Cenozoic carbon fluxes associated with rock weathering, sediment burial, and volcanic degassing are calculated from the mass balance equations coupling marine isotopic records of carbon (both organic and inorganic), strontium, and osmium. The result is confirmed by the good match between modeled carbonate sedimentation rates and carbonate sedimentation rates previously integrated from ocean basins worldwide. The coevolution between weathering and burial of carbonate suggests that marine carbonate accumulation was regulated mainly by the recycling of carbonate rocks, which mediated the bicarbonate ion concentration of the oceans. A reduction in CO2 effusion to the atmosphere caused by reduced volcanic degassing from 52 to 15 Ma and tectonically enhanced organic rock exhumation since 15 Ma is also observed. These changes in CO2 effusion are balanced by concomitant changes in CO2 sequestration by silicate weathering and organic carbon burial. Importantly, we demonstrate a clear decoupling of modeled silicate weathering rates from global climate over the last ∼15 Ma. This observation is inconsistent with temperature-mediated mineral dissolution acting as the key mechanism facilitating the CO2 silicate weathering feedback process. However, we instead observe a clear coupling (positive correlation) between modeled silicate weathering, organic carbon burial, and atmospheric CO2 concentration. We suggest that CO2 fertilization effects on terrestrial biomass productivity and plant weathering could have represented a major negative feedback process helping to balance atmospheric CO2, at least during the Cenozoic ice house periods.
 The intensive interest in present-day greenhouse gas induced global climate change has renewed efforts to understand the mechanisms that modulate the concentration of atmospheric carbon dioxide (pCO2) in the geological past [e.g., Berner and Kothavala, 2001; Wallmann, 2004]. Over long timescales (i.e., >106 years), pCO2 is generally considered to be regulated by variations in rock weathering, sediment burial and volcanic/metamorphic degassing [e.g., Berner et al., 1983]. Through the Cenozoic Era, the well-known long-term decrease in pCO2 (and subsequent cooling) is thought to be the result of a global decrease in volcanic degassing coupled with both tectonically enhanced increases in silicate weathering and elevated organic carbon burial [France-Lanord and Derry, 1997; Raymo et al., 1988; Raymo and Ruddiman, 1992; Wallmann, 2001]. Changes in Cenozoic pCO2 have been documented by both proxy data [Pagani et al., 1999, 2005; Pearson and Palmer, 1999, 2000] and box modeling [Wallmann, 2001]. However, there is still disagreement as to the most significant processes that control its evolution, largely because of the lack of constraints on the ancient carbon cycle.
 Marine isotopic records of carbon and strontium provide valuable archives for ancient carbon cycle processes because carbon fluxes derived from different reservoirs are characterized by distinct δ13C values, and because the processes that control the long-term carbon cycle are also the major modulating factors that control marine strontium isotope evolution [e.g., Francois and Goddéris, 1998]. Nevertheless, ambiguities exist in the precise way in which changes in the above proxies are interpreted. For example, secular variations in marine strontium isotopic composition can be caused either by changes in the relative proportion of strontium fluxes from silicate weathering, carbonate weathering and hydrothermal inputs, or by shifts in 87Sr/86Sr of individual fluxes [e.g., Hodell et al., 1989; Li et al., 2007]. Assumptions, such as prescribing constant hydrothermal inputs or constant 87Sr/86Sr, are frequently employed for box models which use carbon and strontium isotopes. This has the obvious drawback of potentially misrepresenting key model components and increasing uncertainties in reconstructed carbon cycle processes.
 By using a combination of isotopes with different sources to the oceans and different behaviors in the carbon cycle, it is possible to reduce the uncertainties associated with the calculation of ancient carbon fluxes [Burton, 2006; Wallmann, 2004]. In this work, an inverse model has been developed on the basis of marine isotopic records of inorganic and organic carbon, strontium and osmium. Our model enables the calculation of carbon fluxes associated with silicate weathering, exhumation of carbonate and organic-rich rocks, organic and inorganic carbon burial, and volcanic degassing. The factors that control the long-term evolution of the Cenozoic carbon cycle and pCO2 are then discussed on the basis of our results.
