Relationships Among Climate, Erosion, Topography, and Delamination in the Andes: a Numerical Modeling Investigation

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. A plateau ⎛ yy− ⎞ SS=−⎜141max ⎟ if y < ° xe is the distance over which erosion takes exists for most of the model duration, hence max ⎝ yrange ⎠ place on one side of the orogen, Aec is the area the maximum and mean elevations are similar. ρ ρ =≥ of the eclogitic root, e and c are the densities For simplicity, we do not distinguish between SSmin if y41°, (4) of eclogite and crust, respectively (nominally eclogite produced by metamorphic reactions 3 3600 and 2750 kg/m ), x is the half-width of the and that produced magmatically. Although where Smax = 7 km/Ma (for a maximum shorten- orogen, he is the elevation above which precipi- there are signifi cant differences between these ing of 420 km in the central Andes, assuming tation decreases signifi cantly due to orography, two mechanisms, our approach is focused more 60 Ma of convergence, consistent with maxi- and α is the topographic slope of the fl anks of on developing the pressure conditions suffi - mum geologic estimates [McQuarrie, 2002; the orogen. Erosion in the model is assumed cient to maintain eclogite to a point at which Oncken et al., 2006]), Smin = 1 km/Ma, y is to be proportional to P and xe. Precipitation in it becomes gravitationally unstable. Numeri- latitude, ymax = 16° is the latitude of maximum the Andes decreases signifi cantly above 3 km cal models suggest that suffi cient pressure for shortening, and yrange = 25° (Kendrick et al., elevation (Bookhagen and Strecker, 2008) due eclogite production and maintenance (i.e., sta- 2006). The value of Smin is not well constrained, to orography. The distance xe in the model rep- bility of garnet in the lower crust) exists when but we assume a shortening rate of 1 km/Ma for resents the lateral distance over which signifi - the surface elevation reaches 3 km (Quinteros the Andes south of 41°. cant precipitation (and hence erosion) occurs et al., 2008). The root is assumed to delaminate The central Andes contain regionally exten- on the fl anks of the orogen below 3 km. Cor- when its cross-sectional area, Aec, is greater sive marginal marine sedimentary rocks of Maas- relations between long-term erosion rates and than a prescribed threshold value for delamina- trichtian to mid-Paleocene age (El Molino and

MAP rates in the Andes have been documented tion, Ade. If suffi cient pressure exists, eclogite Santa Lucía Formations) (Sempere et al., 1997; by Kober et al. (2007) and can be expected on forms in the model at a rate proportional to the Horton et al., 2001), indicating that the region 2 theoretical grounds (e.g., stream-power models shortening rate, at a rate PeS (in units of km / was near sea level ca. 60 Ma. As such, a reason- of bedrock channel erosion, e.g., Whipple and Ma) where Pe has units of kilometers. Math- able (although simplifi ed) starting point for the Tucker [1999]). Erosion is assumed to occur on ematically, the rate of increase in the area of model is no topography and initiation of short- both sides of the range with comparable rates the eclogitic root, dAec/dt, is given by ening at 60 Ma. The parameters for the model α (leading to the factor of 2 in Equation 1). As reference case are: = 0.025, hpl = 6 km, T = such, the variable E should refl ect a representa- 35 km (Beck et al., 1996), E = 0.0001, h = 3 km 1GSA Data Repository item 2010067, additional ec tive average of erosion rates on both sides of (Quinteros et al., 2008), he = 3 km (Bookhagen discussion of numerical model illustrating the rela- 2 the orogen. tionships among climate, erosion, topography, and de- and Strecker, 2008), Ade = 2500 km , Tde = 3 Ma, Although the modern Andes are an asym- lamination in the Andes, and an animation of the Ce- and Pe = 18 km. These values were determined metric two-sided orogen, here we assume a nozoic topographic evolution of the Andes, with color using empirical data where constraints are avail- symmetric two-sided orogen with topographic representing elevation (black, red is low elevation; able (described in the Data Repository) together α yellow, white is high elevation), is available online at slope = 0.025 (m/m) on the fl anks because www.geosociety.org/pubs/ft2010.htm, or on request with a parameter tuning procedure that simulta- the asymmetric shape of the modern Andes is from [email protected] or Documents Secre- neously honors the modern topography of the likely a relatively recent development (Oncken tary, GSA, P.O. Box 9140, Boulder, CO 80301, USA. Andes along their length from 5° N to 50° S and

