Simulations of glacial/interglacial cycles with simple box-models. The ocean CO2 source during deglaciations

Master in Oceanography Facultad de Ciencias Básicas Universidad de Las Palmas de Gran Canaria Simulations of glacial/interglacial cycles with simple box-models. The ocean CO2source during deglaciations Carmen Herrero i Navarro Contents Abstract iii Resumen iv 1Introduction 1 2Methods 4 2.1 Insolation ..................................... 4 2.2 Optimizations................................... 6 3Models 8 3.1 PP04model.................................... 8 3.2 4⌧model ..................................... 10 3.2.1 Another proxy for I60 .......................... 16 4Results 18 4.1 LMSSmodel ................................... 18 4.2 LMDSmodel ................................... 19 5Discussion 23 Acknowledgements 27 References 28 Appendix 31 i Contents ii Abstract Paillard and Parrenin [2004] model has been modified to obtain a closer fit to 18Oand CO2time-series for the last 800 kyr. Some sub-models have been developed, finding an improvement in performance if CO2sensitivity to I65 insolation is eliminated, and if different response times are assumed for both absorption/emission of CO2and for ablation/accumulation of ice. Correlations between simulated and experimental time-series have increased from 0.64 and 0.61 (for ice volume and CO2) to 0.89 and 0.81, respectively. It has been found that the model is almost insensitive to late Austral summer insolation (60ºS, 21st February) which leads to some conceptual changes, characterized in the Local Model with Double Stratification (LMDS). In LMDS, local proxies for Antarctic temperature have been used and stratification has been described to operate in two different ways: locally via the extent of Antarctic ice sheet and local temperature; and globally through global ice volume, V(which is strongly correlated to temperature changes in Northern Hemisphere), making a interconnection between oceanic pulse of CO2in Southern Ocean (SO) and Northern Hemisphere (NH). According to this model, terminations are produced by I65 amplification, through CO2 Tand TCO2feedback, in synergy with an extra CO2contribution coming from the deep ocean. This CO2pulse may be controlled by variations in the deep water formation rate in the Antarctic shelf, which is strongly dependent on ice volume and sea ice extent, being thus consistent with either a teleconnection mechanism via North Atlantic Deep Water upwelled in the SO (mechanism suggested by Gildor and Tziperman [2001]), or with sea-ice extent controlled by a local temperature (as suggested by Paillard and Parrenin [2004]). iii Resumen El modelo de Paillard and Parrenin [2004] ha sido modificado para obtener un mayor ajuste de las series experimentales de 18OyCO2para los últimos 800 kyr. Se han desarrollado varios sub-modelos, encontrando una mejora en los ajustes si la sensibilidad del CO2a la insolación I65 es eliminada y si se considera distintos tiempos de respuesta para la absorción/emisión de CO2y para la ablación/acumulación de hielo. Las correlaciones entre las series simuladas y experimentales han aumentado de 0.64 y 0.61 (volumen de hielo global yCO2) a 0.89 y 0.81, respectivamente. Se ha encontrado que el modelo es prácticamente insensible a la insolación Austral tardía (60ºS, 21 de Febrero) lo que lleva a ciertos cambios conceptuales, caracterizados en el Modelo Local con Doble Estratificación (LMDS). En LMDS, se han utilizado indicadores locales para la temperatura Antártica y la estratificación ha sido descrita para operar en dos sentidos: localmente mediante la extensión de capa de hielo Antártica y la temperatura local; y globalmente, mediante el volumen global de hielo, V (el cual está fuertemente correlacionado con variaciones de la temperatura en el Hemisferio Norte), dando lugar por tanto a una interconexión entre los pulsos oceánicos de CO2en el Océano Austral y el Hemisferio Norte. De acuerdo con este modelo, las terminaciones están producidas por una amplificación de I65 mediante el feedback CO2TyTCO2, en sinergia con una contribución extra de CO2proveniente del océano profundo. Este pulso de CO2podría estar controlado por variaciones en la tasa de formación de aguas profundas en la plataforma Antártica, la cual es altamente dependiente del volumen de hielo y la extensión de hielo marino, siendo por tanto consistente tanto con un mecanismo de teleconexión mediante la North Atlantic Deep Water aflorada en el Océano Austral (mecanismo sugerido por Gildor and Tziperman [2001]), o con la capa de hielo marino controlada por la temperatura local (tal y como se sugiere en Paillard and Parrenin [2004]). iv 1Introduction Variations of glacial-interglacials states during the Quaternary are ultimately caused by changes in parameters of the Earth’s orbit (Hays et al. [1976]) but other physical mechanisms must be involved