Surface ocean carbon dioxide variability in South Pacific boundary currents and Subantarctic waters

To improve estimates of the long-term response of the marine carbon system to climate change a better understanding of the seasonal and interannual variability is needed. We use high-frequency multi-year data at three locations identified as climate change hotspots: two sites located close to South Pacific boundary currents and one in the Subantarctic Zone (SAZ). We investigate and identify the main drivers involved in the seasonal an interannual (2012–2016) variability of the carbon system. The seasonal variability at boundary current sites is temporally different and highly controlled by sea surface temperature. Advection processes also play a significant role on the monthly changes of the carbon system at the western boundary current site. The interannual variability at these sites most likely responds to long-term variability in oceanic circulation ultimately related to climatic indices such as the El Niño Southern Oscillation, the Pacific Decadal Oscillation and the Southern Annular Mode (SAM). In the SAZ, advection and entrainment processes drive most of the seasonality, augmented by the action of biological processes in spring. Given the relevance of advection and entrainment processes at SAZ, the interannual variability is most probably modulated by changes in the regional winds linked to the variability of the SAM.

and short-term variability of the carbon system to the detection of long-term trends and the complexity of identifying the main drivers of the seasonal and spatial variability.
We describe the variability and drivers of surface-ocean fugacity ( fCO sw 2 ) by using high-frequency data from three moorings located south of Australia: Kangaroo Island (KAI), Maria Island (MAI) and the Southern Ocean (SOTS) (Fig. 1). These moorings are capable of climate quality measurements and are strategically located in climate change hotspots South of Australia: in the Subantarctic Zone (SAZ) and at South Pacific boundary currents. Boundary current systems play crucial roles in transport of heat, water masses and other properties 11 , strongly affecting regional climate and ecosystems and the SAZ is the most important region of the Southern Ocean in terms of CO 2 uptake 12 . The data are integrated into global networks 6,13 and are used for validation and assimilation in current analytical and predictive models 14 . We also analyse ancillary data from hydrographic lines, satellites, and model runs to give more insight into the biological processes and ocean dynamics affecting fCO sw 2 variability at seasonal scales. Furthermore, we investigate the interannual variability of fCO sw 2 , elucidating its main drivers and possible future implications for long-term trends. oceanographic settings KAI (36°S, 136°E) is located on the southern Australian shelf in 105 m of water to the east of the Great Australian Bight (GAB, Fig. 1). The shelf is the largest actively growing carbonate platform on earth and is a region with ecosystems of high ecological and economic importance 15 . The oceanography of the region is highly dynamic, with a seasonal variability linked to the passage of high pressure systems 16 . South-easterly winds in the austral summer (Dec-Mar) transport waters from the Southern Ocean and eastern Tasmania and along the continental slope of the GAB as the Flinders Current 16 (FC, Fig. 1). The winds are favourable to upwelling during these months and drive episodic upwelling events of relatively cold offshore waters onto localized areas of the continental shelf 17 (mostly south of Kangaroo Island), which are essential to the maintenance of the shelf ecosystems 15 . A shift in the winds towards autumn (Mar-Jun) drives the development of an eastward flowing coastal current along the continental shelf ( Fig. 1) that suppresses upwelling, and is strongest in winter (Jun-Sep) 18 . This coastal current is a mixture of waters from the Leeuwin Current (LC, Fig. 1) and entrained shelf waters 16,19 . The LC is the poleward eastern boundary current that flows down the west coast of Australia before turning east and flowing along the southern Australian shelf. The projection of the LC along the southern shelf is strongest during winter when it contributes to the extension and persistence of the coastal current 16 . The link of the LC and the coastal current to the atmospheric systems makes them especially sensitive to climate change, which could change the dynamics of the area, alter the water properties and have diverse impacts on the fisheries and marine organisms 20 .
