a. CSM 1.4 coupled physical model

The core of the coupled carbon–climate model is a modified version of NCAR CSM 1.4, consisting of ocean, atmosphere, land, and sea ice physical components integrated via a flux coupler (Boville and Gent 1998; Boville et al. 2001). The simulations here are integrated with an atmospheric spectral truncation resolution of T31 (∼3.75°) with 18 levels in the vertical, and an ocean resolution of 0.8°–1.8° latitude and 3.6° longitude with 25 levels in the vertical (referred to as T31 × 3). The sea ice component model runs at the same resolution as the ocean model, and the land surface model runs at the same resolution as the atmospheric model. Physical control simulations display stable surface temperatures and minimal deep ocean drift without requiring surface heat or freshwater flux adjustments. The water cycle is closed through a river runoff scheme, and modifications have been made to the ocean horizontal and vertical diffusivities and viscosities from the original version (CSM 1.0) to improve the equatorial ocean circulation and interannual variability.

The 3D atmospheric CO₂ distribution is advected and mixed as a dry-air mixing ratio using a semi-Lagrangian advection scheme; both dry and moist turbulent mixing schemes are used for the transport of water vapor mass fractions. The model CO₂ field affects the shortwave and longwave radiative fluxes through the column average CO₂ concentration.

b. Land carbon cycle model

The CSM 1.4-carbon land carbon module (Fig. 1) combines the NCAR Land Surface Model (LSM) biogeophysics package (Bonan 1996) with the Carnegie–Ames–Stanford Approach (CASA) biogeochemical model (see Randerson et al. 1997). Both the LSM and CASA models are documented extensively in the literature. Here we provide a brief overview of the models and highlight changes that have been made to the standard model dynamics. The land surface is characterized by the fractional coverage of 14 plant functional types (PFTs) and 3 soil textures (Bonan 1996). LSM estimates leaf-level stomatal conductance of CO₂ and water to maximize carbon assimilation for sunlit and shady conditions (Collatz et al. 1990; Sellers et al. 1996). The carbon assimilation is integrated through the canopy using the fraction of sunlit and shade leaves to yield gross primary productivity (GPP). A terrestrial CO₂ fertilization effect arises physiologically in the model because carbon assimilation via the Rubisco enzyme is limited by internal leaf CO₂ concentrations; GPP thus increases with external atmospheric CO₂ concentrations, eventually saturating at high CO₂ levels.

In this implementation, net primary productivity (NPP = F_ab) is assumed to be 50% of GPP calculated by LSM (replacing NPP calculated by CASA). The NPP/GPP ratio has been demonstrated to be constant on annual time scales across a wide range of forests (Waring et al. 1998). While it is well known that autotrophic respiration (R_a) varies seasonally and diurnally, we have not modeled R_a explicitly, as its magnitude as well as sensitivity to temperature and other control variables remain uncertain even in high-frequency flux tower measurements (e.g., Wohlfahrt et al. 2005; Reichstein et al. 2005). The impact of this assumption on modeled CO₂ cannot be readily quantified, as global-scale constraints are available for the seasonal variability of NPP [via satellite observations of the normalized difference vegetation index (NDVI)] and on the net flux (via the seasonal oscillations of atmospheric CO₂), and not for GPP or respiration.

NPP is allocated to three live biomass pools M (leaf, wood, and root) following Friedlingstein et al. (1999), with preferred allocation to roots during water-limited conditions and to leaves during light-limited conditions:

View Expanded

In the CASA formulation, turnover times τ_k of the three live pools are PFT specific but time invariant, with constants ranging from 1.8 yr for leaves in tropical broadleaved evergreen trees to 48 yr for wood in broadleaved deciduous tress. The leaf mortality of deciduous trees is modified to include cold-drought stress to effect leaf fall in 1–2 months, and leaf biomass (kg C m⁻² land) is translated into prognostic leaf area indices (LAI) using specific leaf areas [SLA; m⁻² leaf (kg C)⁻¹] following Dickinson et al. (1998), so that LAI vary with climate. We place limits on LAI, with a minimum of 0.6 to simulate the storage of carbon in photosynthates and a maximum of 6 to simulate light and nutrient limitation. The excess carbon above the maximum M_leaf is added to litterfall M_leaf/τ_leaf.

There are nine dead carbon pools, with leaf mortality contributing to metabolic and structure surface litter (k = 4, 5), root mortality contributing to metabolic and structure soil litter (k = 6, 7), and wood mortality contributing to coarse woody debris (CWD; k = 8). The subsequent decomposition of M_k, k = 4–8 by microbes leads to the transfer of carbon to the dead surface, soil microbial pools (k = 9, 10), and the slow and passive pools (k = 11, 12). A fraction of each carbon transfer is released to the atmosphere via microbial or heterotrophic respiration. This is summarized in Eq. (3):

View Expanded

The first term on the rhs of Eq. (3) is the gain of M_k due to litterfall and the transfer from other dead carbon pools j; the second term is the loss of M_k due to transfer from pool k to other pools n; and the third term is R_h = F_ba, the loss of carbon to the atmosphere via heterotrophic respiration. The transfer coefficients γ_jk are time-invariant constants following CASA.

