Pelletier, J.D., How Do Pediments Form?

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How do pediments form?: A numerical modeling investigation with comparison to pediments in southern Arizona, USA

Jon D. Pelletier

Geological Society of America Bulletin 2010;122, no. 11-12;1815-1829 doi: 10.1130/B30128.1

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How do pediments form?: A numerical modeling investigation with comparison to pediments in southern Arizona, USA

Jon D. Pelletier† Department of Geosciences, University of Arizona, Gould-Simpson Building, 1040 East Fourth Street, Tucson, Arizona 85721-0077, USA

ABSTRACT rocks in the Mojave and Sonoran Deserts of as they downcut? If the pediment is formed pri- southeastern California and southern Arizona. marily by slope retreat, how could the pediment Pediments are gently sloping, low-relief Figure 1 illustrates an example of a pediment on be devoid of alluvium and regolith despite its bedrock erosional surfaces at the bases of the west side of the Santa Catalina Mountains gentle slope? mountain ranges. Pediments tend to form near Tucson, Arizona. The pediment surface, in Pediment studies have a long history in more readily in arid climates and in weather- the foreground, is composed of the same granite the geomorphic literature. Pediments can be ing-resistant lithologies, but the processes re- that makes up the steeper portions of the Santa broadly classifi ed into two main types: plana- sponsible for pediment formation are still not Catalina Mountains to the east. Given that the tion surfaces formed on less resistant bedrock in widely understood after more than a century range and pediment are composed of the same contact with steeper, more resistant bedrock of debate. In this paper, I investigate the be- rock type, what processes account for the abrupt (examples of which were described by, e.g., havior of a coupled numerical model for the slope break between the range and pediment? Gilbert [1877] and Miller [1950], and “rock evolution of mountain ranges and their adja- When the geomorphologists of the early twen- pediments” composed of the same lithology, cent piedmonts that includes bedrock erosion tieth century fi rst came to the southwestern typically granite, granodiorite, or quartz mon- in channels, soil production and erosion on United States, pediments were among the most zonite, as that of the adjacent mountain range hillslopes, and the fl exural-isostatic response striking and puzzling features of the landscape. (Oberlander, 1997). In this paper, I focus on the of the lithosphere to erosional unloading. For If fl uvial channels respond to tectonic uplift by formation of rock pediments (herein referred relatively small values of the fl exural parame- incising, how could the channels draining these to simply as pediments) because these are the ter, erosion of the mountain range leads to suf- ranges have maintained such low-relief surfaces more enigmatic of the two types. fi cient fl exural-isostatic tilting of the adjacent piedmont that a suballuvial bedrock bench is exhumed to form an erosional surface on the piedmont. In addition, slope retreat at the A mountain front and subsequent tilting of the abandoned surface can contribute to pediment formation by lengthening the pediment in the upslope direction. The rate of erosion on the piedmont must also be greater than or equal to the rate of soil production, thereby Figure 1. Aerial photographs creating an erosional surface that has, at (south looking) of the Catalina most, a thin veneer of soil or regolith. The rate pediment near Catalina, Ari- of soil production depends primarily on cli- zona (northwest of Tucson). mate and lithology, with lower soil production The close-up view (B) illustrates rates associated with more arid climates and that the pediment is dissected more resistant lithologies. The model predic- with bedrock channels that tions are compared to morphometric analy- grade into the steeper bedrock B ses of pediments in the southwestern United channels of the Santa Catalina States and to the detailed morphology of two Mountains. The pediment is classic pediments in southern Arizona. bounded on its west side by the Pirate Fault. Aerial Photography INTRODUCTION by Peter L. Kresan ©1990.

A pediment is a gently sloping, low-relief bedrock erosional surface at the base of a moun- Catalina pediment tain range. In the United States, pediments are Pirate fault most commonly formed on weathering-resistant

†E-mail: [email protected]

GSA Bulletin; November/December 2010; v. 122; no. 11/12; p. 1815–1829; doi: 10.1130/B30128.1; 12 ﬁ gures.

Pelletier

The puzzle of pediment formation can per- order to preserve the linear mountain fronts ad- a pediment. Strudley et al. also showed that if haps best be understood by considering why jacent to many pediments (Davis, 1930a, 1930b; a “humped” soil production function is used, pediments do not form along most mountain Rich, 1935; Ruxton, 1958; Ruxton and Berry, tors and inselbergs may form. The Strudley fronts. Pediments can fail to form for at least 1961; Mabbutt, 1966; Warnke and Stone, 1966; et al. model represents an important advance two reasons. First, most piedmonts in the Basin Hadley, 1967). Models that invoke sheetfl ood- in our understanding of pediments, but more and Range are uniformly covered with alluvial ing to form pediment surfaces (e.g., McGee, work is needed. One drawback of the Strudley fan deposits. In areas of rapid late Cenozoic 1897; King, 1949) are also generally regarded et al. approach is that the rate of rock uplift of uplift, rates of alluvial fan deposition are often as unlikely to work (Cooke et al., 1993). The ob- the mountain range adjacent to a pediment (or, suffi ciently high that alluvial fans and bajadas servation that pediments tend to form in granitic equivalently, the rate of base-level lowering of uniformly cover the piedmont. The fact that rocks has led to the hypothesis that pediments the downstream model boundary), is assumed areas of the Basin and Range characterized by form by subsurface weathering (granitic rocks to be a prescribed value independent of other neotectonic activity tend to have continuous are particularly susceptible to this process) processes operating in the model. In most parts alluvial cover suggests that pediment formation (Mabbutt, 1966). Pediment formation by slope of the Mojave and Sonoran Deserts, however, is a post-tectonic process (Dohrenwend, 1994). retreat and exhumation of a suballuvial bedrock active tectonic uplift has not occurred for mil- Second, even if bedrock is exhumed from be- bench was proposed by Paige (1912), Lawson lions or tens of millions of years. Hence, rock neath an initial cover of alluvium on the pied- (1915), and more recently by Cooke (1970). uplift in these regions occurs primarily as the mont, the soil or regolith on that surface may Lawson envisioned that mountain fronts erode fl exural-isostatic response to erosion in the be suffi ciently thick to preclude classifying the primarily by slope retreat, leaving behind an ranges. A second drawback of the Strudley surface as a pediment. For example, the pied- alluvium-mantled bedrock surface. Pediments et al. approach is that it assumes that all chan- mont surface of the eastern United States is a are then exhumed from beneath the alluvium nels in the model are alluvial channels. In fact, regionally extensive, low-relief bedrock surface by tilting or doming. Cooke (1970) favored the most channels on pediments and their adjacent bounded by the Blue Ridge and Appalachian exhumation model because it best explained mountain ranges are bedrock channels. Mountains to the west and the Atlantic Coastal the morphometric correlations he observed be- Figure 2 illustrates the conceptual model of Plain to the east. As such, the piedmont surface tween pediments and upstream drainage basins this paper. In the early stages of pediment de- meets one of the criteria for pediments: it is a in the western Mojave Desert. No clear mecha- velopment, tectonic extension forms a semi- gently sloping, low-relief erosional piedmont nism has been proposed for causing the uplift periodic sequence of basins and ranges. Hillslope surface. Flexural-isostatic tilting has been in- that leads to bedrock exhumation in this model, and channel erosion in these ranges occurs in re- voked as a means to maintain the relief of the however. Uplift cannot simply occur by reacti- sponse to the relief production associated with piedmont surface despite the great age of the vation of range-bounding faults, because that extension. Erosion reduces the topographic load, Appalachian orogeny (Pavich, 1989). This sur- would cause incision of any pediment formed triggering fl exural-isostatic rebound. If the fl ex- face cannot be considered a pediment, however, upslope from the fault and deposition on any ural parameter α (a function of the fl exural ri- because it is covered with regolith that is locally pediment formed downstream of the fault. All of gidity of the lithosphere and the density contrast over 30 m thick (Crickmay, 1935). The great these models remain conceptual, and none has between the crust and the mantle) is relatively thickness of this regolith cover is due, in part, gained widespread acceptance for even a subset large relative to the spacing between ranges, to the relatively humid climate of the eastern of pediments found in nature. isostatic rebound will be uniformly distributed United States. In this paper, I argue that under Strudley et al. (2006; Strudley and Murray, across basins and ranges, resulting in regional conditions of suffi cient erosional unloading and 2007) were the fi rst to model pediment forma- rock uplift with little or no tilting. In the absence low fl exural rigidity, fl exural-isostatic tilting can tion numerically. Numerical modeling is an of tilting, alluvium and/or colluvium will be de- tilt piedmonts to the point of developing an ero- attractive approach to this problem because it posited on the piedmont, thus preventing pedi- sional bedrock surface, by exhumation and/or provides a means of investigating the coupled ment formation. Conversely, if the value of α is by slope retreat, that is steep enough to prevent evolution of geomorphic process zones that is small relative to the spacing between ranges, ero- alluvial deposition. In addition, however, pedi- required to test the conceptual models that have sion will result in concentrated isostatic rebound ment formation requires a suffi ciently arid cli- been proposed over the past century. Strudley beneath the ranges. As a result, the piedmonts at mate and/or a weathering-resistant lithology so et al. (2006; Strudley and Murray, 2007) ap- the fl anks of each range will be tilted, causing a that the rate of erosion on that surface is greater plied the soil production function concept of bedrock surface to be exhumed, if suffi cient tilt- than the rate of soil formation, thereby preclud- Heimsath et al. (1997, 1999) to argue that pedi- ing occurs. ing the accumulation of a thick mantle of rego- ments form, in part, due to a negative feedback Tilting of the piedmont is a necessary but lith over time. between the soil and regolith thickness and the not a suffi cient condition for the formation of Four principal processes have been invoked rate of bedrock weathering. In this feedback, an a pediment according to the conceptual model for pediment formation: lateral corrasion, increase in the thickness of regolith leads to a of this paper. In a relatively humid climate, bed- sheetfl ood erosion, subsurface weathering, and decrease in the bedrock weathering rate, which, rock is weathered more quickly than in an arid exhumation and/or slope retreat. In the lateral under conditions of constant base-level lower- climate, resulting in a thick regolith and soil corrasion model proposed by Gilbert (1877), ing, tends to steepen the piedmont and result mantle on low-relief bedrock surfaces (e.g., the Blackwelder (1931), and Johnson (1931, 1932), in soil and regolith removal. In their model, Appalachian Piedmont surface). Therefore, an channels draining the mountains are thought to this feedback mechanism results in an equi- additional requirement for pediment formation erode laterally as they downcut, thus maintain- librium soil cover on the piedmont in which is that the rate of erosion must equal or exceed ing a planar surface. Later studies concluded the rate of bedrock weathering beneath the the rate of soil production on the piedmont. The that the corrasion model is unlikely to work due regolith matches the rate of base-level lower- rate of soil production is a function of climate to the fact that channels would have to downcut ing. Under certain conditions, this equilibrium (with lower rates in more arid climates), rock with uniform effi cacy within a 180° swath in soil thickness can be relatively thin, leading to type, and soil cover. Therefore, given suffi cient

