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 To investigate the timescales of regolith formation on hillslopes with contrasting topographic aspect, we measured U-series isotopes in regolith profiles from two hillslopes (north facing versus south facing) within the east-west trending Shale Hills catchment in Pennsylvania. This catchment is developed entirely on the Fe-rich, Silurian Rose Hill gray shale. Hillslopes exhibit a topographic asymmetry: The north-facing hillslope has an average slope gradient of ~20°, slightly steeper than the south-facing hillslope (~15°). The regolith samples display significant U-series disequilibrium resulting from shale weathering. Based on the U-series data, the rates of regolith production on the two ridgetops are indistinguishable (40 ± 22 versus 45 ± 12 m/Ma). However, when downslope positions are compared, the regolith profiles on the south-facing hillslope are characterized by faster regolith production rates (50 ± 15 to 52 ± 15 m/Ma) and shorter durations of chemical weathering (12 ± 3 to 16 ± 5 ka) than those on the north-facing hillslope (17 ± 14 to 18 ± 13 m/Ma and 39 ± 20 to 43 ± 20 ka). The south-facing hillslope is also characterized by faster chemical weathering rates inferred from major element chemistry, despite lower extents of chemical depletion. These results are consistent with the influence of aspect on regolith formation at Shale Hills; we hypothesize that aspect affects such variables as temperature, moisture content, and evapotranspiration in the regolith zone, causing faster chemical weathering and regolith formation rates on the south-facing side of the catchment. The difference in microclimate between these two hillslopes is inferred to have been especially significant during the periglacial period that occurred at Shale Hills at least ~15 ka before present. At that time, the erosion rates may also have been different from those observed today, perhaps denuding the south-facing hillslope of regolith but not quite stripping the north-facing hillslope. An analysis of hillslope evolution and response timescales with a linear mass transport model shows that the current landscape at Shale Hills is not in geomorphologic steady state (i.e., so-called dynamic equilibrium) but rather is likely still responding to the climate shift from the Holocene periglacial to the modern, temperate conditions.
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 Chemical weathering breaks down bedrock and generates regolith. The transformation of bedrock to regolith provides nutrients to ecosystems, controls surface water chemistry, regulates atmospheric carbon dioxide, and sculpts landscapes [e.g., Walker et al., 1981; Berner et al., 1983; Pavich, 1986; Heimsath et al., 1997; Gaillardet et al., 1999; Gabet, 2000; Kump et al., 2000; Anderson et al., 2002; Chadwick et al., 2003; Drever, 2004; Derry et al., 2005; Gabet and Mudd, 2009; Hilley et al., 2010; Pogge von Strandmann et al., 2011]. Long-standing research efforts have identified climate, relief, biology, parent material, time, and human impacts as major state factors of regolith formation [e.g., Jenny, 1941; Amundson, 2004]. However, the role of each of these individual factors in governing regolith formation is still not clear. Small catchments have been commonly studied as some of the state factors can be held relatively constant at a catchment scale.
 It has been shown that topographic features such as hillslope gradient and aspect may influence regolith formation by controlling soil physical conditions such as temperature and moisture content at the catchment scale [e.g., Cooper, 1960; Churchill, 1982; Carter and Ciolkosz, 1991; Egli et al., 2007, 2010; Broxton et al., 2009; Li et al., 2010]. However, some previous observations that have used the extents of chemical depletion in regolith to infer regolith formation rates were equivocal with respect to differences between north-facing and south-facing hillslopes [e.g., Cooper, 1960; Hunckler and Schaetzl, 1997; Rech et al., 2001; Egli et al., 2007, 2010]. For example, when soil moisture is not limiting, greater extents of chemical depletion and faster rates of regolith formation have been observed on south-facing slopes and have been attributed to the effect of higher average soil temperatures [e.g., Cooper, 1960; Rech et al., 2001]. In contrast, some have measured enhanced total loss of elements during chemical weathering on north-facing hillslope soils compared to south-facing hillslope and have attributed this more intensive weathering to higher moisture contents of those soils [e.g., Hunckler and Schaetzl, 1997; Egli et al., 2007, 2010]. Underlying these inferences is the assumption that the timescale of regolith formation is similar for north-facing and south-facing slopes in a given location. However, such an assumption is often not easily justified due to the lack of reliable dating tools for Earth surface processes, especially for regions that have been recently disturbed by glaciation. The objective of this study is to investigate the relationship between hillslope aspect and regolith formation at a well-studied temperate catchment in Pennsylvania by incorporating both U-series isotopic disequilibrium measurements and major elemental analyses.
 With the recent advances in understanding the behavior of U-series isotopes in near-surface environments, 238U, 234U, and 230Th are now being utilized to determine the durations of chemical weathering and rates of regolith formation at various spatial scales, such as in weathering rinds, soil profiles, and large watersheds [e.g., Gascoyne, 1992; Plater et al., 1994; Mathieu et al., 1995; Vigier et al., 2001, 2005, 2006; Dequincey et al., 2002; Krishnaswawi et al., 2004; Maher et al., 2004; Depaolo et al., 2006; Dosseto et al., 2006a, 2006b, 2006c, 2008a, 2008b; Chabaux et al., 2003a, 2003b, 2006, 2008; Granet et al., 2007, 2010; Gaillardet, 2008; Pelt et al., 2008; Bourdon et al., 2009; Ma et al., 2010; Pogge von Strandmann et al., 2011]. 238U decays with a half-life (T1/2) of ~4.5 Ga to 234U (T1/2 = 244 ka), which in turn decays to 230Th (T1/2 = 75 ka). The decay half-lives of 234U and 230Th are similar to timescales involved in many Earth surface processes including regolith formation and chemical weathering. For a system remaining undisturbed longer than ~1.3 Ma (i.e., a time equal to 5 decay half-lives of 234U), U-series isotopes achieve secular equilibrium (the daughter/parent activity ratios equal unity: the activity is defined to equal the number of atoms of an isotope in a system multiplied by its decay constant). However, U and Th differ in their solubilities in surface water. In addition, alpha recoil effect occurs during production of 234U from 238U when alpha particles are emitted, damaging the crystal lattice and promoting the preferential release of 234U over 238U to water during water-rock interaction [Langmuir, 1978; Langmuir and Herman, 1980; Fleischer, 1980]. Thus, the relative mobility of U-series isotopes during chemical weathering is generally 234U > 238U > 230Th [e.g., Rosholt et al., 1966; Latham and Schwarcz, 1987a, 1987b; Vigier et al., 2001; Chabaux et al., 2003a, 2008]. Therefore, surface waters are generally characterized by (234U/238U) > 1 and (230Th/238U) < 1 (parenthesis means activity ratio hereafter), and materials such as regolith that have weathered recently generally show (234U/238U) < 1 and (230Th/238U) > 1. More importantly, the creation of U-series disequilibrium in the weathered residuals starts when the major U-bearing phases are exposed to weathering fluids (e.g., at mineral-water interfacial area) and the degree of disequilibrium in regolith is time dependent. The disequilibrium signature is thus inferred to record the time information of the chemical weathering process in the regolith zone and can be modeled to determine the durations and rates of weathering [e.g., Chabaux et al., 2003a, 2008; Dosseto et al., 2008b; Ma et al., 2010].
 Here we present regolith profiles developed on two hillslopes with contrasting aspect, south facing versus north facing, at the Shale Hills catchment in central Pennsylvania. A previous study in the Shale Hills catchment has documented that the regolith samples on the north-facing slope display significant U-series disequilibrium resulting from shale weathering [Ma et al., 2010]. In this study, new regolith samples from the south-facing slope were collected and analyzed for U-series isotopic and chemical compositions. In comparison with the previous study [Ma et al., 2010], the new results demonstrate that regolith production rates, apparent durations of shale weathering, and extents of chemical depletion differ systematically between the two hillslopes, revealing important relationships between hillslope aspect and regolith production at the Shale Hills catchment. In a companion manuscript (West et al., Regolith production and transport at the Susquehanna Shale Hills Critical Zone Observatory: Part 2—Insights from meteoric 10Be, Journal of Geophysical Research—Earth Surface, in review, 2013), we utilize the accumulation of meteoric 10Be along the same hillslope transects to measure the timescales and rates of downslope transport. Comparison of both isotopic systems allows us to determine whether the rates of soil production and downslope transport are in balance or whether regolith is thickening in the field site. Using simple numerical models of soil production and erosion calibrated to these rates, we show that response times to perturbations away from a geomorphologic steady state are long, on the order of 105–106 years. This long response time is consistent with the conclusion that the catchment is probably still responding to the climate shift from periglacial conditions to the present, temperate climate.
