Time evolution of the mineralogical composition of Mississippi Valley ...

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Geochimica et Cosmochimica Acta 74 (2010) 6357–6374 www.elsevier.com/locate/gca

Time evolution of the mineralogical composition of Mississippi Valley loess over the last 10 kyr: Climate and geochemical modeling Yves Godde´ris a,*, Jennifer Z. Williams b, Jacques Schott a, Dave Pollard b, Susan L. Brantley b b

a Laboratoire d’e´tude des Mećanismes et Transferts en Geólogie, CNRS, Universite´ de Toulouse, Toulouse, France Center for Environmental Kinetics Analysis, Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA 16802, USA

Received 30 December 2009; accepted in revised form 16 August 2010; available online 25 August 2010

Abstract Anthropogenic and natural climate change affect processes in the atmosphere, biosphere, hydrosphere, and pedosphere. The impact of climate on soil evolution has not been well-explored, largely due to slow rates and the complexity of coupled processes that must be observed and simulated. The rates of mineral weathering in loess deposited 23 kyr ago and experiencing soil formation for 13 kyr are explored here using the WITCH model for weathering and the GENESIS model for climate simulation. The WITCH model, which uses rigorous kinetic parameters and laws with provision for the effect on rates of deviation from equilibrium, can successfully simulate the depletion profiles in the soil for dolomite and albite if soil CO2 is assumed to rise over the last 10 kyr up to about 30–40 the present atmospheric pressure, and if the solubility product of the Ca-smectite is assumed equal to that of an Fe(III)-rich Ca-montmorillonite. Such simulations document that dissolution behavior for silicates and carbonates are strongly coupled through pH, and for Ca-smectite and feldspars through dissolved silica. Such coupling is not incorporated in simple geometric and analytical models describing mineral dissolution, and therefore probably contributes to the long-standing observation of discrepancies among laboratory and field mineral dissolution rates. Ó 2010 Elsevier Ltd. All rights reserved.

1. INTRODUCTION Continental weathering is a key component of global geochemical cycles. Since the early 80s it has been recognized as a driver for long-term global climate (Walker et al., 1981). However, recent studies have demonstrated its importance for shorter timescales, including for ongoing climate change (Aumont et al., 2001). Furthermore, the response of weathering processes to the changing environment might be much stronger than generally estimated. Recent work shows that weathering rates of small basaltic

⇑ Corresponding author. Tel.: +33 (0)5 61 33 26 15.

E-mail address: [email protected] (Y. Godde´ris). 0016-7037/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2010.08.023

catchments are quickly responding to man-induced climate warming at high latitude (Gislason et al., 2008). At the continental scale, weathering intensity is also changing quickly. The discharge of HCO3 from the Mississippi river, related to chemical weathering, has increased by 25% over the last 40 years in response to land use change and to agricultural practices (Raymond et al., 2008), making weathering processes a potentially non-negligible actor in the global carbon cycle at anthropogenic timescales. Understanding how continental weathering depends on environmental parameters and predicting how it will change under changing boundary conditions (climate, vegetation cover) require the development of mechanistic models of weathering reactions. Recently, we developed a numerical tool called the WITCH model to simulate weathering fluxes

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at the watershed scale (Godde´ris et al., 2006). The WITCH model uses kinetic laws derived from Transition State Theory with kinetic parameters derived from laboratory experiments to simulate the mineral dissolution/precipitation in the weathering profiles, from the surface down to the bedrock. The WITCH model was applied to the Strengbach granitic catchment (80 ha) covered with a temperate forest. We demonstrated the ability of WITCH to reproduce the mean dissolved load of the main stream as well as the chemical composition of the soil solution as a function of depth. In this numerical experiment, the mineralogical composition of the soil layers and their thickness were held constant, a simplification justified by the short simulated time period (1 year). Indeed, at this timescale, the only evolving parameter is the vertical drainage and soil solution chemical composition. At the other end of the complexity scale stands a model able to reproduce the soil growth from bedrock, including geometry changes (such as thickness and porosity evolution) and the evolution through time of the mineralogical composition of the weathering profile as well as that of the draining waters. One main difficulty of such a model lies in the numerical computation of the processes at the bedrock/weathering profile interface where the saprolitic material is developed. Up to now, most soil growth models remain empirical, generally based on an assumed exponential decay of the soil production rate as the soil thickness increases (Minasny et al., 2008). In many of those papers, “soil” is defined as the mobile layer of loose material that moves downslope, and is not strictly defined to include the regolith above bedrock. But promising efforts are now ongoing to investigate bedrock conversion into saprolite (Fletcher et al., 2006; Buss et al., 2008). In this contribution, to overcome the problem of soil generation we study loess profiles along the Mississippi river which formed by the deposition of eolian materials sometime after 23 kyr ago 14C (Muhs et al., 2001; Williams et al., 2010). Since 13 kyr, weathering occurred within these loessic formations causing mineralogical evolution to vary as a function of the location from the North to the South along the Mississippi valley. Given that these loess materials were roughly uniform in mineralogical composition at the time of their deposition (Muhs et al., 2001), they offer a unique opportunity to test our ability to model the mineralogical evolution of weathering profiles as a function of climate at the 104 year timescale. 2. STUDY SITES Geochemical data published for twenty two soil pedons spanning from northeastern Iowa (42°590 N) to south-central Louisiana (30°470 N) were analyzed as a function of depth to differentiate chemical variations between parent lithology (Peoria Loess) and the residual soils. All pedons were classified as very deep, well-drained, non-eroded upland soils (Muhs et al., 2001; Soil-Survey-Staff, 2008) which were derived from identical parent material and weathered for the same duration under different climatic regimes (Ruhe, 1984; Muhs et al., 2001). A subset of samples from two pedons (ie. the most northerly and the most southerly) were characterized for