2. Model Description
 Two approaches are frequently adopted to model the long-term evolution of the carbon cycle. One method is to model certain prescribed physical and chemical processes and then use the model to calculate corresponding isotopic signals. The veracity of the various model components can thus be evaluated by comparing the generated isotopic signals to those obtained from the geological record [e.g., Bergman et al., 2004]. In such a model, feedback processes must be prescribed. For this study, our aim is to specifically elucidate the nature of the major feedback processes that control the evolution of the Cenozoic carbon cycle, and for this reason we have adopted an inverse approach to create a model that uses existing isotopic signals to reconstruct the rates of various carbon cycle processes [e.g., Francois and Goddéris, 1998]. The modeled results can then be compared with independent proxy records of parameters such as seawater palaeotemperature and pCO2 which enable discussion of the likely main feedback processes. As with the GEOCARB type models, our approach assumes that the carbon in the atmosphere-ocean system is in steady state [e.g., Berner et al., 1983]. The relative strength of the five main carbon cycle fluxes of silicate weathering, carbonate and organic-rich rock weathering, organic and inorganic carbon burial, and volcanic degassing are solved from a set of simultaneous equations that couple the cycles and marine isotopic records of carbon, strontium and osmium. Neither pCO2 nor temperature are resolved, nor are any feedback processes involving these.
2.1. Carbon Cycle
 As mentioned earlier, the long-term evolution of the carbon cycle is mainly controlled by the processes of silicate weathering, carbonate sedimentation and dissolution, burial and oxidation of organic carbon, and volcanic CO2 degassing [e.g., Berner et al., 1983; Wallmann, 2001]. Atmospheric carbon dioxide is primarily released from volcanic degassing, carbonate sedimentation and oxidation of organic rocks, whilst its consumption is mainly facilitated by rock weathering and organic carbon burial. Volcanic degassing and weathering of carbonate and organic-rich rocks supply carbon to the exospheric (ocean-atmosphere) system, while burial of carbonate and organic matter remove carbon from it. In this work, we use “C,” labeled by corresponding subscripts, to represent the late Pleistocene volumes of carbon or carbon dioxide associated with these processes (1) Csiliw and Cbasw = CO2 sequestered by silicate and basalt weathering (CaSiO3 + 2CO2 + 3H2O → Ca2+ + 2HCO32− + H4SiO4); (2) Ccarbw and Ccarbb = releasing and sequestration of C and CO2 by weathering and burial of carbonate (CaCO3 + CO2 + H2O ↔ Ca2+ + 2HCO32−); (3) Corgw and Corgb = releasing and sequestration of C and CO2 by weathering and burial of organic carbon (CO2 + H2O ↔ CH2O + O2); (4) Cm/a = CO2 degassing from midocean ridges and subduction arcs; (5) Cplume = CO2 degassing from plumes related volcanoes; and (6) Calter = carbon removal by oceanic crust alteration (CaSiO3 + Ca2+ + 2HCO32− + H2O → 2CaCO3 + H4SiO4).
 Because of the short residence time of carbon in the ocean-atmosphere system, the sinks and sources of carbon and carbon dioxide should be in balance on million-year timescales [Berner and Caldeira, 1997]. The mass balance of CO2 in the ocean-atmosphere system at equilibrium can thus be expressed as
where ksiliw, kc/o, kcarbb, korgb and km/a are normalized fluxes relative to late Pleistocene values for silicate weathering, carbonate and organic-rich rock weathering, carbonate sedimentation, organic carbon burial, and volcanic CO2 degassing from midocean ridges and arcs respectively (Table 1). The left part of the equation represent sinks of atmospheric CO2 by silicate weathering (ksiliwCsiliw), carbonate weathering (kc/oCcarbw), organic carbon burial (korgbCorgb), and weathering of island basalt (km/aCbasw), while the terms in the right part correspond to CO2 sources from organic carbon weathering (kc/oCorgw), carbonate burial (kcarbbCcarbb), degassing at midocean ridges and volcanoes in subduction arcs (km/aCm/a), and plume degassing (Cplume). Fluxes of carbonate weathering (kc/oCcarbw) and organic carbon weathering (kc/oCorgw) are treated in proportion, since on a large-scale carbonate and organic-rich rocks are interbedded in typical marine sedimentary systems, and their weathering fluxes are thus expected to be controlled by the exposure of sedimentary cover [Derry and France-Lanord, 1996]. Also, the volcanic CO2 degassing from midocean ridges and arcs (km/aCm/a) is assumed to be proportional to island basalt weathering (km/aCbasw) since all of them are thought to be regulated by the spreading rate of midocean ridges [Berner and Kothavala, 2001; Wallmann, 2001].
