Oceanic circulation and the carbon cycle play a major role in the regulation of the past and present climate. Heat and carbon dioxide in the atmosphere tend to equilibrate with the ocean surface and are transported down into the deep ocean through the Meridional Overturning Circulation (MOC). Biogeochemical cycling also generates organic carbon that transfers into the deep ocean through particle sinking. Because of this, the strength of the MOC and particle removal participate actively in the regulation of the climate on the Earth.

Trace elements are also affected by these mechanisms and represent useful tools to provide constraints on these processes. The GEOTRACES programme has generated a large unique dataset that can now be used to better understand biogeochemical oceanic processes. Modelling quantifies and provides more information on the processes that control the oceanic distribution of these new observations. In present day climate, it is difficult to measure the MOC strength, and for past climate there are no measurements available at all. Isotopes and trace elements from sediment cores are used as proxies to infer past ocean circulation. Several examples include carbon isotopes , the cadmium/calcium ratio , the ratio between protactinium-231 and thorium-230 (231Pa/230Th) , and the neodymium isotope ratio 143Nd/144Nd . These proxies are affected by dynamical and biogeochemical processes. Including these proxies in a climate model is a way to better understand the climatic signal they register.

We will focus on 230Th and 231Pa because these isotopes are well documented by the international GEOTRACES programme, and they are particularly suitable to study the transfer of particulate matter since the isotopes' source in the ocean is perfectly known: radioactive decay of uranium isotopes. Others have modelled 143Nd and 144Nd , 13C , and 14C . The ratio between 230Th and 231Pa is used as a proxy for past ocean conditions, but this signal is potentially affected by both circulation and biogeochemical changes. Therefore, a correct understanding of the scavenging and underlying particle dynamics is essential in order to better simulate these tracers .

Protactinium-231 and thorium-230 are produced in the ocean by the α decay of uranium-235 and uranium-234, respectively. Because the activity of uranium is approximately uniform in the ocean, 231Pa and 230Th are produced at a relatively constant rate (βPa=2.33×10-3 dpmm-3yr-1 and βTh=2.52×10-2 dpmm-3yr-1; dpm: disintegrations per minute) . They are both scavenged rapidly by the many particles that reside in the ocean and settle towards the sea floor. 231Pa is less sensitive to particle scavenging than 230Th, which is reflected in the longer residence time of 231Pa (80–200 yr) compared to that of 230Th (20–40 yr) . 231Pa and 230Th are radioactive, decaying to radium isotopes and having a half-life of 32.76 and 75.40 kyr, respectively. Each combination of particle–radionuclide adsorption has a different reactivity. Other factors may affect the adsorption of radionuclides onto particles. For example, smaller particles have larger surface area to volume ratios, which results in an increase in the number of these radionuclides adsorbed per particle. Additionally, while the adsorption rate is expected to increase with particle concentration, the adsorption rate may be partly limited by the coagulation of non-filtered particles (or colloids) to filtered particles . The vertical distributions of natural radionuclides, such as 230Th and 231Pa, are hence sensitive to the distribution and mixture of particles. As a consequence of the different particle reactivities of 230Th and 231Pa, the dissolved concentration ratio 231Pa/230Th deviates from the production activity ratio of 0.093 .

As both particle dynamics and circulation of the ocean affect 230Th and 231Pa, numerical biogeochemical general circulation models are used to study the relative contribution of these mechanisms. The isotopes have been simulated in models of intermediate complexity, for instance by (LSG-OGCM), (EMIC 2.5D), (HAMOCC) and . More complex ocean general circulation models have also been used to simulate these tracers, namely by (NEMO–PISCES), , (Bern3D), and (CESM). demonstrated that the particle concentration simulated by the PISCES model in the deep ocean was too low by a factor of 2 in the mesopelagic zone to 50 in the deepest ocean. This led to overestimated radionuclide concentrations in the deep ocean. Therefore, it is crucial to improve the representation of the particles . showed that taking into account additional sinks at the sea floor and at the ocean margins yields an improved agreement with observations, especially for the dissolved phases of 230Th and 231Pa. Particulate ratios improved to a lesser extent; the authors have not presented an evaluation of their simulated particulate concentrations. had similar goals as this study.

