- © 2014 by the Mineralogical Society of America
Landscapes are sculpted by a variety of processes that weather and erode bedrock, converting it into soils and sediments that are moved downslope. Quantifying erosion rates provides important insights into a wide range of questions in disciplines from tectonics and landscape evolution to the impacts of land use. Cosmogenic nuclides contained in quartz sediment provide a robust tool for determining spatially averaged erosion rates across scales ranging from single hillslopes to continental river basins and are providing fundamental clues to how landscapes evolve. Cosmogenic nuclides in buried sediments contain unique information about paleo–erosion rates up to millions of years in the past. This article explores some of the basic ideas behind various methods used to infer catchment-wide erosion rates and highlights recent examples related to problems in tectonics, climate, and land use.
At the grandest scale, Earth's topography represents an accumulation of potential energy from mantle convection and tectonics, balanced by decay from chemical weathering and physical erosion. Over timescales of 103–106 years, hillslope erosion, soil formation, and sediment accumulation define the distribution and fertility of soil upon which our societies depend. There is a critical need to understand how soil erosion from land use is depleting this natural resource and how modern rates compare with those from the past. Climate change also affects erosional processes in complicated ways, which can be difficult to discern without accurate measurements of erosion rates over various timescales.
Curiously, the problem is that the rate of erosion is a tricky thing to measure. It is a measure of something that isn't there anymore, and of how quickly it went away. What is needed is a sensitive way to measure how much material was once at a given place and the rate at which that material was lost to dissolution, erosion, and sediment transport. There have been a number of traditional approaches to the problem. For example, over long timescales (millions of years), one can use thermochronology to infer the rate of rock cooling due to exhumation by erosion from kilometers below the surface (Reiners and Shuster 2009).
Over very short timescales of years to decades, sediment and solute fluxes from a watershed can be monitored, but these measurements are difficult to make with accuracy and may not capture important but infrequent events. A better approach over time scales from decades to millennia is to measure sediment accumulation in lakes and reservoirs or in datable sedimentary deposits, such as alluvial fans. Unfortunately, these measurements require special circumstances and can be subject to considerable uncertainty due to spatial variations in sedimentation rate and in sediment-trapping efficiency.
There is an important middle ground over timescales of 103–105 years in which rocks weather and soils form, climate changes from glacial to interglacial, rivers incise or aggrade, and civilizations rise and fall. This is the timescale that belongs to cosmogenic nuclides. Over the past two decades, cosmogenic nuclides have emerged as the method of choice for inferring erosion rates over spatial scales that can be as small as a single outcrop to as large as watersheds spanning a continent.
DETERMINING EROSION RATES
Theory and Methods
Cosmogenic nuclides such as 10Be (half-life, t1/2, = 1.39 My) and 26Al (t1/2 = 0.702 My) are produced in minerals such as quartz by reactions with secondary cosmic ray neutrons, protons, and muons (for details see Dunai and Lifton 2014 this issue). These nuclides can be used to infer erosion rates because their production rates within a mineral grain depend on their proximity to the Earth's surface. Production rates decrease exponentially with depth in rock or soil (with a mean cosmic ray penetration length of ~60 cm in rock of density 2.6 g cm-3). For an eroding surface, this means that the cosmogenic nuclide concentration integrates the history of a grain's approach toward the surface. In other words, the cosmogenic nuclide concentration contained in a mineral grain today reflects how quickly the overlying mass went away.
Mathematically, it can be shown that the cosmogenic nuclide concentration in an eroding rock is inversely proportional to erosion rate (Lal 1991). Erosion, as used here, refers to the combination of physical erosion and chemical weathering that removes mass near the surface. Early in the development of cosmogenic nuclide applications, it was recognized that bedrock outcrops can be used to determine the denudation history of that particular rock. However, in the mid-1990s researchers realized that cosmogenic nuclides in detrital sediment grains can also be used to determine erosion rates [for reviews see Bierman and Nichols (2004) and Granger and Riebe (2013)].
Two key realizations led to interpreting cosmogenic nuclides in sediment. The first was that for a well-mixed soil eroding at steady state (and in the absence of a high degree of chemical weathering within the soil), the average concentration of cosmogenic nuclides in the soil is the same at all soil depths. This concentration is equal to the concentration contained in the surface of a rock outcrop eroding at the same rate. In other words, for a given erosion rate, a sample of well-mixed soil has exactly the same concentration as exposed bedrock. The effects of chemical weathering are somewhat more complex, as they vary with depth, and an entire research field has emerged dedicated to interpreting weathering rates with cosmogenic nuclides (e.g. Dixon and Riebe 2014 this issue).
