Nakamura et al. Progress in Earth and Planetary Science 2014, 1:9
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RESEARCH

Open AccessDirect comparison of site-specific and basin-scaledenudation rate estimation by in situ cosmogenic
nuclides: an example from the Abukuma
Mountains, Japan
Atsunori Nakamura1,2, Yusuke Yokoyama1,2,3*, Kazuyo Shiroya4, Yosuke Miyairi1 and Hiroyuki Matsuzaki5

Abstract
Accurate determination of denudation rates is important in understanding Earth surface system dynamics. In situ
produced cosmogenic nuclides, such as 10Be and 26Al, provide a valuable insight but are not entirely free fromcomplications. In this study, denudation rates are determined for the Abukuma Mountains, Japan, using bothsite-specific and basin-scale methods. Considered with density measured in the field, distinct and systematic differences
between the two methods are identified. Site-specific rates calculated from depth profiles of cosmogenic nuclides(10Be and 26Al) at topographic highs indicate a rate of 67 to 85 mm/kyr, whereas basin-scale averaged denudation
rates derived from the concentration of cosmogenic nuclides in fluvial sediments show 114 to 180 mm/kyr. This is thefirst comparison of these two commonly used methods in the same region in Japan, where the entire study area ischaracterized by well-developed saprolite. These results indicate that differential denudation rates between topographic
highs and valleys reflect increasing local topographic relief of the study area. Comparison between rates derived from
depth profiles and those applicable to the entire basin is important for understanding landscape development.
Keywords: Denudation rate; Erosion rate; In situ cosmogenic nuclide; 10Be and 26Al; Depth profile; Density

BackgroundSite-specific and basin-scale denudation rates

Quantifying denudation rates is important across a diverse range of disciplines in geology, geomorphology,
and paleoclimatology (Yokoyama et al. 2005; Yokoyama
and Esat 2011). Denudation is often associated withsediment generation, which exposes fresh rock to CO2consuming weathering reactions, and with creating soil,changing landforms, and moving mass from continents
to oceans (Berner et al. 1983; Matsumoto and Yokoyama2013). While numerous studies underline the significanceand complexity of relationships between denudation,
tectonics, and climatic processes (e.g., Granger andRiebe 2007 and references therein; Shiroya et al. 2013),* Correspondence: yokoyama@aori.u-tokyo.ac.jp
1
Atmosphere and Ocean Research Institute, University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8564, Japan2
Department of Earth and Planetary Science, Graduate School of Science,
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Full list of author information is available at the end of the article

determination of long-term denudation rates over thetimescales of soil formation and transport has, until recently, remained difficult. In situ cosmogenic nuclide concentrations such as 10Be and 26Al are directly related todenudation rate, allowing quantification on long-termtimescales (Gosse and Phillips 2001). Initial application ofcosmogenic nuclides to denudation rate determination was
limited to areas of widely distributed, exposed rock, often
at high latitudes or in arid environments (e.g., Nishiizumi
et al. 1986; Cockburn et al. 1999). Later work employedthese methods in more humid regions, where soil covers
much of the land surface (e.g., Heimsath et al. 2001a).
There are two common methods for determining denudation rates using in situ cosmogenic nuclides inhumid regions. One relies on fluvial sediments to obtainbasin-scale averaged rates (Brown et al. 1995; Bierman
and Steig 1996; Granger et al. 1996), and the other uses
depth profiles obtained from topographic highs to determine site-specific rates (Siame et al. 2004; Matsushi
et al. 2006). Combination of these two methods has the© 2014 Nakamura et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction
in any medium, provided the original work is properly credited.

Nakamura et al. Progress in Earth and Planetary Science 2014, 1:9
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potential for providing greater insight into the complex
surface processes and landscape development in any particular region (Brown et al. 1995). In this study, we
present a direct comparison between denudation rates
determined from these two methods in the same lithological region, where the entire study area is characterized by well-developed saprolite.
The regional topographic relief increases if denudation
rates on topographic highs are less than basin-scale averaged rates. In contrast, a reduction in relief occurs if
the rates on topographic highs exceed basin-scale rates.
Comparison of denudation rates from soil-mantled upland obtained from single samples, rather than a depth
profile, with basin-scale averaged rates has been previously performed in the Oregon Coast Range (Heimsath
et al. 2001a), Australian southeastern highlands (Heimsath
et al. 2001b, 2006), and German Black Forest (Meyer et al.
2010). Comparison between summit bedrock and basinaveraged denudation rates has also been performed in the
Negev Desert (Clapp et al. 2000), southern Africa (Bierman
and Caffee 2001), and the Appalachians (Hancock andKirwan 2007; Portenga et al. 2013). The advantage of adepth profile of in situ cosmogenic nuclides is that it
has the potential to provide information about equilibrium conditions, which cannot be obtained from a single
sample.
Denudation rates from in situ cosmogenic nuclides

