Late Cenozoic surface uplift of the southern Sierra Nevada ( California , USA ) : A paleoclimate perspective on lee-side stable isotope paleoaltimetry

Late Cenozoic surface uplift of the southern Sierra Nevada (Sierra; California, United States) is widely debated. Recent interpretations of lee-side isotope records from the southern Sierra suggest that the elevation of the southern Sierra has been sufficiently high to induce atmospheric flow patterns similar to modern patterns since the mid-Miocene, at ca. 12 Ma. The tendency for flow to deflect around a topographic barrier can be determined by the atmospheric stability, barrier height, and incoming wind speed. We test the sensitivity of flow deflection to elevation to determine what elevation would have been sufficiently high to establish modern flow patterns in the mid-Miocene. Using global paleoclimate models and idealized regional weather models, we find that the Miocene atmosphere was more stable than modern. We suggest that in a Miocene climate, flow patterns similar to modern patterns could have been achieved for elevations as low as 2 km, and that while Miocene lee-side isotope records from the southern Sierra may indicate that the southern Sierra has been a longstanding topographic feature, they may not have changed significantly in response to proposed late Cenozoic surface uplift of the southern Sierra.

Late Cenozoic surface uplift of the southern Sierra Nevada (California, USA): A paleoclimate perspective on lee-side stable isotope paleoaltimetry

INTRODUCTION
Several lines of evidence suggest that the southern Sierra Nevada (Sierra; California, United States) has undergone 1-2 km of surface uplift over the past 20 m.y.(Wakabayashi, 2013, and references therein).Interpretations of lee-side stable isotope-based paleoaltimetry studies suggest that the southern Sierra was high enough to induce atmospheric flow trajectories similar to modern trajectories since ca.12 Ma (Mulch, 2016), but the elevation required to support modern flow trajectories is poorly known, and the extent to which lee-side proxies can constrain late Cenozoic surface uplift of the southern Sierra is still debated.Lechler and Galewsky (2013) showed that air parcel trajectories tend to travel around the highest part of the southern Sierran topography, but the focus therein was exclusively on the modern climate, leaving open the key question of whether modern flow deflection observed in the southern Sierra persisted through past climates.If past climates supported significantly less flow deflection than we see today, then lee-side isotope-based proxy records may have had the potential to faithfully record changes in the elevation of the southern Sierra associated with the proposed late Cenozoic surface uplift.The goal of this study is to explore the extent to which paleoclimate may have influenced flow deflection and leeside isotope-based paleoaltimetry proxies in the southern Sierra during the late Cenozoic, a key period for understanding the surface uplift history of the Sierra.

BACKGROUND Miocene Tectonics of the Southern Sierra
The tectonic evolution of the northern and southern Sierra is a topic of considerable debate, and their surface uplift histories are thought to be significantly different from each another (e.g., Chamberlain et al., 2012;Wakabayashi, 2013;Gabet, 2014;Mulch, 2016, and references therein).In this paper we focus exclusively on the southern Sierra, south of the Stanislaus River and north of the Kern River (Fig. 1).Clark et al. (2005) and Wakabayashi (2013) proposed two pulses of surface uplift in the southern Sierra over the past 20 m.y.The first pulse may have been driven by the opening of a slab window during the northward migration of the Mendocino triple junction (Wakabayashi, 2013).The event began in the Kern and Kings river drainages ca.20 Ma, migrated north through the San Joaquin River drainage between 10 and 6 Ma, and then through the Mokelumne and Stanislaus river drainages ca.4-3.6 Ma (Mahéo et al., 2009).The second pulse was relatively synchronous between the southern Sierra river basins and may have been driven by the delamination of high-density material beneath the southern Sierra after 3.6 Ma (Ducea and Saleeby, 1996).
Early interpretations of lee-side isotope records for the southern Sierra suggested that the stability of precipitation d values over time indicated that there may have been relatively little surface uplift since ca.18 Ma (Poage and Chamberlain, 2002;Crowley et al., 2008).More recent interpretations highlight -some of the limitations of the technique (e.g., Mulch, 2016;Chamberlain et al., 2012) and suggest that the southern Sierra may have been sufficiently high to induce flow patterns similar to modern patterns since ca.12 Ma (Mulch, 2016).Here we address the question of how high is sufficiently high to induce flow patterns similar to modern patterns in the southern Sierra and the implications this has for understanding the evolution of the southern Sierra in the late Cenozoic.