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How do pediments form?

A early time where h is local elevation, t is time, U is rock uplift rate, K is the coefﬁ cient of bedrock erodibility, Q is discharge, w is channel width, and x is the along-channel distance (Whipple and suballuvial Tucker, 1999). Scaling relationships between bench discharge, channel width, and drainage area can be used to further simplify (1) to

B late time ∂h ∂h =−UKAm , (2) alluvial ∂t ∂x apron where A is drainage area and m (nominally large α/λ equal to 0.5) is an exponent that combines the scaling relationships between discharge, channel width, and drainage area [note that the coeffi cient K in (1) and (2) have different values C late time soil and different units after (1) is transformed into (2)]. The more general form of the stream- power model includes a power-law relationship between erosion rate and channel slope small α/λ, (with an exponent often assumed to be close to 2 large P0/DX unity, as assumed here) and a fi nite shear stress threshold for erosion (useful if a range of fl ood late time event sizes is prescribed). Here I use the basic D pediment pediment form of the stream-power model exclusively because my purpose is to elucidate the nature of the feedbacks between bedrock channel incision, hillslope erosion, and fl exural-isostatic small α/λ, rebound rather than to calibrate the stream- small P /DX 2 0 power model as precisely as possible for a particular study site. η Hillslopes in upland (soil over bedrock) land- Sp h scapes are composed of a system of two inter- 0 acting surfaces: the topographic surface h(x,y), λ c and the underlying weathering front, given by b(x,y). The difference between these two sur- Figure 2. Schematic diagram of the conceptual model. Early in the model, Basin and Range faces is the soil or regolith thickness, η(x,y). In extension creates a semi-periodic series of basins and ranges. Range-bounding hillslopes this paper, the terms soil and regolith are used and channels respond by backwearing and downwearing. The erosional response to uplift is interchangeably to refer to the unconsolidated accompanied by a fl exural-isostatic rebound. If the value of α/λ is relatively large, isostatic material above the bedrock consisting of mate- rebound will be distributed across basins and range uniformly, resulting in little or no pied- rial weathered in situ and material transported mont tilting (B). As a result, the piedmont will remain covered in alluvium. If, however, the from upslope. The topographic and weathering- value of α/λ is relatively small, the piedmont will tilt. Pediments will form on the tilted pied- front surfaces are strongly coupled because the 2 mont if the value of P0 /DX is relatively small. In that case (D), hillslope and channel erosion shape of the topography controls erosion and on the piedmont will keep pace with soil production, resulting in bare bedrock slopes despite deposition, which, in turn, changes the val- 2 η the low relief (as in Fig. 1). If the value of P0 /DX is relatively large, a soil will form on the ues of (x,y) (Furbish and Fagherazzi, 2001). η η tilted piedmont slope. Also shown in (D) are parameters of the hillslope model (i.e., Sp, , The values of (x,y), in turn, control bedrock λ 2 c, and h0) used to determine the critical value of P0 /DX required for bare slopes to form. weathering and/or soil production rates. The simplest system of equations that describes this feedback relationship between topography, soil aridity, the rate of soil formation will slow to the channel erosion. The classic method for quan- thickness, and the rate of increase of soil thick- point that soil can be transported off the slope at tifying bedrock channel erosion, the stream- ness is given by: the same rate it is formed. Under these condi- power model, assumes that bedrock channel ∂ηρP −ηθη tions, a pediment will form. erosion is proportional to stream power, i.e., =+∇b 0 eDhcos 0 2 , (3) ∂ ρθ the product of unit discharge and channel-bed t s cos MODEL DESCRIPTION slope. In its simplest form, the stream-power ∂b P −η θη model is given by = U − 0 e cos 0, (4) Modeling the erosional response of moun- ∂t cosθ ∂h Q ∂h tain ranges to tectonic uplift requires math- =−UK , (1) ematical models for hillslope and bedrock ∂t w ∂x hb=+η, (5)

