifically
near the Oyashio current and the outflows from the Sea of Okhotsk (see
Fig. S3 in the Supplement). Most models show a *T* dominance in the North Atlantic
basin; only CESM1-BGC and GFDL-ESM2M show a DIC dominance (see
Fig. S4 in the Supplement). The North Atlantic is one of the major sinks of anthropogenic
CO_{2}; however, some models fail to estimate its uptake capacity
(Goris et al., 2018). Goris et al. (2018) found that models with an efficient carbon
sequestration present a DIC-dominated *p*CO_{2} seasonal cycle in
the North Atlantic, but models with low anthropogenic uptake show a *T* dominance in this region.
In the northwestern Pacific, Mckinley et al. (2006)
found that coarse models are not able to capture the intricate oceanographic
features of this area, and therefore the *p*CO_{2} seasonality is
not well captured.

Towards the end of the century (Fig. 3, right column), the
amplification of *δ**p*CO_{2} is caused by an
increase in the DIC_{s} and *T* contributions and to a lesser extent
due to TA_{s} and S_{fw}. Only in the high latitudes does the
TA_{s} contribution reinforce the DIC_{s} effect. The
*δ*DIC_{s} and *δ**T* relative phase and magnitude play an
important role in causing regional differences of future
*δ**p*CO_{2}. For example, between
40 and 60^{∘}, we find a lower amplification factor than at
30–40^{∘} in both hemispheres (Fig. 1c), contrary to what we expected from the general observed larger
amplification at higher latitudes. In this band of lower amplification, the
warm water from subtropical regions meets the nutrient-rich water from the
subpolar regions, but the DIC_{s} and *T* effects are almost 6 months
out of phase, and therefore their cancellation is larger than in the
30–40^{∘} latitude band where, for example, in the
North Atlantic, there is 9-month phase difference between the two contributions.
A clear illustration of this phase effect is found in the Supplement (Fig. S5).

In the Southern Ocean there is a shift in the maximum
*δ**p*CO_{2} occurring from August–September to March–April
(Fig. 3, last row). This shift is generated because the *T* contribution gains
importance over DIC_{s} due to a reduction of
*δ*DIC_{s} magnitude at the same time that *δ**T* increases
(Fig. 5). In the equatorial Pacific region (Fig. 5), *T* dominates
over DIC_{s} but both contributions are
small due to their low seasonality. Therefore, this region will experience a
low amplification in *δ**p*CO_{2}. In this region some
models underestimate the *p*CO_{2} trend (Tjiputra et al., 2014), and
therefore the seasonal amplification might be underestimated too. In the
following sections we conduct further analysis by decomposing each
contribution as the result of three factors: the mean *p*CO_{2}
($\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$), the regional *p*CO_{2}
sensitivities (*γ*_{DIC}, *γ*_{TA},
*γ*_{T},
and ${\mathit{\gamma}}_{{S}_{\mathrm{fw}}}$), and the seasonal cycles (*δ*DIC_{s},
*δ*TA_{s}, *δ**T*, and *δ*S_{fw}) as
determined in Eq. (5).