Sierra
Until recently, one of the major, if implicit, assumptions in lee-side isotope-based paleoaltimetry models is that atmospheric flow around and a mountain range is two-dimensional (2-D), implying that lee-side isotope records come from air masses that have traveled west to east and surmounted the range crest.As an air mass is lifted along the windward side, water vapor condenses, and the heavier isotopes are preferentially rained out.With increasing elevation, and as the air mass reaches the lee side, d values are increasingly more negative.The magnitude of change in the isotopes across the range crest into the lee side is thought to record the maximum elevation along that path (Chamberlain and Poage, 2000).However, the stable isotope composition of waters in the Great Basin is not consistent with 2-D atmospheric flow over the southern Sierra.Most of the precipitation that reaches the eastern Great Basin was deflected to the north or south of the range (Friedman et al., 2002).Modern trajectory analyses for locations on the lee side of the Sierra find that flow is diverted around, rather than over, the highest topography (Lechler and Galewsky, 2013).This is especially true in the southern Sierra, where deflection dominates the flow path for areas above 2.5 km.
Atmospheric flow over topography can be understood in terms of the nondimensional flow parameter Nh/U, where N is the Brunt-Väisälä frequency (s -1 ), h is the mountain height (m), and U is the horizontal wind speed (m/s) (e.g., Epifanio and Durran, 2001).Idealized models of atmospheric flow around topographic barriers suggest that when Nh/U << 1, flow tends to pass over the topographic barrier, but when Nh/U >> 1, flow tends to be deflected around the topographic barrier (Galewsky, 2009).In order for lee-side proxies in the southern Sierra to have quantitatively recorded the highest elevations, Nh/U during the Mio cene needed to be lower than modern.

Atmospheric Stability of the Sierra
To determine how changes in climate influence flow deflection in the Sierra, we calculated the annual and storm average upstream flow parameters for simulations of a preindustrial (PI) and a Miocene climate.The simulations were run using the Community Earth System Model (CESM) version 1.0.5 (Gent et al., 2011).The atmospheric components of our simulations were configured with an ~2° × 2° horizontal resolution and 26 vertical levels.The PI simulation was run with boundary conditions representing the year A.D. 1850.The Miocene simulation was forced with vegetation, topography, and CO 2 representing 20-14 Ma, and was run for >2000 yr to ensure equilibrium.The Miocene simulation was updated from Herold et al. (2011) (more details can be found in the GSA Data Repository 1 ).
The upstream flow parameter calculations apply to both the northern and southern Sierra.We establish a windward and leeward region for both the PI and Miocene Sierra.The windward region is the area to the east of the coastline and the west of the range crest for the length of the Sierra.The leeward region is the area between the range crest and 2° of longitude east for the length of the Sierra.The upstream flow parameters are regional averages from the windward region.Due to the coarse resolution of the CESM simulations we do not calculate the Brunt-Väisälä frequency; instead, we calculate the static stability, a measure of the change in temperature with height that determines the Brunt-Väisälä frequency (Frierson, 2006).The moist static stability (q ez ) is the difference between the saturated equivalent potential temperature at 400 hPa and the equivalent potential temperature at the surface.The dry static stability (q z ) is the difference between the potential temperature at 400 hPa and the potential temperature at the surface (Frierson, 2006).U is an average of the wind speeds between 500 hPa and the surface.Because lee-side isotope records are generated during lee-side precipitation, we calculate storm averages for q ez , q z , and U. A storm was selected if there was precipitation in both the leeward and windward region.

Simulations of Flow Around Idealized Terrain
Using the Weather Research and Forecasting (WRF) model version 3.5.1 (Skamarock et al., 2008) we ran idealized simulations to determine the climate conditions required for the 2-D assumptions used in the lee-side proxies to faithfully record the elevation in two idealized topographic scenarios: (1) a 2.5-km-high uniform ridge (low southern Sierra), and (2) a 2.5-kmhigh ridge with a 4-km-high southern region (high southern Sierra).These are idealized scenarios to develop our intuition about flow over Sierran-scale topography and do not necessarily embody any particular theory for the geological evolution of the Sierra.The model domain is 564 × 250 points with 4 km horizontal grid spacing and 121 unevenly spaced vertical levels extending to 30 km.
First, we tested the sensitivity of flow deflection to the high southern Sierra model to changes in the atmospheric conditions during a storm-like event.The high southern Sierra model topography is based on the modern configuration of the Sierra, and is a 500-km-long by 80-km-wide ridge (Fig. 2A).The atmospheric conditions are set by the moist Brunt-Väisälä frequency (N m ).We used a constant U for all simulations, the average incoming storm wind profile from the PI and Miocene.Surface winds were set at 5 m/s, increasing to 30 m/s at the tropopause (~11 km), and decreasing to 10 m/s at the model top (Fig. 2B).Initial conditions are after Galewsky (2008).Each simulation has an initial relative humidity of 98% and surface temperature of 16 °C.Above the tropopause we use a dry Brunt-Väisälä frequency (N d ) of 0.02 s -1 .
To test the sensitivity of flow deflection to elevation and the low southern Sierra model, we ran simulations of flow deflection around a uniform ridge, ranging in elevation from 1 to 3.5 km, under a less stable climate.We used a low value of N m to quantify flow deflection for low values of Nh/U.The ridge length, width, and the initial atmospheric conditions are the same as in previous simulations.
To quantify flow deflection, we ran a forward trajectory analysis using Read/Interpolate/Plot version 4.6 (www2.mmm.ucar.edu/mm5 /WRF _post /RIP4.htm).The trajectories started 100 km upstream of the ridge and extend from the model surface to 2 km in elevation with 100 m vertical and 4 km horizontal grid spacing.We selected 2 km to capture air masses that travel up the windward face of the topographic barrier.

