**Model description paper**
10 Mar 2022

**Model description paper** | 10 Mar 2022

# Global simulation of dissolved ^{231}Pa and ^{230}Th in the ocean and the sedimentary ^{231}Pa∕^{230}Th ratios with the ocean general circulation model COCO ver4.0

^{231}Pa and

^{230}Th in the ocean and the sedimentary

^{231}Pa∕

^{230}Th ratios with the ocean general circulation model COCO ver4.0

Yusuke Sasaki, Hidetaka Kobayashi, and Akira Oka

**Yusuke Sasaki et al.**Yusuke Sasaki, Hidetaka Kobayashi, and Akira Oka

- Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan

- Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan

**Correspondence**: Akira Oka (akira@aori.u-tokyo.ac.jp)

**Correspondence**: Akira Oka (akira@aori.u-tokyo.ac.jp)

Received: 08 Jan 2021 – Discussion started: 06 May 2021 – Revised: 26 Jan 2022 – Accepted: 03 Feb 2022 – Published: 10 Mar 2022

Sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios provide clues to estimate
the strength of past ocean circulation. For its estimation, understanding
the processes controlling the distributions of ^{231}Pa and ^{230}Th in
the ocean is important. However, simulations of dissolved and particulate
^{231}Pa and ^{230}Th in the modern ocean, recently obtained from the
GEOTRACES project, remain challenging. Here we report a model simulation of
^{231}Pa and ^{230}Th in the global ocean with COCO ver4.0. Starting
from the basic water-column reversible scavenging model, we also introduced
the bottom scavenging and the dependence of scavenging efficiency on
particle concentration. As demonstrated in a previous study, the
incorporation of bottom scavenging improves the simulated distribution of
dissolved ^{231}Pa and ^{230}Th in the deep ocean, which has been
overestimated in models not considering the bottom scavenging. We further
demonstrate that introducing the dependence of scavenging efficiency on
particle concentration results in a high concentration of dissolved
^{230}Th in the Southern Ocean as observed in the GEOTRACES data. Our best
simulation can well reproduce not only the oceanic distribution of
^{231}Pa and ^{230}Th but also the sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios. Sensitivity analysis reveals that oceanic advection of ^{231}Pa
primarily determines sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. On the other
hand, ^{230}Th advection and bottom scavenging have an opposite effect to
^{231}Pa advection on the sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios,
reducing their latitudinal contrast. Our best simulation shows the realistic
residence times of ^{231}Pa and ^{230}Th, but simulation without bottom
scavenging and dependence of scavenging efficiency on particle concentration
significantly overestimates the residence times for both ^{231}Pa and
^{230}Th in spite of similar distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios to our best simulation.

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^{231}Pa and

^{230}Th in the ocean and the sedimentary

^{231}Pa∕

^{230}Th ratios with the ocean general circulation model COCO ver4.0, Geosci. Model Dev., 15, 2013–2033, https://doi.org/10.5194/gmd-15-2013-2022, 2022.

The ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in marine sediments are used for estimating
past ocean circulation strength (e.g., Yu et al., 1996; McManus et al.,
2004; Gherardi et al., 2009; Böhm et al., 2015; Waelbroeck et al., 2018;
Süfke et al., 2020). Alpha decay of ^{235}U and ^{234}U produces
^{231}Pa (half-life of ∼32.5 kyr) and ^{230}Th (half-life
of ∼75.2 kyr), respectively, at an approximately constant
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratio of 0.093 in the ocean (Henderson and Anderson,
2003). ^{231}Pa and ^{230}Th are absorbed onto and desorbed from the
surfaces of sinking particles (reversible scavenging; Bacon and Anderson,
1982) and eventually removed from the water column into marine sediments.
Differential scavenging efficiencies of ^{231}Pa and ^{230}Th result in
differences in their residence times in the ocean; the residence times of
^{231}Pa and ^{230}Th were estimated to be 111 and 26 years in Yu et al. (1996), and 130 and 20 years in Henderson and Anderson (2003). The shorter
residence time of ^{230}Th indicates that ^{230}Th generated from
^{234}U is removed relatively quickly to marine sediments. On the other
hand, the longer residence time of ^{231}Pa indicates that ^{231}Pa
produced from ^{235}U is transported for a longer period by ocean
transport. Therefore, the deviation of the sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios from the constant production ratio of 0.093 has been used as a proxy
for ocean circulation (Yu et al., 1996). For example, the sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios from the Bermuda Rise were closer to 0.093 at
the Last Glacial Maximum (LGM) than today, possibly suggesting that the
Atlantic meridional overturning circulation (AMOC) was weaker at the LGM
(McManus et al., 2004; Böhm et al., 2015). To use the sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios as a proxy for ocean circulation in a more
quantitative manner, modeling about ^{231}Pa and ^{230}Th is important.

For ^{231}Pa and ^{230}Th modeling, one needs to take into account the
different scavenging efficiencies of different marine particle types (e.g.,
particulate organic carbon, calcite, and opal) as well as the distribution
of these particles (Chase et al., 2002; Edwards et al., 2005). Sinking
particles effectively scavenge ^{231}Pa and ^{230}Th in regions with
high particle concentrations. In general, ^{231}Pa has a longer residence
time than ^{230}Th, because sinking particles scavenge ^{230}Th more
efficiently. However, as for opal particles, Chase et al. (2002) argue that
opal scavenges ^{231}Pa more effectively than ^{230}Th. This report is
consistent with observational studies that find high ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios in the Southern Ocean, where opal sinking flux is high (Rutgers van
der Loeff and Berger, 1993; Walter et al., 1997; Chase et al., 2003).

Authors of previous modeling studies have tried to simulate the global
distributions of ^{231}Pa and ^{230}Th by two-dimensional (2D) ocean
models (Marchal et al., 2000; Luo et al., 2010) or three-dimensional (3D)
ocean models of LSG-OGCM (Henderson et al., 1999), Bern 3D (Siddall et al.,
2005; Rempfer et al., 2017), NEMO (Dutay et al., 2009; van Hulten et al.,
2018), CESM (Gu and Liu, 2017) and iLOVECLIM (Missiaen et al., 2020a). There
are also modeling studies that discuss the relationship between the strength
of the AMOC and changes in sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Siddall
et al., 2005; Lippold et al., 2012; Gu and Liu, 2017; Gu et al., 2020;
Missiaen et al., 2020a, b). Siddall et al. (2005) pioneered the 3D
simulation of both ^{231}Pa and ^{230}Th by incorporating reversible
scavenging. Their control simulation appropriately reproduced the observed
distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios; it showed high
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in regions where the sinking opal
particle flux is high. In their control simulation, the concentrations of
dissolved ^{231}Pa and ^{230}Th increased linearly with depth; this
pattern agreed broadly with observed features. However, simulated dissolved
^{231}Pa and ^{230}Th were both higher than observations in the deep
ocean. In addition to reversible scavenging by sinking ocean particles,
several studies (e.g., Anderson et al., 1983; Roy-Barman, 2009; Okubo et
al., 2012) have pointed out the importance of additional scavenging at the
seafloor (bottom scavenging) and the continental boundaries (boundary
scavenging). The bottom scavenging has not been explicitly included in
global 3D ocean models except for Rempfer et al. (2017) which used a
simplified 3D ocean model of intermediate complexity similar to that used by
Siddall et al. (2005) and reproduced the distributions of dissolved
^{231}Pa and ^{230}Th more realistically by introducing the bottom
scavenging. On the other hand, Henderson et al. (1999) reproduced the
distribution of dissolved ^{230}Th in their ocean general circulation
model (OGCM) simulation by changing the efficiency of reversible scavenging
depending on particle concentration; this effect has not been directly
considered by recent modeling studies but some studies have evaluated the
impacts of changes in particle concentration and scavenging efficiency on
the distribution of ^{231}Pa and ^{230}Th (van Hulten et al., 2018;
Missiaen et al., 2020a, b). Recently, the GEOTRACES project has led
to a dramatic increase in the number of observations of dissolved and
particulate ^{231}Pa and ^{230}Th (Schlitzer et al., 2018). The
GEOTRACES database provides an opportunity to test models describing the
cycling of these two radioisotopes in the global ocean. In this study, we
report our model simulation about the global distribution of ^{231}Pa and
^{230}Th in the ocean with COCO ver4.0. Starting from the basic
water-column reversible scavenging model of Siddall et al. (2005), we also
introduced the bottom scavenging and the dependence of scavenging efficiency
on particle concentration. Furthermore, we quantitatively discuss the
processes that control the global distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios; by performing a series of sensitivity
simulations, we discuss how the individual processes (i.e., water-column
reversible scavenging, ocean transport, and bottom scavenging) affect the
global distribution of dissolved ^{231}Pa and ^{230}Th and sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios.