260 GEOLOGY, March 2010 the timing of inferred delamination events in the Figures 2A–2C illustrate the application of the in the central Andes, more time is needed to central Andes, where a late Miocene event has model to the length of the Andes from 5° N to reach the threshold for delamination, and in the been inferred from multiple studies and a mag- 50° S. To obtain these results, shortening rates northern and southern ends of the Andes the matic ﬂ areup at ca. 45 Ma indicates that delami- (Equation 4) and MAP rates (extracted from threshold is never reached. This is consistent nation also may have occurred during the mid Legates and Willmott [1990]; Fig. DR3) for 1° with available data from the Andes, where more Cenozoic (Haschke et al., 2002; DeCelles et al., latitude bins were input into the model. All of recent delamination has been inferred in the 2009). Using the modern topography as a model the remaining parameter values were set equal topographically higher Puna Plateau compared constraint is appropriate given that our goal is to to those of the reference case. Figure 2A (also to the Altiplano, which may be lower because constrain the paleotopographic history and rates see animation in the Data Repository) illustrates the next cycle of eclogite production is already of crustal sources and sinks leading up to the the mean elevation as a function of time and under way (DeCelles et al., 2009). Model results modern state. latitude in the model, illustrating the pulses of for modern topography are shown in Figure 2B surface uplift that result from delamination. The with three different values of E, illustrating the MODEL RESULTS model suggests that delamination events are time robustness of the model with respect to uncer- Example output of the model is illustrated in transgressive, with removal ﬁ rst occurring in the tainty in the erosivity value. In the central Andes, Figure 1B for a relatively humid (P = 3 m/a) and central Andes near 20° S because that region has the mean Cenozoic rate of mass removal by a relatively arid (P = 0.5 m/a) case. The short- undergone the optimum combination of high eclogite production, Ep, is much larger than the ening rate is assumed to be 7 km/Ma in order tectonic shortening rates and aridity. Elsewhere rate of removal by erosion, Eg (Fig. 2C). From to isolate the effects of climatically-controlled 3°S to 36°S, Ep > Eg, while in the northern and erosion in this comparison. Figure 1B illustrates southern Andes erosion is dominant, i.e., Ep < Eg. the maximum and mean elevations as a func- 6 Late Miocene tion of time from the beginning of the model A delamination CONCLUSIONS

(i.e., t = 0). Mean elevation increases through Mid Cenozoic Tectonic shortening, climatically-controlled time until an eclogitic root begins to form at t = delamination erosion, eclogite production, and delamination (km) ca. 4–5 Ma. The negative buoyancy associated h 3 all exert signiﬁ cant control on the evolution of with the eclogitic root keeps the maximum ele- the Andes. These processes are coupled, how- vation close to 3 km until delamination occurs at ever, and hence a multi-disciplinary approach t = ca. 25 Ma in the arid case and t = ca. 30 Ma is needed to understand the feedbacks among in the humid case. In the humid case, eclogite 60 them. Here we described a mass-conservative 30 0 grows more slowly because erosion periodically t (Ma) -50 -40 -30-20 -10 0 model that self-consistently honors the topog- y (o) reduces the surface elevation below the thresh- 3.5 raphy of the modern Andes and the timing of old for eclogite production, thereby delaying E = 0.00005 inferred Cenozoic delamination events. Our 3.0 E = 0.0001 B the delamination event relative to the arid case. E = 0.0002 model illustrates that while erosion likely Delamination triggers maximum surface uplift 2.5 Observed plays a relatively minor role in exporting mass (km) ¯ of 1 km, followed by a second phase of eclogitic h 2.0 from the central Andes, it exerts an additional production (which causes surface elevations to 1.5 control on topography by modulating the tim- increase more slowly or to decrease, depending ing of delamination events. This suggests that 1.0 on climate) until a second, late Cenozoic delam- feedbacks between geomorphic, petrologic, and ination event occurs. Delamination is accompa- 0.5 geodynamic processes play a signiﬁ cant role in 0.0 nied by an abrupt 100 km increase in the width -50 -40 -30-20 -10 0 controlling along-strike variability in the mor- of the orogen (Fig. DR2). An increase in oro- y (o) phology of the Andes. 10,100 E > E 4 gen width accompanies delamination because C p g E - E E < E surface uplift creates gravitational body forces p g p g ACKNOWLEDGMENTS g

E We wish to thank Fritz Schlunegger, Patience /Ma)

- 3 2 m/a) that favor the migration of thrusting to lower p (

E P Cowie, and two anonymous reviewers for comments (km/Ma) S P elevations (Royden, 1996, Hilley and Strecker, (km

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