The second key to interpreting cosmogenic nuclides in sediment is that for well-mixed stream sediment, the average concentration in the sediment yields the average erosion rate in the watershed (Fig. 1). This relies on the assumptions that sediment is supplied at a rate that is proportional to the erosion rate, that the mineral being analyzed (i.e. quartz) is evenly distributed throughout the entire catchment, and that the cosmogenic nuclide in question was absent before the rock approached the surface.
It is worth examining these assumptions in detail. We begin with the idea that detrital sediment from well-mixed soil on a hillslope has a cosmogenic nuclide concentration that is inversely proportional to the hillslope erosion rate. For a watershed that is eroding homogeneously (i.e. everywhere at the same rate), then the concentration in stream sediment is equal to that of the soils on the hillslopes and the stream sediment yields the erosion rate. In most cases we can ignore sediment storage and transport time in the stream system, which occurs much faster than the timescale of erosion rates, that is, the time to erode the landscape by 60 cm. For a watershed that is eroding heterogeneously, a surprisingly simple solution emerges if we consider the flux-averaged cosmogenic nuclide concentration. That is, areas of the landscape that are eroding quickly provide a large fraction of the quartz but have a low cosmogenic nuclide concentration; conversely, areas eroding slowly provide less quartz but have a high cosmogenic nuclide concentration. In this case, the average cosmogenic nuclide concentration in the sediment reflects the spatially averaged erosion rate from the entire watershed. Remarkably, the equation to determine the erosion rate from an entire watershed is functionally identical to the equation used to determine the erosion rate from a single eroding outcrop. For example, the cosmogenic nuclides contained in a single sample of sand can yield the spatially averaged erosion rate of a watershed ranging in size from the catchment of a small upland creek to the entire Amazon River basin (Fig. 2; Wittmann et al. 2011).
While the assumption of well-mixed and representative stream sediment may hold approximately true, landslides or other such episodic events may deliver an overwhelming load of sediment that temporarily biases the average. If the preponderance of a sample comes from just one landslide, then the inferred erosion rate will reflect primarily only that area. Moreover, if the landslide incorporates fresh bedrock or saprolite, then the cosmogenic nuclide concentration will be lowered and the inferred erosion rate will be faster than the long-term average. On the other hand, if landsliding dominates sediment delivery in the watershed, then it is important to sample that material or the inferred erosion rate will be too slow. The best solution is to sample a sufficiently large catchment with enough landslides so that any single event does not significantly influence the average cosmogenic nuclide concentration (e.g. Yanites et al. 2009).
Timescale of Erosion
The timescale over which in situ–produced cosmogenic nuclides measure erosion rates is one of the major strengths of the method, but this also limits the sorts of problems to which cosmogenic nuclides can be applied. Because cosmogenic nuclides integrate the history of production rates and because production rates fall off exponentially with depth, for a steady erosion rate the concentration is equivalent to the mineral residence time within the top 160 g cm-2 (~60 cm in rock of density 2.6 g cm-3, or ~1 m in soil of density 1.6 g cm-3). In other words, the timescale of bedrock erosion is equal to the time it takes to lower the landscape by ~60 cm, roughly equivalent to the timescale of soil formation in many landscapes. This timescale implies that cosmogenic nuclides effectively dampen rapid changes in erosion rate. If erosion rates change suddenly—for example, due to recent land use or climate change—then the cosmogenic nuclide concentration in the soil will change only slowly, with a response time determined by both the soil mixing depth and the time taken to erode ~60 cm of rock (Fig. 3). The damped response time means that the cosmogenic nuclide concentration measured in soils today represents the long-term average erosion rate, which is usually independent of recent changes in land use and soil degradation.
Examples of Catchment-Wide Erosion Rates
Over the past 20 years, erosion rates have been estimated by measuring the cosmogenic nuclides contained in thousands of river-sediment samples from virtually every climatic and tectonic environment in the world (e.g. Portenga and Bierman 2011; Covault et al. 2013 and references therein). Generally, these erosion rates are based on the measurement of 10Be produced in situ in quartz. Several persistent themes have emerged from the data.
