Spatiotemporal variability and long-term trends of ocean acidification in the California Current System

Due to seasonal upwelling, the upper ocean waters of the California Current System (CCS) have a naturally low pH and aragonite saturation state ( arag), making this region particularly prone to the effects of ocean acidification. Here, we use the Regional Oceanic Modeling System (ROMS) to conduct preindustrial and transient (1995–2050) simulations of ocean biogeochemistry in the CCS. The transient simulations were forced with increasing atmospheric pCO2 and increasing oceanic dissolved inorganic carbon concentrations at the lateral boundaries, as projected by the NCAR CSM 1.4 model for the IPCC SRES A2 scenario. Our results show a large seasonal variability in pH (range of ∼ 0.14) andarag (∼ 0.2) for the nearshore areas (50 km from shore). This variability is created by the interplay of physical and biogeochemical processes. Despite this large variability, we find that present-day pH and arag have already moved outside of their simulated preindustrial variability envelopes (defined by ±1 temporal standard deviation) due to the rapidly increasing concentrations of atmospheric CO 2. The nearshore surface pH of the northern and central CCS are simulated to move outside of their present-day variability envelopes by the mid-2040s and late 2030s, respectively. This transition may occur even earlier for nearshore surface arag, which is projected to depart from its present-day variability envelope by the earlyto mid-2030s. The aragonite saturation horizon of the central CCS is projected to shoal into the upper 75 m within the next 25 yr, causing near-permanent undersaturation in subsurface waters. Due to the model’s overestimation of arag, this transition may occur even earlier than simulated by the model. Overall, our study shows that the CCS joins the Arctic and Southern oceans as one of only a few known ocean regions presently approaching the dual threshold of widespread and near-permanent undersaturation with respect to aragonite and a departure from its variability envelope. In these regions, organisms may be forced to rapidly adjust to conditions that are both inherently chemically challenging and also substantially different from past conditions.


Introduction
Since the onset of the industrial era, the oceans have absorbed about one-third of the anthropogenically emitted carbon dioxide . The uptake of anthropogenic CO 2 by the oceans has already reduced the global surface ocean pH by about 0.1 units  and it is projected to decrease another 0.3 to 0.4 pH units by the end of this century under the IPCC 1992 (IS92a) scenario (788 ppm in 2100, Orr et al., 2005). This chemical change, known as ocean acidification, also leads to a decline in the saturation state ( ) of seawater with respect to calcium carbonate minerals, such as calcite or the less stable form aragonite. While this altered carbon chemistry and its effects on marine ecosystems are an ongoing subject of intensive Published by Copernicus Publications on behalf of the European Geosciences Union. scientific research , many (although not all) results have demonstrated that these changes can have deleterious effects on marine-calcifying invertebrates such as corals, coralline algae, oyster larvae and pteropods (Orr et al., 2005;Kleypas et al., 2006;Martin and Gattuso, 2009).
The California Current System (CCS) has a naturally low pH and aragonite saturation state ( arag ), making it particularly prone to the effects of ocean acidification (Feely et al., 2008;Gruber et al., 2012). Seasonal upwelling is induced by equatorward winds in early spring. The upwelling brings cold subsurface water, rich in nutrients and dissolved inorganic carbon (DIC), up to the surface. The high DIC content of the upwelled waters endows them with a low pH and arag . Once close to the surface, the nutrient-rich water triggers the onset of phytoplankton blooms that then draw down oceanic pCO 2 to levels sometimes below atmospheric pCO 2 (Hales et al., 2005), causing an increase in surface water pH and arag . Conversely, remineralization processes of sinking organic matter counteract the effects of production by lowering pH and arag . Physical circulation can affect the duration and magnitude of these biological processes and therefore plays an important role in controlling the evolution and spatial pattern of pH and arag .
These physical and biological features create large spatial and temporal variability in pH and arag in the CCS (Feely et al., 2008;Juranek et al., 2009;Alin et al., 2012). North of Point Conception (34.5 • N), a combination of strong seasonal upwelling events and remineralization trigger a pH drop to 7.65 and arag to 0.8 at the surface in some nearshore environments (Feely et al., 2008). Combined with high biological production, a heterogeneous distribution of pH and arag is created. Offshore pH and arag are not directly influenced by upwelling and remain above 8.0 and 2.2, respectively. Reconstructed pH and arag from temperature (T ) and oxygen (O 2 ) time series from the central Oregon shelf display a seasonal range of arag of 0.8-1.8 at 30 m (Juranek et al., 2009), with lowest levels attained during the upwelling season between spring and fall. South of Point Conception, upwelling-favorable winds are weaker, yet more persistent throughout the year (Dorman and Winant, 1995). In contrast to the area north of Point Conception, reconstructed pH and arag from T and O 2 time series display the highest levels in summer, due to biological drawdown of CO 2 in warm subsurface waters (30 m). Spatial variability is also highest in summer, most likely driven by an interplay of high productivity and upwelling (Alin et al., 2012). At the Santa Monica Bay Observatory (SMBO at 33 • 55.9 N and 118 • 42.9 W), surface pH and arag display a large seasonal variability, ranging by ±0.08 (1 STD) and ±0.4 units, respectively (Leinweber and Gruber, 2013).
In the CCS, the aragonite saturation horizon has shoaled 50-100 m since the preindustrial era (Feely et al., 2008;Hauri et al., 2009;Juranek et al., 2009) and will continue to rise in response to future oceanic uptake of anthropogenic CO 2 . Simulations forced with increasing atmospheric pCO 2 -as projected by the NCAR CSM 1.4 model run under the IPCC SRES A2-scenario (Nakićenović and Swart, 2000) suggest that about 70 % of the euphotic nearshore region of the central US West Coast will become undersaturated with regard to aragonite ( < 1) during the upwelling season by 2050. Within the next 20 to 30 yr this "absolute" threshold of aragonite undersaturation will be reached throughout the year in nearly all habitats along the seafloor (Gruber et al., 2012).
Due to the large "natural" variability of pH and arag , it is conceivable that the organisms of the CCS are not only well adjusted to low levels of pH and arag , but also to a large range of chemical conditions. Therefore, in order to evaluate the impact of ocean acidification, it is also necessary to consider how the chemical conditions evolve in relationship to this "natural"variability. Eventually, the anthropogenic trend of ocean acidification will drive the waters toward levels of pH and arag that are well below those the organism experienced in the preindustrial era. Assuming that the organisms' tolerance for low pH and arag conditions decreases rapidly once it lives below these "natural" levels, we define a "relative" threshold, i.e., by determining how and when future trajectories of pH and arag begin to depart in a significant manner from current and prior conditions. Cooley et al. (2012) and Friedrich et al. (2012) have used global Earth System Models to study this relative threshold. However, their coarsely resolved models are not able to simulate many important local to regional processes, such as coastal upwelling. This in turn leads in these models to an overestimation of pH and arag levels, an underestimation of their temporal and spatial variability, and hence large potential errors in the timing of the crossing of the absolute and relative thresholds.
Here, we use regional model simulations to describe the spatiotemporal variability of pH and arag in the CCS from the Mexican to the Canadian border, and project their future evolution until 2050 using two emissions scenarios. We will investigate whether the CCS, despite its high variability, is projected to approach the combined absolute and relative thresholds of both chemical dissolution of aragonite and a departure from the variability envelopes of pH and arag .

