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Keywords:

  • Southern Sierra Critical Zone Observatory;
  • Luquillo Critical Zone Observatory;
  • cosmogenic nuclide methods;
  • saprolite weathering

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Cosmogenic nuclides in rock, soil, and sediment are routinely used to measure denudation rates of catchments and hillslopes. Although it has been shown that these measurements are prone to biases due to chemical erosion in regolith, most studies of cosmogenic nuclides have ignored this potential source of error. Here we quantify the extent to which overlooking effects of chemical erosion introduces bias in interpreting denudation rates from cosmogenic nuclides. We consider two end-member effects: one due to weathering near the surface and the other due to weathering at depth. Near the surface, chemical erosion influences nuclide concentrations in host minerals by enriching (or depleting) them relative to other more (or less) soluble minerals. This increases (or decreases) their residence times relative to the regolith as a whole. At depth, where minerals are shielded from cosmic radiation, chemical erosion causes denudation without influencing cosmogenic nuclide buildup. If this effect is ignored, denudation rates inferred from cosmogenic nuclides will be too low. We derive a general expression, termed the ‘chemical erosion factor’, or CEF, which corrects for biases introduced by both deep and near-surface chemical erosion in regolith. The CEF differs from the ‘quartz enrichment factor’ of previous work in that it can also be applied to relatively soluble minerals, such as olivine. Using data from diverse climatic settings, we calculate CEFs ranging from 1.03 to 1.87 for cosmogenic nuclides in quartz. This implies that ignoring chemical erosion can lead to errors of close to 100% in intensely weathered regolith. CEF is strongly correlated with mean annual precipitation across our sites, reflecting climatic influence on chemical weathering. Our results indicate that quantifying CEFs is crucial in cosmogenic nuclide studies of landscapes where chemical erosion accounts for a significant fraction of the overall denudation. Copyright © 2012 John Wiley & Sons, Ltd.


Introduction

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Over the last two decades, cosmogenic nuclides have been increasingly used to quantify rates of physical and chemical erosion of saprolite (Heimsath et al., 1997, 2001; Burke et al., 2007, 2009; Dixon et al., 2009a), soils (Riebe et al., 2004b; Green et al., 2006; Yoo et al., 2007, 2009; Ferrier et al., 2011), and entire watersheds (Granger et al., 1996; Riebe et al., 2000, 2004a; Binnie et al., 2007; Norton et al., 2011). The database of denudation rates derived from cosmogenic nuclides has grown to span the globe (Portenga and Bierman, 2011), fueling a revolution in surface processes research (von Blanckenburg, 2005).

Although cosmogenic nuclide measurements are now routine, research continues on the details of how best to employ them in quantifying rates of surface processes (Balco et al., 2008). For example, it has only recently been recognized in the literature that failure to account for chemical erosion from deep saprolite can introduce significant errors in cosmogenic nuclide studies of denudation rates (Dixon et al., 2009a). The complication arises due to shielding by overlying regolith, which prevents mass losses at depth from strongly influencing the buildup of cosmogenic nuclides (Dixon et al., 2009a). Hence, in landscapes where chemical erosion from deep saprolite is a large fraction of the overall erosional flux, cosmogenic nuclides may only weakly reflect landscape denudation rates (Dixon et al., 2009a).

Chemical erosion near the surface introduces additional biases in the buildup of cosmogenic nuclides if it causes the host mineral to become enriched or depleted in regolith relative to bedrock (Small et al., 1999; Riebe et al., 2001a). Such enrichment (or depletion) of a host mineral reflects a longer (or shorter) residence time, relative to the regolith as a whole. This in turn makes it so that the cosmogenic nuclide concentration in the host mineral is not representative of the erosion rate of the surrounding regolith. Rather, host minerals that are relatively soluble (e.g. olivine) will have apparent denudation rates that are unrepresentatively fast, because of faster-than-average chemical erosion that leads to relative depletion in the regolith and thus unrepresentatively low near-surface residence times. Conversely, for host minerals that are relatively insoluble (e.g. quartz), apparent denudation rates will be too slow, because of slower-than-average chemical erosion, which results in residence times and nuclide concentrations that are both unrepresentatively high (Small et al., 1999).

Although previous studies have proposed correction factors that separately adjust for effects of deep and near-surface chemical erosion (Small et al., 1999; Riebe et al., 2001a; Dixon et al., 2009b), there has been no accurate accounting for cases in which both types of chemical erosion are important. There has also been no treatment of effects of chemical erosion on nuclide buildup in minerals other than quartz, although such minerals are now increasingly used in cosmogenic nuclide studies (Gayer et al., 2008). Moreover, few studies have used either the deep or shallow chemical erosion correction factors in their cosmogenic estimates of denudation rates. Here we explore the extent to which such oversights can introduce errors in cosmogenic nuclide studies. We derive a general expression, termed the ‘chemical erosion factor’ (or CEF), which corrects for biases introduced by chemical erosion both at depth and near the surface. Calculating CEF requires measurements of soil thickness and density and also the concentrations of both the host mineral and an insoluble element (or mineral) in soil, saprolite, and unweathered rock. We analyze data from diverse climatic settings and show that CEFs can be as high as 1.87 for cosmogenic nuclides in quartz in intensely weathered soils. This implies that accounting for chemical erosion may often be crucial to the accurate inference of denudation rates from cosmogenic nuclides. Our analysis of climatic effects on weathering indicates it may be possible to estimate CEFs for quartz in granitic landscapes using precipitation as a proxy, thus obviating the many measurements of regolith and bedrock that would otherwise be needed to calculate CEF directly using the formulations presented here.

The Chemical Erosion Factor

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Definitions and nomenclature

Because the terminology of weathering and erosion varies across disciplines, we begin by defining the terms used in our derivation and discussion of the CEF. Table 1 summarizes the nomenclature used in our equations.