 The equilibrium of total carbon in the ocean-atmosphere system can be described by the following expression:
where the left part contains sources of carbon from carbonate weathering (kc/oCcarbw), organic carbon oxidation (kc/oCorgw), degassing at midocean ridges and subduction arcs (km/aCm/a), and plume outgassing (Cplume). The right part of the equation shows the carbon sinks of carbonate burial (kcarbbCcarbb), organic carbon burial (korgbCorgb), and alteration of ocean crust (km/aCalter). Alternation of ocean crust (km/aCalter) is assumed to be proportional to volcanic CO2 degassing from midocean ridges and arcs (km/aCm/a) and island basalt weathering (km/aCbasw) because of their assumed control by spreading rates of midocean ridges [Berner and Kothavala, 2001; Wallmann, 2001].
 The carbon isotopic mass balance associated with equation (2) can be expressed as
where δ13C with corresponding subscripts is carbon isotopic composition of the carbon fluxes. The carbon isotopic compositions of all types of CO2 degassing (δ13Cvolc) are assumed to be equal to the mantle value (−5‰) (Table 1). However, the δ13C of CO2 released from arcs may be offset by the changing proportion of mantle-sourced CO2 involved in arc volcanism, the isotopic compositions of subducted carbonate and organic carbon, and the amount and proportion of carbonate and organic matter submitted to decomposition in subduction zones [Nishio et al., 1998]. The possible influence of this on model result is tested in the discussion section. The δ13C of carbonate precipitated as a product of oceanic crust alteration (δ13Calter) is assumed to be the same as that of biogenic carbonate (δ13Ccarbb) since the carbon isotopic fractionation between seawater and carbonate is small and not particularly temperature sensitive (Table 1).
2.2. Strontium and Osmium Cycle
 The main inputs of strontium and osmium to the oceans are related to continental silicate weathering, weathering of carbonate and organic-rich rocks, diagenetic products of marine sediments, hydrothermal activity, and cosmic flux [Cohen, 2004; Palmer and Edmond, 1989; Peucker-Ehrenbrink and Ravizza, 2000]. As different sources have distinct isotopic values, relative changes of these inputs ought to be reflected by marine strontium and osmium isotopic records based on the following two mass balance equations:
where Sr and Os are late Pleistocene fluxes of strontium and osmium to the oceans associated with different processes labeled by corresponding subscripts, while SrR and OsR represent the 87Sr/86Sr and 187Os/188Os ratio of these fluxes (listed in Table 1). Equation (4) is a transient state solution to the isotopic mass balance equation of marine strontium after Brass  and Hodell et al. , in which Nocean is the amount of strontium in seawater and dSrRocean/dt describes the rate of change of SrRocean. Equation (5) describes the isotopic mass balance of marine osmium, in which the osmium isotopic composition of seawater is equal to the weighted 187Os/188Os ratio of all osmium influxes to the oceans [Cohen, 2004; Peucker-Ehrenbrink and Ravizza, 2000].
3. Data and Parameters
 The relative fluxes of silicate weathering (ksiliw), carbonate and organic carbon weathering (kc/o), carbonate deposition (kcarbb), organic carbon burial (korgb), and volcanic degassing (km/a), can be calculated from the combination of equations (1)–(5) when the other parameters in the equations are known. Most of the parameters, especially those associated with the intensively researched global carbon cycle, and the relevant marine isotopic records required in equations (1)–(5) can be taken directly from the literature with little or no treatment (Table 1 and Figure 1). Strontium isotopic curve (87Sr/86Srocean) is from the updated LOWESS database of McArthur et al. . δ13C data of marine carbonate (δ13Ccarbb) and organic carbon (δ13Corgb) is from Falkowski et al. , and the osmium isotopes of seawater (187Os/188Osocean) are from Burton . Some parameters, such as the proportion of riverine osmium fluxes contributed by silicate weathering and sedimentary rocks, need to be empirically derived because they are poorly constrained because of a lack of adequate investigation or because they are dependent parameters which, to reduce model uncertainties and to facilitate sensitivity analyses, need to be calculated from other independent parameters by equations (1)–(5) under the late Pleistocene condition of k = 1.
