The oxygen minimum zones (OMZ) are especially sensitive to ocean deoxygenation due to the nonlinear dependence of their size on the oxygen inventory. Significant decadal variability has been observed in the extent and intensity of the tropical Pacific OMZ. Here we diagnose the physical and biogeochemical mechanisms behind the interannual and decadal variability of oxygen in the tropical Pacific thermocline using a three-dimensional ocean biogeochemistry model that reproduces the expansion of the tropical Pacific OMZ since the 1980s. On interannual time scales, heat content and respiration rates are strongly influenced by El Niño-Southern Oscillation cycles and the associated changes in upwelling. The resulting changes in solubility and apparent oxygen utilization tend to compensate one another, thus damping the magnitude of oxygen variability. Regional oxygen budget reveals the subtle balance between the lateral and vertical ocean circulation in controlling the physical oxygen supply to the eastern tropical Pacific. Spectral analysis shows that the tropical Pacific oxygen has a stronger variance in decadal time scales than its physical and biological drivers. Our results suggest that the physical oxygen supply and biological oxygen loss are integrated through the finite memory of thermocline waters to produce the multidecadal variability of OMZ.
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 Dissolved oxygen plays a crucial role in numerous chemical and biological processes in the oceans. The oxygen content of seawater controls oxidation reactions and the abundance of trace metals [Morel and Price, 2003] and the marine nitrogen cycling [Codispoti, 1995]. These processes regulate macronutrient and micronutrient content of the surface ocean, potentially limiting its biological productivity. Low-oxygen conditions also severely impact the physiology of marine organisms [Pörtner and Knust, 2007]. Changing oceanic oxygen therefore has far reaching implications for marine ecosystems, fisheries, and biogeochemical cycles.
 Model simulations predict that the ocean's oxygen content is sensitive to climate warming, suggesting 1 to 7% decline of global oxygen inventory by the year 2100 [Keeling et al., 2010; Helm et al., 2011]. In a warming climate, ocean heat uptake decreases the solubility of oxygen. An increased thermal stratification also weakens the downward transport of well-oxygenated surface waters into the interior ocean [Bopp et al., 2002; Keeling, 2002; Plattner et al., 2002; Matear and Hirst, 2003; Oschlies et al., 2008; Frölicher et al., 2009; Duteil and Oschlies, 2011]. These two mechanisms reinforce one another to deplete the subsurface oxygen. This is a qualitatively robust prediction of ocean climate models, although the absolute magnitude of oxygen loss and the relative roles of solubility and ventilation changes are uncertain [Keeling et al., 2010].
 Regions of low-oxygen waters, called oxygen minimum zones (OMZs), may be especially vulnerable to ocean deoxygenation [Stramma et al., 2008], because the volume of low-oxygen waters rapidly decreases with the threshold oxygen concentration [Deutsch et al., 2011]. The volume of seawater around the suboxic threshold (5 μM) exponentially declines as a function of oxygen concentration. Therefore, a uniform 1% decline of oxygen concentration (~1.8 μM) leads to a doubling of the suboxic volume (O2 < 5 μM). Such a global-scale oxygen decline is likely to leave disproportionately large imprint on the suboxic OMZ in the tropical Pacific and Indian Oceans, due to its strong sensitivity to the ambient oxygen concentration.
 Ocean time series observations have shown strong decadal fluctuations superimposed on the long-term decline of oxygen in the North Pacific [Deutsch et al., 2005; Emerson et al., 2004; Ono et al., 2001; Whitney et al., 2007]. The tropical Pacific OMZ has expanded in depth since the 1980s [Stramma et al., 2008], and coastal hypoxic waters have come up closer to the surface [Bograd et al., 2008; McClatchie et al., 2010]. Changes in equatorial upwelling and thermocline depth have reinforcing effects on the depths of hypoxic water through its control over the biological oxygen consumption, and this produces decadal-scale changes in the hypoxic water volume that are significantly correlated with the Pacific Decadal Oscillation (PDO) [Deutsch et al., 2011]. Furthermore, observed physical supply of oxygen to the tropical Pacific OMZ via subsurface zonal jets may have declined over the past several decades [Stramma et al., 2010]. Thus, the expansion of the Pacific OMZ since the 1980s could be driven by the combination of long-term ocean changes as well as natural climate variability on interannual and decadal time scales, which modulates both the physical oxygen supply and biological oxygen loss.
