Concurrent Decadal Trend Transitions of Sea Ice Concentration and Sea Surface pCO₂ in the Beaufort Sea

Highlights

What are the main findings?

• A decadal trend transition in sea surface pCO₂ in the Beaufort Sea was found around 2010–2012 both by observation and via a numerical model.
• The sea surface pCO₂ trend transition was driven by a concurrent trend transition in sea ice cover through changing the seasonal duration of open-water.

What are the implications of the main findings?

• This finding improves our understanding of the decadal-scale response of the Arctic Ocean carbon cycle to climate changes.
• This finding advances our understanding of the influence of seasonal sea ice variabilities on decadal trends in the carbon cycle.

Abstract

Interannual climate changes and increasing atmospheric CO₂ (AtmCO₂) have significantly altered sea surface partial pressure of CO₂ (pCO₂) in the Beaufort Sea (BS). Yet, their decadal variability and underlying mechanisms remain inadequately understood. Using observational data and the Regional Arctic System Model (RASM), a decreasing trend transition of the BS summer surface pCO₂ was identified at around 2010–2012. Sensitivity cases reveal that the decadal trend transition in surface pCO₂ (early: 4.12 ± 0.80 μatm/yr, p < 0.05 and late: 1.23 ± 2.22 μatm/yr, p > 0.05) is driven by interannual climate changes. While the long-term increase in AtmCO₂ does not directly drive surface pCO₂ trend transition, it reduces its magnitude. The sensitivity experiment with no interannual AtmCO₂ changes from 1990 reveals that the statistically significant contributor of the decadal trend transition in surface pCO₂ is the concurrent transition in sea ice concentration (SIC, early: −0.0120 ± 0.0037/yr, p < 0.05 and late: 0.0101 ± 0.0063/yr, p > 0.05). The decadal trend transitions in the subsurface and deep layer pCO₂ are negligible compared to that in the sea surface pCO₂ due to the insignificant influence of interannual climate changes on subsurface and deep layer pCO₂. The surface pCO₂ decadal trend transition is significantly correlated with a trend transition of CO₂ sink. On seasonal timescales, the effects of SIC on the decadal trend transition of pCO₂ occur primarily within the duration of open-water (DOW), and align with the decadal trend transitions in the open-water start day, end day, and DOW. The magnitude of sea surface pCO₂ trend transition increases as the magnitude of the DOW trend transition increases.

1. Introduction

Since the Industrial Revolution, anthropogenic emissions have elevated atmospheric CO₂ (AtmCO₂) from approximately 277 ppm in 1750 [1] to 417 ppm in 2022. This level exceeds the natural range of 180–300 ppm observed over the past 650,000 years [2]. The ocean absorbs about 26% of anthropogenic CO₂ emissions, acting as Earth’s primary CO₂ sink [3,4,5]. The Arctic Ocean covers only 4% of the global ocean, yet it serves as a critical carbon sink accounting for 5–14% of the global oceanic carbon uptake [6,7,8].

The Arctic has experienced rapid climate changes in recent decades, such as warming near-surface air temperature [9], decreasing sea ice cover [10,11], a change from a cyclonic circulation pattern to an anomalous anticyclonic circulation pattern [12], altered surface circulation [13,14,15], and increase in inflow of Pacific summer water [16,17], air–sea CO₂ exchanges [18,19], ocean stratification [20], and net primary production (NPP) [21,22]. These changes affect carbon cycle pathways and magnitude.

The sea surface partial pressure of CO₂ (pCO₂), a critical parameter in the carbon sink, exhibits pronounced spatiotemporal heterogeneity in the western Arctic Ocean [19,23]. From 1994 to 2017, the increasing long-term trend of summer surface pCO₂ in both the Canada Basin and the adjacent Beaufort Sea (BS) was twice that of the atmosphere due to decreased sea ice cover and warmed ocean temperature [19]. In contrast, the increasing long-term trend of summer surface pCO₂ in the Chukchi Sea was insignificant, which was attributed to the increased NPP [19,22] due to an extended duration of open-water (DOW) [24,25] and the enhanced inflow of nutrient-rich Pacific summer water [26].

On seasonal timescales, sea surface pCO₂ in the western Arctic Ocean is significantly influenced by sea ice cover [6,27]. During sea ice formation, solute exclusion elevates surface pCO₂ in the Beaufort Gyre [28]. During sea ice melt, surface pCO₂ is reduced by low-pCO₂ ice meltwater mixing, CaCO₃ dissolution, and photosynthesis in the Amundsen Gulf and BS [29]. During open-water period, the surface pCO₂ is increased by elevated temperatures [30] and air–sea CO₂ exchange in the Canada Basin [31,32,33]. Decreased sea ice cover amplified seasonal surface pCO₂ variability and led to a stronger increasing long-term trend [19].

A decadal trend transition in the sea ice extent in the Canada Basin between 1994 and 2012, and 2010 and 2020 drove a subsequent trend transition in sea surface acidification [27]. However, it remains unclear whether the sea ice and surface pCO₂ in the shelf sea also exhibit a similar trend transition. Extensive research has been conducted on the relationship between sea ice and pCO₂ in terms of long-term trends and interannual variability in the Canada Basin, Chukchi Sea, and BS [19,22,23]. The relationship between the seasonal variability of sea ice and the decadal trend of surface pCO₂ has not been fully elucidated. The surface pCO₂ in the BS has experienced dramatic changes under climate warming and changing interactions of Pacific, Atlantic, and Arctic surface waters, including shelf-break upwelling [34] and wintertime brine rejection-induced sinking [28]. These changes reflect both long-term trend under consistently increasing AtmCO₂ and seasonal to interannual changes in the physical and biogeochemical variables. Therefore, this study focuses on surface pCO₂ changes in the BS from 1990 to 2020. The decadal trend transitions of sea ice concentration (SIC), surface pCO₂, and CO₂ sinks were investigated using the ice–sea–ecosystem coupled model as well as observation. The mechanisms of surface pCO₂ trend transition were explored using sensitivity experiments and multiple linear regression. In addition, the relationship between the decadal trend transition of surface pCO₂ and seasonal-scale sea ice variability is also discussed in terms of days since ice retreat (DSR).