3.1. Parameters Related to Carbon Cycle
 The late Pleistocene release of carbon dioxide from the oxidation of organic matter in sedimentary rocks (Corgw) is calculated from the carbonate weathering flux (Ccarbw) using the method of Derry and France-Lanord , under the assumption made earlier that carbonate weathering and organic carbon oxidation can be treated as being in proportion because of the large-scale coexistence of carbonate and organic rocks in typical sedimentary cover, hence
where Xorg is average proportion of organic carbon in total sedimentary carbon; δ13Ccarbw is the average carbon isotopic composition of sedimentary carbonate; δ13Cvolc is the mean δ13C value of our planet, and Δc–o is the mean carbon isotopic difference between organic matter and carbonate in marine sediments. Using the parameters listed in Table 1, a value of 3.6 × 1012 mol/a can be calculated for Corgw, which is identical to the recent estimates of 3.58 × 1012 mol/a on the basis of the global distribution of fossil organic carbon stored in the first meter of sedimentary rocks [Copard et al., 2007].
 The late Pleistocene fluxes of carbonate deposition (Ccarbb), organic carbon burial (Corgb), and volcanic CO2 degassing (Cm/a + Cplume) are calculated from equations (1)–(3) when k = 1. We note here that the resultant calculated value for total volcanic CO2 degassing of 9.0 × 1012 mol/a is very close to the value ascertained from the recent assessment of carbon degassing from the lithosphere [Mörner and Etiope, 2002]. Since degassing from midocean ridges and arcs (Cm/a) release about 4.7 × 1012 mol CO2 per year at present [Marty and Tolstikhin, 1998], other volcanic CO2 sources, mainly plume related (Cplume), contribute the remaining CO2 degassing of about 4.3 × 1012 mol/a.
3.2. Parameters Related to Strontium Cycle
 Present-day continental weathering contributes a yearly strontium flux (Srw) of about 3.4 × 1010 mol to the oceans [Davis et al., 2003], of which about 31% originates from silicate weathering [Gaillardet et al., 1999]. Thus, the late Pleistocene strontium flux from silicate weathering (Srsiliw) and carbonate weathering (Srcarbw) are 1.1 × 1010 mol/a and 2.3 × 1010 mol/a, respectively. The average 87Sr/86Sr ratio of the carbonate weathering flux (SrRcarbw) is inferred from the strontium isotope curve of marine carbonate [McArthur et al., 2001] using the method employed by Derry and France-Lanord  for the calculation of average sedimentary carbonate δ13C, giving a value of 0.7077. A 87Sr/86Sr ratio of 0.7203 for silicate weathering (SrRsiliw) can then be calculated from the isotopic mass balance of the silicate carbonate mixing model for strontium weathering flux when using an average riverine 87Sr/86Sr ratio (SrRw) of 0.7116 [Davis et al., 2003]. The late Pleistocene hydrothermal strontium flux (Srhy) is calculated from equation (4) under the late Pleistocene condition of k = 1 (Table 1).
3.3. Parameters Related to Osmium Cycle
 At present, osmium weathering budgets are poorly constrained. Nevertheless, a good correlation between SO4−2/Si and Os/Si ratios for large rivers worldwide can be observed on the basis of data compilations from Gaillardet et al.  and Levasseur et al.  (Figure 2). This would suggest the dominant control of sediment weathering on continental osmium flux, since the SO4−2 ion in rivers is derived mainly from weathering of sedimentary rocks, while dissolved silicon is derived mainly from silicate weathering [Gaillardet et al., 1999; Meybeck, 2003]. The slope of the SO4−2/Si-Os/Si correlation indicates the Os/SO4−2 ratio of the sediment weathering flux (ROs-S), while the intercept of the correlation gives the Os/Si ratio of silicate weathering (ROs-Si) (Figure 2). Thus, the contribution from sediment weathering to continental osmium flux (Osc/o) can be calculated by multiplying ROs-S to the riverine SO4−2 flux (Sc/o) giving a value of 1119 mol/a. Similarly, an osmium flux of 553 mol/a derived from silicate weathering (Ossiliw) can be inferred by multiplying ROs-Si to the riverine silicon flux (Sisiliw). The total riverine osmium flux deduced in this work is thus 1672 mol/a. This value is is consistent (within error) with the directly calculated value of 1569 mol/a established from the world's large rivers [Levasseur et al., 1999].