The rates of transfer are climate sensitive, following CASA:

View Expanded

where τ_k0 is the turnover time of pool k at 10°C with no water limitation; τ_k0 ranges from 20 days for the metabolic soil pool to 500 yr for the passive pool. The modulators f (T) and g(w) are functions of soil temperature (T) and an index of soil moisture saturation (w), respectively. Soil temperature and soil moisture are averaged over the top 30 cm (top two model soil layers) of the soil. Here, f (T) is represented by a Q₁₀ of 2, or a rate doubling for every 10°C increase in soil temperature referenced to 10°C, and g(w) is a monotonic function of soil moisture saturation, and ranges linearly between 0 and 1 for w between 0.25 and 0.75.

This version of the model does not include other land surface processes that affect atmosphere–biosphere interactions. These include an explicit nitrogen cycle, fires and other disturbances, herbivory, dynamic vegetation cover, or anthropogenic land cover change.

Carbon fluxes and carbon pools are updated at LSM time steps of 30 min so that the prognostic biogeochemistry is in step with the biogeophysics. The geographic distribution of the net atmosphere–land flux,

View Expanded

is passed to the atmosphere to update atmospheric CO₂ concentration. In this way, changes in leaf areas calculated by CASA influence GPP transpiration and albedo, while changes in temperature and soil moisture calculated by LSM alter NPP, allocation and decomposition rates. Thus, there is full coupling of the energy, water, and carbon cycles.

c. Ocean carbon cycle model

The ocean carbon cycle model is a derivative of the Ocean Carbon Model Intercomparison Project (OCMIP2) biotic carbon model, which is itself a derivative of the model of Najjar et al. (1992), and is described, for instance, in Doney et al. [2003, 2004; see also R. G. Najjar and J. C. Orr 1999, unpublished manuscript (OCMIP-2 Biotic-HOWTO; available online at http://www.ipsl.jussieu.fr/OCMIP/)]. Air–sea fluxes of CO₂ are estimated as

View Expanded

where k_u is the wind-dependent gas exchange coefficient across the air–sea interface, β_T is the temperature-dependent solubility of CO₂, pCO₂^atm and pCO₂^sw are the partial pressures of CO₂ in the lowest two layers of the atmosphere (∼60 mb) and in the top layer of the ocean, respectively, and f_ice is the fractional ice coverage. The pCO₂^sw is calculated from model dissolved inorganic carbon (DIC), alkalinity (ALK), temperature, and salinity according to carbonate chemistry.

The primary differences between the new model (Fig. 2) and the OCMIP-2 BGC model are

• nutrient uptake has been changed from a nutrient restoring formulation to a prognostic formulation,

• iron has been added as a limiting nutrient in addition to phosphate, and

• a parameterization for the iron cycle has been introduced.

1) Nutrient uptake

The parameterization of biological uptake is similar to that used in the Hamburg Model of the Ocean Carbon Cycle (HAMOCC; Bacastow and Maier-Reimer 1990; Maier-Reimer 1993). The uptake of PO₄ is given by the turnover of biomass B, modulated by temperature, macro- and micronutrients, and surface solar irradiance:

View Expanded

Like the OCMIP-2 BGC model, biological uptake only occurs in the production zone (z < z_c), where z_c is the compensation depth (75 m). The temperature limitation function,

View Expanded

is the same that is used in HAMOCC with T (°C). The nutrient limitation term is the minimum of Michaelis–Menten limiting terms for PO₄ and Fe:

View Expanded

where κ_PO4 is 0.05 μmol L⁻¹ and κ_Fe is 0.03 nmol L⁻¹. The light (irradiance) limitation term,

View Expanded

uses I, the solar shortwave irradiance, and a light limitation term κ_I (20 W m⁻²). Irradiance decays exponentially from the sea surface with a 20-m length scale. If the cell is completely contained in the mixed layer z_ml, then I is the average over the entire mixed layer. If the cell is completely below in the mixed layer, then I is simply the average over the cell. For intermediate cases, I is the appropriate weighted average. As a consequence, the light limitation term decays like O(1/z_ml) for z_ml > z_c. B is a proxy for biomass (μmol L⁻¹):

View Expanded

where r_Fe:P is the ratio of Fe to PO₄ uptake 5.85 × 10⁻⁴ (mol/mol), derived by assuming a Fe-to-C uptake ratio of 5.0 × 10⁻⁶ (mol/mol) and a C-to-PO₄ uptake ratio of 117 (mol mol⁻¹). The term max(1,z_ml/z_c) scales the uptake by z_ml when it exceeds z_c; this is meant to implicitly extend the production zone to the base of the mixed layer. Finally, τ is the optimal uptake time scale (15 days).