Table 1. Nomenclature used in derivations
SymbolDescriptionUnits
CEFchemical erosion factorunitless
Dtotal denudation rate, equal to the regolith production rate in steady statet km-2 a-1
Wsap, Wsoilchemical erosion rate from saprolite and soil, respectivelyt km-2 a-1
Esap, Esoilrate of production (i.e. input) and physical erosion (i.e. output) of soilt km-2 a-1
Zrsoil, Zrsap, Zrrockimmobile element or mineral concentrations in soil, saprolite and rockppm
Xsoil, Xsap, Xrockconcentration of mineral X (e.g. quartz) in soil, saprolite and rockg g-1
P(0)nuclide production rate at surface due to one of the production pathwaysatoms g-1 a-1
Λattenuation length scale for nuclide production at depthg cm-2
<P>average nuclide production rate in host mineral in soilatoms g-1 a-1
<N>average nuclide concentration in host mineral in soilatoms g-1
Nsapnuclide concentration in host minerals in top of saproliteatoms g-1
ρ, hsoil density and thickness (note: their product equals soil mass per unit area)g cm-3, cm
τsoilturnover timescale of soil, equal to soil mass per unit area divided by soil denudation rateka
τnuclideradioactive meanlife of a specified nuclideMa
Hregolith thicknesscm
Aareakm2
<D>spatially averaged denudation ratet km-2 a-1
MAPmean annual precipitation ratem a-1

When discussing processes, we use ‘chemical erosion’ to refer to mass loss by alteration and dissolution of minerals during interactions with meteoric water. ‘Physical erosion’ refers to mass loss by physical removal of mineral grains, both when it occurs at the saprolite–soil interface, due to conversion of saprolite to soil, and when it occurs in soil, due to sediment transport (Figure 1). We use ‘denudation’ to refer collectively to physical and chemical erosion.

image

Figure 1. Schematic of mass-balance principles for regolith on a slope. When inputs from conversion of unweathered rock to saprolite (D) are balanced by the sum of outputs from chemical erosion of saprolite (Wsap), chemical erosion of soil (Wsoil), and physical erosion of soil (Esoil), the mass of regolith is steady. Likewise when the production of soil (Esap) is balanced by the sum of Wsoil and Esoil, soil thickness (h) is steady. Unweathered parent rock has concentrations of zirconium and host mineral X of Zrrock and Xrock. The top of immobile regolith (i.e. ‘saprolite’) has concentrations of zirconium, element X and cosmogenic nuclides of Zrsap, Xsap, and Nsap, respectively (see text). The mixed, mobile regolith (or ‘soil’) has average concentrations of zirconium, host mineral X, cosmogenic nuclides, of Zrsoil, Xsoil, and <N>, and an average density and nuclide production rate of ρ and <P>, respectively.

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In defining components of a weathering profile, we use ‘bedrock’ to refer to unweathered rock (i.e. parent material) at the base of the regolith profile. ‘Saprolite’ refers to weathered rock that retains recognizable bedrock structure and has not been physically mobilized, irrespective of its degree of chemical depletion and volumetric strain relative to unweathered rock. Following usage common in the geochemical literature, we use the term ‘soil’ to refer to material that has been physically mobilized, irrespective of its state of weathering or degree of horizonation. Finally, we use ‘regolith’ to refer collectively to the soil and saprolite that blanket unweathered rock at depth.

Geochemical mass balance of regolith

When a regolith profile is in steady state, downward propagation of weathering at the bedrock–regolith interface converts fresh rock into saprolite at a pace equal to the total denudation rate (D), which is the sum of all the regolith's erosional effluxes, including physical erosion of the soil (Esoil) and chemical erosion of both the soil (Wsoil) and saprolite (Wsap) (Figure 1). Similarly, when soil is in steady state, soil production at the saprolite–soil interface (Esap) is equal to the sum of all erosional fluxes from the soil (i.e. Esoil plus Wsoil). We can apply such steady-state, mass-balance principles both to the regolith as a whole and to individual elements and minerals within it as exemplified in Equation (1) for weathering of an element (or mineral) from saprolite:

  • display math(1)

Here WX,sap is the chemical erosion rate from saprolite of the element (or mineral), and Xrock and Xsap are its concentrations in rock and saprolite respectively (Riebe et al., 2003). For insoluble components of the saprolite and soil, chemical erosion rates are zero and Equation (1) can be rewritten and rearranged as shown in Equation (2), after Dixon et al. (2009a).

  • display math(2)

Here, Zrrock and Zrsap are the concentrations in rock and saprolite of an insoluble mineral or element (in this case zirconium). Enrichment of Zr in saprolite relative to rock reflects chemical losses of other, more soluble elements (Nesbitt, 1979; Stallard, 1985).

The mass balance can be recast into similar relationships for soils in steady state, as shown in Equation (3).

  • display math(3)

Here, WX,soil is the chemical erosion rate from soil of an element (or mineral), Xsoil is its concentration in soil, and Esoil is the erosion rate of the soil. For insoluble elements, Equation (3) reduces to

  • display math(4)

Here, Zrsoil is the zirconium concentration in the soil. The mass balance principles embodied in Equations (1)(4) are crucial to solving for the effects of chemical erosion on cosmogenic nuclide buildup, as shown next.

Effects of chemical erosion from deep saprolite and well-mixed soils

To account for the consequences of chemical erosion on cosmogenic nuclide-based estimates of denudation rates, we first write differential Equation (5), which expresses the buildup of cosmogenic nuclides in a host mineral X as a function of inputs and outputs of nuclides from a well-mixed soil (i.e. where nuclide concentrations are homogenized over timescales much shorter than that of nuclide accumulation).