 The average osmium isotopic composition of eolian loess deposits [Peucker-Ehrenbrink and Jahn, 2001] is used here as the mean 187Os/188Os ratio of the continental silicate weathering flux (OsRsiliw = 1.05, Table 1), since loess is assumed to be representative of the exposed upper continental crust [Taylor et al., 1983]. Using the same binary mixing model described earlier for the riverine strontium budget, it is thus simple to calculate a 187Os/188Os ratio of 1.78 for sediment (i.e., carbonate and organic-rich rock) weathering (OsRc/o) using an average riverine 187Os/188Os value (OsRw) of 1.54 [Levasseur et al., 1999].
 A 928 mol/a hydrothermal and cosmic osmium input flux (Oshy + Oscos) is calculated from equation (5) under a late Pleistocene condition where k = 1. Hydrothermal flux (Oshy) contributes about 86% (fhy) to (Oshy + Oscos), with cosmic input (Oscos) contributing the remaining 14% [Levasseur et al., 1999].
 On the basis of the independent equations (1)–(5) described above, the relative intensities of continental silicate weathering (ksiliw), carbonate/organic carbon weathering (kc/o), carbonate sedimentation (kcarbb), organic carbon burial (korgb), and volcanic CO2 degassing (kvolc), can be calculated using the parameters listed in Table 1 and the isotopic curves displayed in Figure 1. The results are illustrated in Figure 3, in which kvolc is relative flux of total CO2 degassing including those released from midocean ridges and arcs (Cm/a), and from other volcanic sources (Cplume) such as plumes. In the model, Cm/a is treated in proportion to km/a, while Cplume kept as constant. Thus, kvolc is equal to (km/aCm/a + Cplume)/(Cm/a + Cplume).
 As the isotopic records that has already been used in the calculation run are not applicable for model testing, here we can help validate our model results by comparing our reconstructed carbonate sedimentation rate against the geological record (Figure 3a). The reconstructed carbonate sedimentation rate matches very well with values previously integrated from worldwide ocean basins [Opdyke and Wilkinson, 1988], especially for the Neogene portion (Figure 3a). This result is encouraging and also lends support to the veracity of other fluxes calculated from the same sets of simultaneous equations. Disagreements between the detailed structure of both data sets likely originate from errors associated with both the model and the methodology employed by Opdyke and Wilkinson .
 Consistent, large-scale shifts are readily observable in all the derived carbon cycle parameters (Figure 3). In particular, all carbon fluxes show decreases during the Paleocene (65–56 Ma), and rapidly recover during the early Eocene (56–52 Ma). Carbonate and organic-rich rock weathering and carbonate sedimentation are characterized by near-constant or slow increases from 52 to 15 Ma and show a rapid increase over the last 15 Ma. Volcanic degassing, silicate weathering, and organic carbon burial all show a clear decrease from 52 to 15 Ma. Over the last 15 Ma, volcanic degassing stays relatively constant whereas silicate weathering and organic carbon burial both show an increase.
5. Error Control and Sensitivity Analysis
 The uncertainties of our model results can be estimated by employing traditional methods of error propagation. The whole process of model calculation can be expressed in the form
where kit is relative intensity of flux i at time t; fit represents the whole calculation process at time t; xnt is the primary parameter n (n = 1, 2, …, 28) used in the calculation (Table 1) (and is time dependent for marine isotope records). The accumulative uncertainties associated with the calculation can be calculated as following:
where σit and σnt are the standard deviations of kit and xnt, respectively. Using the proposed σnt values for the primary parameters listed in Table 1, the time-dependent standard deviations of the modeled results, σit, can be estimated from equation (9). These are displayed as shaded areas on the modeled curves in Figure 3. As is clear from Figure 3, model errors are generally small over the past 15 Ma, but become larger as age increases. Nevertheless, our calculated errors are still small enough not to obscure the evolutionary trends derived from our model for the Cenozoic carbon cycle.
 The sensitivity of the relative flux ki on the accuracy of parameter n, Γin, can be estimated from the average contribution of σnt to the square of σit
The results are illustrated in Figure 4. This analysis demonstrates that the model results are mostly sensitive to uncertainties in present-day CO2 outgassing (Cm/a) and riverine 187Os/188Os ratio (OsRw). Other parameter uncertainties, such as possible changes in global average riverine 87Sr/86Sr value caused by relative 87Sr/86Sr changes of weathered rock [Brass, 1976], or variability in temperature-controlled global weathering kinetics [Li et al., 2007], may be not significant on the basis of the calculated sensitivities.
