Over land, Eqs. (6) and (7) can be expanded to investigate, firstly, the contributions, from changes in live vegetation pools (ΔCV) and dead litter plus soil carbon pools (ΔCS) to the strength of the feedback parameters, since ΔCL=ΔCV+ΔCS. Secondly, Eq. (6) can be further decomposed to gain insight into the reasons for differences across models, in a manner similar to Hajima et al. (2014). 8βL≈ΔCL∗c′=ΔCV∗+ΔCS∗c′=ΔCV∗ΔNPP∗ΔNPP∗ΔGPP∗ΔGPP∗c′+ΔCS∗ΔRh∗ΔRh∗ΔLF∗ΔLF∗c′=τvegΔCUEΔΔGPP∗c′+τsoilΔΔRh∗ΔLF∗ΔLF∗c′9γL≈ΔCL′-ΔCL∗T′=ΔCV′-ΔCV∗T′+ΔCS′-ΔCS∗T′ The superscript ∗ in Eq. (8) implies that the terms are calculated here using the BGC version of the 1pctCO2 experiment. In Eq. (8), ΔNPP and ΔGPP represent the change in net primary productivity (NPP) and gross primary productivity (GPP), ΔLF the change in litterfall flux, and ΔRh the change in heterotrophic respiration, compared to the preindustrial control experiment. The multiplicative terms in Eq. (8) do indeed have physical meaning although they are based on change in the magnitude of quantities as opposed to their absolute magnitudes. We note here explicitly that as such, these terms cannot be compared directly to the terms which are based on absolute magnitudes.

The term ΔNPPΔGPP (fraction) is the fraction of GPP (above its preindustrial value) that is turned into NPP after autotrophic respiratory losses are taken into account. We use the term carbon use efficiency (CUE) but subscripted by Δ (CUEΔ) to represent ΔNPPΔGPP. The subscripted Δ allows CUEΔ to be differentiated from CUE as used in the existing literature (Choudhury, 2000), which represents the fraction of absolute GPP that is converted to NPP rather than its change over some time period, as well as the point that we consider globally integrated rather than locally derived quantities. Similarly, the term ΔCVΔNPP represents a measure of turnover or residence timescale of carbon in the vegetation pool (τvegΔ, years). The term ΔGPPc′ (PgC yr-1 ppm-1) is a measure of the strength of the globally integrated CO2 fertilization effect. However, in the models that dynamically simulate changes in vegetation cover, the effect of changes in vegetation coverage is implicitly included in this term. The term ΔCSΔRh is a measure of the average residence time of carbon in the dead litter and soil carbon pools (τsoilΔ, years). However, as with CUE, this quantity cannot be compared directly to the residence time of carbon in the litter plus soil carbon pool calculated using the absolute values of CS and Rh. Nor can it be compared to the changes in carbon residence time due to the “false priming effect” associated with the increase in NPP inputs, as [CO2] increases, into the dead carbon pools (Koven et al., 2015). ΔRhΔLF (fraction) is a measure of the increase in heterotrophic respiration per unit increase in litterfall rate, and ΔLFc′ (PgC yr-1 ppm-1) indicates the global increase in litterfall rate per unit increase in CO2, which in principle, should be close to the change in net primary productivity per unit increase in CO2, CUEΔΔGPPc′. A comparison of these terms across models can potentially yield insight into the reasons for large differences in land carbon uptake across models.

Assuming changes in the biological organic carbon inventory are small, the change in the ocean carbon inventory, ΔCO, is defined by an integral of the change in the dissolved inorganic carbon, ΔDIC, and density over the ocean volume: 10ΔCO=12gCmol-1∫VΔDICdV×10-15, where ΔCO is in petagrams of carbon; the ocean dissolved inorganic carbon, DIC, is in moles per cubic meter; the ocean volume V is in cubic meters; and the multiplier 10-15 converts grams to petagrams of carbon.