Measuring in situ cosmogenic nuclides in river-born
sediments allows investigation of denudation rates on
drainage basin scales (Brown et al. 1995; Bierman and
Steig 1996; Granger et al. 1996; Riebe et al. 2000; Moonet al. 2011; Siame et al. 2011). If exposure to cosmic
rays is sufficiently long with respect to the denudation
rate, the accumulation of in situ-produced 10Be and26
Al reaches a secular equilibrium, providing information on the maximum denudation rate (Lal 1991). Because rivers carry and mix the sediment produced
within a given drainage basin, denudation rates deduced from river-born quartz were identified as ideal
material for quantifying denudation rates of an entire
watershed (Brown et al. 1995; Bierman and Steig 1996;
Granger et al. 1996).
Although the principle is simple, the culmination of aseries of assumptions and approximations may compound some uncertainty. Stream sediment is not always
representative of the entire watershed, especially withinsmaller watersheds prone to episodic mass wasting(Niemi et al. 2005; Granger and Riebe 2007). Storage andburial of river sediments would also disturb the initialconcentration of cosmogenic nuclides by radioactive
decay, which creates a case where the measured nuclide
concentration underestimates the steady-state nuclide
concentration (Wittmann et al. 2011). This methodology

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has been tested for small (1 to 10 km2; Granger et al. 1996)
and large (102 to 105 km2; Schaller et al. 2001) drainage basins, as well as in different geologic and climatic settings(Portenga and Bierman 2011 and references therein). Manyregional-scale cosmogenic studies indicate that environmental parameters, such as precipitation, temperature, altitude, basin slope, and tectonics, can influence denudation
rates (Riebe et al. 2000; von Blanckenburg 2005; Hencket al. 2011; Moon et al. 2011, Siame et al. 2011). However,quantitative assessment of the contributions from independent environmental parameters is still under debate,
due in part to the lack of direct comparison between basin
scale and site-specific denudation rates.
Depth profiles of in situ cosmogenic nuclides allow determination of site-specific denudation rates in humid
regions without the complex assumptions required forbasin-scale studies (Siame et al. 2004; Matsushi et al.
2006). Topographic highs such as mountain summits,
hilltops, and ridges are appropriate sites for depth profiling due to the minimized influence of along-slope masstransport (Shiroya et al. 2010). Another advantage stemming from the usage of depth profiles is that information regarding nuclide equilibrium is also obtained (seethe following). Cumulative concentration of a particularnuclide at an outcrop is a function of the denudation
rate (D) and exposure age (T), so that measurement of
one nuclide (typically 10Be) at the surface cannot
uniquely identify D and T. The use of depth profiles has
recently been introduced to alleviate this problem(Siame et al. 2004; Braucher et al. 2009). Depth profiles
have been used to determine the ages of fluvial terraces(Hein et al. 2009; Hidy et al. 2010; Rixhon et al. 2011).
In this study, we present denudation rates for a granitic saprolite in the Abukuma Mountains, Japan, using insitu cosmogenic nuclides measured in both depth profileand fluvial sediments. A known saprolite density is required to determine the denudation rate using cosmogenic nuclides. However, previous studies have often
treated density as a free parameter (Siame et al. 2004;
Rixhon et al. 2011). Therefore, we also conduct actual
field measurements of the saprolite density. Together
with 26Al/10Be plots of fluvial sediment, these data indicate that there are distinct variations in denudation rates
obtained from the topographic highs and from basinscale approaches.
Study area and sampling strategy