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Pelletier

ρ ρ where b is the bedrock density, s is the sedi- mont is assumed to store alluvium locally and for selected regions of southern Arizona. The ρ ment density (nominally 1.3 times b), P0 is hence does not erode. edges of the model domain are kept at a fi xed the maximum bedrock lowering rate on a fl at The fl exural-isostatic response to erosion is elevation of zero to represent stable valley-fl oor surface, θ is the slope angle, D is the hillslope included in the model by solving for the defl ec- channels (i.e., they are assumed to neither erode η diffusivity, and 0 is a characteristic soil depth tion of a lithosphere with uniform elastic thick- nor aggrade). The model duration was assumed (Heimsath et al., 1997, 1999). Equation (3) states ness subject to vertical unloading: to be 30 Ma based on the late Oligocene–early that the rate of change of soil thickness with Miocene age of extension in southern Arizona ∇+4 (ρρ −) = time is the difference between a “source” term D wgwqxymc (,), (7) (Dickinson, 1991). Bedrock uplift rates during equal to the rate of soil production associated the active uplift phase of the model (from t = 0 with the bedrock surface lowering and a “sink” where w is the defl ection, D is the fl exural rigid- to t = Tu) were nominally set to U = 1 m/ka, but ρ ρ term equal to the curvature of the topographic ity, c is the density of the crust, m is the density this value was varied to determine the model profi le. The cos θ dependence in Equation (3) of the mantle, g is the acceleration due to grav- sensitivity to this parameter. The duration of originates from the fact that soil production is an ity, and q(x,y) is the weight of the rock removed active uplift, Tu, was chosen to result in 2 km exponential function of soil thickness normal to by erosion (Watts, 2001). Elastic thicknesses of total active uplift (i.e., Tu = 2 Ma for U = the surface. The curvature-based erosion model in the Basin and Range vary from ~3 to 15 km 1 m/ka). This value for UTu produces ranges in Equation (5) is the classic diffusion model of (Lowry et al., 2000). Given a prescribed elastic that have peak elevations of between 2 and hillslope evolution, fi rst proposed by Culling thickness value, the fl exural rigidity, D, can be 3 km in the model, i.e., comparable in relief to (1960, 1963). Equations (3–5) can be solved for computed using the relationship the tallest ranges in southern Arizona. Peak ele- the steady-state case in which soil thickness is vations in the model are larger than 2 km due to ET 3 independent of time: D = e , (8) isostatic rebound of the slowly eroding peaks. 12( 1− ν2 ) The coeffi cient of bedrock erodibility, K, is not η ⎛ ρ P 1 ⎞ η = 00ln b . (6) well constrained for this region, but the time θ ⎝⎜ ρθ−∇2 ⎠⎟ ν cos s Dhcos where E = 70 GPa and = 0.25 (typical values scale of mountain range denudation varies in- for continental lithosphere). Alternatively, the versely with this parameter. As such, an appro- Note that steady state in this context does not fl exural-isostatic calculation can be completely priate value of K can be chosen so that the time mean that the topography is in steady state, but, described with two parameters: the relative scale of denudation down to base level is within rather, that the soil thickness is steady through density contrast between the crust and mantle, the range of 30 to 50 Ma, thereby creating a ma- ρ ρ ρ ρ time as the landscape is denuded (i.e., a “soil- defi ned as ( m − c)/ c (nominally 0.2, e.g., c ture mountain range at the end of 30 Ma of up- 3 ρ 3 thickness steady-state” condition). Equation (6) = 2750 kg/m and m = 3300 kg/m ), and the lift and erosion that still stands high above base illustrates that, if the curvature is negative and fl exural parameter, α, defi ned as level. This constraint provides a reference value –1 greater than a certain threshold value, the sur- 14/ for K equal to 0.0002 ka . Drainage densities ⎛ 4D ⎞ face will be bare of soil because the argument α = . (9) in arid regions are sensitive to vegetation cover ⎜ (ρρ− ) ⎟ of the natural logarithm will approach one. The ⎝ mcg⎠ and hence precipitation. Melton (1957) found analysis of in situ cosmogenic isotope abun- that drainage densities in southern Arizona are η –1 dances indicates that the value of 0 (the soil The fl exural parameter is a length scale propor- typically within the range of X = 0.01–0.1 m , thickness at which bedrock lowering falls to tional to the natural fl exural wavelength of the with higher values in areas of greater aridity. 1/e of its maximum value) is ~0.5 m for several lithosphere (Turcotte and Schubert, 2002). Val- Conceptually, the value of X can be thought well-studied sites around the world (e.g., Heim- ues of α are approximately two to three times of as the inverse of the average lateral distance sath et al., 1997, 1999). larger than those of elastic thickness (Pelletier, between a divide and a channel head for a hill- The transition between hillslopes and chan- 2008). As such, appropriate values of α in the slope with a gradient of 1 m/m (i.e., 45°). As nels in the model occurs where the product of Basin and Range vary from ~6 to more than such, the range X = 0.01–0.1 m–1 corresponds the slope and the square root of contributing 20 km (with lower values in areas of greater to channels with a spacing of between 10 and area is greater than a threshold value given fault density or in close proximity to faults). 100 m on steep slopes. For the reference model, by the inverse of a channelization threshold Equation (8) is solved in the model using the I choose X to be at the high end of this range, X that has units of one over length (so that X Fourier transform technique (Press et al., 1992; i.e., 0.1 m–1. Pelletier and Rasmussen (2009) has the same units as drainage density), i.e., Pelletier, 2008) validated by comparison of the quantifi ed the relationship between P0, mean SA1/2 ≥ X–1. This approach is consistent with the model prediction with analytic solutions for annual temperature, and mean annual precipi- slope and area controls on channel head loca- defl ection beneath a line load (Turcotte and tation for granitic rocks and found P0 to be in tion observed in natural drainage basins (e.g., Schubert, 2002). the range of 0.01–0.1 m/ka in arid climates. In

Montgomery and Dietrich, 1988). The value of The reference case of the model is a the reference case of the model, I assume P0 =

Xc is the square root of the average “support vertically uplifting mountain block 12.8 km × 0.01 m/ka, but this parameter is also varied to area” required to create a channel head on a 12.8 km in extent. The model domain is determine the model sensitivity to variations particular landscape, per unit slope gradient S. 25.6 km × 25.6 km in extent, and periodic in this parameter. Cosmogenic isotope stud- η The value of Xc can be closely approximated boundary conditions are used for the purposes ies constrain 0 to be ~0.5 m (Heimsath et al., by the drainage density of the basin divided by of computing the fl exural-isostatic response of 1997, 1999). Hillslope diffusivities in arid ter- the average slope immediately downslope from the lithosphere. As such, the model effectively rain range from D = 1–10 m2/ka depending on channel heads. On the piedmont, hillslope and assumes an infi nite series of ranges in both di- hillslope sediment texture, vegetation cover, channel erosion are applied to all locations rections with the ranges occupying 1/9 or 11% and other factors. I chose D = 10 m2/ka for where the slope is greater than a threshold of the landscape. This value is comparable to the reference case. Pediments form over a range value given by Smin. Below that value, the pied- the 10% range area estimated by Cooke (1970) of slopes from nearly fl at to ~10° (Strudley and

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How do pediments form?

