Biogeosciences Does atmospheric CO 2 seasonality play an important role in governing the air-sea flux of CO 2 ?

The amplitude, phase, and form of the seasonal cycle of atmospheric CO 2 concentrations varies on many time and space scales ( Peters et al. , 2007). Intra-annual CO2 variation is primarily driven by seasonal uptake and release of CO2 by the terrestrial biosphere ( Machta et al. , 1977; Buchwitz et al., 2007), with a small (Cadule et al. , 2010; Heimann et al., 1998), but potentially changing ( Gorgues et al. , 2010) contribution from the ocean. Variability in the magnitude, spatial distribution, and seasonal drivers of terrestrial net primary productivity (NPP) will be induced by, amongst other factors, anthropogenic CO 2 release ( Keeling et al. , 1996), land-use change ( Zimov et al., 1999) and planetary orbital variability, and will lead to changes in CO atm 2 seasonality. Despite COatm 2 seasonality being a dynamic and prominent feature of the Earth System, its potential to drive changes in the air-sea flux of CO2 has not previously (to the best of my knowledge) been explored. It is important that we investigate the impact of COatm 2 seasonality change, and the potential for carbon-cycle feedbacks to operate through the modification of the COatm 2 seasonal cycle, because the decision had been made to prescribe CO atm 2 concentrations (rather than emissions) within model simulations for the fifth IPCC climate assessment ( Taylor et al. , 2009). In this study I undertake ocean-model simulations within which different magnitude COatm 2 seasonal cycles are prescribed. These simulations allow me to examine the effect of a change in CO atm 2 seasonal cycle magnitude on the air-sea CO 2 flux. I then use an offline model to isolate the drivers of the identified air-sea CO 2 flux change, and propose mechanisms by which this change may come about. Three mechanisms are identified by which co-variability of the seasonal cycles in atmospheric CO 2 concentration, and seasonality in sea-ice extent, wind-speed and ocean temperature, could potentially lead to changes in the air-sea flux of CO2 at mid-to-high latitudes. The sea-ice driven mechanism responds to an increase in CO atm 2 seasonality by pumping CO2 into the ocean, the wind-speed and solubility-driven mechanisms, by releasing CO 2 from the ocean (in a relative sense). The relative importance of the mechanisms will be determined by, amongst other variables, the seasonal extent of sea-ice. To capture the described feedbacks within earth system models, CO atm 2 concentrations must be allowed to evolve freely, forced only by anthropogenic emissions rather than prescribed CO atm 2 concentrations; however, time-integrated ocean simulations imply that the cumulative net air-sea flux could be at most equivalent to a few ppm COatm 2 . The findings presented here suggest that, at least under pre-industrial conditions, the prescription of COatm 2 concentrations rather than emissions within simulations will have little impact on the marine anthropogenic CO2 sink.


Introduction
Rapid cooling, high biological activity, strong winds, and the pumping of surface waters to depth, make the high latitude oceans the planet's major atmospheric CO 2 sinks (Takahashi et al., 2009).Variability in the strength of these sinks is known to be large, but is presently poorly understood (e.g. Watson et al., 2009;Le Quere et al., 2007).Photosynthesis within the large, and extensively vegetated land masses of North America and Eurasia drive a major spring-summer CO 2 uptake in the Northern Hemisphere, with leaf fall and breakdown causing a compensating CO 2 release during autumn and winter (Machta et al., 1977).In high northern latitudes the amplitude of the CO atm P. R. Halloran: CO 2 seasonality and air-sea flux exceeds 15 ppm (Peters et al., 2007), and has increased significantly (+40 % between 1960's and 1990's) over recent years (Keeling et al., 1996).The sign of this change is consistent with the observed lengthening and intensification of the growing season and associated increase in net primary production, occurring in response to warming (White et al., 1999;Goulden et al., 1996), rising concentrations of atmospheric CO 2 (Lewis et al., 2004), and local increases in solar radiation intensity (Graham et al., 2003).Seasonality changes are also a potential driver of glacial-interglacial cyclicity (e.g.Gildor and Tziperman, 2000;Denton et al., 2005), as suggested by the close statistical coupling between variability in the Earth's obliquity, and glacial terminations (Huybers and Wunsch, 2005).High obliquity means high intra-annual variability in high-latitude insolation, and appears to be a precondition for deglaciation (Loutre et al., 2004;Huybers and Wunsch, 2005;Liu et al., 2008).To understand past change, and robustly investigate potential future change, we must therefore understand whether or not interactions between seasonality and the global carbon cycle can have a significant impact on the ocean sink.This challenge is of particular relevance right now because the decision has been made to prescribe CO atm 2 concentrations, rather than emissions, within the main Earth System Model simulations anticipated to contribute to the fifth IPCC climate assessment (Taylor et al., 2009).This decision has been made for good reason, because significant difficulties arise when attempting to undertake multi-model analysis of experiments with interactive carbon cycles seeing only common CO 2 emissions; each model will simulate a different evolution of the CO 2 airborne fraction, meaning that different models will experience different CO 2 radiative forcing histories.Despite being done for very sensible reasons, it is important to understand any potential implications of following this approach.One of the implications will be that the bulk of CMIP5 (5th Climate Model Intercomparison Project) experiments will not simulate or experience any seasonality in atmospheric CO 2 concentrations (Taylor et al., 2009).In this paper I explore the consequences of changes in CO atm 2 seasonality, examining conditions with no seasonal cycle, a preindustrial seasonal cycle, and twice the pre-industrial seasonal cycle.I first explore the air-sea flux change occurring in response to a change in CO atm 2 seasonality by running a physical-biogeochemical ocean model (the ocean component of the HadGEM2-ES Earth System Model -see Sect.2) with different CO atm 2 seasonal cycles.I then show that much of the air-sea CO 2 flux change resulting from a change in CO atm 2 seasonality can be reproduced within off-line calculations, and is therefore not governed by time-dependent processes, such as transport of carbon within the ocean.By holding variables constant within the off-line calculations, I identify the components of the system responsible for the seasonalitydriven change in air-sea flux, and go on to suggest mechanism by which these changes could occur.Finally I quantify the net impact of a change in CO atm 2 seasonal cycle magni-tude on the air-sea CO 2 flux, and consider the importance of simulating these processes interactively in climate-change simulations.