The Abukuma Mountains, a major granitic terrain in
Japan, formed as an uplifted peneplain (e.g., Koike 1968)(Figure 1). The mountains consist of low-relief hills of
granitic saprolite at an elevation of 400 to 600 m above
sea level covered by soil and vegetation. Freshly exposed
bedrock and gully development are not observed. Because the mountains are not steep, landslides are also

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Figure 1 The Abukuma Mountains, a major granitic terrain in Japan, formed as an uplifted peneplain. (a) Location of the study area.
(b) Digital elevation map of the sampling sites. (c) Close-up of the catchments. Elevation data is obtained from ASTER GDEM (http://gdem.ersdac.
jspacesystems.or.jp/). Black dots indicate the sampling sites for depth profiles. Open squares indicate the sampling sites for fluvial sediments.
Catchments of the sites are also indicated as solid lines. Numbers described are denudation rates (mm/kyr) obtained from this study.

not reported in this region (Shimizu and Oyagi 1988).
The Abukuma granitic terrain is petrologically separated
by the N-S trending Hatagawa fracture zone and theFutaba fault (Figure 1). Recent activity of a west-dipping
reverse fault with a dip slip rate of 50 to 100 mm/kyr
has been reported for Futaba fault (Fukushimaken 1999).
Annual mean precipitation is 1,465 mm with a peak in
September, and annual mean temperature is 10.3°C (calculated from 1981 to 2010 at Kawauchi, Japan; http://
www.jma.go.jp/jma/indexe.html).
Depth profile sampling sites, ABK101 (N 37.384, E
140.824) and ABK103 (N 37.482, E 140.778), are roadsideoutcrops covered by approximately 20 cm of black soil andare located near the topographic highs in the eastern partof the Abukuma Mountains at an altitude of 620 and
540 m, respectively (Figures 1 and 2, Table 1). These arerounded, gently sloping, and deeply weathered (>3 mdeep), which indicates no significant influence from catastrophic mass wasting. The saprolite exhibits original granitic textures, also indicating that no significant disturbanceor mixing has occurred during in situ weathering. The
entire study area is characterized by soil of relatively
uniform thickness that is underlain by well-developed
saprolite to appreciable depth. Samples for cosmogenic

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Figure 2 Columnar sections and photographic views of sampling sites.

nuclide measurement were collected from below the soil
horizon. Plastic tubes (5 cm long) were placed into the
granitic saprolite to determine its wet and dry density(Figure 3). Here, we use mean wet bulk density at the
sampling site for calculation because granitic saprolite contains water, in contrast to fresh rock. ABK-R1 (N 37.431,
E 140.754) and ABK-R3 (N 37.450, E 140.807) are thefluvial sites, located in the Takase River (Figure 1, Table 1).
The catchment areas of the fluvial sampling sites are
between ABK101 and ABK103 and do not include the
Hatagawa fracture zone.

Methods
Samples for depth profiles were crushed to a grain sizeof 0.35 to 1 mm, and quartz grains were subsequently

separated by chemical etching following the method ofKohl and Nishiizumi (1992). River sediments were sieved
to 0.35 to 1 mm size fractions for analysis. The purified
quartz samples (approximately 25 g) were dissolved with
HF and spiked with Be carrier (approximately 0.3 mg).
Aliquots for Be and Al were separated by column chromatography and then oxidized for accelerator mass spectrometry (AMS) measurements at the University of Tokyo.
The standards used were 07KNSTD (KNB5-1) for 10Be
(10Be/9Be ratio 2.709 × 10−11; Nishiizumi et al. 2007) andKNSTD (KNA4-2) for 26Al (26Al/27Al ratio 3.029 × 10−11;
Nishiizumi 2004). The decrease in cosmogenic nuclide
concentrations with depth has previously been modeledusing a chi-square (χ2) inversion method (Siame et al.
2004; Braucher et al. 2009). For a surface experiencing

Table 1 Site parameters and geometric properties of the drainage basins sampled for cosmogenic measurements
Site

10

Be production rate (atoms/g/yr)

26

Al production rate (atoms/g/yr) Latitude Longitude Altitude Mean basin Mean slope
°N
°E
(m)
altitude (m)c(deg)

