Sediment 231 Pa / 230 Th as a recorder of the rate of the Atlantic meridional overturning circulation : insights from a 2-D model

A two dimensional scavenging model is used to investigate the patterns of sediment 231Pa/230Th generated by the Atlantic Meridional Overturning Circulation (AMOC) and further advance the application of this proxy for ocean paleocirculation studies. The scavenging parameters and the geometry of the overturning circulation cell have been chosen so that the model generates meridional sections of dissolved230Th and 231Pa consistent with published water column profiles and an additional 12 previously unpublished profiles measured in the North and Equatorial Atlantic. The processes that generate the meridional sections of dissolved and particulate 230Th, dissolved and particulate 231Pa, dissolved and particulate 231Pa/230Th, and sediment 231Pa/230Th are discussed in detail. The results indicate that the relationship between sediment 231Pa/230Th at any given site and the overturning circulation is very complex. They clearly show that constraining past changes in the strength and geometry of the AMOC requires an extensive data set and they suggest strategies to maximize information from a limited number of samples.


Introduction
Ocean circulation plays an important role in climate control by transferring solar heat from low to high latitudes (Ganachaud and Wunsch, 2000).In particular, rapid changes in the strength and geometry of the Atlantic Meridional Overturning Circulation (AMOC) have been invoked to explain the abrupt variations in climate that have punctuated Correspondence to: Y. Luo (yluo@eos.ubc.ca) the last ice age and deglaciation (Schmittner et al., 2002;Clark et al., 2002).However, documenting the link between changes in climate and ocean circulation still remains a major challenge in paleoclimatology (Lynch-Stieglitz et al., 2007).Past changes in circulation were first inferred from the sedimentary records of nutrient proxies (Boyle and Keigwin, 1987).While these tracers provide important information on changes in the geometry of the overturning circulation, they do not constrain changes in the rate of overturning (Legrand and Wunsch, 1995).To address this problem, several kinematic tracers of ocean circulation are being investigated (Lynch-Stieglitz et al., 2007).The 231 Pa/ 230 Th ratio of Atlantic sediments is one of these tracers.This proxy has recently been used to investigate past changes in the rate of the AMOC from the last glacial maximum to present (Mc-Manus et al., 2004;Hall et al., 2006;Gherardi et al., 2005Gherardi et al., , 2009)).Because both 231 Pa and 230 Th have uniform production rates (from the decay of dissolved uranium) and 231 Pa has a longer residence time than 230 Th in the water column, the AMOC exports 231 Pa more effectively from the Atlantic into the Southern Ocean (Yu et al., 1996;Francois, 2007).The modern rate of overturning results in the mean residence time of deep water in the Atlantic roughly equivalent to the mean residence time of 231 Pa in the water column (∼200 years), so that nearly half of the 231 Pa produced in Atlantic water is exported to the southern ocean with the water in which it formed.On the other hand, with its much shorter residence time (∼30 years), nearly all of the 230 Th produced in this water is removed into the sediments of the Atlantic and little is exported to the Southern Ocean.As a result, the 231 Pa/ 230 Th ratio in Atlantic sediments is, on average, about half the production rate ratio of these two isotopes in the water column (0.092 dpm/dpm).Faster rates of overturning export a larger fraction of 231 Pa and further decrease 231 Pa/ 230 Th, while slower rates of overturning increase this ratio (Marchal et al., 2000;Siddal et al., 2007).
Application of this simple principle is, however, complicated by two factors.First, sedimentary 231 Pa/ 230 Th is not only controlled by the rate of overturning, but also by the removal rate of the two isotopes from the water column by particle scavenging.Scavenging rates, which are controlled by the flux and composition of settling particles (Bacon, 1988;Walter et al., 1997;Chase et al., 2002Chase et al., , 2003)), dictate the residence time of 231 Pa in seawater and the extent to which it can be exported from the Atlantic by the AMOC (Yu et al., 1996).On the other hand, 230 Th has a residence time sufficiently short to severely limit its redistribution by circulation and mixing, even when the rate of overturning is fast (Francois et al., 2004).It is possible to assess the impact of changes in particle scavenging by analyzing the composition of the sediment, which informs us on changes in particle flux and composition at the site of study and their possible overprint on sediment 231 Pa/ 230 Th at this location (Gherardi et al., 2009), at least to the extent that we can take into account the effect of diagenesis.However, the extent to which scavenging can also affect sediment 231 Pa/ 230 Th further "downstream" in the overturning circulation cell still needs to be investigated.The second point of contention is the extent to which sediment 231 Pa/ 230 Th integrates circulation rates over the overlying water column.In a recent study using a 1-D scavenging model, Thomas et al. (2006) have argued that sedimentary 231 Pa/ 230 Th may only record overturning occurring in about 1000 m of water overlying the analyzed sediment and shallower overturning cannot be recorded in deep sediments.
Several studies have investigated the distribution of 231 Pa and 230 Th in the ocean using three dimensional circulation models based on simplified dynamics (Henderson et al., 1999;Siddall et al., 2005Siddall et al., , 2007) ) or the primitive equations (Dutay et al., 2009).In this study, we take a very different approach and develop a simple 2-D scavenging model to establish the patterns of 231 Pa/ 230 Th distribution that can be generated by an ascribed overturning circulation.The results provide possible explanations for some of the existing field observations in the water column and sediments and a baseline for further evaluating the influence of the other factors that affect the distribution of 231 Pa/ 230 Th in the real ocean.They also suggest sampling strategies to maximize the information on paleocirculation that could be obtained form a very limited sediment database.

Model descriptions
Water column profiles of dissolved and particulate 230 Th and 231 Pa concentration indicate that these two isotopes are removed from seawater by reversible scavenging (Bacon and Anderson, 1982;Nozaki et al., 1987).We use the same for-malism to describe scavenging imbedded in a 2-D circulation scheme to investigate how the concentration of 231 Pa and 230 Th in the water column and sediments can potentially be affected by changes in circulation and scavenging rate.