  • display math(5)

Here, d<N>/dt is the rate of change of the average nuclide concentration in the host mineral in a well mixed soil, <P> is the depth-averaged nuclide production rate in the soil, Nsap is the concentration of cosmogenic nuclides in host minerals in the top of saprolite, ρ is soil density, and h is soil thickness (Figure 1). In writing Equation (5) we assume that soil mass (i.e. the product of soil density and thickness) is in steady state. This assumption is common to all studies of soil production rates (Heimsath et al., 1997), although practitioners have imprecisely stated that only soil thickness needs to be in steady state. We refer the reader to the literature for comprehensive discussions of the rationale behind steady-state assumptions in soil production rate studies (see, for example, Dietrich et al., 1995 and Heimsath et al., 1997).

Equation (5) is valid for nuclides that are either stable or have a radioactive mean life (τnuclide) that is significantly greater than ρh/Esap, the turnover timescale of the soil (τsoil). This is typically the case in mountainous settings for cosmogenic nuclides in quartz. For example, using typical values of ρ, h, and Esap (e.g. as reported in Riebe et al., 2004a), we find that τsoil generally ranges from 1 to 50 ka, significantly less than either τAl-26 = 1.0 Ma or τBe-10 = 2.0 Ma (Nishiizumi et al., 2007; Chmeleff et al., 2010).

Cosmogenic nuclides are produced in mineral grains by neutron spallation, muon capture, and interactions with high-energy muons (Heisinger et al., 2002a, 2002b). Because cosmic radiation attenuates with passage through matter, cosmogenic nuclide production rates decrease with depth in soil and rock. The precise relationship between production rates and depth remains a subject of research. However, available evidence indicates that the decline in production rates with depth can be expressed to good approximation as a series of exponentials (Granger and Smith, 2000), with <P> computed as shown in Equation (6).

  • display math(6)

Here, Pi(0) is the production rate at the surface due to mechanism i, and Λi is the corresponding scaling factor for the decline in production with depth beneath the surface (in g cm-2; see Supplemental Table 1 in online Appendix for values used here).

If chemical erosion of saprolite occurs at depths greater than a few meters, where cosmogenic nuclide production is minimal, then, in steady state, the concentration of cosmogenic nuclides in host minerals at the top of saprolite is given by Equation (7) (Lal, 1991; Heimsath et al., 1997).

  • display math(7)

Equation (7) is valid for nuclides that are stable or have a radioactive mean life that is significantly greater than Λi/Esap, and thus do not decay significantly over the timescale of nuclide buildup during exhumation to the surface.

In the case of isotopic steady state (i.e. with d<N>/dt = 0), Equation (5) can be solved as shown in Equation (8) after combination with Equations (2), (3), (6) and (7), and collection of terms.

  • display math(8)

The term in curly brackets in Equation (8) represents a series of i = 4 correction factors which correspond (one each) to the exponential decay terms in the relationship between cosmogenic nuclide production rate and depth; each term must be corrected separately because of the dependence on penetration depth (Λi), which differs among the production rate mechanisms (see Supplemental Online Data).

Equation (8) expresses the concentration of cosmogenic nuclides in sediment collected from a well-mixed soil, which is eroding in steady state. Traditionally, erosion rates have been inferred from a much simpler approximation (Lal, 1991), reproduced here in Equation (9).

  • display math(9)

Equation (9) appears in Equation (8) as a prefix. It is convenient to write Equation (10), which re-expresses Equation (8) as a correction factor (i.e. the CEF) that should be applied to denudation rates that have been inferred from Equation (9).

  • display math(10)

It is important to understand the assumptions that have gone into derivation of Equations (8) and (10). First, they are specific to chemical erosion that occurs exclusively in well-mixed soils and in deep saprolite; if significant chemical erosion occurs in shallow saprolite (at overburden depths less than or not too much greater than Λi), then the effects of chemical erosion are more complicated. In that case, the CEF would need to be computed with site-specific information on how chemical erosion varies with depth. Second, our derivation does not capture variations over time in either erosion rates or soil mass; instead, as is the case in most cosmogenic-nuclide-based formulations of erosion rates, Equations (8) and (10) require that erosion is steady over a timescale that is long enough for cosmogenic nuclide concentrations to approach steady state (Lal, 1991). Our analysis requires the additional assumption that both soil mass and its degree of chemical depletion are steady over the timescale of erosion (Heimsath et al., 1997; Riebe et al., 2001b). Estimates of CEF from Equations (8) and (10) will be erroneous to the extent that these assumptions are violated. However, according to a recent sensitivity analysis of the mass balance of eroding regolith, chemical weathering rates inferred from solid phase geochemistry are remarkably insensitive to plausible fluctuations in both soil depth and physical erosion rates, differing from the long-term average by less than 15%, even in the worst-case scenarios (Ferrier and Kirchner, 2008). Hence, Equations (8) and (10), which are based on the same mass balance principles that are used in measuring chemical weathering rates (Brimhall and Dietrich, 1987; Riebe et al., 2001b, 2003; Anderson et al., 2002), should yield estimates of CEF that are likewise robust against plausible changes over time in erosion rate and soil mass. A final note of caution in employing Equations (8) and (10) is that they are only valid for erosion rates that are rapid enough that radioactive decay can be ignored. If this is not the case, then erosion rates will be systematically overestimated due to neglect of radioactive losses of nuclides. In all of the cases discussed later, erosion rates are fast enough that radioactive decay can be ignored without introducing significant errors in the estimation of CEFs.

Simplifications in CEF arising from special circumstances

Equation (10) is a generic formulation of CEF that accounts for the effects of both deep and near-surface chemical erosion on cosmogenic nuclides such 3He, 10Be, 21Ne, 26Al in target minerals such as olivine, quartz, and magnetite. If quartz is the host mineral for the cosmogenic nuclide of interest, as has been the case in the vast majority of previous work on catchment-scale erosion rates, we can use Zrsoil/Zrsap as a substitute for Xsoil/Xsap in Equation (9). This requires the generally reasonable assumption that quartz is insoluble and thus enriched to the same degree as zirconium during chemical erosion (Riebe et al., 2001a). In that case, Equation (8) simplifies to

  • display math(11)

If weathering in the saprolite is minimal, such that Zrsap = Zrrock, Equation (11) reduces further to

  • display math(12)

Equation (12) implies a CEF that is equivalent to the quartz enrichment factor of Small et al. (1999) except here Zr enrichment is used as a proxy for quartz enrichment, as suggested by Riebe et al. (2001a).