Murray, 2007). I choose the minimum slope where U is the rate of active uplift, and Tu is the Equation (13) provides an estimate for the larg- α for pediment formation, Smin, to be 0.02, but duration of active uplift. For the model experi- est value of that will allow pediments to form this value can be expected to vary with allu- ments of this paper, I assume UTu = 2 km and in a Basin and Range system with prescribed ρ ρ ρ α λ α vial texture and drainage basin size. The value ( m − c)/ c = 0.2, so R = 10 km. The factor values of R, , , and Smin. Figure 3 plots c as α ρ ρ ρ λ of was chosen to be 12 km for the reference c/( m − c) in (12) results from the fact that a function of and Smin assuming R = 10 km. case but was varied between 9 and 24 km, with mountain ranges in isostatic equilibrium have Pediments can form for a wider range of values lower values expected in areas of the Basin and buoyant crustal roots that are approximately of α as λ increases (i.e., ranges are more widely

Range with higher fault density. In summary, fi ve times thicker than the height of the over- spaced) and Smin decreases (e.g., sediments the parameter values for the reference case are: lying ranges. In order to erode mountains to eroding from the mountains can be transported λ ρ ρ ρ α = 25.6 km, ( m − c)/ c = 0.2, = 12 km, U = base level, therefore, it is necessary to remove at lower slopes due to fi ner sediment textures –1 –1 1 m/ka, Tu = 2 Ma, K = 0.0002 ka , X = 0.1 m , a thickness of rock equal to approximately fi ve and/or a wetter climate). Pediments can form in η 2 α P0 = 0.01 m/ka, 0 = 0.5 m, D = 10 m /ka, Smin = times as much as the height of the range. It this simplifi ed model, if the value of is below ρ ρ α α 0.02, b/ s = 1.3, and m = 0.5. should be noted that the amount of rock uplift that of c. They will generally not form if is α in (12) is a maximum value. If pediments form, greater than c because insuffi cient tilting takes DESCRIPTION AND RESULTS OF they will usually form prior to the complete de- place to exhume the bedrock surface above the SIMPLIFIED MODELS nudation of the range. alluvial apron. Substituting (11) and (12) into (10) yields In addition to suffi cient tilting, the climate Before describing the results of the fully the following formula for the critical fl exural must also be suffi ciently arid and/or the lithol- coupled numerical model, the conceptual model parame ter for pediment formation: ogy must be suffi ciently weathering-resistant can be further explored using approximate ana- 1/4 to prevent a thick mantle of soil and regolith λ ⎛ 4a ⎞ lytic solutions of simplifi ed models that help α = − 4 , (13) from forming on the pediment surface. Pedi- c ⎝⎜ ⎠⎟ to narrow the range of tectonic and climatic 2 Smin ment surfaces exhumed above the Smin thresh- conditions under which pediments can form. old will erode by bedrock channel and hillslope First, I consider the role of the fl exural-isostatic where processes. Figure 2D illustrates the geometry response to erosion. Pediments can form, if of pediment hillslopes schematically. Soil pro- 2UT ρ fl exural-isostatic tilting causes a portion of the a = uc . (14) duction and erosion on hillslopes will occur λρ( − ρ) piedmont to be steepened beyond Smin, the slope mc via (3–5). The conditions required for bare below which alluvial deposition is assumed to slopes to form can be estimated by assuming occur. The piedmont slope that results from tilting is equal to the ratio of the total rock uplift, R, divided by half of the Basin and Range wave- 40 length, λ/2. Mathematically, this gives the fol- A lowing criterion for pediment formation: 30 2 R CS> . (10) λ min 20 (km)

The factor C in (10) is the compensation ratio, c deﬁ ned as the ratio of subsidence and/or uplift α Figure 3. Plot of the value of the that results from lithospheric loading and un- 10 0.02 critical value of α for pedimen- loading (Turcotte and Schubert, 2002). Math- 0.04 tation, α , as a function of the ematically, C is deﬁ ned as c Smin 0.06 Basin and Range wavelength, 0 0.08 1 λ, and the critical slope for C = . (11) 20 40 60 80 100 4 alluvial deposition, S . The 1 ⎛ 2πα⎞ min λ (km) 1+ ⎜ ⎟ α ⎝ λ ⎠ value of c increases (i.e., pedi- 4 B 0.08 α = ment form under a wider range c 9 km of lithospheric strengths) as λ 0.07 α If the value of C is equal to one, erosion in the c = increases and S decreases. 13 km range will result in uplift of the range only. As min (A) and (B) show the same 0.06 α the value of C decreases (by an increase in the c = data, one as a surface plot and 17 km value of α/λ), isostatic rebound becomes more 0.05 the other as a contour plot.

broadly distributed. If the value of C is close to min zero, isostatic uplift occurs with equal magni- S 0.04 tude in basins and ranges, and little or no tilting occurs. The total rock uplift R of the range 0.03 during the interval from active uplift to erosion 0.02 back down to base level is given by 0.01 ρ 20 40 60 80 100 R = c UT , (12) ρρ− u λ (km) mc

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Pelletier a soil-thickness steady-state condition. In this MODEL RESULTS have been considered pediments, and hence condition, the soil thickness is given by (6). The one could choose η = 1 m, for example, as an curvature of hillslopes on the pediment depends Figure 4 illustrates the results of the refer- alternative since there is no widely accepted on the hillslope relief, h0, and the spacing be- ence case numerical model. Figure 4A presents threshold value. Clearly, the higher one sets λ tween channels, c, according to a color map of the topography following 2 Ma the maximum soil thickness before a piedmont of active uplift and an additional 8 Ma of ero- surface is no longer considered a pediment, the 4h ∇=2h 0 . (15) sion and ﬂ exural-isostatic response to erosion wider the range of tectonic and climatic condi- λ2 c following the cessation of active uplift. In this tions under which pediments can form. For the early phase of the model, a high plateau is still purposes of interpreting the model results, how- Channel heads are located where the product present, and bedrock channels have not had suf- ever, the important thing is to use a consistent of the local slope and the square root of con- ﬁ cient time to propagate back into the central threshold value for soil and regolith cover across tributing area is greater than a threshold value portion of the range. Nevertheless, erosion has the range of model scenarios so that the relative given by X–1. This gives the following relation- triggered a modest degree of isostatic rebound, sizes of the pediments formed in each model can λ ship for c: as illustrated by the “halo” of dark-red colors be compared and the controls on pediment area

− surrounding the range. The piedmont slopes properly identiﬁ ed. λ ≈ 1 cp(SX) , (16) remain sufﬁ ciently small that no portion of the Figure 5 is a plot of the pediment area as a