## 2.1 Ocean general circulation model

The OGCM used in this study is COCO version 4.0 (Hasumi, 2006), the ocean
component of the coupled ocean-atmosphere general circulation model MIROC
version 3.2 (K-1 Model Developers, 2004). The COCO is also used as the ocean
part of the MIROC earth system model (Hajima et al., 2020; Ohgaito et al.,
2021). The model domain is global, with about 1^{∘} horizontal
resolution and 43 vertical layers. The vertical resolution varies from 5 m
(top) to 250 m (bottom). Surface boundary conditions are given from monthly
averages of zonal and meridional components of wind stress, air temperature,
specific humidity, net shortwave radiation, downward longwave radiation,
freshwater flux, and wind speed. These boundary conditions are taken from
the output of a pre-industrial simulation with the MIROC (Kobayashi et al.,
2015; Oka et al., 2012). To calculate ^{231}Pa and ^{230}Th, we perform
“offline” tracer simulation using physical fields obtained in advance by
the COCO (Oka et al., 2008, 2009). The offline means that the
calculation of tracer is separately performed from that of the physical
field; since the distributions of ^{231}Pa and ^{230}Th do not affect
the physical fields at all, the results do not depend on whether the model
is offline or online. The offline tracer model makes it easier to
perform various sensitivity experiments. The tracer model is integrated for
3000 years and tracer fields reach a steady state where changes in ocean
tracer inventory almost vanish (less than 10^{−5} % per 100 years). We
analyze the average of the last 100 years of the integration.

The physical fields used in this study is based on MIROC climate model simulations, and its reproducibility has been discussed and confirmed in a variety of literature (e.g., K-1 Model Developers, 2004; Gregory et al., 2005; Oka et al., 2006; Stouffer et al., 2006). We also note that the physical fields used here are the same as the pre-industrial (PI) simulation reported in Kobayashi et al. (2015) and Kobayashi and Oka (2018). For reference, the Atlantic meridional overturning circulation (AMOC) simulated by the COCO used in this study is shown in Fig. S11.

## 2.2 Particle fields

Following Siddall et al. (2005), the distribution of biogenic particles
(organic carbon, calcite, and opal) is used to evaluate the scavenging of
both ^{231}Pa and ^{230}Th. We define the concentration *M* of each
particle type (g m^{−3}) as $M=F/{w}_{\mathrm{s}}$, where *F* is the particle flux
(g m^{−2} yr^{−1}) and *w*_{s} is the constant settling velocity (m yr^{−1}). The particle flux is calculated using the export flux from the
euphotic zone and an assumed vertical profile of each particle type. The
detailed procedure is explained below.

First, the particulate organic carbon (POC) export flux from the euphotic
zone is calculated by multiplying the distribution of primary production
derived from satellite observations (Behrenfeld and Falkowski, 1997) by the
export ratio (Dunne et al., 2005). From POC export flux and $M=F/{w}_{\mathrm{s}}$,
the concentration of POC at the base of the euphotic zone, *M*_{POC}(*z*_{0}), where *z*_{0} is the depth of the bottom of the euphotic
zone, is obtained. After obtaining *M*_{POC}(*z*_{0}), the POC
concentration in the water column is expressed (Marchal et al., 1998) as

where *ε* is a remineralization exponent for POC.

Next, the calcite and opal export fluxes from the euphotic zone are calculated by multiplying the POC export flux by their rain ratios, which are estimated following formulations of Siddall et al. (2005) and Maier-Reimer (1993); please refer to Eqs. (2)–(5) of Siddall et al. (2005) for detail. The calcite particle concentration is calculated by assuming an exponentially decreasing vertical profile (Henderson et al., 1999; Marchal et al., 2000; Siddall et al., 2005). Thus, we have

where *z*_{p} is the calcite penetration depth. While the opal concentration
is expressed as an exponentially decreasing vertical profile in some
previous studies (e.g., Henderson et al., 1999), we consider opal
dissolution to be dependent on temperature, following Siddall et al. (2005),
as

where *D*_{opal} (yr^{−1}) is the opal dissolution rate, *T*_{0} is the
minimum temperature (^{∘}C) of seawater in the model, and *B* is a
dissolution constant (^{∘}C^{−1} yr^{−1}). Table 1 lists the
parameter values used in this study. Figure S10 shows the distribution of
particle fluxes in the surface ocean.

## 2.3 Reversible scavenging model

We use a tracer model of ^{231}Pa and ^{230}Th based on Siddall et al. (2005). The dissolved concentration (*A*_{d}) and particle concentration
(*A*_{p}) of ^{231}Pa and ^{230}Th are calculated from the following
equations:

In Eq. (4a), the first term on the right-hand side (*β*^{i}) represents
production from uranium (^{231}Pa from ^{235}U; ^{230}Th from
^{234}U), the second term represents radioactive decay, the third term
represents the effect of vertical transport by particle settling, and the fourth term
represents ocean transport by advection and diffusion. The superscript *i*
represents the isotope type (^{231}Pa, ^{230}Th).

By following a reversible scavenging model (Bacon and Anderson, 1982), the
relationship between the radionuclide concentration in the dissolved phase
(*A*_{d}) and particulate phase (*A*_{p}) is represented by the
partition coefficient (${K}_{j}^{i}$) as

where subscript *j* represents the particle type (organic carbon, calcite,
opal) and *C*_{j} is the dimensionless ratio of particle concentration to
the density of seawater. The formulation of the reversible scavenging was
also described in Oka et al. (2009, 2021) and readers can obtain its
detailed description therein. The partition coefficient depends on the type
of particles (Siddall et al., 2005). The partition coefficients of
^{231}Pa and ^{230}Th for each type of particle have been estimated
in previous studies (Luo and Ku, 1999; Chase et al., 2002). Chase et al. (2002) show that opal scavenges ^{231}Pa more efficiently than ^{230}Th,
whereas calcite scavenges ^{230}Th more efficiently than ^{231}Pa. Here
we use partition coefficients following Chase and Anderson (2004), as in
other previous modeling studies (Dutay et al., 2009; Gu and Liu, 2017;
Siddall et al., 2005; Table 2). The model parameters are summarized in Table 1.

## 2.4 One-dimensional reversible scavenging model

In addition to the three-dimensional tracer model based on the OGCM, we use a simple, vertical, one-dimensional model, which was widely used in previous studies (e.g., Bacon and Anderson, 1982), to analyze simulation results in Sect. 4. In the one-dimensional model, we assume a steady state and ignore the effect of ocean transport in Eq. (4a). Furthermore, we do not take the radioactive decay term into account, because it is much smaller than the production term. Under these assumptions, Eq. (4a) becomes

In this one-dimensional model, production by uranium radioactive decay (the
first term on the left side of Eq. 6) is balanced by vertical transport
through particle settling (the second term on the left side of Eq. 6). If
we assume that ${A}_{\mathrm{p}}^{i}$ is zero at the sea surface (*z*=0), then Eq. (6)
can be solved, leading to

Equation (7) shows that the vertical profile of ${A}_{\mathrm{p}}^{i}$ is determined
from two parameters: *β*^{i} and *w*_{s}. From Eq. (5), we have

The dissolved concentration can be obtained from Eqs. (7) and (8):

Equation (9) shows that the vertical profile of ${A}_{\mathrm{d}}^{i}$ is determined
by the particle settling speed, the partition coefficients, and the
concentrations of each particle. By comparing results from the
one-dimensional model and the three-dimensional tracer model, we can isolate
the influence of ocean transport (i.e., advection, diffusion, and
convection) on the simulated distributions of dissolved ^{231}Pa and
^{230}Th (see Sect. 4; Table 3).