The *γ*_{DIC} and *γ*_{TA} are projected to
increase by the end of the century due to a lower ocean buffering capacity
produced by increasing temperature and larger background concentrations of
DIC (Fassbender et al., 2017). This agrees with our results shown in Fig. 4,
which shows that all regions will experience an increase in
*γ*_{DIC} and *γ*_{TA}. Lower buffer factors
(higher sensitivities factors) are found in regions where DIC and TA have
similar values, and they will decrease (increase) as the DIC ∕ TA ratio in the
oceans increases (Egleston et al., 2010). The alkalinity sensitivity is negative,
as *p*CO_{2} decreases with increasing alkalinity, but we show
here the negative *γ*_{TA} for better comparison.
*γ*_{TA} will increase (with negative values) more than the DIC
sensitivity. However, seasonal changes in open-ocean TA_{s} are
small, and therefore the total contribution of alkalinity in our analysis is
negligible compared to the DIC_{s} and *T* contributions.
${\mathit{\gamma}}_{{\mathrm{S}}_{\mathrm{fw}}}$ decreases everywhere except in the Western Pacific
Warm Pool. In this region ${\mathit{\gamma}}_{{\mathrm{S}}_{\mathrm{fw}}}$ increases, probably due
to future changes in precipitation that enhance the freshwater effect. In
Fig. 4, the sensitivities (*γ*) are expressed as a
percentage change in *p*CO_{2} per unit in DIC, TA, *T*, and *S*, respectively. This follows the approach of Takahashi et al. (1993); however, in
their paper the authors compute the Revelle factor, which is related to
*γ*_{DIC} as $R=\mathrm{DIC}\cdot {\mathit{\gamma}}_{\mathrm{DIC}}$. To illustrate
the meaning of the sensitivities, we will focus on the subtropical North
Pacific in the 15–40^{∘} N latitudinal band. In this
region *γ*_{DIC} indicates an average 0.6 % change in
*p*CO_{2} per unit of DIC in 2006–2026. Therefore, for a
*δ*DIC_{s} seasonal cycle amplitude of 40 µmol kg^{−1} and $\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\approx \mathrm{400}$ µatm,
the total *δ**p*CO_{2} amplitude equals
96 µatm. Following the same reasoning, by 2080–2100,
*γ*_{DIC} increases to 0.7 % and *δ*DIC_{s}
decreases to 30 µmol kg^{−1}; therefore, for a
$\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ equal to 800 µatm, the
*δ**p*CO_{2} amplitude due to *δ*DIC amounts to 168 µatm.

Temperature sensitivity has been experimentally determined by Takahashi et al. (1993), who found a value of 0.0423, meaning that
*p*CO_{2} changes by about 4 % for every ^{∘}C. This
value agrees with our global mean ensemble estimate of 0.0428. However, our
analytical expression of *γ*_{T} shows that this value varies regionally
and, for reasons unknown to us, it might decrease in the future to a global
mean value of 0.0415 (Fig. 4c, third column). The *T* sensitivity is larger in colder
regions and lower in the warmer tropics;
however, colder regions will experience a larger reduction in
*γ*_{T}, which locally prevents a larger amplification of the *T* contribution to *δ**p*CO_{2}. In the next section
we show that the *T* seasonality is projected to increase in high latitudes,
strengthening the *T* contribution.

Towards the end of the century, the global mean amplitude of
*δ*DIC_{s} is projected to decrease by
≈26 %–28 % in the high latitudes
(Fig.5a), according to all the CMIP5 Earth system model
simulations used here. In the middle to low latitudinal band there is no agreement
between models; while some show an increase, others project a decrease in
amplitude. As suggested by Landschützer et al. (2018), the larger decrease in the
Southern Ocean may be the result of changes in the shallow overturning
circulation that prevent CO_{2} accumulation in this region. This reduction
may be counteracted by the predicted increase in productivity owing to a
suppression of light and temperature limitations (Bopp et al., 2013; Steinacher et al., 2010).

According to the CMIP5 models, most of the ocean is projected to experience a
slight increase in *δ**T*, as shown in Fig. 5b.
All models show a slight increase in *δ**T*; only one model showed a
slightly decrease in the southern region, and two models showed a decrease in
the equatorial region during October to December. It is important to note
that Fig. 5 shows the seasonal values with the mean *T* removed.
Therefore, when considering the positive *T* trends, the absolute summer values
show an increase and the absolute winter values a decrease. This agrees with
the results of Alexander et al. (2018), who showed that models project a seasonal
intensification of *T* with larger warm extremes and reduced cold extremes.
The authors attributed the *T* seasonality intensification to an increased
oceanic stratification and an overall shoaling of the mixed layer depth,
which confines seasonal changes in a reduced volume of water, producing
larger changes at the surface. They also showed that the intensification
trends are stronger in summer than winter, as the mixed layer depth is
shallower in summer. Moreover, ice-covered regions will experience the
largest increase in *T* seasonality due to the loss of sea ice because the ice
melting and freezing moderates the surface water temperature
seasonality (Carton et al., 2015).