In this study, we try to improve on previous studies that simulate the distribution of 230Th and 231Pa. Our approach is to improve the mechanistic description of the particle and radionuclide cycling, as well as on the side of system design and reusability of the model. We evaluate how well the model fits with observations, but tuning is not one of our main goals. Just like , we use the NEMO–OPA (Nucleus for European Modelling of the Ocean – Océan PAralelisé) ocean general circulation model and the PISCES biogeochemical model . showed that dissolution rates of particulate organic carbon (POC) in PISCES were overestimated, and they improved on this by introducing a spectrum of different labilities. This improved the simulation of both small and big POC significantly, so we use this same model for our simulations. There are several improvements since ; namely, the new model

includes lithogenic particles from dust deposition;

New observations are available from the GEOTRACES programme. Especially the North Atlantic GA03 transects will be used for model validation because on this transect not only dissolved 230Th and 231Pa have been measured , but also their adsorbed forms and biogenic and lithogenic particle concentrations in two size classes .

In order to simulate the biogenic particle dynamics and their interaction with the 230Th and 231Pa trace isotopes, we use the biogeochemical circulation model NEMO–PISCES . This model has been employed for many other studies concerning trace metals, as well as large-scale ocean biogeochemistry e.g.. We force PISCES by a climatological year of circulation fields (including turbulent diffusion) that was obtained from the dynamical component of NEMO. Table  gives an overview of this and other components of the model and their relevant properties.

All model fields are defined on the ORCA2 discrete coordinate system, an irregular grid covering the whole world ocean with a nominal resolution of 2∘×2∘, with an increased resolution in the meridional direction near the Equator and Antarctica and in both horizontal directions in the Mediterranean, Red, Black and Caspian seas. On the Northern Hemisphere, it has two coordinate singularities, one in Canada and the other in Russia, such that both singularities fall outside the computational domain. The vertical resolution of the ORCA2 grid is 10 m in the upper 100 m, increasing downwards to 500 m such that there are 30 layers in total and the ocean has a maximum depth of 5000 m . The time step of the model is 6 h for the dynamics and the radionuclides and 1.5 h for the biogeochemistry (PISCES) and the lithogenic particles. When necessary, sub-time stepping is done for all sinking components in the model.

For the numerical simulations, we forced the just described model, an adjusted version of PISCES with lithogenic particles and radiotracers, with the off-line circulation fields. The model was spun up for 500 years, after which it was in an approximate steady state (decadal drift of -0.002 % for total 230Th and +0.058 % for total 231Pa). Protactinium-231 has a larger drift than thorium-230 because 230Th is more quickly removed everywhere in the ocean because of its high particle reactivity. The lithogenic particles are in a steady state, and the PISCES variables are in an approximate steady state (e.g. phosphate shows a drift of -0.005 % per decade).

The partition coefficients Kij, with i∈{Th,Pa}, depend on the type of particle j and are given in Table .

These coefficients still have large uncertainties, but their values can be constrained by reported values from different experimental studies e.g.. Therefore, we had quite some freedom in prescribing values. The adsorption onto calcium carbonate is a factor of 2 decreased from . This brings the K value of Pa closer to that in based on field measurements, namely 0.9±0.4 Mgg-1 (106 g of seawater per gram of particles), but since we maintained the ratio of K values, the partition coefficient of Th is much smaller than found by . It is consistent with the laboratory results of , but they cleaned the biogenic silica aggressively, bought carbonate that should be organic-free and clay (smectite) was purchased as a commercial standard and not cleaned (; and Walter Geibert, personal communication, January 2018). In the real ocean, solid minerals are not clean but have organic matter around them, giving rise to increased scavenging for diatoms. Therefore, our K values for at least biogenic silica and calcium carbonate may be lower than what is typically considered realistic. The actual reason for the relatively low K values is that we only have fast-sinking biogenic silica and calcium carbonate particles in the model that also represent smaller particles that sink slower. Thus using higher K values would result in too much export of Pa and Th. For small lithogenic particles, K is set about a factor of 5 larger than in the literature , whereas big lithogenic particles have a smaller value than reported in the literature. The Supplement contains a more exhaustive table of information, including an estimated literature range (Table S3). The consequences of the chosen values for the partition coefficients are discussed further in Sect. .