mineralogy (Williams et al., 2010). In our previous work, samples corresponding to the deepest C horizon, the Bt horizon at 0.75 m below surface, and the surface A horizon, were ground with a mortar and pestle to pass through 325 mesh (an equivalent particle size of 45 lm). In addition, an extensive clay characterization was achieved for the northernmost Bt specimen following standard procedures for the removal of organic matter, carbonates, and MnO2 (White and Dixon, 2003). Characterization was accomplished by X-ray powder diffraction (XRD) on zero-background quartz slides. The Scintag PAD V diffractometer was operated at 35 kV voltage and 30 mA current using Cu-Ka1 and Cu-Ka2 radiation and a Ge solid-state detector. Diffraction patterns were collected from a 2° to 70° continuous scan with a speed of 2° per minute. Results document that quartz, albite, K-feldspar and clays were present in each of the samples, confirming compositional uniformity of the soils along the transect (Ruhe, 1984; Pye and Johnson, 1988; Muhs et al., 2001). Only a few of the deeper samples from the pedons were shown to contain measurable dolomite. These XRD results were generally consistent with reported observations for the loessderived soils (Pye and Johnson, 1988). Specifically, XRD documented the presence of dolomite at 3.8 and 3.5 m depths for respectively the most northerly and southerly pedons. By combining data for mineralogical composition observed in the most northerly and southerly pedons based on XRD with the bulk elemental composition and making mineralogical models as described in Williams et al. (2010), we determined reasonable mineral abundances for both pedons (Table 1). These concentrations are plotted as solid symbols on Fig. 3, as described later. 3. THE MODELS 3.1. Modeling setup Since the objective in this contribution is to model the time evolution of all major mineralogical transformations of the loessic profiles along the Mississippi valley since 10 kyr, two numerical models are utilized (Fig. 1). A climate model is used to estimate the evolution of the climate along the soil transect for the past 10 kyr (temperature, drainage, water volumetric content, vegetation cover). These outputs are then used in a geochemical box model, WITCH, that allows the calculation of the amount of dissolved and precipitated mineral phases induced by water vertical drainage within the profiles along the Mississippi valley transect. The climate model is an atmospheric general circulation model (GENESIS) and has been run for three time slices: 0 kyr (present day), 6 kyr, and 10 kyr. The climatic outputs of interest are then interpolated linearly in time to produce a history for each parameter over the last 10 kyr. They are also linearly interpolated in space to produce a climatic history at each site along the Mississippi transect. And finally, they are also linearly interpolated as a function of depth. Indeed, the GCM includes a description of the soil water and heat budget in 6 vertical layers from the surface down to 4.25 m (thickness 0.05, 0.10, 0.20, 0.40, 1.00 and 2.50 m), while the loessic profiles

Modeling climate and weathering processes

initial mineralogical composition is identical for each box (Table 1) for each simulated pedon. This approach relies upon the climate model feeding the geochemical model without any feedback from the geochemistry towards the climate. This means specifically that the drainage and water volumetric content are fixed by the GCM simulation and are not impacted by the dissolution and precipitation of mineral phases inside the weathering profile over the 10 kyr of the simulations.

Table 1 Mineral distribution in the parent soil.

Albite K-feldspar Quartz Kaolinite Camontmoril Dolomite

Volume % abundance North pedon (excl. porosity)

Volume % abundance South pedon (excl. porosity)

11.8 12.6 41.2 10.7 7.8

9.6 10.4 43.7 10.2 7.7

11.5

11.3

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3.2. The climate model

are described in WITCH as a pile of 20 identical boxes (0.20 m thick) from the surface down to 4 m depth. The

A global climate model (GCM) was used to calculate temperature and porefluid advection velocities during the Holocene through model soils along the Mississippi Valley transect. The experiments presented here used the GENESIS

WITCH

Vertical drainage Water volumetric content NPP

Bedrock

Drainage

4m

Loess

GENESIS GCM

Mineralogical composition Water chemistry

Fig. 1. Model structure. The GCM is run for three timeslices (10, 5 and 0 kyr BP) and results for the Mississippi valley are injected into the WITCH model. WITCH calculates the time evolution of the chemistry of the draining waters and of the mineralogical composition for each vertical box. The model is run for two sites (42°590 N and 30°470 N).


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version 2.3 GCM, composed of an atmospheric general circulation model coupled to multilayer models of vegetation, soil and land ice, and snow (Thompson and Pollard, 1997). Sea-surface temperatures and sea ice are computed using a 50-m slab oceanic layer with diffusive heat fluxes. The atmospheric GCM is spectral T31 (3.75°); the surface model grid is 2° 2°. The surface module includes a two-canopy model of physical vegetation and a six-layer soil model (Pollard and Thompson, 1995). The soil model extends from the land surface to 4.25 m depth, with layer thicknesses increasing from 5 cm at the top to 2.5 m at the bottom. Physical processes in the vertical soil column include heat diffusion, liquid water transport, uptake of water by plant roots for transpiration, surface runoff, bottom drainage, and freezing and thawing of soil ice (Clapp and Hornberger, 1978; Cosby et al., 1984; Dickinson, 1984). Three 25-year GCM simulations were run for modern conditions, 6 and 10 ka, with orbital configurations, greenhouse gas amounts and ice sheet extents prescribed for each time period as in Pollard et al. (1998). Predictions of vegetation distributions were modeled interactively by BIOME4 (Kaplan et al., 2003), using changes from modern climate to drive the vegetation (Pollard et al., 1998; Bergengren et al., 2001). To clarify the interpretation of soil chemistry results for this study, uniform soil properties were prescribed within a rectangular area that roughly includes the Mississippi Valley loess deposits (see below). To minimize spin-up transients and interannual variability, all GCM results used are averages over the last 10 years of each simulation.