2 Geological Setting
 The Susquehanna Shale Hills Critical Zone Observatory (or Shale Hills; Figure 1) was established in central Pennsylvania as a part of a network of Critical Zone Observatories (http://criticalzone.org/) to investigate Earth surface processes [e.g., Brantley et al., 2007]. Extensive geochemical, geophysical, and geomorphologic data sets are available at Shale Hills [Lynch, 1976; Lynch and Corbett, 1985; Duffy and Cusumano, 1998; Lin, 2006; Lin et al., 2006; Qu and Duffy, 2007; Jin et al., 2010a, 2010b; 2011a, 2011b; Ma et al., 2010, 2011a, 2011b; West et al., 2011]. Details of the geological setting of this 8 ha watershed have been previously described by Jin et al. [2010a] and Ma et al. [2010, 2011a], and only key factors are listed below for reference.
 Located in the northern part of the Appalachian Mountains, this temperate watershed has a mean annual temperature of 10°C and mean annual precipitation of 1070 mm [NOAA, 2007]. The catchment is characterized by an average local relief of 30 m (Figure 1) and is covered by deciduous trees (maple, oak, and beech), hemlocks and pines [Lynch, 1976; Lin, 2006]. A first-order stream flows within the catchment from east to west (Figure 1).
 The bedrock is a Silurian gray shale, known as the Rose Hill Shale Formation with interbedded Ca-rich carbonate zones [Folk, 1960; Lynch, 1976; Lynch and Corbett, 1985]. Jin et al. [2010a] characterized the parent shale as predominantly composed of illite (58 wt.%), quartz (30 wt.%), and “chlorite” (which is used here to refer to chlorite, vermiculited chlorite, and weathered forms of chlorite including vermiculite and hydroxy-interlayered chlorite, together present at 11 wt.%). Minor mineral phases such as feldspar (plagioclase and K-feldspar), anatase (TiO2), Fe oxides (magnetite and hematite), pyrite, and zircon are also identified in the bedrock [Jin et al., 2010a]. The carbonate mineral ankerite was observed in drilled chips at the northern ridge at ~20 m below land surface. By approximately 22 m depth, the ankerite is completely absent, and above 5 m depth, evidence for the onset of depletion of feldspar is observed [Jin et al., 2011a].
 Regolith, defined here as material that can be hand augered, overlies fractured bedrock throughout the catchment. Thickness of the hand-augerable regolith layer ranges from ~0.3 m at the ridgetop to greater than 3 m in the valley floor and the swales (topographically low areas) (Figure 1a). Material referred to here as bedrock is presumed to have been depleted in minor feldspar and carbonate minerals during subsurface weathering—this cohesive, still aggregated material was referred to as saprock by Jin et al. [2011a] due to this weathering. Weathering in the regolith is dominated by clay transformations: illite and chlorite weather to vermiculite, hydroxyl-interlayered vermiculite, and kaolinite; and extensive chemical weathering of illite is thought to initiate approximately 15 cm below the depth of augering refusal at the ridgetops [Jin et al., 2010a]. The major carrier phases for U and Th are primary clay minerals and Fe oxides [Ma et al., 2010, 2011b]. Weathering of these phases is restricted largely to the regolith depths shallower than 30–50 cm below land surface [Jin et al., 2011a].
3 Samples and Analytical Methods of U-Series Isotopes
 Selected pedons and catenas at sites representing different hydrologic patterns have been chosen to characterize shale weathering and regolith production [Jin et al., 2010a, 2010b; Ma et al., 2010, 2011a, 2011b; West et al., 2011]. We focus here on the U-series isotopic compositions of six weathering profiles along two planar transects (south facing versus north facing) of the catchment (Figure 1). It is noted that at the Shale Hills catchment, the “south-facing” hillslope is located on the northern side of the catchment and the “north-facing” hillslope is located on the southern side (Figure 1). The three profiles collected from the north-facing hillslope were thus named the southern planar ridgetop (SPRT), middle slope (SPMS), and valley floor (SPVF); and the three sites selected from the south-facing hillslope were named the northern planar ridgetop (NPRT), middle slope (NPMS), and valley floor (NPVF).
 Due to the presence of swales, the choice of planar transect locations is limited at Shale Hills, especially for the south-facing slope. Here swales are defined as topographically low areas with planform concavity across the topographic gradient (brown areas in Figure 1a). The south-facing planar hillslope is bounded by two swales, while the north-facing planar hillslope is bounded by one swale on the east (Figure 1a). The two catenas were chosen to be far enough away from the edge of the swales that divergence of soil transport is not a factor. We consider all soil transport along our transects to be parallel to the transect (down the steepest topographic gradient; hence the term, “planar”). Thus, the primary boundary condition for each of our transects should be the lowering rate along the channel, as shown by the parallel contour lines on Figure 1a.
 In addition, a 25 m deep drill core (DC1) obtained using a rotary air drill on the northern ridge of the catchment provided 12 saprock samples which were used to define “parent material” based on elemental analyses [Jin et al., 2010a]. The DC1 samples were considered as representative of the parent material at the Shale Hills catchment because they are relatively uniform in elemental concentrations [Jin et al., 2010a]. For example, the standard deviation around the mean of measured element concentrations was calculated for the 12 DC1 samples: the values ranged from 0.01 to 0.38 wt.% for major elements. The standard deviations are observed to be especially low for elements present at more than 3 wt.% [Jin et al., 2010a]. Furthermore, Jin et al. [2010a] also calculated the average compositions of the deepest, least weathered soils from five regolith cores hand augered throughout the catchment, and they were similar to the DC1 parent composition. Based on these observations, the averaged DC1 composition was used as the composition of the parent material for the following discussion.
 Regolith samples were collected using a 2 in diameter hand auger over about 10 cm intervals at various depths until refusal. Zero depth is defined here as the bottom of the ~3 cm thick organic layer or, equivalently, the top of the mineral soil. Jin et al. [2010a] and Ma et al.  previously reported major element and U-series isotope data, respectively, for SPRT, SPMS, SPRT, and DC1. The analytical procedure we used to analyze the new samples reported here (NPRT, NPMS, and NPVF) is similar to that of Ma et al.  and is only briefly provided below.
 Bulk samples consisting of all rock fragments, sand, silt, and clay recovered during augering were ground for analysis. Chemical analyses of NPRT, NPMS, and NPVF regolith showed little elemental depletion below 40–50 cm of depth [Ma et al., 2011b]. Therefore, for these samples, U-series analyses were restricted to the uppermost 40–50 cm of regolith, where most weathering of clay minerals occurred [Jin et al., 2011a]. This spanned the entire depth interval of regolith for NPRT and NPMS. However, the NPVF augerable regolith extended to a total depth of 120 cm.