piedmont has tilted above the Smin threshold for function of time in the reference model and sev- where Sp is the piedmont slope. Equation (16) subaerial exposure. As such, the piedmont is en- eral alternative models, illustrating the sensitiv- λ assumes that c is equal to the square root of tirely covered with alluvium at this stage. ity of pediment area to variations in individual the contributing area. Depending on the shape By t = 20 Ma (Figs. 4B and 4D), headward- parameter values and time. In the reference of the zeroth-order drainage basin above each eroding bedrock channels have penetrated into model, pediment area increases with time until a λ 1/2 piedmont channel head, c may differ from A the headwaters of the range, and suffi cient maximum area is reached at t = 17 Ma and then by a constant factor close to one [e.g., (π/2)1/2 for isostatic rebound has taken place to tilt the declines back down toward zero. The time scale the case of a semicircular zeroth-order basin]. piedmont above the Smin threshold required for of the waxing and waning of pediment area in By neglecting this factor, the results we obtain subaerial exposure of the initially suballuvial the model is primarily a function of the bedrock are only approximate. Substituting (15) and (16) bedrock bench. Drainage networks have formed erodibility, K, which is the primary control on into (6) gives on the piedmont with second-order channels the time scale of mountain range denudation. draining parallel to the direction of fl exural- The sensitivity of pediment area to individual ⎛ ρ P ⎞ ηη= ln ⎜ b 0 ⎟. (17) isostatic tilting. Periodically spaced, fi rst-order model parameters is illustrated in Figures 5 0 ρ 2 2 α ⎝ sp4Dh0 S X ⎠ channels have formed perpendicular to those and 6. First, I increased the value of from 12 second-order channels. The color map of soil to 18 km. Tilting in the model with α = 18 km The cos θ factors in (6) have been neglected thickness at t = 20 Ma illustrates that soil cover was insuffi cient to steepen any portion of the in (17) because the piedmont slopes are suf- thickens with increasing distance downslope on piedmont above Smin. As a result, no pediment fi ciently small that the approximation cos θ ≈ the piedmont from zero or nearly zero on inter- was formed (Fig. 6B). This extreme sensitiv- 1 holds to a high degree of accuracy. Setting η fl uves in the proximal end of the piedmont to ity of pediment area to α can be understood equal to zero gives the following critical condi- greater than 3 m on the distal end of the pied- as a consequence of the fact that the fl exural- 2 tion for the value of P0/(DX ) required for bare mont. At later stages of the model (i.e., t = isostatic response of the lithosphere is very sen- slopes on the piedmont: 30 Ma, Figs. 4C and 4E), erosion in the moun- sitive to α (i.e., C varies inversely as the fourth tain range and the resulting fl exural-isostatic re- power of α/λ) coupled with threshold nature of P ρ 0 = s 4hS2. (18) bound continue, but at a slower rate. As a result, pediment formation in the model. Second, in- 2 ρ 0 p DX c b soils are thicker everywhere on the piedmont at creasing the value of P0 from 0.01 m/ka (the ref- this time. It should be noted that white areas in erence case) to 0.03 m/ka thickens soils on the For example, given the parameters of the refer- the mountain range do not have thick soils de- piedmont and thereby decreases pediment area 2 ence model (i.e., P0 = 0.01 m/ka, D = 10 m /ka, spite the fact that they are mapped as white in (Figs. 5 and 6C). Third, decreasing the channel- X = 0.1 m–1), pediments will form (given suf- the soil thickness maps of Figures 4D and 4E. ization threshold from X = 0.1–0.05 m–1 results fi cient tilting), if the right-hand side of (18) is This is because areas above 10% slope in the in smaller pediments. In the mountain range, a greater than 0.1. This could occur, for example, model were mapped as white regardless of lower channelization threshold slows erosion ρ ρ with h0 = 10 m and Sp = 0.05, assuming s/ b is the thickness of soil cover so that areas of thin because the ratio of hillslopes to channels in- approximately one. soil (i.e., black areas) could be directly inter- creases with decreasing X, and hillslopes erode The simplifi ed model results of this section preted as pediments in these soil thickness maps. more slowly than channels. As a result, isostatic highlight the importance of a suffi ciently high For the purposes of this paper, it is necessary rebound is also reduced. On the piedmont, lower degree of fl exural-isostatic tilting and a suffi - to choose a critical soil and regolith thickness drainage densities result in thicker soils, thereby ciently low rate of soil and regolith production below which the surface is considered a pedi- resulting in a further reduction in pediment area in order for pediments to form. In the next sec- ment and above which it is not. Here I choose in the X = 0.05 m–1 model relative to the refer- tion, I consider the results of the fully coupled η = 0.1 m as a threshold value, i.e., a surface ence case. Finally, I also considered the effect of model, which contains no approximations and with essentially no soil. This choice is consis- reducing the active uplift rate U by a factor of illustrates how channel, hillslope, and fl exural- tent with the pediments in southern Arizona, 5 but lengthening the duration of active uplift isostatic processes interact to form pediments many of which have essentially no soil cover Tu by the same proportion so that the total active when certain tectonic, climatic, and lithologic (Tuan, 1959). Based on the literature, how- rock uplift remained the same as in the reference conditions are met. ever, piedmonts with a range of soil thicknesses case. A smaller value of U leads to a modest

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How do pediments form?

reduction in maximum pediment area (Fig. 5). A 3 km This result can be interpreted as a consequence of a reduction in mountain front hillslope gra- dients with lower values of U. Mountain front steepness promotes greater slope backwearing relative to downwearing, thus lengthening the pediment surface by slope retreat. α The trends among pediment areas , P0, and X discussed above are also documented in Fig- ure 7, which illustrates the relationship between

pediment area Ap (expressed as a fraction of the α model domain), , and P0 for two representa- elevation tive values of channelization threshold, X. Pedi- ment area decreases steadily with increasing α 0 3000 m t = 10 Ma values of and P0, in the former case because not enough piedmont tilting takes place and in the latter case because there is too much soil B C cover on the piedmont. It should be emphasized that the specifi c thresholds for pediment formation documented in Figure 7 are specifi c to λ = 25.6 km and other model parameters. As such, while it is reasonable to expect that the depen- α dence of Ap on and P0 documented in Figure 7 will hold qualitatively for other parameter values, the specifi c thresholds for pediment formation will differ from those of Figure 7, if any of the other model parameter values deviate from those of the reference case. Pediments in the model can form by ex- huming the suballuvial bench downslope from t = 20 Ma t = 30 Ma the range-bounding fault and/or by retreat of the mountain front upslope from the range- bounding fault. Examples of both mechanisms D E are found among the pediments of the Mojave and Sonoran Deserts. In the model, the relative importance of each mechanism depends sensi-

tively on the value of P0. On the hillslopes of the mountain range, soil cover is negligible due to the steep slopes and relatively low values of

P0 used in the model. As such, slopes erode normal to the hillslope with a rate nearly equal to

the maximum rate of bedrock weathering, P0. The mountain front will therefore retreat later- θ ally with a rate of approximately P0sin , where θ is the hillslope angle. Figure 8 illustrates the model topography at t = 20 Ma for four differ-

t = 20 Ma t = 30 Ma ent values of P0, keeping all other parameters of the model equal to those of the reference case. soil depth pediment If P0 = 0.03 m/ka (Fig. 8A), and the angle of the hillslopes along the mountain front is as- 0 3 m sumed to be 45°, the mountain front wears back, extending the pediment, by ~423 m during the Figure 4. Color maps of output of the numerical model for the reference case. (A) Color map 20 Ma duration of the model illustrated in Fig- of topography at t = 10 Ma (model starts at t = 0 Ma and ends at t = 30 Ma). Flexural-isostatic ure 8. If P0 = 0.05 m/ka (Fig. 8B), the mountain rebound is just beginning, as indicated by the “halo” of dark red surrounding the moun- front is expected to wear back by 705 m in the tain block. (B–E) Color maps of the topography (B and C) and soil thickness (D and E) at same time period. The grayscale map of Figure t = 20 Ma and 30 Ma, respectively, illustrate the maximum and waning stages of pediment 8B, however, indicates that more than 1 km of formation. In (B) and (D), the pediment area (shown in black, indicating less than 10 cm soil mountain front retreat has taken place in the P0 cover) is ~25% of the model domain. At later times where the upland topography is more = 0.05 m/ka case. Similarly, if the value of P0 is subdued, the pediment has retreated toward the mountain as soil thicknesses have increased. raised to 0.07 m/ka, at least 2 km of mountain

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Pelletier

Figure 5. Plot of time series of at fi rst as fl exural-isostatic tilting begins, leaving 0.3 reference case lower U pediment area Ap, expressed (U =0.2m/a) lower portions still buried under alluvium. This as a fraction of the area of the situation is not signifi cantly different from the model domain, for the refer- lower X case of an initially fl at bedrock surface, although

