Abstract

During the Quaternary, extreme floods along the Durack River, in the Kimberley, northern Australia, dislodged, transported, and stacked massive meter-sized boulders from the underlying bedrock channel floor. Field evidence identified a population of the boulders to have been overturned after detachment. We measured in situ cosmogenic 10Be and 26Al concentrations in six imbricated boulders to constrain the timing of flood events. We present a simple numerical model that simultaneously solves the expressions for the predicted nuclide concentrations from the exposed and hidden surfaces of a flipped boulder to calculate the time since it was overturned. The ability of the model to unequivocally discern whether a boulder was overturned depends on boulder thickness and the site-specific steady-state erosion rate. Of the six boulders sampled, our model successfully determined four finite flip ages, whereas the other two boulders indicated steady state and were either not flipped or flipped sufficiently long ago for the nuclide profile to have returned to steady state. While the two older model ages (ca. 150 ka and ca. 260 ka) are strongly sensitive to assumptions made for the local erosion rate correction, the two younger flip ages, 5.6 ± 1.0 ka and 10.3 ± 1.9 ka, are robust against such corrections. Early to mid-Holocene major floods have been recorded in other parts of northern Australia. We suggest that similar Holocene floods occurred in the Kimberley and that such extreme events may have been widespread in northern Australia in the late Quaternary. Our boulder-flip model can be applicable to similar deposits associated with other extreme events such as paleo-tsunamis.

INTRODUCTION

Concentrations of in situ cosmogenic nuclides in bedrock, boulders, and sediments primarily reflect spatial and temporal information on landscape modification depending on the geomorphic context (Lal, 1991; Gosse and Phillips, 2001; Tuniz et al., 1998). While simple models for cosmogenic nuclide exposure dating assume that a sampled surface contains no inherited cosmogenic nuclides (e.g., glacially scoured bedrock or erratic), studies of more complex sedimentary sequences, such as river terraces, glacial tills, and eolian dunes, rely on modeling nuclide depth profiles to constrain simultaneously deposition age, erosion rate, and inheritance (Balco et al., 2005; Braucher et al., 2009; Fujioka et al., 2009). In principle, a depth profile from intact bedrock that has not experienced episodes of burial since its first exhumation can be determined on a single sample collected from shallow depths below the surface. However, when a bedrock slab is detached and overturned, such as is the case of flood-generated boulders in the Durack River, the Kimberley, northern Australia, the predicted depth profile no longer applies, and instead the deviation of a measured depth profile from that predicted can be used to estimate time elapsed since overturning.

In this study, we present a numerical model based on concentrations of in situ cosmogenic radionuclides, 10Be (half-life, 1.387 m.y.) and 26Al (0.705 m.y.), measured from the upper exposed and lower hidden surfaces of massive, flood-flipped boulders, to constrain the timing of extreme floods during the late Quaternary within the monsoon tropics of northern Australia. Records of paleo-floods are generally limited to the Holocene, preventing our ability to correlate changes in paleo-hydrology with different climate states (Nott and Price, 1999; Knutson et al., 2010). The present method has potential to extend the study of paleo-flood records to the past two glacial cycles (∼240 k.y.), providing the possibility to improve our predictions of extreme event frequency in the face of global warming.

BOULDER-FLIPPING MODEL

For a flipped boulder, a previously buried surface becomes exposed and a previously exposed surface is shielded (Fig. 1). The ratio of cosmogenic 10Be concentrations between these two surfaces will then deviate from a value predicted for a profile from intact bedrock (i.e., normal profile; Fig. 1A). For some time after flipping, the 10Be concentration of the currently buried surface (Y in Fig. 1B) must exceed that of the newly exposed surface (X in Fig. 1B). This inverse relationship will, with time, progressively return toward a steady-state profile (i.e., as if the boulder had never overturned), as the newly exposed surface will continue to receive a higher cosmic ray dose than the now-hidden surface (Fig. 1C). Prior to a steady-state profile being established, it is possible to calculate the timing of the overturning event via modeling the evolution of the 10Be concentration ratio between upper and lower surfaces of a flipped boulder.

Cosmogenic 10Be accumulating in a flipped boulder consists of two components: pre-flip (inheritance) and post-flip components. Assuming that initially the “boulder” had been intact within the channel bedrock, the inherited 10Be concentration in the currently exposed (previously hidden) surface, Ntop,inh (atoms g–1), can be determined from the inherited concentration of the hidden (previously exposed) surface, Nbottom,inh (atoms g–1), 
graphic
where ρ, Λ, and h are rock density (g cm–3), spallation attenuation length (g cm–2), and boulder thickness (cm), respectively. The depth profile of inheritance may not have achieved steady state or erosion equilibrium, which is not a prerequisite for our model because the concentration ratio of any two points within an intact bedrock profile will always satisfy Equation 1. Following an exposure of time T (yr) after a flip event, the top and bottom concentrations, Ntop and Nbottom (atoms g–1), respectively, are given by 
graphic
and 
graphic
where P is the site-specific nuclide spallation production rate (atoms g–1 yr–1), λ is the cosmogenic nuclide decay constant, and ε is the surface erosion rate after a flip event (cm yr–1). The first terms in Equations 2 and 3 represent decay-corrected inheritance since the flip event T years ago, with the second terms accounting for post-flip nuclide production at surface and at depth. For simplicity, we consider spallation reactions only (see the GSA Data Repository1).