## 2.5 Experimental design

This study conducts a series of OGCM experiments. First, we perform an
experiment named Siddall_EXP using the same parameters and
formulations as in Siddall et al. (2005). As stated in the Introduction,
Siddall et al. (2005) was a pioneering 3D model for global simulation of
both ^{231}Pa and ^{230}Th. This model is now a relatively old model and
the reversible scavenging model introduced in this model is simpler than
more recent models. However, this model appropriately reproduced the
observed distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios as shown
in their Fig. 2 which appears not necessarily inferior to that in more
recent models. Therefore, in this study, we start with
Siddall_EXP where the most basic reversible scavenging model
of Siddall et al. (2005) is introduced.

Second, we perform an experiment named BTM_EXP, in which we
additionally take bottom scavenging into account. Following Rempfer et al. (2017), we simply set the deepest model grid layer as the nepheloid layer.
The thickness of the nepheloid layer becomes equal to the thickness of the
corresponding deepest model grid layer which varies between 5 and 250 m
depending on the depth. The intensity of the bottom scavenging depends on
two parameters: the partition coefficient (*K*_{bottom}) and the
concentration (*C*_{bottom}) of the bottom particles. Our treatment about
*C*_{bottom} is the same that in Rempfer et al. (2017); we assume a globally
uniform value for *C*_{bottom} ($\mathrm{6.0}\times {\mathrm{10}}^{-\mathrm{8}}$ g cm^{−3}) which
is within the range of $\mathrm{4.0}\times {\mathrm{10}}^{-\mathrm{8}}$ to $\mathrm{1.65}\times {\mathrm{10}}^{-\mathrm{6}}$ g cm^{−3} observed in the benthic nepheloid layers in the North Atlantic
(Lam et al., 2015). As for *K*_{bottom}, because our formulation of the
reversible scavenging is not the same as Rempfer et al. (2017), we needed to
find its appropriate parameter value. For this purpose, we perform a number
of simulations with different bottom scavenging intensities by changing the
value of *K*_{bottom}.

Third, we perform a sensitivity experiment named KREF_EXP
concerned with the reference partition coefficient (*K*_{ref}). In
KREF_EXP, in addition to varying the value of the partition
coefficient for bottom particles (*K*_{bottom}), we also vary the values
of the reference partition coefficients (*K*_{ref}) from those assumed in
Siddall_EXP and BTM_EXP.

Finally, we perform an experiment named PCE_EXP, in which we
incorporate the dependence of scavenging efficiency on particle
concentration. In PCE_EXP, *K*_{ref} is not assumed to be
constant but varies according to the following formulation of Henderson et
al. (1999):

where *C*_{total} [g cm^{−3}] is the total concentration of all sinking
particles(${C}_{\mathrm{total}}={C}_{{\mathrm{CaCO}}_{\mathrm{3}}}+{C}_{\mathrm{opal}}+{C}_{\mathrm{POC}}$) and *C*_{ref}
[g cm^{−3}] is the reference concentration. Note that the value of
*C*_{total} is differently specified on each grid, whereas *C*_{ref} is given
as a globally uniform value. Due to the dependence of *K*_{ref} on
*C*_{total}, the scavenging efficiency becomes lower under higher particle
concentrations and higher under lower particle concentrations. We conduct
several simulations by varying *C*_{ref} between 10^{−9} and
10^{−6} g cm^{−3} (smaller *C*_{ref} value leads to stronger
scavenging). Although the observed decrease of the partition coefficient
with increased bulk particle concentration is not entirely understood (Pavia
et al., 2018), we will show that this particle concentration effect becomes
important for controlling dissolved ^{230}Th in some ocean regions.

## 3.1 Dissolved ^{231}Pa and ^{230}Th along the Atlantic meridional transects

First, we discuss the results of Siddall_EXP, focusing on the
meridional distribution of ^{231}Pa and ^{230}Th in the Atlantic Ocean.
Figure 1 shows the dissolved concentrations of ^{231}Pa and ^{230}Th
simulated in Siddall_EXP along the Atlantic 30^{∘} W
transect, together with GEOTRACES data (see Fig. S1 for the location of
observations referenced in this study). We confirm that the distributions of
dissolved ^{231}Pa and ^{230}Th in Siddall_EXP are
approximately the same as those reported in Siddall et al. (2005; their Fig. 2). Because ^{231}Pa and ^{230}Th exchange reversibly with sinking
particles and are transported to the deep ocean, the dissolved ^{231}Pa
and ^{230}Th concentrations increase with depth, both in the model
simulation and in observations. However, as in Siddall et al. (2005), the
model simulation overestimates dissolved ^{231}Pa and ^{230}Th
concentrations at depths greater than 2000 and 1000 m, respectively. For
quantitative analysis, we perform a linear regression analysis between the
simulation results and observed data from the GEOTRACES GA02 transect; we
calculate the root mean square deviation (RMSD), the correlation coefficient
(*R*), and the slope of the linear regression (*s*) of modeled concentration
versus observed concentration, as summarized in Table S1. The linear
regression line slope indicates the model's ability to reproduce the
observed distribution; it approaches 1.0 when the model simulation
realistically reproduces the target distribution (Dutay et al., 2009; Gu and
Liu, 2017). For Siddall_EXP, the slope of linear regression
line is significantly larger than 1.0 for both ^{231}Pa (*s*=1.88,
*R*=0.72, and RMSD = 0.15) and ^{230}Th (*s*=4.44, *R*=0.89, and
RMSD = 1.31; Table S1). This overestimation in the deep ocean is also found
in other previous model simulations (e.g., Dutay et al., 2009; Gu and Liu,
2017; van Hulten et al., 2018).

Next, to reduce the overestimation of the simulated concentrations in the
deep ocean, we additionally incorporate bottom scavenging in benthic
nepheloid layers (BTM_EXP). The dissolved ^{231}Pa and
^{230}Th distributions are shown in Figs. 2 and 3, respectively. As
expected, the incorporation of bottom scavenging helps reduce ^{231}Pa and
^{230}Th concentrations in the deep ocean, improving the model's agreement
with the data. As for the distribution of dissolved ^{231}Pa, the model
results come relatively close to the GEOTRACES data if ${K}_{\mathrm{bottom}}^{\mathrm{Pa}}$ is set to 5.0×10^{5} (*s*=1.04, *R*=0.90, and
RMSD = 0.05; see CTRL_EXP in Table S1; Fig. 2c and d). This
result confirmed the importance of the bottom scavenging, which was already
reported from a previous global 3D model (Rempfer et al., 2017) and a
regional eddy-permitting model (Lerner et al., 2020). On the other hand, it
is difficult to reproduce the observed distribution of dissolved ^{230}Th
in BTM_EXP. With ${K}_{\mathrm{bottom}}^{\mathrm{Th}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{6}}$, the concentrations of ^{230}Th in bottom waters come close to
observed values (Fig. 3c and d), but the concentrations in the deep ocean
(from 2000 to 5000 m) remain overestimated. In the case of larger ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$, the simulated ^{230}Th concentrations approach observed
values in the deep ocean but are significantly lower than observations in
bottom waters (e.g., ${K}_{\mathrm{bottom}}^{\mathrm{Th}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{7}}$ in Fig. 3g
and h). These results indicate that modification of Siddall_EXP by considering bottom scavenging alone is not sufficient for accurately
simulating ^{230}Th distribution in our model. As shown in Rempfer et al. (2017) and Lerner et al. (2020), the appropriate selection of scavenging
parameter coefficients is required for more realistic simulation. Because
our reversible scavenging model (which is the same as Siddall et al., 2005;
Sect. 2.3) is not the same as Rempfer et al. (2017) and Lerner et al. (2020), we need to discuss the validity of a scavenging parameter
coefficient in our model (i.e., *K*_{ref}). In the following
experiments (i.e., KREF_EXP and PCE_EXP), we
discuss more appropriate treatment about *K*_{ref} by focusing solely on
^{230}Th.