To gain insight into how the ocean carbon distribution is controlled, the ocean dissolved inorganic carbon, DIC, may be defined in terms of separate carbon pools (Ito and Follows, 2005; Williams and Follows, 2011; Lauderdale et al., 2013; Schwinger and Tjiputra, 2018): 11DIC=DICpreformed+DICregenerated=DICsat+DICdisequilib+DICregenerated, where the preformed carbon, DICpreformed, is the amount of carbon in a water parcel when in the mixed layer at the time of subduction and the regenerated carbon, DICregenerated, is the amount of dissolved inorganic carbon accumulated below the mixed layer due to the biological regeneration of organic carbon. The preformed carbon is affected by the carbonate chemistry and ocean physics. To gain further insight into how close the ocean is to an equilibrium with the atmosphere, the preformed carbon, DICpreformed, is further split into saturated, DICsat, and disequilibrium, DICdisequilib, components. The saturated component represents the concentration in surface water fully equilibrated with the contemporary atmospheric CO2 concentration. The disequilibrium component represents the extent that surface water is incompletely equilibrated before subduction, which is affected by the strength of the ocean circulation altering the residence time in the mixed layer and the ocean ventilation rate. Each of these components is affected by the increase in atmospheric CO2 and the changes in climate.

The change in the global ocean carbon inventory, ΔCO, relative to the preindustrial period may then be related to the global volume integral of the change in each of these DIC pools: 12ΔCO=ΔCpreformed+ΔCregenerated=ΔCsat+ΔCdisequilib+ΔCregenerated, where ΔCpreformed is the preformed carbon inventory, ΔCsat is the saturated carbon inventory, ΔCdisequilib is the disequilibrium carbon inventory, and ΔCregenerated is the regenerated carbon inventory.

The simplified expressions for carbon cycle feedback parameters in Eqs. (6) and (7) based on the air–sea flux changes to the ocean may then be approximated by the global ocean carbon inventory changes, which may be expressed in terms of these different global ocean carbon pools (Williams et al., 2019): 13βO≈ΔCO∗c′=ΔCpreformed∗c′+ΔCregenerated∗c′=ΔCsat∗c′+ΔCdisequilib∗c′+ΔCregenerated∗c′,14γO≈ΔCO′-ΔCO∗T′=ΔCpreformed′-ΔCpreformed∗T′+ΔCregenerated′-ΔCregenerated∗T′=ΔCsat′-ΔCsat∗T′+ΔCdisequilib′-ΔCdisequilib∗T′+ΔCregenerated′-ΔCregenerated∗T′. The anomalies for each of these carbon pools are calculated as 15ΔDICregenerated=-RCOΔAOU+12ΔAlk-ΔAlkpre-RNOΔAOU,16ΔDICsat=fpCO2atm,To,So,P,Si,Alkpret-fpCO2atm,To,So,P,Si,Alkpret=0,17ΔDICdisequilib=ΔDIC-ΔDICregenerated-ΔDICsat, where RCO and RNO are constant stoichiometric ratios, ΔAOU is the change in apparent oxygen utilization from its preindustrial value (where preformed oxygen is assumed to be approximately saturated with respect to atmospheric oxygen); ΔAlk is the change in alkalinity; To and So are the ocean temperature and salinity, respectively; P and Si are the phosphate and silicate concentrations; and ΔAlkpre is the change in preformed alkalinity (Ito and Follows, 2005; Williams and Follows, 2011; Appendix of Lauderdale et al., 2013). In Eq. (16), ΔDICsat is calculated using the partial pressure of CO2 in the atmosphere (pCO2atm) and preformed alkalinity as represented by the function f following the iterative solution for the ocean carbon system of Follows et al. (2006) and by considering the small contribution of minor species (borate, phosphate, silicate) to the preformed alkalinity, at time t, and the preindustrial values, at time t=0. In Eq. (16), the calculation uses the preformed alkalinity, the alkalinity at the time of water subduction, instead of the total instantaneous alkalinity to remove the effect of CaCO3 dissolution from the time the water parcel lost contact with the atmosphere. The preformed alkalinity is estimated from a multiple linear regression using salinity and the conservative tracer PO (PO=O2-Ro2:PP; Gruber et al., 1996), with the coefficients of this regression estimated based on the upper ocean (first 10 m) alkalinity, salinity, oxygen, and phosphate in each model. Our diagnostics of the ocean feedbacks and carbon pools depend primarily upon changes in DIC and upon the preformed and regenerated pools, relative to the preindustrial period, although differences in the preindustrial ocean in our suite of models do affect the saturated DIC changes relative to the preindustrial period by ∼5 % or less due to the nonlinearity of the carbonate chemistry.