The TA seasonality is also projected to increase in the high latitudes
according to all models, except CESM1-BGC, which shows a decrease. For
*δ**S* (see Fig. S6 in the Supplement) there is no agreement among
the different CMIP5 models, except in the Southern Ocean where all the models
show a slight decrease. Kwiatkowski and Orr (2018) demonstrated that the
seasonality of the drivers is important to determine future changes in
[H^{+}] seasonality. In the same fashion, our results show that the
four *δ**p*CO_{2} drivers present changes in
seasonality, and in particular *δ*DIC_{s} and *δ**T* changes
are important to explain future projections of the
*δ**p*CO_{2} amplitude. The increase in *δ**T* enhances
the *δ**p*CO_{2} amplification, and the reduction of
*δ*DIC_{s} in the Southern Ocean locally prevents a larger
amplification.

To identify the main cause of the *δ**p*CO_{2} amplification we
use the Taylor series expansion method. With this method we consider the
system's final state (*δ**p*CO_{2} by 2080–2100) as
a perturbation of the initial state (*δ**p*CO_{2}
by 2006–2026), as shown in Eq. (6). The expansion is done
in three groups of variables: the seasonal cycles of DIC_{s},
TA_{s}, *T*, and *S* (*δ**X*), the sensitivities of
*p*CO_{2} to the same four variables (*γ*_{x}), and
the mean *p*CO_{2} ($\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$). Therefore, each
term of the expansion represents how much of the total
*δ**p*CO_{2} change (indicated by
Δ*δ**p*CO_{2} and calculated as the 2080–2100 value
minus the 2006–2026 value) is due to the change in each of these factors. We also
add the second-order terms that come from their combination. The results are
shown in Fig. 6a and they indicate that the leading cause of
the *δ**p*CO_{2} amplification is the change in
$\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ ($\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$), which
confirms previous findings by Landschützer et al. (2018).

It is important to note that our linear Taylor expansion approach neglects
one aspect of the highly nonlinear carbonate chemistry of the ocean: it
assumes $\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ and the sensitivities as independent
variables and therefore does not include the positive feedback between
larger $\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ and increasing *γ*_{DIC}
(decreasing buffering capacity). Hence in the following, we use changes in
$\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ and changes in seawater carbonate chemistry
synonymously, overall resulting in an enhanced response of *δ**p*CO_{2} to seasonal changes in DIC, TA, *T*, and *S*.

Considering regional differences, we note that amplification increases as
we move poleward in spite of decreasing $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$
(see Figs. 1 and 2). This characteristic
geographical pattern of stronger high-latitude amplification is the result of
larger present-day sensitivities (${\mathit{\gamma}}_{\mathrm{DIC}{}_{\mathrm{s}}}$,
*γ*_{T}) and seasonal amplitudes
(*δ*DIC_{s}, *δ**T*) in the high latitudes that
amplify the effect of $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ even when its value
is small compared to other regions (see Eq. 6, first
row term). Some exceptions can be found south of Greenland and near the
subtropical gyres, where $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ reaches higher
values and therefore also presents large amplification. We also found
spatial differences on smaller scales; for example, the western equatorial
Pacific presents lower initial *δ**p*CO_{2} and
amplification than the eastern equatorial Pacific (see Fig. 1).
This is because the eastern side of the basin has larger DIC_{s} and
*T* contributions than the western side (see Fig. S2) as a
consequence of the upwelling of cold, CO_{2}-rich waters in the east, which
lower the buffering capacity and induce larger *δ**p*CO_{2}
amplitude due to the seasonal effects of productivity and solubility
(Valsala et al., 2014).