 Analyses of U and Th isotopes and concentrations were performed at the Laboratoire d'Hydrologie et de Geochimie de Strasbourg, University of Strasbourg (France), following the procedures as described in Granet et al.  and Pelt et al. . Air-dried and ground (sieved to 100 µm) samples were weighed and mixed with an artificial 233U-229Th spike. The samples were then completely dissolved using a three-step procedure with HNO3-HF, HClO4, and HCl-H3BO3 acids. U and Th separation and purification were performed by conventional ion exchange chromatography. Concentrations of U and Th and activity ratios (234U/238U) and (230Th/232Th) were analyzed on a Thermal Ionization Mass Spectrometer (TIMS) Thermo-Scientific Triton [e.g., Ma et al., 2010]. Over the data acquisition period, the mean of the HU1-standard analyses of (234U/238U) was 1.000 ± 0.004 (n = 6, 2σ), in good agreement with the laboratory mean (2008–2009) for (234U/238U) of 0.999 ± 0.005 (n = 32; 2σ) and consistent with secular equilibrium. In addition, three separate analyses of the BEN rock standard, spiked with the 233U-229Th tracer, yielded a mean (234U/238U) of 1.001 ± 0.002 and a mean U concentration of 2.468 ± 0.011 ppm, both of which are consistent with the laboratory long-term mean values—(234U/238U) = 0.999 ± 0.005 (n = 5; 2σ) and U = 2.457 ± 0.013 (n = 5; 2σ) (2006–2009)—and the reference values (U = 2.46 ppm) [Govindaraju, 1994]. The reproducibility of Th isotopic ratio measurements, checked by the in-house standard solution Th-105, is ~1% (n = 5, 2σ). In addition, the three analyses of the BEN rock standard, yielded a mean (230Th/238U) ratio of 1.001 ± 0.009 and a mean Th concentration of 10.66 ± 0.11 ppm, which are consistent with secular equilibrium and the reference values (Th = 10.7 ppm) [Govindaraju, 1994]. The procedure blanks for U-Th analysis were measured at ~30–80 pg for U and ~70–420 pg for Th. They were negligible (<0.5‰) compared to the amount of U and Th analyzed in the samples.
4.1 U and Th Concentrations and Activity Ratios
 U and Th concentrations and activity ratios in the regolith samples on the south-facing hillslope (NPRT, NPMS, and NPVF) are presented in Table 1 along with those for bedrock (DC-1) and the north-facing hillslope (SPRT, SPMS, and SPVF) samples which were previously discussed [Ma et al., 2010]. U and Th concentrations in the new south-facing regolith samples range from 2.6 to 3.0 ppm and 11.6 to 14.9 ppm, respectively. These values are generally lower than the bedrock concentrations (Table 1).
Table 1. U-Th Concentrations and Activity Ratios of Regolith and Bedrock Samples at the Shale Hills Catchment
(234U/238U) activity ratios calculated from measured 234U/235U isotopic ratios assuming that 238U/235U = 137.88 and using the following decay constant: λ238 = 1.551 × 10−10 yr−1 and λ234 = 2.826 × 10−6 yr−1[Akovali, 1994; Cheng et al., 2000]. (230Th/232Th) activity ratios calculated from measured 232Th/230Th isotopic ratios using λ232 = 4.948 × 10−11 yr−1 and λ230 = 9.158 × 10−6 yr−1 [Cheng et al., 2000]. Reported errors are internal precisions (2SE) of single measurements. Analytical uncertainties based on long-term reproducibility of synthetic solutions, rock standards, and rock samples are estimated to be 0.5% for (234U/238U), 0.7% for U content, ~1% for (230Th/232Th), (238U/232Th) and Th content, and ~1.5% for (230Th/238U).
 As shown previously [Ma et al., 2010], (234U/238U) and (230Th/238U) ratios in DC-1 samples taken from 1 and 6 m depth are equal to 1 within error (Table 1 and Figure 2), as expected for Silurian bedrock at secular equilibrium.
 (234U/238U) values of the south-facing hillslope sites (NPRT, NPMS, and NPVF) are all significantly less than 1, indicating U-series disequilibrium (Table 1 and Figure 2). The three south-facing sites show generally upward-decreasing values of (234U/238U) (Figure 3) that are similar to those of the north-facing profiles and are consistent with increasing extent of loss of 234U to fluids during weathering [Ma et al., 2010]. The south-facing and north-facing samples differ in that none of the south-facing samples show (234U/238U) values > 1, whereas significant 234U enrichment over 238U was observed in the north-facing SPVF samples at depth (Figure 2) [Ma et al., 2010]. This 234U enrichment in the deep SPVF profile was previously interpreted to have resulted from U inputs into the profile in addition to U leaching [Ma et al., 2010]. The input of U was attributed to co-precipitation or sorption of U in secondary Fe hydroxides or clay minerals from soil pore waters that contain U characterized by (234U/238U) > 1. Such high (234U/238U) ratios were only observed in the deep SPVF profile, probably related to the local environment conditions that favor U precipitation, e.g., a change of redox conditions and/or formation of secondary minerals due to saturation in soil pore water at depth. Consistent with this, Jin et al. [2010a] documented the evidence for precipitation and accumulation of certain major elements (e.g., Al and Si) in the valley floor soils on the north-facing transect.
Table 2. Regolith Production Rates, Weathering Duration, Leaching Coefficients, and U-Series Inputs Derived from the Model
The model is solved multiple times to obtain 1000 sets of solutions for each profile as described in section B by Ma et al. . The model parameters are taken as the average of the sets of solution values, and the uncertainties are calculated as the standard deviation on the sets of values. 238U0 is initial number of 238U atoms/g in the starting material of the system. The total regolith depth of NPVF profile is 118 cm. Only samples from the upper 50 cm of NPVF were measured for U-series activity ratios and used for calculation of regolith production rate. Total input and output of 238U for each profile along the 2D transect, calculated with the model-derived U input rates and leaching coefficients. Total input and output are described in units of 238U yr−1 where 238U in this table figure is the initial number of 238U atoms in a 10 cm regolith column interval with a unit area.
2.5 × 10−5
3.6 × 10−6
3.49 × 10−5
2.65 × 10−6
2.59 × 10−5
 (230Th/238U) ratios in the NPRT, NPMS, and NPVF profiles range from 0.989 to 1.049; most of these values are greater than the bedrock values (Table 1 and Figure 2). (230Th/238U) activity ratios increase gradually toward the surface and display an opposite trend to the (234U/238U) activity ratios (Figure 3). Indeed, (234U/238U) and (230Th/238U) ratios for the south-facing samples are anti-correlated, as has also been observed in the north-facing samples (Figure 2) [Ma et al., 2010]. However, the variations of (234U/238U) and (230Th/238U) ratios in the south-facing profiles are much smaller than those in the north-facing profiles (Figure 2).
4.2 Extent of Elemental Depletion during Regolith Formation
 For north-facing and south-facing planar transects, regolith density, mineralogy, and mobility of major and trace elements during chemical weathering have been previously discussed [Jin et al., 2010a, 2010b; Ma et al., 2011a, 2011b]. A summary is briefly presented below.
 Concentrations of many elements in the six regolith profiles are characterized as “depletion profiles” [Brantley and White, 2009] because significant losses of the elements have been observed in comparison to immobile elements and underlying parent bedrock chemistry (U profiles also show depletion profiles: Figure 4) [Jin et al., 2010a, 2010b; Ma et al., 2011a, 2011b]. The total mass loss of element j per unit pedon area (ΔMj, regolith) from a regolith profile can be calculated by integration. Specifically, ΔMj, regolith = the numerator in equation ((1)) below, as derived originally by Brimhall and Dietrich  and modified by Chadwick et al.  and Egli and Fitze . By comparing the analogously calculated mass per unit pedon area of element j in the original parent material integrated over the depth range of today's regolith (Mj, parent), the fraction (fj in Brantley and Lebedeva ) of element j lost from a given profile has also been defined:
 Here ε is volume strain; τj, Zr is the mass transfer coefficient for element j calculated with Zr as the immobile element [e.g., Brimhall and Dietrich, 1987; Anderson et al., 2002]; Cj,w and Cj,p and CZr,w and CZr,p are concentrations of j and Zr in regolith (w) and parent material (p), respectively; and ρw and ρp are bulk density in regolith and parent materials, respectively. Equation ((1)) thus represents the fractional relative mass loss of element j integrated over the entire regolith profile (a = 1 to n) where ΔZ is the thickness of each depth interval sampled. (It is important to note that this equation is only justified if the sum over all ΔZ for a given profile equals the total regolith depth at that location: in other words, samples must incorporate all regolith, or concentrations must be extrapolated so that the sum over all intervals equals total regolith depth). Here the fraction of element lost during regolith formation is calculated based on the concentration values reported for the six profiles in Jin et al. [2010a, 2010b] and Ma et al. [2011a, 2011b]. Regolith bulk density (ρw) was calculated with an empirical relationship (see Figure 5 caption) with depth based on field measurements from Lin . Sample depth is listed in Table 1. Zr was chosen as the immobile element because Zr occurs in relatively insoluble and immobile zircon in the Rose Hill shale and is more immobile than other candidates such as Ti [Jin et al., 2010a].