MAI (43°S, 148°E) is located off the east coast of Tasmania in 85 m of water of the South Tasman Sea and is also located in the extensive carbonate producing platform of the southern Australia shelf 15 . The circulation of this region is dominated by the boundary current system of Eastern Australia: the East Australian Current (EAC, Fig. 1). The EAC originates off northeastern Australia at ~20°S, and is fed by waters from the South Pacific subtropical gyre 21 . Near 33-34°S, much of its transport separates from the coast and turns east but a highly-variable tongue, the EAC extension ( Fig. 1), of relatively warm and salty EAC waters extends southward along the East Australian coast as a series of energetic mesoscale features 21 . The EAC extension creates a zonal jet south of Tasmania that connects Pacific and Indian waters, as part of the global thermohaline circulation. Most of this flow follows a northwest direction off southern Tasmania, as part of the FC and the rest goes southward in the form of eddies 22 . The EAC extension is strongest in the austral summer and weakens over winter allowing cooler and fresher modified subantarctic surface waters to spread north and into the vicinity of MAI 23 . The seasonality of the EAC extension influences the regional climate as well as the marine living systems and fisheries of the area near MAI 24 . The region east of Tasmania has shown the highest warming rates observed in the last seven decades in the Southern Hemisphere and the strength of the EAC extension is predicted to increase under future climate scenarios with important implications for fisheries, the marine carbon system and other oceanic processes 20 .
SOTS (47°S, 142°E) is in >4500 m of water in the SAZ, the region of the Southern Ocean between the Subtropical (STF) and Subantarctic (SAF) fronts of the Antarctic Circumpolar Current (ACC) 25 (Fig. 1). The Southern Ocean is the largest net oceanic sink of atmospheric CO 2 and the SAZ is the area responsible for most of this uptake 12 . The waters of the SAZ are influenced by many dynamic processes such as the ACC flow, the mixing between subtropical and subantarctic waters, the subduction of subsurface waters as part of the upper cell of the oceanic thermohaline circulation and the spawning of eddies from the SAF associated with meanders in the front due to the interaction of the SAF with the bathymetry 25 . The SAZ to the south of Tasmania is also affected by the EAC extension 22 (Fig. 1). The interaction between subantarctic and subtropical waters are believed to be contributors to high seasonal primary production in the SAZ 26 . Over recent decades, numerous studies have shown long time-scale variability of the Southern Ocean in terms of atmospheric carbon uptake 10,27 although data from this area is scarce with SOTS being one of the only two high-frequency surface time-series sites located in the Southern Ocean 28 .
The oceanographic settings at the three sites influence the mean de-trended (Eq. 1) annual values and the seasonal amplitude of temperature and salinity ( Fig. 2g-i). The boundary current sites (KAI and MAI) are characterized by warmer and saltier waters with a greater subtropical component than the higher latitude site (SOTS) that is mainly influenced by subantarctic waters. At KAI the influence of South Indian subtropical waters combined with local inputs from the shelf 19 results in higher salinity waters than at the MAI site, which is influenced by western South Pacific subtropical waters 29 (Fig. 2g,h). The seasonal changes in salinity at KAI (Fig. 2g) are less than at MAI and SOTS as these latter two sites have greater amounts of warm and salty subtropical waters present in warmer months and more subantarctic waters in the cooler months ( Fig. 2g-i). These differences also extend to the mean annual values of total alkalinity (A T ), which is related to salinity, and dissolved inorganic carbon (DIC) that decrease and increase, respectively, at higher latitudes ( Fig. 2d-f).  At KAI, fCO sw 2 approaches near-equilibrium values with the atmosphere in late summer (Feb, ∆fCO 2 = −3.1 ± 5.2 μatm), decreases through winter to a minimum in about Aug (∆fCO 2 = −49 ± 4.4 μatm), and increases over the spring-summer to near equilibrium values (Fig. 2a). The rate of change of fCO sw 2 (d fCO obs sw 2 , Fig. 3a) is between −5 and −10 μatm per month from early autumn (Mar) through winter (Aug), before becoming positive from spring until early summer (Dec) (Fig. 3a). At MAI, the fCO sw 2 seasonality is about four months out of phase with that of KAI, with a minimum in Nov and a maximum in Feb and about half the seasonal amplitude as the other sites (Fig. 2b). The smallest sea-air gradient at MAI occurs during winter (∆fCO 2 = −23.4 ± 3.5 μatm) and does not approach equilibrium with the atmosphere as observed at the other sites (Fig. 2c). The monthly rate of change at MAI is also relatively small and typically less than ±5 μatm for most of the year (Fig. 3b). The seasonal amplitude of fCO sw 2 at SOTS (Fig. 2c) is similar to KAI, with the maximum value close to equilibrium with the atmosphere (∆fCO 2 = −8.9 ± 6 μatm). However, fCO sw 2 at SOTS is about 6 months out of phase with KAI and is characterized by a rapid decrease from a maximum in Sep to a minimum in Dec with a more gradual increase from summer through the end of winter (Fig. 3c).