If chemical erosion from soils is minimal, such that Zrsoil = Zrsap, or if the mass per unit area of soil (i.e. ρh) is small compared with the penetration depth for production by cosmogenic nuclides, then Equation (8) reduces to

  • display math(13)

Here, the CEF is simply Zrsap/Zrrock, equivalent to the correction factor of Dixon et al. (2009a) for chemical erosion of deep saprolite. Note that this correction factor is also more generally appropriate for correcting cosmogenic nuclides measured in the top of saprolite (i.e. using Nsap instead of <N>) as originally proposed by Dixon et al. (2009a).

If the host mineral for cosmogenic nuclides is soluble (e.g. as in the case of olivine), and if chemical mass losses in the saprolite are minimal (i.e. Zrsap = Zrrock), Equation (8) reduces to

  • display math(14)

Note that if the host mineral weathers at the same rate as the bulk soil, its concentration will be neither enriched nor depleted in soil relative to bedrock (i.e. Xsoil = Xrock). In that case, Equation (14) shows that CEF would be equal to unity. Thus Equation (10) reduces to Equation (9), the classical formulation of Lal (1991), if weathering of saprolite is negligible and if the host mineral is lost from the soil at a rate that is representative of chemical erosion of the soil as a whole (i.e. all of its minerals on average).

Gauging the Size of the Chemical Erosion Factor

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

How big is the CEF likely to be in landscapes where cosmogenic nuclides have typically been used to measure erosion rates? To find out, we calculated representative CEFs for cosmogenic nuclides in quartz for the suite of climatically diverse granitic landscapes listed in Table 2. Across these landscapes, mean annual temperature ranges from 4 to 25°C, and mean annual precipitation ranges from 0.25 to 4.2 m a-1, including diverse combinations such as cold and dry, at Adams Peak, cold and wet, at McNabb Track, hot and dry, in the Sonora Desert, and hot and wet, at the Luquillo CZO (Table 2).

Table 2. Chemical erosion factors for cosmogenic nuclides in quartz at climatically diverse granitic sites
SiteLocationAverage annualinline image ainline image bFraction of weathering in saprolitecSoil massdCEFe
LatitudeLongitudePrecip.Temp.
°N°Em a-1°C(g cm-2)
  1. All results are calculated from means of element concentrations and other values (e.g. density and depth) according to equations in the text with errors propagated using one standard error of the mean.

  2. a

    Data used in estimates of average Zrrock for each site were reported in Riebe et al. (2004a), except for those from S. Sierra CZO, which we present in the online appendix (Supplemental Table 3). Results used for average Zrsap are reported in the online appendix (Supplemental Tables 2 and 3), Riebe et al. (2001b; for Fort Sage and Adams Peak), and Riebe et al. (2003; for Luquillo CZO).

  3. b

    Data used in estimates of Zrsoil are reported in Riebe et al. (2001b, 2003 and 2004a) and Supplemental Table 3.

  4. c

    Fraction of weathering in saprolite estimated as (1–Zrrock/Zrsap)/(1–Zrrock/Zrsoil), which is the chemical depletion in the saprolite divided by the chemical depletion in the regolith as a whole.

  5. d

    Soil mass is based on data reported by Riebe et al. (2001b, 2003, and 2004a), except for S. Sierra CZO, where it is the product of the average soil bulk density of 1.38 ± 0.09 g cm-3 and average soil thickness of 65 ± 5 cm reported by Johnson et al. (2011) for measurements from 53 widely distributed soil pits.

  6. e

    CEFs are calculated from Equation (10) assuming Xsoil/Xsap = Zrsoil/Zrsap (as may often be the case for quartz) and using the 10Be production rates and penetration length scales reported in the online appendix (see Supplemental Table 1).

  7. f

    Error is substantial but undefined by simple error-propagation techniques.

Luquillo CZO18.300−67.8004.20221.39 ± 0.071.90 ± 0.070.45 ± 0.0686 ± 311.79 ± 0.14
McNabb Track, NZ−41.000172.1334.0081.77 ± 0.111.15 ± 0.090.86 ± 0.08120 ± 381.87 ± 0.13
Chiapas Highlands15.417−92.5003.50191.38 ± 0.071.07 ± 0.080.86 ± 0.1661 ± 171.40 ± 0.07
Jalisco Highlands20.350−105.3001.80231.26 ± 0.111.12 ± 0.080.71 ± 0.2736 ± 91.29 ± 0.11
Panola Mtn.33.633−84.1671.24171.17 ± 0.081.47 ± 0.140.34 ± 0.1460 ± 171.30 ± 0.10
S. Sierra CZO37.053−119.1961.1091.30 ± 0.051.28 ± 0.050.58 ± 0.0890 ± 91.42 ± 0.06
Jalisco Lowlands20.133−105.3000.80251.11 ± 0.051.16 ± 0.040.46 ± 0.2048 ± 121.15 ± 0.05
Adams Peak39.883−120.1170.6041.00 ± 0.041.16 ± 0.050.00f54 ± 141.04 ± 0.04
Sonoran Desert29.367−111.1670.34251.04 ± 0.081.16 ± 0.080.25 ± 0.4424 ± 91.06 ± 0.08
Fort Sage40.083−120.0670.25121.03 ± 0.041.17 ± 0.040.19 ± 0.2142 ± 91.07 ± 0.04