Spallationa

Slow
muonb

Fast
muonb

Spallationa

Slow
muonb

Fast
muonb

ABK101

6.90

0.016

0.045

46.64

1.1

0.093

37.384140.824620--

ABK103

6.49

0.015

0.044

43.82

1.1

0.092

37.482140.778

540--

ABK-R1

7.07

0.016

0.045

47.77

1.1

0.094

37.431140.754

463

649

13.9

ABK-R3

6.58

0.015

0.044

44.43

1.1

0.092

37.450140.807

339

551

12.0

a

Production rates by high-energy spallation are calculated following Stone (2000) for altitudinal and latitudinal scaling. This is the most commonly used scaling
scheme in the existing literature. The scaling factor is a function of atmospheric pressure and geographic latitude; bproduction rates by slow and fast muons arecalculated according to Braucher et al. (2011); cmean altitudes of the catchments are calculated by ArcGIS for production rates of fluvial sediments.

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Figure 3 The sampled saprolite. (a) Plastic tubes were placed into the granitic saprolite. (b) The sampled saprolite shows the original granite
textures, indicating that no disturbance occurred during sampling.

denudation at rate ε (cm/year) during a time interval dt,
the concentration of cosmogenic nuclides C (atoms/g) withtime t (year), and depth x (cm) is described as
−ρx
∂C
∂C
¼ P0 e Λ þ ε
−Cλ
∂t
∂x

ð1Þ

where P0 (atoms/g/year) is the surface production rate,Λ (g/cm2) is the attenuation length, ρ (g/cm3) is thedensity, and λ is the radioactive decay constant (year−1)
for 10Be (5.10 × 10−7) (Nishiizumi et al. 2007) and 26Al
(9.83 × 10−7) (Nishiizumi 2004). Considering the threereaction mechanisms (neutrons, stopping, and fast muons)and assuming constant rates of denudation, Equation 1 issolved as follows using the initial condition at time t = 0
that C = 0.

!
ρε
− λþΛ
t
Pspal Λ−ρxspal
C ðx; t Þ ¼ ρεe spal 1−eΛspal þ λ

!
ρε
− λþΛ
t
P stop Λ−ρx
stop
þ ρε
e stop 1−eΛstop þ λ

!
ρε
− λþΛ
t
Pfast Λ−ρx
fast
þ ρε
e fast 1−eΛfast þ λ

ð2ÞHere, Pspal, Pstop, and Pfast are surface production rates
for the three production mechanisms, and Λspal, Λstop,and Λfast are the effective attenuation lengths, respectively, of those three rates. Production rates for neutrons
are scaled using the method of Stone (2000) based on
the reference 10Be production rate of 4.49 (atoms/g/year)with 26Al/10Be = 6.75 (Balco et al. 2008). Production
rates for muons are calculated following Braucher et al.
(2011). This study uses the values: Λspal = 160 (g/cm2),(Lal 1991; Brown et al., 1995), Λstop = 1,500 (g/cm2),
Λfast = 4,320 (g/cm2) (Heisinger et al. 2002a, b; Braucher
et al. 2011).

The χ2 inversion model (Siame et al. 2004) for best fitting of the model is as follows:N 
X
C i −C ðxi ; ε; t Þ 2
2
χ ¼
ð3Þ
σi
i¼1
Here, Ci and σi are the measured cosmogenic nuclide
concentration and its standard deviation at the depth xi,
respectively, and C(xi, ε, t) is the theoretical concentration computed using Equation 3 with a given timedenudation (ε, t) pair. A nuclide concentration at a variety
of depths below the surface can provide both D and T information. Not only does this approach allow determination of ages (Hein et al. 2009; Hidy et al. 2010; Rixhon
et al. 2011) but also allows testing of the equilibrium condition. On topographic highs, where cosmic ray exposure
is infinitely long, exposure time calculated by the χ2
method is expected to indicate equilibrium. If mass movement has significantly influenced the outcrop, χ2 inversion
would exhibit lower, nonequilibrium values. Therefore,
this method is useful for confirming the existence of theequilibrium condition, which is required to accurately calculate denudation rates. Uncertainties of denudation rates
include both uncertainty of density and uncertainty ofχ2 inversion, determined as χ2 ≤ χ2min + 1 following themethod of Rixhon et al. (2011).
Basin-scale denudation rates from river-born quartz
are also determined following the method of Granger et al.
(1996), where the terms are the same as those listed
previously.
ε¼

P spal Λspal þ P stop Λstop þ P fast ΛfastCρð4Þ

Mean altitudes of the catchments calculated by ArcGIS with ASTER GDEM elevation data (http://www.
gdem.aster.ersdac.or.jp/) are used for production rates offluvial sediments (Table 1). The effects of topographic
shielding are insignificant and therefore not included

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because the production rate is not affected by the lowrelief geometry of the study area.