Table 2 Kinetic dissolution constants at 25 °C (mol/m2/s) and activation energy (kJ/mol) of the dissolution reactions promoted by H+, OH, water (w) and organic ligands (L) (see eq. 3), as used in the WITCH model for the present study for the silicate minerals. Also shown is the reaction order with respect to H+ and OH promoted dissolution (nH, nOH). Symbol “” stands for “no effect”.

Albitea

K-feldsparb

Quartzc

Kaolinited

Ca- montmorillonitese

pkH EaH nH

pkOH EaOH nOH

pkW Eaw

pkL EaL

9.50 60 0.5 9.65 60 0.5 12.45 50 0.38 9.8 48 0.38

9.95 50 0.3 10.70 50 0.3 11.00 85 0.25 10.74 40 0.73

12.60 67

12.96 59

12.85 67

13.40 85

14.43 55

13.9 55

12.1 48.3

a Fitting within the framework of Eq. (3) of data reported by Blum and Stillings (1995) for albite. b Fitting within the framework of Eq. (3) of data reported by Blum and Stillings (1995) for orthoclase. c Dove (1994). d Fitting of data reported by Nagy (1995) for kaolinite. e Holmqvist (2001).

3.3. The geochemical model 3.3.1. Mass balance equations for soil solutions WITCH is a vertical box model that calculates the evolution of the soil solutions as a function of time. Because WITCH is a box model, the compartmentalization process leads to a set of coupled ordinary differential equations that describes the budget of the main conservative species (not involved in fast speciation reactions). Those equations are solved at each time step in each box for each species: nm nm X X dðz h C j Þ ¼ F top F bot þ F iweath;j F iprec;j dt i¼1 i¼1

Rj

ð1Þ

where Cj is the concentration of the species j. WITCH includes a budget equation for Ca2+, Mg2+, K+, Na+, SO42, total alkalinity, total aluminum, total silica, and total phosphorus. z is the thickness of the layer under consideration (here a constant 20 cm in thickness), and h is the water volumetric content. Ftop is the input of species from the layer above the given layer in moles per unit of time through drainage, and Fbot is the removal of water through downward drainage. Both the drainage and the water volumetric content are taken from the GCM output, i.e., they are fluctuating along the Mississippi transect and through time on an annual basis (no seasonal simulations have been performed to avoid excessive computation time). nm is the total number of minerals considered in the simulation,

Fiweath,j is the release of the species j through dissolution of the mineral i in the considered box, and Fiprec,j is the removal of j through precipitation when the solution becomes supersaturated with respect to mineral i (see below). Finally, Rj is the exchange term between the soil solution and the clay–humic complex. This cation exchange flux is set to zero in the present simulations. This is justified here by the length of the simulation (10 kyr), and by the forcing functions which are all defined on a mean annual basis (temperature, drainage, water volumetric content). Once the mass balance equations have been solved, the chemical speciation of the soil solutions for each layer is calculated allowing the determination of pH and concentrations of various species (H2CO3, HCO3, CO32, Al3+, AlOH2+, Al(OH)2+, Al(OH)4, H4SiO4, H3SiO4, H2SiO42, PO43, HPO42, H2PO4, H3PO4 and organic ligands RCOOH and RCOO as described in Section 3.3.3). The proton concentration is calculated by solving the charge balance of the soil solution in each layer of the weathering profile at each time step ½OH þ ½HCO3 þ 2½CO3 2 ½RCOO ½Hþ 3½Al3þ 2½AlOH2þ ½AlðOHÞ2 þ þ ½AlðOHÞ4 þ ½H3 SiO4 þ ½H2 SiO4 þ 3½PO4 3 þ 2½HPO4 2 þ ½H2 PO4 Alk ¼0

ð2Þ


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where Alk is the total alkanity of the soil solution in each layer calculated from the mass balance Eq. (1). The redox potential of the solution is not calculated in the present version of WITCH.

sky et al., 1999; Pokrovsky and Schott, 1999, 2001). Calcite dissolution Fcal is described by: ! ko ð5Þ F cal ¼ k H cal aH þ 1 Xcal 1:0 1 105 þ aCO3

3.3.2. Dissolution/precipitation rates and mineral mass balance The dissolution Fiweath,j and precipitation Fiprec,j terms for silicate minerals are calculated using kinetic laws and parameters derived from the transition state theory (TST; Eyring, 1935) and laboratory experiments, respectively. Within the framework of TST, the rate of an elementary reaction is equal to the product of two terms, the concentration of the activated complex and the frequency with which these complexes cross the energy barrier that separates the reactants from the products. Assuming the activated complexes can be formed by parallel reactions with H+, OH, water and organic ligands, the overall dissolution rate of a mineral can be expressed as (Schott et al., 2009): ! $ % X Ela;g nl;g 0 al finh k l;g exp F g ¼ Ag RT l ð3Þ 1 X1=s g

where kHcal equals 100.659 mol/m2/s and ko 1011 mol/m2/s at 25 °C (Wollast, 1990). The activation energies for rate constants are respectively set to 8.5 and 30 kJ/mol (Alkattan et al., 1998; Pokrovsky et al., 2009). The WITCH model includes kinetic laws and parameters for 32 minerals. Kinetic data for the silicate minerals included in the present study are listed in Table 2. Thermodynamic parameters for the dissociation reaction of these minerals are given in Table 3. In addition, a mass balance for each mineral in each layer has been added, given the precipitation/dissolution flux calculated above. At each time step, the total amount (in moles) of mineral g inside each layer Qg is thus calculated as:

