Erosion at Earth’s surface exposes underlying bedrock to climate-driven chemical and physical weathering, transforming it into a porous, ecosystem-sustaining substrate consisting of weathered bedrock, saprolite, and soil. Weathering in saprolite is typically quantified from bulk geochemistry assuming physical strain is negligible. However, modeling and measurements suggest that strain in saprolite may be common, and therefore anisovolumetric weathering may be widespread. To explore this possibility, we quantified the fraction of porosity produced by physical weathering, FPP, at three sites with differing climates in granitic bedrock of the Sierra Nevada, California, USA. We found that strain produces more porosity than chemical mass loss at each site, indicative of strongly anisovolumetric weathering. To expand the scope of our study, we quantified FPP using available volumetric strain and mass loss data from granitic sites spanning a broader range of climates and erosion rates. FPP in each case is ≥0.12, indicative of widespread anisovolumetric weathering. Multiple regression shows that differences in precipitation and erosion rate explain 94% of the variance in FPP and that >98% of Earth’s land surface has conditions that promote anisovolumetric weathering in granitic saprolite. Our work indicates that anisovolumetric weathering is the norm, rather than the exception, and highlights the importance of climate and erosion as drivers of subsurface physical weathering.

In eroding landscapes, chemical and physical weathering transform unaltered protolith into weathered bedrock, saprolite, and soil as it is exhumed by erosion and gradually exposed to climate. This subsurface weathering weakens the rock (Goodfellow et al., 2016), making it more susceptible to erosion (Dixon et al., 2009), which in turn influences weathering by setting the duration of chemical and physical attack (Yoo and Mudd, 2008). The resulting dissolution and volumetric expansion open subsurface pore space (Callahan et al., 2020), enabling throughflow of ecosystem-sustaining water (Klos et al., 2018), which promotes additional subsurface weathering. Weathering also liberates nutrients, thus influencing biogeochemical cycles (Uhlig et al., 2017) and fueling ecosystem productivity (Hahm et al., 2014), which drives biological subsurface weathering (Brantley et al., 2017). Over millions of years, solutes from subsurface weathering affect atmospheric CO2, which in turn influences Earth’s weathering-climate thermostat (Maher and Chamberlain, 2014). Quantifying subsurface weathering, and its sensitivity to factors such as climate, vegetation, and erosion rates, is therefore important for understanding geomorphological, hydrological, and biogeochemical feedbacks across broad spatiotemporal scales.

Subsurface weathering is commonly studied using the bulk geochemistry of weathered rock and saprolite to quantify chemical mass losses accrued during exhumation of protolith by erosion (Riebe et al., 2017). This mass loss accurately quantifies the chemical part of subsurface weathering but ignores the physical part caused by volumetric strain. Strain can also be quantified if in situ measurements of bulk density are available (Brimhall and Dietrich, 1987), but, compared to bulk geochemistry, bulk density is more difficult to quantify because it requires intact samples collected without disruption that renders volume measurements incorrect. This is particularly problematic in saprolite, which is difficult to sample for bulk density except by expensive push-core extraction. Without bulk density measurements, subsurface weathering studies have assumed volumetric strain is negligible, which also simplifies reactive transport models of chemical weathering (Lebedeva et al., 2007). However, recent modeling of strain caused by freezing, thawing, and frost cracking challenges the assumption of isovolumetric weathering, particularly in climates with seasonal freezing (Anderson et al., 2013; Rempel et al., 2016). In addition, a recent push-core study showed that granitic saprolite doubled in volume during exhumation at a forested site in the Sierra Nevada, California (USA), possibly reflecting seasonal freezing or the effects of other strain-inducing mechanisms such as root wedging, biotite expansion, and exhumation through the ambient stress field (Hayes et al., 2019). Thus, modeling, observations, and the abundance of potential strain-inducing mechanisms suggest that anisovolumetric weathering may be more widespread than previously appreciated.

To explore this possibility, we quantified subsurface porosity, strain, and mass loss using push cores from two sites near the Sierra Nevada site of Hayes et al. (2019), but at lower elevations, thus widening the range of climates spanned by the measurements (Fig. 1). We interpret the results in a nondimensional framework that quantifies the relative contributions of volumetric strain and mass loss to saprolite porosity production. Our analysis shows that volumetric strain has contributed more to porosity than mass loss at all three Sierra Nevada sites, with the highest fractional contribution at the lowest-elevation site, where average precipitation is lowest and temperatures are highest. We also analyzed available volumetric strain and mass loss data from four other granitic sites and found that 94% of the variance in fractional porosity from volumetric strain can be explained by precipitation and erosion rate, despite variations in mineralogy across the sites. Our results indicate that weathering in granitic saprolite is commonly anisovolumetric and that climate and erosion rate strongly regulate the relative importance of subsurface physical and chemical weathering.