Table 2 Summary of density measurements
SampleDepth Wet density 1σ error Dry density 1σ error(g/cm3)(m)(g/cm3)Results

ABK101-8d

39.0

1.64

0.07

1.41

0.06

χ fitting for the depth profiles

ABK101-12d

108.3

1.68

0.07

1.47

0.06

ABK101-20d

248.5

1.65

0.07

1.43

0.06

ABK103-1d

37.2

1.59

0.07

1.43

0.06

ABK103-3d

81.7

1.61

0.07

1.45

0.06

ABK103-8d

193.2

1.62

0.07

1.45

0.06

2

Measured wet bulk densities ranged between 1.59 and1.68 g/cm3 with no systematic depth trend (Figure 4,
Table 2). Similar stability of the dry bulk density indicates constant water content. Therefore, we used theaverage wet bulk density of each sampling site for calculation of cosmogenic nuclide depth profiles. The values
are 1.66 ± 0.07 and 1.61 ± 0.07 g/cm3 for sites ABK101
and ABK103, respectively.
Figure 5 shows that measured 10Be and 26Al concentrations decrease exponentially with depth (Table 3).
Low χ2 values are distributed parallel to the axes of exposure age (Figure 6). Therefore, χ2 fitting indicates thatsteady-state concentrations have been reached. Denudation
rates at site ABK101 are 73 ± 9 and 85 ± 9 mm/kyr for 10Be
and 26Al, respectively, whereas 67 ± 9 and 82 ± 11 mm/kyr
were measured for 10Be and 26Al, respectively, at site
ABK103 (Figures 5 and 6). The uncertainty reflects uncertainties in both measurements of density and χ2 inversion.
Although the modeled curves are not perfectly fit to themeasured concentration, two independent lines of evidence indicate that the derived denudation rates are reliable. First, rates calculated from both 10Be and 26Al areconsistent, and second, both sampling sites exhibit almost
identical denudation rates. Thus, we interpret that thecosmogenic nuclides data accurately represent local denudation rates. It should be noted that relatively large χ2values are observed for 10Be profiles compared with 26Al
profiles at site ABK103 (Figure 6). This might due torelatively high 10Be/9Be ratios for the process blanks(Table 3) compared with those used in recent publications(e.g., Larsen et al. 2014).
Denudation rates from fluvial sediments

Basin-scale denudation rates are calculated from theconcentration of cosmogenic nuclides using Equation 4.
For river sediments, we used 1.63 ± 0.07 g/cm3 as thedensity of the basin, which is the average value of sites
ABK101 and ABK103. This assumption is justified because
these two values are consistent within their uncertainties.
Furthermore, well-developed saprolite is widespread andrepresentative at the scale of the entire catchment, whichallows us to calculate the denudation rates for the basinsusing the measured density at the sites of the depth
profiles. The catchment-averaged denudation rate ofsite ABK-R1 is 123 ± 14 and 114 ± 18 mm/kyr, as obtained from 10Be and 26Al, respectively. ABK-R3 exhibits rates of 167 ± 17 and 180 ± 26 mm/kyr from 10Be
and 26Al, respectively. In most previous studies, only a single nuclide, typically 10Be, is measured for determination

ABK101

1.0 1.2 1.4 1.6 1.8 2.0 0

ABK103102030

1.0 1.2 1.4 1.6 1.8 2.0 0

0

0

50

50

100

100

150

150

200

200

250

250

300

300

dry density

wet density

10

water content

Figure 4 Dry density (open circles), wet density (filled circles), and water content (squares) of the samples.