To reproduce the distribution of ^{230}Th more realistically, we change
the value of the reference partition coefficient (${K}_{\mathrm{ref}}^{\mathrm{Th}}$) in
addition to ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ (KREF_EXP). Figure 4 summarizes
the results of KREF_EXP and shows the simulated vertical
distributions of dissolved ^{230}Th for various values of ${K}_{\mathrm{ref}}^{\mathrm{Th}}$
and ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ (see Fig. 4g). Note that, for example, the simulation
R2_B5 means that ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ is set to 2.0×10^{7} and ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ to 5.0×10^{5}. In the cases
where ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ is set to 5.0×10^{5} (namely,
R2_B5, R4_B5, and R6_B5), the
^{230}Th concentrations systematically change depending on ${K}_{\mathrm{ref}}^{\mathrm{Th}}$;
as the reversible scavenging on sinking particles becomes stronger (i.e.,
for larger ${K}_{\mathrm{ref}}^{\mathrm{Th}}$), the concentrations of dissolved ^{230}Th
become smaller throughout the water column (Fig. 4c, e, and f). As
discussed for BTM_EXP, it is also confirmed that the stronger
bottom scavenging (i.e., larger ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$) leads to the lower
concentrations near the sea bottom (e.g., see R2_B5,
R2_B10, and R2_B20). For some combinations of
water-column scavenging and bottom scavenging, simulations (e.g.,
R6_B5, R4_B5, R4_B10)
reasonably reproduce the observed profile of dissolved ^{230}Th
concentration. Among our KREF_EXP simulations, the
R6_B5 simulation (Fig. 4f) shows the slope of the linear
regression line nearest to 1.0 (*s*=0.88, *R*=0.81, and RMSD = 0.20; Table S1) where ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ is higher (${K}_{\mathrm{ref}}^{\mathrm{Th}}=\mathrm{6.0}\times {\mathrm{10}}^{\mathrm{7}}$) than for Siddall_EXP and BTM_EXP
(${K}_{\mathrm{ref}}^{\mathrm{Th}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{7}}$). In the R6_B5
simulation (Fig. 4f), the vertical profile of dissolved ^{230}Th is
significantly improved from that of Siddall_EXP (Fig. 1d) and
BTM_EXP (Fig. 3). We confirmed that the R6_B5
simulation captures the observed features of the Atlantic transects of the
GEOTRACES data (Fig. 5a). However, the R6_B5 simulation still
underestimates the concentrations of dissolved ^{230}Th from the surface
to intermediate depths (see Fig. 4f). Also, the high concentrations of
dissolved ^{230}Th observed in the Southern Ocean in GEOTRACES data are
not well reproduced (Fig. 5a). To address this issue, we performed
additional simulations by slightly changing the values of ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ and ${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ from the R6_B5 simulation
(not shown), but we found that it is difficult to remove the abovementioned
deficiencies by merely changing the values of ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ and
${K}_{\mathrm{bottom}}^{\mathrm{Th}}$ in KREF_EXP.

Finally, we discuss PCE_EXP, in which the dependence of
scavenging efficiency on particle concentration is taken into account,
according to Eq. (10). We conduct several simulations by varying the value
of the reference concentration (*C*_{ref}) between 10^{−9} and
10^{−6} g cm^{−3}. Among these results, we here discuss the case with
${C}_{\mathrm{ref}}={\mathrm{10}}^{-\mathrm{7}}$ g cm^{−3}, which shows the best agreement with
observations. Compared to the case in which the dependence of scavenging
efficiency on particle concentration is not considered (i.e.,
R6_B5 simulation of KREF_EXP),
PCE_EXP is expected to show smaller (larger) ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ for the higher (lower) concentration of sinking particles. In
Fig. 5, we compare the simulated dissolved ^{230}Th distribution obtained
from PCE_EXP and R6_B5 simulation of
KREF_EXP. Owing to the dependence of scavenging efficiency on
particle concentration, PCE_EXP reproduces the vertical
distribution of dissolved ^{230}Th slightly better than
KREF_EXP (Fig. 5d). The regression analysis also confirms
that the agreement with the GEOTRACES data becomes improved in
PCE_EXP (*s*=0.98 and *R*=0.84; CTRL_EXP in
Table S1). It is worthy to note that the distribution in the Southern Ocean
is significantly improved in PCE_EXP (Fig. 5b) compared to
KREF_EXP (Fig. 5a) as a result of the nonuniform
distribution of the reference partition coefficient ${K}_{\mathrm{ref}}^{\mathrm{Th}}$
(Fig. 5c). In the Southern Ocean, where particle concentration is relatively
higher than in other regions (Honjo et al., 2008), the value of ${K}_{\mathrm{ref}}^{\mathrm{Th}}$ in PCE_EXP is lower than that in the
R6_B5 simulation of KREF_EXP (${K}_{\mathrm{ref}}^{\mathrm{Th}}=\mathrm{6}\times {\mathrm{10}}^{\mathrm{7}}$; i.e., ${K}_{\mathrm{ref}}^{\mathrm{Th}}\sim \mathrm{7.8}$) (Fig. 5c). Therefore, the concentration of dissolved ^{230}Th in
PCE_EXP becomes high compared to the KREF_EXP,
which leads to a more realistic distribution of dissolved ^{230}Th in the
Southern Ocean. The distributions of ^{230}Th simulated in previous
modeling studies (e.g., Figs. 4 and 5 in Dutay et al., 2009; Fig. 2 in
Siddall et al., 2005; Fig. 2 in Gu and Liu, 2017; Fig. 3 in Rempfer et al., 2017;
Fig. 12 in van Hulten et al., 2018; Fig. S3 in Missiaen et al., 2020a) are
basically similar to our result (Fig. 6b); however, our simulation is the
best at reproducing the high concentration in the Southern Ocean. Hereafter,
our best simulation (i.e., ${K}_{\mathrm{bottom}}^{\mathrm{Pa}}=\mathrm{5.0}\times {\mathrm{10}}^{\mathrm{5}}$ case
of BTM_EXP for ^{231}Pa and PCE_EXP for
^{230}Th) is called CTRL_EXP (see Table 2 for parameter
values of CTRL_EXP).

## 3.2 Particulate ^{231}Pa and ^{230}Th

By conducting a series of experiments described above, this study
successfully reproduces the observed distributions of dissolved ^{231}Pa
and ^{230}Th, shown again in Fig. 6a and b, respectively. The model captures the observed
tendency that the concentration becomes higher in the high-latitude Southern
Ocean, as reported in previous studies (e.g., see Fig. 2 in Siddall et al.,
2005). The ratio of ^{231}Pa to ^{230}Th in the particulate phase in
the water column shows low concentrations in the deep ocean, while the ratio
becomes high in the northern North Atlantic Ocean and the Southern Ocean
(Fig. 6f). This feature is consistent with observational findings and recent
modeling studies (e.g., Fig. 2 in Gu and Liu, 2017; Fig. 3 in Rempfer et al.,
2017). Although the number of available observations is limited for the
particulate phase, it is confirmed that our simulation reasonably reproduces
observed distributions for both dissolved and particulate phases.

## 3.3 Sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios

Our CTRL_EXP also well reproduces the global distribution of
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. 6e) consistent with the
reported observations (Mangini and Sonntag, 1977; Müller and Mangini,
1980; Anderson et al., 1983; Shimmield et al., 1986; Schmitz et al., 1986;
Yang et al., 1986; Shimmield and Price, 1988; Lao et al., 1992;
François et al., 1993; Frank et al., 1994; Frank, 1996; Bradtmiller et
al., 2014; Luo et al., 2010, and their supplemental data). Sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios are high along the margin of the North Pacific
and the North Atlantic, as well as in the Southern Ocean, where particle
concentrations are high. On the other hand, sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios are low in the low-latitude regions, including
subtropical gyres, where particle concentrations are low. These simulated
features are consistent with observations (circles in Fig. 6e). Previous
modeling studies reported the similar distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (e.g., Fig. 2 in Siddall et al., 2005; Fig. 11
in Dutay et al., 2009; Fig. 4 in Gu and Liu, 2017; Fig. 10 in van Hulten et al.,
2018; Fig. 1 in Missiaen et al., 2020a) and our Siddall_EXP
also reasonably reproduced the global distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. S4a). However, as shown above, the
distributions of dissolved ^{231}Pa and ^{230}Th in the ocean are
significantly different between CTRL_EXP and
Siddall_EXP. Thus, each experiment implies a different set of
processes controlling the distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios. We will discuss this point later in the next section.