and by now, they remain mostly unknown. Specifically, the role and mechanisms which involved an increase of atmospheric CO2during glacial-interglacial change are not entirely clear, although some exchange mechanisms involving the biological or the physical “carbon pumps” have been proposed to explain it (Skinner [2009]): 1. those involving an increase in the export rate of organic carbon to the deep ocean, either via increased nutrient availability at low latitudes or via increased efficiency of nutrient usage at high latitudes (Broecker [1982]; Knox and McElroy [1984]; Kohfeld et al. [2005]) 2. those involving a reduction in the “ventilation” of water exported to the deep Southern Ocean (SO) (Toggweiler and Sarmiento [1985]; Watson and Garabato [2006]) 3. those involving changes in ocean chemistry and “carbonate compensation”, possibly promoted by changes in the ratio of organic carbon and carbonate fluxes to the deep sea (Archer and Maier-Reimer [1994]). Each of this conceptual models has problems explaining the variation in glacial-interglacial CO2by itself, which probably suggest that none has operated in complete isolation (Archer et al. [2000]; Sigman and Boyle [2000]). What seems to be fundamental to explain CO2 changes during glacial-interglacial states is the balance between biological sink of exported carbon from the surface-ocean and the returned carbon from deep circulation via physical mechanisms. Regarding this physical pump, four main mechanisms have been identified which could modify its efficiency in glacial and interglacial times: (a) Changes in the surface-to-deep mixing rate efficiency (Toggweiler [1999]; Gildor and Tziperman [2001]) and deep ocean stratification (Paillard and Parrenin [2004]). This mechanism is supported by proxies of temperature and salinity of deep water in the last glacial maximum (LGM) (Adkins et al. [2002]), which suggest that the density anomaly between Antarctic Bottom Waters (AABW) and intermediate waters was three times larger in the LGM than it is today. Therefore, if the rate of vertical mixing is inversely proportional to the density difference, the change in stratification of the deep ocean in glacial periods should be able to explain a fraction of the reduction of CO2input to the atmosphere due to diapycnal mixing variation in deep waters (Watson and Garabato [2006]). 1 1. Introduction (b) Sequestration of CO2in deep waters with a standing volume that increases during glacial climates. Southern-sourced deep water was found in the deep North Atlantic up to a water depth of 2.5 km in the past glacial age (Curry and Oppo [2005]) which suggests an increase of southern-sourced water. Skinner [2009] calculates that, for glacial ages, a rising in the level of AABW and Low Circumpolar Deep Water, LCDW (having average total dissolved CO2concentrations of 2280 µmol kg1) from 20 million km3to 70 million km3(a 4-fold increase) at the expense of NADW (having 2180 µmol kg1) would produce an oceanic gain of 63 Gt of carbon. If all this carbon comes from the atmosphere, then atmospheric pCO2would have to drop by 30 ppm, given 1 ppm change per 2.12 Gt carbon removed from the atmosphere. This is equivalent to 34% of the CO2increase observed after glacial-interglacial change. (c) Switching off/on of the Antarctic upwelling at Drake Passage latitudes in cold/warm conditions (Toggweiler et al. [2006]). Any process producing a (global or southern) tropospheric warming would imply poleward-shifted westerlies, possibly through increased evaporation. This would produce stronger wind-stress work at the Drake Passage latitudes and stronger upwelling of deep water at the SO divergence. (d) Extended ice sea in the SO produces a “capping” effect on the CO2release to the atmosphere during winters (Keeling and Stephens [2001]) and a retardation of the overturning rate in the SO due to sea ice control on the residual circulation (Watson and Garabato [2006]; Fischer et al. [2010]). In all of the mechanisms above, an increased CO2release is expected during the change between glacial-interglacial periods, and it is expected to take place mainly in the SO. Interestingly, recent proxies obtained for the temperature at Antarctica show a strong correlation between temperature and CO2concentrations (Siegenthaler et al. [2005]; Fischer et al. [2010]). On the other hand, recent interpretations (Paillard [2010]) of empirical data (Bard et al. [1996]; Monnin et al. [2001]) suggest that the atmospheric CO2concentration increased for several millennial before the melting of the northern hemisphere ice sheets. Both pieces of evidence support the hypothesis that some of the mechanisms mentioned above, taking place essentially in the SO, could be behind the increase of CO2needed to produce glacial-interglacial change. Some simple box models have been proposed to explain this so-commented glacialinterglacial cycles. Some of them, as Pelegrí [2008] and Pelegrí et al. [2011] take into account changes in overturning rate and biological exportation of CO2, reproducing approximately sawtooth-like oscillation of last four glacial cycles but in which physical triggers of glacial-interglacial states remain unexplained. More complex models as Ganopolski et al. [2010] have shown that Earth system models of intermediate complexity (EMICs) as CLIMBER-2 are able to reproduce the major aspects of glacial cycles under orbital and greenhouse forcing rather realistically. However, the CO2forcing has to be introduced independently of the orbital forcing. 