In this study, we will focus on the GEOTRACES GA03 transect in the North Atlantic Ocean. Recently, a large number of measurements on both radionuclides and their carrier particles have been collected on this transect. This unique combination makes it especially useful to evaluate a radionuclide scavenging model. We will also compare our global ocean model with several observational datasets throughout the ocean (Table ). Observations obtained from the GEOTRACES programme are denoted with the respective GEOTRACES transect number .

For the carrier particles most of our data come from , which is a recent GEOTRACES dataset at the GA03 transect in the North Atlantic Ocean. An older compilation of particles is taken from . We use some older data as well (Table ). Particle concentrations were determined by filtering seawater in situ.

Concentrations of both dissolved and particulate phases of 230Th and 231Pa were taken from (GA03) and (Pacific Ocean). Other data are listed in Table .

To evaluate the sediment 231Pa/230Th flux of the model, we will compare with compilations of the Holocene (i.e. top core particulate concentrations) (Table ).

We succeed in generating the global patterns of the dissolved nuclide concentrations. However, we underestimate radioactivities in the surface waters (Figs. a and a). This shortcoming may be due to the instant equilibration between the dissolved and the adsorbed phases . After the decay of U into 231Pa and 230Th, the tracers instantly adsorb onto the particles in the surface ocean and are exported from the mixed layer. The equilibrium scavenging approach is commonly used in Pa/Th modelling . It allows the model to use partition coefficients that can be directly constrained by observations (although consensus values for these coefficients are still not available). A non-equilibrium approach to scavenging could be considered, but it would necessitate the use of adsorption and desorption coefficients (k+, k-) that are currently very poorly constrained by observations. Observations shows equilibrium partition coefficient K values varying (decreasing) with particle flux , and we apply these in our simulation (i.e. lower K values for large, fast-sinking particles). This parameterisation produces effects that are similar to those of a non-equilibrium system for fast-sinking particles.

The reversible scavenging model uses partition coefficients Kij for the different isotopes i and particles j. Many studies provide constraints on these coefficients but estimates vary strongly between different studies. Small particles are the most important scavengers and largely control the shape of the vertical profile of the tracers . This also shows from sedimentary isotope records . This is explained by the specific surface of small particles, which is larger than that of big particles. Therefore, higher adsorption values are set for small particles compared to the bigger particles of the same type (namely, 5 times higher for POC and 10 times higher for lithogenic particles). Compared to , we succeed in simulating the tracer concentrations using reasonable K values. This is due to improvement in (especially small) particle concentrations, which were generated with the lability parameterisation of POC , the change in the CaCO3 dissolution parameterisation and the addition of lithogenic dust in our ocean model. This shows that at least two particle size classes are needed to simulate dissolved and particulate thorium and protactinium. Our model does not include small particles for all types (there are neither small CaCO3 nor small bSiO2 particles), even though we expect that better results can be reached upon adding those particles akin to small POC and small lithogenic particles.

On the GA02 transect, the correlation coefficient r of the data–model comparison of [230Th]D is 0.80, which is close to what was reported by in their simulations without bottom-boundary scavenging. On the GA03 section, r=0.78. The correlations between the model and observations are presented as scatter plots (Supplement Fig. S2).

