We developed a multiple linear regression model to robustly determine aragonite saturation state (Ωarag) from observations of temperature and oxygen (R2 = 0.987, RMS error 0.053), using data collected in the Pacific Northwest region in late May 2007. The seasonal evolution of Ωarag near central Oregon was evaluated by applying the regression model to a monthly (winter)/bi-weekly (summer) water-column hydrographic time-series collected over the shelf and slope in 2007. The Ωarag predicted by the regression model was less than 1, the thermodynamic calcification/dissolution threshold, over shelf/slope bottom waters throughout the entire 2007 upwelling season (May–November), with the Ωarag = 1 horizon shoaling to 30 m by late summer. The persistence of water with Ωarag < 1 on the continental shelf has not been previously noted and could have notable ecological consequences for benthic and pelagic calcifying organisms such as mussels, oysters, abalone, echinoderms, and pteropods.
 Since the preindustrial, atmospheric loading of CO2 from fossil fuel combustion and land use changes has driven an anthropogenic ocean uptake of 146 ± 20 Pg C (updated from Sabine and Feely ) and a corresponding average surface water pH change of 0.1 units [Feely et al., 2004]. Accelerating emission rates and reduced buffering capacity will decrease pH by as much as 0.3–0.4 units by the end of this century under business-as-usual scenarios [Orr et al., 2005]. Effects of these “ocean acidification” changes on marine organisms are still under intense study [Kleypas et al., 2006; Fabry et al., 2008; Doney et al., 2009], but increased ocean CO2 content will result in a reduced saturation state for calcium carbonate minerals and potentially deleterious impacts for organisms that form CaCO3 shells, including corals, pteropods, foraminifera, and commercially important shellfish and their larvae.
 The saturation state (Ω) of CaCO3 minerals is determined by the relationship:
where K′sp, the stoichiometric solubility product, is a function of temperature, salinity, pressure, and the particular mineral phase (aragonite or calcite). In a thermodynamic sense, Ω > 1 indicates mineral precipitation is favored and Ω < 1 indicates dissolution is favored, although biogenic calcification is subject to “vital effects” such as organic shell coatings and species-specific calcification mechanisms, and calcification/dissolution can occur when ambient-water Ω values indicate opposing thermodynamic effects [Langdon et al., 2003; Tunnicliffe et al., 2009]. However, recent experiments indicate that Ω < 1 adversely impacts some organisms; Fabry et al.  reported net dissolution in live pteropods within 48 hours of exposure to undersaturated water. Because aragonitic CaCO3 has a metastable crystalline structure and is ≈50% more soluble than calcite [Mucci, 1983], organisms that form aragonitic shells will likely be affected first, and perhaps most severely, by ocean acidification.
 Transient episodes of reduced aragonite Ω (Ωarag) have already been noted in productive eastern boundary upwelling systems such as the California current system [Feely et al., 2008a]. Understanding the duration, intensity, and overall ecological impact of these events is a key need in economically and socially important coastal fisheries regions. Here we present an approach, updated from Feely et al. [2008b], to determine Ωarag from temperature and O2, using data collected on a 2007 survey of North American Pacific coastal waters. We justify the approach with a statistical evaluation, and apply it to a hydrographic time-series from the central Oregon coast to evaluate seasonal changes in Ωarag.
2. Algorithm Development
 Ωarag is a function of temperature (T), salinity (S), pressure (P), and the [Ca2+] and [CO32−] of seawater (equation (1)). Because [Ca2+] changes are proportionally small in seawater, variations in Ωarag are largely determined by changes in [CO32−], which can be predicted from observations of dissolved inorganic carbon (DIC) and total alkalinity (TA). DIC concentrations are governed by physics (solubility, surface gas exchange) and biology (photosynthesis/respiration) and therefore should be a function of T, S, and either O2 or NO3− [Anderson and Sarmiento, 1994; Lee et al., 2000]. TA can also be modeled as a function of T and S [Lee et al., 2006]. We would therefore expect a predictive relationship for Ωarag as a function of T, S, P, O2, NO3−, or a subset of these parameters.