2) Iron parameterization

There are three conceptual forms of iron in the model: Fe representing dissolved inorganic iron, DOFe representing the iron content of the dissolved organic matter, and POFe representing the iron content of the sinking particles. The following processes govern the iron cycle:

• surface deposition of Fe from the atmosphere,

• biological uptake of Fe, converting Fe into DOFe and POFe,

• remineralization of DOFe into Fe,

• scavenging of Fe into POFe,

• and remineralization of POFe into Fe.

Surface deposition of Fe is derived from the monthly climatological dust flux estimated by Mahowald et al. (2003). The dust is assumed to be 3.5% Fe by weight with 2% of the Fe bioavailable. Biological uptake of Fe is equal to r_Fe:P × J_prod. It is routed to DOFe and POFe using the same partitioning that is used for P, where a fixed fraction σ = 0.67 goes to DOFe and the remainder goes to POFe. DOFe remineralizes into Fe following first-order kinetics with a rate constant κ = 2 yr⁻¹. Since r_Fe:P is constant and σ and κ are the same for the Fe pools as they are for the P pools, DOFe is equal to r_Fe:P · DOP. Because of this relationship, DOFe is not explicitly tracked in the model.

The scavenging of Fe is similar to the single ligand model described in Archer and Johnson (2000). Conceptually, there is a ligand that organically binds to Fe molecules, protecting them from scavenging; Fe that is not bound to ligands is denoted Fe_free and is the positive root of the quadratic equation

View Expanded

where L is the concentration of ligand and K_L is the strength of the binding reaction. We assume a globally uniform ligand concentration of 1.0 nmol L⁻¹ and a K_L = 300 L(nmol)⁻¹. The scavenging of Fe is given by

View Expanded

where C₀ = 0.2 yr⁻¹, α = 200, and z_scav = 250 m.

Scavenged Fe is attached to the sinking particles to form POFe. A fraction (40%) of the scavenged Fe is assumed to be insoluble and is directly lost to the sediments. The remaining 60% can be remineralized back to dissolved form below z_c. The OCMIP-2 model used a single Martin power-law curve (a = −0.9) to describe the vertical POP flux profile over all the full water column. This scheme needs to be modified to a local power law because scavenged Fe is attached to the sinking organic matter throughout the water column. Consider a model cell with a flux F_POFe through the top at z_t. The flux at the bottom (z_b) is then

View Expanded

where 0.6 represents the 60% of the scavenged Fe that is potentially soluble. Of the POFe that reaches the seafloor, that due to biological uptake is remineralized into the bottom cell. This is equivalent to setting the seafloor remineralization of POFe to r_Fe:P times seafloor POP remineralization.

a. Global climate and carbon cycle time series

As shown in Fig. 4, global integral properties such as the average surface temperature, atmospheric CO₂ concentration, and the ocean and land carbon inventories remain approximately stable over the entire 1000-yr coupled carbon–climate control simulation. Global annual mean model surface temperature remains constant within ±0.10 K (1 σ) over the integration, and other global integral physical climate metrics are similarly constant. The stability of the CSM 1 physical climate with fixed atmospheric composition and no flux corrections is documented in Boville and Gent (1998) and Boville et al. (2001). The global annual mean atmospheric CO₂ in the 1000-yr control run displays no long-term trend, and the variations are ±1.2 ppmv (1 σ), small enough that the concomitant alterations in the radiation budget are relatively minor. Thus, the variability in Fig. 4 arises from natural, internal dynamics of the climate system working on the carbon cycle.

The model carbon inventories vary on interannual-to-centennial time scales, reflecting continuous repartitioning of carbon among the atmosphere, ocean, and land reservoirs (Fig. 4c). A dominant feature is the gradual increase in atmospheric CO₂ by ∼4 ppmv in the first 350–400 yr of the integration followed by a comparable decrease over the ensuing 200–250 yr. These changes are tied to oscillations in both the land and ocean inventories and are related to slow adjustments in the physical climate (soil moisture, land and sea surface temperatures, ocean circulation) and, for the oceans, changes in atmospheric CO₂. The 500-yr simulation with CO₂ fertilization also exhibits a stable but somewhat different atmospheric CO₂ trajectory (Fig. 4b); in this case there is an initial transient uptake rather than release from the land biosphere. The magnitude of the interannual-to-centennial variability is quite comparable, however.