Model setup
We use a United States West Coast configuration of the threedimensional Regional Oceanic Modeling System (ROMS) (Marchesiello et al., 2003;Shchepetkin and McWilliams, 2005), which simulates flow and mixing of ocean waters at an eddy-resolving horizontal resolution of 5 km. The model covers a 1300-km-wide section along the US West Coast from the US/Canadian border past the US/Mexican border to 29 • N (Fig. 1). The model grid is defined by horizontal Biogeosciences, 10, 193-216, 2013 www.biogeosciences.net/10/193/2013/ curvilinear coordinates and a terrain-following vertical coordinate (σ ) with 32 depth levels, with enhanced resolution near the surface and nearshore on the shallow shelf (see Gruber et al., 2011;Lachkar and Gruber, 2011, for a detailed description of the model setup). The biogeochemical model used here is a simple nitrogenbased NPZD 2 and is described in detail in Gruber et al. (2006). The analyzed simulations are those presented in Gruber et al. (2012) and use the same biogeochemical parameters as those employed by Lachkar and Gruber (2011). The model considers six pools of nitrogen, i.e., nitrate (NO − 3 ) and ammonium (NH + 4 ), phytoplankton, zooplankton and two types of detritus. The large detritus pool sinks fast (10 m day −1 ) and the smaller one sinks at a slower rate (1 m day −1 ). However, the small detritus pool coagulates with a fraction of phytoplankton to form large detritus, which increases its sinking speed.
The carbon component of the model adds three new state variables to the biogeochemical model, i.e., DIC, Alkalinity (Alk) and mineral CaCO 3 . It is not necessary to add explicit carbon-based state variables to the organic pools, i.e., phytoplankton, zooplankton and the two detrital pools, since they are all assumed to have a fixed C:N stoichiometric ratio of 106 : 16 (Redfield et al., 1963). This also implies that biologically mediated processes with the exception of the biogenic formation of CaCO 3 are assumed to have this stoichiometry as well. DIC is modified by gas exchange, CaCO 3 precipitation and dissolution, and net community production, which is net primary production minus heterotrophic respiration. Alk is primarily governed by the precipitation and dissolution of CaCO 3 . But Alk is also changed by the generation of NO − 3 through nitrification and its removal by new production. The biogenic CaCO 3 formation is tied to net primary production with a fixed production ratio of 7 % (Sarmiento et al., 2002;Jin et al., 2006), i.e., for each mole of organic carbon formed by NPP, 0.07 mol of CaCO 3 is formed. CaCO 3 dissolves at a constant dissolution rate of 0.0057 day −1 and sinks at a velocity of 20 m day −1 , which is twice the sinking velocity of large detritus. Oceanic pCO 2 is calculated from DIC, Alk, T and salinity (S) using the standard OCMIP carbonate chemistry routines 1 . The routines used the carbonic acid dissociation constants of Mehrbach et al. (1973), as refit by Dickson and Millero (1987) and Dickson (1990). The pressure effect on the solubility was taken from Mucci (1983), including the adjustments to the constants recommended by Millero (1995). Gas exchange is parameterized following Wanninkhof (1992), with the gas transfer velocity depending on the square of the wind speed. The reader interested in a more detailed description of the carbon biogeochemistry module is referred to Appendix A. 1 http://ocmip5.ipsl.jussieu.fr/OCMIP/ The light blue line defines the study area of 50 km along the coast. Because of the perpend the regional boundaries the off-shore part of each region's lower boundary lays south of th latitudes. The yellow dots indicate the locations used in the model-observational data spat Sect. 3). The arrow is pointed at the transect used for visual comparison. The Santa Moni Mooring (33 • 55.9 N and 118 • 42.9 W) is shown as a red dot. The northern subregion is defined by the dark blue box and represents the area between the northern boundary of 47.5 • N and a southern boundary at Cape Mendocino (40.5 • N). Between Cape Mendocino and Point Conception (34.5 • N) the central subregion is defined by the orange box. The southern subregion extends southward from Point Conception to 32.4 • N. The light blue line defines the study area of 50 km along the coast. Because of the perpendicular orientation of the regional boundaries, the offshore part of each region's lower boundary lays south of the above mentioned latitudes. The yellow dots indicate the locations used in the model-observational data spatial comparison (see Sect. 3). The arrow is pointed at the transect used for visual comparison. The Santa Monica Bay Observatory Mooring (33 • 55.9 N and 118 • 42.9 W) is shown as a red dot.

Forcing
Our analysis is primarily based on a transient simulation for the years 1995 to 2050 (Gruber et al., 2012), with atmospheric CO 2 following the SRES A2 emissions scenario (Nakićenović and Swart, 2000). We compare these results with those from a time-slice simulation run under preindustrial conditions (Hauri et al., 2009) Risien and Chelton, 2008). The surface heat and freshwater fluxes were derived from the Comprehensive Ocean-Atmosphere Data Set (COADS) data products (da Silva et al., 1994) and applied with surface T and S restoring after Barnier et al. (1995) with a relaxation timescale of three months. To a limited extent, this approach allows implicitly taking into account riverine-driven seasonal variability of S associated with the Columbia River, even though riverine input is not explicitly modeled. The initial and boundary conditions for T , S and nutrients were taken from the World Ocean Atlas 2005 (WOA05) 2 . Monthly means of WOA05 were also used to prescribe T , S, and momentum fluxes along the three lateral open boundaries following a radiative scheme (Marchesiello et al., 2003). Initial and boundary conditions for DIC and Alk were taken from the GLobal Ocean Data Analysis Project (GLODAP, Key et al., 2004). A seasonal cycle was introduced in the DIC and Alk boundary conditions using a monthly climatology of pCO 2 (Takahashi et al., 2006) and a monthly climatology of surface Alk, calculated using T and S following Lee et al. (2006). These seasonal DIC and Alk variations are assumed to occur throughout the upper 200 m, but are attenuated with depth by scaling them to the vertical profile of the seasonal amplitude of T . After a model spin-up of 10 yr, the transient simulation was forced with increasing pCO 2 from 364 ppm in 1995 to 541 ppm in 2050, and increasing DIC concentrations at the lateral boundaries. These atmospheric and lateral boundary conditions were taken from a simulation of the fully coupled Earth System Model NCAR CSM 1.4 , which was forced with the SRES A2 emissions scenario (Nakićenović and Swart, 2000). While the atmospheric pCO 2 was taken directly from the NCAR model, the lateral DIC concentrations were determined by combining the present-day DIC field from GLO-DAP and adding to them the annual increment of DIC from the NCAR CSM 1.4 carbon model simulation. DIC and atmospheric pCO 2 at the lateral boundaries were the only forcings that changed over the years, while the atmospheric physical forcings, as well as the lateral boundary conditions of Alk, T , S, nutrients and circulation remained unchanged from their seasonal climatologies for the entire simulation from 1995 to 2050. For the preindustrial time-slice simulation, the atmospheric pCO 2 was set to a preindustrial value of 280 ppm, and the lateral DIC boundary conditions were taken from the preindustrial fields of GLODAP . In order to analyze the sensitivity of our results toward the chosen SRES emissions scenario, we compared the results of two additional transient simulations that follow both the "high-CO 2 " SRES emissions scenario A2 described above, and the "low-CO 2 " SRES emissions scenario B1 (Figs. A2 and A3). Due to computational constraints, these two addi-2 http://www.nodc.noaa.gov/OC5/WOA05/pr woa05.html tional simulations were conducted with a coarser-resolution setup of 15 km (Gruber et al., 2012). By 2050, atmospheric pCO 2 increased to 492 ppm in the B1 scenario, compared to 541 ppm in the A2 scenario.