Formulation
The scavenging model used for both 231 Pa and 230 Th is shown in Fig. 1.Dissolved 230 Th and 231 Pa concentrations ([X] d ; where X represents 230 Th or 231 Pa) are controlled by the production rates of the respective nuclides (P X ; dpm m −3 y −1 ), their adsorption (K X 1 ) and desorption (K X −1 ) rate constants (y −1 ), and the transport rates imposed by the circulation scheme (V ; m y −1 ), while 230 Th and 231 Pa particulate concentrations ([X] p ) are controlled by the adsorption/desorption rate constants, transport rates and the sinking rates (S; m y −1 ) of the particles that scavenge the two nuclides from the water column.At steady-state, we can write: Where X represents 230 Th or 231 Pa, Z is water depth (m), i is the vertical index, and is an "upwind" difference divided by the grid spacing (Press et al., 1992).The model uses a uniform grid with a horizontal grid spacing of 2.5 degrees latitude and a vertical grid spacing of 250 m.These equations are used to calculate the concentration of dissolved and particulate 230 Th and 231 Pa as a function of depth and latitude.Using the upwind scheme with a horizontal velocity u=5.3×10 −3 m/s and an horizontal grid spacing x=278×10 3 m, the inherent mixing in our model (K diff ) is ∼800 m s −2 (K diff =u x/2; based on equivalence of the upwind scheme applied to an advective-reactive equation and an analytic diffusive-advective-reactive equation; e.g.Press et al., 1992).This is in the upper range of the along-isopycnal tracer diffusivities reported for the southern ocean (100-800 m s −2 ; Zika et al., 2009).Initial tests indicate that using a smaller grid size to decrease the model's diffusivity does not result in significant differences in the model results.

Overturning circulation
The 2-D meridional overturning circulation scheme (control run) used in this study is ascribed within a meridional section in the Atlantic Ocean (constant depth of 5000 m from 70 • N to 70 • S) and based on the meridional overturning transports for the North Atlantic reported by Talley (2003).It consists of two meridional overturning cells flowing in opposite directions (Fig. 2).The Atlantic Meridional Overturning Circulation (AMOC) is initiated by the formation of 20.5 Sv of North Atlantic Deep Water (NADW) (Friedrichs and Hall, 1993;Macdonald, 1998;Talley et al., 2003) resulting from evenly divided into 56×20 grids (20 layers evenly distributed over 5000m depth and 56 columns evenly distributed over the meridional section; 2.5° latitude per column).
Xp's = particulate concentrations (dpm.m -3 ).P X = production rates from U decay (dpm.m -3 .y - ).S = sinking rates of particles (m.y -1 ).V = Transport rates (m.y -1 ) Water from this homogeneous region is then transported horizontally to the south at different rates (Fig. 2b).The depth distribution of lateral transport was chosen so that the model generates dissolved 230 Th and 231 Pa profiles consistent with observations (see below).At 10 • N, the NADW flow increases to 22.5 Sv with the addition of 2 Sv from the Antarctic Bottom Water (AABW) between 10 • N and 35 • N. Two Sverdrups of AABW are added further south, resulting in a total flow of 24.5 Sv of NADW, which is close to the NADW strength (23±3 Sv) estimated from the World Ocean Circulation Experiment (WOCE) data (Ganachaud and Wunsch, 2000).NADW starts to gradually upwell at 42.5 • S towards a mixing zone (i.e. one homogeneous region) located above 1000 m between 67.5 • S and 57.5 • S. Water from this mixing zone feeds surface and intermediate water forming the shallow return limb of the AMOC.
The second overturning cell is initiated by 8 Sv of AABW, originating from the same mixing cell, flowing into the southernmost region (67.5 • -70 • S) and sinking directly to 3500 m.Four Sverdrups are transported northward between 3500 m and 4500 m depth and entrained in the upwelling NADW south of 40 • S. The remaining 4 Sv are transported northward below 4500 m.This northward flow is gradually attenuated by entrainment in the NADW and disappears at 37.5 • N, which is roughly consistent with hydrographic observations (Sloyan and Rintoul, 2001).In this study, we do not specifically represent the Antarctic Intermediate Water (AAIW).Although the rate of AAIW formation may affect the 231 Pa/ 230 Th of sediment deposited at intermediate depths in the South Atlantic, preliminary model runs indicate that this water mass has little or no effect on the 231 Pa/ 230 Th of deep sea sediments.