Porosity in weathered rock (ϕw) equals the initial protolith porosity (ϕp) plus the integrated effects of physical and chemical weathering, which open voids via volumetric strain (ε) and chemical mass losses that can be quantified using τ, the bulk mass transfer coefficient (Ague, 1991). The relationship among these variables, derived from mass balance principles, is shown in Equation 1 (Hayes et al., 2019; see Item S1 in the Supplemental Material1 for details).
A chemical mass loss in the subsurface produces an effective loss of protolith volume equal to the mass loss divided by the density of the protolith. Hence, the production of porosity (i.e., the added fractional volume of voids) associated with the chemical mass loss is equal to the fractional mass loss, represented by −τ. Therefore, when ϕp = 0, the fraction of porosity from chemical weathering (FPC) is equal to −τ/ϕw.
The fraction of porosity from physical weathering (FPP) equals 1 − FPC.

FPP and FPC express the relative importance of physical and chemical weathering in porosity production nondimensionally. When physical weathering dominates, FPP is high, and FPC is therefore low (and vice versa). Thus, quantification of FPP and FPC provides a basis for testing assumptions about isovolumetric weathering in saprolite.

To encompass weathering environments that are likely to include a range of strain-inducing mechanisms, our analysis combined two new sites together with the P301 site of Hayes et al. (2019) to span a range in elevation, and thus climate, in the Sierra Nevada Batholith (Fig. 1). P301, the highest-elevation site, is the coolest and wettest. Soaproot, the middle-elevation site, is warmer and drier but has denser vegetation. Conditions are warmer and drier still, and vegetation is sparsest at Fine Gold, the lowest-elevation site. The three sites have similar erosion rates (Callahan et al., 2019), have tonalitic or granodioritic bedrock (Bateman, 1992), and were not glaciated in the Pleistocene (Gillespie and Zehfuss, 2004), permitting us to focus on climate and vegetation as factors that may influence the relative importance of subsurface physical and chemical weathering.

We quantified strain, mass loss, and porosity in saprolite collected to refusal depth using a Geoprobe 7822DT direct push system during July 2019, which yielded two 2-m-long cores at Fine Gold and one 4-m-long and two 7-m-long cores at Soaproot (see Item S1 in the Supplemental Material for detailed sampling methods). Cores were collected in 0.5 m increments and were weighed after drying for 24 h at 105 °C to obtain dry material mass, which we used with core volume to calculate bulk density. Calculated bulk density was used to estimate ϕw assuming a 2.65 g cm−3 average mineral density. To estimate ε and τ, we used X-ray fluorescence following standard procedures to quantify concentrations of immobile elements (including Zr and Ti) in protolith sampled from outcrops at the surface and in representative saprolite aliquots from cores. A geochemical mass balance shows that ε and τ can be quantified from the immobile element enrichment that occurs in saprolite as soluble elements are dissolved and removed in solution (Brimhall and Dietrich, 1987).

Porosity ranges from 0.15 to 0.78 across the samples and increases toward the surface at both Soaproot and P301, the two sites with saprolite thick enough to show meaningful downhole trends in weathering (Fig. 2A). These trends reflect the cumulative effects of weathering during exhumation, which are also evident in upwards increases in mass loss at Soaproot and strain at both P301 and Soaproot (Figs. 2B and 2C). At Soaproot, FPP is roughly uniform with depth (Fig. 2D), because increases in porosity from strain (Fig. 2B) are matched by increases from mass loss (Fig. 2C). At P301, where mass loss is roughly uniform with depth (Fig. 2C), the increase in strain toward the surface (Fig. 2B) is too small to cause a statistically significant increase in FPP (Fig. 2D), despite contributing to increased porosity (Fig. 2A). This illustrates the greater sensitivity of ϕw to −τ relative to ε in the mass balance formulation (Equation 1) and moreover highlights the value of FPP over either ε or −τ alone in quantifying the relative importance of physical and chemical weathering in saprolite porosity production.

At each site, FPP is greater than 0.5 on average (Fig. 2H). Hence, more than half of porosity production in saprolite at these sites is due to volumetric strain, indicating that weathering can be strongly anisovolumetric across a range of climates. This may reflect a variety of climate-driven, strain-inducing mechanisms. For example, Soaproot and P301 are high enough in elevation to have supported cyclical freezing, thawing, and frost cracking over the glacial part of the 105–106 yr time scales required to produce the thick saprolite of these sites (Callahan et al., 2019). However, the finding that Fine Gold has the highest FPP, even though its elevation is well below the limits of seasonal freezing (both now and in the Pleistocene), indicates that porosity production can be driven by other strain-inducing mechanisms such as root wedging (Brantley et al., 2017), biotite expansion during weathering (Goodfellow et al., 2016), and exhumation through the ambient stress field (St Clair et al., 2015).