One surprising conclusion from these cosmogenic nuclide–based erosion rates is that climate is less important for regulating erosion rates than previously assumed. While erosion rates certainly vary strongly under conditions of climatic extremes where erosional processes are fundamentally different (for example, erosion is slow in hyperarid deserts with little biological activity and fast in glacial and periglacial environments), climate generally plays a secondary role in determining erosion rates over most of the planet. Climate strongly affects the degree of soil weathering (Dixon and Riebe 2014), but the total erosion rate is more commonly determined by factors such as river and hillslope gradients that are adjusted to balance local uplift. Thus, erosion rates on low-relief continental shields are generally slow regardless of climate (~1–10 m/My), while they are much faster (~103–104 m/My) on rapidly uplifting mountain ranges.
The conclusion that landscape erosion rates are ultimately set by tectonics driving river incision and hillslope erosion rather than by climate has a number of implications. Perhaps the most important is that cosmogenic nuclide–based erosion rates can be used as a proxy for local river incision and uplift rates (e.g. Wobus et al. 2005). This is a powerful notion for landscapes at dynamic equilibrium because it suggests that a handful of sand can provide the local incision and uplift rates (Kirby and Whipple 2012).
The numerous cosmogenic nuclide measurements now available allow comparison of erosion rates over different timescales. Catchment-averaged erosion rates from cosmogenic nuclides can be compared to short-term suspended- and dissolved-sediment loads in rivers (e.g. Wittmann et al. 2011; Covault et al. 2013). Interestingly, Covault et al. (2013) found that the vast majority of cosmogenic nuclide–based erosion rates are faster than those inferred from monitored sediment yield. This tendency was first noticed by Kirchner et al. (2001), who invoked the importance of large but infrequent events in sediment delivery. While the abundances of cosmogenic nuclides average such variability, stream-gauging methods are likely to miss the largest and most important events that may happen only once in a decade or a century. In addition, sediment storage in floodplains tends to buffer rapid changes in sediment supply due to land use (Wittmann et al. 2011). Only in the most highly modified landscapes or in landscapes with very low sediment storage capacity do modern erosion rates consistently exceed cosmogenic nuclide–based erosion rates (e.g. Hewawasam et al. 2003).
If modern-day river sediment contains information about the erosion rate of its source area, then sedimentary deposits should be able to tell us about paleo–erosion rates and how erosion rates have varied through time in response to changes in climate or tectonics.
Estimates of paleo–erosion rates provide powerful insights into the behavior of ancient landscapes. It must be recognized, however, that the cosmogenic nuclides that are generally useful for determining erosion rates, such as 10Be and 26Al in quartz, are radioactive. Also, cosmogenic nuclide production does not fully stop even after several meters of burial. Thus, accurate paleo–erosion rate determinations require correcting for loss due to radioactive decay as well as continued production by deeply penetrating muons. The slower the paleo–erosion rate and the more deeply buried the sediment, the further back in time one can infer paleo–erosion rates—generally up to 5–10 million years.
Of course, accurate paleo–erosion rate determinations require knowing the depositional age of the sediment. But what if the age is not known independently? The beauty of cosmogenic nuclides is that it is possible to date the sediment directly using “burial dating.” Measuring at least two nuclides in the same mineral grains (such as 10Be, 26Al, and/or 21Ne in quartz; Balco and Shuster 2009) allows one to solve for the burial age and the paleo–erosion rate simultaneously.
Examples of Paleo–erosion Rates
A good example of how paleo–erosion rates can be estimated over glacial/interglacial timescales comes from the pioneering work of Schaller et al. (2002). In their study of sediments in terraces of European rivers, they found that erosion rates were roughly twice as fast during the Last Glacial Maximum (LGM) as they are today. Estimates show that the ~80 m/My determined for the LGM became much slower, to ~30–40 m/My, through the Holocene to the present. The faster rates may be due to frost-cracking and/or periglacial processes that accelerated erosion and soil transport during the LGM (e.g. Delunel et al. 2010).