 The overall objective of this paper is to use model hindcast simulations to understand the behavior of the tropical Pacific OMZ for the past several decades. Our emphasis is on (1) the physical links between climate and biogeochemical variability on interannual time scale, and (2) the relationship between interannual variability and the decadal changes that has been discussed in previous work [Deutsch et al., 2011]. The paper is structured as follows. In section 2, we describe the model architecture and experimental design and compare simulated oxygen distributions against climatological observations. In section 3, we analyze the interannual and decadal variability of oxygen and its budget components in the tropical North Pacific. In section 4, we summarize our findings and conclude.
2 Model Description
 We employ a global ocean biogeochemistry model based on Massachusetts Institute of Technology general circulation model [Marshall et al., 1997a, 1997b] configured for the 1° × 1° global topography in longitude-latitude grid with 23 vertical levels. We simulate tracer transport and biogeochemistry in offline mode, using precomputed circulation fields from the German Estimating the Circulation and Climate of the Ocean (ECCO) product [Stammer et al., 2002]. At this resolution, the model cannot resolve mesoscale eddies and their effects are parameterized using the isopycnal thickness diffusion scheme [Gent and McWilliams, 1990]. Surface mixed layer processes are parameterized following the K-Profile Parameterization scheme [Large et al., 1994].
 Ocean biogeochemistry is simulated using the OCMIP-2 (Ocean Carbon-cycle Model Intercomparison Project Phase 2) scheme [Najjar et al., 1992], where the biological uptake of nutrient is parameterized as a linear relaxation of surface nutrient to its monthly climatology. The rates of carbon uptake and oxygen production are then calculated assuming a constant stoichiometric ratio as discussed below. The model transports five prognostic tracers: dissolved inorganic carbon, alkalinity, dissolved inorganic phosphorus (DIP), dissolved organic phosphorus, and dissolved oxygen (O2). Biological uptake of DIP is calculated by the restoring of surface DIP concentration toward the monthly climatology above the depth level of 75 m. We modified parameters for the production of dissolved organic matter and the exponent for vertical decay of sinking particulate matter. Of the DIP uptake, 20% turns into dissolved organic matter and the remaining 80% sinks down as particulate organic matter. The Martin exponent of 1.0 is used for the parameterization of the vertical attenuation of sinking particles, and the dissolved organic matter decays back to inorganic nutrient and carbon with the e-folding time scale of 6 months. Remineralization of sinking organic matter and dissolved organic matter consumes oxygen with a globally uniform stoichiometric ratio, P:C:−O2 = 1:110:170. When the model requires respiration in the regions where oxygen concentration is very low (<4 μM), the oxygen utilization is turned off in order to prevent negative oxygen concentration. Air-sea gas transfer of carbon and oxygen is calculated using the gas transfer coefficient that is proportional to the square of surface wind speed [Wanninkhof, 1992].
 The model is initialized from the annual mean climatology based on the World Ocean Atlas for dissolved inorganic phosphorus and dissolved oxygen [Garcia et al., 2006, 2010] and Global Ocean Data Analysis Project [Key et al., 2004] for dissolved inorganic carbon and alkalinity. In order to bring the model to the state of dynamic equilibrium, the model is integrated for 2000 years using the monthly mean climatological circulation fields. The climatological circulation field is computed by taking the monthly averages of the circulation fields between 1962 and 2002. The spin-up period of 2000 years was required to eliminate the model drift in the global inventory of all tracers. In the last century of the spin-up run, the global oxygen inventory drifted by only 0.04%.
 Starting from the spun-up condition, the model is further integrated for 50 years from January 1952 to December 2001 using time-varying circulation field. The first 10 years are discarded as the model may contain some initial adjustment. This operation is somewhat arbitrary, and the overall result does not change regardless of the omission of the first 10 years. Simulated oxygen variability and related three-dimensional physical and biogeochemical fields are recorded at monthly frequency for analysis.