2. Materials and Methods

2.1. Regional Arctic System Model (RASM)

RASM is a coupled ice–ocean–ecosystem model that can be run with either high-resolution (1/12°) in the regional Arctic or coarse resolution (1-degree) in the global domain [35]. RASM is built on the Community Earth System Model (CESM) framework, integrating the Parallel Ocean Program version 2 (POP2) and Community Ice CodE (CICE) sea ice models developed by Los Alamos National Laboratory (LANL) [36,37,38]. RASM improves the simulation of critical physical processes, feedbacks, and their effects on the Arctic climate system, while reducing uncertainties in predictions [39]. Initial conditions for temperature and salinity were obtained from the Polar Science Center Hydrographic Climatology (PHC), with nitrate data sourced from the gridded World Ocean Atlas (WOA2013, https://www.nodc.noaa.gov/OC5/woa13/woa13data.html, accessed on 13 September 2024) provided by NOAA [40,41]. JRA-55 reanalysis data (http://search.diasjp.net/en/dataset/JRA55, accessed on 13 September 2024) was employed as the atmospheric forcing field, featuring a 3 h temporal resolution and a 0.5° spatial resolution [42]. JRA-55 also provides the input of river freshwater runoff for ocean models. The AtmCO₂ from Barrow observatory was employed as the AtmCO₂ forcing field. The marine biogeochemistry (BGC) module was based on a moderately complex Nutrient–Phytoplankton–Zooplankton–Detritus (NPZD) model, incorporating 26 state variables for phytoplankton, nutrients, zooplankton, and other carbon and nutrient reservoirs [43]. Coastal erosions are not included as no interannual varying data of coastal erosions are available. In this study, we analyzed model outputs for summer (July–September) from 1990 to 2020, including temperature (°C), salinity (psu), seawater pCO₂ (μatm), dissolved inorganic carbon (DIC, μmol/kg), total alkalinity (TA, μmol/kg), SIC, mixed layer depth (MLD, m), nitrate (NO₃, mmol/m³), and NPP (mmol/m²/d). The NPP represents the combined net primary productivity of three phytoplankton groups (diatoms, small phytoplankton, and nitrogen fixers) [44].

A control case and two sensitivity cases from RASM were configured (

Table 1. Design of control case and sensitivity cases.

Experiment Name	JRA-55	AtmCO2
case C	with interannual change	with interannual change
case S1	with interannual change	1990
case S2	1990	with interannual change

): (1) control case C includes both interannual change in AtmCO₂ and climate; (2) sensitivity case S1 excludes interannual AtmCO₂ changes (repeats 1990 AtmCO₂ seasonal cycle) from 1990 onward; and (3) sensitivity case S2 excludes interannual climate changes (repeats 1990 JRA seasonal cycle forcing) from 1990 onward. Comparisons among these three cases were employed to evaluate the effects of AtmCO₂ increase and interannual climate changes on decadal trend transition of the BS summer surface pCO₂.

2.2. NSIDC Sea Ice Data and In Situ Observations

The daily SIC data were sourced from the National Snow and Ice Data Center (NSIDC, https://nsidc.org/data/nsidc-0051/versions/2, accessed on 13 June 2025), based on calibrated passive microwave remote sensing retrievals from the Nimbus-7 SMMR, SSM/Is, and SSMIS sensors, with a spatial resolution of 25 × 25 km [45].

Summer sea surface pCO₂ underway data in the BS during the summer from 1997 to 2019 were obtained from international databases, including the China National Arctic and Antarctic Data Center (https://datacenter.chinare.org.cn/data-center/dindex, accessed on 20 July 2025), Surface Ocean CO₂ Atlas (SOCAT v2024, http://www.socat.info, accessed on 5 August 2025), Japan Agency for Marine-Earth Science and Technology (JAMSTEC, https://www.jamstec.go.jp/e/, accessed on 10 August 2025), NSF Arctic Data Center, Carbon Dioxide Information Analysis Center (CDIAC, https://cdiac.ess-dive.lbl.gov, accessed on 10 August 2025), and the United States Geological Survey database (USGS, https://pubs.er.usgs.gov, accessed on 10 August 2025). The spatial distribution of observational sites in the western Arctic Ocean from 1997 to 2019 is presented in Figure 1.