 One might suspect that the release of CO2 into the atmosphere caused by metamorphism of carbonate rocks and decomposition of organic matter in collision zones may affect the carbon isotopic composition of arc-soured CO2 (δ13Carc), which is assumed to be constant in the model's standard run, i.e., δ13Carc = δ13Cvolc = −5.0‰. As alluded to earlier, a global offset in δ13Carc caused by carbonate metamorphism and organic matter decomposition could depend on the proportion of mantle-sourced CO2 involved in arc volcanism, the isotopic compositions of subducted carbonate and organic carbon, and the amount and relative proportion of carbonate and organic matter subjected to decomposition in subduction zones. Generally, organic matter is preferentially decomposed while considerable amounts of carbonate can survive subduction zone and be transported into the mantle [Nishio et al., 1998]. Nevertheless, the influence of δ13Carc offsets on our model results is tested in two scenarios (Figure 3), with δ13Carc positively biased by 3‰ under preferential carbonate metamorphism and with δ13Carc negatively offset by 3‰ under preferential organic decomposition. A positive δ13Carc offset causes both a positive shift of the model results and an increased amplitude in the variability of the parameters, while a negative δ13Carc offset generates a negative shift in the model results but with reduced variability in amplitude (Figure 3). No changes in parameter trends are introduced in these model runs, and the shifts caused are typically within the error of the standard run in any case. Thus, the possible influence of δ13Carc offsets on model results can be neglected in our ensuing discussion on the evolutionary trends of the Cenozoic carbon cycle.
 Another possible influence on model results is the changing strontium isotopic ratio of silicate or carbonate weathering caused by increasing inputs of Tibetan rivers over the past 40 Ma due to uplift of the Tibetan plateau. These riverine fluxes are characterized by having extremely radiogenic strontium isotopic compositions [Galy et al., 1999]. Recent compilations of the eleven major upper streams leading out from Tibetan Plateau show that the Tibetan rivers have radiogenic 87Sr/86Sr ratios of about 0.71448 and a yearly strontium flux of 3.18 × 109 mol (W. Wu et al., Contribution of weathering of the Himalaya and Qinghai-Tibet Plateau to evolution of 87Sr/86Sr in oceans, submitted to Science China Series D, 2009). About 30% of this flux is derived from silicate weathering and the rest from carbonate dissolution [Wu et al., 2008; Wu et al., submitted manuscript, 2009]. The influence of Tibetan rivers on model results is tested by assuming that their contribution to global strontium weathering flux increased from zero to the present condition in a linear fashion since 40 Ma. To investigate this further, two specific scenarios are tested (Figure 3f). The first scenario assumes that carbonate weathering is totally responsible for the high 87Sr/86Sr ratio of Tibetan rivers, thus the global mean 87Sr/86Sr ratio of carbonate weathering (SrRcarbw) will increase from 0.7077 to 0.7081 over the last 40 Ma. The second scenario assumes that silicate weathering is responsible for the high 87Sr/86Sr ratio of Tibetan rivers, thus the global mean 87Sr/86Sr ratio of silicate weathering (SrRsiliw) will be reduced from 0.7203 to 0.7193 without contribution of Tibetan rivers before 40 Ma. Both the scenarios have similar effects on model results in the form of reduced carbon fluxes (Figures 3a–3e). Nevertheless, the offsets created by these modeled curves are still within the error of the standard run, and the shapes are unchanged (Figures 3a–3e). In conclusion, we suggest that the influence of Tibetan riverine 87Sr/86Sr changes would be minor.
6.1. Tectonic Controls on the Cenozoic Carbon Cycle
 The long-term evolution of the Cenozoic carbon cycle is clearly influenced by tectonic changes (Figure 3). For instance, as postulated previously, the decrease in volcanic CO2 degassing we can demonstrate between 52 and 15 Ma is probably caused by a decrease in the spreading rate of midocean ridges and a consequent decline in the subduction rates of convergent margins after the India-Asian collision [Gaina et al., 2007; Klootwijk et al., 1992]. India-Asian collision and subsequent mountain uplift and exhumation of sedimentary cover [England and Molnar, 1990] can also explain the gradual increase in weathering rates of carbonate and organic rocks since 55 Ma. The accelerated rise in sedimentary weathering over the past 15 Ma is coincident with the most intensive period of Tibetan uplift during the Neogene [Tapponnier et al., 2001; Zhao and Morgan, 1985]. The clear coevolution of carbonate burial and sedimentary weathering also points to a fundamental control on carbonate burial via the regulation of bicarbonate/calcium ion flux to the oceans derived from carbonate weathering.