Parameterization
Among all the parameters needed to constrain the model shown in Fig. 1, the production rates for 230 Th and 231 Pa are best known since they are essentially constant and only depend on the well established concentration of 234 U and 235 U in seawater (Delanghe et al., 2002;Robinson et al., 2004).The other parameters, however, are associated with greater variability and uncertainties.
Sinking rate (S): most estimates of the average sinking rate of fine particles (S) obtained from water column profiles of particulate 230 Th (e.g.Krishnaswami et al., 1981;Rutgers van der Loeff and Berger, 1993;Scholten et al., 1995;Moran et al., 2001) range between 400-800 m y −1 .Since there are no clear indications of systematic variability in this parameter, we chose a uniform and intermediate value of 500 m y −1 (Table 1).
K Th 1 and K Th −1 : the adsorption (K 1 ) and desorption (K −1 ) rate constants for 230 Th have been estimated using a reversible scavenging model (Bacon and Anderson, 1982;Nozaki et al., 1987;Clegg and Whitfield, 1991;Clegg et al., 1991) and mostly range from 0.2 to 0.8 y −1 for K Th 1 and 1 to 3 y −1 for K Th −1 .We chose values within this range (Table 1) which generate dissolved 230 Th profiles broadly consistent with water column profiles measured at several locations in the Atlantic and in the Southern Ocean (Fig. 3; Table 2).K Th 1 is lower in the Southern Ocean than in the Atlantic, consistent with the data of Chase et al. (2002).We also used higher K Th 1 in the upper 500m to reflect the increase in K Th 1 with particle concentrations (Bacon and Anderson, 1982).
K Pa 1 and K Pa −1 : the adsorption and desorption rate constants for 231 Pa are even less constrained and we selected their values so as to obtain dissolved 231 Pa concentration profiles (Table 2) and fractionation factors that are also broadly consistent with observations in the field.The fractionation factor is defined as (Anderson et al., 1983): F has been directly measured in the Atlantic and southern ocean (Walter et al., 1997;Moran et al., 2001;Chase et al., 2002).Particle composition affects the fractionation factor (F ) due to the stronger affinity of opal for 231 Pa.In carbonate dominated regions, F is much higher than in opal dominated regions, where F is close to 1.We have adjusted the adsorption and desorption rate constants with latitude (Table 1) to produce systematic variations in the "equilibrium" fractionation factor which broadly reflect the field observations (Moran et al., 2002;Walter et al;1997; Table 3).The "equilibrium" fractionation factor is the fractionation factor that would be measured if particles were in equilibrium with surrounding seawater.In this case ).As we will discuss below, however, F measured in the field is also affected by particle sinking rates and circulation.The "equilibrium" fractionation factors used in our control run are set at 7.8 in all waters situated north of 42.5 • S. Further south, they decrease gradually to reach a minimum of 0.9 south of 50 • S.
In order to calculate the transport rates (V ; m y −1 ) needed to obtain the desired water transport fluxes (Sv), we fixed the width of the Atlantic basin in our model at 3000 km.et al. 1995; 1997; 2002); Western Atlantic: W-A toW-F (Table 2); Eastern Atlantic: E-A to E-F (   (Moran et al., 1995(Moran et al., , 1997(Moran et al., , 2002)); Western Atlantic: W-A to W-F (Table 2); Eastern Atlantic: E-A to E-F (Table 2); Southern Ocean: S (Rutgers van der Loeff and Berger; 1993).
328), and 2005 (ENDEAVOR 407).In this section, we present the fit between field data and those generated by our control run and discuss the processes that generate them.Simple scavenging models using constant S, K 1 and K −1 and neglecting circulation predict a linear increase in   (Bacon and Anderson, 1982;Bacon et al., 1985;Nozaki et al., 1987): Where Z is depth.However, most 230 Th and 231 Pa seawater profiles measured in the ocean display significant deviations from linearity because the effect of circulation can rarely be neglected.The dissolved 230 Th and 231 Pa concentration profiles obtained with our model using the parameters listed in Table 1 also deviate often from linearity and are broadly consistent with observations.
The model reproduces reasonably well the water column profiles measured in the Labrador and Norwegian Sea (Fig. 4).Shallow waters entering the Nordic Seas to produce deep water have low 230 Th and 231 Pa concentrations and deep winter convective mixing results in low and nearly constant concentration profiles.Concentrations are higher at shallow depths and lower in deep waters than predicted by the scavenging model in the absence of vertical mixing.The fit of the modeled 230 Th is best with the profiles measured in the Labrador Sea in 1993 (Moran et al., 1997) and in the Norwegian Sea (Moran et al., 1995).The 230 Th concentrations measured in the Labrador Sea in 1999 are significantly higher and have been attributed to a temporary cessation of deep water convection in the Labrador Sea during that period (Moran et al., 2002).The build-up of 231 Pa resulting from the same effect is expected to be much smaller (the response time depends the residence time and is longer for 231 Pa; see below), and we find a reasonable fit between the model and the 1999 Labrador Sea measurements of dissolved  1995) and the Labrador Sea in 1993 (IOC93-2; Moran et al., 1997) and 1999(Labrador: Moran et al., 2002).
231 Pa (although the model generates somewhat higher concentrations than observed).
The concentration deficit in deep waters generated in the Nordic and Labrador Seas spreads southward with the North Atlantic Deep Water.During transit to the Southern Ocean, the newly formed deep water is continuously subjected to the particle rain that originates from surface waters and which scavenges the 230 Th and 231 Pa continuously produced in the water column.When particles reach the depth of the newly formed deep water where the 230 Th and 231 Pa seawater concentrations are below steady-state concentrations dictated by scavenging, desorption from particles is enhanced and a fraction of the 230 Th and 231 Pa scavenged at shallower depths is released to the deep waters instead of being removed into the underlying sediments.Thus, the 230 Th and 231 Pa concentrations in newly formed deep waters gradually increase during transit to the southern ocean until the concentration at steady state with respect to scavenging is regained, at which point the water column profiles have relaxed back to linearity (Francois, 2007).The gradual relaxation of the profiles to linearity has been described for each isopycnal by adding a lateral transport term to the scavenging model, as first proposed by Rutgers van der Loeff and Berger (1993): Where i [X] t and [X] t are total 230 Th or 231 Pa concentration measured at two locations on the same isopycnal with i [X] t the concentration in the upstream source region and τ w is the "transit time" of water between these two sites.In deep waters, K (=[X] p /[X] t ) is nearly constant.Integrating the above equation thus gives: In the absence of circulation or mixing, and assuming a constant K, the reversible scavenging model predicts that ss [X] t =P X Z/SK, where ss [X] t is the total concentration of 230 Th or 231 Pa in seawater at steady state with respect to scavenging.Z/SK is thus the residence time with respect to addition by uranium decay and removal by scavenging when the profile has regained linearity (i.e. when it has regained steady state with respect scavenging), defined as τ ss = ss [X] t /P X .Therefore, τ ss =Z/SK and: Equation ( 9) predicts that the radioisotope profiles relax back to linearity more slowly with increasing τ ss and therefore water depth.Profile linearity is thus regained closer to the source at shallower depths, and 230 Th regains linearity faster than 231 Pa because of its shorter τ ss .The shapes of the 230 Th profiles measured in the Atlantic are in agreement with this simple conceptual model and are also reproduced in the control run (Figs. 5 and 6).The seawater data show clearly the gradual southward relaxation of the profiles towards linearity.Linearity is regained faster for 230 Th and at shallower depths.We also note that the profiles from the western Atlantic display a greater deficit farther south, reflecting the stronger ventilation of the western Atlantic basins.The profiles obtained from the model (Figs.5c and 6c) show similar trends with dissolved 230 Th and 231 Pa concentrations close to those observed in the ocean.Further south, where the deep waters start to upwell, their relatively high 230 Th concentrations exceed the concentrations predicted by the scavenging model in the absence of circulation, resulting in convex dissolved profiles (Francois, 2007).This is again clearly seen in measured seawater profiles (Rutgers van der Loeff and Berger, 1993) and model results (Fig. 7a).This trend is less apparent for 231 Pa (Fig. 7b)   Anderson et al., 1983;Walter et al., 1997;Moran et al., 2002).These measured values are generally viewed as being mostly controlled by particle composition, with opal having a much lower F than the other major constituents of marine particles (Chase et al., 2002;Guo et al., 2002;Geibert and Usbeck, 2004).Our model reflects the generally accepted view that F is much lower in the opal dominated Southern Ocean than in the carbonate-dominated Atlantic Ocean and we chose adsorption and desorption rate constants to generate "equilibrium" fractionation factor broadly consistent with field observations (Table 3).The fractionation factor generated by the model using Eq. ( 4) indicates, however, that F is also significantly affected by the sinking rate of particles and ocean circulation (Fig. 8).This is because the chemical equilibrium between particles and seawater cannot be reached when particles sink through vertical dissolved 230 Th and 231 Pa concentration gradients.In the absence of circulation, we can rearrange Eqs.
If the two nuclides have identical desorption rate constants, F would be independent of sinking rates in the absence of circulation.However, if 1) then F calculated with sinking particles rises well above equilibrium values and gradually decreases towards the equilibrium value with depth (Fig. 8a).When particles sink through the Atlantic Meridional Overturning cell, the fractionation factors estimated from Eq. ( 4) drop below the equilibrium fractionation factor within the core of the NADW (Fig. 8b).The fractionation factors measured in the field are therefore not directly comparable to those derived from equilibrium absorption experiments conducted in the laboratory (e.g.Geibert and Usbeck, 2004;Guo et al., 2002).
In contrast to the F generated by our model, the fractionation factors measured by Moran et al. (2002) and Scholten et al. (2008) in the equatorial and southern Atlantic increase with depth down to ∼1500 m and stay roughly constant or decrease further down.Also, the natural variability in F is much larger than the range observed in our model.The reason for this discrepancy could be depth variation in particle composition, a factor that is not taken into account in our model.Scholten et al. (2008) invoke a drop in the opal content of particles to explain the trend.However, the few available data on the composition of suspended particles (in the Sargasso Sea, Sherrell and Boyle, 1992; and in the North Pacific, Sherrell et al. 1998) do not show a clear trend with depth (except for one profile taken in spring 1991 in the North Pacific).Clearly, more data are needed before adding this variable in any model and this discrepancy must be left unresolved for now.