 The regolith depletion profiles calculated to the various depths of auger refusal on the north-facing transect all show fj values that document significant loss of major elements during regolith formation: 39–58% total depletion for Al, 42–58% for Fe, 43–63% for K, 42–63% for Mg, and 19–29% for Si (Figure 5a). In contrast, the upper 50 cm of regolith profiles on the south-facing slope documents much less chemical depletion: 12–35% for Al, 13–29% for Fe, 14–42% for K, 16–47% for Mg, and 6–24% for Si (Figure 5a). Similarly, ΔMj, regolith values for the north-facing regolith profiles are also greater than those of the south-facing regolith profiles, indicating more total mass loss of elements from the north-facing slope (Figure 5b).
 All of the north-facing planar transect profiles (SPRT, SPMS, and SPVF) show relatively smooth depletion curves towards the surface (U profiles in Figure 4; and major element profiles in Jin et al. [2010a]). The south-facing NPRT and NPMS show less smooth depletion curves; furthermore, only the top 50 cm of the south-facing NPVF profile shows a depletion curve, whereas samples from 120 to 50 cm depths show an almost vertical profile consistent with limited depletion of U (Figure 4). As mentioned previously, this is consistent with relatively extensive loss of U only in the upper 50 cm samples but onset of U loss deeper than 50 cm.
5.1 Fractionation of U-Series Isotopes
 As we previously observed for the north-facing transect samples, the U and Th concentrations in the south-facing regolith samples are lower than those in the bedrock samples, consistent with loss of both U and Th during weathering. Extrapolation of the isotopic data in Figure 3 to values of (234U/238U) equal to unity are consistent with depths of ~60, 60, and 80 cm, respectively, at sequential locations from ridgetop down to valley floor. These extrapolated depths to secular equilibrium are interpreted as the depths where the preferential loss of 234U begins. Here the extrapolation is based on the implicit assumption that the gradients of 234U loss are similar in the regolith beneath the depth of augering refusal. This is consistent with conclusions of Jin et al. [2010a] who argued that preferential loss of elements in clays in the regolith occurs beneath the depth of augering refusal based on the major element depletion profiles.
 High mobility of U and Th has been observed in this catchment and attributed to two factors [Ma et al., 2010]. First, organic acids measured in the soil water [Andrews et al., 2011] may cause formation of soluble U/Th-organic complexes. However, transport of U and Th is also attributed to micron-sized particles that form as shale bedrock transforms to regolith. These particles have been inferred based on soil and water chemistry to also contribute to preferential loss of major elements with respect to Zr [Jin et al., 2010a]. No evidence for loss of Zr was observed, consistent with Zr deriving from the heavy mineral, zircon.
 (234U/238U) values decrease toward the surface in all three south-facing profiles (Figure 3). Greater loss of the lighter isotope of U (234U) from regolith is expected with enhanced mobility of 234U relative to 238U due to alpha decay-related crystalline damage leading to preferential leaching [Fleischer, 1980; Chabaux et al., 2003a, 2008]. The observed trends of (234U/238U) ratios in the south-facing NPRT, NPMS, and NPVF profiles are thus consistent with (i) increasing weathering extent due to longer duration of exposure toward the surface and (ii) rates of regolith mixing, e.g., due to bioturbation, that are not fast enough to obscure fractionation trends. The linear variation in isotopic ratios with respect to depth as expected from behaviors of U-series isotopes during chemical weathering is also consistent with insignificant deposition of U in dust to soils at Shale Hills.
 In contrast to the decreasing (234U/238U) activity ratios, (230Th/238U) ratios in the NPRT, NPMS, and NPVF profiles increase gradually toward the surface (Figure 3). The difference between these (234U/238U) and (230Th/238U) trends is attributed to the different behaviors of 230Th and 234U [Gascoyne, 1992]. Specifically, Th is “particle-reactive;” i.e., it partitions more with the solid phase than the aqueous phase. Therefore, Th is less mobile than U isotopes. Generally, this results in (230Th/238U) ratios > 1 in the residual weathering products and (230Th/238U) ratios < 1 in the weathering fluids [e.g., Vigier et al., 2001; Dosseto et al., 2006a; Chabaux et al., 2003a, 2008]. Different behaviors of 230Th and 234U during chemical weathering are also documented in the anti-correlation between (230Th/238U) and (234U/238U) (Figure 2). Like the extents of chemical weathering of major elements for north-facing versus south-facing profiles (e.g., Figure 4), the variations of (234U/238U) and (230Th/238U) in the south-facing planar profiles are smaller than those in the north-facing planar profiles.
5.2 Determination of Regolith Production Rates and Duration of Chemical Weathering
 Determination of rates and duration of chemical weathering from U-series disequilibria requires an understanding of U and Th mobility in a regolith profile [e.g., Ghaleb et al., 1990; Scott et al., 1992; Vigier et al., 2001; Dequincey et al., 2002; Chabaux et al., 2003a, 2008; Maher et al., 2004; DePaolo et al., 2006; Dosseto et al., 2008b; Bourdon et al., 2009]. In our previous study [Ma et al., 2010], we modeled the U-series disequilibrium data for the north-facing planar profiles and showed that the isotopic and concentration data for U and Th are consistent with a relatively simple weathering + erosion regime. Because similar U-series fractionation patterns are observed in the new south-facing planar profiles, we apply the same model to solve for rates and duration of chemical weathering on the south-facing hillslope. The model description and assumptions have been described in Ma et al.  and are briefly presented below.
 U is presumed to reside in the primary clay and Fe oxide minerals in the Rose Hill shale, and no other U-containing minerals have been identified [Ma et al., 2010, 2011b]. The interface at depth where these U-containing minerals start to react to measurable extent with chemically non-equilibrated meteoric water is defined as the lower boundary of the U weathering reaction front. This boundary is presumed to lie at the depth where the trends in (234U/238U) extrapolate to unity.
 We envision the systems at the ridgetop, middle slope, and valley floor as experiencing net upward flow of earth material (relative to the surface) and net downward flow of meteoric fluids. The profiles at the middle slope and valley floor sites are also experiencing flow of material from upslope to downslope positions. A system of equations summarized below therefore describes the three profiles—NPRT, NPMS, and NPVF—as one-dimensional systems where regolith material moves “upward” through the weathering front and erodes away at the surface. During “ascent” of particles, the U-series isotopes are differentially lost through weathering and removed from the system by the downward-flowing fluids. The differential loss is a result of the net balance of dissolution + adsorption + co-precipitation onto Fe oxides or clay minerals [Ma et al., 2010]. Furthermore, although preferential loss of U and Th isotopes requires dissolution, the actual transport of U out of the profiles may involve transport of Fe + Si + Al + organic particles that could also contain U or Th isotopes (see discussions by Jin et al. [2010a] and Ma et al. ).
 The mass conservation equations for 238U, 234U, and 230Th for a given profile are expressed as follows:
 Here F238, F234, and F230 (in activity per unit time per unit mass: atoms yr−2 kg−1) represent the input rates of 238U, 234U, and 230Th to each profile, respectively. Only at the ridgetop is the input rate of U-series isotopes equal to zero (e.g., no input from upslope or atmosphere as U concentration in precipitation is generally negligible) [Chabaux et al., 2003a]. F234/F238 and F230/F238 represent the rate ratios of (234U/238U) and (230Th/238U) for the input sources, respectively.
 The parameters k238, k234, and k230 are first-order rate constants (yr−1) for release of 238U, 234U, and 230Th from U-containing minerals [Latham and Schwarcz, 1987a, 1987b; Plater et al., 1994; Vigier et al., 2001]; i.e., U-containing phases are assumed to dissolve and release U or Th at rates equal to k238238U, k234234U, and k230230Th. The terms λ238, λ234, and λ230 are the decay constants for 238U, 234U, and 230Th (yr−1) and “238U,” “234U,” and “230Th” refer to their respective concentrations (e.g., atoms/kg). The time, t, is defined as the duration of weathering (year) of particles in the weathering zone, i.e., the zone in which enough water-rock interaction occurs to preferentially remove 234U over 238U. Simplistically, this time is the residence time of particles in the regolith or the time since formation of enough water-rock interfacial area to fractionate significant 234U. The ratios k234/k238 and k230/k238 describe the relative loss rates of 234U and 230Th, respectively, to 238U during “chemical” leaching. However, “chemical” leaching here includes net transport out of the profile as solutes or as colloidal or micron-sized particles (of composition different from the parent rock).
