Discrepancy between mineral residence time and soil age: Implications for the interpretation of chemical weathering rates Kyungsoo Yoo* University of Delaware, Plant and Soil Sciences Department, Newark, Delaware 19716, USA Simon Marius Mudd* School of GeoSciences, University of Edinburgh, Edinburgh EH9 3JW, UK
Keywords: chemical weathering, soil formation, soil production, mineral dissolution. INTRODUCTION An important component of soil formation is the chemical weathering of primary minerals. In quantifying mineral chemical weathering rates, one approach has been to apply kinetic relationships obtained in the laboratory to the field setting (e.g., Sverdrup and Warfvinge, 1988). Typically, such kinetic relationships only predict the weathering rate as a function of the concentration of solutes in the soil water, the soil’s reactive surface area, and temperature. Recent studies, however, have found that weathering rates also correlate strongly with erosion rates (e.g., Riebe et al., 2004; West et al., 2005) and sediment transport rates (Yoo et al., 2007), an effect that is not predicted by the traditional kinetic relationships (Hodson and Langan, 1999). The relationship between erosion rates and chemical weathering rates has been theorized to be a result of the supply of fresh minerals from parent material to the soil (hereafter referred to as soil production, SP) (e.g., Raymo and Ruddiman, 1992). The freshness of mineral grains in a soil is determined in part by the average time (hereafter residence time) that they spent within the weathering zone, which we define as the soil between the ground surface and the unweathered parent material. According to a recent compilation of field and laboratory based weathering rates (White and Brantley, 2003), the weathering rate of several different mineral species is a power law function of time: older particles are weathered at a rate far slower than younger particles. Laboratory-derived rates reported by White and Brantley (2003) were measured on human time scales. For longer time *E-mails:
[email protected];
[email protected].
scales (thousands to millions of years), weathering rates compiled by White and Brantley (2003) were determined using field-derived data. These rates were calculated through a variety of methods in noneroding landscapes where the soil age is the time elapsed since the stabilization of the geomorphic surface. We propose, however, that the relationships between the mineral weathering rates and soil ages obtained from noneroding surfaces are not directly comparable to similar relationships found in laboratory studies. On a newly stabilized geomorphic surface, the soil grows in thickness as time passes. In an unmixed weathering zone, the youngest material (i.e., the most recent input from parent material to soil) is near the weathering front and the oldest is at the surface; in a mixed soil mineral grains of different residence times are dispersed throughout the profile. Regardless of the degree of mixing there is a range of mineral residence times younger than the soil age. Soil age, consequently, is fundamentally different from the minerals’ weathering exposure time as used in laboratory studies. It is the mineral residence time within the soil layer, rather than the soil age, that relates directly to exposure times in laboratory experiments. Another important issue is that applying the relationship between mineral chemical weathering rate and soil age to eroding or depositional surfaces is problematic. Soils on dynamic geomorphic surfaces do not have ages as defined for the soil chronosequence because they are constantly rejuvenated by erosion or deposition. One can quantify, however, the time mineral grains spend within the physically dynamic soil (e.g., Mudd and Furbish, 2006; Almond et al., 2007). This mineral residence time approach may also be used to simulate geochemical soil development in the chronosequence setting.
Here, using modeling exercises, we demonstrate that the consideration of soil production demands a new way of scaling up the relationship between mineral chemical weathering rate and time from laboratory to field soils. We also demonstrate quantitatively the factors controlling the residence times of different primary mineral species within the soil profile. MODEL DEVELOPMENT AND COMPARISON WITH THE PAST APPROACH We focus on a soil in which the soil production occurs at the boundary between the soil and the parent material (Fig. 1). To avoid the complication due to depth-dependent soil mixing, we consider the depth-integrated masses of bulk soil (Ωs is in the dimensions of mass per length squared [ML–2]. Hereafter dimensions are given in dimensions of mass [M] length [L] and time [T]; the dimensions follow each variable within square brackets as unitalicized text.) and a mineral of interest (Ωj, s with the dimension of ML–2, where j represents a primary mineral species j and s represents soil material) per unit area of soil surface: ∂Ωs = ρr P − w, ∂t
Soil
(1)
∂Ω s ∂t =
Total mass per unit area of soil on landscape surface: Ω s
ABSTRACT Virtually all soil chronosequence studies have equated the degree of mineral weathering with the soil age, which is equal to the time since the cessation of erosion or deposition. The primary minerals from the parent material, however, enter the soil as the weathering front propagates downward and are depleted via chemical weathering. The residence time of minerals is thus a function of both the rate of conversion of parent material to soil (i.e., soil production) and the minerals’ susceptibility to chemical weathering reactions. We find that mineral residence times are significantly shorter than the soil age. By mathematically considering the interactions among soil production and chemical weathering, we demonstrate that traditional estimates of mineral-specific chemical weathering rates from soil chronosequences may diverge by several orders of magnitude from the actual weathering rates.