To further disentangle which of the two main drivers (DIC_{s} or *T*)
is most affected by $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$, we decomposed the
DIC_{s} and *T* contributions into their sensitivity, seasonal cycle, and
$\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ components. Figure 6b shows the
total DIC and *T* components together with the
$\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ and seasonal cycle effects on them. The
effects from the sensitivities are not depicted, as they only play a minor
role. Only the Δ*γ*_{DIC} term gains importance in the
Southern Ocean (not shown). In most of the ocean, the
$\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ effect on *T* contribution is the leading
cause of amplification. This effect is the result of seasonal solubility
changes acting over a larger [CO_{2}] (Gorgues et al., 2010). In the northern high
latitudes, an increase in *δ**T* reinforces the amplification. In
general, the Δ*δ**T* contribution gains importance as we
move poleward in both hemispheres and therefore the second-order terms
originating from $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}\cdot \mathrm{\Delta}\mathit{\delta}T$ also
reinforce the amplification. Interestingly, in the high latitudes, the
amplification through second-order terms is as important as the change in the
seasonality of the drivers.

The Southern Ocean is an exception to the *T* dominance; in this region the
$\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{p{\mathrm{CO}}_{\mathrm{2}}}$ effect on the DIC_{s} contribution
dominates, and the regional amplification is reinforced by low values of the
mean buffering capacity (high ${\mathit{\gamma}}_{\mathrm{DIC}{}_{\mathrm{s}}}$). This result agrees
with the findings of Hauck and Völker (2015). In this area the amplification is
counteracted by a reduction in *δ*DIC_{s}.

4 Conclusions

Back to toptop
In this study, we used output from seven CMIP5 global models, subjected to the
RCP8.5 radiative forcing scenarios, to provide a comprehensive analysis of
the characteristics and drivers of the intensification of the seasonal cycle
of *p*CO_{2} between present (2006–2026) and future (2080–2100)
conditions. By 2080–2100 the *δ**p*CO_{2} will be 1.5–3
times larger compared to 2006–2026. The projected amplification by the
Earth system models and the possible causes of it are consistent with
observation-based amplification for the period from 1982 to 2015
(Landschützer et al., 2018). However, the models slightly overestimate the present-day amplification, probably due to the larger *p*CO_{2} trends in
models than observations (Tjiputra et al., 2014).

The models confirm the well-established mechanisms controlling present-day
*δ**p*CO_{2} (Fay and McKinley, 2017; Sarmiento and Gruber, 2006; Takahashi et al., 2002).
DIC_{s} and *T* contributions are the main counteracting terms
dominating the seasonal evolution of *δ**p*CO_{2}.
Furthermore, the models show that under future conditions the controlling
mechanisms remain unchanged. This result confirms the findings of
Landschützer et al. (2018) that identified the same regional controlling mechanism
for the past 30 years. The relative role of the DIC and *T* terms is regionally
dependent. High latitudes and upwelling regions, such as the California
current system and the coast of Chile, are dominated by DIC_{s} and
the temperate low latitudes are driven by *T*. Only in the North Atlantic and
northwestern Pacific do the models show a dominance of thermal effects over
nonthermal effects, which is in disagreement with observations. This further
illustrates the urgent need for models to accurately represent regional
oceanographic features to accurately reproduce the
*δ**p*CO_{2} characteristics.

In agreement with Landschützer et al. (2018), the model projections towards
the end of this century also demonstrate that the global amplification of
*δ**p*CO_{2} is due to the overall long-term
increase in anthropogenic CO_{2}. A higher oceanic background CO_{2}
concentration enhances the effect of *T*-driven solubility changes on
*δ**p*CO_{2} and alters the seawater carbonate chemistry,
also enhancing the DIC seasonality effect. The spatial differences of
*δ**p*CO_{2} amplification, however, are determined
by the regional sensitivities and seasonality of *p*CO_{2}
drivers. For example, polar regions show larger sensitivity to DIC and *T* and
larger seasonal cycles of DIC and *T*. Therefore, these areas present a strong
enhancement of *δ**p*CO_{2} in spite of smaller
changes in mean *p*CO_{2}.