The Sierra Nevada sites show several other potentially climate-related differences in subsurface weathering. For example, Fine Gold has the lowest annual average precipitation (AAP), highest mean annual temperature (MAT), and lowest forest cover, and it also has the lowest near-surface porosity (Fig. 2E), the lowest mass loss (Fig. 2G), and the shallowest refusal depths. This may reflect precipitation and vegetation limitations on subsurface chemical weathering at low elevations within the range (Dixon et al., 2009), which may also help to explain why FPP at Fine Gold is greatest on average (Fig. 2H). Meanwhile, average porosity, strain, and mass loss are all greatest at Soaproot (Figs. 2E–2G), where forest cover is also greatest due to trade-offs in moisture and cold limitations that maximize ecosystem productivity at midelevations in the region (Goulden et al., 2012). We hypothesize that this climatic optimum for vegetation also promotes a vegetation-weathering feedback that maximizes porosity, volumetric strain, and mass loss at midelevations. This optimum in weathering is broadly consistent with altitudinal trends in soil production, clay content, and exchangeable iron in the region (Dahlgren et al., 1997; Dixon et al., 2009).

The finding that average FPP is highest where AAP is lowest raises the possibility of climatic control on the relative importance of physical and chemical weathering. To explore this possibility, we compiled available data on strain and mass loss in granitic saprolite—i.e., from below the top 1–2 m of soil. This yielded estimates of average FPP from four additional sites, including Rio Icacos, in Puerto Rico, and three sites in the southeastern United States (Table 1). These sites encompass a wider range of climates and erosion rates and thus span a wider range of weathering conditions that might influence the relative importance of physical and chemical weathering.

FPP is greater than zero on average at all sites in the compilation, ranging from 0.12 to 0.77 (Fig. 3A). This suggests that anisovolumetric weathering is widespread, arising from a diversity of physical and chemical mechanisms acting across the climates and biomes spanned by the sites (Fig. 3B). FPP correlates strongly with AAP across the sites (Fig. 3C), and the residuals of a semi-log regression between FPP and AAP correlate strongly with erosion rates (Fig. 3D). When combined together in a multiple regression model (Fig. 3E), AAP and erosion rate explain 94% of the variance in FPP, indicative of strong climatic and erosional control on the relative importance of physical and chemical weathering in saprolite (see the Supplemental Material for details). The predicted FPP from the model shows that FPP = 1, corresponding to physical weathering without mass loss, when erosion rates are high or when AAP is low (Fig. 3E). Conversely, purely chemical, isovolumetric weathering, with FPP = 0, is predicted where AAP > 3000 mm/yr, which occurs across <2% of Earth’s surface (cf. Figs. 3B and 3E). Hence, the model predicts that anisovolumetric weathering is the norm rather than the exception at granitic sites around the world.

The fraction of porosity from physical weathering, FPP, can be calculated from estimates of volumetric strain and mass loss and provides a framework for quantifying the relative contributions of physical and chemical weathering to saprolite porosity production. Despite differences in mineralogy across the seven granitic sites where both strain and mass loss data are available, 94% of the variance in FPP can be explained by differences in average precipitation and erosion rate. This may reflect a moisture limit on chemical depletion at relatively arid sites and a time limit on chemical weathering at rapidly eroding sites (Ferrier et al., 2016). Although FPP is lower at wetter, more slowly eroding sites, volumetric strain is predicted to be a nonnegligible part of granitic saprolite porosity production in climates that prevail across >98% of Earth’s land surface. To test these predictions, new measurements of both strain and mass loss are needed to quantify the relative importance of physical processes such as freezing, thawing, frost cracking, root wedging, mineral expansion, and exhumation through the ambient stress field. These processes are widespread in mountain landscapes irrespective of lithology, indicating that anisovolumetric saprolite weathering is common and should replace isovolumetric weathering as the a priori assumption.

Funding was provided by the National Science Foundation grants EAR-1331939 and EAR-2012357; National Aeronautics and Space Administration grant NNX15AI08H; and Natural Sciences and Engineering Research Council of Canada grant RGPIN-2019–05501. Field help was provided by M. Elliot, M. Thompson-Munson, M. Gilmore, and E. Stacy. Site access was granted by the Sierra Foothill Conservancy. We acknowledge three anonymous reviewers for helpful comments.

1Supplemental Material. Supplemental methods and Tables S1–S4. Please visit to access the supplemental material, and contact with any questions.
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