Study area
As our primary interest is the nearshore area, we largely restricted our analyses to the first 50 km in an east-west direction along the coast (Fig. 1, within light blue line). With regard to depth, we analyzed pH and arag at two distinct depths, i.e., the surface and 100 m, in order to retain the full spatial variability of pH and arag , which would have been lost by averaging over the euphotic zone. We also divided the CCS into three subregions defined by Dorman and Winant (1995), based on distinct regional differences in the wind and temperature patterns that potentially affect the dynamics of pH and arag . The region north of Cape Mendocino (40.5 • N) is subsequently denoted as the "northern" (blue), the region between Cape Mendocino and Point Conception (34.5 • N) as the "central" (orange) and the region south of Point Conception as the "southern" (red) subregion ( Fig. 1).

Temporal resolution of model output
Our analyses of the modeled evolution of pH and arag from 2005 to 2050 are based on monthly averages, with the temporal resolution primarily having been determined by computational and storage constraints. Although such a monthly time averaging reduces the aliasing of unresolved timescales that would result from the analysis of monthly time-slices, it fails to capture the full variability. In order to determine the degree to which the monthly averages represent the full variability, we conducted a spectral analysis of the two-day model output that we had generated for a limited time period only (2006)(2007)(2008)(2009)(2010). Such a two-day output captures nearly all of the variability in our model, because in our climatologically forced simulations, all of the simulated high-frequency variability is driven by mesoscale processes with characteristic time scales of between a few days and several weeks.
For the spectral analysis, we calculated the Welch power density spectrum (PDS) of the Fourier transform of the detrended time series data from each grid cell using a Hann window (Glover et al., 2011). The interval for the frequencies (f ) captured with monthly output was set to a = 0.2 yr −1 and to b = 6 yr −1 , according to thresholds given by the Nyquist-Shannon sampling theorem. For the frequencies captured with two-day output, the upper boundary was set to c = 90 yr −1 . We quantified the amount of total variability across all frequencies from a to c and compared it to the amount of variability occurring in the frequencies from a to b. We define M as the percentage of the total variability of surface pH or arag that occurs at frequencies less than b as follows: (1) Biogeosciences, 10, 193-216, 2013 www.biogeosciences.net/10/193/2013/ A plot of M at the surface (Fig. 2a) reveals that in most areas (98.5 %) along the US West Coast, the majority of variability of surface-modeled pH and arag occurs at frequencies less than b and can be captured by monthly model output. However, as will be discussed in Sect. 4.1, highfrequency variability can lead to very low pH and arag in some nearshore surface areas. These few areas are limited to about 1.5 % of the nearshore 50 km along the US West Coast. There, less than 50 % of the total variability of surface pH can be captured with monthly model output (Fig. 2a, blue).
The time series (Fig. 2b) and the PDS of the Fourier transform ( Fig. 2c)  At 100-m depth, the majority of variability of modeled arag occurs at frequencies less than b (Fig. 3a). Thus the low-frequency variability of arag is the most dominant mode along the entire US West Coast (Fig. 3c) and can be very well captured by the monthly averages.
To account for areas where the model variability of pH and arag are not fully captured with monthly average output, we introduce a correction factor (var cf ): where σ 2 two-day is the temporal variance of the two-day output of model year 2010 and σ 2 month is the temporal variance of the monthly averaged, two-day output data of the same year. The correction factor var cf varies between 1.2 in the northern and southern CCS and 1.4 in the central CCS and is used to correct the variability envelopes in Sect. 4.4.
Additional high-frequency variability, such as due to synoptic wind-driven upwelling events, for example, cannot be captured with either model output type due to our choice of monthly climatological wind forcing (see Sects. 3 and 5 for further discussion).