where Fg is the overall dissolution rate of mineral g inside a given layer. The sum accounts for the four parallel rate controlling elementary reactions that are assumed to describe dissolution promoted by H+, OH, H2O and organic ligands for feldspars. In this relation al and nl,g stand for the activity of the lth species and the reaction order with respect to the lth species, respectively. For organic ligands, al equals the activity of a generic organic species RCOO (conjugate of RCOOH). kl,g is the rate constant of mineral g dissolution reaction promoted by species l, and Ela,g is the activation energy of this reaction. finh stands for inhibitory effects (i.e. by aqueous Al). The last factor in Eq. (4) describes the effect on rate of the departure from equilibrium where Xg is the solution saturation state with respect to mineral g (Xg = Q/Kg where Q is the activity quotient and Kg is the equilibrium constant for mineral g dissociation reaction), and s, the Temkin’s coefficient number, is the stoichiometric number of moles of activated complex formed from one mole of the mineral. Precipitation terms are calculated in the same way, but Xg is then >1. A0 is the reactive surface (see below). Carbonate mineral dissolution/precipitation has been added to WITCH and modeled within the framework of TST and surface coordination chemistry concepts (Pokrovsky et al., 1999; Pokrovsky and Schott, 1999, 2001). Dolomite dissolution rate Fdol is modeled as: " F dol ¼ k H

dol

aH

0:75

1 Xdol 1:9

þ k Mg

dol

1:575 109 9 1:575 10 þ 3:5 105 þ aCO3 aCa

!#

dQg ¼ Fg dt

ð6Þ

Fg is either positive or negative during the simulation, depending on the chemical saturation state of the solution with respect to the given mineral g. Note that only clay minerals and calcite are allowed to precipitate. When chemical equilibrium is reached with respect to primary silicate minerals or dolomite, their respective dissolution rates are set to zero without allowing precipitation. Reactive surface is calculated separately for non-clay and clay minerals. In each layer i, total reactive surface of non-clay minerals Ai,p is calculated according to: Ai;p ¼ r

Mi M0

where Mi is the total volume of non-clay mineral in layer i, and M0 is the initial volume of material prior to any dissolution. r is a constant fixed so that the initial reactive specific surface of the primary minerals in layer 1 equals 13 106 m2/m3 corresponding roughly to the specific BET surface area typical for loess (Kahle et al., 2002). Reactive surface is thus assumed to evolve linearly with the volume abundance through time. Part of this total reactive surface is then assigned at each time step to each primary mineral depending on their relative volume abundance. Total reactive surface for clay minerals Ai,s (m2/m3) in layer i is estimated from a parametric relationship between grain size fraction and reactive surface (Sverdrup and Warfinge, 1995; Sverdrup et al., 2002), accounting only for the clay grain size fraction: Ai;s ¼ 8 nclay 1000 qi

ð4Þ

where aH, aCO3 , a Ca stand respectively for the H+, CO32, and Ca2+ activities. kHdol equals 103 mol/m2/s, and kMgdol 108.2 mol/m2/s at 25 °C. The activation energy for kHdol and kMgdol is set to 40 and 60 kJ/mol, respectively (Pokrov-

ð7Þ

Si M0

ð8Þ

where nclay is the fraction of clay-size grain in the loessic profile (fixed to 0.12), qi is the pedon density (fixed to 1700 kg/m3) and Si is the total volume of clay minerals in each layer at each time step. The factor 1000 is a conversion factor and 8 is a parameter of the transfer function (Sverdrup and Warfinge, 1995).


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Table 3 Equilibrium constants at 25 °C and enthalpies of reaction for dissolution of minerals involved in the present study. Unless otherwise specified, data for minerals and aqueous species are from EQ3/EQ6 database (Wolery et al., 1990) revised by Wolery in 1998 and 2002 (slop98.dat and SPEQ02.dat) except for Al3+ (Castet et al., 1993; Wesolowski and Palmer, 1994) and H4SiO4 (Walther and Hegelson, 1977). Albite K-feldspar Quartz Kaolinitea Halloysitea Ca-montmoril Calcitea Dolomitea a

Dissolution reaction

pKeq

DHR0 (kJ/mol)

NaAlSi2O8 + 4H2O + 4H+ ? Na+ + Al3+ + 3H4SiO4 KAlSi3O8 + 4H20 + 4H + ? K+ + Al3+ + 3H4SiO4 SiO2 + 2H2O ? H4SiO4 Al2Si2O5(OH)4 + 6H+ ? 2Al3+ + 2H4SiO4 + 2H2O Al2Si2O5(OH)4 (Halloysite) + 6H+ ? 2Al3+ + 2H4SiO4 + 2H2O Si4O10(OH)2Mg0.33Al1.67Ca0.165 + 6H+ + 4H2O ? 4H4SiO4 + 1.67Al3+ + 0.33Mg2+ + 0.165Ca2+ CaCO3 ? Ca2+ + CO32 CaMg(CO3)2 ? Ca2+ + Mg2+ + 2CO32

2.29 0.022 3.98 7.435 12.5 2.53

73.82 49.93 25.06 147.7 166.6 81.65

8.48 17.09

9.61 39.48

Drever (1997).

3.3.3. Below ground carbon The total organic acid [RCOO] content (in mol/l) in each layer is calculated from a prescribed and fixed dissolved organic carbon (DOC) content (expressed in g/m3) (Oliver et al., 1983; Alveteg, 1998; Alveteg and Sverdrup, 2002): 6