2.3. Air–Sea CO₂ Fluxes (FCO₂), CO₂ Sink, and Ekman Pumping Velocity (EPV)

The air–sea CO₂ flux (FCO₂, mmol C/m²/ d) is calculated as follows [46]:

$${\mathrm{F}\mathrm{C}\mathrm{O}}_2={\mathrm{k}}_{\mathrm{s}}\times {\mathrm{K}}_0\times {(p\mathrm{C}\mathrm{O}}_{2,\mathrm{s}\mathrm{e}\mathrm{a}}-{p\mathrm{C}\mathrm{O}}_{2,\mathrm{a}\mathrm{i}\mathrm{r}})$$

(1)

where ${p\mathrm{C}\mathrm{O}}_{2,\mathrm{s}\mathrm{e}\mathrm{a}}$ and ${p\mathrm{C}\mathrm{O}}_{2,\mathrm{a}\mathrm{i}\mathrm{r}}$ represent the CO₂ partial pressure in seawater and atmosphere, respectively. ${\mathrm{K}}_0$ represents CO₂ solubility, influenced by temperature and salinity [47], and ${\mathrm{k}}_{\mathrm{s}}$ is the gas transfer velocity, calculated from wind speed and modulated by sea ice as follows [46]:

$${\mathrm{k}}_{\mathrm{s}}=-0.251\times {{\mathrm{U}}_{10}}^2\times {\left(\mathrm{S}\mathrm{c}/660\right)}^{-0.5}\times \left(1-\mathrm{S}\mathrm{I}\mathrm{C}\right)$$

(2)

where ${\mathrm{U}}_{10}$ (m/s) represents the wind speed at 10 m (from JRA-55 in this study), SIC represents sea ice concentration, ranging from 0 to 1, and $\mathrm{S}\mathrm{c}$ is the Schmidt number, influenced by temperature [46].

The CO₂ sink (Tg C/yr) is calculated as follows [23,48]:

$${\mathrm{CO}}_2 \mathrm{Sink}=\iiint {\mathrm{F}\mathrm{C}\mathrm{O}}_2\left(\mathrm{x},\mathrm{y},\mathrm{t}\right)·\mathrm{A}\left(\mathrm{x},\mathrm{y}\right)\mathrm{d}\mathrm{x} \mathrm{d}\mathrm{y} \mathrm{d}\mathrm{t}$$

(3)

where x and y represent the horizontal grid indices of the model domain, A represents area of the corresponding grid, and t represents the time index.

In a complex environment with partial sea ice coverage, the calculation of the EPV (cm/d) intensity index must account for both the atmospheric–seawater stress and the sea ice–seawater stress effects [49]. The EPV is calculated as follows [50]:

$$\mathrm{E}\mathrm{P}\mathrm{V}=\left(\nabla \times \overrightarrow{\mathsf{\tau }}\right)/\left(\mathsf{\rho }\mathrm{f}\right)$$

(4)

where $\overrightarrow{\mathsf{\tau }}$ represents the total surface stress (N/m²), $\mathsf{\rho }$ represents density of seawater (kg/m³), and f is the Coriolis coefficient (s⁻¹). The total surface stress is calculated as $\overrightarrow{\mathsf{\tau }}=\left(1-\mathsf{\alpha }\right)\overrightarrow{{\mathsf{\tau }}_{\mathrm{a}\mathrm{i}\mathrm{r}}}+\mathsf{\alpha }\overrightarrow{{\mathsf{\tau }}_{\mathrm{i}\mathrm{c}\mathrm{e}}}$ [49]. The atmospheric stress is given by $\overrightarrow{{\mathsf{\tau }}_{\mathrm{a}\mathrm{i}\mathrm{r}}}={\mathrm{C}}_{\mathrm{D}}{\mathsf{\rho }}_{\mathrm{a}\mathrm{i}\mathrm{r}}\overrightarrow{{\mathrm{U}}_{10}}\left|\overrightarrow{{\mathrm{U}}_{10}}\right|$, where ${\mathrm{C}}_{\mathrm{D}}$ is the drag coefficient, set to 0.00125 [51], ${\mathsf{\rho }}_{\mathrm{a}\mathrm{i}\mathrm{r}}$ is the air density, set to 1.225 kg/m³, and $\overrightarrow{{\mathrm{U}}_{10}}$ is the wind speed at 10 m (m/s). The sea ice stress is expressed as $\overrightarrow{{\mathsf{\tau }}_{\mathrm{i}\mathrm{c}\mathrm{e}}}={\mathrm{C}}_{\mathrm{I}\mathrm{D}}{\mathsf{\rho }}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}\left(\overrightarrow{{\mathrm{U}}_{\mathrm{i}\mathrm{c}\mathrm{e}}}-\overrightarrow{{\mathrm{U}}_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}}}\right)\left|\left(\overrightarrow{{\mathrm{U}}_{\mathrm{i}\mathrm{c}\mathrm{e}}}-\overrightarrow{{\mathrm{U}}_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}}}\right)\right|$, where ${\mathrm{C}}_{\mathrm{I}\mathrm{D}}$ is the sea ice drag coefficient, set to 0.0055 [52], ${\mathsf{\rho }}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$ is the seawater density, $\overrightarrow{{\mathrm{U}}_{\mathrm{i}\mathrm{c}\mathrm{e}}}$ is the sea ice velocity, $\overrightarrow{{\mathrm{U}}_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}}}$ is the ocean current velocity, with seawater density, sea ice velocity, and ocean current velocity derived from RASM outputs [44].

2.4. Multiple Linear Regression and Temperature-Normalized pCO₂

According to previous studies, seawater pCO₂ can be calculated from temperature, DIC, TA, and salinity [53]. Other potential drivers (e.g., biological activity, mixing processes) also influence seawater pCO₂ through these four variables. DIC can be affected by temperature, salinity, SIC, EPV, MLD, AtmCO₂, NPP, and NO₃ [54,55]. TA can be affected by temperature, salinity, and SIC [56]. Therefore, we selected temperature, salinity, SIC, EPV, NPP, MLD, NO₃, and AtmCO₂ as the predictors. In order to understand the mechanisms underlying the influence of interannual climate changes on the decadal trend transition in surface pCO₂, we normalized (values subtracted by the mean and divided by the standard deviation) the trends in the selected predictors from case S1 and then performed multiple linear regression on the summer mean (July–September) from 1990 to 2012 and 2010 to 2020, respectively. These two periods were first introduced in the west Arctic Ocean by Qi et al. [27], and in this study, this trend transition is further confirmed with both the NSIDC SIC and modeled surface pCO₂ in the BS in the Section 3.2. In the final regression, we retained SIC, EPV, NPP, and MLD as predictors. AtmCO₂ was excluded due to no interannual AtmCO₂ changes in case S1. Temperature and salinity were excluded because they are significantly correlated with SIC and their seasonal variability in the surface Beaufort Sea is predominantly driven by sea–ice processes. Similarly, NO₃ was removed due to its strong correlation with NPP that more directly represents biological production.