Given measurement of boulder thickness and cosmogenic 10Be concentrations in both surfaces (Ntop, Nbottom), three unknowns remain: Nbottom,inh, ε, and T. If ε is independently determined from local bedrock with similar lithology at erosional equilibrium, then the flipping age T and inheritance Nbottom,inh can be obtained by simultaneously solving Equations 2 and 3. If a normal, exponential depth profile is observed, we cannot uniquely distinguish whether the boulder had been overturned in the distant past or had never been overturned. Model sensitivity to determine a finite flip age depends largely on boulder thickness and time since flipping compared to time for arriving at erosion equilibrium in a given locality and lithology. Our model can determine flip ages up to ca. 250 ka for sandstone boulders ∼1 m thick in northern Australia, where erosion equilibrium is attained at 2–5 mm k.y.–1 (Heimsath et al., 2009; Ward et al., 2005).

SITE AND SAMPLE DESCRIPTION

The Kimberley, northern Australia, has a tropical, semi-arid climate with monsoonal rainfall and frequent storms during the austral summer. Jack’s Waterhole (15.83°S, 127.41°E, ∼220 m above sea level), located in an ∼500-m-wide, ∼1.5-km-long sandstone gorge (Derrick et al., 1969) of the Durack River, is ∼70 km from the Cambridge Gulf and fed by a 12,000 km2 upstream catchment (Fig. DR1 in the Data Repository). On the eastern flank of the gorge, a wide flat bedrock platform, a few meters above the modern channel, contains numerous sets of hydraulically plucked rock slabs, which have been transported and stacked into imbricated piles (Fig. DR2A). The boulder piles are arced concave downstream (Fig. DR2B), indicating that massive flooding funneled through the gorge can attain sufficient power to pluck slabs out of the bedrock channel floor (Wende, 1999). Layered sandstone bedding and vertical jointing result in platy imbricated slabs ranging in thickness from 0.5 to 2 m, and with surface areas of ∼5–25 m2. Distinct differences in their upper and lower surface morphology (e.g., sharp, fresh joint breaks, fracturing, dissolution pits, rock vanish) as well as orientation of bedding patterns between fractured and intact faces (Fig. DR2) indicate that a population of the boulders has overturned.

We collected thin fragments (∼2–4 cm thickness) from exposed and hidden surfaces of six boulders deemed from field observations to have been overturned (Table DR1; Figs. DR2 and DR3). Two samples (JW-1-P and JW-2-P) were collected from exposed bedrock platforms adjacent to flipped boulders JW-1 and JW-2 that represent the original intact surfaces from which these boulders had been plucked. A third bedrock sample (JW-4-BR) was taken from an extended surface, ∼20 × 50 m in area, void of imbricated boulders, further downstream within the gorge. This surface is elevated by ∼1–2 m above the mean height of the boulder field and is heavily jointed to a depth of ∼1 m, with numerous potholes and dissolution pits (Fig. DR2H). Although fluvially eroded, the surface has not been affected by hydrological plucking of bedrock slabs and hence best represents continuously eroded intact bedrock with the same lithology as the sampled boulders. All 15 boulder and bedrock samples were analyzed for 10Be and 26Al (Fink and Smith, 2007; Mifsud et al., 2013; Table 1; see the Data Repository for details). Four of the six boulders (JW-1, JW-2, JW-5, and JW-7) were unequivocally identified to have been overturned (Fig. 2A). Two boulders (JW-3 and JW-6) show a steady-state profile, and therefore we cannot ascertain whether they were flipped sufficiently long ago so that the nuclide profile has returned to steady state, or never flipped (Fig. 2B). Concordant 10Be and 26Al concentrations for sample JW-4-BR indicate an absence of prolonged burial (>∼300 k.y.; Granger and Muzikar, 2001) and a steady-state erosion rate of 2.3 ± 0.3 mm k.y.–1 (Table 1).

DISCUSSION

Model Flip Ages

Flip ages are numerically modeled by solving two simultaneous equations, one for each surface of a flipped boulder (Equations 2 and 3), for two unknowns, viz., inheritance of the previously exposed (currently hidden) surface and flip time. Calculations were made under three progressively more sophisticated scenarios: spallation production only with no erosion (model A); spallation and muon production with no erosion (model B); and as for model B, but with a nonzero erosion rate (model C) (see the Data Repository for details). For model C, we applied an erosion rate of 2.3 ± 0.3 mm k.y.–1 as determined in bedrock sample (JW-4-BR), which limits the range of model flip ages at this site to ca. 250 ka and younger. Results of the model calculation are shown in Table 1. Based on measured 10Be concentrations, model C flip ages for the four flipped boulders, JW-1, JW-2, JW-5, and JW-7, are 10.3 ± 1.9 ka, 146 ± 26 ka, 256 ± 45 ka, and 5.6 ± 1.0 ka (1σ), respectively.

