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Understanding earth's eroding surface with Understanding earth's eroding surface with
1010
Be Be
Eric W. Portenga
University of Vermont
Paul R. Bierman
University of Vermont
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Portenga EW, Bierman PR. Understanding Earth’s eroding surface with 10 Be. GSA today. 2011
Aug;21(8):4-10.
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4 AUGUST 2011, GSA TODAY
Understanding Earth’s eroding surface with
10
Be
Eric W. Portenga, Dept. of Geology, University of Vermont, 180
Colchester Ave., Burlington, Vermont 05405, USA, eporteng@
uvm.edu; Paul R. Bierman, Dept. of Geology and Rubenstein
School of the Environment and Natural Resources, University of
Vermont, 180 Colchester Ave., Burlington, Vermont 05405, USA,
pbierman@uvm.edu
ABSTRACT
For more than a century, geologists have sought to measure the
distribution of erosion rates on Earth’s dynamic surface. Since the
mid-1980s, measurements of in situ
10
Be, a cosmogenic radionu-
clide, have been used to estimate outcrop and basin-scale erosion
rates at 87 sites around the world. Here, we compile, normalize,
and compare published
10
Be erosion rate data (n = 1599) in order
to understand how, on a global scale, geologic erosion rates inte-
grated over 10
3
to 10
6
years vary between climate zones, tectonic
settings, and different rock types.
Drainage basins erode more quickly (mean = 218 m Myr
−1
;
median = 54 m Myr
−1
) than outcrops (mean = 12 m Myr
−1
; median
= 5.4 m Myr
−1
), likely reflecting the acceleration of rock weathering
rates under soil. Drainage basin and outcrop erosion rates both
vary by climate zone, rock type, and tectonic setting. On the global
scale, environmental parameters (latitude, elevation, relief, mean
annual precipitation and temperature, seismicity, basin slope and
area, and percent basin cover by vegetation) explain erosion rate
GSA Today, v. 21, no. 8, doi: 10.1130/G111A.1
Figure 1. Geographical distribution of cosmogenic
10
Be erosion rate data (see supplemental data Tables DR1–DR3 [see text footnote 1]). (A) Location of
studies compiled in this paper. (B) Distribution of outcrop samples and (C) drainage basin samples. Symbols sized to reflect the number of samples per
study and colored to indicate relative erosion rate. Note: Citations included within this figure are listed with the supplemental data text.
GSA TODAY, AUGUST 2 011 5
1
GSA supplemental data item 2011216, reference list for text Figure 1, erosion rate recalculation methods, ArcGIS data extraction methods, statistical
methods, results of statistical analyses (including Figs. DR1–DR4), and bedrock and drainage basin erosion rate data tables (Tables DR1–DR5),
is online at www.geosociety.org/pubs/ft2011.htm. You can also request a copy from GSA Today, P.O. Box 9140, Boulder, CO 80301-9140, USA;
gsatoday@geosociety.org.
variation better when they are combined in multiple regression
analyses than when considered in bivariate relationships. Drainage
basin erosion rates are explained well by considering these envi-
ronmental parameters (R
2
= 0.60); mean basin slope is the most
powerful regressor. Outcrop erosion rates are less well explained
(R
2
= 0.32), and no one parameter dominates. The variance of ero-
sion rates is better explained when subpopulations of the global
data are analyzed. While our compilation is global, the grouped
spatial distribution of cosmogenic studies introduces a bias that
will only be addressed by research in under-sampled regions.
INTRODUCTION
Accurate global mapping, understanding, and prediction of geo-
logic or background erosion rates is important because erosion is
the means by which sediment is generated, fresh rock is exposed
to CO
2
-consuming weathering reactions, soil is created, landforms
change over time, and mass is moved from the continents to the
oceans and eventually recycled via the process of subduction and
volcanism. Earth’s ability to support billions of inhabitants depends
critically on the resiliency of the soil system and the purity of sur-
face waters, both of which erosion affects directly. Thus, measur-
ing the rate and spatial distribution of erosion on millennial time
scales is fundamental to understanding how landscapes evolve
through time and for placing human environmental impacts in
context (Hooke, 1994, 2000).
Yet, geoscientists are largely lacking the data to develop a global
model that can predict, with accuracy or precision, the background
rate and spatial distribution of erosion on Earth’s dynamic surface.
It is even more difficult to predict how erosion rates respond to
changes in boundary conditions including tectonic and climatic
forcing. Understanding how rates of erosion are related to com-
plex, non-linear feedbacks between multiple Earth systems includ-
ing the solid Earth (tectonic regime), the climate (precipitation and
temperature), and the biosphere (vegetation) is prerequisite to de-
veloping such a model.