The final regression equation was calculated as follows:

$${p\mathrm{C}\mathrm{O}}_2=\mathrm{a}+{\mathrm{b}}_1\mathrm{S}\mathrm{I}\mathrm{C}+{\mathrm{b}}_2\mathrm{E}\mathrm{P}\mathrm{V}+{\mathrm{b}}_3\mathrm{N}\mathrm{P}\mathrm{P}+{\mathrm{b}}_4\mathrm{M}\mathrm{L}\mathrm{D}$$

(5)

To remove thermal effect, the modeled sea surface pCO₂ were normalized to a constant temperature following the widely adopted approach [57,58,59]:

$${p\mathrm{C}\mathrm{O}}_{2,\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}-\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}}={p\mathrm{C}\mathrm{O}}_2\times \exp \left({\mathsf{\gamma }}_{\mathrm{T}}\times \left(\overline{\mathrm{S}\mathrm{S}\mathrm{T}}-\mathrm{S}\mathrm{S}\mathrm{T}\right)\right)$$

(6)

where ${\mathsf{\gamma }}_{\mathrm{T}}$ represents the temperature sensitivity of CO₂ of 0.0423/°C [53], and $\overline{\mathrm{S}\mathrm{S}\mathrm{T}}$ represents the multi-year mean SST.

2.5. DSR and Contribution Decomposition to pCO₂ Seasonal Variability

The day of ice retreat is defined as the day when the modeled BS mean SIC first falls below 0.15 in the melting season, and DSR is the days since the day of ice retreat [33] with a range of −80 < DSR < 90. The years 1991, 1992, 1996, and 2018 are excluded from the analysis due to the absence of ice retreat in the BS mean daily SIC on a seasonal timescale. The seasonal decline range is defined as the period starting from DSR = −80 until the first increase in pCO₂. Following this, the period during which pCO₂ rises continuously until DSR = 40 is defined as the seasonal increase range. The results are not sensitive to the spatial resolution of the SIC data.

The total seasonal surface pCO₂ variability within the study period is as follows:

$${∆p\mathrm{C}\mathrm{O}}_2={p\mathrm{C}\mathrm{O}}_{2,\mathrm{e}\mathrm{n}\mathrm{d}}-{p\mathrm{C}\mathrm{O}}_{2,\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}$$

(7)

where the subscripts ‘initial’ and ‘end’ represent the variables from the model at the initial and end times of the study period, respectively.

The contributions of air–sea CO₂ exchange and biological production to surface DIC variability within the study period are as follows [19,27,33]:

$$∆{\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{G}}=\int {\mathrm{F}\mathrm{C}\mathrm{O}}_2/(\mathrm{M}\mathrm{L}\mathrm{D}·\mathsf{\rho })\mathrm{d}\mathrm{t}$$

(8)

$${∆\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{B}}=\int \mathrm{N}\mathrm{C}\mathrm{P}/(\mathrm{M}\mathrm{L}\mathrm{D}·\mathsf{\rho })\mathrm{d}\mathrm{t}$$

(9)

where $∆\mathrm{D}\mathrm{I}\mathrm{C}$ with subscripts ‘G’, ‘B’ represents the changes in DIC induced by air–sea CO₂ exchange and biological production, respectively. NCP represents net community production (mmol/m²/d), which is approximated here using NPP following Yang et al. [33].

The contributions of thermal effect, biological production, air–sea CO₂ exchange, and water mixing to ${∆p\mathrm{C}\mathrm{O}}_2$ are calculated as follows [33]:

$${∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{T}}=\mathrm{F}\left(\overline{\mathrm{D}\mathrm{I}\mathrm{C}},\overline{\mathrm{T}\mathrm{A}},{\mathrm{S}\mathrm{S}\mathrm{T}}_{\mathrm{e}\mathrm{n}\mathrm{d}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)-\mathrm{F}\left(\overline{\mathrm{D}\mathrm{I}\mathrm{C}},\overline{\mathrm{T}\mathrm{A}},{\mathrm{S}\mathrm{S}\mathrm{T}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)$$

(10)

$${∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{G}}=\mathrm{F}\left({\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}+{∆\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{G}},\overline{\mathrm{T}\mathrm{A}},\overline{\mathrm{S}\mathrm{S}\mathrm{T}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)-\mathrm{F}\left({\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}},\overline{\mathrm{T}\mathrm{A}},\overline{\mathrm{S}\mathrm{S}\mathrm{T}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)$$

(11)

$${∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{B}}=\mathrm{F}\left({\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}+{∆\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{B}},\overline{\mathrm{T}\mathrm{A}},\overline{\mathrm{S}\mathrm{S}\mathrm{T}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)-\mathrm{F}\left({\mathrm{D}\mathrm{I}\mathrm{C}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}},\overline{\mathrm{T}\mathrm{A}},\overline{\mathrm{S}\mathrm{S}\mathrm{T}},\overline{\mathrm{S}\mathrm{S}\mathrm{S}}\right)$$

(12)

$${∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{M}}={∆p\mathrm{C}\mathrm{O}}_2-{(∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{T}}+{∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{G}}+{∆p\mathrm{C}\mathrm{O}}_{2,\mathrm{B}})$$

(13)

where ${∆p\mathrm{C}\mathrm{O}}_2$—with subscripts ‘T’, ‘G’, ‘B’, and ‘M’—represents changes in sea surface pCO₂ induced by thermal effect, air–sea CO₂ exchange, biological production, and water mixing, respectively. The variables with an overline represent their mean values from model over the study period. The function F is calculated through CO₂SYSv3.1.2 in MATLAB version R2019a [60,61].