 Similar to the previous model [Ma et al., 2010], we define the average integrated regolith production rate P (m/Myr) in the weathering profiles as
 The same equation was used in Ma et al.  in which t is the elapsed time for a particle moving from a reference position to its present position and h is the vertical distance between positions. An implicit assumption underlying equation ((7)) is that chemical weathering is isovolumetric. Such an assumption has been discussed and justified for the weathering profiles at Shale Hills [Ma et al., 2010]. Briefly, it has been shown that the relative variation in strain during the regolith expansion is less than ~18% within the profile regolith volume from depths of 17 to 54 cm for north-facing profiles, much smaller than the error estimates of the production rates. Only in the upper 3 cm layer has volume expanded significantly beyond 18% due to addition of organic matter [Jin et al., 2010a].
 The model was solved using the same approach as that of Ma et al. : equations ((4))–((7)) were solved analytically, and the solutions were rearranged as functions between (234U/238U) and (230Th/238U) ratios and unknown parameters (F238, F234, F230, k238, k234, k230, and t or P). With the measured (234U/238U) and (230Th/238U) ratios as input values for each regolith profile, the unknown parameters (F238, F234, F230, k238, k234, k230, and P) were solved using the MatlabTMlsqnonlin function (Table 2; Appendix B in Ma et al.  for details). The function calculates output parameters such that they fit the observed activity ratios within approximately 1%. The model calculation was performed 1000 times to obtain a set of possible solutions. The average of these solutions and their standard deviations are presented in Table 2.
 The unknown parameters (F238, F234, F230, k238, k234, k230, and P) are assumed to be constant over time for each weathering profile [e.g., Ghaleb et al., 1990; Dequincey et al., 2002]. We assume that the production rate P is constant for each profile and then solve for P, instead of solving the system of equations at multiple values of t [Ma et al., 2010]. P is thus an average over the depth interval of the samples: in other words, if P is constant, then P is an average over the timescale, h/P. Of course, vertical transport of particles is strictly only true for the NPRT profile. Therefore, the effects of lateral transport of particles that are not described explicitly in the model are lumped into the F and k parameters for the NPMS and NPVF profiles.
5.3 Regolith Production Rates and Duration of Chemical Weathering at SSHO
 The (234U/238U) and (230Th/238U) activity ratios calculated as a function of regolith depth are shown in Figure 3 as gray lines. The curves agree well with the measured ratios. P derived from the model is the same for each site within error: ~40 ± 22 m/Ma at NPRT, ~52 ± 15 m/Ma at NPMS, and ~50 ± 15 m/Ma at NPVF (Table 2 and Figure 3). The model lines can be extrapolated downward to the point where activity ratios equal unity: 60 cm at RT, 60 cm at MS, and 80 cm at VF (i.e., deeper than the augerable depth). Using the derived value of P, the residence time that particles have remained in the window of preferential 234U loss was calculated using equation ((7)) by setting h to those values. These residence times in the depth zone of 234U loss are the same at each site within error: ~15 ± 8 ka for NPRT, ~12 ± 3 ka for NPMS, and ~16 ± 5 ka for NPVF (Table 2).
 Regolith production rates of the south-facing regolith profiles are the same within error to the rate previously determined from U-series disequilibrium at the north-facing ridgetop (SPRT: ~45 ± 12 m/Ma) but much greater than the values for the north-facing mid-slope (~18 ± 13 m/Ma) and valley floor (~17 ± 14 m/Ma) [Ma et al., 2010]. The residence times for chemical weathering of the south-facing regolith (~12–16 ka) are also similar to the SPRT site (~17 ka), but much shorter than the SPMS and SPVF sites (43 ka and 39 ka, respectively), calculated with extrapolated depth and P values from Ma et al. .
 Model-derived k238 values vary in the range 0.5–0.6 × 10−5 yr−1 (Table 2), similar to the parameters in Ma et al. . Model-derived k234/k238 ratios from the three profiles are all greater than one, varying from 1.4 to 1.9 (Table 2). These greater-than-one ratios are consistent with the fact that 234U isotope is preferentially lost to the weathering fluids compared to 238U [e.g., Fleischer, 1980; Vigier et al., 2001; Dequincey et al., 2002; Dosseto et al., 2008b; Andersen et al., 2009].
 Values of the ratios of k230/k238 from the model range from 0.3 to 0.7 at SSHO (Table 2), consistent with less mobility for 230Th during weathering than 238U. However, these values suggest that 230Th is not completely immobile. Loss of 230Th may be consistent with colloidal or micron-sized particle transport [e.g., Viers et al., 2000; Ma et al., 2010].
 Using a similar approach to that described in Ma et al.  (Table 2), we calculate the 238U mass balance for the south-facing transect to test whether these 238U fluxes could be U carried downslope from NPRT to NPMS to NPVF. We assume that U input from wet precipitation or dust is negligible [e.g., Chabaux et al., 2003a]. Thus, U-series isotopes are lost through weathering and radioactive decay at the NPRT profile without addition of U. For the downslope locations (NPMS and NPVF), the U input to each downslope profile is non-negligible and we can check if it can be provided by the output calculated from upslope positions. Our model results show that U inputs calculated by the model are accounted for with the U outputs from the site above (Table 2). This calculation demonstrates that no additional U input fluxes must be invoked to explain the U mass balance. A similar conclusion was reached in the previous study [Ma et al., 2010].
5.4 Elemental Release Rates During Chemical Weathering
 The release of elements from weathering profiles at Shale Hills is mostly controlled by weathering of primary clay minerals such as illite and chlorite [Jin et al., 2010a]. The element release rates can be calculated from the chemical weathering gradients, which are defined by the change in the element contents with depth in weathering profiles (e.g., Figure 4), and regolith production rates, according to the following equation [White, 2002]:
 Here rs is the element release rate per unit volume of regolith (mol m−3 s−1), ρw is regolith bulk density (1.8 g cm−3 at SSHO), P is regolith production rate (m s−1) which is here determined from U-series isotopes, and bs is the chemical weathering gradient for the element of interest (m kg mol−1). The weathering gradient is the slope of a plot of concentration (or relative concentration) of element (x axis) versus depth (y axis).
 Release rates for U, Al, Fe, K, Mg, and Si for regolith profiles on both transects are calculated (Figure 6). Elemental release rates are generally much greater for profiles on the south-facing planar transect than the north-facing planar transect (Figure 6). It is noted here that equation ((8)) describes the simplest scenario for steady state weathering [White, 2002] and is strictly only true for the RT profiles where no contributions from upslope have occurred. The release rates for the MS and VF profiles are calculated here with equation ((8)) for the purpose of comparison only.
5.5 The Influence of Aspect on Regolith Formation and Chemical Weathering
 The two hillslopes have similar topographic gradients: ~15° (south facing) versus ~20° (north facing); relief: ~31 m (south facing) versus ~22 m (north facing); and hillslope length: ~110 m (south-facing) versus ~75 m (north facing) (Figure 1). However, the south-facing hillslope is closer to a linear profile (Figure 1b). In contrast, the north-facing hillslope is convex at the top, linear at middle slope, and concave near the valley floor (Figure 1c). Neither of these profiles suggests a simple steady state convex landform predicted by geomorphic transport laws. This conclusion is true regardless of whether the regolith flux is considered to be a simple, linear function of slope [e.g., Culling, 1960; Mckean et al., 1993; Dietrich et al., 2003] or a nonlinear function [e.g., Roering et al., 1999; Gabet, 2000]. The difference in elevation at the bottom of each hillslope (Figures 1b and 1c) is due to the fact that the location of the south-facing transect is ~200 m upstream (as measured along the channel) compared to the north-facing transect (Figure 1d).