 The modeled oxygen distribution is first compared against the observational climatology [Garcia et al., 2010] to evaluate the mean state of the model. Figure 1 compares the distribution of climatological oxygen field interpolated on the isopycnal surface σθ = 26.8, which lies close to the base of the ventilated thermocline in the North Pacific. The model spin-up captures the large-scale climatological oxygen distribution including near saturation condition at the isopycnal outcrop, relatively high values in the ventilated subtropical thermocline, and strong O2 depletions in the poorly ventilated tropics (Figure 1). The modeled volume of waters with the threshold oxygen value of 5 μM is 1.2 × 1015 m3. Observational estimates based on Bianchi et al.  are 2.45 × 1015 m3. In comparison, the simulated volume of low-O2 waters from the CMIP-5 (Coupled Model Intercomparison Project Phase 5) present-day runs ranges from 1.01 × 1015 m3 to 39.9 × 1015 m3 with a median value of 6.55 × 1015 m3 [Cocco et al., 2013]. In this metric, our simulation is similar to the best performing CMIP-5 simulations. In the tropical subsurface, oxygen concentrations are in reasonable agreement with the observation, but the shape of the low-O2 waters is less zonally elongated than observed. These deficiencies are also found in other coarse-resolution general circulation models [Deutsch et al., 2011]. We therefore do not focus on the specific shape or distribution of tropical oxygen minimum zone in this study, but rather, we use the oxygen inventory and the volume of low-oxygen water as the integrative metrics of oxygen variability. In the supporting information, we further demonstrate that the model can reproduce the overall interannual variability of tropical thermocline as measured by the time series of the Warm Water Volume in the Tropical Atmosphere-Ocean Project. The rest of our analysis will focus on the domain enclosed by 5°S and 115°W line, which contains the majority of suboxic/hypoxic waters in the tropical North Pacific (Figure 1b, white line).
 When forced by varying circulation, the thickness of the OMZ in the eastern tropical Pacific varies substantially over time (Figure 2a). The thickening of the low-oxygen condition is previously reported based on the historic observations [Stramma et al., 2008]. In our simulation, however, its behavior before the 1980s is opposite such that the thickness of the low-oxygen water slightly declined. In this manuscript, we focus on the temporal variability of oxygen minimum zone by subtracting the long-term trend. The magnitude of the subtracted trend is equivalent to 0.2 μM yr−1. Figure 2b shows the time evolution of the suboxic/hypoxic volume diagnosed from the model simulation. The detrended fractional change in the suboxic/hypoxic volume is normalized by the respective long-term average values over the simulation interval (1962–2002). Three oxygen thresholds are used to calculate the volume of low-oxygen waters including 5 μM, 20 μM, and 40 μM. Between the early 1980s and the late 1990s, the volume of suboxic zone (<5 μM) is more than doubled. Comparing the three lines in Figure 2b, it is clear that the amplitude of the variability becomes greater as lower oxygen thresholds are used to define the low-O2 volumes. Considering the climatological distribution of oxygen, the volume of suboxic water is two orders of magnitude smaller than that of hypoxic waters. Thus, relatively small change in the regional oxygen inventory can cause a major volumetric change in the suboxic waters [Deutsch et al., 2011].
 To diagnose the mechanisms responsible for the O2 variability in this region, we construct a control volume in the region bounded by 5°S and 115°W line within the depth range of 185 m to 710 m as shown in Figure 3. This control volume contains more than 99% of suboxic volume in the model. While the exact shape of this boundary is somewhat arbitrary, the alignment with the native grid allows accurate diagnostics of tracer mass balance. On average, this region receives a net horizontal convergence of mass, balanced by a net vertical divergence. Climatological upwelling rate at the top of the control volume is approximately 1.1 sverdrup. This upwelling water is mainly fed by zonal flow from the west, primarily in the intense subsurface jet under the equator, the Equatorial Undercurrent. The zonal advection also supplies oxygen to this region, balanced by the respiratory oxygen utilization. Each of these fluxes can vary significantly over time, as shown in the oxygen budget that is discussed in section 3.