Superposed on the very low-frequency variations are centennial and shorter time-scale signals, which dominate the variability in the last 400 yr of the 1000-yr control simulation. Because it is difficult to separate the effects of model drift from natural variability on the millennial time scale with only a 1000-yr simulation, we focus our analysis on centennial and shorter time scales. These variations in atmospheric inventory appear to be driven primarily by changes in the land inventory, with net terrestrial carbon uptake and release events as large as 5–10 Pg C on decadal scales. On these same scales, the ocean carbon inventory is positively correlated with the atmosphere and anticorrelated with the land, but with a smaller amplitude signal (∼10%–20%). The dynamics controlling this variability are discussed in more detail in section 5.

b. Physical climate drift and biases

Similar to previous physics-only CSM 1 solutions, the carbon–climate control simulation is not completely stationary, exhibiting long-term drift in some physical properties. There is a vertical redistribution of salt in the ocean with the surface ocean freshening (∼0.035 psu century⁻¹) and a corresponding increase of deep-water salinity. A small net heat flux imbalance leads to a weak ocean warming (∼0.02 K century⁻¹ averaged over a full water column). The surface warming and freshening would both contribute to a small ocean CO₂ outgassing, but the flux is small relative to the internal variability of the model or the anthropogenic fluxes explored in Fung et al. (2005). The global storage of soil moisture and the biogeochemical moisture dependence term show little or no long-term drift. Nonnegligible patterns of regional climate drift occur but do not significantly impact our main findings.

There are also a number of biases in the spatial patterns of the physics in the CSM 1.4 coupled model that impact the biogeochemical solution. Model surface temperatures are too cold in the Northern Hemisphere continental interiors relative to observations (Fig. 5a). Although some of the cooling may be ascribed to the fact that our control run has preindustrial atmospheric CO₂ concentrations, other simulations with greenhouse forcing equivalent to the late twentieth century also show similar biases from −2 to −6 K (Boville et al. 2001; Dai et al. 2001). The CSM 1.4 solutions produce an unrealistic precipitation pattern in the equatorial Pacific pattern with a double intertropical convergence zone (ITCZ) and bands of excess rainfall north and south of the equator (Boville and Gent 1998; Dai et al. 2001). Significant biases exist in tropical and temperate land precipitation with too wet conditions in central Africa, western South America, western North America, and parts of Indonesia, and with overly dry conditions in parts of Amazonia and eastern North America. In the model ocean, the double ITCZ leads to bands of too fresh and vertically stratified surface waters in the Pacific and to an off-equator shift in the maxima of interannual air–sea CO₂ flux variability (section 5b). On land, the temperature and precipitation biases result in corresponding anomalies in the simulated spatial patterns of NPP, LAI, and carbon storage.

c. Land carbon dynamics

The net terrestrial CO₂ flux ΔF_land, or net ecosystem production (NEP), reflects the lag on seasonal interannual out to centennial time scales between NPP and heterotrophic respiration R_h. The global mean terrestrial NPP is 66.74 ± 0.88 Pg C yr⁻¹ in the 1000-yr control run. We note that the simulation is not directly comparable with contemporary observations because of land cover changes and climates forcings in the past two centuries, but the modeled NPP is within the range simulated by dynamic vegetation models forced by the climate of the nineteenth and twentieth centuries (Cramer et al. 2001). The geographic distribution of the simulated NPP (Fig. 6a) is not inconsistent with in situ measurements and satellite observations of the NDVI (e.g., Tucker et al. 2005). The latitudinal gradient of NPP is steeper than observed, with an underestimation at high latitudes due to the small area of boreal forests in the LSM prescriptions of plant functional types, the high-latitude cold bias in CSM 1.4, and an overestimation at low latitudes of excessive stomatal conductance under diffuse radiation. Some obvious blemishes in the simulated NPP field, such as the relatively low simulated values along the coast of eastern South America or in Indochina, are a direct result of biases in the coupled model precipitation field (Fig. 5b).

With the turnover times τ specified via the land carbon module [Eqs. (2)–(4)], the simulated NPP field yields reasonable distributions of living biomass and detrital/soil carbon—871 ± 2.4 and 1086 ± 2.0 Pg C, respectively (Figs. 1 and 6b). Substantial terrestrial carbon storage occurs in the regions of high NPP in the Tropics and subtropics, mostly in living biomass. Elevated carbon inventories are found as well along a band of boreal forests in the Northern Hemisphere associated with cooler temperatures and a larger fraction of storage in the detrital and soil pools. While the model inventories are reasonable to the lowest order, it is difficult to directly compare the model detrital and soil carbon distribution against the observations. The model soil carbon pools represent only the organic material in the upper 20 cm of the soil, and the model does not account for carbon storage in high-latitude peats, for example.

d. Ocean carbon dynamics

The geographic pattern of the average annual net air–sea flux (Fig. 7a) from the control simulation broadly resembles that compiled by Takahashi et al. (2002) for the contemporary ocean, showing net outflux of CO₂ from the equatorial regions and Southern Ocean and net invasion of CO₂ into the temperate and subpolar North Pacific and North Atlantic. Some differences in the spatial distribution, such as the larger net CO₂ efflux from the model Southern Ocean, are expected since the model represents preindustrial conditions. The patterns and integrated magnitude (8.94 ± 0.10 Pg C yr⁻¹) of the simulated sinking particulate organic matter export (Fig. 7b) are also generally consistent with the more limited observational constraints on this quantity (Doney et al. 2003), except for the equatorial Pacific problems already mentioned. So, too, are the water column DIC and nutrient distributions, which are governed by a combination of air–sea exchange, biological uptake and export, subsurface remineralization, and ocean circulation.