 Although the hillslope transects are located at different distances from the mouth of the watershed, several lines of evidence suggest that that they have not experienced significantly different erosion histories through time. First, we do not observe evidence in the shape of the modern longitudinal channel profile for convexities associated with transient incision (Figure 1d). The channel profile is smooth and has a concave-up shape for most of its length, consistent with equilibrium or “graded” profiles [Mackin, 1948; Whipple and Tucker, 1999]. Second, there are no prominent knickpoints in the modern channel except a ~1 m high knickpoint between transects A' and B (Figure 1d); anecdotal evidence from observations in the late 1960s and 1970s suggest that this knickpoint is a recent feature (C. Duffy, personal communication). Considering that the relaxation time on the hillslope of this catchment is ~1 Ma (section 6.2.3), it is thus unlikely that any recent channel changes would have led to a systematic difference in the two transects. Hence, we suggest that the knickpoint is not the primary control on erosion and regolith production on the north- and south-facing slopes.
 Considering the similar topographic features, channel incision history, regional climate, and parent material for the two hillslope transects, it is reasonable to hypothesize that the difference in aspect could account for the different rates of regolith formation and extents of chemical weathering. The effect of slope aspect on rare earth element (REE) release rates has been discussed previously for the same two hillslopes at Shale Hills: consistent with results reported here, faster REE release rates were observed on the south-facing hillslope [Ma et al., 2011a]. The same arguments used by Ma et al. [2011a] can be invoked here to explain the U-series isotope data. For example, it has been shown that for mid-latitude regions, different soil temperature and moisture content could be generated by aspect through controls on the amount of solar radiation at the catchment scale [e.g., Cooper, 1960; Churchill, 1982; Carter and Ciolkosz, 1991; Desta et al., 2004; Egli et al., 2007, 2010; Burnett et al., 2008; Li et al., 2010]. Specifically, the south-facing slope is generally characterized by higher and more variable soil temperatures (because it is sun-facing) and lower and more variable soil moisture contents.
 On the two ridgetops, the rates of regolith production are indistinguishable (40 ± 22 versus 45 ± 12 m/Ma). However, when downslope positions are compared, regolith production rates are higher (50–52 m/Ma) on the south-facing as opposed to the north-facing side (17–18 m/Ma). In addition, using equation ((8)), the faster regolith production rates on the south-facing hillslope are consistent with faster rates of elemental release during chemical weathering, i.e., higher values of rs (mol m−3 s−1) (Figure 6). Thus, the north side is weathering faster and is producing regolith faster. The mechanism of this faster weathering on the south-facing hillslope could be due to faster weathering kinetics driven by higher soil temperatures [e.g., Cooper, 1960; Rech et al., 2001].
 However, although the weathering rates are faster on the south-facing side of the catchment, the fractional extents of chemical weathering for major elements down to auger refusal (fj; Figure 5a) are lower on that side. Nonetheless, this difference in extent of chemical depletion can also be explained by aspect. Specifically, higher soil temperatures generally lead to higher evapotranspiration and less water percolating through the regolith on the south-facing side compared to the north-facing side of a catchment. Given that the average solute concentrations in soil pore water from both sides are similar [Herndon, 2012], the lower through flux of water on the south-facing side could explain the lower extent of weathering on that side. Conversely, the high degrees of chemical depletion on the north-facing slope can be attributed to lower evapotranspiration and higher through flux of water. Following these arguments, we hypothesize that the observed differences in both regolith formation rate and chemical weathering processes at Shale Hills may be adequately explained by differences in microclimatic conditions on the south-facing side compared to the north-facing side.
 An alternative (or additional) explanation is also possible. Specifically, differences related to aspect at Shale Hills might have caused different physical erosion rates on the two sides of the catchment. For example, the higher frequency of freeze/thaw, dry/wet cycles, and the shorter durations of snow would arguably have led to higher sediment yields and higher soil erosion rates on the south-facing side as has been reported in semi-arid, alpine, and polar regions [Marques and Mora, 1992; Munro and Huang, 1997; Descroix and Mathys, 2003; Zhang et al., 2007; Istanbulluoglu et al., 2008; Li et al., 2010]. As previously argued [Ma et al., 2011a], such a hypothesis is consistent with two other observations at SSHO: (1) more variable regolith thickness on the south-facing compared to the north-facing side, and (2) more and deeper swales on the south-facing side throughout the catchment (Figure 1).
 West et al. (in review, 2013) measured meteoric 10Be concentrations in regolith on the north- and south-facing hillslopes to elucidate patterns of regolith transport at SSHO. If meteoric 10Be delivery to the regolith profiles has been constant over time and balanced by erosive removal at Shale Hills, then the 10Be inventories reflect minimum regolith residence times of ~9 ka for the north-facing planar ridgetop and ~11 ka for the south-facing planar ridgetop (West et al., in review, 2013). The similar depths of regolith and these similar residence times are not supportive of different erosion rates on the two sides of the catchment today. In addition, West et al. (in review, 2013) calculate creep velocities and mass flux rates that are identical within error on the south- and north-facing slopes at Shale Hills based on 10Be inventories.
 We thus conclude that today's rate of erosion that is documented in the measured 10Be data is the same on the north-facing side versus the south-facing side of the catchment. The data of West et al. (in review, 2013) do not preclude, however, that erosion rates may have differed on the two sides of the catchment during the recent periglacial conditions in the Holocene. Freeze-thaw and solifluction were probably extensive in this region prior to ~15 ka and may have enhanced the rates of erosion [e.g., Walder and Hallet, 1985; Gardner et al., 1991]. Moreover, it is possible that erosion was more intensive on the south-facing slope and the ridges during periglacial conditions [Jin et al., 2011a]. Indeed, south-facing slopes in alpine and polar regions have been commonly observed to have higher sediment yields and erosion rates [Marques and Mora, 1992; Munro and Huang, 1997; Descroix and Mathys, 2003; Zhang et al., 2007; Istanbulluoglu et al., 2008; Li et al., 2010].
 It is even possible that the regolith that existed prior to ~15 ka was completely removed from the south-facing ridgetop and mid-slope positions due to high erosion rates during vigorous periglacial activity but that some remained on the north-facing hillslope. Under that scenario, the regolith profile on the south-facing slope would represent only formation after the periglacial period. This would be consistent with the observation that the duration of chemical weathering on the south-facing slope is only ~12–16 ka based on U isotopes (Table 2). A similar “reset” of the regolith profile by glaciation has been previously hypothesized for the Mackenzie Basin (Northern Canada), as U-series disequilibria in river sediments showed that duration of chemical weathering was short compared to the time since the last glaciation in that region [Vigier et al., 2001]. It is noted that such a complete removal of regolith by periglacial activity is not supported by our data for the north-facing slope, as the duration of chemical weathering on the north-facing middle slope and valley floor is ~34–40 ka [Ma et al., 2010]. Furthermore, as described by West et al. (in review, 2013), colluvial material has been identified under some of the regolith on the north-facing side of the catchment, including the SPVF site of Ma et al. , but this layer is absent under most of the south-facing hillslope.
 High rates of erosion during periglacial activity could also explain the observed difference between the upper 0–50 cm and the lower 50–120 cm of the NPVF profile (e.g., Figure 4). The total depth of the NPVF (120 cm) is much greater than all the other regolith profiles (30–67 cm), and only the upper 50 cm of the NPVF profile shows a clear depletion trend. In fact, the lower 50–120 cm shows only limited depletion (Figure 4). Based on all the observations, we infer that the upper 0–50 cm of the NPVF profile represents weathering of clay minerals since the periglacial period, similar to the NPRT and NPMS residual regolith profiles. The deeper part of the NPVF profile most likely represents the accumulation of the eroded (and more or less homogenized) sediments that were transported downslope on the south-facing side by the intensive erosive activity during the periglacial time. Finally, deep sediments observed under the valley floor may also represent channel aggradation in response to high sediment loads during periglacial time (West et al., in review, 2013).