3. Results

3.1. Model Validation

The RASM (case C) results (sea surface pCO₂, SIC, SST, and SSS) and remote sensing data (SIC) are interpolated to the spatiotemporal locations of the underway data (sea surface pCO₂, SST, and SSS) for model validation in the BS during the summer (July–September) from 1997 to 2019. The modeled sea surface pCO₂ exhibited an increasing trend (3.02 ± 1.46 μatm/yr, p > 0.05), comparable to the observational trend (2.28 ± 0.91 μatm/yr, p < 0.05) with a significant correlation (r = 0.80, p < 0.001) and a root mean square error (RMSE) of 27.37 μatm (Figure 2a). The modeled SIC exhibited an increasing long-term trend (0.0044 ± 0.0050/yr, p > 0.05) comparable to remote sensing data (0.0028 ± 0.0036/yr, p > 0.05) with a significant correlation (r = 0.93, p < 0.001) and an RMSE of 0.0746 (Figure 2b). The modeled and observational SST were significantly correlated (r = 0.88, p < 0.001) with an RMSE of 1.78 °C (Figure 2c). However, the modeled SST exhibited a lower long-term trend than the observed. The modeled and observational sea surface salinity (SSS) were insignificantly correlated (r = 0.34, p = 0.182) with an RMSE of 1.99 (Figure 2d), possibly due to model errors in capturing enhanced surface freshwater accumulation in the Beaufort Gyre [44]. Nevertheless, the modeled long-term trend in SSS remains consistent with observational data with the decreasing trend of −0.02 ± 0.03/yr (p > 0.05) and −0.05 ± 0.05/yr (p > 0.05), respectively. When using RMSE to represent the model uncertainty, and the standard deviation of observations to represent the magnitude of interannual variability, the model uncertainties are less than the magnitude of interannual variability for pCO₂, SIC, and SST. The model uncertainty for SSS is larger than the magnitude of interannual variability, primarily due to the model’s inability to capture the sustained low values of SSS during the 2010–2013 period. Overall, the model’s long-term trends for sea surface pCO₂ and SIC as well as decadal trend for surface pCO₂ align with observations in the BS during the summer from 1997 to 2019. Therefore, the RASM results were adequately used to explore the mechanisms of the decadal trend transition in surface pCO₂. Model validation for the subsurface and deep layer is presented in the Supplementary Materials.

3.2. Decadal Trend Transition in Sea Surface pCO₂

Sea ice plays a critical role in regulating the carbon cycle in the Arctic Ocean. The mean SIC in the BS from remote sensing exhibited a decadal trend transition from a rapid decrease (−0.0115 ± 0.0043/yr, p < 0.05) during 1990 to 2012 to a slight increase (0.0064 ± 0.0093/yr, p > 0.05) with strong interannual variability during 2010 to 2020 (Figure 3a). The decadal trend transition in SIC may be associated with a southeastward shift in the Beaufort Gyre that facilitates the transport of sea ice from high latitudes to the BS during the summer [15,62,63]. Despite the increasing trend in SIC during the late period, the mean value in SIC (0.1264) remained lower than that of the early period (0.2090). The model reproduced the SIC trend transition, from a decreasing trend of −0.0120 ± 0.0037/yr (p < 0.05) in the early period to an increasing trend of 0.0101 ± 0.0063/yr (p > 0.05) in the late period. Additionally, the modeled mean sea surface pCO₂ exhibited a corresponding decadal trend transition (Figure 3b) from a rapid increasing trend (4.12 ± 0.80 μatm/yr, p < 0.05) in the early period to a more moderate increasing trend (1.23 ± 2.22 μatm/yr, p > 0.05) in the late period. The sea surface pCO₂ and SIC were actually significantly correlated over the entire period (r = −0.83, p < 0.001). This is similar to the reported trend transitions in both sea ice extent and sea surface acidification in the Canada Basin between 1994 to 2012 and 2010 to 2020 [27]. This event was also accompanied by a strong correlation between the two variables in both periods: sea ice extent decreased rapidly and sea surface acidification increased rapidly in the early period, whereas both exhibited slower rates in the late period. The modeled BS surface pCO₂ data averaged over the entire model grid (Figure 3b) show a different trend from those averaged over the spatiotemporal locations of the underway (Figure 2a), i.e., during 1997–2005. This is because the trends in Figure 2a include large impacts from spatiotemporal coverage differences in the sparse observations between years, highlighting the advantage of model data in the long-term analysis.