The differences in the de-trended seasonal changes of fCO sw 2 at the sites are due to shifts in the timing and relative importance of the physical and biological drivers (Eqs 2 and 3). To describe these differences, first we computed (Eq. 2) the changes in fCO sw 2 due to sea-air uptake ( − d fCO air sea sw 2 ) and changes in sea surface temperature (d fCO   Fig. 3a). In autumn (Mar-Jun), regional winds pile water up along the coast favouring the development of the coastal current 16 (Fig. 4). This retraction of shelf waters to the coast promotes the northward transport or advection of water coming from offshore 19,30 . The offshore waters are modified subantarctic waters including FC water and cause a decrease in temperature, salinity and A T , while DIC increases (Fig. 4d). The increase of DIC by advection ( Fig. 3d) partially counteracts the effect of temperature (Fig. 3a). A progressive deepening of the mixed layer (MLD, Fig. 2j) due to the strengthening of the winds allows DIC-rich deeper water to be entrained into the mixed layer tending to increase fCO sw 2 , although the net effect of the entrainment is small (at the limit of its uncertainty, Fig. 3d).
In winter, a combination of stronger winds and more negative ∆fCO 2 increases the net flux into the ocean (Fig. 2m) Fig. 3a). The opposing effect of decreasing temperature prevails and the values of fCO sw 2 continue to decrease through the winter. In July-August, the coastal current peaks (Fig. 4b) and widens 16,30 , affecting the area around KAI and causes an increase of salinity and A T (Fig. 2d,g). The coastal current dissipates quickly towards the end of winter 19 and over Dec-Feb the advection of warmer and saltier subtropical Indian waters, with relatively high A T and low DIC could possibly act to limit the increase of fCO sw 2 caused by warming surface waters (Fig. 3a,d, notice that the changes in − d fCO sw dyn bio 2 are almost below its uncertainty for the first part of the year). For the KAI region, the relative increase in salinity and A T during summer may also be related to the outflow from the nearby coastal embayments 31 due to the relaxation of the coastal current and the prevailing upwelling-favourable winds. Upwelling does occur in the vicinity of KAI, although the upwelling at the site remains subsurface 32 and the effect on surface-layer primary production and fCO sw 2 is negligible (Fig. 3d). At MAI, the role of temperature on fCO sw Fig. 3b) is counteracted by the seasonal extension and contraction of subtropical waters associated with the EAC extension. During autumn and winter, a greater proportion of modified subantarctic waters occur at the site 23 causing an increase in DIC (Fig. 4) and decreases in salinity, A T , and temperature (Fig. 2e,h). The action of advection increases fCO sw 2 , offsetting the effect of decreasing temperature in autumn (Fig. 3b,e). The impact of advection of modified subantarctic waters diminishes over winter and the seasonal cooling leads to a decrease in fCO sw 2 (Fig. 3b,e). From spring to summer, the EAC extension intensifies 23 (Fig. 4a), bringing subtropical waters to the area with relatively higher A T and lower DIC (Fig. 2h,e). The increased transport of the subtropical waters into the region during spring offsets the warming www.nature.com/scientificreports www.nature.com/scientificreports/ effect and causes a slight decrease in fCO sw 2 . Our calculations indicate that the effect of the biological driven changes (d fCO bio sw 2 ) at MAI is negligible during this period, which is consistent with the reported low to moderate primary production in the region 32 .