20

30

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00
ABK101

50

50

100

100

Depth (cm)Depth (cm)ABK101

Denudation rate150

73 ± 9 mm/kyr

200

85 ± 9 mm/kyr

200
250

250

300

300
2

0

4
6
8 10 12 14
104
Be concentration (10 atoms/g)

10

ABK103

50

50

100

100

Denudation rate150

67 ± 9 mm/kyr

200
250

2
26

Depth (cm)Depth (cm)Denudation rate

150

3

4

5

6

7

5

Al concentration (10 atoms/g)

ABK103

Denudation rate150

82 ± 11 mm/kyr

200
250

300

300
2

1

4
6
8 10 12 14
104
Be concentration (10 atoms/g)

2
26

3

4

5

6

7

5

Al concentration (10 atoms/g)

Figure 5 Depth profile of cosmogenic nuclides (circles) with model-best-fit (curve) concentrations based on steady denudation(Equation 2). Error bars show analytical uncertainties (1σ).

Table 3 Summary of sample data from the Abukuma Mountains
SampleDepth Dissolved(cm) quartz (mg)

ABK101-8

39.0

25,028.70

10Be/9Be 1σ error(10−14) (10−14)
10.63

0.66

10

1σ error
Be concentration(104 atoms/g)(104 atoms/g)
8.43

0.53

26

Al/27Al 1σ error(10−13) (10−13)
2.37

0.14

26

1σ error
Al concentration(105 atoms/g)(105 atoms/g)
4.38

0.26

ABK101-10

73.6

25,020.16

6.35

0.48

5.05

0.38

1.73

0.14

3.02

0.24

ABK101-12

108.3

24,973.98

4.59

0.41

3.68

0.33

1.70

0.13

3.57

0.28

ABK101-14

142.9

25,009.59

-

-

-

-

1.32

0.12

2.47

0.23

ABK101-17

194.9

25,012.77

4.81

0.41

3.82

0.33

1.09

0.12

2.15

0.23

ABK101-20

248.5

24,978.36

-

-

-

-

0.99

0.11

1.91

0.21

ABK103-1

37.2

25,007.06

16.63

0.92

13.05

0.72

2.40

0.18

5.57

0.42

ABK103-3

81.7

25,003.43

5.24

0.39

4.17

0.31

1.34

0.12

3.07

0.28

ABK103-5

126.3

24,997.33

-

-

-

-

1.29

0.15

2.53

0.29

ABK103-12

282.4

22,166.50

3.44

0.33

3.08

0.29

0.87

0.14

2.03

0.33

ABK-R1-

29,839.39

10.42

0.53

6.96

0.36

2.98

0.30

5.29

0.52

ABK-R3-24,123.85

5.83

0.26

4.80

0.22

2.01

0.17

3.16

0.26

Background values of 10Be and 26Al are subtracted using the value of each process blank, which is treated in the same batch. 10Be ratios of process blanks for depth
profile and river sediment are 2.63 ± 0.20 × 10−14 and 2.13 ± 0.12 × 10−14, respectively. These values are indistinguishable from the value of 10Be/9Be of added commercial
100 ppm Be carrier (Wako Co., Ltd.; 2 × 10−14), and the long-term average value of the process blank (2 × 10−14). 26Al ratios of process blanks for depth profile and river
sediment are 5.28 ± 0.74 × 10−15 and 7.12 ± 7.12 × 10−16, respectively. Counting errors (1σ) of standards and process blanks measured with AMS are propagated to thecounting uncertainty on the sample ratios. We do not have Be data for ABK101-14, −20, and ABK103-5 because sample treatment was unsuccessful.

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Figure 6 Contour plots of the log(χ2) based on Equation 2. Blue areas indicate where equilibrium conditions are reasonable.

ABK-R110

Bezero erosion lineAl/

ABK-R326of catchment-averaged denudation rate. However, denudation rates derived from a single nuclide may be biased bycomplex exposure histories (Wittmann et al. 2011). In
order to test the steady-state denudation model, thedata are plotted on an ‘erosion-island’ graph (Lal 1991)(Figure 7). The plots show close agreement between denudation rates based on 10Be and 26Al, within error
limits, inside the ‘erosion-island’ area, supporting thatthese samples do not record complex exposure histories.
Although complex histories of sediment transportation
cannot be ruled out completely because of the large uncertainties, the combination of 10Be and 26Al results indicates negligible Myr-scale sediment burial. The large
uncertainties are more likely the result of low cosmogenic nuclide concentration, resulting from the fast denudation rate taking place in low elevation area, whichleads low nuclide production.

