The impact of depth-dependent water content on steady state weathering and eroding systems
Introduction
Many researchers have investigated how regolith forms from bedrock by chemical and physical weathering, but the mechanisms and feedbacks remain puzzling. The long residence time of regolith in many locations points to the coupled nature of weathering and erosion. Several models have been developed to understand these processes. Geomorphological models usually consider empirical relations between the erosion rate at the land surface and the regolith thickness and assume a steady state evolution in which the erosion rate equals the soil production rate at the interface with saprolite or bedrock (Anhert, 1994, Heimsath et al., 1997, Burke et al., 2007, Odoni, 2007, Gabet and Mudd, 2009, Hilley et al., 2010, Phillips, 2010). On the other hand, geochemical models describe the spatial variation of physical and chemical parameters that locally depict the state of the regolith (Li et al., 2017). The chemical aspects of weathering and water transport are then used to predict the evolution of reaction fronts (Lichtner, 1985, Lichtner, 1988, Knapp, 1989, Chamberlain et al., 2005, Lebedeva et al., 2007, Maher, 2010, Lebedeva et al., 2010, Moore et al., 2012, Li et al., 2014a, Steefel et al., 2015, Lebedeva and Brantley, 2017). Quantitative description of data in a given site typically requires complex models that account for particular properties of the rock and of the regolith, which is possible with specialized computer codes (Steefel and Lasaga, 1994, Lichtner, 2007). On the other hand, to seek an explanation of universal trends in data from various sites and climates requires identification and modeling of only the main mechanisms of transport and reaction. For instance, some weathering models are one-dimensional and account for a single reactive mineral and transport of a single chemical species (Lebedeva et al., 2010, Li et al., 2014a, Reis and Brantley, 2017). They treat chemical weathering and land surface erosion as independent processes that may dynamically couple to form a steady state.
With no erosion at the land surface and with advective transport, the reaction front (RF) attains a steady state in which its thickness and its velocity have intrinsic values that depend on the reaction kinetics and fluid transport properties. This is described as a quasi-stationary state for the weathering system because the thickness of the weathered zone (i.e. the remaining material after the RF has passed) increases in time (Lichtner, 1985). If a small erosion velocity is imposed and the fluid velocity is independent of the regolith thickness, neither the RF thickness nor the RF velocity changes in this state. In such cases, there is continuous regolith thickening; see e.g. the discussion in Li et al. (2014a). A steady state can only occur when the erosion velocity equals or exceeds the intrinsic velocity of the RF, and only in this situation is there a coupling between the erosion and the chemical weathering.
An important feature of almost all geochemical models to date is the assumption that all water infiltrated at the land surface reaches large depths. However, this assumption is not reasonable for thick regolith, even with a flat topography, nor is it reasonable for regolith with complex spatial variations in permeability. Instead, part of the infiltrated water flows to neighboring channels or rivers before reaching the regolith-bedrock interface. The deviation of flow is significant especially when water reaches layers with high permeability contrast, which can often be zones of mineral reaction (Brantley et al., 2017). At the same time, when some previous models have been applied to observations of real regolith, the fits were possible only with the assumption that the vertical advection velocity of water was less than mean annual precipitation minus evapotranspiration for a given locality (Brantley et al., 2008, Moore et al., 2012). The treatment of these and other hydrological effects in geochemical or geomorphological models was also explored in recent works (Pandey and Rajaram, 2016, Braun et al., 2016, Harman et al., 2017, Ameli et al., 2017, Lebedeva and Brantley, 2018).
In this work, we introduce a reactive-transport model that represents the decreasing volumetric water content with depth in regolith. The crucial novel feature of this approach is that water entering the soil does not infiltrate to all depths because of lateral flow within the regolith. The conceptual model of Brantley et al. (2017) shows that this feature is necessary to explain how regolith might attain steady state thickness and mineralogy. We introduce an infiltration length to provide a simple description of the water distribution in the regolith. On the other hand, the interplay of dissolution and vertical water transport is characterized by an equilibration length which has the same dependence on dissolution rates and advection velocity as proposed in previous geochemical models. We analyze the possible steady states with a focus on the relations between these two lengths, discuss connections with published geomorphological examples, and propose applications.
This paper is organized as follows. In Section 2, we present the models for depth-dependent volumetric water content and chemical weathering. In Section 3, we study the steady state regolith evolution in the case of constant advection velocity through the regolith thickness. First the analytical solution is presented and then the features of each type of mineral depletion profile (completely developed and incompletely developed) and shown. In Section 4, we discuss consequences of those results: the distinct features of cases of infiltration control and reactive-transport control, the application to a site with a completely depleted profile, and suggestions of applications to incompletely developed profiles. Section 5 presents our conclusions. Appendix A presents the general solution of the model, which includes cases with depth-dependent advection velocity, and Appendix B presents a brief numerical study of such cases.
A list of symbols used in this paper is presented in Table 1 with the corresponding physical dimensions.
Section snippets
Basic definitions and approximations
We define bedrock as unaltered protolith and regolith as all bedrock material that has been physically or chemical altered. Regolith extends from the land surface (interface S) to the interface with the bedrock (B), respectively at positions and , as shown in Fig. 1. Interface S moves with constant velocity as the land surface erodes (the erosion rate may be set by an uplift rate). The x axis also moves down with velocity and we set . The position is defined by boundary
Results
Here we study only the case of constant advection velocity [ in Eq. (11)].
Facile infiltration versus limited infiltration
Here we analyze the results for , which corresponds to very slow dissolution at interface B (). This is the case of red, blue, and orange curves in Fig. 5 and of all curves in Fig. 6: the regolith begins at great depth but the reaction of mineral M does not proceed to great extent until shallower depths, where this reaction accelerates. We discuss separately the endmembers and . In Appendix B, we show that the qualitative results discussed here generalize to cases of depth
Conclusion
We introduced a reactive-transport model to describe mineral weathering with a depth-decreasing volumetric water content. This model was developed in response to many observations in the literature showing that weathering profiles at ridgetops lose water laterally and that not all the water entering the top of the profile advects out the bottom of the profile. The study of the case of depth-independent advection velocity was emphasized, but results for depth-decreasing velocities are
Acknowledgment
FDAAR thanks the Earth and Environmental Systems Institute of Pennsylvania State University, where part of this work was done, for the hospitality, and acknowledges support by Brazilian agencies CNPq (304766/2014-3) and FAPERJ (E-26/202941/2015). This material is based on work supported by the Department of Energy Office of Basic Energy Science Grant DE-FG02-OSER15675 to SLB. SLB acknowledges many conversations with M. Lebedeva, V. Balashov, R. Fletcher, L. Li, and C. Steefel.
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