For all but one of the sites in Table 2, the thickness of soil and immobile element concentrations in both rock and soil were measured in previously published cosmogenic nuclide studies of denudation rates (Riebe et al., 2001b, 2003, 2004a). Nevertheless, only three of the sites (Fort Sage, Adams Peak, and the Luquillo CZO) have sufficient previously published information about saprolite weathering from Zr enrichment (White et al., 1998; Riebe et al., 2001b, 2003) to estimate average CEFs. Fortunately, for all but one of the other sites, we have a sufficient bank of previously unpublished data on saprolite geochemistry to calculate Zrsap/Zrrock (see Supplemental Table 2 for raw data) and thus complete the calculation of CEF. For one site, the Southern Sierra Critical Zone Observatory (Bales et al., 2011; Johnson et al., 2011), all data are new, reported for the first time here based on samples of soil, saprolite, and rock, and data on depth and density from soil pits from widely distributed locations within a series of steep headwater catchments. Concentrations of Zr in 220 samples of soil, 20 samples of saprolite, and 105 samples of rock from the Southern Sierra CZO are reported in the online appendix, along with all other measurements necessary for calculating CEF at the site. The reader is referred to previous publications (Granger et al., 1996; Riebe et al., 2001b, 2003, 2004a) and the online appendix for detailed descriptions of our sites.

To calculate the CEF for quartz at each site, we use Equation (10), assuming that Zrsoil/Zrsap = Xsoil/Xsap. This should be reasonable, even in the intense weathering environment of Luquillo, where minor quartz weathering has been documented (Schulz and White, 1999); quartz enrichment in the Luquillo soils is equivalent, within uncertainties, to Zr enrichment (Ferrier et al., 2010). Our calculations show that CEFs range from 1.03 to 1.87, implying that denudation rates need to be adjusted upwards, in some cases by nearly twofold, due to effects of chemical erosion on cosmogenic nuclide buildup in quartz across our sites (Table 2). This clearly illustrates that quantifying CEFs can be crucial to accurate assessment of denudation rates in landscapes.

To explore how the relative importance of deep versus near-surface chemical erosion varies across our sites, we display the percentage error introduced by neglecting CEF as contours on a plot of immobile element enrichment in saprolite (which gauges weathering at depth) versus immobile element enrichment in soil (which gauges weathering near the surface) (Figure 2(A)). In computing values for CEF shown in Figure 2(A), we set total soil mass (ρh) equal to 100 g cm-2, approximating conditions at the Southern Sierra CZO, Luquillo CZO, and McNabb Track, NZ, and thus enabling visual comparisons of the relative importance of deep and near-surface weathering across a subset of our sites. Although neglecting CEF would introduce similar overall errors in cosmogenic-based denudation rates at the Luquillo CZO and McNabb Track NZ, the errors arise from differing amounts of deep versus near-surface weathering (Figure 2(A)). At the Luquillo CZO, enrichment and thus chemical mass loss near the surface is relatively high (with Zrsoil/Zrsap = 1.90 and Zrsap/Zrrock = 1.39; Table 2) compared with McNabb Track, NZ, where most of the enrichment and chemical mass loss occurs at depth (with Zrsap/Zrrock = 1.77 and Zrsoil/Zrsap = 1.15; Table 2). At the Southern Sierra CZO, the overall CEF is lower than it is at either the Luquillo CZO or McNabb Track NZ and the effects of deep and near-surface weathering are more balanced (with Zrsap/Zrrock = 1.30 and Zrsoil/Zrsap = 1.28; Table 2). If the host mineral for cosmogenic nuclides is soluble in soil (i.e. with Xsoil/Xsap < 1.0, as we might expect for olivine, for example), then the effect of dissolution at depth, which causes denudation rates to be underestimated, will be at least partly offset by near-surface weathering, which causes denudation rates to be overestimated, due to relatively fast depletion (Figure 2(A)).

image

Figure 2. Percentage error in denudation rate due to neglecting CEF expressed as a surface on plots of (A) immobile element enrichment in saprolite versus host mineral enrichment (or depletion) in soil and (B) soil mass versus host mineral enrichment (or depletion) in soil. In (A), soil mass is held constant at 100 g cm-2, thus representing conditions similar to those at the Luquillo CZO, the Southern Sierra CZO, and the McNabb Track, NZ (see Table 2). In B, Zr enrichment in saprolite is set at 1.3, consistent with conditions at the Luquillo CZO, the Sierra Nevada CZO, Chiapas Highlands, and Jalisco Highlands. Errors introduced by neglecting CEF are as high as 100% across the sites considered here. The contribution to CEF due to deep weathering is greatest at McNabb Track NZ for the subset of sites shown here. The contribution due to weathering near the surface is greatest at the Luquillo CZO. Note that here we consider the host mineral quartz and so plot Zr ratios on the abscissae. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

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Figure 2(B) shows how the percentage error in D varies with soil mass and immobile element enrichment in soil. These two factors together govern variations in the part of CEF that arises due to near-surface chemical erosion (see Equation (10)). The contours in Figure 2(B) represent percentage error in denudation rate for a fixed value of deep chemical erosion, in this case reflected by Zrsap/Zrrock = 1.3, which approximates the deep chemical erosion observed at the Southern Sierra CZO, Jalisco Highlands, Chiapas Highlands, and the Luquillo CZO. Examination of the plotting space shows that the error is relatively insensitive to observed differences in soil mass when weathering in soil is minimal (e.g. compare Jalisco Highlands with Chiapas Highlands) and more sensitive to observed differences in enrichment of the host mineral in the soil (compare the Luquillo CZO with the other sites).