Methods
All calculations and simulations presented in this study are undertaken using, or using equations from components of, the 2nd Hadley Centre General Environmental Model, with Earth System components (HadGEM2-ES, Collins et al., 2011).Importantly for this investigation, HadGEM2-ES simulates a fully interactive and coupled ocean and terrestrial biogeochemistry (The HadGEM2 Development Team, 2011;Collins et al., 2011), and a fully coupled and well validated sea-ice component (McLaren et al., 2006).Improvements (with respect to the 3rd Hadley Centre Climate Model with low resolution but carbon cycle components HadCM3-LC, Cox et al., 2000) to the leaf phenology (Cadule et al., 2010) within the model now allow for good reproduction of the CO atm 2 seasonal cycle (Collins et al., 2011) (Fig. 1).Improvements to the physical-ocean and oceanbiogeochemistry within HadGEM2-ES lead to good agreement between the modeled and observed spatial pattern of air-sea CO 2 flux (Fig. 2).
TRIFFID (Top-down representation of interactive foliage and flora dynamics), the terrestrial carbon cycle component of HadGEM2-ES, contains five plant functional types and five soil carbon pools (Cox, 2001).Vegetation change is driven by carbon fluxes, with photosynthesis and respiration dependent on the climate and atmospheric CO 2 concentrations.The ocean biogeochemistry of HadGEM2-ES is simulated by the Diat-HadOCC sub-model, an extension of the original Hadley Centre Ocean carbon Cycle model (HadOCC) (Palmer and Totterdell, 2001) now including a diatom functional type, silica and iron cycling and dimethylsulphide production (Halloran et al., 2010) in addition to the generic macronutrient, phytoplankton, zooplankton and detritus simulated in the original version of the model.
Within this study, air-sea fluxes of CO 2 have been calculated using the following approach, and using values from Nightingale et al. (2000): Where F is the air-sea CO 2 flux, P v the piston velocity (a function of the surface atmosphere wind speed), Sc the Schmidt number, a function of surface ocean temperature, and [CO 2 ] ocn and [CO 2 ] atm the concentration of CO 2 in the ocean and atmosphere in equilibrium with the surface ocean, respectively.Within this study, model formulations of two different levels of complexity (biogeochmical-physical ocean-model and off-line calculations) are used to identify and quantify the impact of changing CO 2 seasonality on ocean carbon uptake.(Peters et al., 2007).Seasonal cycle calculated from detrended monthly values and presented as an anomaly from the annual mean at that latitude.(b) Pre-Industrial latitudinally averaged surface atmospheric CO 2 seasonal cycle simulated in the HadGEM2-ES model when run with interactive carbon cycle components.For consistency with calculations presented in this study, only CO 2 concentrations above the ocean have been considered.Note that although the relative magnitude of changed described by the color scale is identical in both panels, the left panel shows anomalies from zero, and the right, absolute values.This has been done to allow comparison between pre-industrial and detrended present-day values.The left panel shows the observed seasonal cycle at each latitude as an anomaly from its annual mean of zero, whereas annually averaged values for any given latitude in the right panel are not necessarily identical.
Results from fully coupled (ocean-atmosphere Earth System Model) simulations are used only to provide driving variables for ocean-model and off-line calculations, and to provide reference values against which to analyse the simulated air-sea CO 2 flux change.Model configurations and CO atm 2 forcings are documented in Table 1.

Ocean model experiments
A set of four ocean-model experiments are used to examine whether a change in the atmospheric CO 2 seasonal cycle has a net impact on the air-sea CO 2 flux, then to calculate the time-integrated air-sea CO 2 flux occurring in response to this change.Here the ocean component of HadGEM2-ES was run with monthly physical surface flux forcing data taken from the fully coupled pre-industrial control run (see below), are averaged to produce a repeating 12 monthly cycle.The atmospheric CO 2 concentrations seen by these experiments are transformations of the CO atm 2 simulated by the HadGEM2-ES model when run under pre-industrial forcings with a fully interactive ocean and terrestrial carbon cycle, and consequently where the CO atm 2 seasonal cycle is an emergent property of the model.Note that the temporal and spatial structure of CO atm 2 variability simulated by the Earth System Model compares well with that observed in the real world (Fig. 1).Manipulation of the seasonal cycle of CO atm 2 were achieved by multiplying the difference between individual monthly CO atm 2 values and the annual average CO atm 2 con-centrations in each latitude-longitude box, by the specified factor (zero, one or two), and adding that to the annual mean value at that grid-point.Within this paper, "1× seasonal cycle" therefore refers to the seasonality simulated for the preindustrial period within the HadGEM2-ES model when run with fully interactive carbon cycle components (Fig. 1b), "0× seasonal cycle" refers to a situation without any temporal variability, and "2× seasonal cycle" considers the annual variability at each point to be twice that simulated for the pre-industrial period.The chosen seasonal cycle magnitudes represent conditions as they may be specified in Earth System Model simulations with CO 2 prescribed as in the bulk of CMIP5 experiments (Taylor et al., 2009), as they would be simulated by a fully interactive Earth System Model for the pre-industrial, and at an arbitrarily chosen value representing a significant increase over the pre-industrial seasonal cycle to ensure a clear signal.The global annual average CO atm 2 seen by all simulations is adjusted to be exactly 286 ppmv; the pre-industrial CO atm 2 concentration specified in the fixed CO 2 control simulation.