2 Paillard and Parrenin [2004] also proposed a simple box-model (PP04 model hereafter) but taking into account the mechanism of dense water formation in the Southern Ocean. In this model the Antarctic ice-sheet extent is proposed as a new mechanism able to link climatic and CO2glacial-interglacial changes. The clue of their results is the identification of ocean-CO2switch based on the vertical density structure of the deep ocean as the largest non linearity of the system. In spite of its simplicity, this model is the first one to accurately reproduce pace and termination times of all glacial-interglacial cycles during Quaternary, as well as the whole set of maxima and minima of the 18O(Lisiecki and Raymo [2005]) oscillations observed in the past 5 million years. This may be a sign of the crucial role played by the stratification and Southern Ocean CO2pulse in the onset of glacial-interglacial change. García-Olivares and Herrero [2011] (shown in Appendix) generalizes and calibrates PP04 model to the 18Oand CO2time-series available for the last 800 kyr (Lisiecki and Raymo [2005]; Monnin et al. [2001]; Petit et al. [1999]; Pepin et al. [2001]; Siegenthaler et al. [2005]; Luthi et al. [2008]) with the aim of analyzing how different generalizations, such as export production or the strength of deep stratification, could affect some improvements at experimental fits. It was observed that the PP04 model performance can be improved if its CO2sensitivity to insolation is eliminated and if different response times were assumed both for absorption/emission of CO2and for ablation/accumulation of ice. We will refer to this model hereafter as 4⌧(Herrero et al. [2010, 2011]) PP04 and specially 4⌧model are fully explained, mathematically and dynamically, on following sections. 3 2Methods In this section are specified the different software and methods applied to obtain the results. 2.1 Insolation To calculate insolation at different latitudes the software used was Berger [1978a], with a modified script made by Olivella [2009] In this work, different insolation data have been used to cover time domain between -800 kyr and 0 yr (present time) with time steps of 100 yr. On one hand, insolation regarding one single day of the year at one specified latitude, this is Northern Hemisphere summer insolation (65ºN on 21st June) and late Austral summer insolation (60ºSon21st February), both of which are calculated directly with Berger’s software (Figure 2.1.1) Figure 2.1.1: Northern Hemisphere summer insolation (top) and late Austral summer insolation (bottom). On the other hand, we have calculated average insolation of Austral summer (shown in Figure 2.1.2), from 21st November to 21st March. To do so, two different files have been generated with Olivella’s script: a file with monthly insolation of November and December 4 3.2 4⌧model However, two response times for emission (⌧C2)andabsorption(⌧C1) of atmospheric CO2 are harder to explain. Archer et al. [2009] reviewed literature on the carbon cycle and discussed some models, getting to the conclusion that it will take a timescale of 2 to 20 centuries for the ocean to absorb the surplus atmospheric CO2, and even when the equilibrium would be reached, a substantial fraction (20-40%) of this CO2would remain in the atmosphere awaiting slower chemicals reactions. These results are apparently coherent with the situation proposed here, where ⌧C2>⌧C1, but further investigation is needed to have a precise understanding of the long-term carbon cycle. Daily insolation for the last 800 kyr is obtained from the Berger [1978b, a] software as it is shown in section 2. Insolation is normalized with its standard deviation to obtain I65 and I60. No lower bound is imposed on the V,Cand Avariables. Note that all results of the model have been normalized by their standard deviation before plotting. Parameter PP04 Model 4⌧Model with ↵4⌧Model without ↵ ⌧V115000 13297.6 16342.12 ⌧V22437.42 3641.46 ⌧C15000 5353.01 12036.02 ⌧C210503.07 19282.14 ⌧A12000 9424.83 6159.27 x1.3 0.753 1.288 y0.5 0.646 0.65 z0.8 1.199 1.173 ↵0.15 0.218 - 0.5 0.631 0.386 0.7 2.312 1.922 0.4 0.528 0.169 a0.3 0.711 0.833 b0.7 1.399 1.599 c0.01 0.011 0.126 d0.27 0.486 0.637 ⇢V0.64 0.88 0.89 ⇢C0.61 0.80 0.81 Table 3.1: Parameter values used in each model. ⇢Vand ⇢Crepresent the correlation between experimental and modeled data for Vand Crespectively. In original Paillard and Parrenin [2004], parameter had a value of 0.5 due to a mistake. Noticed by Michael Crucifix and Didier Paillard in a later revision, the correct value is 0.7. The original PP04 model includes direct forcing of the I65 insolation on the CO2response (↵parameter on Eq. 3.1.5). The physical interpretation of this forcing is not clear, given that the CO2response to temperature is already included in the model. 