At SOTS, the net sea-air fluxes ( − d fCO air sea sw 2 , Fig. 3c) have a more significant effect on the variability of fCO sw 2 than at the two shelf sites and can approach the influence of temperature (d fCO T sw 2 ). The SAZ is one of the most important areas in terms of oceanic carbon uptake 12 and it can be seen in the values of the sea-air fluxes that achieve the highest negative values of all the locations (Fig. 2o). The high sea-air fluxes are favoured by the cold subantarctic waters and strong winds that are characteristic of this region 25 . The strengthening of winds also deepens the mixed layer at SOTS (Fig. 2l) mixing high DIC waters into the surface layer and increases the entrainment term in autumn (d fCO entr sw 2 , Fig. 3f). The sea-air fluxes and entrainment cause most of the increase in fCO sw 2 , and exceed the decrease in fCO sw 2 due to cooling (Fig. 3c,f). The impact of the sea-air fluxes, temperature and entrainment diminishes through winter, while the role of the advection, that is related to the northward transport of DIC-rich subantarctic waters 33 increases and acts to maintain the increase of fCO sw 2 (Fig. 3c,f). In spring at SOTS, the seasonal increase of temperature tends to increase fCO sw 2 while advection and primary productivity cause a decrease in fCO sw 2 (Fig. 2c,f). The advection processes during this season are related to the arrival, in the form of eddies 22 , of subtropical waters (with low DIC and high salinity and A T ) that mix with subantarctic waters. The impact of primary production during spring is comparable to that of advection (Fig. 3f). Previous studies at SOTS and the Southern Ocean have highlighted the relevance of the primary production and its effect on the carbon cycle during spring to early-summer 10,34 . Over summer, the effect of the primary production and advection diminishes and the combined action of the sea-air fluxes, temperature and entrainment results in a net increase of fCO sw 2 (Fig. 3c,f).

Interannual Variability of fCO sw 2
There is significant interannual variability superimposed on the seasonal changes described above indicating that there are additional processes acting at longer than seasonal time scales that are influencing the CO 2 variability 9 .
In order to assess the interannual variability we used de-seasonalized data (first term in Eq. 1) from KAI and MAI. We contrasted the interannual variability at KAI and MAI between 2012 and 2016. This period was covered by the data at both sites, with the exception of the period from Jun-2013 to May-2014 at KAI when no data were collected (Fig. 5). The SOTS data contained a number of gaps that doesn't allow for a similar assessment at this site (see Methods). At KAI, the de-seasonalized series (trend in Fig. 5a) can be approximated to a linear trend of ~2.0 ± 0.6 μatm yr −1 for the period 2012-2016, which would indicate that the increase in fCO sw 2 at this site is lower than expected if surface waters tracked the atmospheric CO 2 increase 35 of ~2.5 ± 0.2 μatm yr −1 . This is not surprising since recent studies have pointed out the difficulty of separating the anthropogenic signal from the natural variability www.nature.com/scientificreports www.nature.com/scientificreports/ in the air-sea carbon fluxes 4 with the time of emergence of the anthropogenic signal in certain areas of the ocean being higher than three decades. The 5-year trend in salinity is small (−0.0103 ± 0.0001 y −1 ) and has little effect on fCO sw 2 over the period of measurements d fCO ( S sw 2 , Fig. 5a). The observed interannual change in sea-surface temperature (d fCO T sw 2 ) over the period corresponds to a net 5-year decrease of −0.3183 ± 0.0017 °C y −1 and has a stronger effect than salinity. The cumulative monthly change in the de-seasonalized values of fCO sw 2 between 2012 and 2016 (Fig. 5b) indicates that most of the change occurs in autumn and winter. The corresponding monthly changes of salinity and temperature show similar patterns to that of fCO sw 2 , with salinity showing a higher decrease and temperature a lower decrease in autumn (Fig. 5b). The similarity in the monthly changes in salinity and temperature suggests that the 5-year change in fCO sw 2 is not only driven by the atmospheric CO 2 increase and the temperature changes but also by changes in the regional circulation.