3.1 Solubility and Apparent Oxygen Utilization Variability
 Oxygen inventory can be separated into two components, the solubility (O2sat) and apparent oxygen utilization (AOU) components. Oxygen saturation is a known function of temperature and salinity [Garcia and Gordon, 1992], and AOU is defined as the difference between oxygen saturation and oxygen.
 AOU is an estimate of the integrated effect of respiration along the ventilation pathways assuming that the water parcels were in saturation with the overlying atmosphere at the time of water mass formation [Ito et al., 2004]. The oxygen inventory and its two components are plotted in Figure 4.
 On the interannual time scale, the solubility and AOU changes tend to mutually compensate, leading to a relatively weak oxygen variability. The net effect is slightly dominated by the AOU component but its amplitude is significantly weaker than the amplitude of AOU component itself. The correlation coefficient between solubility and AOU components is 0.75, which is significant at 99% confidence interval. What causes the compensation between the solubility and AOU component on the interannual time scale? To understand this behavior, we must examine the relationship between the solubility, heat content, and AOU.
 The solubility of oxygen is primarily and inversely related to the temperature of seawater. As a result, the oxygen saturation inventory is almost perfectly anticorrelated to the heat content of the water mass (Figure 5). In turn, the variability of heat content is closely related to the dominant mode of climate variability in the tropical Pacific, the El Niño-Southern Oscillation (ENSO). During an El Niño event, zonal tilt of the thermocline decreases, causing the regional thermocline to deepen in the eastern equatorial Pacific. Since the control volume is located in the eastern tropical thermocline, the regional depression of thermocline due to El Niño events leads to an increase in the regional heat content and a decrease in the oxygen saturation.
 The recharge-discharge oscillator theory [Jin, 1997; Meinen and McPhaden, 2000] predicts that the integrated volume of warm water in the tropical Pacific increases several months prior to an El Niño event. Indeed, we find that the heat content and oxygen saturation slightly lead the Nino3.4 SST index. Simultaneous correlation between the regional oxygen saturation and Nino3.4 index is −0.56 (P < 0.01) and increases to −0.65 when oxygen saturation leads the Nino 3.4 index by 2–3 months. This lead period is shorter than the classical lag of 7 months [Meinen and McPhaden, 2000] between the warm water volume and the El Niño event.
 The AOU variability is also related to ENSO (Figure 6), albeit with a lower correlation than for O2sat. The AOU time series shows the peaks corresponding to most El Niño events but it also shows low-frequency variability that is not captured by the Nino3.4 index on the time scale of decades. Specifically, there is a decadal-scale AOU trend that changes its sign before and after the early 1980s. Because AOU is the time integral of biological oxygen utilization rate (OUR) along the ventilation pathway, its variability reflects changes in OUR both within and outside the tropics, which may explain the relatively weak correlation with the surface climate variability.
 AOU variability can be associated with changes in water mass ages. If the ventilation rate of water masses changes, it is possible to alter AOU without any OUR variability. To address this issue, we simulated an ideal age tracer along with the biogeochemistry. The variability of ideal age should correlate with any change in AOU solely due to the ventilation changes. Ideal age is moderately anticorrelated with Nino3.4 index (R = −0.34, not shown), indicating a link between tropical thermocline ventilation and climate variability. In a La Niña condition, zonal advection and upwelling are stronger in the eastern tropical Pacific, leading to the stronger upwelling of older waters. Conversely, an El Niño condition weakens the upwelling of older waters, leading to a relatively younger age.
 Changes in OUR also have a direct effect on AOU variability. In our simulation, OUR is calculated from the restoring of surface macronutrient to climatology, and a simple remineralization profile using a power function. The upwelling of excess nutrient results in elevated uptake and export. Thus, the OUR variability is controlled by the rate of upwelling and entrainment of nutrients from the thermocline to the surface waters. The OUR time series for the eastern tropical Pacific box (Figure 7) has a strong seasonal cycle associated with the drawdown of surface nutrients. We estimate the model seasonal cycle by calculating the monthly averages of OUR from the 40 year simulation period. When the mean seasonal cycle is removed, the variability of OUR is negatively correlated with the Nino3.4 index. When an El Niño condition is developing, the upwelling of subsurface nutrient is suppressed. As a result, anomalously weak export production occurs, which then decreases the OUR throughout the water column. Conversely, developing La Niña condition enhances the nutrient upwelling to the surface, leading to the enhanced oxygen consumption under La Niña conditions [Deutsch et al., 2011]. The correlation coefficient between the deseasonalized OUR and Nino 3.4 index is −0.73 (P < 0.01).