 To summarize, the different observations on the two hillslopes are most consistent with the hypothesis that aspect induces different microclimate conditions that affect chemical weathering and that may have led to different rates of erosion during the periglacial period. The importance of temperature, evapotranspiration, flow paths, surface stability, and residence times for weathering minerals have been previously noted to be important in determining the relative contribution of chemical weathering and physical erosion [e.g., Anderson et al., 2002; 2007; West et al., 2005; Gabet and Mudd, 2009]. The relationship between mineral supply and control of chemical weathering has also been documented for catchments by Riebe et al. [2001, 2004] and for a hillslope by Yoo et al.  and Dixon et al. .
 A final comparison can also be made between the U-series inferences and those based on 10Be (West et al., in review, 2013). If we use simply the residence times from 10Be to calculate steady state erosion rates (i.e., depth of regolith/residence time), we calculate values of ~19 ± 6 m/Ma for SPRT and ~16 ± 6 m/Ma for NPRT. These values are within error of the values determined from U-series isotopes at SPRT (~45 ± 12 m/Ma) and NPRT (~40 ± 22 m/Ma) [Ma et al., 2010]. However, as discussed by West et al. (in review, 2013), a more likely interpretation is that the production rates on the SSHO ridgetops are higher than the erosion rates and that regolith on the SSHO ridges is still thickening in response to the change from Late Pleistocene to Holocene climate states.
6 Landscape Evolution and Response to Changes in Channel Incision Rates
 Here we explore the regolith production function and landscape evolution at Shale Hills using a simple hillslope evolution model [e.g., Culling, 1960; Roering et al., 2001; Mudd and Furbish, 2007]. The model is based on parameters and information constrained by the available U-series disequilibrium [Ma et al., 2010; this study] and cosmogenic 10Be data (West et al., in review, 2013). By using a relatively simple model for weathering and erosion, we seek to explore how the current landscape at Shale Hills may have responded to perturbations from Holocene climate conditions and evaluate the corresponding hillslope response timescales.
6.1 Regolith Production Function at Shale Hills
 Collectively, the U-series data presented here implies that the regolith production rate varies with regolith thickness at Shale Hills (Figure 7) according to the following equation:
 Here P is the regolith production rate (m/Ma), h is the regolith thickness (cm), P0 is the apparent regolith production rate (m/Ma) at zero regolith thickness, and α is the depth scaling factor (cm−1) (Figure 7). Similar functions, including other non-exponential relationships, have been used to explain the production rate of mobile soil from underlying saprolite in previous studies [e.g., Cox, 1980; Heimsath et al., 1997; Dietrich et al., 2003]. The parameters in this function were calculated from the three profiles from the north-facing hillslope, i.e., P0 = 100.8 m/Ma, α = 0.028 cm−1 [Ma et al., 2010]. For the south-facing hillslope, only the ridgetop site (NPRT) is consistent with that exponential function, whereas the NPMS and NPVF sites do not show any relationship between regolith thickness and production rate (Figure 7). Such an observation may be consistent with the inference discussed earlier that most of the south-facing hillslope is still adjusting to the perturbations in Holocene (i.e., the north side of catchment is a regolith surface newly formed after the periglacial period). Regardless, the regolith thickness on the north-facing hillslope and both north and south ridgetops may be well described by the regolith production function parameterized by Ma et al.  for the north-facing slope.
6.2 Landscape Response to Changes in Channel Incision Rates
6.2.1 Linear Geomorphic Transport Law
 The change in regolith thickness over time depends on both regolith production, i.e., transformation of saprolite/saprock/bedrock to regolith, and regolith loss, i.e., chemical and physical denudation [Carson and Kirkby, 1972; Heimsath et al., 1997; Minasny and McBratney, 1999; Roering et al., 2001; Mudd and Furbish, 2007]. This relationship can be expressed by the following equations as previously stated by many studies:
 In equation ((10)), h is regolith thickness (m); z is elevation of land surface (m), and e is elevation of the chemical weathering front (m); D is erosive diffusivity of regolith (m2 yr−1); ρb and ρr are density of bedrock and regolith, respectively (kg m−3); t is time (year); and x is the horizontal axis for a cross section (m); thus, is the curvature of the land surface (m−1). The term is the change in elevation of the weathering front with time. Here this term is assumed to be equivalent to the regolith production function (equation (9)) derived from the U-series disequilibrium. Equation ((11)) describes the movement of materials along a slope as diffusive transport [Culling, 1960], where qs is the volume of material that flows along a slope profile per unit width per unit time (m3 m−1 yr−1) and ∂ z/∂ x is the slope gradient of the land surface.
 The above geomorphic transport law assumes the downslope movement of regolith driven by a slope-dependent linear diffusion transport process [Culling, 1960; Carson and Kirkby, 1972; Heimsath et al., 1997; Minasny and McBratney, 1999]. Such a linear diffusion process does not include local disturbances such as biologic activity that may result in a nonlinear transport law at large slope angles [Roering et al., 1999]. Such nonlinear transport processes are important for hillslopes when slopes increase beyond a certain critical angle [e.g., Roering et al., 2001]. However, given the observation that hillslope gradients in our study area are rather gentle (<20°), we consider it likely that gradients are beneath the threshold and therefore that a linear transport law is reasonable. Similarly, the meteoric 10Be data presented in West et al. (in review, 2013) suggest that a slope-dependent transport model adequately describes regolith transport over most of the SSHO.
6.2.2 Steady State Elevation Profiles in the Linear Transport Model
 Many studies have derived steady state elevation profiles from equation (11) using the linear transport model [e.g., Culling, 1960; Roering et al., 2001; Mudd and Furbish, 2007]. For example, an expression for a steady state convex hillslope is shown by Roering et al. :
 Here I0 is the constant channel incision (or base level lowering) rate along the hillslope margin (m yr−1) and c is constant. The definition of other terms is the same as above. The diffusivity (D) can be derived from a steady state elevation profile with a channel incision rate. The diffusivity is assumed here to be spatially and temporally constant.
6.2.3 Landscape Response to Reduced Channel Incision
 Given that the top portion of the north-facing profile is close to a convex steady state hillslope, we first fit equation (12) with the measured elevation data (x = 0 to 30 m in Figure 1c) and a channel incision rate (I0 = 44 m/Ma) that is equal to the regolith production rate at the SPRT (assumed to be at steady state). The derived D value from equation (12) (0.0036 m2 yr−1) is within the range of erosive diffusivity values reported from various studies of soil transport [Fernandes and Dietrich, 1997; Minasny and McBratney, 1999] and is also consistent with the value derived from the cosmosgenic 10Be data at Shale Hills (West et al., in review, 2013). Other parameters used in the model are also listed in Table 3.
Table 3. Parameters used in the Geomorphic Mass Transport Model
 Instead of following the convex steady state hillslope (red dashed line in Figure 8a), the lower portion of the north-facing hillslope (x = 30 to 75 m, blue line in Figure 8a) shows a concave-up curve and reduced relief. We consider the possibility that present-day hillslope relief and gradients reflect the response of a previously steady state landform to a reduction in channel incision rates at the bottom of the hillslope [Mudd and Furbish, 2007]. The response time (τa) of a hillslope to transient channel incision rates can be evaluated using the following expression [Mudd and Furbish, 2007]:
 Here λ is the length of the hillslope (m). The definition of other terms is the same as above. For the north-facing hillslope, the calculated response time τa is ~900 ka (Table 3), which describes the time required for the entire hillslope to adjust to a new steady state landform under a new channel incision rate. Another important timescale as shown by Mudd and Furbish  is the time it takes a signal caused by a change in the channel incision rate to propagate from the channel to the ridgetop; this timescale is approximated by Mudd and Furbish  as τa/9 and is ~100 ka for the north-facing hillslope at Shale Hills. According to these arguments, perturbations associated with the last 100 ka BP (e.g., the periglacial period) could still be influencing the distribution of regolith production within Shale Hills.