–w + Expansion of the : ρrP weathering zone (leads to introduction of fresh material into the soil)
Unweathered Bedrock
Figure 1. Schematic of Equations 1 and 2 (see text). Mass in the soil is added through expansion of weathering zone, and is lost due to chemical weathering. Expansion of weathering zone adds young minerals to the soil. Our approach integrates masses over the soil, so soil properties are obtained by integrating samples from individual layers over the entire soil.
© 2008 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or
[email protected]. GEOLOGY, January 2008 Geology, January 2008; v. 36; no. 1; p. 35–38; doi: 10.1130/G24285A.1; 4 figures; 2 tables; Data Repository item 2008011.
35
and ∂Ω j,s ∂t
= Cj,r ρr P − wj ,
(2)
where t is the soil age [T], ρ is bulk density [ML–3], P is the SP rate [LT–1], w is the rate that mass is lost via chemical weathering [ML–2T–1], C is the mass concentration [MM–1], the subscript j represents a primary mineral species, and the subscripts s and r represent soil and parent material, respectively. The SP rate has been modeled as a function of the soil thickness (soil production function, SPF). Because some biophysical activities (e.g., burrowing) decrease with soil depth (e.g., Gabet et al., 2003), soil production rates have been considered to exponentially decrease with soil thickness (e.g., Heimsath et al., 1997). Other processes, such as freeze and thaw, are thought to be most effective in breaking up parent material at an intermediate soil depth (e.g., Anderson, 2002). The two SPFs may be expressed as exponential SPF, −
h
P = P0 e γ ,
(3)
⎛ h − hp ⎞ P −P P = min ⎜ P0 + p 0 h, Pp e− γ ⎟ , hp ⎝ ⎠
(4)
and peaked SPF,
where P0 is the rate of SP at zero soil thickness [LT–1], Pp is the peak rate of SP [LT–1], γ is a length scale describing how the rate of SP decreases with increasing depth [L], h is the soil thickness [L], hp is the soil thickness at the peak SP rate [L], and the function min takes the minimum value of the two equations within the brackets. Although field data for SP rates on noneroding surfaces are lacking, many soil chronosequence studies show that the thickness of soil (A + B horizons) rapidly increases during initial soil formation, and the rate of thickening decreases with increasing soil age. In addition, the theoretical bases for the two SPFs do not require erosion or deposition. We thus use model parameters for the SPF that are within the range of empirically measured values for eroding landscapes (Table 1). Because of the large discrepancy between laboratory weathering rates and field weathering rates (e.g., Anderson et al., 2004) and the apparent correlation between fresh mineral supply via erosion and basin-wide chemical weathering rates (e.g., Riebe et al., 2004; West et al., 2005), a number of authors have suggested that mineral weathering rates are a function of time spent in the weathering zone (e.g., Hodson and Langan, 1999; White et al., 1996; White and Brantley, 2003). We follow the approach of White and Brantley (2003) and assume that, as a first
36
approximation, the relationship between weathering rate and surface area as a function of time can be described using power law relationships (e.g., R = aτ α and λ = bτ β, where R is the chemical weathering rate in moles reacted per mineral surface area per time [mol L–2 T–1], τ is the time that minerals have been exposed to chemical weathering, λ is the mineral roughness that is the dimensionless ratio between geometric mineral surface area and reactive mineral surface area, and a, b, α, and β are mineral specific empirical coefficients [values of which are given in Tables 1 and 2]). Thus, the mass loss rate per unit ground surface area (wj) of minerals of species j with grains of initial diameter D nonlinearly decreases as a function of its weathering exposure time (see the GSA Data Repository1) wj = −
∂m j ∂τ
=
6 ajb jω j Djρμ , j
τ
α j +β j j
species j, which entered the soil between the soil ages of t and t + Δt (i.e., mj, t = CjrρrPΔt), is exposed to chemical weathering for the time span of τ = T – t, which is the residence time of the mineral mass. A fraction of this mass of mineral j survives chemical weathering and persists when the age of the soil is T (mj, t → T, with the unit of mass per ground surface area). To correctly calculate the chemical weathering mass loss rate of the mineral species, j, from the soil profile of age T using the dissolution rate law (Equation 5), we need to add the chemical weathering rates across the mineral grains incorporated into the soil at different times (for detailed derivation and complete form of equation, see the GSA Data Repository): wj =