Model evaluation
The model's performance for simulating observed sea surface T , surface chlorophyll and the mixed layer depth was already evaluated in Lachkar and Gruber (2011) and Gruber et al. (2006Gruber et al. ( , 2011. The model simulates the observed annual and seasonal patterns of surface temperature well with correlations of ρ = 0.98 and ρ = 0.95, respectively. It also captures successfully the offshore extent of the cold upwelling region. The modeled annual mean mixed-layer depth has a correlation of 0.70 with observational data, but has a substantially higher standard deviation relative to the observations. The annual mean pattern of chlorophyll a compares well with the SeaWiFS data set (ρ = 0.80), but the model underestimates chlorophyll a in the nearshore 100 km and has a poorer representation of its seasonal cycle (ρ = 0.46). The current paper will supplement these earlier evaluations by comparing the model to in situ data with an emphasis on vertical and cross-shore variability of the key carbonate chemistry properties in the upper ocean (also see Gruber et al., 2012).
First, we evaluate the modeled spatial variability of pH, arag , DIC, Alk, T and S by comparing it to data from the North American Carbon Program (NACP) West Coast Cruise (Feely et al., 2008) (Fig. 1, yellow dots, lines 4-11). The observational data were sampled between May and June 2007. For the comparison, we averaged model output of May and June from 2006 through 2010 and linearly interpolated it to a vertical grid with 1 m resolution. The model data were averaged over this 5-year period in order to remove any modelbased interannual variability that could bias the results of the model evaluation.
A visual comparison of the modeled versus observed vertical distributions of the studied variables, along a representative transect line (off Pt. St. George, California, Fig. 1, yellow arrow), indicates that the offshore pattern between 0 and 100 m is captured well (Fig. 4). However, the model underestimates the magnitude of the vertical difference of DIC (∼ 20 µmol kg −1 ) in waters deeper than ∼ 125 m. In the nearshore region between 0 and 250 m depth, the model underestimates Alk by 10-35 µmol kg −1 and especially DIC by 40-150 µmol kg −1 . The larger bias (b) in DIC is the primary cause of the overestimation of the simulated pH (b pH ∼ 0.2) and arag (b arag ∼ 0.5), since their sensitivities toward changes in Alk and DIC are similar. As a result, our modeled aragonite saturation horizon is typically 60 m deeper than the observed one, and up to 150 m deeper during the strongest upwelling events. There is no obvious difference in model performance between subregions, i.e., pH and arag are modeled equally well for all three subregions, with a Pearson correlation coefficient of about ρ pH = 0.89-0.90 between observed and modeled pH and ρ arag = 0.88-0.90 for arag (Fig. 5). The normalized standard deviations, correlation coefficients and biases between all observed and modeled properties can be found in Table A2.
The nearshore positive bias of pH and arag may be partially a result of transect line 5 having been sampled during strong upwelling conditions (Feely et al., 2008). Our model does not simulate such events since it is only forced with a monthly climatology of wind, but not with specific weather patterns and variability. The absence of such an intense upwelling event can be observed in all simulated variables shown in Fig. 4. The observed, strong outcrop nearshore indicates a vigorous upwelling, which is considerably underestimated by our model. This caveat was described by       (2011) and we focus on the implications of this discrepancy in the Discussion.
We evaluate the temporal variability of pH, arag , Alk, DIC, T and S by comparing our model results to a seasonal climatology from the Southern California Bight, generated from roughly bi-weekly samples obtained from the Santa Monica Bay Observatory Mooring at 33 • 55.9 N and 118 • 42.9 W from 2003 to 2008 (Leinweber and Gruber, 2013). The model-based climatology for the same site and time-period underestimates pH and arag at depth (Fig. 6) as evidenced already in the comparisons with the NACP West Coast Cruises. In addition, the observations show high temporal variability at the surface (σ pH = 0.08, 1 STD for the full observational record and σ arag = 0.40) and at depth (σ pH = 0.07 and σ arag = 0.20), which is underestimated by the model by a factor of about 7 for surface arag and by a factor of about 3.5 for surface pH and both variables at 100 m. The observed high spatial and temporal variability of pH and arag of the southern CCS is dominated by highfrequency winds (Capet et al., 2004) that are not resolved in our current forcing files. Moreover, in the model, the bottom topography is smoothed over the continental shelf to prevent numerical instabilities associated with complex bathymetry. Therefore, the variability resulting from the interaction of the flow field with the observed bathymetry, particularly in the southern CCS, is not fully represented.
Better agreements with the observed temporal variability is achieved by the model for most other regions for which data are available. A comparison with new pH and arag data derived from a surface mooring off Newport, OR (44 • 38 0 N 124 • 18 13 W, Harris et al., 2013) from 2009 to 2011 demonstrates that the modeled temporal variability (σ pH = 0.10 and σ arag = 0.32, 1 STD) agrees well with the observed temporal surface variability (σ pH = 0.11 and σ arag = 0.37, 1 STD). Also, the model is in better agreement with the temporal variability of pH and arag in nearshore subsurface regions just north of Point Conception (Alin et al., 2012) than in the southern CCS. Alin et al. (2012) estimated pH and arag based on seasonal hydrographic data from Cal-COFI line 76.7 from 2005 to 2010. Their estimated temporal variability of σ pH = 0.09 and σ arag = 0.32 at 30 m depth are by a factor of 1.2 and 1.5, respectively, greater than the modeled temporal variability (σ pH = 0.07 and σ arag = 0.21). The model-data misfit increases with depth. At 100 m depth, the model underestimates the temporal variability of arag by a factor of 2 and by a factor of 5.5 for pH.
In summary, there are two main model shortcomings that influence the results presented here (also see Discussion). pH and arag are overestimated at depth and in nearshore surface areas, resulting in a deeper aragonite saturation horizon than observed. Secondly, the modeled temporal variability of pH and arag is underestimated. According to available observations, this bias is largest in the southern CCS and at depth and decreases toward the north. Due to the limited spatial and temporal coverage of observational data in the CCS, this model-data comparison serves as preliminary

Results
Here, we discuss the range and magnitude of changes in pH and arag and explore the drivers and mechanisms of the temporal and spatial variability in the nearshore environment of the CCS. We then present projections of the evolution of pH and arag until 2050 and determine the timing of when the chemical characteristics within the different subregions move outside of their modeled preindustrial and present-day variability envelopes (relative threshold). Finally, we project when the absolute threshold of aragonite undersaturation is reached.

Spatial and temporal patterns of modeled pH and arag
Examples of the modeled monthly averages for surface pH of model year 2011 (pCO 2 ∼ 395 ppm) show that the waters within the first 50 km of the CCS experience a wide range of surface pH from 7.85 to 8.15 (Fig. 7a). Spatial variability of surface pH is highest in the central subregion (σ pH = 0.10, 1 STD) around July, while it is small and constant in the southern subregion ( Fig. 8a and b). In the central nearshore CCS, the lowest surface pH (pH min = 7.85) is simulated between June and September. The highest nearshore surface pH (pH max = 8.15) is reached between November and March in the northern subregion, while the central CCS only experiences high surface pH (pH max = 8.05) during three months (January-March). In the central CCS, surface pH decreases to 7.95 around June and increases to around 8.05 in January. Farther off the coast, surface pH of the northern subregion remains at around 8.10, while in the central and southern CCS it drops from 8.15 to 8.00. At 100 m depth, low pH of about 7.75 extends to about 300 km offshore all year round and in the entire CCS, except along the Washington coast, where pH remains close to about 8.10 between April and July, and drops to about 7.65 between August and October (not shown). The seasonal evolution of surface arag (not shown) behaves similarly to surface pH. The modeled monthly means do not show undersaturation at the surface. However, model results from averaged two-day model output reveal that north of Cape Mendocino, surface pH can drop down to 7.72 (Fig. 7c) and surface arag to 0.93, below the values captured by the monthly mean outputs. In nearshore areas at 100 m depth, aragonite undersaturation is also simulated in late fall, most likely due to the remineralization of the sinking organic matter that was produced during the summer phytoplankton blooms (Fig. 7b). Spatial variability of both parameters and along the entire US West Coast is constant and small ( Fig. 8a and b).

Spatially averaged seasonal cycle of pH and arag for each subregion
The range of the mean seasonal cycle of pH and arag varies from region to region in the CCS ( Fig. 8a and b) and is more pronounced at the surface than at 100 m. The northern subregion has the highest annual mean surface pH (pH = 8.07) and the most distinct seasonal cycle (Fig. 8a), with a range of about 0.14 pH units. In the central and southern CCS, the average surface pH is pH = 8.00 with a range of 0.09 and 0.04, respectively. While surface pH is lowest in August and September in the northern subregion, the central subregion shows the lowest surface pH (pH min = 7.95) in June. The annual mean surface arag is 2.02 in the northern and 1.88 in central CCS and is highest ( max arag = 2.14) in the southern subregion (Fig. 8b). Surface arag decreases to 1.85 in August and September in the northern subregion. The central subregion shows the lowest surface arag ( min arag = 1.73) in June. In the southern CCS, surface arag increases slightly during the summer months. At 100 m depth, average pH remains around 7.8 and average arag around 1.1 in all three subregions.