) –1 ence case and three alterna- 2 0.2 (X = 0.05 m ) in the case of a rough surface the pediment may tive models with lower U, be spatially discontinuous. In the case of an ini- /km 2 lower X, and higher P0. In each tially fl at bedrock surface, fl exural-isostatic tilt- case, pediment area increases ing triggers bedrock channel incision, increasing (km as incipient canyons erode p 0.1 relief and/or slopes at the hillslope scale. A pedi- A headward thereby triggering higher P0 ment forms, if relief reduction (by weathering fl exural-isostatic rebound. After (P0 = 0.03 m/a) and/or slope retreat) occurs suffi ciently fast to a maximum pediment area balance relief production by bedrock channel in- is achieved (ranging from t = 0.0 cision. In the case of an initially rough bedrock 10 15 20 25 30 15–25 Ma), the rate of fl exural- t (Ma) surface, relief already exists at the hillslope scale isostatic rebound decreases and (and hence may not be increased by bedrock soils accumulate on the piedmont. The model with α = 12 km is not shown because the plot is channel incision), but the large-scale relief is indistinguishable from Ap = 0 (i.e., the x axis). the same in both cases because it is controlled by the magnitude of fl exural isostatic tilting

above the level set by Smin, the gradient at which front retreat takes place in the same time inter- maximum value of 0.5 m/ka, thereby yielding alluvium is deposited, not the initial relief of val. The reason for this apparent nonlinear in- a maximum rate of U = 1 m/ka (i.e., equal to the buried surface. It should also be noted that crease in slope retreat rate with P0 can be traced that of the reference case). As in the earlier ex- the ability of weathering to reduce the relief of to the fact that once the mountain front becomes periment performed with U = 0.2 m/ka, the dura- slowly tilted landscapes (whether the initially embayed by bedrock channels, slopes retreat tion of uplift was lengthened so that the total buried surface is fl at or rough) does not require back into the mountain range and laterally away uplift integrated over the mountain range was the presence of regolith. Even in the absence from the incised bedrock canyons. The effect equal to that of the reference case. In the meta- of regolith cover, relief reduction occurs be- of an embayed mountain front on the effec- morphic core complexes of southern Arizona, cause weathering takes place normal to the tive rate of mountain front retreat is illustrated asymmetric tectonic tilting has played a sig- surface, thereby including a 1/cos θ component schematically in Figure 8D, where the retreat of nifi cant role in the development of drainage that causes high-relief areas to be eroded more a linear mountain front is compared to that of a architecture (Pelletier et al., 2009), and its role rapidly than low-relief areas. sinusoidal mountain front in map view. In an in pediment formation is suggested by asym- embayed mountain front, slope retreat from two metric pediment development on the margins COMPARISON TO PEDIMENTS IN adjacent embayments can sum together to re- of many metamorphic core complexes of south- SOUTHERN ARIZONA θ treat the slope back at a rate that exceeds P0sin . ern Arizona. Figure 9 illustrates the topography In this fi gure the length of the arrow between and soil thickness predicted by this asymmet- Southern Arizona is home to many of the the dashed lines, which represents the effective ric tilt block model. Pediments are best devel- classic pediments of the southwestern United retreat rate of the embayed mountain front, is oped on the north, west, and east sides of the States. Descriptive studies by Paige (1912), longer than the length of all other arrows in the mountain range, i.e., the directions opposite Bryan (1922), Gilluly (1937), and Tuan (1959), θ fi gure, which represent the rate P0sin . This ef- to the direction of tilting. This result can be among others, have made the pediments of this fect can also be understood in terms of an in- understood as a consequence of the fact that region type localities. In this section, I use geo- crease in the overall length of the mountain front the center of mass of the eroded material has graphic information system (GIS) data sets and θ over time. P0sin is the rate of slope retreat per shifted northward in this case, thereby shifting fi eld observations to relate the predictions of the unit mountain front length. As the mountain the maximum isostatic rebound and center of numerical model to observed trends in the oc- front lengthens and develops embayments, the tilting northward as well. currence and size of pediments in this region. effective rate of mountain front retreat must also In the model, I assume the bedrock surface In order to map pediments within a GIS increase. The results illustrated in Figure 8 are exhumed from beneath the suballuvial bench is framework, it is necessary to develop geographi- broadly consistent with empirical studies of em- fl at. This surface need not be fl at, however, and cally co-registered data sets for topographic bayment formation in arid regions. Parsons and hence it is reasonable to ask whether exhumation slope and the presence and/or absence of crys- Abrahams (1984), for example, documented of a rough bedrock surface from beneath some talline bedrock. Pediments can then be mapped the importance of slope retreat in contributing initial cover of alluvium will also form a pedi- by identifying all pixels with slopes less than a to the formation of mountain front embayments ment. Model experiments with an initially rough certain threshold value (nominally 10%) that are in the Mojave and Sonoran Deserts. bedrock surface indicate that the answer is yes, a also composed of crystalline bedrock. To obtain The assumption of uniform vertical uplift is pediment still forms. The reason a pediment still a slope map for southern Arizona, I began with clearly an idealization. In order to determine forms is that, even if the bedrock surface is ini- a 90 m/pixel digital elevation model (DEM) of the effect of tectonic tilting on the distribu- tially rough, the large-scale relief of the surface southern Arizona obtained from the U.S. Geo- tion of pediments around a mountain range, I in either case (initially fl at or initially rough) is logical Survey (USGS). U.S. Geological Survey performed a numerical experiment in which controlled by the magnitude of fl exural-isostatic DEMs have well-known slope artifacts associ- the active uplift was prescribed to have a uni- rebound, not by the initial relief of the buried sur- ated with contour lines. To minimize this prob- form “background” value of 0.5 m/ka and an face. In the case of an initially rough surface, only lem, I averaged the slope map produced from additional asymmetric tilt component with a the top-most portions of the surface are exhumed the DEM using a 5 × 5 (or 450 × 450 m) moving

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How do pediments form?

A X = 0.05 m–1 A 3 km B 0.4

0.3 A p (km too much 0.2

soil cover 2 /km 0.1 2 9 ) 12 15 0.0 18 0.1 α (km) 21 0.05 24 0.02 not enough 0.01 tilting P0 (m/ka) reference case α = 18 km B X = 0.1 m–1 0.4 C D

0.3 A p (km 0.2 2 /km

0.1 2 ) 9 12 15 0.0 18 0.1 α (km) 21 0.05 24 0.02 0.01 P0 (m/ka)

Figure 7. Plots of maximum pediment area, –1 P0 = 0.03 m/ka X = 0.05 m α Ap, as a function of and P0 for (A) X = 0.05 m–1 and (B) X = 0.1 m–1. Other model pediment soil depth parameters are equal to those of the reference case. In both cases, maximum pedi- 0 3 m ment area decreases with increasing α (due to not enough tilting of the piedmont) and Figure 6. Color maps of soil thickness near the point of maximum pediment area for (A) the P (due to too much soil cover). Increasing reference model, and alternative models illustrating the sensitivity of pediment area to varia- 0 the value of X leads to larger pediments for tions in individual parameter values. (B) α = 18 km, (C) P = 0.03 m/ka, and (D) X = 0.05 m–1. 0 otherwise similar parameter values, both In cases (B) and (C), virtually no pediment forms because not enough tilting takes place in because erosion of the highlands proceeds (B), and there is too much soil cover in (C). In (D), the lower drainage density slows erosion faster (hence tilting is enhanced) and pied- of the mountain block and decreases hillslope incision on the piedmont, thus decreasing the mont soils are thinner. amount of tilting and increasing the thickness of soils on the piedmont, resulting in smaller pediments.