 We illustrate this possibility using a simple numerical model of hillslope evolution with solutions derived by Mudd and Furbish  for a soil-mantled hillslope. We consider the response of a hillslope to a reduction in channel lowering rate, as might be expected during efficient removal of regolith from adjacent hillslopes. We choose an initial condition such that the hillslope topography is in equilibrium with an initial channel incision rate of I0 (m/Ma); in our simulation, we choose I0 = 44 m/Ma, D = 0.0036 m2/yr and hillslope length = 75 m (Table 3) to approximate an initial condition in our study area, as described above. We then allow the hillslope to evolve under a reduction in lowering rate at the channel; we choose I = 17 m/Ma, which is assumed to be the average lowering rates at present [Jin et al., 2010a; West et al., 2011]. The solutions for our north-facing hillslope (i.e., equation (7) as in Mudd and Furbish ) are presented in Figure 8b as the surface topography with elevation measured relative to the channel. We show that from a steady state convex landform (Figure 8b), if the channel incision rate is reduced, the land surface near the ridgetop will still remain a convex landform due to delayed response while the land surface near the valley floor will rise quickly over time in response to the accumulation of eroded sediments from upslope. The valley floor evolves toward a concave-up slope, similar to the current land surface at the north-facing transect (Figure 8a). The relief of the hillslope is also reduced as expected from 35 to ~17 m (Figure 8b). This simulation is again consistent with the suggestion that the current land surface at Shale Hills is in a transient state.
6.2.4 An Alternative Landscape Evolution Scenario
 In the previous landscape evolution scenario, we assumed that the erosion rate (I0 = 44 m/Ma) at the ridgetop is at steady state with respect to the local regolith production rate (44 m/Ma). However, the companion 10Be study (West et al., in review, 2013) shows some of the first direct evidence that the erosion rates are ~19 ± 6 m/Ma for SPRT and ~16 ± 6 m/Ma for NPRT and the regolith production rates are reported here as ~45 ± 12 m/Ma for SPRT and ~40 ± 22 m/Ma for NPRT [Ma et al., 2010; and this study]. Given the large error bars, we are unable to distinguish whether the regolith on ridge crests in the SSHO has reached a steady state. As discussed earlier and by West et al. (in review, 2013), our preferred interpretation is that regolith production on the SSHO ridgetops may outpace erosion, in response to the change from Late Pleistocene to Holocene climate states. Below, we illustrate this possibility using an alternative landscape evolution scenario on the north-facing hillslope.
 We consider here the response of a hillslope to an increase in regolith production rate, as might be expected after extensive removal of regolith from the hillslope during periglacial erosion. We choose an initial condition such that the hillslope topography is in equilibrium with an erosion rate I0 = 17 m/Ma, D = 0.0012 m2/yr and hillslope length of 75 m in our study area, as described above for the north-facing hillslope. The erosion rate of the hillslope is set to be constant at 17 m/Ma, which is assumed to be the average lowering rate at present [Jin et al., 2010a, 2010b; West et al., in review, 2013]. We then allow the hillslope to evolve as the regolith production rate increases in response to a significant reduction in regolith thickness caused by erosion. We initiate the simulation with a uniform initial regolith thickness of 1 cm on the hillslope after the glacial period. The regolith production rate is calculated as a function of the regolith thickness from equation ((9)). The numerical solutions of equation ((10)) for our north-facing hillslope (i.e., with a finite-difference forward-time–central-space approach in Minasny and McBratney ) are presented in Figure 8c.
 The results of this simulation again show that the current land surface at Shale Hills is in a transient state, consistent with the previous scenario. However, in this case, the evolution of topography and regolith thickness is characterized by a reduction in the convexity of the initial steady state hillslope profile (Figure 8c) that involves lowering of the ridge crests and slight aggradation near the toe of the slope in response to the accumulation of eroded sediments (Figure 8c). The valley floor evolves toward a concave-up slope, similar to the previous model scenario (Figure 8b). The relief of the hillslope is reduced as expected from 50 m to about 35 m (Figure 8c), similar to the present-day relief in SSHO today. As discussed in the companion paper (West et al., in review, 2013), this scenario reconciles both the rates of soil production and downslope transport and honors the long residence times of regolith (30–40 ka) [Ma et al., 2010] along the southern valley mid-slope and valley floor positions. Thus, we consider it a more likely scenario that describes the general response of catchment topography and regolith thickness in response to the change from periglacial to modern climatic conditions at Shale Hills.
 These simulations illustrate that the response time of hillslopes in Shale Hills to a perturbation of channel incision rate or regolith production rate is relatively long; our constraints on erosion and soil production rates suggest that the Shale Hills landscape will approach a new steady state in about 900 ka. We note that variations in erosion rates in response to changes in climate, biological succession, or human activities can often occur more frequently than this timescale [e.g., Fernandes and Dietrich, 1997; Roering et al., 1999, 2001; Riebe et al., 2003; Mudd and Furbish, 2007]. For instance, it has been documented that Earth's climate fluctuated between warming and cooling phases over the last million years with strong periodicities ranging from about 1500 years to about 105 years [Alley and Clark, 1999]. Such high-frequency changes in climate likely cause changes in the regolith erosion and transport. As the climate system changes on a timescale much shorter than 105–106 years, we tentatively conclude that Shale Hills is unlikely to have been in a steady state during the Quaternary. Rather, erosion rates in the catchment are more likely driven toward a new steady state dictated by fluctuating climate, vegetative, and hydrologic regimes.
 Here we measured U-series isotopes in three new regolith profiles along a south-facing hillslope developed on shale in central Pennsylvania. Similar to the previously studied north-facing hillslope [Ma et al., 2010], new regolith samples show significant U-series disequilibrium and these activity ratios display depth trends consistent with the relative mobility of U and Th isotopes decreasing in the order 234U > 238U > 230Th. Apparent equivalent regolith production rates calculated with U-series isotopes for the two ridgetop profiles are the same within error (40–45 m/Ma). In contrast, rates calculated for downslope profiles on the south-facing side range from 50 ± 22 to 52 ± 15 m/Ma, much greater than the rates on the north-facing slope, 17 ± 14 to 18 ± 13 m/Ma [Ma et al., 2010].
 The regolith profiles on the south-facing hillslope are thus characterized by faster regolith production rates, faster rates of chemical weathering, and shorter durations of chemical weathering compared to the north-facing, more shaded hillslope. Furthermore, lower degrees of chemical depletion are observed on the south-facing hillslope where regolith experiences less time for chemical weathering, while the north-facing profiles are generally characterized by high degrees of chemical depletion with long chemical duration. These observations are consistent with the hypothesis that aspect exerts an important control on the regolith formation at the Shale Hills catchment. Although topographic aspect induces different microclimatic conditions today that can explain the differences in chemical weathering, our determinations of the rates and timescales of soil formation and transport imply that the best explanation of the differences in regolith formation rates is that these reflect significant differences in erosion rate during the last periglacial. In other words, even though erosion rates are the same between north and south today (West et al., in review, 2013), we infer that erosion may have been much faster on the north side during last glacial maximum. Our study illustrates how aspect can create differences in erosion and chemical weathering that causes development of asymmetric hillslopes. The regolith production function determined from the U-series disequilibrium also allows for an analysis of the hillslope evolution and response times. Today, the hillslopes are responding to the last periglacial perturbation 15 ka ago. The model emphasizes that the catchment most likely has always been out of steady state since the timescales of readjustment of regolith thickness or landscape geometry to a perturbation is much longer than the timescales of climate change.
 We would like to thank A. Densmore and S. Mudd for their editorial handling and insightful comments. Constructive and insightful reviews from three anonymous reviewers are also acknowledged. Discussions with R. Slingerland, C. Duffy, T. White, and A. Dere from PSU are acknowledged. We thank Z. Ruge and B. Ketchum for the help with regolith sampling. Logistical support and/or data were provided by the NSF-supported Susquehanna/Shale Hills Critical Zone Observatory. We thank E. Pelt, M. Granet, and E. Blaes from the University of Strasbourg for their help during U-series analyses. Financial support was provided by National Science Foundation Grant CHE-0431328 to SLB for the Center for Environmental Kinetics Analysis and Grant EAR-0725019 to C. Duffy (Penn State) for the Susquehanna Shale Hills Critical Zone Observatory.SLB and LM were partially funded by Department of Energy Grant DE-FG02-05ER15675 to SLB. Funding from the Region Alsace, France, and the Laboratory network “REALISE” for LHyGeS (EOST), University of Strasbourg and CNRS, to FC and LM is also acknowledged. Partial support to LM from CEEIR at UTEP is acknowledged.