½RCOO ¼

7 10

k ac DOC k ac þ aH

ð9Þ

where kac is the equilibrium constant for the organic acid dissociation reaction and aH the activity of H+. DOC levels have not been reported for the loess soils and we therefore use typical values for temperate environments (20 g/m3 at 0.20 m depth, then rapidly decreasing to 0 at 1 m depth, and kept to 0 below this level) (Dambrine et al., 1995). So far, WITCH does not include a carbon budget for the below-ground solutions. This means that the mineral dissolution reactions do not impact the below-ground partial pressure of CO2. This approximation results in a slight overestimation of the weathering rates since PCO2 is not decreasing as the dissolution reactions proceed. However, it must be kept in mind that the processes of biological production and diffusion of CO2 largely hide the CO2 consumption by weathering. With these assumptions, soil CO2 pressure is thus prescribed, and the speciation of carbon in solution is calculated from this value and from the alkalinity of the solutions calculated by the mass balance equations at each time step. In its previous published version, WITCH was fed by the output of ASPECTS, a numerical model of biospheric productivity (Rasse et al., 2001), to calculate the chemical exchanges between the soil solutions and the dead and living biomass, as well as the below-ground CO2 level (Godde´ris et al., 2006). This cannot be achieved here because ASPECTS cannot be run for long time periods without very detailed meteorological data and biospheric parameters. Here soil CO2 levels are calculated based on the net primary productivity calculated by GENESIS above each pedon. The diffusion coefficient Ds CO2 (cm2/s) of gaseous CO2 in the weathering profile is assumed to be linearly dependent on soil porosity (/ fixed to 0.43) and soil tortuosity (Hillel, 1998). s is the ratio of a straight flow path to the average roundabout path (Hillel, 1998) and is fixed here

to 0.45, assumed to be a standard value in the absence of constraint (Gwiazda and Broecker, 1994) Ds CO2 T 2 ¼ / s Da CO2 273:15

ð10Þ

where Da CO2 is the diffusion coefficient of gaseous CO2 in air at 273.15 K and is set to 0.139 cm2/s (Mattson, 1995). The maximum CO2 pressure reached below the root zone PCO2max in ppmv (assumed to be the only CO2 production zone) is calculated as (Van Bavel, 1951): 2 5:7 107 CO2 pr rootdepth PCO2 max ¼ PCO2 atm þ ð11Þ 2 / Ds CO2 where PCO2atm is the atmospheric pressure in ppmv, rootdepth is the root depth calculated by the GCM at each time step and for each pedon in cm, and CO2pr is the production of CO2 in the root zone in gC/m2. This latest value is assumed to be 75% of the NPP (Gwiazda and Broecker, 1994). To save computation time, a power function of the depth is used to define the CO2 profile from the surface (atmospheric value) down to the root depth (PCO2max) instead of solving the complete diffusion equation. CO2 aqueous speciation is deduced from CO2 profile and calculated solution pH using Henry law and CO2 dissociation constant. Additional details about the WITCH model can be found in Godde´ris et al. (2006, 2009). 4. KEY PARAMETERS: A PRELIMINARY OVERVIEW Any complex suite of models implies the existence of a non-negligible set of parameters that must be tested. All three models, the GCM, BIOME4, and WITCH have their own sets of parameters. Crossed sensitivity tests would result in excessive computation time. Partly for this reason, but also because the Genesis GCM and BIOME4 models have been extensively tested elsewhere, we focus on the sensitivity of the geochemical model in this contribution. The number of critical parameters for the geochemical simulations might be suspected to be high, but this is not the case. We briefly describe here what the key parameters are, and whether they were tested or not in this study:


(1) The mineralogical composition. Here, the mineralogy is fixed based on field observations and thus was not tested. (2) The water volumetric content and the drainage of the weathering profile. The hydrological behavior of the weathering profile is a first order controlling parameter of the weathering processes. It depends on the characteristics of the material (mainly porosity, which is fixed in this study, based on reported values for loess). Another strong control on hydrology is exerted by the vegetation through the evapotranspiration process. In the present study, water volumetric content and vertical drainage are calculated by the GCM and transferred to the WITCH model. As mentioned above, we use the GCM output as a forcing function for the geochemical model with only one test simulation. We are fully aware that this is an important limitation, but given the computational time constraints, this limitation was necessary. (3) The solubility product of the mineral phases. This product is generally well constrained for primary minerals and for some secondary phases (including kaolinite). But previous work performed with the WITCH model (Godde´ris et al., 2006, 2009; Roelandt et al., 2010) explored the role of the solubility product of some secondary minerals, including smectites, showing that this is a critical parameter. It was thus tested extensively as explained below. (4) Soil CO2 pressure. This parameter, an important control on the proton concentration in the weathering profile, ultimately depends on the vegetation productivity which is calculated by the GCM. This parameter also depends upon the texture of the soil and the water volumetric content, both of which control the diffusion of gaseous CO2. Its precise estimation is not easy to assess and tests to the soil CO2 levels were therefore performed. (5) The dependence of the dissolution rates on the soil solution pH: albite dissolution rates were particularly explored. A systematic study of all those parameters to explore the full range of possible values was not possible (one 10 kyr simulation takes 15 h computing time). Rather we followed a step by step method in which we started from a first simulation, and then explored the sensitivity of our results to the various parameters around this first guess. Then, crossed sensitivity tests (several parameters changed at the same time) were performed, improving the agreement between model output and field data. This method allowed us to reach step by step the best agreement with the data. 5. RESULTS 5.1. Pedon 42° lat N 5.1.1. Climatic output Over the course of the simulation, the calculated temperature doubles in the profile of the most northerly pedon (42°590 N, Fig. 1) , from about 4 °C at 10 kyr BP to more

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than 8 °C today (Fig. 2). The water volumetric content also rises through time in all layers. The mean annual drainage of the pedon rises by 45% over the simulated period, increasing from 52 to 75 mm/yr . Finally, calculated partial pressure of CO2 from the GCM NPP rises from 300 up to 650 ppmv in the upper layer, and from 300 to more than 900 ppmv below the root zone. The root zone depth deepens from 20 cm at 10 kyr BP down to almost 2 m at present day. 5.1.2. Geochemical output 5.1.2.1. Run #1. We started with a first “blind” simulation: the run #1 simulation has been performed with standard thermodynamic data and kinetic parameters derived from laboratory experiments (Tables 2 and 3). This simulation was used to fix the geochemical state of the weathering profile around which sensitivity studies were performed. All mineralogical abundances are plotted normalized to the quartz abundance (Brimhall and Dietrich, 1987; Anderson et al., 2002): sm ðz; tÞ ¼