average. Other smoothing algorithms could also of this analysis, I mapped crystalline bedrock counts for most but not all of the granite in this be used, but the 5 × 5 pixel moving average as all pre-Cenozoic map units that are not sedi- region. Figure 10A illustrates a shaded relief im- worked adequately at minimizing contour arti- mentary rock. In southern Arizona, nearly all age of the DEM. The pediment map (Fig. 10B) facts while also minimizing the artifi cial steep- basalt, sediment, and sedimentary rocks are obtained by identifying all crystalline bedrock ening of piedmonts close to mountain fronts Cenozoic in age. As such, the pre-Cenozoic areas with a slope less than or equal to 10% is that is unavoidably introduced by smoothing. criterion works well for distinguishing crystal- illustrated in Figure 10B. Pediments of one size A “mask” grid of the presence and/or absence line rocks (excluding basalt) from sedimentary or another occur adjacent to nearly all mountain of crystalline bedrock was obtained by project- rocks in this region. Planation surfaces can ranges in southern Arizona. In this paper I chose ing the Arizona digital geologic map (Hirsch- form in sedimentary and basaltic rocks, but to highlight two specifi c pediment regions for berg and Pitts, 2000) to the same projection these are usually associated with the differential discussion: the Catalina and Oracle pediments and resolution as the DEM. The Arizona digi- erosion of strata or basalt fl ows, and hence are on the west and north sides of the Santa Catalina tal geologic map contains data on the lithology not included within the defi nition of pediments Mountains, respectively, and the Sierrita pedi- and age of all bedrock and sediment in the state adopted in this paper. Some granites in southern ment on the north side of the Sierrita Mountains resolvable at 1:500,000 scale. For the purposes Arizona are Cenozoic in age, so this map ac- (locations shown in Fig. 10A).

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Pelletier

A 3 km B outline of region A of active uplift

elevation U t = 20 Ma 0 3000 m P0 = 0.03 m/ka P0 = 0.05 m/ka x C D B θ P0sin

mountain front

t = 20 Ma P0 = 0.07 m/ka Figure 9. Grayscale maps of (A) topogra- Figure 8. Grayscale maps of model topography at t = 20 Ma for (A) P0 = 0.03 m/ka, phy and (B) soil thickness for a model with (B) P0 = 0.05 m/ka, and (C) P0 = 0.07 m/ka. (D) Schematic diagram illustrating how, once an the same total uplift as the reference model embayed mountain front forms, the effective rate of slope retreat increases. For this reason, but with a component of asymmetric tilting slope retreat in the model is a nonlinear function of P0, as illustrated in (A–C). [inset graph in (A)]. Pediments are best developed on the steep sides of the mountain block away from the direction of tilting. The pediments of the Santa Catalina Moun- syntectonic sediment deposition, burial, and ex- tains are best developed on the west and north humation. Most of the piedmont on the east side sides of the range (Fig. 11). These pediment of the range is a planation surface, and hence the 1991). In the second, post–mid-Miocene tec- surfaces are composed of the same granite that pediment is restricted to a small area on this side tonic event, faulting occurred along the high- makes up the steeper portions of the range. of the range because of this lithologic contrast. angle Pirate fault in a manner similar to the The pediment surface is dissected by bedrock The Santa Catalina Mountains are primarily block faulting associated with classic Neogene channels that are locally incised by as much as composed of granite and to a lesser extent by Basin and Range extension (Davis et al., 2004; tens of meters. These channels are also clearly mylonitic gneiss on the south side of the range. Wagner and Johnson, 2006). The initial phase infl uenced by the jointed structure of the Cata- The Santa Catalina Mountains are bounded on of extension was accompanied by tilting to the lina granite (Bezy, 1998; Pelletier et al., 2009; the south side by the low-angle Catalina detach- southwest, resulting in relatively steep western, Fig. 1B). Figure 1B indicates that the pediment ment fault (Fig. 11A) and on the west side by northern, and eastern edges of the range and a surface is characterized by a high drainage den- the high-angle Pirate fault (Figs. 1B and 11A). relatively gently dipping south and southwest- sity, i.e., despite the gentle slope of the surface Offset along these faults occurred in two sepa- ern fl ank characterized by larger drainages. The (<10%), channels are separated by ~10 m, im- rate intervals of deformation and uplift. In the model results illustrated in Figure 9 provide a plying values of X in the range of 0.1–1 m–1. The initial phase, late Oligocene–early Miocene basis for interpreting the asymmetry of the pedi- high drainage density on this surface may be offset occurred primarily along the Catalina ments fl anking the Santa Catalina Mountains the result of a combination of the lack of rego- detachment fault. Extension along an ~240° in terms of the south and southwesterly tilting lith and the jointed nature of the bedrock. On azimuth was accompanied by tectonic tilting of of the range during the initial phase of exten- the east side of the range, late Oligocene–early an extension-parallel topographic ramp and by sion. In the model of Figure 9, south-directed Miocene sedimentary rocks have been exhumed antiformal arching along a direction approxi- tilting leads to the development of steep moun- along the mountain front following a cycle of mately orthogonal to extension (Dickinson, tain fronts and well-developed pediments on

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How do pediments form?

114°W 113°W 112°W 111°W 110°W of the Santa Catalina Mountains in that it is characterized by relief on the order of meters rather 20 km A than tens of meters and because it has a discontinuous cover of alluvium that thickens downslope 34°N N into an alluvial apron (Bengert, 1981). As such, the boundary between the pediment and the alluvial apron is gradational in this case (Fig. 11). Tuan (1959) argued that the gradational nature of this contact suggests that the Sierritta Moun- tain pediment is an exhumed suballuvial bedrock bench. More generally, Tuan concluded, “care- ful observation of the pediments of southeastern 33°N Arizona reveals that most of them bear evidence of exhumation” (Tuan, 1959, p. 124). The Sier- rita pediment is more similar to the results of the model illustrated in Figure 4 than is the Catalina pediment. In the model, pediments are formed on the proximal end of the piedmont, giving way SCM to thicker soils and ultimately an alluvial apron with increasing distance downslope. The Cata- 32°N lina pediment, in contrast, is bounded abruptly SM on its eastern side by the Pirate fault. The Sierrita pediment is best expressed on its northern side shaded relief of DEM (Fig. 10B). This fact can be understood, in part, as a consequence of the fact that pediments re- B quire a suffi ciently low value of α/λ to generate suffi cient tilting to become erosional surfaces. If a range is separated from its neighboring ranges by varying distances, the model of this paper predicts that pediments will be most well developed on the side that is separated from its neighboring ranges by the largest distance (hence minimizing the value of α/λ, assuming uniform α). In the case of the Sierrita Mountains, the northern side of the range has the greatest distance from surrounding ranges, hence the pediment is expected to be most well developed on that side of the range. The fl exural-isostatic modeling of this paper can be tied more explicitly to the landscapes of southern Arizona by calculating the fl exural- isostatic response to erosion in southern Arizona. The erosion rates of different ranges are not precisely known, of course. Nevertheless, it is pos- pediment map sible to assume a uniform rate of erosion in all of the steep (>10%) portions of the region and then Figure 10. (A) Grayscale shaded relief map of southern Arizona. (B) Map of pediments to model the relative rates of fl exural-isostatic (white areas) in southern Arizona. Pediments were mapped as areas of crystalline bedrock rebound that would result from such erosion. with a slope of less than 10%. Focus areas (SCM—Santa Catalina Mountains, SM—Sierrita Figure 12 illustrates color maps of the fl exural- Mountains) located in (A). isostatic uplift in southern Arizona, expressed as a fraction of the total erosion, for different values of the fl exural parameter α. For α = 9 km (Fig. 12B), isostatic rebound ratio approaches the north, west, and east sides of the range. The The Sierrita Mountains were formed during its maximum (Airy isostatic) value of ~0.8. For pediments of the Santa Catalina Mountains have the same late Oligocene–early Miocene exten- larger values of α, the peak isostatic rebound a similar asymmetric distribution. This suggests sion that uplifted the Santa Catalina Mountains (and hence degree of piedmont tilting) decreases that tilting of the mountain block during late (Stavast et al., 2008). They did not take part in as the fl exural-isostatic response becomes more Oligocene–early Miocene extension is a likely late Miocene high-angle faulting and uplift, spatially distributed. For α = 17 km (Fig. 12D), cause for the asymmetric pediment distribution however, and hence they have lower relief. The for example, the maximum compensation is ap- on the fl anks of the Santa Catalina Mountains. Sierrita Mountains pediment differs from those proximately half of its value for α = 9 km, and