Offline experiments
Secondly, I take the surface ocean and atmosphere physical and chemical fields relevant to CO 2 exchange (ocean and atmospheric CO 2 concentration, temperature, salinity, windspeed and sea-ice concentration) from the HadGEM2

Fig. 2.
Comparison of latitudinally averaged (above ocean) airsea CO 2 fluxes calculated from an observation-derived climatology (Takahashi et al., 2009) (black), and from climate simulations using the HadGEM2-ES model (red).Earth system model simulations were forced using greenhouse gas, anthropogenic aerosol, volcanic aerosol, land-use change and solar cycle data from the years 1860-2005 (Taylor et al., 2009;Jones et al., 2011).The observation-based climatology has been calculated to represent the conditions in the year 2000, but to avoid sampling internal variability, the model results have been presented as a mean value from the years 1980-2000.The model's ensemble mean has been calculated as the average of three historical simulations started at 50 yr intervals from the pre-industrial control simulation, and is therefore considered to sample well the model's internal variability.prescribed external forcings), and undertake air-sea CO 2 flux calculations offline (based on Eq. 1).Within my offline calculations, I have varied the values relating to the atmospheric CO 2 concentration, to simulate an increased or decreased CO atm 2 seasonal cycle magnitude (relative to pre-industrial).The different magnitude CO atm 2 seasonal cycles were calcu-lated as described in Sect.2.1.The calculations undertaken for this part of the study vary from those undertaken within the fully coupled model only in that monthly mean input values, rather than daily mean values, for physical and chemical fields where supplied.In all situations, using monthly mean values instead of continuous seasonal cycles will decrease the seasonal cycle's total magnitude, and therefore the magnitude of the results can be considered conservative.The result from these offline calculations will represent an instantaneous value for the air-sea CO 2 flux immediately after the seasonality change, rather than an estimation of the net ocean-atmosphere carbon exchange occurring in response to a change in CO atm 2 seasonality.These offline calculations have been designed to facilitate exploration of the mechanisms at play rather than accurately simulating the real-world air-sea CO 2 flux response.

Coupled ocean-atmosphere earth system model experiments
Surface atmosphere and ocean conditions required by the ocean-model and off-line simulations were provided from a pre-industrial control simulation using the fully coupled interactive carbon-cycle configuration of HadGEM2-ES (Jones et al., 2011).A minimum of 270 yr of control run simulation were used to produce all monthly and annual means.
Where comparisons are made to the mean or standard deviation of the air-sea CO 2 flux simulated by the fully coupled Earth System model, the standard pre-industrial CMIP5 setup in which atmospheric CO 2 concentrations are specified at 286 ppmv throughout the year at every grid-point has been used.The decision to benchmark change against the prescribed atmospheric CO 2 concentration simulation was made because by definition these experiments will not contain feedbacks occurring in response to CO atm 2 seasonal cyclicity., 9, 2311-2323,  seasonal cycle amplitude on the air-sea flux of CO 2 calculated as averages over the first perturbed year of ocean-model simulations (solid black and red lines), and instantaneously after the CO atm 2 perturbation using off-line calculations (dashed black and red lines).CO 2 air-sea flux difference calculated between the model's preindustrial atmospheric CO 2 seasonal cycle and a situation with no seasonal cycle (black), and between two times the model's preindustrial atmospheric CO 2 seasonal cycle and a situation with no seasonal cycle (red).Positive values represent a relative flux into the ocean.It can be seen that by increasing the seasonal cycle magnitude (but keeping the annually averaged value at individual points, and therefore globally, constant), the ocean takes up additional CO 2 in the mid-to-high latitudes, and takes up less CO 2 in the high latitudes.The enhanced relative CO 2 in-and out-gassing occurring in the mid and high Northern Hemisphere is a response to the larger seasonal cycle of atmospheric CO 2 in this hemisphere, and a tighter coupling between wind-speed, ocean CO 2 solubility, sea-ice change and atmosphere CO 2 concentration seasonality (see Figs. 8, 9 and 7 and accompanying text), relative to that in the low latitudes and Southern Hemisphere.The model-simulated latitudinally averaged pre-industrial air-sea flux of CO 2 is plotted in the dotted gray line for reference.Note the order of magnitude of increase in scale when considering the absolute air-sea flux, compared to that used for changes in flux.

Biogeosciences
Non-pre-industrial climate simulations have only been used for comparison of model-simulated air-sea fluxes with an observation-based climatology (Fig. 2).These simulations were undertaken according to the CMIP5 protocol, as described in Jones et al. (2011), and experience anthropogenic greenhouse gas and aerosol emissions and anthropogenically generated changes in land-use as well as natural volcanic and solar forcings.All coupled Earth System Model simulations used in this study are freely available from www.earthsystemgrid.org.

Results
The global spatial variability in the air-sea flux of CO 2 (Takahashi et al., 2009) highlighted here latitudinally (Fig. 2 black line) reflects a complex interplay of physical and biological processes.In a pre-industrial world, carbon would have been passed from the ocean to the atmosphere in areas of upwelling, then extracted from the atmosphere as biological activity took up carbon through photosynthesis and exported it to depth through sinking; as warm water moved poleward, CO 2 solubility increased and temperature driven changes in the partitioning of carbon between the reservoirs of carbonic acid, carbonate and bicarbonate allowed the water to hold more CO 2 prior to sinking to depth.The increase in the atmospheric concentration of CO 2 since industrialisation has moved this system out of equilibrium, reducing the out-gassing of CO 2 at upwelling regions, increasing the airsea gradient of CO 2 elsewhere, modifying the temperaturedriven uptake, and altering the balance of carbon species (Revelle and Suess, 1957).Despite the large anthropogenic perturbation to the system, the general features of the preindustrial carbon cycle remain prominent, with out-gassing in equatorial upwelling zones, and in-gassing under highly productive regions such as the lower latitude Southern Ocean and mid-to high latitude Atlantic and Pacific, then temperature driven CO 2 uptake where surface waters move polewards and cool as in the North Atlantic (Takahashi et al., 2009).The close agreement between the present-day air-sea CO 2 flux calculated by the Earth System Model (Fig. 2 redline), and the observational estimate of that flux (Fig. 2 black line) suggests that the HadGEM2-ES model is, to a first order, reproducing the dominant components of the natural carbon cycle operating over the timescales of interest.