There are a couple of interesting features to note on the comparisons. Firstly, the hydrothermal plume over the ridge results in 230Th-poor seawater that is not reproduced by the model (red triangle in Fig. S2, GA03). Secondly, in the western boundary currents, very low dissolved 230Th concentrations are observed due to strong nepheloids and/or possibly strong deep ventilation from the north. Neither of these processes is represented in the model. The lack of nepheloids has an especially large impact on the GA02 transect, which has a relatively large number of measured profiles near the western boundary. Finally, between 32 and 20∘ W, the model tends to underestimate 230Th. The value of the correlation index is not that important because the goal of this study is not to give a perfect model–data comparison.

The provided dust flux does not distinguish between different dust particle sizes or types. Furthermore, dust deposition is uncertain; therefore, we chose a dust flux that was available to the ORCA2 configuration of NEMO, and its biogeochemistry has been tested with that dust flux. However, given the significant impact of dust particles on thorium and protactinium concentrations, it would be useful to look into the effect of different dust deposition fields and using different dust particle size classes. A good model of 230Th (and other isotopes of thorium) could even constrain the sporadic and uncertain dust deposition, but all this falls outside the scope of the present study.

Our model adds 80 % of the dust deposition into the fast-sinking lithogenic particle compartment (corresponding to ∅>51 µm), and only 20 % goes into the slowly sinking compartment (corresponding to ∅≤51 µm). This is necessary to reproduce the distributions of lithogenic particles. However, airborne dust particles typically have a diameter smaller than 20 µm and thus fall clearly within the small size class of less than 50 µm. Recently, there have been observations of aerosols larger than 20 µm , but they do not reach far enough into the atmosphere above the open ocean to explain the high concentration of big lithogenic ocean particles. The explanation for the apparently required high fraction of big lithogenic particles is that smaller aerosols aggregate in the upper layers of the ocean. Moreover, though more hypothetically, there may be strong aggregation with biogenic particles just below the surface, below which the aggregates partly disaggregate again to result in the ∼0.2 big lithogenic fraction in the deep ocean (Fig. f).

The underestimation of lithogenic particle concentrations at the western boundary is expected. The reason is that we only have dust deposition as a source of lithogenic particles, whereas nepheloid layers are not included. Nepheloid layers are at least locally an important source of lithogenic (and biogenic) particles . With the transport of 230Th and 231Pa through the western boundary current, a significant portion may be scavenged. Moreover, the periodic transport through the North Atlantic Gyre would result in lower [230Th]D and [231Pa]D throughout a large part of the North Atlantic Ocean, possibly improving the concentrations in the deep ocean. Therefore, it will be useful to include nepheloid layers in the future. We have not done this so far because we do not know how to model nepheloid layers. Except for trivial models, like the one of , who forced an additional constant scavenging rate in the bottom box of the ocean model, no large-scale prognostic nepheloid models have been developed.

We overestimate the radionuclide activity in the deep ocean, which is partly because we underestimate particle concentrations. Thorium adsorbs especially well onto lithogenic particles, which are underestimated in the western Atlantic Ocean (in the subsurface, west of about 43∘ W, Fig. e). Below 2 km of depth, POC is also underestimated (Fig. a), even though the lability parameterisation improved the distribution by over an order of magnitude compared to previous versions of PISCES . Small POC and the small lithogenic particles are the only small particles. The overall underestimation of small particles in the deep ocean results in an overestimation of the radionuclides in the deep ocean. In our simulation, [230Th]D is not that much overestimated (outside the Arctic Ocean). However, [231Pa]D is strongly overestimated in the deep Pacific and Atlantic Ocean.