 AOU can be changed by both the water mass ages and the regional OUR. Overall, the two mechanisms work together to decrease AOU during El Niño condition and to increase it during La Niña, explaining the anticorrelation between AOU and Nino3.4 index. The deseasonalized OUR time scale correlates better with the Nino3.4 index relative to the ideal age tracer. This indicates that the respiration variability may be the primary driver, which is reinforced by the variability of water mass ages. In the next section, we quantify the relative role of physical circulation and biological respiration by diagnosing the oxygen budget in the model.
 As summarized in Figure 8, there is a strong influence of El Niño-Southern Oscillation on the variability of oxygen inventory in the eastern tropical North Pacific through both solubility and AOU. The red circles indicate El Niño events, defined by the model Nino3.4 SST anomalies greater than +1 standard deviation. Blue circles indicate La Niña events as defined by the model Nino 3.4 SST anomalies being smaller than −1 standard deviation. Most of the data points remain within ±2 μM range parallel to the zero line. Because of mutually compensating anomalies in saturation and AOU, the net effect is controlled by the relatively small residual between the AOU and solubility change. There are many overlapping data points near the center of the domain, which are either El Niño, La Niña, or neutral. During El Niño events, marked by red circles, the regional thermocline is depressed, and the temperature-solubility relation decreases the oxygen inventory due to the increased regional heat content. However, this thermodynamic response is accompanied by the decline in AOU with a slightly greater magnitude. The cause of AOU change is due to the combined effects of changes in water mass age and OUR. During an El Niño event, the weakened upwelling and depressed thermocline weakens the nutrient supply for biological productivity. It decreases the sinking organic flux and OUR. Also, the weaker upwelling prevents the old waters from upwelling into this region. These processes working in concert decrease the AOU during El Niño events. As a result, oxygen inventory tends to slightly increase during an El Niño event because the magnitude of decrease in AOU is slightly larger than the decrease in oxygen saturation. This is indicated by the cluster of red circles in the lower left quadrant of Figure 8.
3.2 Budget Analysis
 Thermocline oxygen shows a strong multidecadal variability, which modulates the interannual variability driven by the ENSO cycle. The recent expansion of the tropical Pacific OMZ since the 1980s may be a part of the underlying multidecadal variability. What drives this variability? As a first step to address this question, we perform a regional oxygen budget analysis for the eastern tropical Pacific box (Figure 3). We diagnose the oxygen transport convergence as well as biological oxygen consumption in the region.
 We diagnose the transport fields at every time step during the model simulation, and the transport fields are associated with the resolved circulation (uO2) and subgrid-scale parameterization terms (F) including Gent-McWilliams scheme [Gent and McWilliams, 1990]. The control volume is located below the euphotic layer, and so the predominant biological oxygen tendency is the loss due to respiration of sinking particulate matter and of dissolved organic matter. The growth of oxygen inventory is balanced by the transport convergence and the biological oxygen sink. Mathematically, our oxygen balance can be written as follows.
 The left-hand side is the growth term, and the first two terms of the right-hand side represent the transport convergence. The last term reflects the volume-integrated OUR, measuring the integrated effect of respiration. Each term is calculated at every time step during the simulation, and the respective monthly mean fields are recorded for analysis. Figure 8 shows the time series of each term in equation (2) for the simulation period including the seasonal cycle and long-term trend. We are able to reconcile more than 99% of the regional oxygen budget in the control volume. Among the components of the transport convergence (Figure 9), the resolved advective transport clearly dominates the overall transport variability and oxygen growth (R = 0.97), while subgrid-scale transport convergence is much less variable and is not significantly correlated to the oxygen growth (R = −0.17, see Figure 10). The variability of the oxygen growth is strongly correlated to the transport convergence (R = 0.98). Averaging over a full seasonal cycle, the transport convergence supplies oxygen to this region, compensated by the biological consumption. However, the compensation between physical supply and biological consumption do not occur on the monthly time scale, leading to the fluctuation of oxygen inventory.