Discussion

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Across the diverse range of sites considered here, CEFs vary widely, from 1.03 to 1.87, implying corrections of as much as a factor of two at some sites. Yet, the effects of chemical erosion have only rarely been accounted for in cosmogenic nuclide studies of denudation rates. To put this oversight into context, we note that in all of the cases considered in Table 2, the estimated CEF is at least as big as, and in many cases markedly greater than, typical slope correction factors (Dunne et al., 1999; Balco et al., 2008), which have been measured as a standard practice in nearly every cosmogenic nuclide study in the literature over the last decade (beginning with Dunne et al., 1999).

Errors due to neglecting chemical erosion from saprolite

Most studies that have attempted to make corrections for chemical erosion (Riebe et al., 2000, 2003, 2004a, 2004b) did so prior to recognition of the potential importance of deep weathering in saprolite (Dixon et al., 2009a), and thus were in error to the extent that chemical erosion from deep saprolite accounts for a significant fraction of the overall erosion from regolith. How big could these errors be? To find out, we used Equations (11) and (12) to compute the error introduced by failing to account for deep weathering and instead erroneously attributing all chemical depletion in the regolith to chemical erosion near the surface (in the soil alone). Results are plotted in Figure 3 as a function of weathering intensity in saprolite (y-axis) and soil (x-axis) for a soil mass equal to 100 g cm-2. Errors increase with increasing chemical erosion in saprolite but are less than 40% in all cases evaluated here, including McNabb Track NZ, an extreme example wherein 86% of its chemical erosion occurs in saprolite (Table 2). Even at the Luquillo CZO, the error in using the near-surface-based quartz enrichment factor (Equation (12)) rather than the more general CEF (Equation (11)) is only ~17%, despite the fact that deep weathering removes nearly all of the rock's Ca and Na at the regolith–rock interface (White et al., 1998; Riebe et al., 2003; Buss et al., 2008). This implies that use of the quartz enrichment factor instead of CEF in previous studies has usually led to biases that are small compared with other sources of error, such as those associated with uncertainties in production rates and how they have changed over time (Lifton et al., 2008; Goehring et al., 2010) . Nevertheless, when accurate results are desired, Figure 3 illustrates that the full form of CEF should be quantified to account for effects of deep saprolite weathering as well as weathering near the surface.

image

Figure 3. Percentage error in denudation rate due to ignoring weathering in saprolite and instead quantifying CEF as if it arose solely due to weathering in soil. This emulates the oversights of Riebe et al. (2000, 2003, 2004a, 2004b) in their accounting for effects of chemical erosion on cosmogenic nuclide-based estimates of denudation rates. Errors are as big as 37% for the extreme case of McNabb Track NZ, where 86% of chemical erosion occurs in saprolite. For the rest of the sites, errors are less than 17%. For accurate assessment of CEF, it is generally necessary to account for weathering in deep saprolite using measurements of immobile element enrichment in saprolite relative to unweathered rock. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

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Errors due to neglecting chemical erosion from soil

It has recently been proposed that denudation rates can be corrected for effects of chemical erosion with a simple, multiplicative factor Zrsap/Zrrock (Dixon et al., 2009a; Rasmussen et al., 2011). This approach fails to account for weathering in soil, and thus leads to errors in denudation rates, to the extent that soils are thick and weathering within them is significant. We compute the size of the error introduced by this simplification using Equations (11) and (13). Results are plotted in Figure 4 as a function of soil mass and the ratio of host mineral enrichment (or depletion) in soil relative to saprolite for a constant condition of deep weathering (with Zrsap/Zrrock = 1.3). Errors due to the simplification increase with increasing relative enrichment in soil and increasing mass of soil, up to a maximum of 30%, at the Luquillo CZO for the cases considered in Table 2. This implies that near-surface weathering will generally need to be accounted for to accurately estimate hillslope-scale erosion rates from soils and basin-scale erosion rates from alluvial sediment. To accomplish this, our formulations show that measurements of the thickness, density, and degree of weathering of soil will be needed. We stress that when soil weathering is significant, use of the simple multiplicative factor Zrsap/Zrrock alone is only strictly appropriate for estimating total denudation rates from cosmogenic nuclides in saprolite.

image

Figure 4. Percentage error in denudation rate due to ignoring weathering in soil and instead quantifying CEF as if chemical erosion occurred solely in saprolite. This emulates errors introduced by the simplifications of Dixon et al. (2009a) and Rasmussen et al. (2011) in correcting denudation rates for effects of chemical erosion. Errors are as big as 30% for the extreme case of the Luquillo CZO, where Zr enrichment of soil relative to saprolite is 1.9. This suggests that accurate measurements of denudation rates will generally require measurements of soil thickness, soil density, and immobile element enrichment in soil, in addition to immobile element enrichment in saprolite. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

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Deep versus near-surface weathering in saprolite

Our derivation of CEF assumes that chemical erosion from saprolite occurs at depths greater than a few meters, where minerals are shielded from significant cosmogenic nuclide production. If chemical losses from saprolite instead (or also) occur close to the surface, and thus significantly influence cosmogenic nuclide buildup, then accounting for effects of chemical erosion of saprolite is more complicated than indicated by Equations (5)(13), both in the initial collection of samples and the final computation of CEFs from geochemical measurements. During sampling, it would be necessary to collect saprolite from multiple depths, to quantify how the degree of immobile element enrichment (and thus chemical erosion) varies with depth near the surface. During computation, it would be necessary to use the measured variations in immobile element enrichment to numerically solve for the denudation rate that best explains the observed nuclide concentration in the context of inferred chemical losses in near-surface saprolite. In practice, the relative importance of deep versus near-surface weathering of saprolite will generally need to be evaluated on a case-by-case basis, either directly, using measurements of immobile element enrichment, or indirectly, from observations of the thickness and degree of weathering of regolith.