Results from observation analysis and high resolution modelling suggest that an increase in the transport and eddy kinetic energy of the LC and FC driven by a wind change has occurred in response to a climate regime shift in the Pacific 20,36,37 . This change in the Pacific climate regime has been linked to the variability of major sources of inter-and intra-decadal global climate variability, in particular, the El Niño Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) 20,36. Cold periods of PDO, such as it occurred during the observational period 20 , are associated with the poleward extension of the EAC and the enhancement of wind curls over South Australia 36 . The poleward extension of the EAC would imply an increase in the contribution of East Tasmanian waters to the FC which, added to the wind curl increase, would result in the enhancement of the volume transport of the FC into the region 20 . An enhanced FC could bring DIC-rich cooler waters from the south to the KAI region that would produce a general cooling, freshening and an increase in DIC and fCO sw 2 especially in summer, when the coastal current is weaker (Fig. 5b). During the observational period, the ocean was under La Niña conditions that are linked to an increase in the volume transport of the LC 36,37 and consequently its intrusions into the GAB in autumn and winter (Fig. 1). In addition, the invigoration of the LC has been associated with anomalous warming and freshening 38,39 . The warming and freshening of the LC flow would explain the higher increase of fCO sw 2 as well as the relative lower decrease of temperature observed during autumn and winter and the relative higher decrease of salinity in autumn (Fig. 5b).
At MAI, the interannual increase in fCO sw 2 between 2012 and 2016 (trend in Fig. 5c) can be linearly approximated to a value of 1.7 ± 0.3 μatm yr −1 , which is less than at KAI, and is also less than the increase expected due to the increase in atmospheric CO 2 . The 5-year trend in salinity corresponds to an increase of 0.0174 ± 0.0001 y −1 and does not have a significant effect on fCO sw 2 (Fig. 5c). The temperature increase for the period 2012-2016 (0.0745 ± 0.0003 °C y −1 ) dominates the interannual variability of fCO sw 2 limiting a direct response to the atmospheric CO 2 increase (Fig. 5c). The net monthly increase in fCO sw 2 at KAI between 2012 and 2016 is stronger in summer and autumn in agreement with the highest increases in temperature and salinity for this period (Fig. 5d).
A long-term warming has occurred at MAI over the last seven decades due to a poleward shift and intensification in the transport and eddy kinetic energy of the EAC 20,40,41 . The EAC strengthening and poleward shifting has been related to the multi-decadal spin-up of the Pacific subtropical gyre, associated with the variability of the PDO and ENSO 20,40,41 . This intensification is transferred into the EAC extension as an increased transport of warm-core eddies that also bring low-DIC waters into the region displacing relatively cooler and high-DIC subantarctic waters. The EAC extension is greatest in summer to early autumn and coincides with the largest increase in fCO sw 2 found for the period 2012-2016 (Fig. 5d) that is linked to the warming influence of the EAC on fCO sw 2 . Although small, the general increase in salinity (Fig. 5d) also supports our reasoning of an increase in the component of subtropical waters at the MAI region due to the intensification of the EAC extension.

summary and Global Connections
Changes in volume transport, poleward extension and warming rates at oceanic boundary currents have been linked to shifts in climate regimes over large areas of the ocean 20,36 . These climate regime shifts are ultimately related to inter-and intra-decadal variability of climate indices such as the PDO, ENSO or the Southern Annular Mode (SAM) 36 .
Our results for the South Pacific boundary current sites (KAI, MAI) show that the seasonal variability of the carbon cycle is temporally different between regions but mainly controlled by changes in sea surface temperature (Fig. 6). Advection processes have also a relevant role on the seasonal variability of fCO sw 2 , specifically for west boundary currents, such as the EAC (Fig. 6). The warming associated with boundary currents, that is expected to increase in future scenarios 36 , would consequently have a relevant effect on the carbon system of these and other similar regions. The most probable change will be a reinforcement of the increase in the amplitude of the seasonal variability that has been observed for more than 30 years 42 . Some hints of this were noticed in the mathematical fit done to separate seasonal from multi-year variability (Eq. 1), where adding the variability in the seasonal amplification improved the fit. Unfortunately, the time coverage of the time series is too short to allow for a deeper discussion on this issue.
The variability of climatic indices has a major role on the interannual variability of fCO sw 2 , lowering the expected response of the carbon system to the anthropogenic increase of atmospheric CO 2 . This strong role of the multiyear atmosphere-ocean variability indicates that the variability over a 5-year period is only representative of this period and that the interannual variability in a future 5-year period could be totally different if the climatic indices were under new phases. This result is a good motivation for maintaining long-term high-frequency oceanic observations to elucidate better the response of the marine carbon system to the atmospheric CO 2 increase.