 A hydrographic survey of the U.S. west coast in 2007 [Feely et al., 2008a] allowed an opportunity to develop predictive relationships for Ωarag based on contemporaneous T, S, P, O2, and NO3− measurements. We first evaluated a linear additive model of the following form:
where Ωarage is the empirically predicted aragonite saturation state, and the coefficients βi are empirical constants. We determined coefficients for equation (2) using an ordinary least-squares regression of Ωarag observations collected in the Pacific Northwest (PNW) region (transects of Washington, Oregon, and N. California coastal waters, Figure 1a), using only data in the 30–300 m depth range to minimize localized effects of surface warming, gas exchange and riverine inputs and to include only relevant source water masses for the shelf/slope region. Although all resulting regression coefficients were significant, tests of collinearity among the independent variables (via pair wise regression and the variance inflation factor test, see Table 1) indicated that S, O2, and NO3− were too closely related, leading to potential errors in least-squares regression coefficients [Kutner et al., 2004]. Stepwise regression and regression statistics (R2, RMS error) subsequently identified O2 as the most robust predictor of the three collinear variables.
Table 1. Summary of Model Parameters, Coefficients, and Indicators Used in Model Selectiona
Bold denotes selected model. 227 observations used in each model.
VIF: Variance inflation factor. See Kutner et al.  for a full description, but briefly, the VIF is an objective measure of the inflation in coefficient uncertainty from poorly scaled or singular matrices (e.g., due to rounding errors during matrix inversion). The VIF is calculated as (1−R2)−1 for the regression of each variable versus the remaining independent variables; values given in the order parameters are listed. Values >5 indicate potential collinearity among predictor variables.
Coefficients with standard error estimates for robust-fit multiple linear regression, which reduces the weight of outliers in the regression analysis. Coefficients correspond to order in which parameters appear. Following equations (2) and (3) in text, β and α values are coefficients for regressions without/with a reference value subtracted.
 A multiple linear regression of T, P, and O2 yielded significant regression coefficients and reasonable regression statistics (Table 1). However, residuals for this relationship showed a strong bias, i.e., overestimation of Ωarage at minimum and maximum T and O2 (see Figure S1 of the auxiliary material). This bias is likely the result of the non-linear dependence of CO32− on TA and DIC, which arises in coastal waters with high pCO2 and significant contributions to TA from non-carbon species. We examined several possible non-linear terms and found that the bias could be minimized through the addition of an interaction term between T and O2 (Figure S1); when this term is added, P and T are no longer significant as predictor variables. To reduce large magnitudes of the product of T · O2 and subsequent errors in the least-squares regression analysis (Table 1) [Kutner et al., 2004], we normalized each term by subtracting a reference value for each variable, i.e.,
Where α's indicate regression coefficients and Tr and O2,r are values representative of upwelling source water in the PNW region (Tr = 8°C and O2,r = 140 μmol/kg, see Figure 2 and Table 1). The resulting model had improved regression statistics (Table 1) and resulted in Ωarage predictions that correctly reproduce both the magnitude and depth-distribution of Ωarag observations for the effective range experienced over the shelf/slope areas (≈0.6 to 2.2) of the PNW region (Figure 1).
3. Model Evaluation and Caveats
 We evaluated the skill of the model described by equation (3) by comparison of the unexplained error in Ωarage and the ability to constrain Ωarag given analytical uncertainties in DIC and TA (2 and 3 μmol/kg, respectively [Feely et al., 2008a]). Uncertainty in Ωarag was determined by a Monte Carlo approach, in which DIC and TA inputs into the Matlab® program CO2SYS [van Heuven et al., 2009] were varied randomly about chosen values for the PNW data, with standard deviations equal to analytical uncertainties. The 1σ values of 1000 individually calculated Ωarag determinations, 0.017/0.034 for minimum/maximum Ωarag values in the PNW data (0.61/2.22, respectively), represent the theoretical lower limit for unexplained random error, ɛ, in any model used to predict Ωarage. The RMS error determined for the equation (3) model is close to, but still slightly higher than, the limit calculated for analytical uncertainties alone (ɛ). Although adding new terms to the regression model causes the RMS error to approach ɛ, the contribution of these additional terms to the explained variance is marginal (Table 1). To avoid overfitting, we rejected these models. A simple model based only on O2, which was the strongest predictor variable of Ωarage (R2 = 0.946, RMS error 0.088; Table 1) was also considered. However, the O2 model had a higher RMS error and a strong bias in residuals similar to that observed for the multiple linear regression of T, P, and O2 (Figure S1). Based on these observations, we chose the equation (3) model.