mj ,
6a jb jω j t = T
(5)
Djρμ , j
∫
t=0
⎡(T − t )α j +β j m j,t→T ⎤ dt . (6) ⎣ ⎦
In Equation 6, the term (mj, t → T) depends on the mass input rate of mineral j via soil production at time t (Equations 2 and 3) and the weathering susceptibility of the minerals. The model also requires characterizing the diameter of the mineral grains entering the soil via SP. The diameter is considered uniform as an approximation of a soil forming on well-sorted material. The chemical weathering rate (Equation 6) and SPF (Equations 3 and 4) complete the mass balance describing the geochemical evolution of a bulk soil above the weathering front (Equations 1 and 2). This implicitly assumes that the extent of weathering for two mineral grains that have been entrained in the soil coevally is the same regardless of the random paths taken by the grains in the soil as a result of bioturbation. In addition, the model does not disregard the translocation of colloids; rather, it assumes that all translocation occurs within the soil and thus does not affect the depth-integrated mass balance.
where mj is the present mass of mineral j per ground surface area, D is the particle diameter, ρμ is the mineral density, and ωj is the molar weight of the mineral j. Equation 5 is effectively a linear dissolution rate law with a timedependant decay coefficient. Applying a functional relationship between mineral chemical weathering rates and weathering exposure time (e.g., Equation 5) to a soil chronosequence, or vice versa, requires considering the mineral residence time in the soil zone. We consider the soil to be the entire weathering profile, including the saprolite layer. In a soil of age T, for example, the mass of mineral 1 GSA Data Repository item 2008011, detailed derivation of Equations 3 and 4 and procedures of numerical calculations, is available online at www. geosociety.org/pubs/ft2008.htm, or on request from
[email protected] or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA.
TABLE 1. SOIL PRODUCTION AND GENERAL PARTICLE PARAMETERS Run number 1† 2§
P0 (m/yr)
Pp (m/yr)
hp (m)
γ (m)
b* (dimensionless)
β* (dimensionless)
0.5 × 10−4 1.0 × 10−6
n/a 0.41 × 10−4
n/a 0.2
0.5 0.5
13.6 13.6
0.2 0.2
Note: For the definitions of all parameters and variables, see text. *For λ = b τβ, τ is in units of years. Parameters based on White and Brantley (2003). Exponential soil production function (SPF) parameters based on Heimsath et al. (2000). § Peaked SPF, parameters P0 and Pp are selected such that the soil profile after 200 k.y. would have the same thickness as the soil in run 1 after the same time period. Parameter hp is based on Anderson (2002). †
TABLE 2. MINERAL PROPERTIES Mineral Quartz K-feldspar Plagioclase
Initial mass fraction
wm (kg mol–1)
ρm (kg/m3)
Log10 (a)*
α†
0.35 0.16 0.39
0.06001 0.27822 0.26302
2600 2600 2600
0 –12.49 –12.46
0 –0.647 –0.564
Note: For the definitions of all parameters and variables, see text. *The units of a are mol m–2 s–1; parameters based on White and Brantley (2003). † For exponent α, residence time used is in units of years; parameters based on White and Brantley (2003).
GEOLOGY, January 2008
GEOLOGY, January 2008
100
plagioclase
100
fine sand
10–2 10–4 10
medium silt
–6
1
10 Soil age (k.y.)
100
chemical weathering across diverse settings, including laboratory, soil chronosequence, and eroding and depositional soils. In our modeling scheme, the factors controlling the mineral residence time include the soil production, the mineral specific susceptibility to chemical weathering, and soil age. In the model, quartz is assumed to be immune to chemical weathering mass loss, so the residence time of quartz reflects only the impact of soil production (Fig. 3A). The quartz residence time, regardless of the types of SPF, is consistently less than the soil age because of the continuous introduction of quartz into the soil layer as time progresses. Additionally, the quartz resi-
A
140
al
ti en
on
p
F
ed
SP
k ea
p
20 40
80 120 160 Soil age (k.y.)