Mechanisms influencing the seasonal cycle in pH and arag
To understand the mechanisms causing the seasonal changes in pH and arag across the three subregions, we investigate their sensitivity to the seasonal variations in Alk, DIC, T and S. To do so, we estimate the contribution of changes in each property to the total change of pH and arag . The change in pH and arag can be "separated" using a Taylor The partial derivatives quantify the differential changes in carbon chemistry due to small changes in DIC, Alk, T and S and are derived from model equations and annual means of a modeled climatology (2006)(2007)(2008)(2009)(2010). s DIC and s Alk are the salinity normalized deviations from the annual means of DIC and Alk; DIC s and Alk s are deviations from the annual means due to freshwater input, and FS pH and FS are the total contributions of freshwater input to the change in pH and arag , respectively. Residuals (= Res.) capture the error when the left-and right-hand side of the equation are not equal. The seasonal variations in pH and arag are driven by a combination of seasonal changes in DIC, Alk and T . These parameters are altered by upwelling and eddies, which differ in magnitude and timing from region to region (Figs. 9 and 10). In addition, Alk changes due to the precipitation or dissolution of CaCO 3 , and due to nitrification and nitrate assimilation during new production (see Sect. 2.1, Appendix A). DIC changes due to CaCO 3 calcification and dissolution, net primary production and heterotrophic respiration. Surface temperature reflects changes in the incoming solar radiation and heat exchange with the atmosphere. Figures 9 and 10 show the contributions of changes in DIC, Alk, S and T to changes (relative to the annual mean) in pH and arag , respectively. Each colored component represents the corresponding term in Eqs. (4) and (6). Components that plot in a positive direction have a positive effect on pH or arag . Therefore, the sum of all components lead to the total effect of pH and arag , resulting in either an addition or cancellation of the effect on pH or arag . pH is negatively correlated to changes in DIC, T and S, but has a positive correlation with changes in Alk. While the correlations for arag with Alk, DIC and S are the same as for pH, changes in arag are positively correlated to changes of T .
In the northern CCS, the effects of the changes in DIC and T on surface pH are counteracted by changes in Alk at the beginning of the upwelling season in spring and amplified in late summer and early fall (Fig. 9a). With a small delay, T amplifies the effect of changes in DIC on surface pH throughout the year. The upwelling of DIC-rich water decreases surface pH beginning in April. Upwelled subsurface waters increase Alk at the surface during upwelling. The increase in Alk compensates for the upwelled DIC-rich water and warming of the surface waters until Alk reaches its peak in June. By August, Alk has declined to a minimum, which then amplifies the effects of DIC and T to create the pH minimum.
In the central CCS, upwelling starts in March, one month earlier than in the northern subregion (Fig. 9). The upwelled, DIC-enriched subsurface waters decrease surface pH to its minimum in June. In spring, DIC is the main driver of seasonal changes of pH. Increased primary production (Fig. A1a) decreases DIC as from June. Warming of surface waters in late summer delays the effect of declining DIC on pH. In winter, T and Alk both amplify the effect of DIC, leading to a pH maximum in February.
In exchange with the atmosphere (Fig. 9e), which decreases pH in summer, when sea surface temperature increases. The seasonal cycle of DIC is out of phase with the seasonal cycle of surface T and slightly counteracts the effect of T on pH. The warming of the surface waters lead to a late summer pH minimum. At 100 m depth, the effects of Alk in the northern CCS ( Fig. 9b) are in concert with the seasonal effects of DIC. Changes in temperature play a minor role. The absence of upwelling in the winter months leads to high pH levels in all subregions. Upwelling starts earlier in the southern (Fig. 9f) than northern CCS, shown by the earlier increase of DIC (decrease of pH) in the southern than in the northern subregion. In the central (Fig. 9d) and southern subregions, DIC is the main driver of pH, except during the upwelling season, when cold, upwelled waters counteract the effect of DIC on pH. The cold temperature of the upwelled waters dampen the early summer pH decrease in the central and southern CCS. Nitrification (Fig. A1b) sets in in March (southern CCS), in April (central CCS) or in June (northern CCS), decreases Alk, amplifies the decreasing effect of DIC on pH and counteracts the cold temperature effect.
The analysis of the contributions to the seasonal changes in arag reveal that Alk has a much higher influence on arag in the northern subregion than it does in the central or southern CCS (Fig. 10). Upwelling brings waters enriched in DIC and Alk to the surface. In the northern CCS, the resulting increase in surface DIC is substantially mitigated by the strong positive net community production that removes most of the "new" DIC provided by upwelling. In contrast, the upwelling-induced increase in Alk is barely mitigated, as the relatively small reduction in Alk caused by the net formation of CaCO 3 is in part offset by the increase in Alk caused by the positive net community production. Taken together, during spring the changes in arag are driven primarily by the upwelling of Alk (Fig. 10a). The decrease of surface arag is thus delayed and changes in arag are suppressed. In July, Alk decreases rapidly, which amplifies the effect of rising DIC concentrations on arag , thereby causing its minimum. In the central and southern CCS, surface arag is mainly driven by the changes of DIC (Fig. 10c and  e). Upwelling in the central subregion starts in March and increases surface DIC and thus decreases arag . From June to August, primary production causes a decrease in DIC, and an increase in arag . Unlike for pH, surface water warming has a positive effect on arag in the southern CCS and amplifies the effects of the seasonal cycle of DIC.
At 100-m depth, Alk amplifies the effects of DIC on arag in all subregions (Fig. 10b, d, f). Respiration of sinking particles from the surface, coupled with high levels of nitrification, cause a decrease in Alk which amplifies the effects of Biogeosciences, 10, 193-216, 2013 www.biogeosciences.net/10/193/2013/ the upwelled DIC-rich water on arag , which leads to a minimum of arag at the end of the season (Fig. A1b).