e. Atmospheric CO₂ distributions

The time–space distribution of atmospheric CO₂ integrates land and ocean fluxes on regional to global scales. Because our model tracks the 3D atmospheric CO₂ tracer field, we can utilize the model atmospheric CO₂ field to assess the skill of simulated surface fluxes. Surface CO₂ fluxes are reflected in spatial patterns in the mean atmospheric surface CO₂ distribution (lowest ∼60 mb; Fig. 8a). Over land, net long-term fluxes into and out of the land biosphere are approximately zero, and the elevated CO₂ levels found in the Tropics and Northern Hemisphere temperate zone arise from the so-called “rectifier effect” associated with seasonal correlations between surface CO₂ fluxes and atmospheric convection and mixing (Denning et al. 1995). Over ocean, the model exhibits a peak due to equatorial CO₂ outgassing regions (Fig. 7a). Atmospheric CO₂ is also slightly higher in the Southern Hemisphere than in the Northern Hemisphere because of the large uptake of CO₂ in the North Pacific and North Atlantic formation sites and subsequent southward lateral transport and release in the equatorial and Southern Oceans (Broecker and Peng 1992). The simulated mean spatial patterns in the model cannot be directly compared to modern observations, which are strongly influenced by fossil fuel emissions and fluxes due to current and past land use change.

The seasonal cycle of CO₂ at Mauna Loa, Hawaii, provides a useful measure of the seasonal imbalances between NPP and R_h of the Northern Hemisphere land biosphere (e.g., Fung et al. 1983; Randerson et al. 1997) and is thus an indirect constraint on the bulk turnover time of soil carbon. The 1000-yr mean CO₂ seasonal cycle at the location of Mauna Loa in the model resembles that observed (Fig. 8b). Both the modeled and observed cycles peak in May and have a trough in September–October; the simulated peak–trough amplitude is ∼4 ppmv, somewhat smaller than the observed value of ∼6 ppmv, which also includes the small but nonnegligible effects of seasonal transport of fossil fuel CO₂ (Randerson et al. 1997). The model underestimation of the CO₂ amplitude is also partially due to the underestimation of NPP at northern high latitudes. The agreement suggests that the seasonal dynamics of both photosynthesis and decomposition are reasonably well captured in the model, and that known deficiencies in the physical climate model have not impaired gross features of terrestrial carbon dynamics. The spatial patterns of the seasonal atmospheric CO₂ amplitude (not shown) are consistent with modern observations, increasing from <1–2 ppmv over the Southern Ocean to 5–15 ppmv over high-terrestrial NPP regions in the Tropics and Northern Hemisphere temperate zone. (Fig. 6a).

a. Global surface CO₂ flux variability

Time series of the global integrated, annual net CO₂ surface fluxes from the land ΔF_land and ocean ΔF_ocean (Fig. 9) highlight the high-frequency, interannual variability in surface–atmosphere exchange. The rms variability (1σ) in the annual net global fluxes is ±0.69 Pg C yr⁻¹ and ±0.10 Pg C yr⁻¹, for ΔF_land and ΔF_ocean, respectively. For monthly, deseasonalized anomalies, the corresponding rms variability increases to ±1.40 Pg C yr⁻¹ and ±0.19 Pg C yr⁻¹. As with the low-frequency signal, interannual variability in terrestrial exchange dominates over that of the ocean by almost an order of magnitude, in part because of the chemical buffering of the carbon dioxide system in seawater, with year-to-year shifts from the terrestrial biosphere as large as ±2 Pg C.

The interannual variability in the simulated terrestrial flux is comparable to the value of ±2.0 Pg C yr⁻¹ inferred from the contemporary atmospheric CO₂ record (Bousquet et al. 2000). Some care is required in a direct model data comparison, as the contemporary fluxes include processes [such as often human-ignited fire contributions (Langenfelds et al. 2002; Randerson et al. 2005) and variability in climate due to volcanic eruptions and the subsequent impact on terrestrial carbon storage (Angert et al. 2004)], that are not explicitly treated in CSM 1-carbon. The modeled variability is also comparable to, albeit at the low end of, that simulated in an intercomparison of terrestrial ecosystem models (Dargaville et al. 2002). Note that the simulated pentadal variability in ΔF_land is similar to the inferred magnitude of the anthropogenic terrestrial carbon sink; thus, the attribution of the contemporary carbon sink to processes other than climate variability remains a statistical challenge. The simulated ocean variability is considerably smaller than that inferred from atmospheric inversions but is consistent with estimates derived from historical reconstructions using ocean-only biogeochemical models [monthly global anomalies: ±0.20 Pg C yr⁻¹ (Le Quere et al. 2000); ±0.23 Pg C yr⁻¹ (Obata and Kitamura 2003)].