 Weakened volcanic CO2 degassing between 52 and 15 Ma and increased organic-rich rock weathering over the past 15 Ma are mostly balanced by concomitant changes in silicate weathering and are partly reconciled by variations in organic carbon burial (Figure 3). The contribution of silicate weathering to the balance is more important than organic carbon burial since the variation of carbon flux associated with silicate weathering is much larger than that of organic carbon burial. The coupled evolution of silicate weathering, organic carbon burial and atmospheric carbon dioxide concentration can be clearly observed, with enhanced silicate weathering and organic burial always accompanied by high pCO2 (Figure 5). The pCO2 record cited here is based on plankton carbon isotope fractionation measurements on alkenones [Pagani et al., 1999, 2005]. The data show that pCO2 decreases rapidly between during ∼35 and ∼15 Ma, and show a slight increase over the past 15 Ma (Figure 5). This pattern is consistent with other pCO2 proxies such as those derived from paleosols, stomatal index and boron isotope [Royer, 2006].
 The well defined increase in both silicate weathering and organic carbon burial over the last 15 Ma is coincident with the period of rapid Tibetan uplift [Tapponnier et al., 2001; Zhao and Morgan, 1985]. However, the possible direct control of uplift on silicate weathering and organic carbon burial is unlikely since this hypothesis potentially implies a decoupling between pCO2 and the rates of silicate weathering and organic carbon burial [France-Lanord and Derry, 1997; Raymo et al., 1988; Raymo and Ruddiman, 1992], i.e., high CO2 sink flux maintained by low pCO2 level. Also, the hypothesis of tectonic uplift facilitated silicate weathering by exposure of fresh rock surface is based on the transport-limited regime of global weathering and surveys show that the global silicate weathering flux is largely weathering limited [e.g., Kump et al., 2000]. The increasing physical erosion caused by tectonic uplift and glacial erosion during the late Cenozoic would lead global weathering to be more weathering limited [West et al., 2005].
6.2. Role of CO2 Fertilization
 Although tectonics is clearly a major factor driving the shifts in Cenozoic carbon cycle, tectonic changes alone cannot account for the rapid adjustment of weathering rates to the mass balance of entire carbon cycle that we recognize in our model results. The coevolution between silicate weathering and pCO2 (Figures 5 and 6) supports the notion that the adjustment of silicate weathering and the long-term equilibrium of the entire carbon cycle is maintained by the negative feedback between pCO2 and silicate weathering [e.g., Berner et al., 1983]. In such a feedback, any tiny imbalance of carbon cycle will cause dramatic change in pCO2, which then will drive the system back into equilibrium by modulating silicate weathering rate through greenhouse/icehouse effects. It has been proposed that the effects of greenhouse/icehouse condition on silicate weathering rate are mainly achieved by temperature induced kinetic control on mineral dissolution rate, temperature modulated global runoff and hence erosion rate, and CO2 fertilized plant weathering [Berner and Kothavala, 2001]. Global climate is indicated by deep sea foraminifera δ18O, with higher δ18O means lower temperature and more continental ice volume [Zachos et al., 2001]. The moderately good, positive correlation between global temperature, as proxied by increase in benthic foraminifera δ18O [Zachos et al., 2001], and silicate weathering between 65 and ∼25 Ma may be explained by this mechanism (Figure 5). However, after 25 Ma, δ18O is poorly correlated with silicate weathering and pCO2, and after 15 Ma, these parameters appear inversely correlated (Figure 5). Thus, it seems that temperature changes and associated runoff variation induced by pCO2 fluctuations are not the major factors that control the Cenozoic silicate weathering rate and global carbon equilibrium, at least for the past 15 Ma.
 We propose here that the coupled evolution of organic carbon burial, silicate weathering and atmospheric CO2 concentration demonstrated in our model is maintained by CO2 fertilized bioproductivity and plant weathering. Terrestrial plants take up CO2 primarily by diffusion, and increasing atmospheric CO2 generally has a positive effect on photosynthesis, productivity and growth [Ainsworth and Long, 2005]. CO2 fertilized bioproductivity and plant weathering has been observed in many experimental studies [Andrews and Schlesinger, 2001; Baars et al., 2008]. Previous carbon cycle models have also included terms implicating that the efficiency of CO2 fertilization of terrestrial plants is a key factor controlling the long-term evolution of silicate weathering and pCO2 [e.g., Berner and Kothavala, 2001]. Thus, any excess of CO2 emission will initiate an increase in pCO2, which can then accelerate CO2 drawdown by enhanced organic carbon burial (caused by enhanced bioproductivity) and fertilized plant weathering of silicate minerals, which prevent the atmospheric CO2 concentration running out of control, and vice versa.