Paleo–erosion rates can also be determined from buried sediment over much longer timescales of millions of years to decipher how landscapes have responded to climate change and tectonic uplift (Schaller et al. 2004). Paleo–erosion rates (and burial dates) allow one to explore how erosion rates and valley-incision rates have varied at the same site over millions of years, and thus to quantify how landscapes have responded to long-term climate change and uplift. For example, a compilation of paleo–erosion rate determinations that span million-year timescales (Fig. 4) records the varied responses of landscapes to the expansion of Northern Hemisphere glaciation near 2.5 My ago. Together these types of studies provide an opportunity to examine the influence of long-term climate change on hillslope erosion rates.
Measurements of cosmogenic nuclides also show that erosion rates have increased in many glaciated or partially glaciated watersheds, even during interglacials. This is true in the northern Swiss Alps (Haeuselmann et al. 2007), the Sierra Nevada of California, USA (Stock et al. 2004), and the Tian Shan in China (Charreau et al. 2011) (Fig. 4). Erosion rates have increased in some unglaciated watersheds as well, particularly in areas subject to a periglacial climate. Schaller et al. (2004) found increased erosion in the Meuse River, the Netherlands, likely due to both climate change and uplift of the Ardennes Mountains. A dramatic increase in erosion rate is documented in an unglaciated valley in the Sangre de Cristo Range, Colorado, USA (Refsnider 2010). Anthony and Granger (2007) studied sediment in caves along the Cumberland Plateau in the unglaciated southeastern United States and showed that paleo–erosion rates systematically increase in the Pleistocene hundreds of kilometers south of the Laurentide ice sheet margin. Interestingly, data from Mammoth Cave in central Kentucky (Granger et al. 2001) do not show any change in paleo–erosion rates across this same climatic transition, even though the site is closer to the ice margin.
DEVELOPING TRENDS: METEORIC 10BE
While the discussion thus far has focused on 10Be produced in situ within mineral grains, there is another, much larger, inventory of meteoric 10Be in soil. 10Be is produced in the atmosphere and delivered to the surface by wet and dry deposition (e.g. Dunai and Lifton 2014). As a fallout radionuclide, meteoric 10Be is incorporated into a variety of archives, including snow and ice; lacustrine, estuarine, and marine sediment; manganese nodules on the sea floor; and soil. Measurements of meteoric 10Be have been used to address a wide range of geologic problems, from snow and ice accumulation to sediment recycling in subduction zones. We focus here on the specific use of meteoric 10Be for determining erosion rates. For recent reviews, see Willenbring and von Blanckenburg (2010), Graly et al. (2010), and Granger et al. (2013).
Meteoric 10Be is a particle-reactive species that adsorbs strongly to mineral grains, particularly clays, for soil pH greater than about 6. Unlike in situ–produced 10Be, the meteoric variety migrates within the soil profile, to a depth determined largely by soil pH, soil texture, and grain size. More recently, the 10Be/9Be ratio of beryllium adsorbed to sediment has been used to simultaneously determine the erosion rate and the degree of chemical weathering of bedrock within a watershed. The 10Be is derived from meteoric fallout while the 9Be comes from the chemical weathering of bedrock (von Blanckenburg et al. 2012). Advantages of the meteoric technique are that only ~1 gram of fine-grained material is required and that the 10Be/9Be ratio is nearly independent of lithology.
During the early years of cosmogenic nuclide applications, meteoric 10Be was widely used for exploring surface processes because of its relatively high atmospheric concentrations. This approach, however, was largely eclipsed by measurements of the in situ–produced variety in the early 1990s as methods were developed for determining 10Be contained in quartz. Recent years have seen a resurgence in the meteoric variety's popularity, but one must recognize that beryllium mobility in the environment can be complex and is still poorly understood. Meteoric 10Be holds great promise for exploring erosion rates and sediment transport, as well as changing environmental conditions.
Cosmogenic nuclides are now the “gold standard” for determining erosion rates of rocks and watersheds. The method is rooted in the physics of energetic-particle attenuation, which allows geologists to query a rock about the material that used to be on top of it and the rate at which the material was lost. A handful of sand from a riverbed can tell us about the average erosion rate upstream. Sedimentary archives offer a unique record of how erosion rates have changed through time. Cosmogenic nuclides are finally allowing geologists to answer age-old questions about how the landscapes and soils around us reflect their combined legacy of climate, tectonics, and land use.
We would like to acknowledge the helpful comments by the guest editors as well as reviews by P. Belmont, B. Bookhagen, and V. Godard.