B PF
F
one
exp
SP
0.6 0.4 0.2 0 0
5 4 3
40
pea
ked
1 0 0
80 120 160 Soil age (k.y.)
200
C
2
40
0.7
exp one ntia l SP F
SPF
80 120 160 Soil age (k.y.)
0
200
lS ntia
0.8
0.8
0.6
1.2 1.0
0.9
200
0
40
80 120 160 Soil age (k.y.)
200
E
peaked SPF
0
exponential SPF 40 80 120 160 Soil age (k.y.)
0
0
200
F
3
ex
40
0
SP
Weathering rate per unit mass (kg yr –1 kg –1 ) 4× 2× 10 10 –5 –5
e
80
0
D
1.0 Fraction of mass remaining
F
100 60
dence time depends on the SPF (Fig. 3A). The parameters for the SPFs were adjusted such that the soil depths were the same after 200 k.y. of soil development (Fig. 3B; Table 1). For soils with the peaked SPF (Fig. 3C), the supply of fresh minerals increases in time until the soil thickness is equal to the peak soil production depth, hp. Over this time period, the growing amount of quartz minerals entering the soil causes the quartz residence time to remain low relative to the soil with an exponential SPF (Fig. 3A). Because the weathering rates of minerals depend on their residence time, which is influenced by the rate of SP, different SPFs will impart different weathering characteristics to the
peaked SPF
120
Total weathering rate from soil profile (kg yr –1 m–2 ) 6× 3× 9x 10 10 10 –3 –3 –
Factors Controlling Mineral Residence Time Mineral residence time is the measure of time that allows the consistent description of the time-dependent characteristics of mineral
10 Soil age (k.y.)
ential expon SPF
True versus Chronosequence-Derived Chemical Weathering Rates Soil age–based estimations (using Equation 7) have significant errors (Fig. 2) because they assume that the entire parent material has been subject to weathering reactions since the initiation of soil formation. In fact, some of the minerals are younger than the soil age due to weathering front propagation. The errors are amplified with decreasing mineral diameter (Fig. 2). The finer the mineral particles, the greater the exposed mineral surface area per given mineral mass to chemical reactions, which further shortens their residence time. Our simulation (Fig. 2) shows that factoring the mineral residence time into the method should precede any efforts to understand the soil profile–scale chemical weathering from the mineral grain scale relationship between chemical weathering and weathering exposure time. We note, however, that the approach described by Equation 7 is internally consistent such that it can be used to compare weathering rates from soils with similar development histories. However, in eroding landscapes there is no way to define a soil age; therefore prediction of weathering rates must be carried out by relating weathering rates to mineral residence times and explicitly accounting for soil production.
10–2 1
lin
SIMULATION RESULTS AND DISCUSSION By combining published parameters (Table 1 and 2) and the preceding equations, we examine how much error in mineral chemical weathering rate is caused by incorrectly equating mineral residence time with soil age. We then identify and assess the factors affecting the mineral residence time and their significance. The detailed procedure of the calculation can be found in the GSA Data Repository.
Figure 2. Ratio between weathering rate predicted by treating the soil as having a uniform age that is determined by cessation of erosion or deposition, and true weathering rate of soil that has a distribution of residence times due to the downward propagation of the weathering front at times ranging from 0 to 200 k.y. Parameters, excluding diameter, are listed in Tables 1 and 2. Fine sand indicates particle diameters of D = 0.0002 m and medium silt indicates particle diameters of D = 0.00002 m.
medium silt
1
where mj is ρsCj, sh.
10–1
ak ed
(7)
fine sand
pe
mj,
k-feldspar
100
1:
α j +β j
Predicted weathering rate based on soil age True weathering rate of soil made up of minerals of varying residence time
Dj ρμ , j
T
Quartz residence time (k.y.)
6a jb jω j
Soil thickness (m)
wj =
Soil production rate (cm k.y.–1 )
The concept described in Equation 6 is fundamentally different from the way that time in noneroding landscapes has been related to mineral specific chemical weathering rates. If soil age is considered instead of mineral age, the chemical weathering rate integrated over the soil profile of mineral species j is directly obtained by replacing the weathering exposure time in Equation 5 by soil age (for the complete form of equation, see the GSA Data Repository) as
pea ked
SPF
expo nenti a
l SPF
40
80 120 160 Soil age (k.y.)