230 Th and 231 Pa distribution in the control run
Since our control run is broadly consistent with the limited water column data that are available, we can discuss the general distribution of 230 Th and 231 Pa generated by the model with some level of confidence.

Dissolved 230 Th
The model clearly generates the downward penetration of low dissolved 230 Th by deep convection in the high northern Atlantic (Fig. 9a).The horizontal isolines between 20 • N and 30 • S indicate however that the vertical dissolved 230 Th profiles quickly regain linearity, as is observed in the field data.South of 30 • S, dissolved 230 Th concentrations start to increase at all depths as a result of deep water upwelling (Fig. 2).The increase in dissolved 230 Th concentration is enhanced south of 50 • S by the lower adsorption rate constants imposed in this region to reflect the dominance of biogenic silica (Table 1), while the formation of AABW results in dissolved 230 Th maxima at intermediate depths, similar to observations (Fig. 7a).In surface water, dissolved 230 Th concentration is significantly higher in the southern ocean, as has been noted in field data (Rutgers van der Loeff and Berger, 1993;Walter et al., 2001;Chase et al. 2003)

Particulate 230 Th
The pattern of distribution of particulate 230 Th concentration (Fig. 9b) is similar to that of dissolved 230 Th.There is a conspicuous maximum in particulate 230 Th just north of the southern opal belt, which is a result of the increase in dissolved 230 Th concentration resulting from deep water upwelling.The sharp drop in particulate 230 Th further south is  a direct consequence of the lower K Th 1 in the southern ocean.Total 230 Th concentration profiles measured in the western (Table 2; Fig. 10) and eastern (Scholten et al., 2008) South Atlantic display a near bottom maximum similar to that generated by the model.This result may help explain the presence of a near-bottom maximum in total 230 Th when there is no clear evidence for the presence of a nepheloid layer (Scholten et al., 2008).However, our model generates these near-bottom maxima further south than observed, suggesting that a better representation of the AMOC in our model may require that the shoaling of the deep limb of the overturning cell starts further to the north.
The fraction of total 230 Th in particulate form generated by the model ([ 230 Th] p / [ 230 Th] t ) ranges from 0.18 to 0.22 at low latitude (Fig. 9c), which is also conforming to field observations (Bacon and Anderson, 1982;Moran et al., 2002).In the Southern Ocean below 1000m, the model produces somewhat lower fractions in particulate form (0.16-0.18), reflecting the lower affinity of biogenic silica for Th (Table 1).Somewhat higher fractions are generated in the upper water column of the Southern Ocean (0.22) and in the Nordic Sea (0.28) reflecting deep convection and longer residence time of particles in these waters.

Dissolved 231 Pa
As for dissolved 230 Th, the model produces a clear downward penetration of low dissolved 231 Pa by deep convection at high northern latitudes (Fig. 9d).However, following expectations and observations, the minimum associated with the core of the NADW propagates much further south, reaching the southern ocean.South of 30 • S, dissolved 231 Pa concentrations start to increase as a result of deep water upwelling but the effect is not as pronounced as for 230 Th because of the higher adsorption rate constants imposed in the southern ocean to reflect the dominance of biogenic silica (Table 1).Surface water dissolved 231 Pa concentrations are significantly higher in the southern ocean, but the effect is less pronounced than for 230 Th because of the higher scavenging rate of 231 Pa.

