Relationships among climate, erosion, topography, and delamination in the Andes: A numerical modeling investigation Jon D. Pelletier*, Peter G. DeCelles, and George Zandt Department of Geosciences, University of Arizona, Gould-Simpson Building, 1040 East Fourth Street, Tucson, Arizona 85721–0077, USA ABSTRACT Cordilleran orogenic systems such as the Andes are controlled by shortening rates, climat- 1994; Beck and Zandt, 2002). The coupling ically-controlled erosion rates, and, in some cases, eclogite production and delamination. All between these processes makes any argument of these processes are coupled, however, making it diffi cult to uniquely determine the relative based solely on one or the other process incom- importance of each process and the feedbacks among them. In this paper we develop a mass- plete, however. Periodic cycles in Cordilleran balanced numerical model that couples an actively-shortening orogen and crustal root with systems involving shortening, arc magmatism, eclogite production, delamination, and climatically controlled erosion. The model provides a and the formation and subsequent gravitational fi rst-order quantifi cation of the sources (shortening) and sinks (erosion and eclogite produc- foundering of eclogite may exist and have a tion and delamination) of crustal volume during the Cenozoic in the Andes as a function of controlling infl uence on changes in retroarc and latitude and time. Given reasonable estimates for the rates of eclogite production and the forearc tapers and elevation (DeCelles et al., threshold size of the eclogitic root required for delamination, the model suggests that, in the 2009). Our goal here is to provide a fi rst-order central Andes between 5° S and 32° S, the orogen has grown to a suffi cient height to produce quantitative assessment of the potential magni- and maintain eclogite, which in turn has promoted delamination in the lower crust and man- tudes of these effects in a coupled model that tle. In this region, climatically controlled erosion rates infl uence the size of the orogen through can be used in testing the general concept of two separate mechanisms: by exporting mass via surface processes and by controlling the Cordilleran cyclicity. lithostatic pressure in the lower crust, which modulates the rates of eclogite production and/or delamination. To the north and south of the central Andes, relatively low shortening rates and MODEL DESCRIPTION high precipitation and erosion rates have slowed eclogite production such that delamination The numerical model of this paper is a two- likely has not occurred during the Cenozoic. dimensional representation of the Andes at a given latitude (Fig. 1A). The model is applied to INTRODUCTION poraneous with an eastward shift in the loca- different latitudes using tectonic data (i.e., short- The roles of tectonics, climate, and ero- tion of thrusting from the Eastern Cordillera to ening rates) and climatic data (i.e., mean annual sion, as well as the feedbacks among them, the Subandes in Bolivia. This interpretation is have attracted a great deal of interest in the controversial because the paleoelevation proxy past decade. As a modern convergent orogen data may partly refl ect a climatic signal (Ehlers A x h e that spans a wide range of climatic zones, the and Poulsen, 2009). Nevertheless, rapid eleva- pl h EPx EPx h e e Andes Mountains are an ideal natural labora- tion gain in the central Andes is also consistent e α tory for examining these processes and feed- with the isostatic response to delamination of x β S T backs. Shortening rate is clearly a fi rst-order a dense eclogitic root, the occurrence of which A w Mantle Crust control on the morphology of the Andes (Isacks, has been deduced independently from petro- lithosphere 1988; Kley and Monaldi, 1998; Oncken et al., logic, seismologic, and geodynamic studies Mantle P S 2006). The Andes achieve their greatest height (e.g., Kay and Abbruzzi, 1996; Beck and Zandt, e and width in the central region, where short- 2002; Sobolev and Babeyko, 2005; Schurr et Aec Eclogite ening rates (both long-term and measured by al., 2006). In Cordilleran systems, eclogite global position system [GPS]) are also highest forms by pressure-dependent phase transitions Delamination (McQuarrie, 2002; Kendrick et al., 2006). (Sobolev and Babeyko, 2005) and by magmatic 6 Arid The importance of climatically-controlled differentiation (Ducea, 2002). Eclogite forma- 5 Humid erosion on the morphology of the Andes has tion by both mechanisms, and subsequent grav- 4 also been emphasized in recent years (Hor- itational removal, may have signifi cant conse- (km) ¯ h ton, 1999; Montgomery et al., 2001; Strecker quences for topography. , 3 et al., 2007). Although climate and topogra- Because eclogite can only form when suf- h phy are closely correlated in many mountain fi cient lithostatic pressure exists, erosion may 2 belts