Throughout the twentieth century, geologists used a variety of
tools to measure rates of erosion (e.g., Saunders and Young, 1983).
The most common approach equated sediment yield with erosion
rate (Dole and Stabler, 1909; Judson, 1968). Such an approach pre-
sumes that human impact is inconsequential and that short-term
measurements of sediment flux are representative of long-term flux
rates, but both assumptions have been repeatedly questioned (e.g.
Kirchner et al., 2001; Trimble, 1977; Wilkinson, 2005), and various
modeling approaches have been implemented (Syvitski et al., 2005)
to overcome the limitations of sediment yield data.
Geologic erosion rates are useful for placing human impact on
the sedimentary system and global environment in context. Until
recently, no one method of measuring geologic erosion rates
directly was globally applicable. The development of Accelerator
Mass Spectrometry (AMS) allowed rapid, high-precision, low-
detection limit measurement of in situ–produced cosmogenic radio-
nuclides (Elmore and Phillips, 1987), the concentration of which
reflects near-surface residence time and thus the pace of surface
processes (Bierman and Nichols, 2004). In situ–produced
10
Be, ex-
tracted from purified quartz, is now routinely used to estimate how
quickly outcrops and drainage basins erode over geomorphically
meaningful time scales (e.g., Bierman and Caffee, 2001; Bierman
and Steig, 1996; Brown et al., 1995; Granger et al., 1996; Nishiizumi
et al., 1986; Schaller et al., 2001; Small et al., 1997).
The method relies on the observation that cosmic rays interact
with Earth’s surface, producing
10
Be, an otherwise exceptionally
rare isotope. The production of
10
Be occurs predominantly within
a few meters of Earth’s surface and decreases exponentially with
depth. Thus, the concentration of
10
Be in outcropping rock or in
fluvial sediment reflects near-surface residence time. Cosmogenic
rate estimates reflect the time it takes to erode several meters of
rock or sediment, typically 10
3
to 10
6
years, the integration time
being inversely proportional to the erosion rate. In bedrock out-
crops, erosion rates are inferred, assuming erosion occurs steadily
through time. Sampling river sand presumes that stream networks
mix and deliver sediment from the entire basin. Because soils are
typically well-stirred by physical and biological processes, shallow,
human-induced soil erosion does not typically affect cosmogenic
estimates of basin-scale erosion rates.
Many local and regional-scale cosmogenic studies (now 87) in-
dicate that individual environmental parameters can influence
millennial-scale erosion rates, although the results are not uniform.
Parameters considered in the past include latitude, elevation, re-
lief, seismicity, basin slope and area, percent basin cover by veg-
etation, and mean annual precipitation and temperature. In order
to understand the relationship between erosion rates and environ-
mental parameters, we compiled all publicly available outcrop and
drainage basin erosion rates inferred from measurements of
10
Be
(Fig. 1). After standardizing the data for changes in
10
Be half-life
(Nishiizumi et al., 2007), production rate (Balco et al., 2008), and
scaling schemes (Lal, 1991) used over the past 24 years, we com-
pared erosion rates and a variety of environmental parameters,
both individually and using multivariate statistical methods. The
result is a description, at a global scale, of the relationship between
these parameters and the erosion rate of both outcrops and drain-
age basins. Such relationships are important for understanding the
behavior of Earth’s sedimentary system over a variety of spatial
and temporal scales as geologists attempt to make sense of human
impacts on erosion and sediment generation (Hooke, 1994; Mont-
gomery, 2007; Wilkinson, 2005).
We recognize that a spatial bias introduced to our analyses is due
to the small number of studies carried out in South America, Africa,
the Middle East, and the polar latitudes as well as the fact that the
number of samples from each study varied in size. Our compilation
and analyses are carried out using available data, however, and fur-
ther sampling in under-studied regions can only improve our under-
standing of how different factors control erosion rates.
METHODS
We compiled all publicly available in situ
10
Be erosion rate data
(Fig. 1; Tables DR1–DR3
1
). We included only unshielded outcrop-
ping bedrock samples collected from horizontal or subhorizontal
surfaces and modern stream sediment samples from drainage ba-
sins that did not experience extensive recent glacial cover. For
each sample, we collected data necessary to recalculate erosion
rates (Table DR1). In some cases, information was provided in the
original publications; in other cases, we contacted authors directly.
Samples in this compilation required recalculation because con-
straints on production rates, neutron attenuation path length, and
6 AUGUST 2011, GSA TODAY
the
10
Be half-life have improved over time and values used in indi-
vidual studies varied widely.