steady state erosion line

complex exposure history

10

Discussion
Density dependence of nuclide concentration profiles

Denudation rates calculated from Equations 2 and 4 arehighly sensitive to density variation, with large changes
resulting from reasonable density adjustments. For example, substitution of 2.00 g/cm3 for the measured value

26

10

Be (atoms/g)

Figure 7 Plot of Al/ Be ratios versus 10Be concentration of
fluvial samples with 1σ errors. 10Be concentrations are normalized
for values at sea level and high latitude. Zero denudation andsteady-state denudation lines are shown as solid lines. 26Al/10Be
ratios indicate that these samples do not have complex exposure
histories detected by the 26Al/10Be system.

Nakamura et al. Progress in Earth and Planetary Science 2014, 1:9
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89 ± 3 mm/kyr for 10Be and 26Al-based determinations,
respectively. These values are 1.4 times larger than theinitial values reported by Shiroya et al. (2010), indicatingthat direct density measurements are indeed crucial for
determining accurate denudation rates. These reanalyzed values are consistent with values obtained fromsites ABK101 and ABK103 in the present study. Hence,
the three sampling sites at topographic highs in the Abukuma Mountains show consistent values between 67 and
89 mm/kyr.
Comparison between depth profile and fluvial methods

Denudation rates deduced from analyses of fluvial sediments are 1.3 to 2.7 times larger than those determinedfrom depth profiles (p < 0.01). Multiple depth profiles ofcosmogenic nuclides provide the denudation rate of thesummit plane, whereas fluvial sediments represent abasin-scale average. Thus, our measurements show that
there are contrasts in denudation rates between topographic highs and the entire basin as a whole, primarily
due to differences in surficial gradient. This supports
previous studies that found that the slope angle of abasin significantly affects the overall denudation rate
(Riebe et al. 2000; von Blanckenburg 2005). However, it
should be noted that the mean basin slope is 13.9° and
12.0° for ABK-R1 and ABK-R3, respectively (Table 1), indicating that fluvial denudation rates are not sensitive tosmall differences in slope angles in the study area before
the threshold for hill slope stability is reached. The slow
upper stream denudation rate is also not attributed tothe spatial distribution of the slope angle because thetwo basins exhibit a similar slope pattern (Figure 8). The

ABK-R1
ABK-R3Frequencyof 1.66 g/cm3 changes the 10Be denudation rate of
ABK101 from 73 to 54 mm/kyr, a 25% change resulting
from only a 0.34 g/cm3 shift in density. This underscores
the importance of accurate density measurements, as
has been previously reported by several authors.
Braucher et al. (2009) suggested that the density usedby Hidy et al. (2005) was too high and advocated consideration of density as a free parameter for denudationand time. Hidy et al. (2010) measured density by inserting a pliable plastic bag into the sampling hole and filling it with a measured quantity of water to determine
the volume of the excavated mass of rock. They statethat density measured in the field should be considereda maximum value because excavation of a very coarse
boulder to gravel-sized fillings may lead to systematic
error. They therefore allowed the density to vary randomly using Monte Carlo simulations. Rixhon et al.
(2011) treated density as a free parameter, adjusting it
within a 1.8 to 2.4 g/cm3 range.
Although these studies have attempted to identify
density variations, accurate measurement of density forterrace sediments is complicated by the presence ofboulders. In contrast, we successfully measured density
by employing the newly developed technique of using
constant volume plastic tubes for granitic saprolite.
Time-dependent variation in density (Rodés et al. 2011)is negligible in the study area because of the homogeneous distribution of granitic saprolite with little differential weathering. Measured density exhibits a constantvalue with depth, indicating that chemical weathering
gradients are not significant for the time scale of interest. In addition, granitic saprolite is widely and homogenously distributed at scales larger than outcrop size(>3 m deep, >10 m wide). Therefore, denudation rates
determined in our study are indicative of those following
saprolite formation. Note that the density of soil above
the saprolite was not measured because plant roots
blocked the sampling tube. Nevertheless, density of soil
does not affect our interpretation because its thickness
is only 20 cm and its density, typically regarded as 1.4–
1.8 g/cm3 (Siame et al. 2011; Heimsath et al. 2012), is indistinguishable from that of the saprolite.
We reanalyzed the denudation rates reported by
Shiroya et al. (2010) in the western part of the Abukuma Mountains using actual measured density. They
determined denudation rates from the depth profile ofa quartz vein in granitic saprolite along a mountainridge assuming 2.2 g/cm3 for the density of wet granitic
saprolite. The reported denudation rates were 61 + 6/–4
and 62 + 4/–3 mm/kyr based on 10Be and 26Al depth
profiles, respectively. In the current study, we applied theactual density of the rock at this site (1.76 ± 0.03 g/cm3)
and parameters described in Shiroya et al. (2010) forrecalculation, which resulted in rates of 86 ± 2 andPage 9 of 11