For many of the sites in Table 2, we can be reasonably certain that deep weathering dominates in the chemical erosion of saprolite. For example, previous work at the Luquillo CZO has shown that most of the weathering in saprolite occurs within a few tens of centimeters of the regolith–bedrock interface (White et al., 1998; Buss et al., 2008), which is often shielded by 8 m or more of overlying regolith (White et al., 1998). At McNabb Track NZ, Chiapas Highlands, and Jalisco Highlands, our observations of exposed weathering profiles in previous work suggest that much of the measured saprolite weathering occurs at depths greater than a few meters (see supplemental information in Riebe et al., 2004a). At the Southern Sierra CZO, evidence from seismic refraction and resistivity surveys indicates that weathering profiles are commonly thicker than 10 m across a wide range of landscape positions, including divergent ridgetops, adjacent planar hillslopes, and convergent meadows (Holbrook et al., in review), implying that our assumption of deep weathering in saprolite is reasonable in our estimate of a representative CEF for the site.

For sites where the assumption of deep weathering of saprolite is not valid, CEFs estimated from the equations derived above will overestimate the true correction factor for chemical erosion effects. However, errors due to incorrectly attributing a deep origin to near-surface chemical erosion of saprolite will be small, to the extent that weathering in saprolite does not significantly enrich its Zr concentrations relative to bedrock (as appears to be the case at Fort Sage, Adams Peak, and Sonoran Desert in this analysis; see Table 2).

The CEF and catchment-wide denudation rates

The complications discussed above apply to vertically mixed soils, as illustrated in the conceptual diagram of Figure 1. Chemical erosion introduces an additional complication for cosmogenic-nuclide-based estimates of catchment-wide denudation rates from laterally mixed soils and sediment (Brown et al., 1995; Bierman and Steig, 1996; Granger et al., 1996). If sediment is mixed according to its contributing area (Aj) and its local denudation rate (Dj), the average nuclide concentration in the host mineral in laterally mixed sediment is given by Equation (15) (after Granger et al., 1996).

  • display math(15)

Here, Nj is the local nuclide concentration in the host mineral for area j, Pj is the local production rate at the surface, and CEFj is the local chemical erosion factor. The spatially averaged denudation rate (<D>) is given by

  • display math(16)

Hence, if CEF is spatially uniform, Equation (15) reduces to

  • display math(17)

If CEF is not spatially uniform, but instead varies, then Equation (15) cannot be readily simplified without a priori knowledge of how CEF varies with Dj. If Equation (17) is nevertheless used to estimate <D> it would be biased towards areas with relatively high CEFs. To minimize potential for this type of bias, it may help to choose sites across which CEF is likely to be roughly uniform, as may be the case in catchments that are small enough to have uniform weathering, due to uniform lithology, climate, and vegetative cover.

Making measurements and computing CEFs

Our derivations show that quantifying CEF requires measurements of immobile element concentrations in both saprolite and rock, except in the special case of Equation (12), when weathering in saprolite is minimal and the bulk geochemistry of saprolite is the same as the bulk geochemistry of bedrock. In addition, measurements of CEF require estimates of soil thickness, soil depth, and the concentrations of an immobile element or mineral in soil – except in the special case of Equation (13), when weathering in soil is minimal, and when cosmogenic nuclides are measured in host minerals that are prone to dissolution (i.e. the general case of Equation (10)). The concentrations of immobile elements in samples of soil, saprolite, and rock can be measured straightforwardly by x-ray fluorescence (Riebe et al., 2001a, 2001b) or ICP-MS. In the more general case of a soluble target mineral, such as olivine, it is also necessary to measure its concentrations in soil and saprolite, using, for example, quantitative X-ray diffraction (Chipera and Bish, 2002; Ferrier et al., 2010).

In practice, if Zr concentrations are to be used as proxies for quartz concentrations, it is important that Zr and quartz are distributed homogeneously in the underlying bedrock. They also need to occur together, correlating with one another in all portions of the weathering profile. This avoids complications due to physical fractionation and mixing from compositionally different sources. However, because the composition of geologic materials is almost always variable to some degree, it is crucial to take multiple samples of soil, saprolite, and bedrock to constrain mean element and mineral concentrations that are geochemically representative of both the parent material and the daughter regolith in which nuclides are to be measured (Riebe et al., 2001a). Likewise, if CEF is to be measured at the hillslope or catchment scale, it will generally be necessary to make spatially distributed measurements of soil thickness and density for estimation of representative averages. The required number of measurements will vary on a case-by-case basis, depending on the degree of variability in the factors of interest. In our experience, at least three to as many as 10 or more distributed samples of each geochemical reservoir (i.e. the soil, saprolite, and bedrock) are generally needed to constrain its mean concentration of Zr for estimates of chemical weathering rates (Riebe et al., 2004a) and CEFs.

Effects of climate on CEF

Across the 10 sites considered here (Table 2), CEFs for quartz increase systematically with mean annual precipitation (Figure 5), presumably because higher precipitation corresponds to higher subsurface flow of meteoric water and thus more intense weathering in both saprolite and soil. A linear, least-squares-error, inverse-variance-weighted regression to the data is plotted in Figure 5 and expressed mathematically in Equation (18).

  • display math(18)
image

Figure 5. CEF (calculated from Equation (10), for cosmogenic nuclides in quartz) increases systematically with mean annual precipitation across the ~20-fold range of Table 2. Dashed lines show 68% (±1 σ) prediction interval for individual points in the regression. The regression slope indicates that CEF increases at a rate of 0.15 ± 0.03 for every m a-1 increase in precipitation. This correlation presumably arises due to higher throughput of meteoric water, which leads to enhanced chemical weathering in regolith. To the extent that the correlation shown here holds across other sites with granitic bedrock, it may be possible to use the regression parameters, together with measurements of mean annual precipitation, to crudely estimate CEF.