PI and Miocene Atmospheric Stability
Our first goal was to determine whether the climate during the Miocene was sufficiently different from modern and whether that climate supported 2-D or 3-D atmospheric flow in the southern Sierra.We calculated the annual and storm average upstream flow parameters for the Sierra for both the PI and Miocene simulated climates.For the PI simulation, the annual average q ez = 28 K and q z = 23 K.The annual average U = 5.6 m/s.For the Miocene simulation the annual average q ez = 48 K and q z = 29 K.The annual average U = 5.4 m/s.For the PI simulation the storm average q ez = 32 K and q z = 26 K.The storm average U = 9.2 m/s.For the Miocene simulation the storm average q ez = 46 K and q z = 31 K.The Miocene storm average U = 8.2 m/s.Both Miocene q ez and q z were higher than the PI, meaning that the Miocene Sierran climate was more stable than modern.From relative values of Nh/U for the Miocene and PI climates, assuming a high southern Sierra, Nh/U would have been greater during the Miocene.Thus, the Miocene climate as simulated here was even more stable than modern, and would have supported even greater flow deflection around a modern southern Sierra topographic configuration.Although the Miocene simulation is forced with climate conditions for 20-14 Ma, there is no evidence to suggest that after 14 Ma it was significantly less stable than modern.

Simulations of Flow Deflection
Although our results suggest that Miocene climate was more stable than modern, there is still a question of whether a less stable climate would support 2-D flow in the southern Sierra.
Here we quantify the degree of flow deflection around the high southern Sierra model for a range of stabilities.As the threshold elevation and Nh/U increase, the percentage of trajectories that surmount the high ridge decreases (Fig. 2C).When Nh/U > 1.1, none of the trajectories surmount the 4 km ridge crest.When Nh/U < 1.1, <5% of trajectories surmount the 4 km ridge crest.For a threshold elevation of 2.5 km, very few of the trajectories surmount the highest elevations of the ridge crest; <15% of trajectories surmount 2.5 km when Nh/U > 1.1.
We also tested the sensitivity of flow deflection to changes in elevation.For simulations of flow around a uniform ridge, as elevation increases, the percent of trajectories surmounting the ridge crest decreases (Fig. 3).For a ridge with a maximum elevation of 2.5 km, <50% of trajectories surmount the ridge crest.For a 2 km ridge where N m = 0.0075 s -1 , near low modern storm values (see the Data Repository), 42% of trajectories surmount the 2 km ridge crest.For a low ridge under modern conditions, >50% of atmospheric flow would be deflected around the mountain range, suggesting that modern patterns of flow deflection could have been established before late Cenozoic uplift of the southern Sierra.

DISCUSSION
Our results are summarized in Figure 4, which outlines the two idealized topographic models of the southern Sierra and the changes in atmospheric flow under modern and Miocene climates.Figures 4A and 4B represent the modern Sierra in a modern climate.Under modern conditions, Nh/U is high and atmospheric flow is deflected around the high southern Sierra (Lechler and Galewsky, 2013;Friedman et al., 2002).Under modern conditions we would not expect air masses to surmount the southern crest or for lee-side precipitation isotopic composition to record the elevation of the southern Sierra.Instead, air masses travel up the windward face to 2-2.5 km, and deflect around the southern crest before reaching the lee side, recording the degree of flow deflection.In order for lee-side isotope proxies to quantify the extent of late Cenozoic uplift, incoming air masses must travel perpendicular to the range and over the southern crest before reaching the lee side.Therefore, Miocene Nh/U needed to have been significantly lower than modern.This was not the case.greater.If the southern Sierra were 2-2.5 km high during the Miocene, deflection may have already dominated the flow path.
In a 2-D model of purely orographic precipitation, the incoming air is lifted and cooled, and the heavier isotopes are preferentially condensed and rained out along the windward path.Subsidence in the lee may then suppress further precipitation downstream.In this case, there may be no leeside record of elevation in meteoric waters.Pure orographic precipitation is rare, however; more typically, precipitation in the Sierra is orographically enhanced within a larger scale weather system (e.g., Galewsky and Sobel, 2005).If the storm traveled west to east and over the range crest, downstream d values in the remaining water vapor may retain a signal of elevation, and would be more negative than if that same storm was deflected around the south of the range.
Although there are many reasons why orographic precipitation d values may not strictly record the elevation of a range crest (e.g., Rohrmann et al., 2014;Insel et al., 2012), we focus here solely on the influence of flow deflection.Nh/U determines the tendency of an air mass to surmount a topographic barrier; when Nh/U is high, air masses tend to be deflected around the barrier and there is limited orographic influence on the isotopic composition.Precipitation from an air mass traveling perpendicular to the range front and deflected around the crest would have higher d values than an air mass that traveled over the range crest to that same lee-side location.If deflection around the range crest was the primary pathway through time, the d values on the lee side might change relatively little with changes in elevation.Mulch (2016) suggested that the southern Sierra was high enough to induce air mass trajectories similar to modern trajectories since ca.12 Ma.Our results suggest that the modern pattern of flow deflection around the southern Sierra may have been established when the southern Sierra exceeded an elevation of 2-2.5 km and that such conditions would have been the case since the Miocene.The proposed late Cenozoic surface uplift of the Sierra Nevada is thought to have increased the elevation of the southern Sierra from 2 km to 4 km (Wakabayashi, 2013).Our results suggest that lee-side proxy records would thus have been dominated by flow deflection even before such surface uplift occurred, and may simply reflect the long-term presence of topography in the southern Sierra.