Ocean model experiments
The first question to explore is whether a change in the CO atm 2 seasonal cycle will have an impact on the air-sea CO 2 flux.Looking at the average difference between an ocean-model simulation seeing no seasonality in CO atm 2 and one seeing the (Earth System Model's) pre-industrial CO atm 2 seasonal cycle (1× the seasonal cycle minus 0× the seasonal cycle), and then the difference between no seasonal cycle and double the seasonal cycle (black and red solid lines respectively in Fig. 3), we see that, averaged over the first year of a simulations, the increase in the seasonal cycle amplitude promotes a relative flux of CO 2 into the ocean in the mid-tohigh latitudes, and a small out-gassing of CO 2 at the highest latitudes.The average flux over the first year after the CO atm 2 seasonal cycle perturbation is approximately one order of magnitude smaller than the natural carbon cycle's latitudinal air-sea CO 2 flux variability (gray line in Fig. 3, note that the scale on the axis relating to this curve (right hand side) is an order of magnitude larger than that used to examine the change in CO 2 flux (left hand side)).Although approximately the same pattern of response is seen in the Northern and Southern Hemispheres, the magnitude of the response is considerably larger in the Northern hemisphere; presumably reflecting the much larger seasonal cycle in the Northern Hemisphere (Fig. 1).Spatially, the change in airsea CO 2 flux resulting from the change in CO atm 2 seasonality indicates that the switch from a relative in-gassing, to a relative out-gassing, occurs at the winter sea-ice edge (Fig. 4, top row), with an weak additional ocean CO 2 uptake occurring in the northern Indian Ocean.It is also interesting to note that the change from zero to one times the CO atm 2 seasonal cycle magnitude promotes a small out-gassing in the Southern Ocean, whereas the larger change, from zero to two times the CO atm 2 seasonal cycle magnitude, promotes in in-gassing (Fig. 3).The contrasting behavior depending on the magni-tude of the seasonality change most likely reflects the nonlinearity in the sensitivities of the opposing mechanisms at play (discussed in Sect.3.2) to a change in CO atm 2 seasonal cycle magnitude.
The results above represent the difference between simulations where the intra-annual variability of the CO atm 2 concentration is being changed at each grid-point, but the annually averaged CO atm 2 at each point is remaining constant.It should however be noted that if one compares the ocean-model simulation with a constant CO atm 2 concentration throughout the year at each individual grid-point (as described above), to one with a constant CO atm 2 concentration in space as well as time (i.e.all grid points and all months having identical CO atm 2 , equal to the spatial and annual average value from the experiments described above (following CMIP5 protocol)), a further difference in air-sea CO 2 flux arises (Fig. 5a).Here the change in air-sea CO 2 flux is occurring because the annually averaged CO atm 2 is not equal at all latitudes.Observationally, and to a large extent in the Earth System Model, we see that the average CO atm 2 concentration over the midto-high southern latitudes is 3-4 ppm lower than that in the Equatorial and Northern latitudes; presumably reflecting the large natural oceanic CO 2 draw-down occurring in the Southern Ocean (Fig. 5b).Note that comparison of the model and observations in Fig. 5b is complicated by the fact that ocean simulations have been undertaken with pre-industrial boundary conditions, and observations have been made in the present day, and consequently the observations will include an additional signature pertaining to the latitudinal distribution of anthropogenic CO 2 emissions -potentially explaining the disagreement between model and observations in the Northern Hemisphere.

It is inherently difficult to isolate and identify the individual mechanisms behind any change within an Earth System
Model because the model represents a myriad of processes which all interact with varying degrees of non-linearity.To isolate the variable(s) driving the change(s), one would ideally want to run a matrix of parallel simulations, each holding a different single variable constant; this is, however, often technically and/or computationally unfeasible.Here, I investigate to what degree we might be able to represent the changes identified within the ocean-model experiments in off-line calculations.Within such calculations one has the luxury of holding constant or manipulating individual vari- 2 seasonal cycle amplitude, presented as anomalies between that calculated with a pre-industrial CO atm 2 seasonal cycle (as calculated interactively by HadGEM2-ES) and no CO atm 2 seasonal cycle (black), and twice the pre-industrial CO atm 2 seasonal cycle, and no CO atm 2 seasonal cycle (red).
ables, and consequently isolating their contribution to the overall process in question.
First I test whether it is possible to accurately reproduce the Earth System Model simulated natural air-sea flux using off-line calculations, given that it is not practicable to output data from the Earth System Model at the frequency at which it undertakes the calculations (every simulated hour).I find that using the same equations as those used in the Earth System Model (see Methods section), but using monthlyaveraged, rather than hourly averaged input variables (ocean and atmosphere CO 2 concentrations, surface ocean temperature and salinity, wind-speed and sea-ice concentration) the offline calculation does a good job of replicating the Earth System Model simulated air-sea CO 2 flux (Fig. 6   During the year, high atmospheric CO 2 concentrations occur around the time of maximum ice-cover, and are therefore prevented from exchanging freely with the ocean, whereas at times of low atmospheric CO 2 concentration, there exists no barrier to exchange.The result of this synchronicity between the seasonal cycles of atmospheric CO 2 concentration and sea-ice extent is that the annually averaged atmospheric CO 2 concentration seen by the ocean is reduced relative to that its full annual mean value, as the amplitude of the atmospheric CO 2 seasonal cycle is increased.The solid black and red curves represent the idealised annual cycles in atmospheric CO 2 concentration at one and two times the seasonal cycle amplitude respectively.The dotted black line represents the full annually averaged atmospheric CO 2 concentration.The dashed black and red lines represent the partial average of atmospheric CO 2 concentrations for the two different seasonal cycle amplitudes, over the ice-free period. cycle magnitude.This second question is tricky, because the off-line calculations are an estimate of the instantaneous response of the system, i.e. the response before the ocean has had any opportunity to come towards a new equilibrium; conversely, the ocean-model results can only tell us the average response over the first year (because a full seasonal cycle must be simulated), over which time the interactively modeled ocean will be rapidly moving towards a new equilibrium.Despite the fact that it is not possible to directly compare the two experiments, we can see if the features simulated by the ocean-model are recreated by off-line model, and indeed we find that they are (Fig. 4, comparing the top, and second-from-top rows), although in terms of the magnitude of the response and the detailed spatial structure, differences are unsurprisingly present (Fig. 3).Given the similarity of the spatial structures simulated by the on-line and off-line models, it is reasonable to assume that by identifying the mechanism driving the change in the off-line model, we will have a good appreciation of the mechanisms operating in a full Earth System Model, and then perhaps the real Earth System.Further, because the change in flux simulated by the on-line and off-line models are structurally similar, we can infer that to a first order the change is not driven by time-dependent processes, such as the transport of carbon within the ocean.
Working from the premise that the off-line calculations are sensibly representing the interactively modeled change in airsea CO 2 flux occurring in response to a change in CO atm 2 seasonality, one can now explore the drivers of that change.I recalculate the change in air-sea flux moving from zero to one times the magnitude of the CO atm 2 seasonal cycle (black) and zero to two times the magnitude of the seasonal cycle (red); individually holding each of the components of the airsea flux calculation constant at each grid-point throughout the annual cycle (variously dotted/dashed lines in Fig. 6b).I find that the change can be accounted for by the interaction of annual variability in wind-speed, sea-ice and to a much smaller degree, surface ocean temperatures with the annual cycle of atmospheric CO 2 .Applying the annually averaged wind-speed to each month of the off-line simulation one finds that there is no change in the air-sea CO 2 flux between 60 • S and 50 • N (Fig. 6b dotted lines), telling us that the interaction of the seasonal cycle in CO atm 2 and wind-speed over these is the sole driver of the change over those latitudes.North of 50 • N and south of 60 • N the dotted line in Fig. 6b deviated from the zero line, representing the influence of all factors other than wind-speed on the change in air-sea CO 2 flux.It turns out that the deviation of the dotted line from zero in Fig. 6b is essentially representing the sea-ice driven contribution to the change in air-sea CO 2 flux, since individually holding all the other remaining variables constant has a negligible impact on the off-line calculation of the air-sea flux, the only minor exception being when holding temperature constant.When applying the annually averaged temperature at each point to each month in the off-line calculation, a small deviation from the results of the full off-line calculation occur between about 50 and 60 • N (Fig. 6b dash-dot-dash line).I will next explore how and why the interaction between the seasonality of the identified variables and the seasonality of CO atm 2 concentrations might bring about the simulated change in air-sea CO 2 flux.