## 4.1 Comparison with previous modeling studies

We demonstrated that our CTRL_EXP can reproduce a more
realistic distribution of dissolved ^{231}Pa and ^{230}Th along the
Atlantic meridional transects than Siddall_EXP by considering
the bottom scavenging and the dependence of scavenging efficiency on
particle concentration. Here, we compared our results with previous modeling
studies which showed their model results along with Atlantic meridional
transects (GEOTRACES GA02 section).

As far as we know, Rempfer et al. (2017) was the only 3D global ocean model
which introduces the bottom scavenging, and in our study, we introduced the
bottom scavenging into the global OGCM for the first time. Models without
the bottom scavenging tend to overestimate the dissolved ^{231}Pa and
^{230}Th in the deep ocean as in our Siddall_EXP. For
example, in Gu and Liu (2017) in which ^{231}Pa and ^{230}Th tracers are
introduced into CESM1.3, their simulated ^{231}Pa and ^{230}Th
concentrations are significantly overestimated in the deep ocean along the
GEOTRACES GA02 section (their Fig. 2). In Dutay et al. (2009) in which
^{231}Pa and ^{230}Th tracers are introduced into NEMO-PISCES, influences
of particle size and type on ^{231}Pa and ^{230}Th are discussed by
performing several sensitivity simulations, but all of their simulations
overestimate ^{231}Pa and ^{230}Th concentrations in the deep Atlantic
Ocean (their Figs. 4 and 5, respectively). In van Hulten et al. (2018) which
was the updated ^{231}Pa and ^{230}Th simulation with NEMO-PISCES, the
model still overestimates ^{231}Pa and ^{230}Th concentrations in the
deep Atlantic Ocean (their Fig. 12), because particles in the nepheloid
layers (i.e., bottom scavenging) are not included in their model.

Although the incorporation of bottom scavenging is important for controlling
the scavenging efficiency, it is worthy to note that bottom scavenging is
not the sole process that controls the scavenging efficiency. Therefore, for
example, the model which specified the relatively stronger affinity to the
particle can lead to smaller tracer concentration even if the model does not
include the bottom scavenging. In fact, in Missiaen et al. (2020a), their
simulated ^{231}Pa and ^{230}Th are underestimated in both the upper and
deep oceans (their Fig. S3 in the Supplement) even if the bottom scavenging was
not included in their model. This is because their specified scavenging
parameters are relatively stronger than the other models (see their Table 2)
as a result of their parameter tuning without the bottom scavenging.

In the Re3d_Bt_Bd simulation reported in
Rempfer et al. (2017) where the bottom scavenging process is considered, the
abovementioned overestimation in the deep ocean was relaxed and their
simulated distribution appears similar to our CTRL_EXP. Their
study is the first 3D model demonstration about the importance of the bottom
scavenging process, which is confirmed again in our study (e.g., from
comparison with Siddall_EXP and KREF_EXP).
However, their model still tends to somewhat overestimate the dissolved
^{231}Pa compared with GEOTRACES GA02 data (their Fig. 3). Because the
formulation of the reversible scavenging and their model parameters are not
the same as our CTRL_EXP, we expect that different choice of
model parameter values leads to such differences; more specifically, our
choice of ${K}_{\mathrm{ref}}^{\mathrm{Pa}}$ is based on Chase et al. (2002) and Siddall
et al. (2005), whereas the scavenging efficiency parameters in Rempfer et al. (2017) are similar to those in Luo et al. (2010) and Marchal et al. (2000).
In addition, as for ^{230}Th, the high concentration in the Southern Ocean
is not reproduced in their model, whereas this is reproduced in our
CTRL_EXP by considering the dependence of scavenging
efficiency on particle concentration. Although the dependence of scavenging
efficiency on particle concentration was already introduced in Henderson et
al. (1999), our study demonstrates its importance for reproducing high
concentrations in the Southern Ocean reported in GEOTRACES GA02 data for the
first time.

This study newly introduces a ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ model to the existing
global three-dimensional OGCM. Based on the reversible scavenging model,
this study well reproduces the distribution of dissolved concentration of
^{231}Pa and ^{230}Th by considering the bottom scavenging and the
dependence of the scavenging efficiency on particle concentration. The
importance of bottom scavenging on the dissolved concentration of ^{231}Pa
and ^{230}Th is already discussed in previous studies (Rempfer et al.,
2017; Lerner et al., 2020). Therefore, our result should be viewed as a
confirmation of these previous results. However, we emphasize that this
study provides a new estimate of the contribution of bottom scavenging to
the distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios compared to
other processes such as advection and water-column scavenging. Rempfer et
al. (2017) evaluated the performance of their ^{231}Pa and ^{230}Th
simulations based on the root mean squared deviation normalized by the
standard deviation of observations. In our control experiment
(CTRL_EXP), the RMSD between the available GEOTRACES data is
0.57 for dissolved ^{231}Pa and 0.51 for dissolved ^{230}Th. These
values lie in the range of values for the “standard” and “optimal”
experiments by Rempfer et al. (2017), the latter of which considers both
bottom scavenging and boundary scavenging (see Fig. 5 in Rempfer et al.,
2017). Lerner et al. (2020) use a regional eddy-permitting ocean circulation
model and focus on the western North Atlantic. They also point out that
removal in the nepheloid layer significantly impacts the basin-scale
distribution of dissolved and particulate phases of ^{231}Pa and
^{230}Th. In line with these previous studies, our result confirmed the
importance of boundary scavenging. Recently, Gardner et al. (2018) reported
data on the distribution of particles in benthic nepheloid layers. If such
datasets become available for specifying the global distribution of
particles in nepheloid layers, the effect of bottom scavenging can be
introduced more realistically. It is also expected that additional
consideration about boundary scavenging helps to improve our model
simulation.

In addition to the bottom scavenging, our study highlights the importance of
the dependence of scavenging efficiency on particle concentration. Although
the decrease of the partition coefficient with increased bulk particle
concentration has been reported from observations, the dependence of
scavenging efficiency on particle concentration considered in
PCE_EXP is not entirely understood (Honeyman et al., 1988;
Henderson et al., 1999; Hayes et al., 2015). Recently, the particle
concentration effect on ^{231}Pa and ^{230}Th partition coefficients in
the open ocean along the GEOTRACES GA03 transect has been reported (Hayes et
al., 2015; Lerner et al., 2017). Their study suggests that the dependency in
the open ocean may deviate from Eq. (10). In discussing the factors
responsible for the particle concentration effect, Pavia et al. (2018) point
out the possibility that the particle concentration effect is an artifact
caused by filtration. Further research is needed to elucidate the mechanisms
that control the particle concentration effect.

As pointed out in previous studies (Rempfer et al., 2017; Lerner et al.,
2020), the distributions of particle phases of ^{231}Pa and ^{230}Th are
difficult to be reproduced in the model compared with the dissolved phases. Part of the error could be related to the particle fluxes that
we give as an empirical distribution based on satellite observations. A
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ modeling study using an ecosystem model that considers
six different particles well reproduces the distribution of ^{231}Pa and
^{230}Th with a simple reversible scavenging model (van Hulten et al.,
2018); such detailed treatment of particles might be helpful for more
realistic simulation of particulate ^{231}Pa and ^{230}Th. Furthermore,
by examining the response of ^{231}Pa and ^{230}Th to freshwater forcing
into the North Atlantic, Missiaen et al. (2020b) show that changes in
biogenic particle fluxes may have caused 30 % of the changes in the
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios during the Heinrich stadial 1.
Also, in Gu and Liu (2017), the particle change due to freshwater and its
impact on sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios is examined. Therefore,
the role of particle fields on the distribution of ^{231}Pa and
^{230}Th, which was not directly investigated in this study, needs to be
further discussed in a future study.

## 4.2 Reproducibility along GEOTRACES GA03 and GP16 transects

So far, we have compared our model results with observations by focusing on the Atlantic meridional GEOTRACES transects (i.e., GA02 and GIPY05). Here, we will compare our CTRL_EXP with other available GEOTRACES transects: GA03 in the subtropical North Atlantic (Hayes et al., 2015) and GP16 in the South Pacific (Pavia et al., 2018).