 Because the only Ωarag data available for algorithm development in this region are from late May 2007, we note there may be important caveats to a seasonal application of equation (3). However, three lines of evidence indicate seasonal application is justified. First, biologically-driven changes in Ωarag for the 30–300 m depth range (i.e., due to remineralization of organic matter over the productive summer months) are to a first order driven by changes in DIC rather than TA, since diatoms typically dominate coastal upwelling systems [Lassiter et al., 2006]. DIC and O2 changes are expected to be proportional in remineralization zones that are not anoxic [Hales et al., 2005; Anderson and Sarmiento, 1994], and therefore changes in DIC should be inherently captured in an algorithm involving O2. Second, the T-S (and T-O2) range experienced spatially in the PNW data is similar to the range observed seasonally near Newport (see Figure S2), suggesting that the water masses present in the seasonal data are present in the regional PNW data. Finally, algorithm developments for the Southern California Bight region suggest no significant bias of algorithm development using only late May data (i.e., difference of measured and predicted values for August 2008 was 0.075 (S. Alin, unpublished data, 2009)). As more Ωarag data become available, the algorithm for this region can be tested and refined. Nevertheless, these arguments point toward the ability to model the seasonal Ωarag dynamics near Newport with the data in hand.
 One potential time frame when algorithm predictions could deviate from observations is between February and May. PNW coastal waters experience intense river inputs during the rainy winter months, and the TA:DIC signature of these freshwaters is often different than in the open ocean [Park et al., 1969]. Proportionality of [Ca2+] to salinity, an assumption used in calculating Ωarag, may also change during these months. Consequently, we do not present predictions for this time period.
4. Seasonal Evolution of Ωarage on the Oregon Coast
 We calculated the seasonal evolution of Ωarage on the shelf and slope near Newport, Oregon with the model described by equation (3) and a time-series of T and O2 data (described by Peterson and Keister ) collected on biweekly to monthly intervals in 2007. The central Oregon coast is located in the northern end of the California Current system and experiences seasonal upwelling during spring and summer months. The region has been well-studied with regard to the physical forcing driving seasonal and interannual variability in water properties (cf. the 2006 Geophysical Research Letters special issue devoted to this region). Selected sections of Ωarage (Figure 2) show a distinct seasonal cycle that is tightly coupled to upwelling dynamics near Newport. In January, the Ωarage = 1 saturation horizon sits near the shelf break (≈125 m), roughly at the depth horizon of the 140 μmol/kg O2 contour and the 9°C isotherm. The 1.5 Ωarage horizon is 25 m shallower, at ≈100 m. The onset of upwelling season begins in early May with the physical spring transition [Huyer et al., 1979], during which wind forcing becomes predominantly equatorward, and offshore transport becomes positive. The offshore transport is compensated by the upwelling of cold, dense waters that are rich in DIC and nutrients, and poor in O2. The strong upwelling event in mid-May (strongly negative N wind stress, blue lines in Figure 2 (top)) results in sharply up-warped iso-surfaces, and the outcropping of the 0.8 Ωarage horizon to the upper 30 m from the mid-shelf (80 m isobath) to the coast. After the spring transition, persistent upwelling-favorable winds pull the 1.0 Ωarage and the 140 μmol/kg O2 contour onto the shelf where they remain through mid-November (Figure 2). Occasional poleward wind stress events (Figure 2, top) result in relaxation from upwelling, but the source water remains over shelf/slope regions. The late May transect used to formulate the algorithm (Figure 1b) occurred during one of these relaxation events.
 Throughout the remainder of the season Ωarage and O2 distribution show depletion on similar hydrographic surfaces, presumably as a result of biological activity (e.g., 1.0/1.5 Ωarage and 140/220 μmol/kg O2 contours retain similar behavior). Between May and November the 1.0 Ωarage contour reaches 30 m near-continuously over the inner shelf (i.e., from the 80 m isobath shoreward), with the exception of early October, when a strong downwelling event confines the low-Ωarage water to the shelf-bottom (not shown). Over the outer shelf and slope, the 1.5 Ωarage horizon shoals to less than 30 m by mid-July and the 1.0 horizon shoals to 50 m by mid-August (Figure 2). After the onset of persistent downwelling-favorable winds in mid-November the 1.0 Ωarage and 140 μmol/kg contours retreat back to the shelf-break/slope region, similar to conditions predicted for January 2007.