The modeled sea surface pCO₂ in the BS reduced the increasing trend following the transition rather than reversing as in the SIC trend transition, due to increasing AtmCO₂ and air-sea pCO₂ flux maintaining an increasing trend of surface pCO₂ [44]. This is further elucidated by the comparison of the control case with sensitivity cases excluding interannual changes of AtmCO₂ (case S1, Figure 3c) or climate (case S2, Figure 3d). When long-term increase in AtmCO₂ was excluded from 1990 (case S1), the sea surface pCO₂ still exhibited a strong trend transition from fast increase (2.85 ± 0.77 μatm/yr, p < 0.05) during the early period to moderate decrease (−0.90 ± 1.94 μatm/yr, p > 0.05) during the late period (Figure 3c). In contrast, the case S2 was characterized by a near-linear increase in the sea surface pCO₂ with very small interannual fluctuations (Figure 3d). The magnitude of sea surface pCO₂ trend transition in case S1 (the absolute difference between the late and early trends, 3.75 μatm/yr) was even larger than that in case C (2.89 μatm/yr). This indicates that the long-term AtmCO₂ increase did not lead to a sea surface pCO₂ trend transition but reduced the magnitude of the trend transition. Comparison of case C, S1 and S2 indicates that the decadal trend transition in sea surface pCO₂ is primarily driven by interannual climate changes rather than increasing AtmCO₂. In the case C, the decadal trend transitions of pCO₂ in the subsurface (20–50 m, magnitude of trend transition: 0.74 μatm/yr) and deep layer (50–120 m, magnitude of trend transition: 0.07 μatm/yr) were negligible compared to that in the sea surface (Figure 4a,e). Moreover, the transitions in these two layers remained relatively small in sensitivity cases (Figure 4).

3.3. Mechanisms Driving the Decadal Trend Transition in Sea Surface pCO₂

After standardizing all variables in Equation (5), a multiple linear regression was performed using sensitivity case S1 to identify the primary climate variables driving the sea surface pCO₂ variability in the BS. The regression results (

Table 2. Multiple linear regression coefficients for the trends of sea surface, subsurface, and deep layer pCO₂ in the BS during summer (July–September) between 1990 and 2012, and 2010 and 2020, based on standardized variables in case S1 (bold represents p < 0.05). Percentages indicate the relative contributions of influencing factors and they are calculated as the square of its regression coefficient divided by the sum of the square of regression coefficients of all statistically significant variables, and then adjusted by the sign of the regression coefficient.

Layer	Period	R2	SIC	EPV	NPP	MLD
Surface	early (1990–2012)	0.87	−0.674 −85.2%	0.063 0.7%	−0.113 −2.4%	0.249 11.6%
	late (2010–2020)	0.94	−0.714 −84.6%	−0.052 −0.4%	−0.231 −8.9%	0.192 6.1%
Subsurface	early (1990–2012)	0.45	−0.591 −93.3%	0.105 2.9%	−0.103 −2.8%	0.060 0.9%
	late (2010–2020)	0.38	0.190 7.0%	0.351 23.9%	−0.580 −65.3%	0.139 3.7%
Deep layer	early (1990–2012)	0.38	−1.636 −76.7%	−0.370 −3.9%	−0.665 −12.7%	−0.484 −6.7%
	late (2010–2020)	0.40	−0.072 −1.0%	0.039 0.3%	−0.702 −98.7%	−0.003 0.0%

) indicate that sea surface pCO₂ was significantly influenced solely by SIC among the 4 climate variables in the regression, with relative contributions of −85.2% in the early period and −84.6% in the late period, respectively. Note that SST is significantly correlated with SIC and it can also represent the interannual climate changes influencing sea surface pCO₂, although it was not used in the regression. Correlation analysis between SIC and sea surface pCO₂ (both original and temperature-normalized) in case C shows that SIC was significantly correlated with original surface pCO₂ (r = −0.88, p < 0.001) and temperature-normalized surface pCO₂ (r = −0.79, p < 0.001) in the early period. This indicates that SIC influenced surface pCO₂ through thermal and non-thermal effects (Figure 5a). In the late period, SIC retained a significant correlation with original surface pCO₂ (r = −0.82, p = 0.002) but lost significance with temperature-normalized surface pCO₂ (r = −0.17, p = 0.621). This indicates that SIC primarily influenced surface pCO₂ via thermal effect during this period (Figure 5b). Therefore, the trend transition in sea surface pCO₂ in the BS is primarily driven by the decadal climate changes represented by SIC and SST during the summer between 1990 and 2012, and 2010 and 2020.

Similar regressions for the subsurface and deep layer from sensitivity case S1 indicate that pCO₂ was only significantly influenced by SIC during the early period in the deep layer with relative contributions of −76.7%, but insignificantly influenced by the 4 variables during other periods and in other layers.

The CO₂ sink from control case C also exhibited a trend transition from a fast decrease (−0.04 ± 0.01 Tg C/yr², p < 0.05) during the early period to a moderate increase (0.01 ± 0.04 Tg C/yr², p > 0.05) during the late period (Figure 6). The direction and timing of decadal trend transition in CO₂ sink are comparable to those derived from in situ observations during July to October between 1994 and 2012, and 2010 and 2019 [23]. Additionally, the CO₂ sink and sea surface pCO₂ were significantly correlated in the early (r = 0.64, p = 0.001) and late periods (r = 0.83, p = 0.001), and their magnitude and timing of the trend transition were comparable. This reveals that the SIC-driven trend transition in sea surface pCO₂ drove a subsequent trend transition in the air–sea CO₂ sink.

3.4. Modulation of Sea Ice Retreat Timing on the pCO₂ Trend

Since the influences of SIC variability on the BS surface pCO₂ are most significant during ice melting season, here a seasonal timescale defined by DSR was used to examine the influences (Figure 7).