Equations (8) and (9) in Sect. 2.1.1 are used to gain insight into reasons for differing responses of land models. In the BGC–COU approach and assuming T∗=0 (Eq. 8), the carbon uptake in the BGC simulation is used to calculate the carbon–concentration feedback parameter (βL). Figure 7 shows how this carbon uptake over land is separated into vegetation and soil + litter components both in absolute (panel a) and fractional (panel b) terms. Figure 7b shows that models vary widely in terms of how the carbon uptake over land is split into vegetation and soil + litter components. The model mean values indicate that slightly more of the carbon sequestered is allocated to vegetation (55 %) than to the soil + litter pools (45 %).

Figure 8 shows the individual components of Eq. (8) which contribute to terms corresponding to changes in vegetation (ΔCV) and soil + litter (ΔCS) carbon pools. Figure 7a is repeated in Fig. 8 for the easy matching of individual components of Eq. (8) with their corresponding models. The model mean values of individual terms do not take into account the results from the BCC-CSM2-MR model as explained in the figure caption. In essence, the terms in Fig. 8 are emergent properties of the land models of the individual ESMs and result from their multiple interacting processes. The comparison of the individual terms of Eq. (8) provides additional insight into the reasons for differences in land models. For example, the CNRM-ESM2-1 model has the highest land carbon uptake among all models in the BGC simulation. However, this is not caused by a strong CO2 fertilization effect (the ΔGPPc′ term) but rather by the relatively high τvegΔ and τsoilΔ values. The CO2 fertilization effect is strongest for the three models that simulate vegetation cover dynamically (NOAA-GFDL-ESM4, MPI-ESM1.2-LR, and UKESM1-0-LL) since the ΔGPPc′ term also implicitly includes the effect of increasing vegetation cover as CO2 increases. The tree cover in the NOAA-GFDL-ESM4 model, for example, increases in the BGC simulation – particularly in dry, high-latitude regions above 50∘ N (not shown). However, these models do not simulate the largest land carbon uptake because of their lower-than-average τvegΔ and τsoilΔ values. The ΔGPPc′ term is unable to capture the CO2 fertilization effect separately from increasing vegetation cover, and this illustrates the challenge in comparing models that do and do not simulate vegetation cover dynamically. The CanESM5 model exhibits higher-than-average land carbon uptake despite its near-average strength of the CO2 fertilization effect and τvegΔ and τsoilΔ values. However, its CUEΔ is the highest, and therefore a much larger fraction of GPP is converted to NPP. Although CUEΔ is not the same as CUE, we found that CUEΔ and CUE (calculated at the end of the 1pctCO2 simulation at 4×CO2) are strongly correlated with a correlation of around 0.90 (not shown). Similarly, τvegΔ is strongly correlated, with a correlation of 0.96, to τveg = CV / NPP calculated at the end of the simulation. The ACCESS-ESM1.5 model exhibits the lowest land carbon uptake because of its weak CO2 fertilization effect and the lowest CUEΔ of all models. Finally, the ΔRhΔLF term shows the least variability across models, which is reflective of the fact that the magnitude of the heterotrophic respiration flux is dominated by NPP inputs into the dead carbon pools (Koven et al., 2015). Several of these individual terms are strongly correlated. The ΔGPPc′ and ΔLFc′ terms have a correlation of 0.77, and CUEΔ ΔGPPc′ and ΔLFc′ have a correlation of 0.94, since a stronger CO2 fertilization effect also implies a larger litterfall flux per unit CO2. Surprisingly, CUEΔ and τvegΔ are negatively correlated (correlation = -0.49) across models, indicating that models which retain a higher fraction of GPP as NPP typically get rid of vegetation carbon sooner via litterfall as indicated by a faster turnover of vegetation (lower τvegΔ), thereby partially compensating for higher CUEΔ.

Figure 9 investigates the reasons for varying magnitudes of the carbon–climate feedback over land (γL). In Eq. (9), γL is a function of change in land carbon (divided into vegetation and soil + litter components) in the COU relative to the BGC simulation and the temperature change in the COU simulation (T′). Over land, the higher temperatures in the COU relative to the BGC simulation affect not only both autotrophic and heterotrophic respiratory fluxes, from live and dead vegetation pools, respectively, but also gross photosynthesis rates. The primary effect of this temperature change in COU versus the BGC simulation is the loss of carbon from the soil + litter carbon pool (hence the negative sign of γL for most models; Fig. 6b and d), but changes in the vegetation carbon pool also occur. Although γL also depends on T′, Fig. 9 arranges models in order from the largest to smallest loss of land carbon in COU relative to the BGC simulation to illustrate the varying response of the models. This ordering of models changes slightly if the carbon loss (or gain in the CanESM5 model) is divided by the temperature change T′ in the COU simulation (yielding the value of γL which assumes T∗=0 as in Eq. 9).