4⌧model has been run with both possibilities (including and not including ↵as a parameter), given that 11 3. Models Figure 3.2.1: 4⌧model with ↵over the last 800 kyr. Top, modeled ice volume (blue) and 18Oexperimental time-series obtained by Lisiecki and Raymo [2005] (black, thin line); below, simulated CO2levels (red) and experimental time-series obtained by Luthi et al. [2008] (black, thin line); below, modeled Antarctica area (black); and bottom, critical parameter F (green) and the state of the ocean (blue): glacial or interglacial. the best fits were obtained when this forcing is zero (Table 3.1 ), hereafter when we will be referring to 4⌧model it will be without ↵parameter. It is interesting how ↵parameter is responsible of high-frequency oscillations in CO2, making visually modeled and experimental curve seem more different, although the correlation obtained is slightly higher (Figures 3.2.1 and 3.2.3) As can be observed in Figures 3.2.2, 3.2.3 and 3.2.4, 4⌧model is much more like a sawtooth oscillation, like experimental data, than PP04 model does. The Cseries presents a saw-shaped form also, which is produced by the feedback V-C(through ) in conjunction with the large value used for the parameter ⌧C2. Is interesting how the introduction of two different response times, as well the suppression of ↵parameter affects the shape and high-frequency of the CO2oscillations. Both models have some problems simulating the maxima of 500 kyr BP, as well as terminations VII and VIII, which none of the models are able to reproduce shape nor timing. In 4⌧model, many details of the high-frequency oscillations of the experimental ice volume are better simulated than in PP04. The shape of the cycles I, III, IV and VII BP are also adequately simulated. However, it can be observed that both models have difficulty simulating the glacial cycle between 600 and 700 kyr BP, specially the timing of its termination, but 4⌧model is able to predict accurately the timing of Terminations II and IV. This is probably a shared limitation of both model and 18Orecords. As has 12 3.2 4⌧model Figure 3.2.2: Model results for PP04 as shown in Paillard and Parrenin [2004]. Top, modeled ice volume (blue) and 18Oexperimental time-series obtained by Lisiecki and Raymo [2005] (black, thin line); below, simulated CO2levels (red) and experimental time-series obtained by Luthi et al. [2008] (black, thin line); below, modeled Antarctica area (black); and bottom, critical parameter F (green) and the state of the ocean (blue): glacial or interglacial (zero value). been suggested by Paillard, almost all paleoclimatic records are, in some way, tuned to the astronomical forcing by using implicitly or explicitly a simple model of ice ages. In other words, it is not clear that the time scale of the data is better or worse than the time scale of the model (within, lets say, a quarter period of the fastest forcing, the precession, i.e. ±6 kyr). This is particularly true for the timing of terminations which may not be constant versus the forcing (see e.g. Parrenin and Paillard [2003] ). For this reason, a "better fit" of the timing of terminations of the 18Odata may not be an improvement, since the data are not necessarily very accurate and may be biased by assumptions that are too simple. As shown, in Table 3.1, parameter c, which relates the efficiency of dense water formation with late Austral summer insolation, is relatively small. Curiously, an almost identical optimum can be found with a set of parameters that does not use the I60 forcing (i.e. c=0). This result can be interpreted in three alternative ways: i. I60 is not a good proxy for Southern Ocean temperature; ii. The formation of dense water and/or CO2release in the Southern Ocean is not controlled by local temperature; iii. The release of CO2in the SO is not controlled by deep water density, and the function F(V,A)in our models represents a different process. 13 3. Models Figure 3.2.3: 4⌧model with ↵=0. Top, modeled ice volume (blue) and 18Oexperimental time-series obtained by Lisiecki and Raymo [2005] (black, thin line); below, simulated CO2levels (red) and experimental time-series obtained by Luthi et al. [2008] (black, thin line); below, modeled Antarctica area (black); and bottom, critical parameter F (green) and the state of the ocean (blue): glacial or interglacial (zero value). Figure 3.2.4: Comparison between Global ice volume (top) predicted by PP04 (blue), 4⌧ (red) and 18Oexperimental time-series obtained by Lisiecki and Raymo [2005] (black) and CO2(bottom) predicted by PP04 (blue), 4⌧(red) and experimental time-series obtained by Luthi et al. [2008] (black). 