The contributions of thermal effect, biological production, air–sea CO₂ exchange, and water mixing to surface pCO₂ on a seasonal scale were calculated according to Equations (10–13) in Section 2.5. In −80 < DSR < 40, the BS surface pCO₂ first underwent a seasonal decline by −40.27 μatm in the early period (−80 < DSR < −38) and by −55.11 μatm in the late period (−80 < DSR < −26). The contributions to sea surface pCO₂ were mainly by biological production (early: −40.81 μatm and late: −59.32 μatm) and water mixing (early: −15.68 μatm and late: −22.22 μatm), and secondly by thermal effect (early: 8.95 μatm and late: 14.97 μatm) and air–sea CO₂ exchange (early: 7.27 μatm and late: 11.46 μatm) (Figure 7b and

Table 3. In the case C, the contributions of thermal effect, biological production, air-sea CO₂ exchange and water mixing to the seasonal decline and increase of sea surface pCO₂ within the −80 < DSR < 40 during the early and late periods in the BS.

	DSR Range	Contributions (μatm) to Sea Surface pCO2
		Total	Thermal Effect	Biological Production	Air-Sea CO2 Exchange	Water Mixing
seasonal decline in the early	−80 < DSR < −38	−40.27	8.95	−40.81	7.27	−15.68
seasonal decline in the late	−80 < DSR < −26	−55.11	14.97	−59.32	11.46	−22.22
seasonal increase in the early	−38 < DSR < 40	45.10	38.23	−58.05	82.32	−17.41
seasonal increase in the late	−26 < DSR < 40	51.52	49.48	−60.38	65.25	−2.83

). As the sea ice further melted to a complete retreat (DSR = 0), sea surface pCO₂ experienced a seasonal increase by 45.10 μatm in the early period (−38 < DSR < 40) and by 51.52 μatm in the late period (−26 < DSR < 40). The contributions to sea surface pCO₂ were mainly from thermal effect (early: 38.23 μatm and late: 49.48 μatm) and air–sea CO₂ exchange (early: 82.32 μatm and late: 65.25 μatm), and secondly by biological production (early: −58.05 μatm and late: −60.38 μatm) and water mixing (early: −17.41 μatm and late: −2.83 μatm). This pattern aligns with the 1-D mass balance model results reported for the Canada Basin [27,33], but the contribution of biological production is higher in the BS than in the Canada Basin.

The day of ice retreat (DSR = 0) from 1990 to 2020 exhibited a trend transition from a decreasing trend (−0.76 ± 0.67 d/yr, p > 0.05) in the early period to a near flat trend in the late period (Figure 8a). Additionally, the open-water end dates also exhibited a trend transition from an increasing trend (0.67 ± 0.56 d/yr, p > 0.05) in the early period to an insignificant decreasing trend (−0.56 ± 0.78 d/yr, p > 0.05) in the late period (Figure 8b). The DOW exhibited a trend transition from an increasing trend (3.09 ± 1.14 d/yr, p < 0.05) in the early period to an insignificant decreasing trend (−3.51 ± 3.70 d/yr, p > 0.05) with strong interannual fluctuation in the late period (Figure 8c).

Sea surface pCO₂ trends on each DSR in the early and late periods (Figure 7c) indicate that, prior to sea ice retreat (DSR < 0), the mean sea surface pCO₂ trends exhibited almost no decadal trend transition, as they were comparable between the early (3.05 ± 0.51 μatm/yr, p < 0.05) and late periods (3.16 ± 1.56 μatm/yr, p > 0.05). However, during the DOW, sea surface pCO₂ exhibits a sharp decreasing decadal transition, from 3.19 ± 0.69 μatm/yr (p < 0.05) in the early period to 2.36 ± 1.51 μatm/yr (p > 0.05) in the late period. The differences in sea surface pCO₂ trend transition between the two sea ice stages suggest that the trend transition was primarily contributed during the DOW on a seasonal scale and aligns with the concurrent decadal trend transitions in the day of ice retreat, open-water end dates, and the DOW. The decadal trend transitions in the DOW and sea surface pCO₂ are not only concurrent in time, but also proportional in magnitudes; for example, the magnitudes of trend transitions in the DOW and sea surface pCO₂ are both smaller (0.08 d/yr and 0.18 μatm/yr, Figure 3d and Figure 8d) in case S2 than those (6.60 d/yr and 2.89 μatm/yr, Figure 3c and Figure 8b) in case C. This indicates that the stronger the magnitude of the DOW trend transition, the stronger the magnitude of the sea surface pCO₂ trend transition.

4. Discussion

In sensitivity case S1, AtmCO₂ follows the repeating seasonal cycle of 1990 without any interannual increase, whereas the control case C uses the observed time-varying CO₂ from Barrow observatory, which includes both seasonal and interannual components. The difference between cases C and S1 thus isolates the effect of interannual AtmCO₂ increase. The shape and amplitude of the seasonal CO₂ cycle vary slightly from year to year, and these intra-annual differences (STD = 5.42 μatm) are small compared with the large interannual rise in AtmCO₂ (STD = 17.17 μatm) over the 1990–2020 period. The resulting nonlinear biogeochemical effects are negligible relative to the dominant interannual signal. Consequently, further decomposition of AtmCO₂ into separate seasonal-fluctuation and interannual-trend components was not performed, as it would not materially alter the attribution of the observed decadal pCO₂ trend transition.

The BS surface pCO₂ in summer exhibits a decadal trend transition around 2010–2012, changing from a rapid increase of 4.12 ± 0.80 μatm/yr (p < 0.05, 1990–2012) to a much weaker increase of 1.23 ± 2.22 μatm/yr (p > 0.05, 2010–2020). This slowdown closely tracks the trend transition in SIC from –0.0120 ± 0.0037/yr (p < 0.05) to 0.0101 ± 0.0063/yr (p > 0.05). This trend transition mirrors the previously documented finding on sea–ice extent and ocean acidification in the Canada Basin [27]. There are significant differences in both the magnitude of the sea–ice transition and the direction of the trend following the transition. The southeastward shift in the Beaufort Gyre position over the past decade may be the primary cause of this discrepancy, as it has altered the sea–ice transport from high latitudes to the BS [15]. Two RASM sensitivity cases were conducted and the comparison with control case revealed that the decadal transition in BS summer sea surface pCO₂ is primarily driven by interannual climate changes. The long-term increase in AtmCO₂ is at almost linear change. Therefore, increasing AtmCO₂ does not directly drive this trend transition, but reduces the magnitude of the trend transition from 2.89 μatm/yr in case C to 3.75 μatm/yr in case S1.