 We investigated the oxygen transport in and out of the control volume. The vertical convergence of oxygen transport is calculated by taking the difference between area-integrated vertical oxygen flux at the top and bottom boundary of the control volume. Similarly, the horizontal convergence is calculated by taking the difference between area-integrated horizontal oxygen flux at the eastern and southern boundaries. The horizontal and vertical components of oxygen transport are negatively correlated (R = −0.58, P < 0.01), and they tend to mutually compensate one another (Figure 11). Red circles indicate that the net oxygen transport convergence is greater than 1 standard deviation. Likewise, blue circles indicate that the net oxygen transport convergence is less than −1 standard deviation. While zonal advection brings in higher oxygen concentration from the western tropical Pacific, the upwelling tends to advect older, oxygen-depleted waters from below. The net oxygen supply to the region depends on the subtle balance between the two opposing tendencies in the horizontal and vertical transport.
 In summary, the budget analysis reveals a close connection between the physical oxygen supply and biological oxygen consumption and their variability. There is a significant month-to-month variability in oxygen transport convergence, which is a residual between the upwelling and zonal advection. Upwelling tends to bring up old, oxygen-depleted waters vertically, which is counteracted by the zonal influx of oxygen-rich waters from the western Pacific. Because of this compensation, the correlation between physical oxygen supply and the ENSO cycle is very weak (R = −0.24). The rate of oxygen consumption (OUR) is significantly correlated with the ENSO cycle (R = −0.73, Figure 7), and this climatically modulated rate of biological oxygen consumption controls the time rate of change in AOU.
 The relationships between sources and sinks of oxygen and tropical climate variability diagnosed above arise from circulation and biogeochemical variability across a wide range of time scales. Figure 12 shows the temporal spectrum of oxygen inventory and its physical and biological drivers. Discrete Fourier Transform (DFT) is applied to the monthly time series of heat content, oxygen inventory, and advective and biological tendencies of oxygen in the control volume. This analysis includes the seasonal cycles and long-term trends. Prior to the application of DFT, anomaly time series are first constructed by subtracting the long-term mean value. Then the anomaly time series are normalized by its standard deviation.
 On the interannual time scale, the spectrum of physical oxygen supply peaks at about the time scale of 1 year, while that of biological oxygen consumption saturates at about the time scale of a few years. On the decadal time scale, the variance of oxygen and heat content generally increases toward long time scales, indicating that it has an elevated low-frequency variability. The largest variance at the lowest frequency (40 years) comes from their long-term trends, which has little statistical meaning. It is difficult to interpret the spectrum in the decadal band because of the small number of realization.
 The temporal spectrum of oxygen inventory (Figure 12b) shows significantly more variance in the decadal frequency relative to its physical and biological drivers. This is consistent with the theoretical study of Ito and Deutsch  that the subsurface oxygen variability integrates physical and biological forcing through the slow ventilation of thermocline waters, leading to the reddening of the resulting oxygen spectrum. This study is different from Ito and Deutsch  in that we explicitly simulate the physical and biological forcing of the oxygen variability and their spectrum can differ from white noise.
4 Discussion and Conclusion
 Natural climate variability significantly modulates the variability of the OMZ through a number of processes including the regional heat inventory, biological respiration, and the ventilation by subsurface ocean circulation. Previous studies identified large temporal change of the North Pacific OMZ [Stramma et al., 2008; Bograd et al., 2008; Keeling et al., 2010] which may be due to the combination of natural variability and ocean heat uptake [Frölicher et al., 2009; Deutsch et al., 2011; Czeschel et al., 2012]. We used a numerical ocean biogeochemistry model to better understand the mechanism controlling the temporal variability of the tropical Pacific OMZ, separate from the long-term trend. Global biogeochemistry simulation is performed in the offline mode using the German ECCO product, and simulated oxygen cycling is analyzed in detail. Our particular simulation captures the expansion of OMZ after the 1980s. Interannual variability of oxygen utilization rate is strongly correlated with the ENSO cycle as it regulates the upwelling supply of nutrients to the surface euphotic layer. This effect is partially compensated by the change in heat content associated with fluctuations in the thermocline depth. During an El Niño event, thermocline deepens in the eastern tropical thermocline, simultaneously decreasing the solubility and sinking organic flux. The former decreases the thermocline oxygen inventory, and the latter increases it. The net effect is a slight increase in the oxygen inventory. This physical-biogeochemical mechanism is driven by the fluctuations in the upwelling and thermocline depth. We identified significant transport variability of oxygen into the eastern tropical Pacific associated with the lateral subsurface circulation due to the equatorial zonal jet. However, there is a significant compensation between the horizontal and vertical transport of oxygen, and the transport-driven oxygen variability is relatively weak in comparison with the biologically driven variability.