The mechanisms
In the high latitudes, particularly of the Northern Hemisphere, the seasonal cycles of CO atm 2 concentration and seaice extent vary approximately in phase.The reason for the synchronous change is that they share a common driving mechanism, light.During the winter months, little light is available for either photosynthesis or heating of the surface ocean; vegetation growth therefore slows or vegetation dies back causing a net release of CO 2 , and (due to the cooling) sea-ice forms.Conversely, in the spring and summer, vegetation begins to draw-down CO 2 from the atmosphere, and, as more light reaches the ocean, sea-ice begins to melt.As a consequence of the seasonal cycles of CO atm 2 concentration and sea-ice extent varying in phase, when CO atm 2 is high, an ice-barrier limits CO 2 exchange with the ocean, and when sea-ice is not present, CO atm 2 concentrations are low and the air-sea pCO 2 gradient (and therefore CO 2 flux) is reduced.Making the first order assumption that sea-ice is impermeable to CO 2 (although some CO 2 flux through continuous ice has been observed (e.g.Zemmelink et al., 2006)), the average CO atm 2 concentration that the ocean sees is therefore reduced relative to its full annual average (Fig. 7).A caveat here is that the seasonal melting of sea-ice can leave behind a stratified low-salinity lid which could limit the volume of water and modify the chemistry of that water, which may come into equilibrium with the atmosphere (Cai et al., 2010).The potential suppression of air-sea exchange in heavily stratified seasonally ice-covered waters may weight the net air-sea flux change towards that occurring in response to changes in the solubility mechanism.This component of the mechanism can not be addressed in the off-line model.I propose that the mechanism described here explains the change in air-sea CO 2 flux seen between the off-line model calculations with and without sea-ice concentrations held temporally constant.