Figure 3. Bulk behavior of the modeled soil system and bulk chemical weathering rates with exponential and peak soil production functions as functions of soil age. The bulk properties plotted in A–F may be found on the ordinate axes. The soil age is the time elapsed since the stabilization of the geomorphic surface (see text for discussion). Mineral properties are given in Table 2 and soil properties are given in Table 1. This simulation is limited to the sand-size parent material (D = 0.0002 m) to illustrate the potential impact of soil production functions (SPF) on a soil’s geochemical development.
200
37
CONCLUSIONS Despite the usefulness of the soil chronosequence approach in quantifying the rates of mineral chemical weathering and geochemical soil formation, this study reveals that some of
38
D = 0.0002 m
tz ar
qu
1: 1
lin
e
120 80
e
las
c gio
40 0
pla
0
K
80 120 160 Soil age (k.y.)
D = 0.00002 m lin
e
120
40
ar
sp
ld -fe
200
tz
ar
qu
1: 1
Residence time of individual minerals (k.y.) Residence time of individual minerals (k.y.)
soils. For the exponential SPF, both the fraction of primary mineral mass remaining (the total primary mineral mass in the soil divided by the total primary mineral mass introduced into the soil by SP) and the total chemical weathering rate per unit primary mineral mass decline monotonically as the soil ages (Figs. 3D, 3E). For the peaked SPF, the fraction of mass remaining and the weathering rate per unit mass remains relatively constant leading up to the peak in SP, because an increasing amount of primary minerals is being introduced into the soil to offset the decline in weathering rate of the older minerals. The total weathering rate from the soil profile (Fig. 3F) depends both on the mass-normalized weathering rate of the minerals (Fig. 3E) and the total mass of the minerals in the soil. In a young soil, there are high rates of mineral weathering because the mineral residence time is relatively short, but there is only a small amount of minerals to be weathered in the soil. As the soil reaches an intermediate age, the weathering rate per unit mass is lower than in the young soil, but more mineral mass contributes to the weathering flux. When the soil is relatively old, the soil has the greatest mass of minerals but the residence times of these minerals are long and the total weathering flux from the soil is thus low. This process leads to the peak in weathering flux at an intermediate soil age. In our simulation, the minerals’ susceptibilities to chemical weathering decrease in the order of plagioclase, K-feldspar, and quartz (Table 2). Plagioclase has a younger residence time than quartz and K-feldspar (Fig. 4). The mineral weathering rates derived using soil age (Equation 7) diverge from the true weathering rates to a greater degree for plagioclase than for K-feldspar (Fig. 2). This is because more weatherable minerals disappear quickly, leading to a greater discrepancy between soil age and mineral residence time (Fig. 4). The impact of minerals’ weatherability on their residence time is also shown by comparing two different mineral sizes. The medium silt-size minerals, with greater surface area per mass exposed to chemical reaction, show much shorter residence time than the sand-size minerals, except for chemically nonreactive quartz. The mineral residence times increase with increasing soil age (Fig. 4). Thus the morphological characteristics of mineral grains, e.g., roughness, may continue to change as the soil ages. Fine-sized minerals with high weathering susceptibilities, however, may eventually reach steady-state residence time as the soil ages (Fig. 4).
80
K-feldspar
40
plagioclase
0
0
40
80 120 160 Soil age (k.y.)
200
Figure 4. Residence time for the mineral species with different susceptibility to chemical weathering and particle diameters (D) as a function of the soil age. The simulation is made with exponential soil production function. Mineral properties are given in Table 2 and soil properties are given in Table 1.