Particulate 231 Pa
The most prominent feature in the distribution of particulate 231 Pa concentration is the concentration maximum in the southern ocean (Fig. 9e), resulting from the higher K Pa 1 used in this region.The fraction of particulate 231 Pa generated by the model north of 45 • S remains uniform between 0.04 and 0.05 (Fig. 9f), in general agreement with observations (Moran et al., 2002), while the higher values generated in the southern ocean (0.16-0.20) are consistent with some of the extreme values reported by Rutgers van der Loeff and Berger (1993).Profiles of total 231 Pa generated in the south Atlantic in the model are intermediate between measurements made in the western and eastern side of the basin (Fig. 11).The lower concentrations measured in the western Atlantic suggest that the Deep Western Boundary Current rather than boundary scavenging plays a major role in controlling the distribution of 231 Pa in the water column of this region.The model also predicts that the highest ratios would be found in the surface water of the South Atlantic (Fig. 9g).2) and in the eastern South Atlantic (Scholten et al., 2008) compared to model results at 40°S.  2) and in the eastern South Atlantic (Scholten et al., 2008) compared to model results at 40 • S. Walter et al. (2001) report an increasing trend in surface water dissolved 231 Pa/ 230 Th from 0.5 to 2.0 between 65 • S and 40 • S (their Fig. 4c).However, water column profiles from the South Atlantic available to date (Moran et al., 2002) 2).
and 231 Pa concentrations are advected north.Since 230 Th is more quickly removed by scavenging, dissolved 231 Pa/ 230 Th initially increases to eventually decrease farther north as the scavenging of 231 Pa "catches up" with that of 230 Th.Evidently, the complexity of surface water movement in the South Atlantic cannot be fully captured in our simple 2-D model and these very high surface values may be artifacts of our simplified circulation.This question needs to be further explored with three dimensional models.

Particulate 231 Pa/ 230 Th
The distribution of particulate 231 Pa/ 230 Th generated by the model is shown in Fig. 9h.We can take these values as representing the 231 Pa/ 230 Th that sediments would have if they were deposited at a given depth and latitude.However, as mentioned when discussing the fractionation factors, settling particles in our model are not in chemical equilibrium with surrounding waters.When particles reach the seafloor, they could possibly come into equilibrium with bottom waters.Whether they do or not depends on how long they are in contact with bottom waters before burial as a result of sedimentation and bioturbation.With the rate constants used in our model, it would take 1-3 years (depending on initial conditions) for surface sediments to be within 95% of their equilibrium value with bottom waters.We can calculate sediment 231 Pa/ 230 Th at equilibrium with bottom waters using for 230 Th and 231 Pa (Fig. 9i).Partial equilibration would result in sediment 231 Pa/ 230 Th intermediate between values reported in Fig. 9h and i.The difference is relatively small in deep water but significantly larger in shallower waters.This is consistent with the observation of Scholten et al. (2008) who remarked that, at shallow depths, 231 Pa/ 230 Th in suspended particles are significantly lower than 231 Pa/ 230 Th in surface sediments (their Fig. 5) and suggest that surface sediments do reach equilibrium with bottom water.The distribution of particulate (Fig. 9h) and sediment (Fig. 9i) 231 Pa/ 230 Th generated by the model is clearly controlled both by circulation and particle composition.We find the lowest values near the base of the two overturning cells just downstream of the sites of deep water formation and the highest values in the Southern Ocean.The low values are clearly generated by the overturning circulation cells, while the high values in the southern ocean are a direct consequence of the particle composition.
Sediment 231 Pa/ 230 Th generally decreases with depth, a pattern dictated by trends in dissolved 231 Pa/ 230 Th which is generated by the overturning circulation.A similar decreasing trend from ∼0.13 at ∼1000 m to ∼0.04 at ∼5000 m has been reported by Scholten et al. (2008) for surface sediments in the South Atlantic.Holocene 231 Pa/ 230 Th from the five North Atlantic cores discussed by Gherardi et al. (2009) also show a similar trend, with values approaching the production rate ratios for the two shallower cores and lower values for the three deeper cores (Table 4).Values reported for core tops from the Nordic Seas range from 0.07 to 0.09 (Yu et al., 1996).Our model generates these values with an equilibrum fractionation factor of 7.8, somewhat higher than the fractionation factors measured in the Labrador Sea (3-7; Moran et al., 2002).Significantly higher sediment 231 Pa/ 230 Th have been reported, however, just south of Iceland and the Denmark Strait (0.10-0.15;Yu et al., 1996;R. F. Anderson, personal communication, 2009) but they are generally found in sediments deposited between 1500 m and 2000 m water depth and seems confined to a relatively small area where Leinen et al. (1986) report opal concentration (carbonate-free wt %) of up to 20%.With the fractionation factors reported in Table 3 and Fig. 8, our model generates sediment 231 Pa/ 230 Th below the production rate ratio at this depth range just south of the site of deep water formation (Fig. 9i).The model generates the high values reported in this region only if we lower the equilibrium fractionation factor to 3.9 (Fig. 13).