C m ðz; tÞ C quartz ðparentÞ 1 C m ðparentÞ C quartz ðz; tÞ

ð12Þ

Here sm(z,t) is the relative abundance of mineral m at depth z and time t, Cm(z,t) its concentration at depth z and time t, and Cquartz(z,t) the concentration of quartz at depth z and time t. Cm(parent) and Cquartz(parent) are respectively the concentrations of mineral m and quartz in the parent material. These latter concentrations are equal to the concentrations throughout the profile at t = 10 kyr before present, i.e., at the time of deposition of the loess. Normalization by quartz concentration is based upon the implicit assumption that quartz is neither added nor removed from the profiles to any significant extent during weathering over the timescale of interest. Plots of s versus depth have been observed to fall into generalized end-member categories depending upon the reactions occurring (Brantley et al., 2008; Brantley and White, 2009). For example, minerals that are neither removed nor added to the soil plot as inert profiles such that s = 0 at all depths. Depletion profiles show s < 0 above the C horizon and decreasing upward. In contrast, addition profiles show s > 0 above the C horizon and increasing upward. Combinations of these profile types are also common: depletion-enrichment profiles show s < 0 at the surface and s > 0 at depth due to leaching in the surface and reprecipitation at depth, while biogenic profiles show the reverse due to biocycling of nutrient elements (s > 0 at the surface and s < 0 at depth). s profiles for albite, K-feldspar, kaolinite Ca-montmorillonite, and dolomite after 10 kyr show many of these characteristics in both simulations and data from present day (Fig. 3). Owing to its very low dissolution rate, quartz abundance (not shown) remains very close to its initial abundance (an inert profile), justifying the use of quartz as an immobile phase in Eq. (12) (after 10 kyr, only 0.6% of the initial abundance has been calculated to be lost in the top layer). Similarly, in agreement with soil observations, simulations of K-feldspar abundance at 10 kyr show only a slight depletion of this mineral (s 0.1) in the top

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Fig. 2. Calculated time evolution of the temperature, water volumetric contents, soil CO2 pressure and vertical drainage for the Northern pedon (42°590 N).

50 cm returning almost to initial abundance at 90 cm depth. In contrast, simulations indicate that dolomite has been completely dissolved down to 1.50 m depth where it displays a very sharp weathering front; below this depth dolomite is present at its initial abundance. However, the most striking feature of the results is the difference between the calculated and observed profiles for clay minerals and albite. Soil data for albite show the characteristics of a depletion profile – maximum depletion at the top of the profile (s 0.3), and then a more or less linear increase in s with depth. A slight relative increase in albite concentration at the surface of the soil is documented by the sparse concentration data; however, such changes at the surface can be spurious due to anthropogenic disturbances or small atmospheric inputs. In contrast to these observations, the model at 0 kyr predicts a very strong depletion and a reverse profile such that s values 0.4 at the surface and 0.6 at 4 m depth. Note however that the profile displays again a tiny positive slope below 1.5 m depth, below the dolomite weathering front where pH shifts suddenly from values around 6.5 to more than 8. The model also fails to reproduce the observed depletion profile for Ca-montmorillonite and the depletion-enrichment profile for kaolinite. It predicts significant Ca-montmorillonite precipitation (with s values around 1.3–1.5 below 1 m depth) while soil data do not record any increase in this mineral abundance. Opposite results are obtained for kaolinite with a marked increase of kaolinite soil abundance at 0.5–2 m depth (s reaches values of 0.8) but no kaolinite precipitation according to the simulations. The “reverse” albite profile simulated by the model results from (i) the strong impact of dolomite on soil solution pH and thus on the reactions among primary and secondary silicate minerals and (ii) the marked dependence on pH of the dissolution rate law selected for albite (Table 2 and Fig. 4). First, the presence of dolomite in the soil profile

forces the pH of the soil solution to be close to 8 whereas dolomite removal from the profile allows pH to drop to 6.5. Albite dissolution rate decreases with pH in acid solution, reaches a minimum around pH 6.0 and rises by about 0.3 order of magnitude at pH 8 (Brantley et al., 2008). As a result, albite dissolves faster in soil horizons where dolomite is present than in horizons where it has been removed. This induces a rapid removal of albite from the soil as illustrated on Fig. 3 by the large migration of s towards negative values at depths where dolomite is present in the soil. When dolomite disappears from the top layers, the rate of removal of albite from these horizons causes the decrease in s to slow down as a result of the decrease in pH. As a result, the s profile for albite develops into a “reverse profile” during the run. Given the similarities between Na- and K-feldspar dissolution, K-feldspar might also be expected to develop a reverse profile. However, this is not displayed in the 10 kyr run (Fig. 3) although the K-feldspar dissolution rate exhibits the same pH dependence as albite with a minimum dissolution rate around pH 6.8. The explanation for this divergence lies in the value of the saturation state (Xg) of the soil solutions with respect to albite and K-feldspar. Solution saturation state with respect to albite never exceeded 0.03 at the end of the simulation (Fig. 5a). The maximum Xg value is reached at the dolomite weathering front where pH abruptly rises to values close to 8. The solution saturation state with respect to K-feldspar, which is much less soluble than albite (its solubility product is about two orders of magnitude lower), is much higher (Fig. 5a). Below 1.50 m depth, for example, where dolomite is still present, Xg value for K-feldspar is above 0.5, reaching almost 1.0 at the base of the pedon profile (4 m depth). As a result, unlike albite, the dissolution rate of K-feldspar is low because soil solutions are close to equilibrium at depth. At the top of the soil profile, the solution saturation state with respect


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Fig. 3. Measured and calculated mineralogical profiles for the Northern pedon (42°590 N) at 10, 5 and 0 kyr BP for the run #1.