Temporal and spatial variability vs. future trends
In this section, we determine the timing of when the trajectories of pH and arag diverge from the ranges of variability that occurred during the preindustrial and the present-day time periods. To accomplish this, we defined preindustrial (1750), present-day (2011), and future variability envelopes. These variability envelopes were calculated by first computing the moving average (over a 10-yr window) of the regionally averaged monthly time series from the model. Secondly, we added and subtracted the ten-year moving standard deviation of the detrended regionally averaged monthly time series. As noted in Sect. 2, we corrected the magnitude of these modeled variability envelopes by a factor var cf that accounts for the underestimation of variability due to the usage of monthly model output instead of the more variable two-day output. In a manner similar to Blackford and Gilbert (2007) and Cooley et al. (2012), we define the midpoint of a 10-yr transition period (transition decade) as the point in time when the future envelope of pH or arag diverges from the preindustrial or present-day envelopes. While we report individual years for these transition decades below, it is important to recognize that these years represent the midpoint of 10-yr windows within which these transitions are projected to take place.
Simulations following the SRES A2 emissions scenario show that increasing atmospheric CO 2 concentrations cause the pH and arag of the nearshore regions along the US West Coast to move out of their modeled preindustrial and projected present-day variability envelopes before 2050 (Figs. 11 and 12, orange and blue lines). By model year 2011, nearshore waters along the US West Coast have already moved out of the preindustrial envelope. In the northern CCS, pH has only recently departed from the preindustrial variability range due to its large temporal variability (Fig. 11a, upper panel). The fast progression of ocean acidification forces the pH of the northern subregion to move out of its modeled present-day variability envelope by 2045, despite the large temporal variability. Surface pH in the central subregion is projected to depart from its present-day envelope by 2037 (Fig. 11a, center panel). Surface arag is projected to move out of its present-day envelope earlier than pH (Fig. 12a). Already by 2030, the northern CCS is projected to be exposed to lower levels of surface arag than experienced in 2011 (Fig. 12a, upper panel). Similarly, surface arag of the central subregion will depart from its present-day envelope by 2035 (Fig. 12a, center panel).
By 2023, surface pH and surface arag of the southern subregion are projected to decrease below the range of their relatively small, modeled present-day temporal variability (Figs. 11a and 12a, lower panels). However, these results have to be taken with caution, since our model does not re-produce the large variability observed in the southern CCS. We therefore expect that pH and arag in the southern subregion will remain within their variability envelopes longer than projected by the model (see Sect. 3 and Discussion).
At 100 m depth, pH and arag of the northern CCS are projected to depart from their modeled present-day variability envelopes by 2033, while in the central and southern CCS this transition is projected to take place already a decade earlier (Figs. 11b and 12b). In addition, permanent undersaturation of arag at 100 m is projected before 2025 in the central and 2035 in the southern and northern CCS.
In a second simulation under which atmospheric CO 2 concentrations follow the "low-CO 2 " (B1) emissions scenario, surface pH of the northern subregion is not projected to move out of its present-day envelope before 2050 (see Fig. A2, upper panel). The projected lower atmospheric CO 2 concentrations, however, do not affect the timing of transition of arag in the north (Fig. A2, upper panel), and pH and arag in the central and southern CCS (Figs. A2a and A3a, center and lower panels). This is because their variability range is low, leading to a departure from their variability envelopes before the atmospheric pCO 2 paths of the two emissions scenarios diverge around 2035 (Fig. S5 in Gruber et al., 2012).
The high spatial variations in the temporal variability within each subregion (especially the northern subregion) leads to a large spatial difference in the timing of the transition outside the variability envelope. Figures 13 and 14 illustrate the percentage of overlap between the variability range (mean ± (1 STD × var cf )) of a detrended 10-yr period from 2005 to 2015 of pH and arag , and the variability range for 10-yr periods of pH and arag for each following decade. The years 2020, 2030 and 2040 are chosen as midpoints for each 10-yr period. Nearshore areas, especially in the northern subregion, retain more than 50 % range overlap until 2030. These areas are exposed to the strongest upwelling and experience the largest range of pH and arag due to the upwelled cold, DIC-and nutrient-rich water. However, areas in the central CCS, south of Monterey Bay (36 • 48 N, 121 • 54 W), are projected to experience pH and arag values outside of the present-day envelope by 2030. At 100 m depth, nearshore areas of the central and southern CCS are projected to be exposed to levels outside of the present-day range by 2020, while offshore areas retain some degree of overlap of range until 2030. In the northern subregion, the present-day range of pH and arag in nearshore regions still overlap by about 50 % until 2030.

Shoaling of the aragonite saturation horizon
In the central subregion, the modeled aragonite saturation horizon has already shoaled into the upper 100 m of the water column and is projected to reach a depth of 50 m by 2050 (Fig. 15a). The aragonite saturation horizon in the northern and southern CCS are projected to reach a depth of 100 m by 2025 and shoal to ∼ 70 m depth by 2050. Figure 15b   shows that after reaching the upper 100 m, the shoaling of the aragonite saturation horizon slows down substantially in all subregions. The saturation horizon is highly sensitive to changes in the concentration of CO 2− 3 where the gradient of CO 2− 3 concentration with respect to depth is small (Fig. 15). Conversely, when the CO 2− 3 concentration gradient with respect to depth is strong, the saturation horizon is less sensitive to small changes of CO 2− 3 concentration. As a result of these sensitivity differences, the aragonite saturation horizon shoals rapidly from 250 to 100 m because the CO 2− 3 concentration gradient with respect to depth is small in this depth range. Once the saturation horizon enters the upper 100 m, it requires larger changes in CO 2− 3 to lead to an equivalent shoaling of the aragonite saturation horizon. This explains why shoaling is initially rapid, and then slows down by about 2025, when the aragonite saturation horizon enters a depth range with larger gradients in CO 2− 3 concentration.