The effect of AMOC on sediment 231 Pa/ 230 Th
In the absence of any circulation, the model generates a field of constant sediment 231 Pa/ 230 Th equal to the production rate ratio (0.092).In this case, changes in the fractionation factor (Table 3) produce changes in the dissolved 230 Th and 231 Pa fields but not in the particulate fields.The distribution of particulate and sediment 231 Pa/ 230 Th reported in Fig. 9h, i should thus provide information on the ocean overturning circulation.The model results clearly indicate, however, that the relationship between sediment 231 Pa/ 230 Th at any given site and the overturning circulation is very complex, as was also noted by Siddall et al. (2007).Sediment 231 Pa/ 230 Th depends not only on the rate of the overturning and particle scavenging, but also on the detailed geometry of the overturning cell and the distance between the coring site and the site of deep water formation.Sediment 231 Pa/ 230 Th reaches a minimum at a depth dictated by the geometry of the overturning cell and at latitude dictated by the position of the site of deep water formation and the strength of the overturning circulation (Fig. 14).Clearly, it is impossible to constrain the history of changes in the AMOC from the evolution of 231 Pa/ 230 Th at one site, as was attempted by McManus et al. (2004).According to Eq. ( 9), the 231 Pa profiles relax back to linearity at a rate that decreases with τ ss (the residence time with respect to addition by uranium decay and removal by scavenging in the absence of circulation or mixing), which is proportional to water depth.Therefore, if the rate of lateral volume transport were the same at all depths, the fraction of the 231 Pa production that is laterally transported with the water would increase with depth.This effect contributes to the general decrease with depth in dissolved and particulate 231 Pa/ 230 Th generated by the model (Fig. 9g-i) and measured in sediments (Table 4).Very little 231 Pa can be laterally exported by circulation at shallow depths but an increasing   Latitudinal changes in sediment 231 Pa/ 230 Th at the depth where the minimum ratio is reached documents an initial decrease with distance from the site of deep water formation, followed by an increase (Fig. 14c).Dissolved 230 Th and 231 Pa concentrations are low throughout the water column at the site of deep water formation (Fig. 4).Because of its shorter τ ss , 230 Th concentration increases faster to reach its steady-state concentration with respect to scavenging (Eq.9), thereby gradually decreasing dissolved, particulate and sediment 231 Pa/ 230 Th.Once dissolved 230 Th has reached its maximum value, the slower increase in dissolved 231 Pa results is a slow increase in 231 Pa/ 230 Th further downstream.5) the largest decrease in sediment 231 Pa/ 230 Th downstream of the deep water formation zone is found in the Southern and equatorial region (Fig. 14c).Even without changing the geometry of the overturning cell and particle scavenging, the same value of sediment 231 Pa/ 230 Th can be generated at one site by different rates of overturning.For instance, the same value of 0.052 is produced at latitude 36.25 • N at 3635 m with overturning rates of 10.25 Sv and 30.75 Sv (Fig. 14c).This observation reinforces the fact that sediment 231 Pa/ 230 Th at one site cannot constrain uniquely the rate of the AMOC.these simple systematic trends can be reproduced in more complex circulation models, however, still needs to be verified.16).The process whereby AABW is producing these low sediment 231 Pa/ 230 Th is the same as for the northern overturning cell but the effect is found at greater depth and is less pronounced because of the smaller flow of water involved and the higher initial dissolved 230    As already indicated above, in the presence of circulation and/or mixing, localized changes in particle composition and fractionation factors produce dramatic but localized changes in sediment 231 Pa/ 230 Th (Fig. 13).Such changes can be taken into account by analyzing the opal content of the sediment from which the 231 Pa/ 230 Th record is obtained (Gherardi et al., 2009) with, however, one important caveat.Opal is undersaturated throughout the ocean and much of it dissolves before burial.Below a certain threshold in opal flux and sediment mass accumulation rates, opal is not preserved in sediments but the 231 Pa/ 230 Th generated by the presence of opal in sinking particles could persist.We could further address this question by using a diagenetic model (e.g.Khalil et al., 2007) to estimate the opal concentration in sinking particles reaching the seafloor from sediment mass accumulation rates and use this information to estimate the range of possible fractionation factors to be applied at this site using the sediment trap data compilation of Chase et al. (2003).However, distinguishing between the importance of changes in circulation and opal flux will eventually be best addressed by generating a database large enough to obtain a near-synoptic view of the spatial distribution of sediment 231 Pa/ 230 Th for each time slice of interest, since the distribution generated by the overturning circulation is clearly distinct from the distribution generated by the distribution of opal productivity in the ocean.While Fig. 13 clearly demonstrates the potential impact of localized variations in fractionation factors, it also shows, and maybe more importantly, that such changes in the North Atlantic have little impact on the 231 Pa/ 230 Th deposited downstream ( 231 Pa/ 230 Th<0.002;Fig. 13b).This is however not the case when we change the fractionation factor in the Southern Ocean (Fig. 17  fractionation factor in the Southern ocean from 0.9 to 1.8 not only decreases sediment 231 Pa/ 230 Th in the Southern Ocean from ∼0.3 to ∼0.2 but also uniformly increases sediment 231 Pa/ 230 Th along the latitudinal transect of the Atlantic by nearly ∼0.01.Reducing the fractionation factor increases the Southern Ocean 231 Pa sink and decreases 231 Pa/ 230 Th in the Atlantic.However, the slope of the latitudinal gradient of sediment 231 Pa/ 230 Th in the Atlantic is not significantly affected and could still be used to constrain the rate of the overturning.Nonetheless, accurately assessing the extent of the southern ocean 231 Pa sink will be important to evaluate the rate of AMOC.