In the SAZ, the seasonal variability of fCO sw 2 is mainly controlled by advection and entrainment processes, with an important role of biological processes in spring (Fig. 6). The processes of entrainment and advection in the SAZ are modulated by the action of the westerly winds over the region, closely linked to the variability of the SAM 33,43,44 . Observation analysis have already shown the link between the SAM and changes in the surface ocean www.nature.com/scientificreports www.nature.com/scientificreports/ carbon system of the Southern Ocean 10,45 . Changes in surface ocean properties have also being considered the most probable cause behind the increase in the amplitude of the seasonal variability 42 . Climate models predict intensification of the westerlies and enhanced warming under a more positive phase of the SAM 36 , suggesting that the amplitude of the seasonal variability of fCO sw 2 is likely to increase. Nevertheless, this conclusion remains difficult to foresee due to the high uncertainties in the climatic projections 36 and in the data-limited observational analysis and the different relative weights of the drivers in the seasonal variability (Fig. 6).

Methods
High frequency (~3-hourly) surface measurements of salinity (S), temperature (T) and the mole fraction of CO 2 (XCO 2 ) in atmospheric air and air equilibrated with surface seawater were obtained from autonomous sensors at each mooring site using SBE16PlusV2 (from Seabird Electronics Inc) and MapCO2 sensors 6  fCO sw 2 was calculated from XCO 2 at T, S and pressure at the sea surface. The accuracy of fCO sw 2 was estimated to be ±2 μatm in all moorings 6 and verified against zero CO 2 and reference CO 2 gas samples run before each 3 hr sampling point. Laboratory validations of the MapCO2 systems before deployment and after retrieval of the sensors confirmed measurement accuracy. S and T sensors calibrations were also confirmed before deployment and after retrieval at a National Association of Testing Authorities facility at CSIRO Oceans and Atmosphere in Hobart, Tasmania.
In addition to the moored sensors, surface water samples were collected at 1-2 month intervals from the Australian National Reference Stations 46 (NRS) for KAI and MAI sites and from approximately 6 monthly CTD stations at SOTS. These samples were analysed for DIC by coulometry, and for A T by potentiometric titration 47 . Certified reference materials and duplicate samples confirmed that the accuracy and precision of both measurements were ±2 μmol/kg. A stepwise linear regression of measured A T values against S and T was used to establish a best fit linear equation to estimate A T . Including T did not improve the fit and two equations with salinity resulted: A T (KAI) = 566 + 50 ·S for KAI, with residuals of ±3 μmol kg −1 and A T (MAI_SOTS) = 787 + 44 ·S for both MAI and SOTS, with residuals of ±1.9 μmol kg −1 . MAI and SOTS sites have a similar salinity range (34.5-35.7 and 34.1-35.1, respectively), while KAI salinities are higher (35.4-36.5). The moored sensor S measurements were then used to estimate 3-hourly A T values, and the A T and fCO sw 2 pair used with measured S and T in the CO2sys program [48][49][50][51][52][53] to estimate DIC. The calculated DIC agreed to within ±3 μmol/kg with measured values.