worldwide, in some cases that correla- modulate the occurrence and timing of delami- 1 tion may be a result, not a cause, of mountain nation, establishing the possibility of feedbacks B 0 building (Molnar and England, 1990). Recent among climate, erosion, and eclogite produc- 02010 30 40 50 60 studies have also emphasized the role of lower tion and delamination. Geomorphologists tend t (Ma) crustal and upper mantle petrologic and geo- to conclude that erosion is the predominant Figure 1. A: Schematic diagram of the model, dynamic processes in controlling the evolution secondary mechanism controlling the morphol- illustrating key geometric and rate param- of the central Andes. Paleoelevation proxies ogy of the Andes (after differences in shorten- eters and infl ows and outfl ows of crustal indicate that the Altiplano-Puna region gained ing rate) (e.g., Montgomery et al., 2001; Meade volume (see text for defi nitions). B: Plots− 1.5–3 km in elevation during late Miocene and Conrad, 2008) while geophysicists and of maximum and mean elevation, h and h, produced by the model for a relatively humid time (Garzione et al., 2008), an event contem- petrologists tend to conclude that the presence (mean annual precipitation, P = 3 m/a, gray or absence of eclogite production and delami- line) and a relatively arid (P = 0.5 m/a, black *E-mail: [email protected]. nation is the key secondary factor (Kay et al., line) case with shortening rate, S = 7 km/Ma. © 2010 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. GEOLOGY,Geology, March March 2010; 2010 v. 38; no. 3; p. 259–262; doi: 10.1130/G30755.1; 2 fi gures; Data Repository item 2010067. 259 precipitation [MAP] rates) specifi c to that lati- et al., 2006). This value for α was chosen to dA ec =<≥PSif A A and h h tude. The model tracks the rate of change of match data for the ratio of the mean height to dt eecdeec crustal mass as the difference between infl ows the width of the modern Andes. Figure DR1 in =<< 0 ifAAec de and hhec 1 (shortening) and outfl ows (erosion, eclogite the GSA Data Repository plots this data from − A removal) and partitions the crust into changes in the model (applied to the length of the Andes = de if AA≥ . (3) T ec de orogen height and width according to isostatic from 5° N to 50° S) using α = 0.025 (m/m). de balance and a prescribed topographic slope at While the ratio of mean height to width is the fl anks of the orogen until the orogen grows guaranteed to match the average value for the In the model, delamination and the accompa- high enough for a plateau to form. Once a pla- modern Andes, the absolute height and width nying surface uplift and thrust-tip propagation teau forms, the topography becomes trapezoidal of the model at different latitudes are emergent take place over a time scale tde = 3 Ma, consistent in cross section and an increase in the cross- properties that depends on sources and sinks of with geophysical models (Molnar and Garzione, sectional area of the crust manifests itself as an crustal volume and their variation with latitude 2007) and paleoelevation proxies (Garzione et increase in the orogen width without an increase and time. An increase in crustal mass translates al., 2008). Geometric relations and isostatic in maximum height because gravitational poten- into an increase in orogenic half-width via balance (see the Data Repository) provide the tial energy limits the maximum elevations of (DeCelles and DeCelles, 2001) remaining equations. orogens (Molnar and Lyon-Caen, 1988). When applying the model to the Andes, input The rate of increase (t, time) of the cross- data are needed for the latitudinal variation in dx 1 dA sectional area (A) of the crust, dA/dt, is the sum = , (2) shortening rates. Kendrick et al. (2006) used dt x()αβ+ dt of the product of shortening rate, S, and the GPS measurements to infer a linear decrease thickness of the crust in the foreland, T, minus in convergence and/or shortening rates from a erosion and the conversion of crust to eclogite: where β is the slope at the base of the crust. The maximum value at 16° S to a value one fi fth as value of β is allowed to vary as determined by great at 34° S. Schellart (2008) also documented dA ρ dA dA isostatic balance of the topographic load and the a linear relationship between convergence rate =−ST20 EPx −eecif ec > e ρ crustal and eclogitic roots. and lateral slab edge distance. These studies dt c dt dt In cross section, an eclogitic root grows in suggest that the most appropriate functional dA =− eec < ST2 EPxe if 0 , (1) the model when the maximum elevation (a form for shortening rate is given by a piecewise dt proxy for lithostatic pressure) is greater than a linear function of latitude, i.e., α where xe = min(x,he/ ), E (dimensionless) is the certain threshold value, hec, required for eclog- erosion rate per unit precipitation rate P (m/a), ite production and maintenance.