Conclusions
We have developed a simple 2-D scavenging model to address some of the questions that have been raised concerning the use of sediment 231 Pa/ 230 Th as a paleocirculation tracer (Keigwin and Boyle, 2008;Scholten et al., 2008;Lippold et al., 2009).Although our circulation model is clearly too simple to capture all the complexity of ocean circulation, it reproduces many of the features observed in the distribution of dissolved 230 Th and 231 Pa and sediment 231 Pa/ 230 Th and provides a tool to start assessing the relative importance of circulation and particle scavenging in controlling the distribution pattern of sediment 231 Pa/ 230 Th in the Atlantic.
The circulation scheme imposed in our model broadly reflects the flow of the main deep Atlantic water masses (NADW, AABW).The detailed geometry of the two overturning cells and the parameters of the imbedded scavenging model have been tuned to reproduce the broad features of the distribution of dissolved 230 Th and 231 Pa and fractionation factors measured in the water column to date.The model produces a general decrease in dissolved, particulate and sediment 231 Pa/ 230 Th with depth, which is consistent with field observations (Fig. 12; Scholten et al., 2008;Gherardi et al., 2009).It also produces patterns in the distribution of sediment 231 Pa/ 230 Th which could be used to distinguish the circulation signal from the effect of particle scavenging.The model output also suggests sampling strategies to optimize the information in past circulation that could be derived from sediment 231 Pa/ 230 Th.The most robust circulation signals generated by the model are the vertical and horizontal sediment 231 Pa/ 230 Th gradients, which changes systematically with the rate and geometry of the AMOC (Figs. 14,15).However, we still need to establish whether these diagnostic trends can also be produced with more complex 3-D circulation models.
We have used our 2-D model to test the extent to which changes in fractionation factor can obliterate the patterns of sediment 231 Pa/ 230 Th generated by the overturning circulation.While it is clear that changes in particle composition in the North Atlantic can change sediment 231 Pa/ 230 Th locally, our model indicates that the 231 Pa/ 230 Th pattern generated by circulation further downstream is not significantly affected.This may be different for the Southern Ocean, which is the main sink for 231 Pa in our model.Changing the fractionation factor in the Southern Ocean offsets 231 Pa/ 230 Th but has little impact on the gradients below 1500 m, and the information on the rate and geometry of the overturning circulation is still preserved.
Our 2-D model largely corroborates the results from the 1-D model of Thomas et al. (2006) and indicates that the sediment 231 Pa/ 230 Th signal is rapidly attenuated in sediment deposited below the base of the overturning cell.Finally, low sediment 231 Pa/ 230 Th in the South Atlantic (Scholten et al., 2008) appears to be due to the formation of AABW, which suggest that the 231 Pa/ 230 Th sedimentary record in this region, just north of the zone influenced by biogenic silica, could be used to constrain past changes in the rate of formation of this water mass.

Fig 1
Fig 1 The scavenging model consists of a meridional section (from 70°N to 70°S)

Fig 2 .
Fig 2. (a)Velocity vector plot.Size of the arrows is proportional to the transport rates used in the model.(b) Overturning fluxes in the model at the equator.

Fig. 2 .
Fig. 2. (a) Velocity vector plot.Size of the arrows is proportional to the transport rates used in the model.(b) Overturning fluxes in the model at the equator.

3
Fig. 3: Station locations for the water column profiles used to constrain the paramete in the model.Nordic Seas: N-A, N-B, N-C(Moran et al. 1995; 1997; 2002); Western
230 Th and 231 Pa concentrations versus depth

Fig. 5 .
Fig. 5. Dissolved 230 Th measured (a) in the western Atlantic, (b) in the eastern Atlantic, and (c) produced with the control run.

Fig. 6 .
Fig. 6.Dissolved 231 Pa measured (a) in the western Atlantic, (b) in the eastern Atlantic, and (c) produced with the control run.

Fig. 7 :Fig. 7 :
Fig. 7: Concentration profiles of dissolved 230 Th and 231 Pa measured (Rutgers van der Loeff and Berger, 1993) and modeled (control run) in the southern ocean

Fig. 8 :
Fig. 8: Distribution of fractionation factors: (a) obtained in our model with sinking particles but without circulation (b) obtained with sinking particles in the control run with AMOC (NADW: 21.5 Sv; AABW: 8 Sv).Note that sinking rates and circulation significantly affect the fractionation factor defined as ( 231 Pad/ 230 Thd)/( 231 Pap/230Thp) [see text for explanation].

Fig. 8 .
Fig. 8. Distribution of fractionation factors: (a) obtained in our model with sinking particles but without circulation (b) obtained with sinking particles in the control run with AMOC (NADW: 21.5 Sv; AABW: 8 Sv).Note that sinking rates and circulation significantly affect the fractionation factor defined as ( 231 Pa d / 230 Th d )/( 231 Pa p / 230 Th p ) (see text for explanation).

Fig. 9c .
Fig. 9c.Fraction of total 230 Th associated with particles generated by the model.

Fig. 9f .
Fig. 9f.Fraction of total 231 Pa associated with particles generated by the model.

Fig. 9i .
Fig. 9i.Sediment 231 Pa/ 230 Th section generated by the model assuming that sediment reach equilibrium with bottom water (see text for explanations).

Fig. 10 :
Fig. 10: Total 230 Th concentration measured in the Southwestern Atlantic at 29°32'S; 43°20'W (Station KNR06-3; Table2) showing a near-bottom maximum similar to that generated in the South Atlantic by our model.

6
Sediment 231 Pa/ 230 Th: data-model comparison In this section, we compare the distribution of sediment 231 Pa/ 230 Th generated by the model with 231 Pa/ 230 Th measured in Atlantic sediments as a test for further validation.
The use of sediment231 Pa/ 230 Th to reconstruct past changes in the AMOC relies on the longer residence time of 231 Pa in the water column.While the short residence time of230 Th severely limits the extent to which it can be laterally transported after its production by uranium decay, the longer residence time of 231 Pa results in its extensive redistribution by ocean circulation.

Figure 13 :
Figure 13: (a) Sediment 231 Pa/ 230 Th generated with an opal belt just south of the site of deep water formation.(b) Difference in the sediment 231 Pa/ 230 Th field generated in with and without the northern opal belt

Fig. 13 .
Fig. 13.(a) Sediment 231 Pa/ 230 Th generated with an opal belt just south of the site of deep water formation.(b) Difference in the sediment 231 Pa/ 230 Th field generated in with and without the northern opal belt.