a

b

Fig. 4. (a) Dissolution rate of albite as a function of pH for two different fits of the experimental data. +: Chou and Wollast (1985), *: Chou and Wollast (1984), h : Holdren and Speyer (1987), : Casey et al. (1991), }: Knauss and Wolery (1986). (b) Dissolution rates of albite and K-feldspar as a function of pH.

to K-feldspar slightly decreases as pH is driven down by the disappearance of dolomite. At that point, feldspar dissolution rates increase. The control of K-feldspar and albite dissolution by chemical affinity and solution pH, respectively, explains why the K-feldspar abundance displays a normal profile and the albite a reverse one. These results illustrate the complex behaviors of the coupled dissolution rates of silicate minerals in the presence of dissolving carbonate minerals. The contrasting behaviors of albite and K-feldspar, where dissolution of the latter mineral occurs near equilibrium, has been previously noted (White, 2008). Based on these first results, several modifications can be considered to improve the calculated profiles for albite and clay minerals. (1) The increase in the dissolution rate of albite at high pH is a common feature documented by all experimental investigations of feldspar dissolution (Bandstra et al., 2008). But the precise pH value at which albite dissolution rate reaches a minimum is difficult to assess from experimental data because of the extremely slow kinetics (Bandstra et al., 2008), as well as the precise slope of the function of the dissolution rate vs pH at alkaline pH. Different fitting functions in the 5–9 pH range might be used, so that the dissolution rate of albite will be lower or the same at pH 8 (in the presence of dolomite) than at pH 6.5 (the pH recorded in a pure silicate environment). (2) We have seen that the preservation of dolomite in the weathering profile after a 10 kyr run facilitates the reversal of the s profile for albite, because high pH conditions persist even at shallow depth. If dolomite is removed faster, acidic conditions may be reached earlier, forcing the albite profile back toward a normal slope for a mineral experiencing only dissolution. (3) The abundant precipitation of

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Fig. 5. Calculated saturation indexes for albite as a function of depth at 10, 5 and 0 kyr BP in the Northern pedon. (a) run#1, (b) run Ksp where solubility product of montmorillonite has been increased from 102.53 to 107 (see text).

Ca-montmorillonite predicted by the model also contradicts field observations. This contradiction originates from the large oversaturation of soil solutions with respect to this mineral (saturation state around 10). Furthermore, silica removal from soil solution by smectite precipitation induces a strong undersaturation of soil solution with respect to the primary minerals, including albite. Limiting the Ca-montmorillonite precipitation by an increase in its solubility product may favor both kaolinite precipitation as recorded in the field and may help to solve the albite reverse profile problem, allowing the soil solution to be closer to equilibrium with albite, thus reducing the dissolution rate of this mineral at high pH. These 3 modifications are explored below. 5.2. Dissolution rate of albite above pH 6.5 In order to decrease the dissolution rate of albite at high pH, we chose to use a fit of experimental data at high pH from the dataset by Knauss and Wolery (1986). This dataset displays lower dissolution rates than other published experiments above pH 6.0 (Fig. 4a). The albite dissolution rate as a function of pH is thus assumed to be a mix between the function used in the original WITCH formulation in the acidic domain (pkH = 9.50, slope nH = 0.5) and a fit of only the few Knauss data points in the basic domain (pkOH = 10.55, nOH = 0.33) (Fig. 4a). This shifts the minimum in the log rate–pH curve from pH 6 to 7 and results

in albite dissolution rate at pH around 6.5 to be close to that at pH 8 (i.e. the pH expected in the presence of carbonate minerals). As a result of running WITCH with this new albite dissolution rate model, the albite profile is now almost vertical (Fig. 6) thus removing the reverse trend calculated in run #1. However, there is still a general leftward drift of the s profile, because there is now continuous albite dissolution at constant rate during the 10 kyr of the run, whether dolomite is present or not (Fig. 6). An alternative solution could be to assume a pH-independent albite dissolution rate in the 5–8 pH range. Indeed, several experimental datasets (Chou and Wollast, 1985; Knauss and Wolery, 1986) can be fitted by a constant dissolution rate (at 25 °C) in this pH range. A set of two simulations were performed (Knauss cste and Chou cste) where the dissolution rate of albite was held constant at respectively 1012.3 moles/m2/s (Knauss and Wolery, 1986) and 1011.96 moles/m2/s (Chou and Wollast, 1985). The calculated albite profiles after a 10 kyr run display in both case a uniformly depleted profile from the surface down to 4 m depth (Fig. 6). As documented in those simulations, the higher dissolution rate resulted in more depletion. Although the reverse profile has disappeared, the model was not able to produce a depleted profile at the top, and a preserved abundance of albite at depth. For both simulations, the profiles were uniformly depleted in albite. Changing the albite dissolution rate law at 5 < pH < 8, either by decreasing it above pH 7 or by fixing it at a constant value


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a

b

Fig. 6. Measured and calculated K-feldspar (a) and albite (b) profiles for the Northern pedon at 0 kyr for various sensitivity tests.

throughout the range, did not produce model outputs that adequately match the mineral abundance data and this option was not further explored below. 5.3. Removing dolomite from the profile (High pCO2 run) Removing dolomite more rapidly from the loess profile can be achieved by increasing the below-ground CO2 level, which will provide more protons to the solutions. However, estimating below-ground CO2 level is a difficult task, either based on the data (there are no measurements of soil solution chemistry) or the modelling. At the end of the simulations described so far, the model is predicting PCO2 levels that reach a maximum value of 3.3 the pre-industrial atmospheric pressure (i. e. 920 ppmv). In contrast, available field measurements often display higher PCO2 values (Jassal et al., 2004, 2005). Furthermore, the CO2 level calculated by the model relies fully on the net primary productivity estimated by the GENESIS GCM, which is obviously subject to caution. In this test, we therefore increased the maximum CO2 partial pressure at the base of the root zone by a factor of 10, allowing PCO2 to reach 33 the atmospheric pressure at the end of the simulation (i. e. 9200 ppmv).