Moreover, the *p*CO_{2} seasonal cycle amplitude depends on the
relative magnitude and phase of the contributions. The models ensemble mean
reproduces the highly effective compensation of DIC_{s} and *T* contributions when they are 6 months out of phase, confirming previous
studies (Landschützer et al., 2018; Takahashi et al., 2002). The compensation of DIC and *T* prevents a larger amplification of *δ**p*CO_{2},
even when both contributions are largely amplified.

The amplification of the TA and *S* contributions has a small impact on
*δ**p*CO_{2} in most regions, except in the high
latitudes at which the TA contribution complements the DIC one, enhancing the
nonthermal effect in this region.

The use of Earth system models allowed us to state the importance of
including future changes in driver seasonalities for future
*δ**p*CO_{2} projections. The *T* seasonality is
projected to increase in most of the ocean basins, thereby reinforcing the
*δ**p*CO_{2} amplification. The *δ**T*
increase is consistent with an increase in stratification that will confine
the seasonal changes in net heat fluxes to a shallower mixed layer
(Alexander et al., 2018). The DIC_{s} seasonality decreases in some cold
areas and its reduction prevents a larger amplification. For the
sensitivities, while *γ*_{DIC} increases, *γ*_{T} decreases. The
latter phenomenon needs further study.

The increasing amplitude of *δ**p*CO_{2} might have
implications for the net air–sea flux of CO_{2}, in particular in regions
where there is an imbalance between winter and summer values
(Gorgues et al., 2010). Examples of such behavior can be found in the Southern
Ocean (between 50 and 60^{∘} S) (Takahashi et al., 2014a) and in the
latitude band from 2–40^{∘} in both hemispheres
(Landschützer et al., 2014). Moreover, seasonal events of high
*p*CO_{2} could have an impact on acidification, aragonite
undersaturation events (Sasse et al., 2015), and hypercapnia conditions
(McNeil and Sasse, 2016). Therefore, understanding the drivers of future
*δ**p*CO_{2} may help to better assess the response
of marine ecosystems to future changes in carbonate chemistry. Finally, our
complete analytical expansion of *δ**p*CO_{2} in terms of
its four variables provides a practical tool to accurately and quickly
diagnose temperature and salinity sensitivities from observational or
modeling data sets.

Data availability

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Data availability.

The CMIP5 data used in the analysis were obtained from
https://esgf-node.llnl.gov/projects/esgf-llnl/ (last access: June 2017; Taylor et al., 2012).
The Landschützer et al. (2017)
*p*CO_{2} data product is available at
https://www.nodc.noaa.gov/archive/arc0105/0160558/3.3/data/0-data/ (last
access: May 2018); *p*CO_{2} data estimates from
Takahashi et al. (2014b) were obtained at
http://cdiac.ess-dive.lbl.gov/ftp/oceans/NDP_094/ (last access: May
2018).

Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/bg-15-5315-2018-supplement.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

Back to toptop
Acknowledgements.

This work was supported by the National Science Foundation under grant no.
1314209 and by the Institute for Basic Science (IBS), South Korea, under
IBS-R028-D1. We thank Peter Landschützer for kindly providing his data sets
of thermal and nonthermal components of the *p*CO_{2} seasonal
cycle.

Edited by: Katja Fennel

Reviewed by: two anonymous referees

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Short summary

It is projected that the summer–winter difference in *p*CO_{2} levels will be larger in the future. In this paper, we study the causes of this seasonal amplification of *p*CO_{2}. We found that anthropogenic CO_{2} enhances the effect of seasonal changes in temperature (*T*) and dissolved inorganic carbon (DIC) on *p*CO_{2} seasonality. This is because the oceanic *p*CO_{2} becomes more sensitive to seasonal *T* and DIC changes when the CO_{2} concentration is higher.

It is projected that the summer–winter difference in *p*CO_{2} levels will be larger in the future....

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