CONCLUSIONS
The goal of this paper was to determine the elevation at which atmospheric flow patterns similar to modern patterns would have been established for the southern Sierra Nevada, and to explore the implications of that result for understanding the late Cenozoic geodynamic evolution of the southern Sierra.Our results suggest that Miocene climate was even more stable than modern and that atmospheric flow deflection in the Miocene could have dominated flow patterns for elevations as low as 2 km.As a result, leeside isotope records for the southern Sierra may only indirectly record late Cenozoic surface uplift due to the 3-D nature of flow in the southern Sierra.We conclude that flow patterns similar to modern patterns in the southern Sierra could have been achieved for elevations as low as 2-2.5 km during the Miocene and that lee-side isotope records may only indicate that the southern Sierra has been a longstanding topographic feature.We further conclude that there may be no conflict between lee-side isotope records in the southern Sierra and the body of evidence in support of late Cenozoic uplift of the southern part of the range.

Figure 1 .
Figure 1.Topography of the Sierra Nevada (California, USA).The late Cenozoic surface uplift of the southern Sierra is focused on the region to the south of the San Joaquin River and to the north of the Kern River.The solid lines are major rivers: 1-Mokelumne; 2-Stanislaus; 3-San Joaquin; 4-Kings; 5-Kern.Dashed line marks the Sierra range crest.Stars mark the d 18 O sampling locations for the southern Sierra (Poage and Chamberlain, 2002).The enclosed dashed line marks the region where low dD values from 17 volcanic glass samples (Mulch et al., 2008) are interpreted as indicating the establishment of similar-to-modern flow deflection since ca.12 Ma (Mulch, 2016).
Figure 2. A: Model domain and idealized terrain.Topographic setup for the high southern Sierra (California, USA) model: the high ridge is 4 km and the low ridge is 2.5 km; contour intervals are 500 m.The gray region is the initial trajectory positions; the arrow indicates the direction of the incoming winds.B: Initial vertical wind conditions.C: Points indicate the percentage of trajectories that pass over the threshold elevation for the idealized high Sierra.Low values of modern Nh/U (N is the Brunt-Väisälä frequency, h is the mountain height, and U is the horizontal wind speed) calculated from North American Regional Reanalysis (http:// www .emc.ncep.noaa.gov /mmb /rreanl/) are in gray.Note that the y-axis only extends to 15%.

Figure 3 .
Figure 3. Percent of trajectories that surmount the ridge crest for a uniform ridge of different elevations.Moist Brunt-Väisälä frequency (N m ) and horizontal wind speed (U ) are the same for all simulations.Gray region marks the transition to flow paths that are dominated by deflection.

Figure 4 .
Figure 4. Summary of atmospheric flow deflection for the high and low southern (S.) Sierra models.Contours are for a simplified Sierra topography at 1 km intervals.Star marks an example location for lee-side proxies.Conditions for both the high and low southern Sierra models in the modern are the same; atmospheric flow deflection dominates the flow path to the lee side of the southern ridge.A: High southern Sierra model.B: Low southern Sierra model.C: For the high southern Sierra model, flow deflection would have been greater than modern.D: For the low southern Sierra model, flow deflection was likely >50% for a 2-2.5-km-high ridge.Due to the threedimensional nature of flow during Miocene and modern climates, lee-side isotope records for the southern Sierra m-ay only indirectly record late Cenozoic surface uplift.