As shown in Fig. 9, all models lose carbon from the soil + litter carbon pool but with widely varying magnitudes. Although typically smaller than the change in the soil + litter carbon pool, the change in the vegetation carbon pool in the COU relative to the BGC simulation is not of the same sign across models. Of the 11 participating models, 6 lose carbon in the vegetation pool in the COU relative to the BGC simulation, thereby contributing to increasing the absolute magnitude of γL, while the remaining 5 exhibit an increase in the vegetation carbon pool, thereby decreasing the absolute magnitude of γL. The largest increase in the vegetation carbon pool is seen in the CanESM5 model that more than compensates for the carbon loss from the soil + litter carbon pool, yielding a positive value of γL in contrast to other models. This case is one of the few times a positive value of γL is seen in an Earth system model. Thornton et al. (2009) reported positive γL after their first attempt to include N cycle in the CLM. Preliminary analysis of CanESM5 data shows the increase in vegetation carbon in the COU relative to the BGC simulation is caused by the increase in GPP and the resulting vegetation growth at middle to high latitudes in response to warming temperatures and increasing CO2. Interestingly, this response is not seen at 2×CO2 (see Table A1 in the Appendix), and γL is still negative for CanESM5.

The loss in land carbon in the COU relative to the BGC simulation (except for the CanESM5 model that gains carbon), indicated by the dark orange bars in Fig. 9, is strongly correlated with the carbon gain in the BGC simulation (Fig. A1e; correlation is 0.59 for all models and 0.87 when CanESM5 is excluded) but not with the absolute amount of total land carbon. Figure A3 in the Appendix shows the absolute amount of carbon in soil + litter and vegetation pools, and their change from the beginning, for the BGC simulation. The models vary widely in terms of the absolute size of the carbon pools, especially for the soil + litter pool. There are two implications of models losing more carbon in the COU relative to the BGC simulation when they take up more carbon in the BGC simulation alone. First, the transient behaviour of a model is determined primarily by its response to CO2 and temperature perturbations and not by the absolute amount of land carbon. Second, carbon–concentration (βX) and carbon–climate (γX) feedback parameters must be correlated as well. Indeed, this is not only the case over land for both CMIP5 and CMIP6 models but also true for ocean feedbacks although the correlations are somewhat weaker over the ocean. These correlations are shown in Table 3 and are negative since higher positive values of βX are correlated with higher negative values of γX, indicating that models that take up more carbon with increasing CO2 also release more carbon when they “see” the associated higher temperatures.

The time-integrated air–sea flux of carbon provides the dominant contribution to the increase in global ocean carbon through changes in the DIC inventory. However, the global ocean carbon inventory is also affected by the land-to-ocean carbon flux from river runoff and the carbon burial in ocean sediments (see Table A2 in the Appendix).

Ocean carbon cycle feedbacks are defined in terms of ocean carbon inventory changes for the COU simulation and by the differences in COU relative to the BGC simulation. To fully understand the ocean carbon cycle feedbacks, it is necessary to understand the ocean carbon distributions for the preindustrial period and then analyze the carbon anomalies relative to the preindustrial period for these climate model experiments.

The ocean dissolved inorganic carbon, DIC, distribution is controlled by a combination of physical, chemical, and biological processes. For the preindustrial period, there is less DIC in the warmer waters of the upper ocean and more DIC in the colder mid-depth and bottom waters (Figs. 10a, 11a; illustrated here for UKESM1-0-LL as a representative example, and Figs. S1 to S7 show similar distributions for all the diagnosed Earth system models). The vertical extent of the low DIC follows the undulations of the thermocline, which is defined by strong vertical temperature and density gradients, and is deeper over the subtropical gyres at 30∘ N and 30∘ S and shallower in the equatorial zone and at high latitudes. The greater DIC at depth is a consequence of greater solubility in colder waters and the accumulation of DIC from the regeneration of organic matter.