Discussion
The comparison of our model results with the available observations of nearshore carbon properties shows that the model is able to generally reproduce the large-scale spatial and seasonal patterns of contemporary pH and arag . However, the following caveats need to be borne in mind while discussing the annual cycle and future trajectories of pH and arag : (1) the model overestimates pH and arag offshore and at a depth of 100-250 m, and in nearshore regions; (2) the model is forced with monthly climatologies of wind and cannot reproduce weather induced, high-frequency events; (3) the riverine input is not explicitly parameterized; (4) consequences of global change such as changes in T , winds or precipitation are not taken into account; (5) interannual processes such as El Niño/La Niña events are not resolved by the model; and (6) ocean acidification-induced changes to important biological processes, such as calcification, photosynthesis and nitrification are not considered by the NPZD 2 ecosystem model.
Since the model overestimates pH and arag along the entire US West Coast, the annually averaged depth of the aragonite saturation horizon is about 60 m shallower in reality. Consequently, we expect that summertime undersaturation of surface waters in nearshore subregions of the northern and central CCS will happen more frequently and with a greater spatial extent than simulated by our model. Comparison to a arag time series derived from O 2 and T variability emphasizes this bias (Juranek et al., 2009) the central Oregon shelf (∼ 100 m) during the majority of the upwelling season. The depth bias between the observed and modeled aragonite saturation horizon is expected to decrease with time, because the shoaling of the aragonite saturation horizon is expected to slow down as it approaches shallower depths (see Sect. 4.5). In our simulations, day-to-day wind variability was not taken into account since the model was forced with a monthly climatology of momentum fluxes from QuickSCAT-based ocean winds. This does not present a large problem in the northern and central subregions where strong seasonal wind patterns prevail (Dorman and Winant, 1995). However, in the southern CCS, synoptic variability dominates (Leinweber et al., 2009;Dorman and Winant, 1995), which is not well captured by our monthly wind climatologies. As a result, the southern subregion is forced with unrealistically smooth wind patterns. Comparison with the SMBO mooring data (Leinweber and Gruber, 2013) underlines this shortcoming of our model for the southern CCS. The model underestimates pH variability (1 STD) by a factor of ∼ 3.5. This implies that the projected transition decades would occur about 20 yr later than inferred from our model results. Considering this caveat, the pH of the southern CCS would move out of its preindustrial envelope around 2020 and depart from the present-day levels shortly after 2050. The temporal variability of surface arag is underestimated in the model by a factor of ∼ 7 at the SMBO mooring, implying that the southern subregion will likely not move out of its preindustrial envelope before 2050. The comparison with observational data derived from the recently deployed mooring off Newport, Oregon (Harris et al., 2013, see Sect. 3) and reconstructed pH and arag from T and O 2 time series (Alin et al., 2012) indicate that our modeled size of the variability envelopes is in better agreement with the limited available data in the northern and central CCS than they are in the southern subregion. Taking advantage of the fast-growing US carbon mooring network in the future will help to further constrain the model bias and better predict the present-day variability envelope. Forcing the model with wind products at daily or higher temporal resolution could help to better simulate the observed high temporal variability in the winds and sporadic, strong upwelling events that cause extremely low levels of pH and arag .
Riverine input of nutrients, DIC and freshwater can increase the range of pH variability by up to about 1 unit (Hinga, 2002). Since the riverine input is not explicitly modeled in this study, pH and arag may not be accurately represented in close proximity to the Columbia River mouth, especially during the rainy months (February-June). Other small rivers along the coast can influence DIC and Alk, but their influence is likely small and often limited to infrequent storm events. The surface T and S restoring described in Sect. 2 improves the mean state, but does not capture the natural variability.
Our study accounted for changes of pH and arag due to atmospheric pCO 2 increase. However, additional consequences of the anthropogenic pCO 2 increase through its effects on the Earth's radiation balance were not taken into account. These include changes in upwelling intensity, strengthened stratification, warming of surface waters, the deepening of the thermocline (King et al., 2011) and thus potential changes in the seasonal cycle. Integrated effects of global change could possibly accelerate the progression of ocean acidification described here. For example, a time series  of upwelling favorable winds and sea surface T suggests that a strengthening of large-scale pressure gradient fields led to increased and protracted upwelling in parts of the central CCS (García-Reyes and Largier, 2010), which in turn would lead to lower surface pH and arag , further exacerbating the effects of increasing pCO 2 on the CCS. In addition to increased aragonite undersaturation, shoaling of low oxygen waters further minimizes habitats of sensitive organisms (Bograd et al., 2008;McClatchie et al., 2010). Oxygen declines in the CCS result from decreasing concentrations of oxygen in the Equatorial and Eastern Pacific (Stramma et al., 2008(Stramma et al., , 2010Bograd et al., 2008). These oxygen declines are thought to be due to increased stratification resulting from global warming (Stramma et al., 2008). As a result of continued global warming and intensified upwelling, hypoxic areas are expected to further expand in the CCS in the future.
The dynamics of the CCS is strongly modified by interannual to decadal climate modes such as El Niño/La Niña events or the Pacific Decadal Oscillation, which are not resolved by our model. The La Niña event in 2010 uplifted the isopycnals in late summer and doubled the period of normal seasonal exposure to undersaturated conditions on the continental shelf off California (Nam et al., 2011). The season of occurrence of La Niña events is variable. It is therefore possible that La Niña amplifies the effect of natural seasonal upwelling, leading to more extreme hypoxic and aragonite undersaturated conditions. As a result, variability envelopes would be widened and the transitions toward the conditions outside these envelopes would be delayed, while seasonal aragonite undersaturation would occur earlier.
Ocean acidification may trigger several physiological responses in organisms, some of which may lead to significant changes in the DIC and Alk concentrations. However, none of these potential responses are represented in our simple NPZD 2 ecosystem model. Ongoing research suggests that several biological processes can be affected by ocean acidification (reviewed in e.g., Doney et al. 2009) with calcification likely being the most relevant. Coccolithophores as the dominant calcifiers show a wide range of responses in their calcification rates to ocean acidification (e.g., Riebesell et al., 2000;Langer et al., 2006;Iglesias-Rodriguez et al., 2008), with possible effects on the vertical distribution of Alk (Ilyina et al., 2009). Here, calcium carbonate formation was kept at a fixed rate, introducing additional uncertainty to the study. But given the limited importance of calcification in controlling pH and arag in the CCS, we consider the potential impact of changes in calcification on our results to be relatively limited.
We found that the CCS is approaching the combined thresholds of both chemical aragonite dissolution and the departure from its variability envelope with respect to pH and arag . The CCS thus joins the Arctic and the Southern oceans as one of only a few known ocean regions presently approaching this dual threshold Mc-Neil and Matear, 2008). Therefore, organisms in these regions must adapt to conditions that are both inherently chemically challenging and significantly different from present conditions. In contrast, while locations such as ocean station ALOHA are projected to depart their variability envelope by 2020 (Cooley et al., 2012), the inherent chemical properties at these sites leave them far from aragonite undersaturation.
This study gives new insights into the spatial and temporal dynamics of pH and arag along the US West Coast. It further enables us to relate the present-day high spatial and temporal variability of pH and arag to their modeled preindustrial and projected future ranges of pH and arag . While a few nearshore areas of the central and northern subregions are presently exposed to temporary undersaturation, our results also highlight the fact that the nearshore ecosystems along the US West Coast are already exposed to pH and arag levels outside of the modeled preindustrial variability envelope. Additionally, as early as ∼ 2040, surface pH and arag of the nearshore US West Coast are projected to move out of the modeled present-day variability envelope under increasing atmospheric CO 2 concentrations as projected from the IPCC SRES A2-Scenario.
The combination of naturally high DIC and the oceanic uptake of anthropogenic CO 2 drives the CCS toward undersaturation faster than other coastal areas (Blackford and Gilbert, 2007) and on a similar timescale as the Arctic and Southern oceans (Gruber et al., 2012). Despite the high annual variability, the absolute decrease of pH and arag is fast and significant enough to cause a departure from its presentday range by 2040. We conclude that these types of changes put the CCS particularly at risk to the effects of ocean acidification. Given the imminent departure from preindustrial envelopes, we speculate that these effects may already be well underway.
Marine ecosystems of the CCS are exposed to a variety of stress factors, many of which are projected to increase in the future. Along with the developing problem of ocean acidification, organisms will have to deal with warming of the waters, an expansion of hypoxic areas and changes of the vertical structure of the water column (Gruber, 2011;Doney et al., 2012). Furthermore, non-climate change-related impacts, such as pollution, eutrophication and overfishing further increase the vulnerability of the CCS ecosystems. Together, these stressors compound the challenges that many organisms of the CCS will face in the coming decades and will necessitate rapid migration, acclimation or adaptation in order to cope with these changing environmental conditions.