Fig. 14 .
Fig. 14.(a) Lateral velocity profile in the control run between 60 • N and 35 • N. (b) Vertical sediment 231 Pa/ 230 Th bathymetric profiles generated by the model at different rates of overturning and at the latitude where the lowest sediment 231 Pa/ 230 Th is found.(c) Latitudinal sediment 231 Pa/ 230 Th profiles for different rates of overturning at the depth where the lowest sediment 231 Pa/ 230 Th is found (3625 m) (red symbols represent the lowest depth of maximum lateral velocity (a), minimum 231 Pa/ 230 Th (i.e. the depth for the latitudinal profiles) (b) and latitude of minimal 231 Pa/ 230 Th (i.e. the latitudes for the vertical profiles) c).
Increasing the rate of overturning in the control run without changing the geometry of the overturning cell has several effects on the distribution of Atlantic sediment 231 Pa/ 230 Th:(1) it pushes the zone of minimum 231 Pa/ 230 Th farther away from the site of deep water formation (Fig.14c);(2) the lati-tudinal minimum in sediment 231 Pa/ 230 Th does not decrease, but instead increases (Fig.14b, c) (3) sediment 231 Pa/ 230 Th also increases at the site of deep water formation and directly south of it (Fig.14c); (4) the vertical gradient of sediment 231 Pa/ 230 Th at the latitude corresponding to the minimum sediment 231 Pa/ 230 Th increases (Fig.14b); ( Fig. 15: (a) Contrasting lateral velocity profiles between the control run (20.5 Sv), the overturning profiles from the ECCO consortium (14 Sv; Wunsch and Heimbach, 2006) and an arbitrary shallower overturning cell (20.5 Sv).(b) Vertical sediment 231 Pa/ 230 Th bathymetric profiles generated by the three overturning profiles at the latitude where the lowest sediment 231 Pa/ 230 Th is found.(c) Latitudinal sediment 231 Pa/ 230 Th profiles generated by the three overturning cells at the depth where the lowest sediment 231 Pa/ 230 Th is found.[Red symbols represent the lowest depth of maximum lateral velocity or the base of the shallow overturning cell (a), minimum 231 Pa/ 230 Th (i.e. the depth for the latitudinal profiles) (b) and latitude of minimal 231 Pa/ 230 Th (i.e. the latitudes for the vertical profiles) (c)]

Fig. 15 .
Fig. 15.(a) Contrasting lateral velocity profiles between the control run (20.5 Sv), the overturning profiles from the ECCO consortium (14 Sv; Wunsch and Heimbach, 2006) and an arbitrary shallower overturning cell (20.5 Sv).(b) Vertical sediment 231 Pa/ 230 Th bathymetric profiles generated by the three overturning profiles at the latitude where the lowest sediment 231 Pa/ 230 Th is found.(c) Latitudinal sediment 231 Pa/ 230 Th profiles generated by the three overturning cells at the depth where the lowest sediment 231 Pa/ 230 Th is found (red symbols represent the lowest depth of maximum lateral velocity or the base of the shallow overturning cell (a), minimum 231 Pa/ 230 Th (i.e. the depth for the latitudinal profiles) (b) and latitude of minimal 231 Pa/ 230 Th (i.e. the latitudes for the vertical profiles) (c)).
Figure9iclearly indicates that the overturning cell initiated in the Southern Ocean by the formation of AABW significantly contributes to lowering sediment 231 Pa/ 230 Th in the South Atlantic.If we eliminate the formation of AABW, sediment231 Pa/ 230 Th in the South Atlantic significantly increases (Fig.16).The process whereby AABW is producing these low sediment 231 Pa/ 230 Th is the same as for the northern overturning cell but the effect is found at greater depth and is less pronounced because of the smaller flow of water involved and the higher initial dissolved 230 Th and 231 Pa in the water that generates AABW.The low sediment 231 Pa/ 230 Th (<0.05) in the deep Southeast Atlantic(Scholten et al., 2008) are consistent with the importance of AABW in generating low 231 Pa/ 230 Th in the South Atlantic and suggest that sedimentary records in this region, if unaffected by changes in opal flux, could generate important constraints on variations in the rate of formation of this important water mass.

Fig. 16 .
Fig. 16.Sediment 231 Pa/ 230 Th field generated in the control run without formation of AABW.
Fig. 17: The influence of Southern Ocean fractionation factor on the sediment 231 Pa/ 230 Th in Atlantic sediments.(a) Lateral velocity field used to conduct the experiments.(b) Vertical sediment 231 Pa/ 230 Th gradient generated by the control run (1xFF) and when the Southern ocean equilibrium fractionation factor (FF = 0.9) is doubled (2xFF) or halved (0.5xFF).(c) Sediment 231 Pa/ 230 Th produced in the North Atlantic and the Southern Ocean under these three scenarios.

Fig. 17 .
Fig. 17.The influence of Southern Ocean fractionation factor on the sediment 231 Pa/ 230 Th in Atlantic sediments.(a) Lateral velocity field used to conduct the experiments.(b) Vertical sediment 231 Pa/ 230 Th gradient generated by the control run (1•F F ) and when the Southern ocean equilibrium fractionation factor (F F = 0.9) is doubled (2 • F F ) or halved (0.5 • F F ). (c) Sediment 231 Pa/ 230 Th produced in the North Atlantic and the Southern Ocean under these three scenarios.

Table 1 .
List of abbreviations and values for the model parameters.
Dissolved 231 Pa/ 230 Th profiles measured at 9 stations in the North and Equatorial Atlantic (Table2).
fail to document the predicted large ratios in surface water.High ratios are generated in our model because surface waters from the southern ocean with relatively high dissolved 230 Th www.ocean-sci.net/6/381/2010/Ocean Sci., 6, 381-400, 2010 OS-2009-78-revised.doc48 Figure 12:
(Scholten et al., 2008)ter that generates AABW.The low sediment 231 Pa/ 230 Th (<0.05) in the deep Southeast Atlantic(Scholten et al., 2008)are consistent with the importance of AABW in generating low 231 Pa/ 230 Th in the South Atlantic and suggest that sedimentary records in this region, if unaffected by changes in opal flux, could generate important constraints on variations in the rate of formation of this important water mass. OS-2009-78-revised.doc