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Here MAP is mean annual precipitation in m a-1 and uncertainties express one standard error of the fitted regression parameters. The slope of the regression between CEF and mean annual precipitation indicates that CEF increases at a rate of 0.15 ± 0.03 for each 1 m a-1 increase in mean annual precipitation. The correlation shown in Figure 5 is fairly strong (adjusted r2 = 0.68) and the regression parameters are highly significant (e.g. P = 0.0021 for the regression slope). The apparently close coupling between CEF and precipitation is broadly consistent with our previous analyses of climatic effects on weathering and erosion across the sites; we found that the relative importance of chemical and physical erosion (measured by the ‘chemical depletion fraction’, which is similar to CEF in the way it gauges chemical erosion intensity in regolith) is sensitive to variations in climate and insensitive to variations in denudation rates over the wide range of climatic and erosional settings, including all but one of the sites in Table 2 (Riebe et al., 2004a).

Evidently, modern climatic conditions are a first-order predictor of CEF (Figure 5). This is remarkable given the likely influences of past climates on saprolite geochemistry; for samples collected at the surface, we estimate that deep weathering at the rock–regolith interface probably occurred tens-of-thousands to hundreds-of-thousands of years ago (i.e. likely under a different climate regime), based on the timescales implied by available 10Be-based erosion rates, which are typically ~100 m Ma-1, and our best estimates of regolith thickness (i.e. H in Figure 1), which are of order 10 m at several of these sites. Nevertheless, the empirical relationship of Figure 5 appears robust, to the extent that it is derived from a range of climatic settings from around the globe.

To the extent that Equation (18) generally describes how CEFs for quartz vary with climate across granitic landscapes, it may be possible to use it to crudely correct cosmogenic nuclide estimates of denudation without cumbersome, yet otherwise necessary measurements of soil depth and thickness and immobile element concentrations in soil, saprolite, and rock. However, the best use of Equation (18) may be in its ability to discriminate between sites where chemical erosion is likely to be important from those where it may be safe to ignore. For example, if one is willing to accept a 10% or less error due to chemical erosion, then Equation (18) and Figure 5 suggest that CEF can be ignored for precipitation rates less than about 0.5 m a-1. Given the wide prediction intervals implied by Figure 5, we suggest that additional measurements are needed to refine the regression and ensure that it is robust enough for widespread use in correcting for weathering-related biases in soil and saprolite. Notwithstanding the uncertainties in the regression, we point out that, without guidance from Figure 5, it would be difficult to know, a priori, whether CEF is small enough to ignore. Moreover, we stress that the climatic dependence of CEF implied by Figure 5 and Equation (18) clearly indicates that it will be especially important to quantify CEF in studies that seek to measure how cosmogenic nuclide-based erosion rates vary across climate gradients (Riebe et al., 2000, 2004a, 2004b; von Blanckenburg, 2005; Dixon et al., 2009a, 2009b; Moon et al., 2011; Rasmussen et al., 2011; Ferrier et al., 2012).

Conclusions

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Here we present a new formulation, termed the chemical erosion factor (CEF), which can be used to correct for effects of chemical erosion on the buildup of cosmogenic nuclides in saprolite and soil on hillslopes. Our formulation of CEF is general enough to work when weathering from soil dominates, when weathering from deep saprolite dominates, and when both types of weathering are important in determining the consequences of chemical erosion for cosmogenic nuclide buildup in regolith. Our analysis of data from diverse climatic settings indicates that accounting for chemical erosion effects is important; when ignored, they can introduce biases as big as a factor of two for cosmogenic nuclides in quartz in intensely weathered granitic soils and saprolite. Quantifying CEFs for quartz requires measurements of soil depth and density as well as concentrations of an immobile element in soil, saprolite, and parent material. However, our formulation of CEF is not specific to quartz, unlike the quartz enrichment factor of previous work. Rather, it is generic enough that it can also be applied to relatively soluble host minerals, such as olivine, if representative concentrations of the mineral can be measured in saprolite and soil. Our analysis indicates that if CEF is spatially variable in a catchment, cosmogenic-based measurements of catchment-wide denudation rates will tend to be biased towards areas with higher CEFs. This suggests that it may be important to choose study catchments with uniform climate, lithology, and topography, and thus minimize the possibility that chemical erosion rates are variable enough to bias cosmogenic estimates of denudation rates. Across the climatically diverse granitic sites considered here, CEF increases systematically with mean annual precipitation, underscoring the importance of quantifying CEFs in studies that seek to measure how denudation rates vary across climatic gradients. To the extent that the measured correlation between CEF and precipitation is representative of effects of chemical erosion on cosmogenic nuclides in other granitic landscapes, it may be possible to use it as a predictor of CEF at sites where it is not tractable to quantify the correction factor directly using measurements of regolith and parent material.

Acknowledgements

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

We thank S. Araki, C. Bechtel, M. Cargill, L. Glaser, B. Jessup, M. Johnson, N. Lester, T. O'Flannigan, J. Schmidt, M. Smith, T. Teague, N. Swoboda-Colberg, R. Valenzuela, S. Varten, R. Wardner, and W. White for assistance in the laboratory and C. Bechtel, N. Brozović, A. Dosseto, M. Fantle, B. Jessup, J. Jessup, M. Johnson, P. McIntyre, M. Meadows, T. Ramírez, M. Smith, and F. Solis for assistance in the field. We improved the manuscript with the help of thoughtful comments from S. Binnie, S. Lane, and an anonymous reviewer. Some of the saprolite weathering data published here were measured nearly 10 years ago under the auspices of NSF EAR 0000999 to J. Kirchner. Additional financial support for collection and analyses of samples from the Southern Sierra CZO was provided by NSF EAR 0725097 to Riebe.

References

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Supporting Information

  1. Top of page
  2. ABSTRACT
  3. Introduction
  4. The Chemical Erosion Factor
  5. Gauging the Size of the Chemical Erosion Factor
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Supporting information may be found in the online version of this article.

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esp_3339_Supplemental_Information.docxWord 2007 document142KSupporting Information

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