14 3.2 4⌧model To explore the third possibility, we conjectured that F(V, A, I60)may be a proxy for the change of CO2release due to variations in upwelling intensity at Drake Passage latitudes. Upwelling intensity should increase when atmospheric convective cells intensify due to increased global and local evaporation; therefore, in our model, it should decrease with V and rise with I60. If this conjecture were correct, then Equation 3.2.2 would be unnecessary, and the system of Equations 3.2.1, 3.2.3, 3.2.4 and 3.2.5 may also have a good fit using adifferent set of parameter values. Consequently, we explored the new equations system for a wider region of the parameter space. However, no fit was found that could reproduce the pace of the last glacial cycles. Another possible interpretation is that F(V, A, I60)could be a proxy for a rate of emission of CO2that is controlled directly by sea ice area, A, and local temperature. Local temperature could be controlled by global temperature more strongly than by I60.One possible mechanism able to produce this effect was proposed by Gildor and Tziperman [2001]: stratification in the SO is composed of cold, fresh and therefore light water above warm, salty and therefore dense water. Glacial conditions in the northern hemisphere cool the North Atlantic Deep Water (NADW) and, consequently, via the southward flow and upwelling of NADW, lower the deep temperature in the SO. Because of permanent ice cover over Antarctica, surface ocean temperature in the SO near Antarctica is close to freezing point during the entire glacial cycle, so that it cannot cool very much even during glacial conditions. Glacial conditions, therefore, increase the density of deep SO water but not of surface SO water and this strengthens the vertical stratification there. As a result, vertical mixing in the SO is expected to be reduced. This mechanism implies that temperature changes in the northern hemisphere (strongly correlated with global ice volume V) lead to CO2changes in the southern hemisphere. To test if Ais sensitive to I60,Equation 3.2.2 of the model was modified in the following way: dA dt =(VAcI60) ⌧A (3.2.7) However, the best fits obtained after this change did not improve upon those obtained by 4⌧model. These results are consistent with the following conclusions: An Avariable, probably related to sea ice extent that follows the evolution of Vwith a delay of 5 to 15 kyr seems necessary to obtain good fits. CO2release to atmosphere in the SO may be controlled either by density of deep water or by sea ice extent or both. However, none of the two mechanisms seems to be sensitive to I60 insolation. Either some of these mechanisms are not sensitive to SO temperature, which is difficult to conceive, or I60 is not a good proxy for SO temperature. Huybers and Denton [2008] have pointed out an important fact that had passed unperceived and that could be coherent with these conclusions: Antarctic summer duration is highly correlated with I65 insolation. In addition, it is plausible that Antarctic climate remains in near radiative equilibrium with local heat accumulation, which is controlled by 15 3. Models Figure 3.2.5: 4⌧model with ↵=0 and IAV 60 . Top, modeled ice volume (blue); below, simulated CO2levels (red); modeled Antarctica area (black); and bottom, critical parameter F (green) and the state of the ocean (blue): glacial or interglacial (zero value). summertime duration. In contrast, northern changes are mediated through the response of the northern ice sheets, which are much more sensitive to insolation at the solstice (I65) than to summertime duration. Thus, SO temperature could be a crucial variable that controls either the southern sea ice or the density of deep water or both; but this southern temperature does not need to be controlled via teleconnection with the north. It may responds directly to local astronomical forcing different to I60. Some simulations have been done with other proxies for I60, for instance using integrated insolation of Austral Summer (IIN 60 ) or averaged insolation of Austral Summer (IAV 60 ), in order to have some light on the subject. 