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Pelletier

A D 2 km C D N

C Pirate fault (high angle)

Catalina detachment fault pediment map w/ shaded relief

B E F

pediment map w/ shaded relief

Figure 11. Pediment maps overlain on shaded relief images for (A) Santa Catalina Mountains and (B) Sierrita Mountains. (C and D) Aerial photographs of pediments on the (C) west and (D) north side of the Santa Catalina Mountains, illustrating the low-relief, dissected nature of these pediments. In contrast, the Sierrita Mountains pediments (E and F) have a thin, discontinuous veneer of regolith and alluvium with tors and inselbergs dotting the landscape (E). the isostatic response to erosion within some of DISCUSSION must have undergone greater tectonic tilting in the more narrow ranges in southern Arizona is order to explain this lack of correlation between distributed across one or more adjacent ranges Cooke (1970) performed a detailed statistical pediment slope and length, a conclusion consis- and their intervening basins. Of the three maps analysis of 53 pediments in the western Mojave tent with the model of this paper. Cooke (1970) presented in Figure 12, the map in Figure 12C Desert in an attempt to develop diagnostic re- also documented essentially no correlation be- (corresponding to α = 13 km) produces a pattern lationships between the morphology of pedi- tween the area of the pediment and the area of of tilting most similar to the distribution of pediments and the mountain range drainage basins the drainage basins upslope from them in the ments in Figure 10B. This result lends support to upslope from them. Cooke documented a poor mountain range. If pediments expand primar- the value of α (i.e., 12 km) chosen for the model correlation between pediment length and slope, ily by backwearing of the mountain front, one reference case. The ﬂ exure maps in Figure 12 a surprising result considering that pediments would expect a negative correlation between cannot be used directly to reproduce the pedi- generally decrease in slope with increasing dis- pediment area and upstream drainage basin area. ment map of Figure 10B due to spatial variations tance downstream (hence, one would expect a Cooke (1970) interpreted the lack of such a cor- in α, mountain block erosion rates, etc. that are negative correlation between pediment length relation to imply that pediments grow primarily not well constrained using existing data. and slope). Cooke argued that longer pediments by exhumation of the suballuvial bench, not by

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How do pediments form?

A B 40 km

Figure 12. (A) Thresholded slope map for southern Arizona, used as input to the ﬂ exural- isostatic model. (B–D) Color maps of isostatic rebound, ex- SCM pressed as a fraction of the total erosion in the ranges, for thresholded slope map SM α = 9 km (B) α = 9 km, (C) α = 13 km, and (D) α = 17 km. As the value of α D increases in the model, tilting is C reduced (i.e., yellow and white colors, indicative of high mag- nitudes of isostatic rebound, are no longer present), and the isostatic rebound becomes more uniformly spatially distributed.

isostatic rebound (m/m)

0 0.8 α = 13 km α = 17 km

retreat of the mountain front. Cooke (1970) con- ing framework of this paper (which assumes a surface runoff, most likely increasing D and de- cluded: “the exhumation hypothesis for pedi- continuous elastic lithosphere). Never theless, creasing Smin (higher discharges require lower ment development deserves close examination the presence of pediment-bounding faults will threshold slopes to entrain sediment of a given in the western Mojave Desert” (Cooke, 1970, decrease the value of α locally, hence a predic- texture). Wetter climates generally have lower p. 36). The role of fl exural-isostatic rebound in tion of the model is that pediments are more drainage densities, X, within arid to semiarid pediment formation has not yet been proposed likely to form in areas of pervasive faulting. climates (e.g., Melton, 1957) because increas- in the pediment literature. As such, the model Pediment formation can also be infl uenced ing vegetation density increases soil resistance of this paper fi lls an important gap in the ex- by the rate of active uplift, U (as illustrated in to erosion. Given the sensitivity of X and espe- humation hypothesis since it provides a widely Fig. 5) and the angle of faulting. Higher uplift cially P0 to climate, it is reasonable to expect applicable mechanism for piedmont tilting. At rates and steeper faults both encourage pedi- that the climatic dependence of P0 and X (with larger spatial scales, fl exural-isostatic rebound ment formation because they promote greater greater aridity promoting pediment formation) has been recognized as an important process in channel and slope backwearing (which tends will dominate over the tendency for decreases

“pediplanation.” For example, ﬂ exural isostasy to lengthen the pediment) over downwearing in D and increases in Smin to prevent pediment has been invoked as a necessary component for (which does not). development in more arid climates. the formation of the stepped landscape of south- Climate controls pediment formation princi- Rock type also controls the values of P0, ern Africa (Pugh, 1955). pally through its control on the maximum rate Smin, X, and D. Rocks that are more resistant to

The model of this paper provides a working of bedrock weathering, P0. Pelletier and Ras- weathering have lower values of P0, and hence hypothesis for the relative roles of tectonics, mussen (2009) quantiﬁ ed the relationship be- are more likely to form pediments than less re- climate, and rock type in controlling the occur- tween P0, mean annual temperature, and mean sistant rocks. Rock type also controls Smin via rence of pediments. The tectonic style of a re- annual precipitation for granitic rocks based the texture of detritus that the rock weathers to gion controls the values of α and λ. Regions that on an analysis of cosmogenic-radionuclide– (on the hillslope) and abrades to (in the channel) are more extensively faulted are characterized derived erosion rates compiled from the lit- (Abrahams et al., 1985; Parsons and Abrahams , α by lower values of and hence are more likely erature. In ﬁ gure 3 of that paper, they showed 1987). Rock types that minimize both P0 and to form pediments under otherwise similar that P0 varies by several orders of magnitude Smin are ideal for pediment formation. The pres- conditions. This is consistent with correlations between arid and humid conditions. For this ence of granite, for example, facilitates pedi- between pediment occurrence and the presence reason, I emphasize the importance of climatic ment formation because it often weathers to of faults in the Mojave and Sonoran Deserts control on P0 as the principal role of climate on small particles (grus) (Pye, 1986) and there-

(Mammerickx, 1964; Cooke, 1970). The oc- pediment formation even though climate also fore results in lower values of Smin and possibly currence of faults that bound pediment surfaces controls the values of Smin, X, and D in the higher values of D (smaller particles are more cannot be explicitly accounted for in the model- model of this paper. Wetter climates increase readily transported).

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Pelletier

Pediment formation can occur for a range of production function compared to a humped pro- ACKNOWLEDGMENTS 2 values of P0/DX . As noted above, if the maxi- duction function. Nevertheless, bare slopes will mum soil thickness for classifying a piedmont form in either case provided that the value of I wish to thank Sebastien Castelltort and an anony- 2 mous reviewer for comments that helped improve the as a pediment is increased, e.g., from the 0.1 m P0/(DX ) is suffi ciently low. manuscript and Peter Kresan for permission to use his used here to the 2–4 m used by Strudley and The model of this paper has a number of limita- photographs in Figure 1. 2 Murray (2007), the range of P0/DX values tions. Most importantly, the model does not treat conducive to pediment formation will also in- erosion and deposition in a mass-conservative REFERENCES CITED crease. More work is needed, however, to nar- manner. 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