 The coupling of low Ωarag state and physically-driven upwelling dynamics would be expected, given the high DIC (low pH) signature associated with upwelling source waters [Hales et al., 2005]. The absolute magnitude of Ωarag over the coastal shelf regions, however, is largely unknown, due to a lack of depth-resolved DIC and TA measurements. This model therefore provides previously unattainable insight into both the magnitude of Ωarag and how it relates to seasonal hydrography changes on the central Oregon shelf. The range in Ωarage experienced seasonally over the shelf (e.g., 0.5–1.4 and 0.8–1.8 for the mid-shelf at 80 and 30 m, respectively) is also much greater than the uncertainty in model predictions (0.053). This favorable signal to noise ratio makes the region particularly amenable to this approach, compared to open ocean subtropical regions where the seasonal range is considerably less [Doney et al., 2009].
 An obvious question to ask is: What is the anthropogenic contribution to Ωarag on the central Oregon shelf? We used the density-anthropogenic CO2 relationship presented by Feely et al. [2008a, supplement] to correct observed DIC in PNW waters for anthropogenic CO2 input (20–40 μmol/kg) and calculated a “preindustrial” Ωarage for our data. A parallel algorithm with the same form as equation (3) was fitted to the data (R2 = 0.989) and used to predict the preindustrial Ωarage = 1 horizon for the time-series data (Figure 2). This preindustrial Ωarage = 1 threshold very closely follows the 2007 Ωarage 0.8 isoline. Therefore, within the ability to estimate anthropogenic CO2 content in coastal waters (±50% [Feely et al., 2008a]), undersaturation over shelf/slope bottom waters is likely a natural phenomena, but an anthropogenic reduction in Ωarag by 0.2 units has caused a shoaling of the 1.0 horizon by ≈25m (shelf/slope) to ≈40m (offshore). Exposure of pelagic communities to undersaturated water may therefore be lengthened or intensified by anthropogenic CO2 input.
 The persistence of water with Ωarag < 1 over the shelf throughout the May–November upwelling season has not been previously noted. Although it is unclear how organisms on the central Oregon coast are directly affected by these conditions, laboratory experiments have indicated potentially deleterious impacts for organisms exposed to waters with Ωarag < 1 [Kleypas et al., 2006; Fabry et al., 2008; Doney et al., 2009]. A clear application of the regression model presented here is to explore effects of low Ωarag on shelf communities when DIC and TA data are unavailable. Preliminary examination of historical pteropod abundance data from the Oregon coast from the last 20 years (B. Peterson, unpublished data, 2009) indicates that pteropods are generally found where upwelling water is not; their abundances are maximum in offshore waters outside of the upwelling region and peak over the shelf only during winter or El Nino events, when upwelling is suppressed. In-depth examination of these data and other historical records may provide insight into adaptations organisms use to cope with low Ωarag conditions.
Bakun  and Snyder et al.  have suggested that upwelling intensity is likely to increase under future warming climate scenarios. Because the transit time of upwelling source waters from last atmospheric exposure to the sites of local upwelling are on the order of decades [Feely et al., 2008a], additional anthropogenic CO2 is already “in the pipeline” in the ocean interior, and will continue to decrease coastal Ωarag well into this century, regardless of atmospheric CO2 rise scenarios. Impacts of these changes will be better understood as studies of the seasonality in Ωarag and effects on coastal organisms emerge. The Ωarage relationship presented here (equation (3)) will need to be adjusted on 5–10 year intervals to account for the additional anthropogenic CO2 input.
 A key advantage of the ability to estimate Ωarag using commonly available hydrographic parameters (T, O2) is the capability to hindcast Ωarag from historical datasets to explore relationships with previously documented ecological/physical observations, provided corrections for reduced anthropogenic CO2 in prior data, if significant, can be taken into account. For example, regression model development efforts by T. Kim et al. (Prediction of East/Japan Sea acidification over the past 40 years using a multiple-parameter regression model, submitted to Global Biogeochemical Cycles, 2009) highlight the importance of ventilation events for determining subsurface (50–500 m) Ωarag in a 50-year hydrographic time-series in the East/Japan Sea. Continued refinement of Ωarage regression models for the PNW and other coastal regions (Kim et al., submitted manuscript, 2009; S. R. Alin et al., manuscript in preparation, 2009) as more Ωarag data become available will significantly enhance our understanding of the sensitivity of coastal regions to future CO2-chemistry changes and warming.
 Financial support for this work was provided by NOAA Global Carbon Cycle Program Grant GC05288 to RAF, CLS, and BH. LWJ was supported by a NRC Postdoctoral Fellowship. Partial support for KL was made possible by the NRL program of KOSEF. This is NOAA/PMEL contribution 3418.