Clearly the model does not remove 231Pa efficiently enough from the deep ocean (Figs. c, d, b and a). Two likely reasons may be that the waters are not well ventilated in the model (older than in reality) or that there is not enough scavenging. The Atlantic OSF (Fig. S1) shows that the upper overturning cell is too shallow compared to observational studies, so there is too little ventilation. This means that 231Pa can build up in the deep water due to sluggish ventilation of the physical model . Moreover, the AABW has weakened in the deep North Atlantic Ocean near the high [231Pa]D region (Fig. a), which may also contribute to the high dissolved 231Pa concentrations. The volume transport of the lower cell is about 6 Sv near 20∘ N and still 2 Sv near 40∘ N, which is in the order of magnitude of what is reported by the literature. Moreover, the relationship between sediment 231Pa/230Th at any given site and the overturning circulation is very complex. In general, any increased opportunity for protactinium to scavenge would increase the sedimentary 231Pa/230Th ratio. Specifically, a slower overturning would mean more Pa scavenging and a higher ratio “just downstream of the sites of deep water formation” . Similarly, relatively stronger scavenging of Pa means a higher sedimentary 231Pa/230Th, which we can see in the Southern Ocean and some coastal areas where the concentration of bSiO2 is high. For these reasons, it is not obvious whether the weak overturning is large enough to explain the discrepancy between the modelled and the observed [231Pa]D.

In reality, there are many regions in the North Atlantic Ocean where there is sediment resuspension and where there are nepheloid layers . This is consistent with the fact that our model underestimates lithogenic particle concentrations in the western Atlantic Ocean (Fig. e). The additional lithogenic particles would scavenge more 231Pa, resulting in lower [231Pa]D. Even though the enforced scavenging occurs near the floor and the western boundary of the ocean, a strong flux of water passes through the latter region and is transported through the North Atlantic Gyre and through the rest of the Atlantic, diluting high tracer concentrations. The small POC and lithogenic particles are now underestimated in much of the deep ocean. They would contribute to lower radio tracer concentrations as well. confirmed that an additional bottom sink affects 231Pa and 230Th significantly. They used a homogeneous extra scavenger in their model grid's bottom grid cell. Therefore, it would be worth testing if a realistic distribution of nepheloids would result in the right amount of scavenging.

Other particles may include resuspended (nepheloidal) biogenic particles, but also manganese and iron hydroxides that are not included in our model, and a smaller class of calcium carbonate and biogenic silica particles in addition to the big particle classes that are already in the model. Manganese oxides are especially available near hydrothermal vents, but also throughout the Pacific Ocean in low concentrations but much higher than in the Atlantic Ocean. Indeed, it has been argued that hydrothermal inputs may provide additional removal of 231Pa and 230Th , and recently this has been confirmed based on an analysis of the ∼10∘ S zonal GP16 transect in the Pacific Ocean .

Finally, the particle concentration effect should be taken into account in future models, particularly when regions of high particle concentration (e.g. ocean margins and nepheloid layers) are included.

The purpose of this study is two-fold. Firstly, we set out a model of 231Pa and 230Th, complete with all the necessary particle improvements and additions. This includes improved underlying particle dynamics from NEMO–PISCES and the addition of lithogenic particles. We have succeeded in this, and the model has been presented and implemented such that it can be used for future studies, including for the modelling and validation of ocean circulations in the past, present and future.

Secondly, this model helps us to study the interplay between the particle and water transport that controls the 231Pa and 230Th profiles. We have shown that, by improving on the particles, we improved the radionuclide distributions and fluxes. We have also shown to what extent the different particle phases drive the scavenging of 231Pa and 230Th.

Dissolved 230Th and 231Pa concentrations are realistic in the intermediate-depth ocean (big improvement compared to ) but not in the upper part of the ocean. A finite equilibration time between the different radionuclide phases may help. The model can be extended to include this in future versions. It would double the number of adsorption and desorption parameters whose values should be determined through a careful literature and model sensitivity study.

In the deep ocean, the overestimation of 230Th and 231Pa in several regions is likely to be caused, at least partly, by missing nepheloid particles, but manganese oxides (from hydrothermal vents) may also improve the distributions. Of course, reported adsorption and desorption parameters vary a lot between different studies, meaning that a different, yet still plausible, combination of partition coefficients could better describe the available data. Additionally, the circulation may be too weak, not freshening AABW fast enough, and hence 230Th and 231Pa concentrations become too high near the ocean floor.