3.2.1 Another proxy for I60 As is shown in Figure 2.1.3, three different insolation sets have been generated, all of which have almost exact shapes. It is said above and according to Huybers and Denton [2008], that the duration of Southern Hemisphere summer is what probably controls Antarctic climate. In spite of having generated two new sets of insolation (IIN 60 and IAV 60 ), and despite having been used both in 4⌧model, here are shown the results using IAV 60 instead of I60, since the similarity between sets of insolation ( IIN 60 or IAV 60 ) provides no differences when running the model. It can be noticed that there is no real difference between using IAV 60 or I60 (Figure 3.2.5), which was actually expected due to both sets of insolation have almost same shape. The conclusion to be drawn have been mentioned before: I60 clearly is not a good proxy for 16 3.2 4⌧model Southern Ocean temperature, for which is necessary more investigation, that will lead us to change some concepts of the model. In line with Gildor and Tziperman [2001], other expressions for local temperature have been searched for. On the other hand, it will be interesting explore with further research how a set of summertime, instead of late Austral summer insolation, affects the model, as Huybers and Denton [2008] had proposed, being this the subject of future work. 17 4Results Some proxies have been proposed to replace I60, since it has been demonstrated that it is not a good proxy for Southern Ocean temperature. Here we show two different models both of which are based on local proxies. 4.1 LMSS model In this Local Model with Simple Stratification (LMSS hereafter) the insolation in the Southern Hemisphere (SH) has been substituted for modeled variable C. Since atmospheric CO2can be considered as temperature proxy (depending on location, temperature often looks like CO2, for instance in the Antarctic deuterium record) and due to oceanic CO2 pulse takes place in SO, variable Ccan be considered as a valid proxy of local temperature in SH. This model proposed here, takes into account a simple mechanism of stratification through the extent of Antarctic ice sheet and local temperature, C. Basically, the “salty bottom water formation efficiency parameter”, F, is only controlled by local mechanisms in the SO, and so does oceanic pulse of CO2which could be responsible of changes in glacial-interglacial states. The mathematical expression follows. dV dt =(VrV) ⌧V (4.1.1) dA dt =(CA) ⌧A (4.1.2) dC dt =(CrC) ⌧C (4.1.3) Vr=xC yI65 +z(4.1.4) Cr=V+H(F)+(4.1.5) F=bA cC +d(4.1.6) Here, the Antarctic ice sheet reference, represented before by V, has been changed to 18 4.2 LMDS model Figure 4.1.1: LMSS model over the last 800 kyr. Top, modeled ice volume (blue); below, simulated CO2levels (red); below, modeled Antarctica area (black); and bottom, critical parameter F(green) and the state of the ocean (blue): glacial or interglacial (zero value). Cin Equation 4.1.2 and similarly, insolation of Southern Hemisphere has been replaced by Cin Equation 4.1.6, as well as the dependency F(V)has been removed. 4.2 LMDS model Another possibility, following previous line, is to consider stratification dependent on local and global variables. Thus, a Local Model with Double Stratification (LMDS hereafter) has been developed, in which structure is virtually identical to LMSS except that stratification operates in two different ways: locally via the extent of Antarctic ice sheet and local temperature; and globally through global ice volume, V(which is strongly correlated to temperature changes in Northern Hemisphere), making a interconnection between oceanic pulse of CO2and Northern Hemisphere (NH). Mathematical expression is the following. dV dt =(VrV) ⌧V (4.2.1) dA dt =(CA) ⌧A (4.2.2) dC dt =(CrC) ⌧C (4.2.3) 19 4. Results Figure 4.2.1: LMDS model over the last 800 kyr. Top, modeled ice volume (blue); below, simulated CO2levels (red); below, modeled Antarctica area (black); and bottom, critical parameter F(green) and the state of the ocean (blue): glacial or interglacial (zero value). Vr=xC yI65 +z(4.2.4) Cr=V+H(F)+(4.2.5) F=aV bA cC +d(4.2.6) Note that difference with LMSS remains in Fparameter, where the dependency with V has been added. As shown in Figures 4.1.1 and 4.2.1, both models are extremely similar; in fact, LMSS gives slightly better results than LMDS, but this last one has more physical consistence, due to the agreement with recent interpretations (Paillard [2010]) of empirical data (Bard et al. [1996]; Monnin et al. [2001]) which suggest that the atmospheric CO2concentration increased for several millennial before the melting of the northern hemisphere ice sheets, being this impossible to explain with LMSS. They both reproduce more high frequency than 4⌧model does in CO2curve, specially LMDS, and it is able to better reproduce the timing of almost all cycles, except IX, where it has problems reproducing shape and time. In LMDS, pace and timing of ice volume for 20 Acknowledgements This work is a contribution to the project MOC-2 funded by the Spanish R+D Plan 2008-2011. I would like to thank Antonio García-Olivares and Josep Lluís Pelegrí for their great support, help, and confidence; as well to Eva Calvo and Carles Pelejero for their interesting suggestions and help with experimental data; and to Didier Paillard, for his useful comments. I wish to dedicate this work to my family, for their unconditional support and patience. 