Biogeosciences
In the mid-to-high latitudes, equatorward of the maximum seasonal extent of sea-ice, I find that the change in air-sea CO 2 flux resulting from a change in CO atm 2 seasonality is driven by two factors: the intra-annual variability in CO 2 solubility and the correlation between seasonal wind-speed and CO atm 2 change.By far the dominant mechanism is the co-variability of wind-speed and CO atm 2 (Fig. 6b).In common with the sea-ice mechanism, in the mid-to-high latitudes, particularly in the Northern Hemisphere, the seasonal cycle of surface wind-speed varies approximately in phase with the seasonal cycle of CO atm 2 concentrations (Fig. 8).Stronger winds when the CO atm 2 is highest allow a greater flux of CO 2 into the ocean (assuming under-saturation of CO ocn 2 persists) than would occur if wind-speed was highest when CO atm 2 concentrations were low.The correlation between wind-speed and CO atm 2 concentration throughout the year (Fig. 8) occurs because the winter-hemisphere decrease in insolation, which results in net respiration over photosynthesis, and therefore terrestrial CO 2 release, also drives an increased latitudinal thermal gradient, an increased equator-topole pressure difference, and increased wind-speeds.I propose that this wind-driven mechanism accounts for the difference between off-line calculations undertaken with temporally fixed and varying wind-speed, and therefore a large component of the CO atm 2 seasonality-driven air-sea CO 2 flux.Similarly, the seasonal cycle of CO 2 solubility varies approximately in phase with the seasonal cycle of CO atm 2 concentrations (Fig. 9).CO 2 solubility and the CO atm 2 concentration in the high (particularly northern) latitudes share a common driver, incident light (and therefore heat).A high CO 2 solubility when the CO atm 2 concentration is high, and a low CO 2 solubility when the CO atm 2 concentration is low, promotes an increased ocean-atmosphere pCO 2 gradient relative to a situation where high solubility occurs when CO atm 2 is low, and vice versa.The increased pCO 2 gradient increases the flux of CO 2 .This solubility change mechanism can account for the air-sea CO 2 flux difference between the fixed and temporally varying temperature simulations seen between 50- 2 seasonality accentuating these relationships between sea-ice, wind-speed and temperature driven CO 2 variability, and the seasonality of CO atm 2 will enhance/reduce the importance of the discussed mechanisms.
Individually, none of these three mechanisms are likely to have a large impact on CO atm 2 concentrations.Assuming no feedbacks operate, after a change in seasonal cycle amplitude, the new equilibrium CO atm 2 concentration would be unlikely to shift by more than the high latitude CO 2 seasonal cycle amplitude change.Considering the sea-ice mechanism, the dashed black line in Fig. 7 represents the average atmospheric CO 2 concentration initially in equilibrium with the underlying seawater, the red dashed line then represents the average atmospheric CO 2 concentration after a change in seasonal cycle magnitude, but prior to reaching a new air-sea equilibrium.The ocean will undergo a relative release of CO 2 to the atmosphere until the atmospheric CO 2 concentration average over the ice-free period is in equilibrium with the seawater again.If we were to assuming that the air-sea CO 2 flux change has only a negligible effect on oceanic CO 2 concentrations, the new equilibrium would be reached when the dashed red line had raised to the concentration shown by the dashed black line, i.e. atmospheric CO 2 increased until the CO atm 2 experienced by the ocean during the ice-free months was again equal to the ocean CO 2 concentration.The problem with this reasoning is that the present high-northern-latitude ocean is not in equilibrium with the atmosphere, and is still taking up CO 2 until it sinks (Takahashi et al., 2009).The steady-state atmospheric CO 2 concentration resulting from a change in the magnitude of the CO atm 2 concentration seasonal cycle would therefore be a function of (to a first order) circulation, temperature change with latitude, the wind-driven rate of air-sea CO 2 exchange, time, and the spatial pattern of air-sea flux change (Volker et al., 2002).Consequently, this analysis of the off-line experiments will never completely represent the changes seen in ocean-model Latitudinal dependence of the phase synchronicity between the seasonal cycle of atmospheric CO 2 concentrations and the solubility of CO 2 in seawater.Correlation coefficients between observed monthly averaged atmospheric CO 2 concentration seasonal cyclicity and the calculated monthly averaged seasonal cycle of CO 2 solubility in seawater are plotted against observation latitude.Points relate to all CarbonTracker flask measurement sites containing at least five years worth of data (Peters et al., 2007), as present in http://www.esrl.noaa.gov/gmd/ccgg/carbontracker on 11 August 2010.Atmospheric CO 2 observations were detrended using a third-order polynomial, fitted (using the least squares method) to all observations at each individual site.Detrended data were averaged into a typical annual cycle, then the correlation coefficient calculated between the 12 average months of atmospheric CO 2 data and 12 months of latitudinally averaged CO 2 solubility, calculated at the latitude corresponding to the relevant atmospheric CO 2 measurement site.CO 2 solubilities in seawater were calculated from World Ocean Atlas 2009 surface temperature and salinity climatologies (Locarnini et al., 2009;Antonov et al., 2009).The solid line depicts a cubic-spline interpolated 6-point moving average through all of the data.High correlation values indicate that the annual cycles in atmospheric CO 2 concentration and CO 2 solubility in seawater vary in phase at that latitude.
experiments, which themselves are still one step removed from fully coupled Earth System model experiments.

Towards the equilibrium response
Analysis of the off-line simulations allow us to understand the factors driving the air-sea CO 2 flux response to a perturbed CO atm 2 seasonal cycle, but does not allow us to ask whether changes in CO atm 2 seasonality might be responsible for significant cumulative changes in ocean carbon uptake; therefore, whether it is important for this reason to undertake coupled simulations with a fully interactive carbon cycle, rather than simulations essentially separating the ocean and terrestrial systems by prescribing atmospheric CO 2 concentrations.Examined as a global average, the deviations between the air-sea CO 2 flux in parallel sections of the zero and one-times CO atm 2 seasonal-cycle simulations, we see a maximum annually averaged out-gassing of carbon of 0.025Gt during the year after the seasonal cycle change is enforced (Fig. 10).Figure 10 presents the global air-sea CO 2 flux calculated with the ocean-simulation with each grid point seeing the annual average CO atm 2 for that grid-point simulated in the preindustrial fully-coupled control simulation (i.e.zero seasonal cycle) minus the control simulation with constant CO atm 2 seen by all grid-points (blue line).The out-gassing reflects the fact that in the Southern Ocean and high North Atlantic, the CO atm 2 seen by the ocean is less than the global average and consequently out-gassing occurs (see Sect. 3.4 and Fig. 5).The black and red line in Fig. 10 (difference between 1× and 0× seasonal cycle, and 2× and 0× seasonal cycle, respectively) do not show the signal of the background latitudinal CO 2 variability because they are presented as a difference of two simulations both containing this feature.The timescale over which this perturbation to the carbon cycle would come into equilibrium is unclear from simulations of the length undertaken here (50 yr), but a timescale of centuries appears likely.Given an average out-gassing of CO 2 of around 0.01 Gt yr −1 over a couple of centuries, and assuming no mitigating terrestrial carbon cycle response, we might expect these processes to alter the background atmospheric CO 2 concentration by a small number of parts per million.The short timescale response is however considerably less than the inter-annual variability in the air-sea CO 2 flux (Fig. 10), so it is unlikely to contribute towards any rapid airsea CO 2 flux changes or significant inter-annual variability.