Figure S5 shows the results of CTRL_EXP along with the
GEOTRACES GA03 data. For dissolved ^{231}Pa, the model shows a high
concentration around a depth of about 3000 m and higher concentrations on
the eastern/southern side of the basin as in observations (Fig. S5a). This
feature was also well reproduced in the Re3d_Bt_Bd simulation of Rempfer et al. (2017) as shown in their
Fig. 2 but not in other previous models (e.g., Fig. 8 in van Hulten et
al., 2018; Fig. 3 in Gu and Liu (2017)). This confirms that the consideration
of the bottom scavenging is helpful for improving the model result along the
GEOTRACES GA03 section. For dissolved ^{230}Th, features similar to
^{231}Pa are also found in both the model and observations although the
model appears to underestimate north–south or west-east differences
(Fig. S5b). For particulate ^{231}Pa and ^{230}Th, the model tends to
simulate high concentration near the sea bottom and the continental margins
where the particle concentration becomes high, but such features are not
necessarily clear in the GEOTRACES data (Fig. S5c and d). Our model may
not sufficiently reproduce the bottom and boundary scavenging associated
with terrestrial particles in this region. More sophisticated treatment of
bottom and boundary scavenging might be required for addressing these
issues.

Figure S6 shows the results of CTRL_EXP along with the
GEOTRACES GP16 data. As with the other section data, CTRL_EXP
approximately reproduces the distribution of ^{231}Pa and ^{230}Th. The
observational data show a clear signal associated with hydrothermal vents:
low concentrations of dissolved ^{231}Pa and ^{230}Th and high
concentrations of particulate ^{231}Pa and ^{230}Th, which are not
simulated in our model. It has been pointed out that trace metals from
hydrothermal activities may cause additional removal of ^{231}Pa and
^{230}Th (Shimmield and Price, 1988; Lopez et al., 2015; Rutgers van der
Loeff et al., 2016; German et al., 2016). Along the GEOTRACES GP16 section,
^{231}Pa and ^{230}Th have been found to decrease with increasing trace
metals of iron and manganese supplied from hydrothermal vents (Pavia et al.,
2018). Processes related to the hydrothermal vents are not explicitly
incorporated in the present ^{231}Pa and ^{230}Th model simulations; its
detailed treatment is beyond the scope of this study but appears necessary
for more realistic simulations.

## 4.3 Processes controlling sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios

In this subsection, we discuss the processes controlling the global
distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. For this purpose,
we decompose the processes controlling sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios simulated in our best simulation CTRL_EXP into three
parts: water-column reversible scavenging, three-dimensional ocean
transport, and bottom scavenging. To evaluate how these three processes
affect the distribution of ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios, we conduct two
additional experiments (see Table 3). The first experiment is
3D_EXP, which is the same as CTRL_EXP except
that bottom scavenging is not taken into account (i.e., we set
${K}_{\mathrm{bottom}}^{\mathrm{Pa}}={K}_{\mathrm{bottom}}^{\mathrm{Th}}=\mathrm{0}$ in 3D_EXP). The second is
1D_EXP, which is the one-dimensional reversible scavenging
model experiment described in Sect. 2.4. The tracer distribution in
1D_EXP is determined solely by the one-dimensional vertical
process of reversible scavenging; the strength of scavenging changes
spatially through changes in the partition coefficient (${K}_{j}^{i}$ of Eq. 9 in Sect. 2.4) that depends on the specified three-dimensional particle
concentration (*C*_{j} of Eq. 9). By using results of CTRL_EXP, 3D_EXP, and 1D_EXP, we can extract the
influence of three processes: the influence of the one-dimensional vertical
reversible scavenging is revealed by 1D_EXP, the influence of
bottom scavenging is revealed by the difference between CTRL_EXP and 3D_EXP, and the influence of ocean transport is
revealed by the difference between 3D_EXP and
1D_EXP. When we focus on sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios, each process described above can be further examined for ^{231}Pa
and ^{230}Th individually. For example, the difference in
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios between CTRL_EXP and
3D_EXP represents the influence of bottom scavenging of both
^{231}Pa and ^{230}Th, whereas the influence of bottom scavenging of
^{231}Pa alone can also be evaluated from CTRL_EXP and
3D_EXP (i.e., ^{231}Pa(CTRL) $/$ ^{230}Th(3D) minus
^{231}Pa(3D) $/$ ^{230}Th(3D)).

In 1D_EXP, the particulate concentration is obtained from Eq. (7); the particulate concentration increases linearly with depth (Fig. S2c
and d). The dissolved concentration is calculated from Eq. (9), suggesting
that the concentration becomes higher for a lower partition coefficient
(${K}_{j}^{i}$ in Eq. 9) and for a lower particle concentration (*C*_{j} in
Eq. 9). Mainly due to the dependency on *C*_{j}, the dissolved
concentration becomes higher (lower) in the area with lower (higher)
particle concentration in 1D_EXP. As a result, the dissolved
concentration becomes very high in the deeper ocean, where the particle
concentration becomes lower for both ^{231}Pa and ^{230}Th (Fig. S2a
and b). It is interesting to point out that the spatial pattern of
dissolved ^{231}Pa and ^{230}Th (Fig. S2a and b) is similar to that
of *K*_{ref} in PCE_EXP (Fig. 5c), because both are
affected by the amount of particle concentration. More importantly, although
it is well known from previous studies, we emphasize here that the
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in 1D_EXP become
uniform everywhere (0.093; Fig. S2e), because, as confirmed from Eq. (7), the
ratio of particulate ^{231}Pa to particulate ^{230}Th amounts everywhere
to ${\mathit{\beta}}^{Pa}/{\mathit{\beta}}^{Th}=\mathrm{0.093}$, regardless of geographic location
(Fig. S2f).

In 3D_EXP, three-dimensional ocean transport operates, in addition to water-column scavenging considered in 1D_EXP (Fig. S3). As described above, the influence of ocean transport can be evaluated from the difference between 3D_EXP and 1D_EXP (Fig. 7). On the other hand, the influence of bottom scavenging can be obtained from the difference between CTRL_EXP and 3D_EXP (Fig. 8). Note again that since the sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in 1D_EXP are globally uniform (${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ = 0.093), their spatial distribution is controlled not by the one-dimensional vertical process but by the ocean transport. Figure 7e and f demonstrate that the ocean transport effect captures the overall features of CTRL_EXP (Fig. 6e and f). On the other hand, bottom scavenging tends to cancel the effects of ocean transport and weaken the spatial contrast of ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios simulated in CTRL_EXP (Fig. 8e and f).

To evaluate the above processes controlling the sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in more detail, we further decompose the ocean
transport contribution into those from ^{231}Pa and ^{230}Th, separately
(Fig. 9a for ^{231}Pa and Fig. 9b for ^{230}Th). Similarly, we further
decompose the contribution of bottom scavenging into those for ^{231}Pa
and ^{230}Th (Fig. 9c and d, respectively). In Fig. 9a, we demonstrate
that ocean transport solely from ^{231}Pa (i.e.,
^{231}Pa(3D) $/$ ^{230}Th(1D)) can reproduce the overall distribution of the
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in CTRL_EXP (Fig. 6e). This result confirms that ocean transport of ^{231}Pa primarily
controls the distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios,
consistent with previous studies (Yu et al., 1996; Marchal et al., 2000).
These previous studies suggest that the distribution of ^{231}Pa mainly
determines the global distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios, because the residence time of ^{231}Pa is longer than that of
^{230}Th.