Description of the carbon biogeochemistry module
The carbon biogeochemistry module adds the three new state variables DIC, Alk and CaCO 3 (D CaCO 3 ) to the model. The conservation equation for any tracer concentration B is given by where K is the eddy kinematic diffusivity tensor, ∇ is the 3-D gradient, ∇ h is the horizontal gradient, u denotes the horizontal and w the vertical velocities of the fluid, and w sink is the vertical sinking rate of all particulate pools, except zooplankton (see Table A1). J (B) denotes the source minus sink term for each tracer, which is described in detail for DIC, Alk and D CaCO 3 in the following. The remaining source minus sink terms for the other model state variables are defined in Gruber et al. (2006). The sources and sinks of DIC include net community production, gas exchange, and CaCO 3 formation and dissolution: This equation follows the nomenclature used in Gruber et al. (2006). Symbols with parentheses, such as µ max P (T , I ) represent functions of the respective variables. J Gas is the gas exchange flux described below (Eq. A3). The state variable associated with the function/parameter is denoted in the subscript, while the corresponding process is given in the superscript. The variables in the equation denote the following: I and T are light and temperature, respectively, P is the phytoplankton pool, Z is the zooplankton pool, D S is the small detritus pool, D L is the large detritus pool, D CaCO 3 is the CaCO 3 pool in the water column, S D is the nitrogen and S CaCO 3 is the CaCO 3 pool in the sediment. All relevant parameters are described in Table A1. The carbon fluxes are tied to those of nitrogen with a fixed stoichiometric ratio r C : N of 106 : 16 (Redfield et al., 1963).
Net primary production is the sum of regenerated and new production and decreases the DIC pool. Depending on  whether phytoplankton (P ) take up NH + 4 or NO − 3 , nitrogen adds to either the regenerated or the new production flux, respectively. The modeled phytoplankton growth is limited by temperature (T ), light (I ) and the concentrations of NO − 3 and NH + 4 . µ max P (T ,I ) is the temperature-dependent, light-limited growth rate of P under nutrient replete condition. γ (NO − 3 , NH + 4 ) is a non-dimensional nutrient limitation factor, with a stronger limitation for nitrate than ammonium, taking into account that P take up NH + 4 preferentially over NO − 3 and that the presence of ammonium inhibits the uptake of nitrate by P . For a more detailed description of these limitation factors the reader is referred to Gruber et al. (2006).
Formation of D CaCO 3 also decreases the DIC pool and is parameterized as 7 % of the net primary production, such that for each mole of organic carbon formed by net primary production, 0.07 mol of D CaCO 3 are formed. D CaCO 3 dissolves at a fixed first order rate of 0.0057 day −1 . This process releases CO 2− 3 , and thus adds to the DIC pool. The full source minus sink equation for D CaCO 3 is described below (Eq. A6).
Zooplankton (Z) are parameterized with one size class (mesozooplankton). The Z respiration from basal metabolism and remineralization processes increases the total DIC pool. Large detritus (D L ) is remineralized at a rate of 0.01 m day −1 and small detritus (D S ) at a rate of 0.03 m day −1 . The different sinking speeds and remineralization rates of small and large detritus result in a large difference of the remineralization length scales of 30 m for D S and 1000 m for D L . As a consequence, D L is rapidly transported to depths below the euphotic zone, while D S is subjected to offshore transport and is absent in the ocean interior (Gruber et al., 2006).
The sediment is parameterized as a simple one layer model added to the bottom layer (k = 1) of the model. The sediment is represented by the state variables S D (mmol N m −2 ) and S CaCO 3 (mmol C m −2 ). Once organic matter and CaCO 3 arrive at the sediment surface they are accumulated in the sediment layer. The accumulated organic matter and CaCO 3 are subjected to first-order decomposition reactions that release dissolved material into the deepest model layer k = 1 and thus back into the water column.
CO sol 2 is the temperature and salinity dependent solubility of CO 2 , pCO 2 air is the CO 2 partial pressure in the atmosphere and pCO 2 ocean is the partial pressure of CO 2 in seawater. Oceanic uptake of CO 2 increases DIC, while it does not influence Alk. Oceanic pCO 2 is calculated from DIC, Alk, temperature and salinity using the standard OCMIP carbonate www.biogeosciences.net/10/193/2013/ Biogeosciences, 10, 193-216, 2013 Table A2. Evaluation of model with regard to its spatial variability: Shown are the normalized model standard deviation (norm. STD.), the correlation coefficient and bias of observed and modeled pH, arag , Alkalinity, DIC, Temperature and Salinity. A five-year average of modeled parameters over May andJune (2006-2010) are compared to observations sampled between May and June 2007 (Feely et al., 2008), for all sampled locations (CCS), the subregions north, central, southern, for 0-100 m, 100-250 m and 500-5000 m. The modeled standard deviations were normalized relative to the observed standard deviations from Feely et al. (2008)  chemistry routines 3 . The routines used the carbonic acid dissociation constants of Mehrbach et al. (1973), as refit by Dickson and Millero (1987) and Dickson (1990). The pressure effect on the solubility was estimated from the equation of Mucci (1983), including the adjustments to the constants recommended by Millero (1995). k is the gas transfer coefficient given by equation three in Wanninkhof (1992), which is dependent on the square of the instantaneous wind speed (u) and the temperature dependent Schmidt number (Sc). Alk increases due to the removal of NO − 3 (new production) and dissolution of CaCO 3 and decreases due to the formation of NO − 3 (nitrification) and formation of CaCO 3 : J (Alk) = + 2 · k diss CaCO 3 D CaCO 3 dissolution (A5) + µ max P (T , I ) · γ (NO − 3 ) · P · r C : N new production + 2 · k diss S CaCO 3 S CaCO 3 sediment dissolution at k=1 − 2 · k form CaCO 3 · µ max P (T , I ) · γ (NO − 3 , NH + 4 ) · P · r C : N Nitrification is light-limited (I ) and parameterized at a rate of 0.05 day −1 (see Gruber et al., 2006). CaCO 3 formation and dissolution processes change Alk twice as much as DIC. This can be explained from the definition of alkalinity (Dickson, 1981) where the addition (removal) of 1 mol of CO 2− 3 results in a 2 mol change in Alk. The concentration of CaCO 3 (mmol C m −3 ) is dependent on net primary production and dissolution: J (D CaCO 3 ) = k form CaCO 3 · µ max P (T , I ) · γ (NO − 3 , NH + 4 ) · P · r C : N CaCO 3 formation − k diss CaCO 3 D CaCO 3 dissolution .
CaCO 3 increases by 0.07 mol (k form CaCO 3 ) for each mole of organic carbon produced by net primary production and it dissolves at a fixed rate of 0.0057 day −1 (k diss CaCO 3 ) in the water column and at 0.002 day −1 (k diss