Discussion
Despite being unlikely to alter global CO atm 2 concentrations significantly, the consequences of the operation of the seaice, wind-speed and solubility mechanisms, described here, under changing CO atm 2 seasonal cycle amplitude are interesting spatially and temporally.Firstly, an increase in the CO atm 2 seasonal cycle magnitude and a decrease in sea-ice extent (Intergovernmental Panel on Climate Change, 2007) over the coming decades, if acting alone, would cause the seasonalsolubility driven oceanic CO 2 uptake to increase and move to higher latitudes, and an increased intensity but reduced area, of seasonal-sea-ice driven relative out-gassing at the highest latitudes.Secondly, abrupt changes in the terrestrial biosphere, whether through natural variability (e.g.drought) or anthropogenic land-use change (e.g.deforestation), without necessarily impacting the annually averaged CO atm 2 concentration, could drive locally important changes in the highlatitude air-sea flux of CO 2 .It is also possible that yearto-year changes in the CO atm 2 seasonal cycle, rather than in annually averaged CO 2 concentrations, could account for a small component of the observed, but largely unexplained high latitude air-sea CO 2 flux variability (e.g. Watson et al., 2009;Le Quere et al., 2007).A further point to note is that, assuming the CO atm Fig. 10.Globally averaged air sea flux of CO 2 calculated as a difference between an ocean-model simulation seeing constant atmospheric CO 2 for 286 ppmv at all points, and spatially varying, but temporally constant (zero seasonal cycle) CO atm 2 (blue).Globally averaged air-sea flux of CO 2 calculated as a difference between the annual cycle of pre-industrial CO atm 2 generated by the Earth System Model control run (and adjusted so that the annual global mean is exactly 286 ppmv) (black).Globally averaged air-sea flux of CO 2 calculated as a difference between two times the annual cycle magnitude of pre-industrial CO atm 2 generated by the Earth System Model control run (and adjusted so that the annual global mean is exactly 286 ppmv, and the annual mean at each point equals the annual mean of that grid-point in the Earth System Model control run) (red).The dashed lines represent one standard deviation of the globally annually averaged air-sea CO 2 flux calculated over 270 yr of the fixed CO atm 2 pre-industrial Earth System Model control run.
system (rather than for example, an anthropogenically imposed change in land use), the ocean ecosystem, and factors impacting the air-sea flux (e.g.temperature and wind speed) may respond themselves to the climate forcing, modifying and potentially dominating the response to the change in CO atm 2 seasonality.One aspect of the seasonality and air-sea flux feedback mechanisms not discussed here is that of shifts in seasonal cycle phase, rather than amplitude.Various mechanisms, such as changing precipitation pattern or intensity, could shift the CO atm 2 cycle phase independently from the sea-ice and seawater CO 2 solubility cyclicity.The theory behind how changing CO 2 seasonal cycle amplitude impacts on the CO 2 air-sea flux, presented here, could equally be used to understand the response of the air-sea CO 2 flux to changing CO atm 2 seasonal cycle phase.A relative shift in the phase of the seasonal cycles of CO atm 2 concentration, and sea-ice extent or wind-speed or seawater CO 2 solubility may have the capacity to produce much larger changes in ocean in/out-gassing than changes in CO atm 2 concentration seasonal cycle amplitude.A relative shift in phase between these variables might be expected if a change in phase of the CO atm 2 seasonal cycle, as observed over the last few decades (Keeling et al., 1996), was to occur in response to changing CO 2 fertilisation of the ter-restrial biosphere, rather a change in temperature (which may be expected to impact all of the cycles in the same sense).
Presently, the seasonal cycle in earth system model CO atm 2 concentrations is often considered a way of diagnosing and bench-marking changes in model terrestrial net primary production (e.g.Cadule et al., 2010;Heimann et al., 1998), rather than as critical prognostic variability in its own right.
Given the identification of mechanisms by which CO atm 2 may feed back (at least locally) on air-sea CO 2 fluxes, it is important that the terrestrial biosphere components of earth system models consider the seasonal cycle of CO atm 2 as more than a diagnostic tool, and are developed, validated, and explored accordingly.

Conclusions
Despite being a prominent and dynamic feature of the carbon cycle, the climatic influence of the CO atm 2 concentration seasonal cycle has, to the best of my knowledge, not previously been explored.In Northern Hemisphere seasonally ice-covered waters, the air-sea flux change seen here appears to occur as a consequence of the synchronicity between the CO atm 2 and sea-ice seasonal cycle.Equatorward of the maximum sea-ice extent, the change in air-sea flux appears to results from of synchronicity between the seasonal cycles of CO atm 2 and the seasonal cycles of wind-speed and seawater CO 2 solubility.The operation of the described mechanisms could allow the sign of the net air-sea flux change to switch depending on the maximum sea-ice extent.Despite demonstrating that changes in the amplitude of the CO atm 2 seasonal cycle can impact the mid-to-high latitude air-sea flux of CO 2 , at least at a global level the impact of this change is marginal.
Given the small impact on globally averaged air-sea CO 2 fluxes found to occur in response to a change from a spatially and temporally constant CO atm 2 to the observed seasonal cycle, it appears that little error will be introduced to simulations, via the mechanisms discussed in this paper, by the decoupling of ocean and terrestrial carbon cycle components through the prescription of CO atm 2 concentrations, rather than allowing the modeled carbon cycle to generate its own CO 2 concentration, seasonality and distribution from specified CO 2 emissions.

Fig. 1 .
Fig. 1.(a) Observed atmospheric CO 2 seasonal cycle at latitudes with CarbonTracker flask measurement sites containing at least five years worth of data(Peters et al., 2007).Seasonal cycle calculated from detrended monthly values and presented as an anomaly from the annual mean at that latitude.(b) Pre-Industrial latitudinally averaged surface atmospheric CO 2 seasonal cycle simulated in the HadGEM2-ES model when run with interactive carbon cycle components.For consistency with calculations presented in this study, only CO 2 concentrations above the ocean have been considered.Note that although the relative magnitude of changed described by the color scale is identical in both panels, the left panel shows anomalies from zero, and the right, absolute values.This has been done to allow comparison between pre-industrial and detrended present-day values.The left panel shows the observed seasonal cycle at each latitude as an anomaly from its annual mean of zero, whereas annually averaged values for any given latitude in the right panel are not necessarily identical.