Here, we further discuss how the ocean transport of ^{231}Pa controls the
distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. Since changes in
sedimentary ^{231}Pa correspond to particulate ^{231}Pa changes in the
bottom ocean, we focus the ocean transport effect on particulate ^{231}Pa
(Fig. 7c). Consistent with Fig. 9a, Fig. 7c indicates that ocean transport
acts to decrease (increase) particulate ^{231}Pa in lower (higher)
latitudes. We also found that particulate ^{231}Pa changes (Fig. 7c) are
similar to those in dissolved ^{231}Pa (Fig. 7a). Because most of
^{231}Pa are in the dissolved phase, the advection of particulate
^{231}Pa itself is very small compared with that of dissolved ^{231}Pa,
and ocean transport takes place mainly in the form of dissolved ^{231}Pa.
Therefore, it is interpreted that ocean transport first controls the
dissolved ^{231}Pa, and then the corresponding changes in particulate
^{231}Pa take place so that the relationship between dissolved and
particulate ^{231}Pa (i.e., Eq. 5b) is satisfied. In other words, the
changes in particulate ^{231}Pa take place as a result of changes in
dissolved ^{231}Pa. Therefore, we need to focus on the processes that
control the dissolved ^{231}Pa changes (Fig. 7a). As previously mentioned,
in the case of no ocean transport (i.e., 1D_EXP), the
dissolved ^{231}Pa concentration near the seabed in lower latitudes
becomes very high (Fig. S2a). Ocean transport, which includes both advection
and diffusion, reduces high concentrations of dissolved ^{231}Pa in low
latitude oceans by transporting dissolved ^{231}Pa from lower latitudes to
higher latitudes. As a result of the change in the dissolved ^{231}Pa
(Fig. 7a), the changes in particulate ^{231}Pa (Fig. 7c) also take place
by satisfying Eq. (5b); this leads to lower sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in lower latitudes and higher ratios in higher
latitudes (Fig. 7e and f).

Contrary to ^{231}Pa, the influences of ^{230}Th transport on
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios have been usually regarded as small
because ^{230}Th is generally assumed to be scavenged very quickly
everywhere. However, our results demonstrate that ocean transport of
^{230}Th also affects the distribution of sediment ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
to some extent. As a matter of fact, ^{230}Th ocean transport acts in the
opposite direction of ^{231}Pa ocean transport, reducing the spatial
contrast in sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. 9b). However, an
exception is found in the Southern Ocean, where the ^{230}Th ocean
transport contributes to higher sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios, in
the same way as the ^{231}Pa ocean transport. Because opal scavenges
^{231}Pa more effectively than ^{230}Th (Chase et al., 2002), ^{231}Pa
transported toward the Southern Ocean is expected to be quickly removed
there due to the high opal flux. Therefore, previous studies concluded that
ocean transport of ^{231}Pa explains high sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in the Southern Ocean. On the other hand, in
addition to ocean transport of ^{231}Pa, our results suggest that ocean
transport of ^{230}Th also contributes to the high ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios in the Southern Ocean. This result implies that scavenging of
^{230}Th is not so efficient in the Southern Ocean as previously expected
due to the dependence of scavenging efficiency on particle concentration.
This interpretation is consistent with the high concentration of dissolved
^{230}Th in the Southern Ocean (Fig. 6b). Missiaen et al. (2020a)
demonstrated that the dissolved ^{230}Th concentration in the Southern
Ocean will increase if the effect of particle scavenging is halved and that
most of this effect comes from POC and opal. This implies the scavenging of
^{230}Th is controlled also by the opal in the Southern Ocean. Together
with their and our results, quantification about scavenging of ^{230}Th by
opal in the Southern Ocean may be a key for a more accurate understanding of
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in the global ocean.

Bottom scavenging promotes the removal of both ^{231}Pa and ^{230}Th
near the seafloor and tends to cancel the influence of ocean transport.
Namely, the bottom scavenging of ^{231}Pa reduces the contrast among
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. 9c), whereas the bottom
scavenging of ^{230}Th increases this contrast (Fig. 9d). Because the
influences of bottom scavenging of ^{231}Pa tends to be stronger than that
of ^{230}Th, bottom scavenging overall results in reducing the contrast of
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. 8e and f). Precisely speaking, the
actual processes of the bottom scavenging effect on the sedimentary
^{231}Pa and ^{230}Th appear somewhat complicated compared with those of
the ocean transport effect. The effect of the bottom scavenging is twofold.
First, extra particles in the bottom ocean lead to an increase of
sedimentary ^{231}Pa and ^{230}Th (e.g., positive values near the bottom
in low latitudes in Fig. 8c). Second, the bottom scavenging removes
^{231}Pa and ^{230}Th from the ocean, which reduces the concentration of
dissolved ^{231}Pa and ^{230}Th in the ocean interior (Fig. 8a and b).
The changes in dissolved-phase concentration then lead to changes in
particulate-phase concentration in a way such that the Eq. (5b) is
satisfied. The former leads to higher sedimentary ^{231}Pa and ^{230}Th,
whereas the latter leads to lower sedimentary ^{231}Pa and ^{230}Th. Our
results indicate that the former process becomes more important than the
latter in the low latitudes, and the sedimentary ^{231}Pa increases there.
In contrast, the latter dominates in the high latitudes, and the sedimentary
^{231}Pa decreases there by the bottom scavenging effect. The effect of
bottom scavenging on ^{230}Th is also basically similar to ^{231}Pa.

## 4.4 Residence time of ^{231}Pa and ^{230}Th

Additional insights into the simulated distribution of ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios can be obtained from a comparison of CTRL_EXP with
Siddall_EXP which reproduces sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios (Fig. S4a) as realistically as does
CTRL_EXP (Fig. 6e). In this subsection, we discuss this point
by focusing on the difference in the residence time of ^{231}Pa and
^{230}Th between CTRL_EXP and Siddall_EXP.
Assuming the mass balance of ^{231}Pa and ^{230}Th are in a steady
state, we calculate the residence time of ^{231}Pa and ^{230}Th from the
following formulas:

In Eq. (11a) and (11b), the integral domain is global and the parameters are
described in Table 1. The residence times of ^{231}Pa and ^{230}Th are
calculated to be 103 and 21 years, respectively, in CTRL_EXP,
whereas they are 211 and 89 years, respectively, in Siddall_EXP (Table S2). By incorporating bottom scavenging and modifying the
partition coefficient of ^{230}Th, the modeled residence time in
CTRL_EXP comes close to the previous estimate based on data:
111 years for ^{231}Pa and 26 years for ^{230}Th in Yu et al. (1996) and
130 years for ^{231}Pa and 20 years for ^{230}Th in Henderson and
Anderson (2003). Because the reference partition coefficients for ^{231}Pa
of Siddall_EXP and that of CTRL_EXP are the
same value (i.e., ${K}_{\mathrm{ref}}^{\mathrm{Pa}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{7}}$), the influence
of ocean transport on ^{231}Pa is identical in both experiments (Fig. 9a).
Therefore, the difference in the ^{231}Pa distribution between the model
experiments must come from the bottom scavenging, which is included in
CTRL_EXP but not in Siddall_EXP. The bottom
scavenging reduces the residence time of ^{231}Pa in CTRL_EXP (103 years) compared to Siddall_EXP (211 years). The
difference in the ^{230}Th distribution between CTRL_EXP
and Siddall_EXP mainly comes from the difference in reference
partition coefficients (${K}_{\mathrm{ref}}^{\mathrm{Th}}$). The reference partition coefficient
${K}_{\mathrm{ref}}^{\mathrm{Th}}$ of CTRL_EXP, which depends on particle
concentration, is larger than that of Siddall_EXP
(${K}_{\mathrm{ref}}^{\mathrm{Th}}=\mathrm{6.0}\times {\mathrm{10}}^{\mathrm{7}}$) in most of the ocean. Therefore,
the contribution from the ocean transport of ^{230}Th becomes larger in
Siddall_EXP (Fig. S4b) than in CTRL_EXP (Fig. 6b). Together with additional contribution from the bottom scavenging effect
on ^{230}Th (Fig. 9d), the residence time of ^{230}Th in
CTRL_EXP (21 years) is shorter than that in
Siddall_EXP (89 years). Since the residence time is
overestimated for both ^{231}Pa and ^{230}Th in Siddall_EXP compared to CTRL_EXP, the distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in Siddall_EXP ends up similar
to that in CTRL_EXP. The residence time in
CTRL_EXP is similar to the residence time of their control
simulation in Gu and Liu (2017), which does not include the bottom
scavenging process. Therefore, total scavenging efficiency in the ocean is
more important than the introduction of bottom scavenging to reproduce
residence time. Compared with Siddall_EXP based on Siddall et
al. (2005), our CTRL_EXP can realistically simulate not only
oceanic distribution of ^{231}Pa and ^{230}Th but also their residence
time by introducing the bottom scavenging and the dependence of scavenging
efficiency on particulate concentration.