We used the CRONUS online calculator for erosion rate esti-
mates (Balco et al., 2008; http://hess.ess.washington.edu/). Effec-
tive elevation, or the production-rate weighted average elevation
for a basin, and effective latitude were determined (see supple-
mental data methods section [footnote 1]), enabling us to use the
CRONUS calculator for determining drainage basin erosion rates.
CRONUS-calculated erosion rates for outcrops and basins strongly
and significantly correlate to their original published erosion rates
(Figure DR1).
We compared erosion rates for outcrops and drainage basins to
latitude (°N or °S), elevation (meters above sea level [masl]), mean
annual precipitation (MAP; mm yr
−1
) and temperature (MAT; °C),
seismicity (peak ground acceleration [PGA; see supplemental data
{footnote 1}], where seismically active sites have PGA >2), basin
area (km
2
), mean basin slope (°), and percent basin coverage by
vegetation. These parameters are used because they are the most
commonly analyzed metrics in cosmogenic erosion rate literature
to date. We extracted data from global datasets using ArcGIS (Ta-
ble DR4). Not all global coverages extend to Antarctica. Antarctic
climate data were modified from Monaghan et al. (2006), and be-
cause seismicity data were not available for Antarctica, those sites
are excluded from some of our analyses. See the supplemental
data for details regarding these parameters.
We used a variety of statistical methods (see supplemental data
[footnote 1]). These parametric statistical tests assume a normal
sample distribution. Because both outcrop and drainage basin ero-
sion rate distributions are highly skewed (Fig. 2), we log-trans-
formed (base 10) all erosion rate data before performing statistical
tests; this transformation produced a more normally distributed
dataset. Bivariate analyses were carried out for numeric parame-
ters, and we completed analyses of variance and Student’s t-Tests
for nominal data. We also performed forward stepwise regressions
for each global dataset and for each subgroup of nominal data
categories. Parameters were entered into the regression based on
their ability to statistically improve the regression. If a variable did
not significantly improve the regression, it was omitted.
RESULTS
Outcrop Erosion Rates
Outcrops (n = 450) erode at an average rate of 12 ± 1.3 m Myr
−1
.
The median erosion rate is 5.4 m Myr
−1
, reflecting the highly
skewed distribution (Fig. 2B). In bivariate global comparisons
(Fig. DR2), outcrop erosion rates are unrelated to absolute latitude,
elevation, or seismicity. Globally, outcrop erosion rates co-vary
weakly with relief and MAP; the highest outcrop erosion rates oc-
cur where MAT is ~10 °C.
Analysis of variance (ANOVA) shows that outcrops in seismically
active regions erode similarly (14 ± 1.6 m Myr
−1
; n = 55) to those
in seismically inactive areas (13 ± 1.4 m Myr
−1
; n = 395) but that
outcrop erosion rates differ by lithology and climate (Fig. 3). Erosion
rates of sedimentary (20 ± 2.0 m Myr
−1
; n = 118) outcrops are faster
than metamorphic outcrops (11 ± 1.4 m Myr
−1
; n = 102) and igne-
ous outcrops (8.7 ± 1.0 m Myr
−1
; n = 230), which are statistically
similar. The average outcrop erosion rate in temperate climates
(25 ± 2.5 m Myr
−1
; n = 85) is significantly higher than those in any
other climate zone except for erosion rates in tropical zones.
Outcrops in polar climates erode most slowly (3.9 ± 0.39 m Myr
−1
;
n = 31). Median values show similar trends (Fig. 4).
Figure 2. Erosion rate data. (A) Exceedance probability for compiled erosion rates. (B) Histogram of outcrop erosion rates. (C) Histogram of drainage basin
erosion rates. (D) Histograms of erosion rates after being log-transformed (base 10) showing normally distributed datasets for statistical analyses; outcrops
are green lines and drainage basins are red lines.
Figure 3. Analysis of variance (ANOVA) for the log-transformed CRONUS
erosion rates on outcrop and drainage basin samples categorized by rock
type, climate zone, and tectonic regime. Letters below each box-plot rep-
resent the results from paired Student’s t-Tests—categories linked by a
similar letter are similar at p <0.05. Green lines are means; red lines are
medians. Box defines 25th and 75th percentiles. Whiskers represent data
range, excluding statistical outliers.
GSA TODAY, AUGUST 2 011 7
A forward stepwise regression shows that 32% of the variation in
the global population of outcrop erosion rates can be described by
five parameters; MAP is the most important regressor (Fig. 4). For
individual climate zones, lithologies, and seismic regimes, the rele-
vant parameters and their weighting vary greatly (Fig. 4; Table DR5).