b. Spatial patterns in CO₂ flux variability

The geographic distribution of the rms variability in the annual means of ΔF_land and ΔF_ocn (1σ standard deviation of the time series at each individual grid point) is shown in Fig. 10a. Variability in ΔF_land is largest in the Tropics, with peak values exceeding 100–200 g C m⁻² yr⁻¹, and is elevated (20–100 g C m⁻² yr⁻¹) across temperate North America and Eurasia. The tropical variability maxima occur in bands of moderate NPP surrounding the terrestrial NPP maxima in Amazonia, Central Africa, and Indonesia (Fig. 6a). Locally, the air–sea CO₂ flux variability of the annual means ranges from 1 to >10 g C m⁻² yr⁻¹ in the coupled model, with maxima in the subpolar North Atlantic and North Pacific, Southern Ocean, and in two off-equatorial bands in the tropical Pacific. There is a general correspondence between the locations of the maxima in air–sea CO₂ flux variability and the regions of strong CO₂ uptake and degassing (Fig. 7a).

The largest variability in our air–sea flux is in the Southern Ocean and North Atlantic. This is in contrast to most modeling and observational studies that show the highest air–sea CO₂ flux variability to be associated with El Niño–Southern Oscillation (ENSO), accounting for the majority of the total global variability in ocean-only simulations [70%, (Le Quere et al. 2000); >50% (Obata and Kitamura 2003)] and coupled ocean–atmosphere simulations (e.g., Jones et al. 2001). This could be because these ocean-only models underestimate high-latitude ocean dynamics and biology. It could also be because of overly weak vertical gradients in DIC in the upper thermocline in the CSM 1.4-carbon model Tropics, caused by overly strong iron limitation and, therefore, low surface biological uptake (Fig. 7b). In contrast to the model results, equatorial Pacific observations show that the highest interannual variability in air–sea CO₂ flux occurs on or near the equator. In the field data, it appears to be driven primarily by the shoaling and deepening of the thermocline in the central and eastern basin, which in turn alters the magnitude of subsurface inorganic carbon upwelling. The model simulations include corresponding changes in thermocline depth (20°C isotherm). The variability in simulated monthly sea surface temperature anomalies (±0.72 K) in the central equatorial Pacific in the 1000-yr control agrees well with observations (±0.82 K), suggesting that our low tropical variability is not an issue of thermocline variability or physical upwelling (Otto-Bliesner and Brady 2001). The problem appears instead to be that the vertical inorganic carbon gradients are too weak so that even with thermocline shoaling or deepening, there is insufficient variability in the inorganic carbon concentrations of the upwelled source water.

Not surprisingly, the model regions with high surface CO₂ flux variability create corresponding areas of elevated variability in the overlying surface atmospheric CO₂ field (Fig. 10b). Rms variability (1σ) in the spatial anomalies in annual surface CO₂ concentrations (after removal of global mean) range from <0.2 ppmv over oceans to 0.2–0.5 ppmv over northern Eurasia and eastern North America to as high as 0.5–1.0 ppmv in the Tropics. The spatial patterns in the annual mean and rms spatial variability in surface atmospheric CO₂ are almost identical between the cases with and without land CO₂ fertilization.

c. Terrestrial variability mechanisms

Terrestrial photosynthesis and decomposition are enhanced by positive temperature and soil moisture anomalies (unless thresholds are exceeded), and the net effect on NPP and R_h depends on their synergistic or competing effects. Over land, the interannual variability of surface air temperature and soil moisture is positively correlated (warm–wet and cool–dry) when mean air temperature is low (e.g., temperate latitudes in winter and polar regions in the summer) and negatively correlated (warm–dry and cool–wet) when the mean air temperatures are high (Tropics all year and temperate bands in the summer). These distinct regional/seasonal patterns are illustrated in Fig. 11a, which is a spatial map of the air temperature–soil moisture correlation for the Northern Hemisphere summer. Interannual variations in simulated NEP tend to be controlled by summer moisture stress (annual mean stress in the case of the Tropics) rather than temperature stress (Fig. 11b). An exception is in the polar Northern Hemisphere, where temperature and moisture effects are synergistic and comparable in size.

Because the turnover time of vegetation carbon is shorter than that of soil carbon, NPP is slightly more sensitive to climate perturbations than R_h, ±0.88 Pg C yr⁻¹ versus ±0.54 Pg C yr⁻¹ (1σ rms, global net annual mean), respectively. Thus, NPP decreases faster than R_h with climate stress and increases faster than R_h under favorable climate conditions (Fig. 12a). NPP and R_h covary on subannual time scales. Globally, however, the linkage of land photosynthesis to respiration is considerably weaker on interannual time scales because regional flux anomalies tend to cancel.