## 4.5 Remaining issues

Although our model was able to generally reproduce the basin-scale
distributions of ^{231}Pa and ^{230}Th, there are still some mismatches
between the model results and observations. For dissolved ^{231}Pa,
introducing bottom scavenging helped to reproduce the concentrations seen in
the data at depths below 3000 m (Fig. 2). However, the model tends to
simulate lower concentration than the observations below 3000 m in Fig. 2c
and d, which needs to be improved. The improvement was not possible simply
by reducing the bottom scavenging (i.e., specifying smaller
${K}_{\mathrm{bottom}}^{\mathrm{Pa}}$ than in Fig. 2c and d), therefore more fundamental
improvement appears to be required. The dissolved ^{230}Th simulated in
CTRL_EXP (Fig. 5b) also tends to underestimate the observed
concentration near the sea bottom. One possibility is that our treatment of
the nepheloid layer (i.e., the thickness of the ocean deepest layer) may be
too simple and needs to be modified so that the thickness of the nepheloid
layer is more realistically specified. The introduction of more realistic
bottom scavenging and the consideration of the effects of particles from the
continental shelf and hydrothermal vents may also help to improve the
model–data agreement for both ^{231}Pa and ^{230}Th.

In this study, particle fields were not calculated in the model but
specified as boundary conditions in our approach where the specified
distribution of biological particles is taken from satellite-based
estimation. Since the bias of the particle field affects the distribution of
^{231}Pa and ^{230}Th, our approach has advantages over the other
studies where the particles are explicitly simulated in the model. However,
satellite-based estimation referenced here may also contain some errors, and
understanding about the influence of the particle field on sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios, which was not seriously discussed in this
study, is also important as the previous studies pointed out (e.g., Missiaen
et al., 2020b; Dutay et al., 2009; van Hulten et al., 2018).

To reconstruct past sedimentation flux, ^{230}Th normalization was used.
Recently, the influence of lithogenic and authigenic ^{230}Th on
^{230}Th in sediments was evaluated (Missiaen et al., 2018; Costa et al.,
2020). This is not a direct topic of our study, but we need to care about
such processes which also affect the ratio of ^{231}Pa and ^{230}Th
obtained from marine sediments. As more observational data and their
modeling become available, we expect to make further progress in
quantitative understanding of the processes governing ^{231}Pa and
^{230}Th in the ocean.

In this study, we performed OGCM experiments that incorporated the bottom scavenging and the dependence of scavenging efficiency on particle concentration together with the water-column reversible scavenging. We quantitatively evaluated the processes that determine the global distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios, which is used as a proxy for the strength of paleo-ocean circulation.

First, we performed an OGCM experiment using the same model settings and
parameters as Siddall et al. (2005), which only introduced the water-column
reversible scavenging (Siddall_EXP). In
Siddall_EXP, the simulated concentrations of ^{231}Pa and
^{230}Th increase with depth, consistent with data; however, this
experiment significantly overestimated the concentrations observed in the
deep ocean. By incorporating bottom scavenging in nepheloid layers following
Rempfer et al. (2017) (BTM_EXP), we reduced this
overestimation and successfully reproduced the vertical profile of dissolved
^{231}Pa. However, this experiment had difficulty in reproducing the
observed vertical profile of dissolved ^{230}Th. Therefore, we modified
the parameters associated with the strength of water-column scavenging
(i.e., *K*_{ref}: the reference partition coefficient for sinking
particles) with the consideration of the bottom scavenging
(KREF_EXP). When we increased the reference partition
coefficient of ^{230}Th (${K}_{\mathrm{ref}}^{\mathrm{Th}}=\mathrm{6.0}\times {\mathrm{10}}^{\mathrm{7}}$) from that used
in the Siddall_EXP with the consideration of bottom
scavenging (${K}_{\mathrm{bottom}}^{\mathrm{Th}}=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{7}}$), dissolved ^{230}Th was
found to be more realistically simulated, but significant underestimation in
the Southern Ocean remained. We found that the underestimation in the
Southern Ocean can be improved by introducing dependence of *K*_{ref} on
particle concentration which was used in Henderson et al. (1999)
(PCE_EXP). Although most of the previous ^{231}Pa and
^{230}Th model results showed significant overestimation in the deep ocean
(e.g., Siddall et al., 2005; Dutay et al., 2009; Gu and Liu, 2017; van
Hulten et al., 2018), our best OGCM simulation considering the reversible
scavenging, bottom scavenging, and the dependence of scavenging efficiency
on particle concentration (CTRL_EXP) can reproduce the
distributions of dissolved ^{231}Pa and ^{230}Th consistently with
GEOTRACES data, together with the realistic distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios.

We also made a quantitative assessment about the processes that determine
the global distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios by
decomposing the processes affecting the sediment ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$
ratios into three parts: water-column scavenging, ocean transport (advection
and diffusion), and bottom scavenging. We confirmed that the global
sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in our best model
(CTRL_EXP) are primarily determined by ocean transport of
^{231}Pa, as shown in previous studies. Contrary to ^{231}Pa, ocean
transport of ^{230}Th tends to reduce the spatial contrast of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. However, we found that this is not the case
for the Southern Ocean; ^{230}Th advection increases the sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in the Southern Ocean and strengthens the
observed high ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios there. This means that not only
^{231}Pa advection but also ^{230}Th advection contributes to the high
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in the Southern Ocean. This result implies that
scavenging of ^{230}Th is not much efficient in the Southern Ocean as
conventionally thought when we consider the dependence of scavenging
efficiency on particle concentration. We also show that bottom scavenging
works opposite to ocean transport and decreases the spatial contrast of
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios; bottom scavenging promotes the removal of
^{231}Pa near the sea bottom more efficiently than that of ^{230}Th, and
the total effect of bottom scavenging reduces spatial contrasts of the
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. Our best simulation shows the realistic
residence times of ^{231}Pa and ^{230}Th, but simulation without bottom
scavenging and dependence of scavenging efficiency on particle concentration
significantly overestimates the residence times for both ^{231}Pa and
^{230}Th in spite of similar distribution of sedimentary
${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios to our best simulation.

The model developed in this study is useful not only for simulating ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios in the present-day ocean but also in different climates such as glacial periods. Our OGCM experiments using the present-day physical fields can clarify the processes governing the global distribution of sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios. A similar analysis using the physical ocean fields during glacial periods may help climate scientists to understand the mechanisms for glacial changes in the sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratio observed in sediment cores. Although simulated sedimentary ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ under glacial times are also discussed in a 2D model (Lippold et al., 2012) and recently in a 3D model (Gu et al., 2020), there is insufficient discussion of the mechanism of change in the three-dimensional distribution. Simulation of ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ ratios under glacial climates (e.g., Oka et al., 2011; Kobayashi and Oka, 2018) is an exciting avenue of future study.

The ${}^{\mathrm{231}}\mathrm{Pa}{/}^{\mathrm{230}}\mathrm{Th}$ model code and data used to produce the results in this study are available at the repository website Zenodo: https://doi.org/10.5281/zenodo.4600287 (Sasaki et al., 2021a) and https://doi.org/10.5281/zenodo.4655883 (Sasaki et al., 2021b), respectively. COCO is an ocean component of MIROC and the code of COCO4 is included as a part of MIROC-ES2L. The source code of MIROC-ES2L can be obtained from https://doi.org/10.5281/zenodo.3893386 (Ohgaito et al., 2020).

The supplement related to this article is available online at: https://doi.org/10.5194/gmd-15-2013-2022-supplement.

All the authors contributed to the interpretation of the simulation results. YS performed the numerical simulations. AO designed and supervised the study. YS and HK analyzed the results. YS wrote the first draft, and the final draft was prepared with the inputs from all the co-authors.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors acknowledge many constructive comments from reviewers, which significantly improved the article.

This work was supported by JSPS KAKENHI (grant no. JP19H01963).

This paper was edited by Paul Halloran and reviewed by two anonymous referees.

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^{230}Th and

^{231}Pa in the ocean, we highlight the importance of the removal process of

^{231}Pa and

^{230}Th at the seafloor (bottom scavenging) and the dependence of scavenging efficiency on particle concentration. We show that consideration of these two processes can well reproduce not only the oceanic distribution of 231Pa and 230Th but also the sedimentary

^{231}Pa/

^{230}Th ratios.

^{230}Th and

^{231}Pa in...