Drainage Basin Erosion Rates
On average, sampled drainage basins erode at 218 ± 35 m Myr
−1
(n = 1149). The distribution is highly skewed, with a median ero-
sion rate of 54 m Myr
−1
(Fig. 2C). At the global scale, basin slope
yields the strongest bivariate correlation, with erosion rates (R
2
=
0.33, Fig. 5; Fig. DR3). Basin relief, mean elevation, and seismicity
also have significantly positive, bivariate correlations. MAT has a
very weak negative correlation. There is no significant bivariate
correlation between basin erosion rates and latitude, MAP, or basin
area (Fig. DR3).
Analysis of variance (Fig. 3) indicates that the average erosion
rate for seismically active basins (367 ± 55 m Myr
−1
; n = 221)
is significantly higher than in seismically inactive basins (182 ±
30 m Myr
−1
; n = 928). The average drainage basin erosion rate in
polar climates (537 ± 125 m Myr
−1
; n = 71) is higher than in all
other climate zones. Arid region drainage basins erode most slowly
(100 ± 17.3 m Myr
−1
; n = 229). Results are less clear for lithology.
On average, metamorphic terrains erode more rapidly than
other lithologies, but this is not reflected in ANOVA results on log-
transformed data (Fig. 3).
Forward stepwise regressions of basin erosion rates show that
all nine parameters together significantly describe 60% of variabil-
ity in the global data set (Fig. 4). For nearly every basin-scale
subcategory, basin slope is the most significant regressor (Fig. 4).
The remaining parameters are highly variable in terms of their re-
gression power. Basin area, MAT, and elevation have low weights
for nearly all subcategories in which they appear.
DISCUSSION
While summaries of
10
Be erosion rate data have been presented
in the past (e.g., Bierman and Nichols, 2004; von Blanckenburg,
2005), our compilation of 1599 measurements of in situ–produced
10
Be provides the first broad, standardized view of pre-human,
geologic erosion rates (Figs. 1 and 2). Compiled outcrop erosion
rates are slow and do not exceed 140 m Myr
−1
, similar to rock
weathering rates measured in the past (Saunders and Young,
1983). Some cosmogenic studies in tectonically active zones (i.e.,
Binnie et al., 2006, 2008; DiBiase et al., 2009) indicate drainage
basin erosion rates higher than previously reported (Saunders and
Young, 1983).
Spatial Distribution of Existing Samples
Our compilation is global; however, large portions of Earth re-
main unsampled, meaning that the data are not randomly distrib-
uted (Fig. 1). Drainage basin cosmogenic data represent only 2.3%
of the world’s land area. Latitudes with large sample populations,
between 30°–50° north and south, correspond to Europe, the
United States, and Australia—easily accessible locations. There are
Figure 5. Mean basin slope and erosion rate co-vary. Correlation is scale-
dependent and decreases with increasing area included in the sample:
Appalachian Plateau within the Susquehanna River Basin (red squares;
Reuter, 2005); Appalachian Mountains crest data (green triangles; Matmon
et al., 2003; Reuter, 2005; Sullivan, 2007); and global data set (gray circles;
references in Table DR1 [supplemental data; see text footnote 1]).
Figure 4. Forward stepwise regressions for outcrop
and drainage basin datasets considered globally
and by subdivisions of categorical data. Colored
boxes indicate parameters that significantly ex-
plain erosion rate variance. The number in each
colored box is the amount of the overall R
2
value
contributed by the corresponding parameter.
The R
2
value listed at the bottom of each column
represents the total amount of variation in the
data that is explained by the significant parame-
ters. Regressions use log-transformed CRONUS
erosion rates. Mean and median values calculated
from CRONUS erosion rates.
![Figure 5. Mean basin slope and erosion rate co-vary. Correlation is scaledependent and decreases with increasing area included in the sample: Appalachian Plateau within the Susquehanna River Basin (red squares; Reuter, 2005); Appalachian Mountains crest data (green triangles; Matmon et al., 2003; Reuter, 2005; Sullivan, 2007); and global data set (gray circles; references in Table DR1 [supplemental data; see text footnote 1]).](/figures/figure-5-mean-basin-slope-and-erosion-rate-co-vary-2sy26ook.webp)
![Figure 1. Geographical distribution of cosmogenic 10Be erosion rate data (see supplemental data Tables DR1–DR3 [see text footnote 1]). (A) Location of studies compiled in this paper. (B) Distribution of outcrop samples and (C) drainage basin samples. Symbols sized to reflect the number of samples per study and colored to indicate relative erosion rate. Note: Citations included within this figure are listed with the supplemental data text.](/figures/figure-1-geographical-distribution-of-cosmogenic-10be-19h2nznu.webp)