To gain insight into how the ocean carbon distribution is controlled, the DIC is separated into three pools, DICsat, DICdisequilib, and DICregenerated, as defined earlier. The DIC distribution for both the preindustrial period and after 140 years in the 1pctCO2 simulation reveal the following key features for each of these carbon pools (Figs. 10a, b and 11a, b):

The saturated carbon pool provides the dominant contribution to the DIC, holding more than 2.15 mol C m-3, particularly within cooler waters below the thermocline.

Next we consider the anomalies in the DIC at year 140 in the COU configurations of the 1pctCO2 simulation calculated relative to the preindustrial period. The carbon anomaly, ΔDIC, in the COU configuration is positive over the upper thermocline over the Atlantic and Pacific basins, reaching +0.3 mol C m-3, coinciding with regions that are well ventilated. This gain in carbon is made up of an increase in the saturated carbon over all depths due to higher atmospheric CO2. There is a dipole in the disequilibrium anomaly (Figs. 10b, c and 11b, c); it is generally weakly positive in the upper ocean and more strongly negative in deeper waters below the thermocline reaching up to -0.2 mol C m-3. This negative disequilibrium anomaly in deeper waters is smallest in the relatively well-ventilated mid-depth waters of the North Atlantic but extends over nearly all of the more poorly ventilated mid-depth waters of the Pacific (Figs. 10b and 11b).

The regenerated carbon anomaly is relatively small in magnitude, reaching less than 0.05 mol C m-3, and varies regionally, enhanced within much of the North Atlantic and the thermocline of the Pacific but with little change in the deep waters of the Pacific (Figs. 10b and 11b). The increase in regenerated carbon is due to a weakening of ocean overturning leading to an increase in residence time and an associated accumulation of DIC from the regeneration of biologically cycled carbon (Bernardello et al., 2014; Schwinger et al., 2014). The regenerated carbon signal does not change in the mid-depths and deep Pacific as 140 years is too short an integration timescale for any effect to be detected.

To diagnose the carbon cycle feedback parameters, the ocean carbon response needs to be considered for the BGC configuration where there is only limited warming from the increase in atmospheric CO2 and therefore limited change in climate and ocean circulation. The resulting DIC anomalies are generally very similar to those for the COU configuration (Figs. 10b, c and 11b, c), which is to be expected as the dominant effect for the ocean carbon response is the enhanced ocean uptake of carbon in response to the increase in [CO2]. There is a weakening in ventilation in the COU configuration due to the additional radiative forcing. In comparison, in the BGC configuration, there is no change in the circulation as there is no radiative warming effect, so there is slightly more carbon uptake in the northern North Atlantic, such as revealed at around 50∘ N, compared with the COU configuration. For the BGC configuration, the saturated carbon pool is slightly greater at depth due to the water masses being cooler than in the COU configuration, the disequilibrium anomaly shows a less negative anomaly in the northern North Atlantic because there is little or no change in ventilation, and there are only slight differences in the regenerated pool.

The climate response to rising [CO2] is now considered in terms of the difference in the COU and BGC configurations, which includes the combined effects of warming and circulation changes (Figs. 10d and 11d). The surface warming drives a decrease in solubility, an increase in stratification, and a reduction in ventilation, which leads to an overall decrease in carbon uptake over the Southern Ocean and Pacific basins and much of the Atlantic basin. There is a decrease in the saturated carbon pool associated with the warming acting to inhibit carbon uptake. The regenerated carbon anomaly is enhanced in the deep northern North Atlantic and in the Southern Ocean. The regenerated carbon anomaly for this climate response is very similar to that for the COU configuration, suggesting that the regenerated carbon anomaly is mainly due to circulation changes: the gain in the regenerated carbon anomaly is consistent with the expected longer residence time from weaker overturning and ventilation. There is a more negative disequilibrium anomaly in the deep waters of the North Atlantic, which is a consequence of weaker ventilation.

To gain more insight into the disequilibrium response, the ocean DIC response is also considered for the radiatively coupled integration (RAD), where the ocean biogeochemistry does not see the increase in [CO2]. The warming in the RAD simulation leads to a weakening in the overturning, which enhances the residence time in the surface waters and so generally decreases the magnitude of the disequilibrium anomaly in the North Atlantic (Fig. S8), making the disequilibrium less negative relative to the preindustrial period and so forming a positive disequilibrium anomaly at year 140. In comparison the COU–BGC approach captures the effect of the warming under rising [CO2], leading to the disequilibrium anomaly instead becoming more negative at depth, since the weakening in the ventilation leads to more of the anthropogenic carbon remaining at the surface rather than being transferred into the deeper ocean (Schwinger et al., 2014).