the fundamental mechanisms of soil formation with potentially significant impacts on quantifying these rates have not been considered. The traditional approach to estimate mineral chemical weathering rate using soil chronosequences is not compatible with mineral grain scale relationships between weathering rates and time measured in laboratory settings. In comparing the field data to laboratory data, and applying the results from stable terrain to geomorphically dynamic terrain, the mineral residence time must be used. It is critical to consider soil production in order to bridge the long-known discrepancy between laboratory versus field measured mineral chemical weathering rates. ACKNOWLEDGMENTS This work was funded by University of Delaware College of Agriculture and Natural Resources seed grant to Yoo and the National Science Foundation (grant EAR-0125843). We thank Ronald Amundson for his constructive criticism on the early manuscript and Emmanuel Gabet and Peter Almond for their thoughtful and thorough reviews. REFERENCES CITED Almond, P., Hales, T.C., and Roering, J.J., 2007, Using soil residence time to delineate spatial and temporal patterns of landscape disequilibrium: Journal of Geophysical Research– Earth Surface, v. 112, F3, p. F03S17, doi: 10.1029/2006JF000568. Anderson, R.S., 2002, Modeling the tor-dotted crests, bedrock edges, and parabolic profiles of
high alpine surfaces of the Wind River Range, Wyoming: Geomorphology, v. 46, p. 35–58. Anderson, S.P., Blum, J., Brantley, S.L., Chadwick, O., Chorover, J., Derry, L.A., Drever, J.I., Hering, J.G., Kirchner, J.W., Kump, L.R., Richter, D., and White, A.F., 2004, Proposed initiative would study earth’s weathering engine: Eos (Transactions, American Geophysical Union), v. 85, p. 265, 269. Gabet, E.J., Reichman, O.J., and Seabloom, E.W., 2003, The effects of bioturbation on soil processes and sediment transport: Annual Review of Earth and Planetary Sciences, v. 31, p. 249–273, doi: 10.1146/annurev.earth.31.100901.141314. Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., and Finkel, R.C., 1997, The soil production function and landscape equilibrium: Nature, v. 388, p. 358–361, doi: 10.1038/41056. Heimsath, A.M., Chappell, J., Dietrich, W.E., Nishiizumi, K., and Finkel, R.C., 2000, Soil production on a retreating escarpment in southeastern Australia: Geology, v. 28, p. 787–790, doi: 10.1130/ 0091–7613(2000)282.0.CO;2. Hodson, M.E., and Langan, S.J., 1999, The influence of soil age on calculated mineral weathering rates: Applied Geochemistry, v. 14, p. 387–394, doi: 10.1016/S0883–2927(98)00052–3. Mudd, S.M., and Furbish, D.J., 2006, Using chemical tracers in hillslope soils to estimate the importance of chemical denudation under conditions of downslope sediment transport: Journal of Geophysical Research, v. 111, p. F02021, doi: 10.1029/2005JF000343. Raymo, M.E., and Ruddiman, W.F., 1992, Tectonic forcing of late Cenozoic climate: Nature, v. 359, p. 117–122, doi: 10.1038/359117a0. Riebe, C.S., Kirchner, J.W., and Finkel, R.C., 2004, Erosional and climatic effects on long-term chemical weathering rates in granitic landscapes spanning diverse climate regimes: Earth and Planetary Science Letters, v. 224, p. 547–562, doi: 10.1016/j.epsl.2004.05.019. Sverdrup, H., and Warfvinge, P., 1988, Weathering of primary silicate minerals in the natural soil environment in relation to a chemicalweathering model: Water, Air, and Soil Pollution, v. 38, p. 387–408. West, A.J., Galy, A., and Bickle, M., 2005, Tectonic and climatic controls on silicate weathering: Earth and Planetary Science Letters, v. 235, p. 211–228, doi: 10.1016/j.epsl.2005.03.020. White, A.F., and Brantley, S.L., 2003, The effect of time on the weathering of silicate minerals: Why do weathering rates differ in the laboratory and field?: Chemical Geology, v. 202, p. 479–506, doi: 10.1016/j.chemgeo.2003.03.001. White, A.F., Blum, A.E., Schulz, M.S., Bullen, T.D., Harden, J.W., and Peterson, M.L., 1996, Chemical weathering rates of a soil chronosequence on granitic alluvium. 1. Quantification of mineralogical and surface area changes and calculation of primary silicate reaction rates: Geochimica et Cosmochimica Acta, v. 60, p. 2533–2550, doi: 10.1016/0016–7037(96)00106–8. Yoo, K., Amundson, R., Heimsath, A.M., Dietrich, W.E., and Brimhall, G.H., 2007, Integration of geochemical mass balance with sediment transport to calculate rates of soil chemical weathering and transport on hillslopes: Journal of Geophysical Research, v. 112, p. F02013, doi: 10.1029/2005JF000402. Manuscript received 19 April 2007 Revised manuscript received 23 August 2007 Manuscript accepted 27 August 2007 Printed in USA
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