In order to evaluate the seasonal variability, measured and estimated data from KAI and MAI were fit to a harmonic equation that simultaneously separates the long-term trend and the seasonal cycle:  where y t ( ) represents the predicted time series of a variable and t is the time expressed as a fraction of year based on the number of data since the start and end dates of the time series. The coefficients a i , b hj and c hj , d hj and e hj were linearly obtained. The first term of Eq. 1 represents the data trend 54 . The sequence of five harmonics (j) represents the annual cycle 54 and includes harmonics with constant (h = 0) and variable amplitude 54 . (h = 1, 4). The variability in the amplitude of the harmonics was considered because it increased the fit between the time series and Eq. 1. The residuals from the fit between Eq. 1 and the time series were filtered in the time domain using two different low-pass filters and then added to the function 55 . The data gap at KAI adds some uncertainty to the estimated coefficients in Eq. 1. The coefficients of determination (R 2 ) of the fits between the time series and Eq. (1) for KAI and MAI were: 0.74, 0.78 for S; 0.93, 0.95, for T and 0.86, 0.87 for fCO sw 2 (see Suplementary Fig. S1). The mean seasonal variability for each variable is obtained from the second and third terms of Eq. 1, or − ∑ = y t a t ( ) The scarcity of the data from SOTS does not allow us to use Eq. 1 and the mean seasonal variability of the variables was obtained by estimating monthly means without considering interannual variability. The uncertainties added by using this approximation require care to be taken when considering the role of the different processes in the seasonal variability of fCO sw 2 at SOTS. The seasonal variability of fCO sw 2 in the ocean surface is mainly due to changes in thermohaline properties, air-sea fluxes and to processes associated with ocean dynamics and biology: . For MAI and KAI the MLD on site was estimated from NRS stations using a threshold density value (0.03 kg m −3 ) 58 . We also considered the MLD immediately off-shore of these two sites on the shelf edge using a monthly climatology derived from Argo floats 58 . For SOTS, we used the MLD on site obtained from SOTS temperature sensors 59 . Although the uncertainty in the estimate of the MLD could be lower for SOTS 34 , we considered an error of 25% in the estimate of MLD for the three sites due to the higher errors of the climatology 58  the effect of entrainment, advection and diffusion processes. These variables were first estimated as changes in DIC and then transformed to changes in fCO sw 2 using the CO2sys program.
The term d fCO bio sw 2 in Eq. 3 represents the effect of the net community production (NCP) on fCO sw 2 and was estimated from net primary production (NPP) data obtained from MODIS and the CbPM algorithm 60 . We assume the error of the NPP from the CbPM algorithm to be of ~35% 60 . NCP was used as the amount of DIC consumed by the marine organisms and transformed into a change in fCO sw 2 using CO2sys. We assumed that NCP constitutes ~15% of NPP 61,62 for KAI and MAI sites and 55% for SOTS site 43 63 , which accounts for the exchange of DIC between the mixed layer (DIC) and the underlying seasonal thermocline waters (DIC tc ) as the mixed layer depth changes with time ( dMLD dt ). We assumed that DIC, obtained from fCO sw 2 and A T , was representative of the mean value in the mixed layer. For KAI and MAI, the monthly values of DIC below the MLD (DIC tc ) were obtained from measurements at the sites. For SOTS, we obtained averaged winter and summer values of DIC below MLD from repeats of the nearby WOCE SR03 hydrographic section 64  www.nature.com/scientificreports www.nature.com/scientificreports/ the monthly surface flow, v, was estimated using modelled flow from the B-SOSE simulation 14 63 with vertical diffusivity coefficients of K z = 0.5 10 −4 m 2 s −1 for SOTS, K z = 0.6 10 −4 m 2 s −1 for KAI and K z = 0.8 10 −4 m 2 s −1 for MAI 66 . The vertical gradient of DIC ( dDIC dz ) was obtained from the measurements at the sites for KAI and MAI and from the repeats of the WOCE SR03 hydrographic section for SOTS. The mean uncertainty (propagated) of d fCO dif sw 2 is ±3 μatm, being DIC the major contributor.
The interannual variability of fCO sw 2 was only analysed for KAI and MAI because of the discontinuity in SOTS data. The interannual trend for the period 2012-2016 was obtained from the first term of Eq. 1. The effect of temperature d fCO T sw 2 and salinity d fCO S sw 2 on the interannual change of fCO sw 2 between 2012 and 2016 was examined using the CO2sys program by having the correspondent variable follow the observed changes while keeping all other variables constant. Monthly differences between 2016 and 2012 in fCO sw 2 , temperature and salinity were also computed.

Data Availability
The KAI and MAI data are available through Australia's Integrated Marine Observing System data portal (https:// portal.aodn.org.au). The SOTS CO 2 data are available via the NOAA National Centers for Environmental Information data portal (https://www.nodc.noaa.gov/ocads/oceans/Moorings/SOFS.html). Data from other SOTS sensors are available through Australia's Integrated Marine Observing System data portal (https://portal.aodn. org.au).