Slope (deg)Figure 8 Spatial distribution of slope angle.

Nakamura et al. Progress in Earth and Planetary Science 2014, 1:9
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lower basin-scale denudation rate of ABK-R1 comparedwith ABK-R3 is likely derived from localized low denudation rates due in part to its location proximal to theridgeline.
Subtraction of the site-specific denudation rate fromthe basin-scale rate (29 to 113 mm/kyr) represents therate of change of local topographic relief. Overall, local
topographic relief of the Abukuma Mountain is interpreted to be increasing. This is the first comparison ofthese two methods in the same lithological region in
Japan, which allows us to quantitatively investigate regional landscape evolution. Yamamoto (2005) showedthat fluvial incision rates, based on tephrostratigraphy,
are 80 to 150 mm/kyr during the Late Quaternary according to the relative height of fluvial terraces. This isconsistent with our results. Comparison between rates
derived from depth profiles and those applicable to theentire basin is important for understanding landscapedevelopment. This requires careful site selection of topographic highs in order to obtain denudation rates thathave minimal potential slope influence.

Conclusions
We compare denudation rates derived from cosmogenic
nuclide data from the Abukuma Mountains between
summits and catchments. This is the first comparison ofthese two methods in the same lithological region, where
the entire study area is characterized by well-developed
saprolite. Slope angle strongly affects the basin-scale averaged denudation rates by as much as 1.3 to 2.7 times,
whereas rates derived from depth profiles at summit
sites are unaffected. The importance of physical density
measurements, as opposed to modeled values, to obtainaccurate denudation rates is demonstrated. Denudation
rates of topographic highs inferred from depth profilesof cosmogenic nuclides are 67 to 85 mm/kyr, whereas
basin-scale denudation rates derived from concentrationof cosmogenic nuclides in fluvial sediments indicate 114
to 180 mm/kyr.
Competing interests
The authors declare that they have no competing financial interests.
Authors’ contributions
AN collected the samples, performed experiments, analyzed data, and wrote
the paper. YY designed and directed the project, collected the samples, andcontributed in writing the paper. KS and YM collected the samples with AN.
HM conducted accelerator mass spectrometry experiments along with AN.
All authors participated in the data analysis and interpretation of the results.
All authors read and approved the final manuscript.
Acknowledgements
This work was supported by JSPS NEXT program GR031 and GCOE program.
We thank Dr. L.L. Siame and an anonymous reviewer for their insightfulreviews. We thank A. Suzuki, A. Horio, and S. Ochiai for their assistance and
S.P. Obrochta for discussing the manuscript.

Page 10 of 11

Author details
1
Atmosphere and Ocean Research Institute, University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8564, Japan. 2Department of Earth andPlanetary Science, Graduate School of Science, University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. 3Institute of Biogeoscience, Japan
Agency of Marine Science and Technology (JAMSTEC), 2-15 Natsushima-cho,
Yokosuka, Kanagawa 237-0061, Japan. 4Geological Survey of Japan, National
Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba
Central 7, 1-1-1 Higashi, Tsukuba 305-8567, Japan. 5Department of Nuclear
Engineering and Management, The University of Tokyo, Yayoi 2-11-16, Bunkyo-ku, Tokyo 113-0032, Japan.
Received: 6 December 2013 Accepted: 23 April 2014
Published: 21 May 2014
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Cite this article as: Nakamura et al.: Direct comparison of site-specificand basin-scale denudation rate estimation by in situ cosmogenic
nuclides: an example from the Abukuma Mountains, Japan. Progress inEarth and Planetary Science 2014 1:9.

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