 The formula proposed in GEOCARB III model is adopted here to describe the CO2 fertilized plant weathering [Berner and Kothavala, 2001]
where pCO2 is the concentration of atmospheric carbon dioxide; 280 indicates preindustrial pCO2 level; n is the exponent representing the efficiency of CO2 in fertilizing plant growth globally. The value n = 0 means no fertilization globally, where a value of n = 1 mean that all plants globally respond to CO2 fertilization. In the equation, plant productivity is assumed to no more than double worldwide in response to the increasing CO2. Theoretically, the term kpre should be equal to 1. However, the best fit for the correlation between ksiliw and pCO2 in this work results in a smaller kpre of 0.85 (Figure 6a), which may be caused by the model error or limitations of the proxy pCO2 record. Although the resulting n value of 0.59 is a little higher than that used in the GEOCARB III model (n = 0.4), our estimate is reasonable since this parameter is poorly constrained [Berner and Kothavala, 2001].
Equation (11) can also be used to describe CO2 fertilized organic carbon burial, with a resulting n value of 0.32 (Figure 6b). Because the largest portion of organic carbon burial is marine, the lower n value of the korgb-pCO2 correlation than that of the CO2 modulated plant weathering may resulting from the difference in the sensitivity of CO2 fertilization between terrestrial plants and marine phytoplankton. Unlike terrestrial plants, which take up CO2 primary by diffusion, most marine phytoplankton have concentrating mechanisms that actively take up inorganic carbon, either as CO2 directly or as bicarbonate ions (HCO3–), or both. Thus, as they actively physiologically concentrate CO2, changes in the ambient CO2 content of the water have less effect on their photosynthesis efficiency [Giordano et al., 2005]. Another possible explanation for the low n value of the korgb-pCO2 correlation is that marine productivity is largely nutrient limited [e.g., Tyrrell, 1999].
 The proposed hypothesis is that CO2 fertilized plant productivity should control both silicate weathering and organic carbon burial. Thus, silicate weathering and organic carbon burial would be correlated. However, between 52 and 34 Ma this is not the case. Two possibilities can explain the mismatches: (1) the large uncertainties of the model results in this portion or (2) the difference in the sensitivity of CO2 fertilization between terrestrial plants and marine phytoplankton (as mentioned above).
 Cenozoic carbon fluxes related to silicate weathering, carbonate/organic carbon weathering, marine carbonate accumulation, organic carbon burial and volcanic degassing were calculated from the marine carbon (both inorganic and organic), strontium, osmium isotopic records based on an inverse model. We found a good match between reconstructed carbonate sedimentation rates and those previously integrated from ocean basins worldwide. The coupled evolution of continental carbonate exhumation and marine carbonate accumulation suggests that the deposition of marine carbonate is mainly controlled by the recycling of terrestrial carbonate rocks. Our model supports tectonic changes as the major driver for the long-term evolution of the Cenozoic carbon cycle, which is responsible for reduced volcanic degassing after the collision of the Indian-Asian continents between 52–15 Ma and the enhanced exhumation of sedimentary cover during the Himalayan orogeny.
 The balance of atmospheric CO2 in the Cenozoic is maintained by the rapid adjustment of silicate weathering and organic carbon burial to changes in volcanic degassing and organic carbon oxidation. In our consideration of the coevolution of atmospheric carbon dioxide level, silicate weathering and organic carbon burial, we suggest that rapid adjustments of silicate weathering and organic carbon burial are facilitated by CO2 fertilization of terrestrial and marine biomass, and associated plant weathering effects of land plants.
 We greatly thank Hongfei Ling and Yige Zhang for stimulating discussions. The paper has been improved immensely by the reviews of Corinne Le Quere (AE), Klaus Wallmann, and another anonymous reviewer. This work was supported by the National Basic Research Program of China (2004CB720204), the National Natural Science Foundation of China (40331001, 40473009, and 40625012), and Scientific Research Foundation of Graduate School of Nanjing University. D.B.K. acknowledges receipt of a Girton College Research Fellowship.