Variations in simulated terrestrial NEP can be driven by NPP, R_h, or both. In our model formulation, the climate modulations are the same for all the dead carbon pools [cf. Eq. (4)]. The respiratory fluxes from the fast (τ_k < 5 yr) pools are in step with NPP and cancel 50%–60% of the NPP. It is the variation of wood biomass, CWD, and the “leakage” of dead carbon from the litter to the slow pool that determine NEP on decadal- to-centennial time scales. Unlike the fluxes, the variability of these pools is comparable on interannual and interdecadal time scales (Fig. 4c), with 1σ rms for global annual means of ±1.51, ±0.63, and ±0.95 Pg C for wood, CWD, and the slow pool, respectively. Figure 12b shows squared coherence versus frequency for NEP against NPP and NEP against R_h; the squared coherence varies from 0 (completely incoherent or uncorrelated at all phase lags) to 1 (fully coherent) and indicates the fraction of variance that can be accounted for between the two time series with a linear model. NEP, the noncancellation between NPP and R_h, is essentially uncorrelated with R_h on all time scales shorter than 10 yr. But R_h is coherent with both NPP and NEP on centennial time scales, lagging by about a decade (turnover time of CWD), and largely tracks the variations in net accumulation–loss of soil/detrital carbon [cf. Eq. (3)].

d. Ocean variability mechanisms

Several competing mechanisms govern oceanic CO₂ flux variability in the 1000-yr control, and the relative magnitudes (and even the signs) of the interactions differ from region to region and by time scale. The variability in net air–sea CO₂ flux ΔF_ocn (Fig. 10a) can be analyzed in terms of the components contributing to the model air–sea flux parameterization [Eq. (5)]. The transfer velocity k_u depends on the square of 10-m wind speed U². Wind-driven variability contributes to high-frequency flux variability everywhere, with the sign of the U²–ΔF_ocn correlation depending on mean net air–sea flux patterns (Fig. 7a). Sea ice coverage plays a role at high latitude both in terms of capping gas exchange and altering stratification. The impact of low-frequency variations in pCO₂^atm on ΔF_ocn is discussed in section 5e; the high-frequency atmospheric signal is small enough over the ocean (Fig. 10b) to have little impact on air–sea flux.

Variability in surface water pCO₂^sw is governed by thermal solubility and freshwater inputs (cooling and freshening decrease pCO₂), biological uptake and particle export that draw down DIC and alkalinity with the net effect of reducing pCO₂, and mixing/circulation that can bring up subsurface waters with elevated DIC, alkalinity, nutrients, and pCO₂ (metabolic CO₂) due to respiration of organic matter at depth. The interplay of these different factors is shown in a set of ΔF_ocn versus property covariance maps (Fig. 13). Interannual variations in freshwater fluxes associated with the model ENSO lead to surface freshening, warming, stratification, and negative CO₂ flux anomalies (uptake), driving the large off-equator variability in the tropical Indo-Pacific (Fig. 10a). Net freshwater input to the surface ocean lowers sea surface salinity (SSS), reducing both DIC and alkalinity by dilution. The thermodynamics of the ocean carbonate system is such that dilution (negative SSS anomaly) lowers surface water pCO₂ and drives a downward (negative) CO₂ flux anomaly, which accounts for the large positive SSS–CO₂ flux covariance in Fig. 13c. Note that the SST–CO₂ flux covariance in these regions is negative, opposite that of thermodynamics (warming leading to increased seawater pCO₂), and demonstrates that haline forcing dominates over thermal.

The effects of particle export and circulation are often opposed to each other because the same enhanced mixing or upwelling that brings nutrients to the surface to enhance production (lower pCO₂ and positive, downward ocean CO₂ uptake anomaly) also brings DIC that increases pCO₂. In the deep-mixing zones of the Southern Ocean and North Atlantic, upwelled DIC from deeper mixing overwhelms enhanced biological drawdown, leading to positive CO₂ flux anomalies (outgassing). In the Southern Ocean, deeper mixing is associated with colder SSTs, while the opposite pattern occurs in the subpolar North Atlantic, where mixing is governed by sea ice distributions and surface salinity.

e. Ocean damping of land-driven atmospheric CO₂ variability

The power spectral densities (Pg C yr⁻¹)² cpy⁻¹ in the simulated global net land and ocean CO₂ fluxes are plotted in Fig. 14a versus the log of frequency (cpy). The spectral analysis utilizes monthly, deseasonalized anomalies where a mean seasonal climatology has been removed from the global time series of ΔF_land and ΔF_ocean. Figure 14b displays the spectrum for the total flux (land + ocean) but it is plotted in a variance-preserving form where the area under any frequency band is proportional to variance in that band (Emery and Thomson 1998). The spectral analysis illustrates several features: terrestrial variability dominates over ocean variability at all frequencies; the spectra are white on time scales beyond a few years and thus, most of the variance is concentrated at high frequencies (frequency >0.25 cpy; time scale <4 yr); and on a relative basis, the ocean has more variability than the land at low frequencies (frequency <0.1 cycles yr⁻¹; time scale >10 yr).