As a result, the dolomite front at the end of the simulation is shifted downward by about 1.30 m. It is now located at 2.70 m depth, in close agreement with the observed front around 3.20 m depth. The calculated K-feldspar s is almost unchanged, only displaying a slight shift towards more depleted values. But the albite s profile is deeply modified (Fig. 6). First it shifts towards less depleted values. Indeed, higher CO2 values lead to more acidic conditions so that dolomite is faster removed from the profile in the high CO2 run than in run #1. Since albite dissolution rates are lower at acid conditions (pH around 6.2) than at alkaline conditions in the presence of dolomite (pH around 7.8), s values are less negative. But a reverse profile is still calculated. The time period covered by the simulation is indeed too short to remove the imprint of the initial basic conditions on the s profile for albite. 5.4. Increasing Ca-montmorillonite solubility product (Ksp run) The solubility product of clay minerals is difficult to accurately characterize because solubility heavily depends both on mineral crystallinity and chemical composition. Godde´ris et al. (2006) have recently demonstrated the impact of clay solubility products on the export of dissolved

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cations and silica by a small catchment. Maher et al. (2009) came to the same conclusion while modelling weathering rates in soil profiles. A recent contribution also emphasized the potential key role played by the precipitation clay phases on the overall dissolution rate of primary minerals in the field (Zhu and Lu, 2009). The importance of clay solubility has been also explored in marine sediments (Maher et al., 2006) and was previously explored through the modeling of granitic weathering (Steefel and Van Cappellen, 1990). Reported values for the Ca-montmorillonite solubility product show it heavily depends on Fe3+ content, ranging from 102.53 for a well crystallized Fe-free Ca-montmorillonite (Si4O10(OH)2Al1.67Mg0.33Ca0.165: EQ3/EQ6 database, see Table 3) to 1014.1 for the iron rich Clay Spur smectite (Si3.93Al0.07O10(OH)2Al1.52Fe3+0.24Mg0.33Ca0.19Na0.02K0.02: (Huang and Keller, 1973; Kudrat et al., 2000) thus spanning almost 12 orders of magnitude. Because there is a significant amount of Fe3+ in the parent soils (i.e. about 3 and 4 wt.% Fe2O3 in the north and south pedon, respectively), one can test the effect of increasing the Ca-montmorillonite solubility product in connection with its inferred Fe3+ content. Increasing Ca-montmorillonite solubility product yields both (i) a decrease of the saturation state of the percolating waters with respect to this mineral and a decrease or even cessation of montmorillonite precipitation and (ii) an increase of silica and aluminum concentrations in soil solutions and consequently the increase of the solution saturation states with respect to the other aluminosilicate phases. This saturation increase leads to a decrease in the disequilibrium between the soil solutions and the reacting primary silicate minerals and thus a slow down in the rate of dissolution and removal of albite at depth whether dolomite is present or not. A large range of solubility product values for Ca-montmorillonite was therefore tested from 102.58 up to 1014. Here we present the results for an intermediate value, 107, which corresponds to a plausible content of Fe3+ in the montmorillonite (note that for this calculation we did not specify Fe3+ concentration in the montmorillonite as we have no data allowing the computation of soil solution redox and aqueous Fe3+ activity). Such a value has an important impact on the calculated s profile for albite as can be seen in Fig. 6. First, the reverse profile has now disappeared, and the results display a normal depletion profile as a function of depth. This is accompanied by a considerable increase in the saturation state of the percolating waters with respect to albite (Fig. 5b). 5.4.1. Reference simulation for the northern pedon (best fit) The reference simulation for the 42°N pedon has been performed assuming a solubility product for Ca-smectite equal to 107 and a high below-ground CO2 level (33 times the atmospheric level below the root zone at the end of the simulation, i.e. at present day). This simulation yields results for albite, K-felspar, and dolomite that match observations adequately (Fig. 7). The Ca-smectite profile is almost not affected by weathering all along the simulation (s = 0). This result is in agreement with the data below 1 m depth, but the data show depletion in smectites above this level. Despite the fact that the model also calculates dis-

solution of Ca-smectite above 1 m depth, the calculated depletion remains underestimated. Similar to the observations, the model also predicts accumulation of kaolinite in the profile below 50 cm depth, and a dissolution trend above it, but the amplitude of these trends are underestimated by WITCH. The calculated chemical composition of the percolating waters at 0 kyr display large changes with depth, especially around the dolomite front around 3 m depth (Fig. 8). The Ca2+ concentration rises from about 30 lmol/l above the front to more than 1000 lmol/l below the front. The same increase is predicted for Mg2+. Dissolved Na+ and H4SiO4 concentrations display a smooth increase from the top of the profile to the dolomite front. This behavior documents the progressive accumulation through silicate mineral dissolution. Below the dolomite front, the concentrations in Na+ and H4SiO4 remain constant because of the slow down of the albite dissolution at high pH (for Na+), and because the waters become saturated with respect to smectite (for H4SiO4). Four additional sensitivity tests have been performed. First we have tested the impact on feldspar profiles of the value of the Temkin’s stoichiometric coefficient (s) in the (1 X1/s) term of Eq. (3) that describes the consequence of departure from equilibrium on mineral dissolution rate (labelled in Fig. 9 “Temkin” simulation). According to TST (see above), s is equal to 3 for albite and K-feldspar (Gautier et al., 1994; Oelkers et al., 1994; Schott et al., 2009). It can be seen on Fig. 9 that changing the value of s from its reference value of 3 to 1 significantly degrades the simulated albite profile by moving it towards much more negative s values. In contrast, changing the value of s only weakly impacts the K-feldspar profile because, with the exception of the shallowest samples (depth