The ocean carbon–concentration feedback parameter, βO, is diagnosed from the changes in the ocean carbon inventories for the BGC configuration, which does not include radiative warming due to increasing [CO2] (Eq. 13). There is a consistent increase in ocean carbon storage across all models with a model mean value of around 670 PgC (Fig. 12, turquoise bars). This increase in ocean carbon storage is made up of an increase in the saturated carbon inventory, ΔCsat, by about 3100 PgC from the increase in [CO2] (Fig. 12, red bars). This increase is partly offset by a more negative disequilibrium carbon, ΔCdisequilib, of typically -2500 PgC (Fig. 12, blue bars), representing how the ocean carbon uptake cannot keep up with the rate of [CO2] increase. There is relatively little change in the regenerated carbon inventory, ΔCregenerated. The resulting βO is positive and mainly explained by the chemical response involving the rise in ocean saturation with no significant biological changes, although the physical uptake of carbon within the ocean is unable to keep pace with the rise in [CO2].

The ocean carbon–climate feedback parameter, γO, is diagnosed from the difference between the COU model configuration and the BGC configuration and so includes the effect of an increasing surface warming under rising [CO2] (Eq. 14). There is a broadly consistent response across models, with a model mean decrease in carbon inventory of around 80 PgC due to the additional warming in the COU configuration relative to the BGC configuration (Fig. 13, turquoise bars). The effect of this additional warming and the associated climate change leads to a decrease in both the saturated carbon and disequilibrium carbon of typically -60 and -70 PgC (Fig. 13, orange and blue bars), representing the decrease in solubility and decreased ocean ventilation. There is an increase in the regenerated carbon of typically 50 PgC (Fig. 13, green bars), which is due to a weaker circulation leading to a longer residence time of thermocline and deep waters, so there is more time for the accumulation of regenerated carbon below the mixed layer. The resulting γO is negative, indicating that the ocean takes up less carbon in response to the combination of surface warming and a weakening in ocean ventilation. This response involves a combination of chemical, physical, and biological changes where the warming reduces the solubility of the carbon in the ocean and a weakening in the circulation decreases the disequilibrium pool but lengthens the residence time and so increases the regenerated pool.

Overall, the ocean carbon inventory increases in the BGC configuration by 666 ± 53 PgC (model mean ± standard deviation) and decreases in COU relative to BGC by -80 ± 15 PgC. The resulting βO is very similar across all the models (0.78 ± 0.06 PgC ppm-1), reflecting not only the strong control of carbonate chemistry by rising atmospheric CO2 (Katavouta et al., 2018) but also the use of similar carbonate chemistry schemes and bulk parameterizations of air–sea CO2 fluxes across marine biogeochemical models (Séférian et al., 2020). The dominant contributions are composed of a positive contribution from the saturated carbon (3.66 ± 0.16 PgC ppm-1) and a negative contribution from the disequilibrium carbon (-2.98 ±  0.16 PgC ppm-1; see Table A3 in the Appendix); these intermodel differences are relatively small with ratios of the standard deviation to model mean of only 0.05 and 0.06, respectively. The regenerated contribution is over 2 orders of magnitude smaller than the sum of the saturated and disequilibrium contributions and so may be neglected for evaluating βO.

The values of γO differ more strongly across the models (-16.95 ± 5.62 PgC ∘C-1) and arise from differences in the extent of the surface warming and the dynamical changes in the ocean circulation and resulting changes in ventilation, residence time, and biological regeneration (Table A3). The contributions to γO include negative contributions from the saturated (-12.78 ± 2.50 PgC ∘C-1) and disequilibrium (-16.36 ± 5.31 PgC ∘C-1) components, which are partly opposed by a positive contribution from the regenerated component (12.25 ± 8.53 PgC ∘C-1). The largest intermodel differences are in the regenerated and disequilibrium responses and a relatively small spread in the saturated response, with the ratios of the standard deviation to the model mean being 0.70, 0.33, and 0.20, respectively (Table A3).