 Previous study has shown that slow ocean ventilation integrates the energetic interannual and shorter time scale variability of regional physical and biogeochemical processes, leading to the pronounced decadal variability of thermocline oxygen [Ito and Deutsch, 2010]. Our results are consistent with this view that low-frequency variability of oxygen inventory is elevated relative to the physical and biogeochemical forcing. The elevated variance of oxygen inventory on the decadal time scale may be related to the Pacific Decadal Oscillation (PDO) [Deutsch et al., 2011; Czeschel et al., 2012], whereby decadal-scale fluctuations of low-O2 volume are correlated with the depth of thermocline and associated respiration variability. This study confirms this relationship between the thermocline depth, regional heat content, oxygen utilization rate, and the volume of low-O2 water. The common result between this study and the previous studies is that the thermocline oxygen shows opposite sense of change relative to the thermodynamic effect of ocean heat content. Solubility of oxygen decreases with temperature; however, our model shows that warmer and deeper tropical thermocline contains greater amount of oxygen. This is due to the corresponding changes in the biological oxygen consumption facilitated by the reduction in nutrient supply to the surface ocean.
 As the climate warms and the upper ocean will be more stratified in the future, it is possible that the long-term change in OUR may be controlled by the weakened nutrient supply to the euphotic layer, which leads to an increase in thermocline oxygen particularly in the tropics. Consistent with this mechanism, simulated oxygen trend from numerical ocean models can show a long-term oxygen increase in the tropical thermocline [Stramma et al., 2012; Cocco et al., 2013].
 However, the comparison of modeled and observed oxygen shows that the models perform poorly in reproducing the decline of oxygen in the tropics over the past few decades and that the model performance changes significantly depending on the diapycnal mixing rate in the model [Duteil and Oschlies, 2011; Stramma et al., 2012]. The issue of mixing and its impact on tropical oxygen trend is clearly a crucial topic for further study.
 There are several caveats in our model simulations. The parameterization of biological productivity used in this study is highly idealized including the restoring of a macronutrient toward monthly climatology. This parameterization strongly couples upwelling and export production so as to keep the surface nutrient constant, which may generate the variability of biological oxygen consumption that is too strong. However, the nutrients upwelling in the tropical Pacific are eventually be fully utilized by the time the surface water gets to the oligotrophic subtropics. Thus, in a regional integral sense, the upwelling variability indeed controls the productivity. It is of great interest to compare this study with more mechanistic models of biological productivity. The oxygen budget analysis in the tropical Pacific OMZ highlights the importance of advective oxygen supply maintained by the zonal jets in the equatorial current system. Previous study highlights the importance of equatorial zonal jets in supplying oxygen to the OMZ [Stramma et al., 2010]; however, our model does not fully resolve the equatorial current system and its variability. Similarly, mesoscale eddies are not explicitly resolved in our simulation, but they are crudely parameterized. Eddy stirring and bolus transport may play important role in the physical supply of oxygen and nutrients [Resplandy et al., 2011]. Additional work, such as a suite of sensitivity experiments at a higher resolution and different diapycnal and isopycnal mixing rates would be necessary in order to isolate the different physical processes contributing to the variability of OMZ.
 We appreciate two anonymous reviewers who provided constructive and thorough comments on the earlier version of the manuscript. We thank the U.S. National Science Foundation for funding support. This work is supported by NSF grant OCE-0647979 to T.I. and OCE-0550771 to C.D.