In order to identify the main drivers of the interannual climate changes, multiple linear regression between pCO₂ and climate-related variables (SIC, EPV, NPP, MLD) are conducted using RASM case S1. The results indicate that sea surface pCO₂ in the BS was significantly influenced solely by SIC with a relative contribution of −85.2% in the early period and −84.6% in the late period, indicating that the interannual climate changes are mainly contributed by SIC among the 4 variables in the regression. In the early period, the decline in SIC drove the increase in surface pCO₂ through both thermal and non-thermal effects (e.g., biological production, air–sea CO₂ exchange, and water mixing). In the late period, the rebound in SIC moderated this pCO₂ increase predominantly by thermal effect, likely because the lower mean SIC reduced the sensitivity of non-thermal processes to further SIC changes. Since SST is significantly correlated with SIC in the BS in the summer, it is not used in the regression. However, it is important to note that the interannual climate changes can also be represented by SST. Therefore, the decadal trend transition in BS surface pCO₂ is mainly driven by the decadal trend transition in SIC (and SST) induced by interannual climate changes. Furthermore, case S1 results also show that subsurface pCO₂ was insignificantly influenced by climate-related variables during both the early and late periods. Deep layer pCO₂ was significantly influenced solely by SIC during the early period and was not significantly influenced by climate-related variables during the late period. The generally insignificant influence of interannual climate changes on subsurface and deep layer pCO₂ is likely due to the strong ocean stratification [20] that slowed the pCO₂ response to climate changes. Thus, the decadal trend transitions in the subsurface and deep layer of the BS are close to none compared to that in the sea surface pCO₂.

The surface pCO₂ trend transition is one of the reasons for the CO₂ sink trend transition in the BS during the summer. In case C, the CO₂ sink exhibits significant interannual correlations with sea surface pCO₂ and has comparable magnitudes and timing of decadal trend transition (early: −0.04 ± 0.01 Tg C/yr², p < 0.05 and late: 0.01 ± 0.04 Tg C/yr², p > 0.05) during both periods. The decadal trend transition and its timing in CO₂ sink in model case C is comparable to those by Ouyang et al. [22] using in situ observations between 1994 and 2010, and 2010 and 2019. If the ongoing rebound in trend of SIC persists and continues to moderate the increasing trend of surface pCO₂, the CO₂ sink is likely to remain on an increasing trend in the future of the BS.

How the variability of SIC influences the BS surface carbon sink and pCO₂ are therefore investigated on a seasonal timescale in terms of DSR. The case C results indicate that, within the −80 < DSR < 40, sea surface pCO₂ initially decreased (due to biological production and water mixing), and then increased (due to air–sea CO₂ exchange and SST increase). This aligns with the seasonal variations in surface pCO₂ reported in the Canada Basin using a 1-D mass balance model [27,33]. The mean sea surface pCO₂ trends did not show any transition between the early and late periods before ice retreat (DSR < 0), but exhibited a notable transition afterwards during DOW (DSR from 0 to open-water end dates). This suggests that the decadal trend transition of the BS surface pCO₂ is primarily contributed during the DOW, and aligns with the decadal trend transition in the day of ice retreat, open-water end dates, and DOW. A comparison between two cases with different SIC evolutions (cases C and S2) reveals that the magnitude of sea surface pCO₂ trend transition increases as magnitude of DOW trend transition increases.

5. Conclusions

In recent decades, the rapid decline in the arctic sea ice has driven dramatic changes in the carbon sink capacity of the western Arctic Ocean. The response and its mechanism of sea surface pCO₂ to long-term SIC trend variability in the BS are analyzed in this study. The RASM was validated well with observed patterns of sea surface pCO₂ variability in response to sea ice changes. Building on this, the response mechanism of sea surface pCO₂ to SIC trend variability in the BS during the summer of 1990–2020 was quantified using numerical model sensitivity studies and multiple linear regression methods. The primary conclusions are as follows:

Underway data from the BS during the summer of 1997–2019 reveal a generally increasing trend in sea surface pCO₂, with a notable trend transition around 2010–2012. The RASM successfully reproduced this trend transition and the accompanying SIC changes. Therefore, the RASM are used as a tool to explore the mechanisms driving the decadal trend transition in sea surface pCO₂ variability.

RASM control and sensitivity cases, combined with multiple linear regression analyses, reveal a notable decadal transition in BS summer surface pCO₂. This transition is driven mainly by interannual climate changes, particularly the trend transition in SIC from a strong decrease to a slight increase around 2010–2012. The long-term increase in AtmCO₂ does not induce the transition but reduces its magnitude. The surface pCO₂ trend transition further drives a concurrent transition in the summer CO₂ sink, while subsurface and deep layer pCO₂ exhibit negligible trend transitions due to the generally insignificant influence of interannual climate changes on these layers.

On the seasonal timescale in terms of DSR, the decadal pCO₂ transition occurs mainly during the DOW and closely tracks the marked slowdown in open-water season lengthening after this transition. The magnitude of the decadal surface pCO₂ trend transition scales directly with the magnitude of the trend transition in open-water season duration.