27 Bibliography Adkins, J. F., K. McIntyre, and D. P. Schrag, The salinity, temperature, and 18oofthe glacial deep ocean, Science,298(5599), 1769–1773, 2002. Archer, D., and E. Maier-Reimer, Effect of deep-sea sedimentary calcite preservation on atmospheric co2concentration, Nature,367(6460), 260–263, 1994. Archer, D., A. Winguth, D. Lea, and N. Mahowald, What caused the glacial/interglacial atmospheric pco2cycles?, Rev. Geophys.,38(2), 159–189, 2000. Archer, D., et al., Atmospheric lifetime of fossil fuel carbon dioxide, Annual Review of Earth and Planetary Sciences,37(1), 117–134, 2009. Bard, E., B. Hamelin, M. Arnold, L. Montaggioni, G. Cabioch, G. Faure, and F. Rougerie, Deglacial sea-level record from tahiti corals and the timing of global meltwater discharge, Nature,382(6588), 241–244, 1996. Barker, S., P. Diz, M. J. Vautravers, J. Pike, G. Knorr, I. R. Hall, and W. S. Broecker, Interhemispheric atlantic seesaw response during the last deglaciation, Nature,457(7233), 1097–1102, 2009. Berger, A., A simple algorithm to compute long term variations of daily or monthly insolation., vol. 18, 18 ed., Contribution de l’Institut d’Astronomie et de Geophysique, Universite Catholique de Louvain. Louvain-la-Neuve. Belgium, 1978a. Berger, A., Long term variations of daily insolation and quaternary climatic changes, Journal of the Atmospheric Sciences,35(12), 2362–2367, 1978b. Broecker, W. S., Glacial to interglacial changes in ocean chemistry, Progress In Oceanography,11(2), 151 – 197, 1982. Charbonneau, P., An introduction ot genetic algorithms for numerical optimization, High Altitude Observatory, National Center for Atmospheric Research. Boulder, Colorado., 2002. Curry, W. B., and D. W. Oppo, Glacial water mass geometry and the distribution of 13c of co2in the western atlantic ocean, Paleoceanography,20(1), PA1017–, 2005. Fischer, H., et al., The role of southern ocean processes in orbital and millennial co2 variations - a synthesis, Quaternary Science Reviews,29(1-2), 193 – 205, 2010. 28 Bibliography Ganopolski, A., R. Calov, and M. Claussen, Simulation of the last glacial cycle with a coupled climate ice-sheet model of intermediate complexity, Climate of the Past,6(2), 229–244, 2010. García-Olivares, A., and C. Herrero, Fitting the last pleistocene delta o-18 and co2timeseries with simple box models, Scientia Marina,2011. Gargett, A., Vertical eddy diffusivity in the ocean interior, Journal of Marine Research, 42(2), 359–393, 1984. Gildor, H., and E. Tziperman, Physical mechanisms behind biogeochemical glacialinterglacial co2variations, Geophys. Res. Lett.,28(12), 2421–2424, 2001. Hays, J. D., J. Imbrie, and N. J. Shackleton, Variations in the earth’s orbit: Pacemaker of the ice ages, Science,194(4270), 1121–1132, 1976. Herrero, C., A. García-Olivares, and J. L. Pelegrí, El ciclo glacial-interglacial. análisis y mejora del modelo de paillard, in IEncuentro de la Oceanografía Física Española (EOF). Barcelona, Spain. Poster,2010. Herrero, C., A. García-Olivares, and J. L. Pelegrí, Simulations of glacial/interglacial cycles with simple box-models. key triggers for deglaciations, in Goldschmidt Conference. Prague, Czech Republic. Poster,2011. Huybers, P., and G. Denton, Antarctic temperature at orbital timescales controlled by local summer duration, Nature Geosci,1(11), 787–792, 2008. Karsten, R. H., and J. Marshall, Constructing the residual circulation of the acc from observations, J. Phys. Oceanogr.,32(12), 3315–3327, 2002. Keeling, R. F., and B. B. Stephens, Antarctic sea ice and the control of pleistocene climate instability, Paleoceanography,16(1), 112–131, 2001. Knox, F., and M. B. McElroy, Changes in atmospheric co2: Influence of the marine biota at high latitude, J. Geophys. Res.,89(D3), 4629–4637, 1984. Kohfeld, K. E., C. L. Quere, S. P. Harrison, and R. F. Anderson, Role of marine biology in glacial-interglacial co2cycles, Science,308(5718), 74–78, 2005. Kuhlbrodt, T., A. Griesel, M. Montoya, A. Levermann, M. Hofmann, and S. Rahmstorf, On the driving processes of the atlantic meridional overturning circulation, Rev. Geophys., 45(2), RG2001–, 2007. Laepple, T., M. Werner, and G. Lohmann, Synchronicity of antarctic temperatures and local solar insolation on orbital timescales, Nature,471(7336), 91–94, 2011. Lisiecki, L. E., and M. E. Raymo, A pliocene-pleistocene stack of 57 globally distributed benthic delta o-18 records, Paleoceanography,20(1), PA1003–, 2005. 29 Bibliography Luthi, D., et al., High-resolution carbon dioxide concentration record 650,000-800,000 years before present, Nature,453(7193), 379–382, 2008. Lynch-Stieglitz, J., et al., Atlantic meridional overturning circulation during the last glacial maximum, Science,316(5821), 66–69, 2007. McManus, J. F., R. Francois, J.