Fig. 3 .
Fig.3.Latitudinally averaged impact of changing atmospheric CO 2 seasonal cycle amplitude on the air-sea flux of CO 2 calculated as averages over the first perturbed year of ocean-model simulations (solid black and red lines), and instantaneously after the CO atm 2 perturbation using off-line calculations (dashed black and red lines).CO 2 air-sea flux difference calculated between the model's preindustrial atmospheric CO 2 seasonal cycle and a situation with no seasonal cycle (black), and between two times the model's preindustrial atmospheric CO 2 seasonal cycle and a situation with no seasonal cycle (red).Positive values represent a relative flux into the ocean.It can be seen that by increasing the seasonal cycle magnitude (but keeping the annually averaged value at individual points, and therefore globally, constant), the ocean takes up additional CO 2 in the mid-to-high latitudes, and takes up less CO 2 in the high latitudes.The enhanced relative CO 2 in-and out-gassing occurring in the mid and high Northern Hemisphere is a response to the larger seasonal cycle of atmospheric CO 2 in this hemisphere, and a tighter coupling between wind-speed, ocean CO 2 solubility, sea-ice change and atmosphere CO 2 concentration seasonality (see Figs. 8, 9 and 7 and accompanying text), relative to that in the low latitudes and Southern Hemisphere.The model-simulated latitudinally averaged pre-industrial air-sea flux of CO 2 is plotted in the dotted gray line for reference.Note the order of magnitude of increase in scale when considering the absolute air-sea flux, compared to that used for changes in flux.

Fig. 4 .
Fig. 4. Spatial maps showing the impact of changing atmospheric CO 2 seasonal cycle amplitude on the air-sea flux of CO 2 (top four figures), and the background (calculated from the first 200 yr of the control simulation) annually averaged air-sea flux and standard deviation in that flux (bottom two figures).Ocean model results (top row) have been calculated over the first 12 months after the CO atm 2 seasonal-cycle perturbation.Off-line calculations (second row from top) show an instantaneous estimate of the flux after the seasonal-cycle perturbation.

Fig. 5 .
Fig. 5. Average air-sea CO 2 flux simulated during the first year after moving from the model ocean seeing a spatially and temporally homogeneous CO atm 2 concentration of 286 ppm to seeing annual mean (i.e.without a seasonal cycle) CO atm 2 simulated interactively by the HadGEM2-ES model, but still with a global mean of 286 ppmv (left).The latitudinal variability in annually averaged CO atm 2 calculated for the pre-industrial by the fully coupled HadGEM2-ES model (solid line), and observations (dots) presented as an anomaly from the globally averaged CO atm 2 during that model or observational year (right).
Fig. 6. (a)Latitudinally and annually averaged air-sea CO 2 flux simulated in (and calculated interactively by) the HadGEM2-ES pre-industrial interactive-CO 2 control simulation (gray), and offline calculation of that air-sea flux from annually averaged temperature, salinity, wind-speeds, sea-ice concentrations, and atmosphere and ocean CO 2 concentrations (dashed blue line).(b) Offline calculations showing the impact on the air-sea CO 2 flux of changing the CO atm 2 seasonal cycle amplitude, presented as anomalies between that calculated with a pre-industrial CO atm 2 seasonal cycle (as calculated interactively by HadGEM2-ES) and no CO atm 2 seasonal cycle (black), and twice the pre-industrial CO atm 2 seasonal cycle, and no CO atm 2 seasonal cycle (red).

Fig. 7 .
Fig.7.Explanation of how a change in the magnitude of the atmospheric CO 2 seasonal cycle can change the air-sea CO 2 flux in seasonally sea-ice covered waters.During the year, high atmospheric CO 2 concentrations occur around the time of maximum ice-cover, and are therefore prevented from exchanging freely with the ocean, whereas at times of low atmospheric CO 2 concentration, there exists no barrier to exchange.The result of this synchronicity between the seasonal cycles of atmospheric CO 2 concentration and sea-ice extent is that the annually averaged atmospheric CO 2 concentration seen by the ocean is reduced relative to that its full annual mean value, as the amplitude of the atmospheric CO 2 seasonal cycle is increased.The solid black and red curves represent the idealised annual cycles in atmospheric CO 2 concentration at one and two times the seasonal cycle amplitude respectively.The dotted black line represents the full annually averaged atmospheric CO 2 concentration.The dashed black and red lines represent the partial average of atmospheric CO 2 concentrations for the two different seasonal cycle amplitudes, over the ice-free period.

Fig. 8 .
Fig. 8. Correlation coefficient between average monthly latitudinally averaged wind-speeds and CO atm 2 concentrations, as simulated in the fully coupled Earth System Model pre-industrial simulation.
Fig. 9.Latitudinal dependence of the phase synchronicity between the seasonal cycle of atmospheric CO 2 concentrations and the solubility of CO 2 in seawater.Correlation coefficients between observed monthly averaged atmospheric CO 2 concentration seasonal cyclicity and the calculated monthly averaged seasonal cycle of CO 2 solubility in seawater are plotted against observation latitude.Points relate to all CarbonTracker flask measurement sites containing at least five years worth of data(Peters et al., 2007), as present in http://www.esrl.noaa.gov/gmd/ccgg/carbontracker on 11 August 2010.Atmospheric CO 2 observations were detrended using a third-order polynomial, fitted (using the least squares method) to all observations at each individual site.Detrended data were averaged into a typical annual cycle, then the correlation coefficient calculated between the 12 average months of atmospheric CO 2 data and 12 months of latitudinally averaged CO 2 solubility, calculated at the latitude corresponding to the relevant atmospheric CO 2 measurement site.CO 2 solubilities in seawater were calculated from World Ocean Atlas 2009 surface temperature and salinity climatologies(Locarnini et al., 2009;Antonov et al., 2009).The solid line depicts a cubic-spline interpolated 6-point moving average through all of the data.High correlation values indicate that the annual cycles in atmospheric CO 2 concentration and CO 2 solubility in seawater vary in phase at that latitude.

Halloran: CO 2 seasonality and air-sea flux
top panel).Secondly, we must ask if the off-line calculations adequately recreate the change in the air-sea CO 2 flux simulated by the ocean-model as a response to a change in the CO atm 2 seasonal www.biogeosciences.net/9/2311/2012/Biogeosciences, 9, 2311-2323, 2012 P. R.