A cross-spectral analysis of the model global net ocean and land CO₂ fluxes is presented in Fig. 15. The first panel displays the squared coherence versus frequency; squared coherence varies from 0 (completely incoherent or uncorrelated at all phase lags) to 1 (fully coherent) and indicates the fraction of variance that can be accounted for between the two time series with a linear model. The average coherence of ΔF_land and ΔF_ocean on the subannual time scale is low, essentially indistinguishable from zero at the 95% confidence level. The global time series are strongly coherent on time scales of 2–100 yr, and the land CO₂ fluxes can explain 40%–90% of the variance in the ocean fluxes.

The mechanism and relationship between ΔF_land and ΔF_ocean vary with time scale. The second panel (Fig. 15b) displays the phase difference (in degrees) between ΔF_land and ΔF_ocean (solid line) and ΔF_ocean and atmospheric CO₂ inventory (circles) as a function of frequency. Assuming that the pairs of time series are coherent (Fig. 15a), a phase of 0° occurs when the time series are perfectly correlated (peaks matching peaks) and +/−180° when perfectly anticorrelated (peaks matching troughs). Negative phases mean the ocean lags either the land fluxes or atmosphere CO₂. On time scales of a few years (frequency 0.25–0.50 cycles yr⁻¹), the ocean and land fluxes are approximately in phase (∼+50°), with the ocean somewhat leading the land by a few months. Although the land and ocean CO₂ fluxes partially amplify each other with respect to their impacts on atmospheric CO₂, the two carbon reservoirs are only indirectly coupled via the biogeochemical responses to regional and global physical climate modes [ENSO, North Atlantic Oscillation (NAO), etc.; Wang and Schimel (2003)].

The small positive ocean–land phase difference in the model is somewhat counter to the expectation based on ENSO observations. During an El Niño, negative ocean CO₂ flux anomalies (reduced outgassing) arise in the equatorial Pacific a few months prior to the larger positive terrestrial flux anomalies (e.g., Jones et al. 2001). The along-equator upwelling-driven interannual variability in our model simulations is too small and the different land–ocean interannual variability phasing is governed by the ENSO response of the off-equator variability bands (salinity forcing) and model ENSO teleconnections on temperate ocean biogeochemistry variability.

On decadal and longer time scales, ΔF_land and ΔF_ocean are closer to being anticorrelated (Fig. 15b), and the land–ocean carbon coupling occurs more directly through variations in atmospheric CO₂. At a phase of +180°, the troughs in ocean CO₂ flux would exactly line up with the peaks in the land flux (and vice versa); since the land–ocean phase difference is ∼+150°, the ocean troughs somewhat lag the land peaks by ∼1 to 10 yr on decadal-to-centennial time scales, respectively. Correspondingly, the ocean troughs somewhat lead the atmospheric CO₂ peaks by a roughly similar amount of time. The strong land–ocean coherence (Fig. 15a) and phasing (Fig. 15b) suggest that global low-frequency carbon cycle variability originates on the land and then propagates into the atmosphere and ocean. For example, a CO₂ release from the terrestrial biosphere results in the growth of atmospheric CO₂ that in turn drives a net air–sea CO₂ flux into the ocean; the maximum ocean uptake occurs prior to the peak in atmospheric concentrations when the temporal gradient is largest (Fig. 16). The strength of this ocean damping of land-induced atmospheric CO₂ variability is about 20%–25% on multidecadal scales.

Direct comparison of the estimated multidecadal to centennial variability from CSM 1-carbon against contemporary observations is complicated by the limited temporal duration of data records (a few decades at most) together with the large impacts of anthropogenic activities on the carbon cycle (including fossil fuel emissions, land use, and climate change). For the preindustrial period, perhaps the best datasets with sufficient time resolution and global scale are atmospheric CO₂ time series from bubbles trapped in high-deposition ice cores [e.g., Law Dome (Etheridge et al. 1996), Taylor Dome (Indermühle et al. 1999), and Dronning Maud Land (Siegenthaler et al. 2005)]. The simulated peak to peak centennial-scale variability from CSM 1.4-carbon (∼5 ppmv CO₂) is comparable to that from ice core records (e.g., ∼6 ppmv CO₂; Siegenthaler et al. 2005), but the agreement may be misleading because of drift issues in the model simulations, the omission of external volcanic and solar climate–carbon perturbations (Gerber et al. 2003; Trudinger et al. 2005), and possible analytical errors in the ice record. The validation problem is even more challenging on decadal scales because of limited temporal resolution and low precision for the ice core data.