-M. Gherardi, L. D. Keigwin, and S. Brown-Leger, Collapse and rapid resumption of atlantic meridional circulation linked to deglacial climate changes, Nature,428(6985), 834–837, 2004. Monnin, E., A. Indermuhle, A. Dallenbach, J. Fluckiger, S. Bernhard, T. F. Stocker, D. Raynaud, and J.-M. Barnola, Atmospheric co2concentrations over the last glacial termination, Science,291, 112–114, 2001. Negre, C., R. Zahn, A. L. Thomas, P. Masque, G. M. Henderson, G. Martinez-Mendez, I. R. Hall, and J. L. Mas, Reversed flow of atlantic deep water during the last glacial maximum, Nature,468(7320), 84–88, 2010. Olivella, R., Modelizacion de la respuesta glacial-interglacial del co2atmosferico mediante un modelo fisiologico oceanico, Master’s thesis, Universidad de Las Palmas de Gran Canaria, 2009. Paillard, D., The timing of pleistocene glaciations from a simple multiple-state climate model, Nature,391(6665), 378–381, 1998. Paillard, D., Climate and the orbital parameters of the earth, Comptes Rendus Geoscience, 342(4-5), 273 – 285, 2010. Paillard, D., and F. Parrenin, The antarctic ice sheet and the triggering of deglaciations, Earth and Planetary Science Letters,227(3-4), 263 – 271, 2004. Parrenin, F., and D. Paillard, Amplitude and phase of glacial cycles from a conceptual model, Earth and Planetary Science Letters,214(1-2), 243 – 250, 2003. Pelegrí, J. L., A pysiological approach to oceanic processes and glacial-interglacial changes in atmospheric co2,Scientia Marina,72, 185–202, 2008. Pelegrí, J. L., R. Olivella, and A. García-Olivares, A simple metabolic model of glacialinterglacial energy supply to the upper ocean, Earth System Dynamics Discussions,2(1), 271–313, 2011. Pepin, L., D. Raynaud, J. M. Barnola, and M. F. Loutre, Hemispheric roles of climate forcings during glacial-interglacial transitions as deduced from the vostok record and lln-2d model experiments, Journal of Geophysical Reviews,106, 31,885–31,892, 2001. Petit, J. R., et al., Climate and atmospheric history of the past 420000 years from the vostok ice core antarctica., Nature,399, 429–436, 1999. 30 Bibliography Shackleton, N. J., M. A. Hall, and E. Vincent, Phase relationships between millennial-scale events 64,000-24,000 years ago, Paleoceanography,15(6), 565–569, 2000. Siddall, M., B. Honisch, C. Waelbroeck, and P. Huybers, Changes in deep pacific temperature during the mid-pleistocene transition and quaternary, Quaternary Science Reviews, 29(1-2), 170 – 181, 2010. Siegenthaler, U., et al., Stable carbon cycle-climate relationship during the late pleistocene., Science,310, 1313–1317, 2005. Sigman, D. M., and E. A. Boyle, Glacial/interglacial variations in atmospheric carbon dioxide, Nature,407(6806), 859–869, 2000. Sigman, D. M., M. P. Hain, and G. H. Haug, The polar ocean and glacial cycles in atmospheric co2 concentration, Nature,466(7302), 47–55, 2010. Skinner, L. C., Glacial-interglacial atmospheric co2change: a possible "standing volume" effect on deep-ocean carbon sequestration, Climate of the Past,5(3), 537–550, 2009. Stephens, B. B., and R. F. Keeling, The influence of antarctic sea ice on glacial-interglacial co2variations, Nature,404(6774), 171–174, 2000. Toggweiler, J. R., Variation of atmospheric co2by ventilation of the ocean’s deepest water, Paleoceanography,14(5), 571–588, 1999. Toggweiler, J. R., and J. L. Sarmiento, Glacial to interglacial changes in atmospheric carbon dioxide: The critical role of ocean surface water in high latitudes. in the carbon cycle and atmospheric co2: Natural variations archean to present, Geophys. Monograph, American Geophysica Union,32, 163 – 184, 1985. Toggweiler, J. R., J. L. Russell, and S. R. Carson, Midlatitude westerlies, atmospheric co2, and climate change during the ice ages, Paleoceanography,21(2), PA2005–, 2006. Waelbroeck, C., L. Labeyrie, E. Michel, J. Duplessy, J. McManus, K. Lambeck, E. Balbon, and M. Labracherie, Sea-level and deep water temperature changes derived from benthic foraminifera isotopic records, Quaternary Science Reviews,21(1-3), 295 – 305, 2002. Watson, A., and A. C. N. Garabato, The role of southern ocean mixing and upwelling in glacial-interglacial atmospheric co2change, Tellus B,58(1), 73 – 87, 2006. Wunsch, C., Determining paleoceanographic circulations, with emphasis on the last glacial maximum, Quaternary Science Reviews,22(2-4), 371 – 385, 2003. 31 Corrigendum Msc Thesis. Universidad de Las Palmas de Gran Canaria Simulations of glacial/interglacial cycles with simple box-models. The ocean CO2source during deglaciations Carmen Herrero i Navarro January 24, 2012 •In Figure 2.1.1 the y axes Northern Hemisphere Summer Insolation (W/m²)and Late Austral Summer Insolation (W/m²)shall be replaced by Northern Hemisphere Summer Insolation and Late Austral Summer Insolation. •In Equations 3.1.5, 3.2.5, 4.1.5 and 4.2.5 the parameter H(F)shall be replaced by H(F).