Results from models A and B indicate that muon contributions reduce model ages by ∼3%, whereas the impact of surface erosion (model C) depends on the magnitude of erosion rate and flip age (Fig. 3). Older model B flip ages (no erosion), ca. 110 ka (JW-2) and ca. 160 ka (JW-5), increase considerably in model C, by ∼30% and ∼60%, respectively (Table 1), with an erosion rate of 2.3 mm k.y.–1. Erosion rates higher than ∼4 mm k.y.–1 for JW-2 and ∼3 mm k.y.–1 for JW-5 would result in indeterminate flip ages (Fig. 3). In contrast, the young flip ages of 10 ka (JW-1) and 6 ka (JW-7) are unaffected by any choice of erosion correction within the range of bedrock erosion rates observed across Australia (≤1–10 mm k.y.–1; Fig. 3), and therefore are more robust than the older flip ages. Importantly, the nuclide concentration of platform sample JW-1-P, equivalent to the original upper surface of the JW-1 boulder, is also consistent with model prediction (i.e., sum of decayed bottom inheritance and post-flip production; see the Data Repository, and Table DR2 therein, for details). This latter result further supports our confidence in the model flip age of 10.3 ± 1.9 ka for boulder JW-1.

Complex Flip Scenarios

Model flip 26Al ages are essentially consistent with corresponding 10Be ages within 2σ uncertainties (Table 1). However, on closer inspection, average measured 26Al/10Be concentration ratios for top surfaces (-T suffix on sample number) (6.0 ± 0.8) are generally higher than those for bottom surfaces (-B) (5.3 ± 0.9) (Table 1). Specifically, two of the six exposed (JW-5-T, JW-6-T) and four of six hidden surface samples (JW-1-B, JW-2-B, JW-5-B and JW-6-B) have 26Al/10Be ratios somewhat lower (i.e., by more than 2σ of their respective errors) than the nominal 26Al/10Be production rate ratio of 6.7 (Balco et al., 2008), a value commonly expected for continuously exposed eroding surfaces. 26Al/10Be ratios lower than the nominal 6.7 might suggest that some boulders have undergone a complex exposure history, such as one including burial. However, these boulders have undergone at least two stages of exposure history (pre- and post-flipping), and, therefore, without knowing a detailed pre-detachment exposure history, one cannot simply relate depressed 26Al/10Be ratios to burial.

Depressed 26Al/10Be ratios may be caused by boulder burial after flipping. This would reduce production and increase the time required to return to a normal depth profile. Under this scenario, our model flip ages should be regarded as minimum ages. Field observations record a total absence of fluvially deposited sediment or gravel within the waterhole. The flat open spaces bordered by arced stacks of imbricated boulders are void of fragmentary debris (cf. Fig. DR2), and our sampled boulders were fully exposed within a stack. Intense monsoonal rainfall would make sediment storage a short-lived feature within the confined gorge. Moreover, burial after flipping would depress the 26Al/10Be ratio for both surfaces, contradicting our result showing higher mean ratios for top surfaces. Two of the three bedrock samples (JW-4-BR and JW-1-P), which were taken from surfaces that, at present, are fully exposed without sediment cover, exhibit 26Al/10Be ratios indistinguishable from a simple exposure (6.7 ± 0.5 and 6.4 ± 0.6, respectively; Table 1; Table DR2). These results suggest that boulder stacks at Jack’s Waterhole have been free of extensive long-term sediment cover. Depressed 26Al/10Be ratios may be caused by exposed bedrock having been buried prior to flipping. For reasons given above, pre-flip burial of an intact “boulder” in the original bedrock surface is also unlikely.

In theory, 26Al/10Be concentration ratios can range between 6.7 (the production rate ratio) to 3.4 (zero erosion saturation). Depressed inherited (pre-flip) 26Al/10Be ratios may thus arise if channel bedrock history prior to flipping incurred a prolonged non-buried exposure (∼500 k.y.) and/or low steady-state erosion (<10 mm k.y.–1). As post-flip exposure proceeds, the reduced top-surface ratio increases to 6.7 more rapidly than that of the lower surface where production is reduced due to shielding. Hence the likelihood of observing reduced ratios is higher for bottom surfaces, consistent with the observed trends in the 26Al/10Be ratios. Regardless of the process causing inherited 26Al/10Be ratios to be depressed, model flip ages are based on the concentration ratio of the single nuclide (either 10Be or 26Al) between the top and bottom surfaces (cf. Equation 1), which must be preserved during any pre-flip burial.

To conclude, other complex scenarios, such as multiple flip events with intermediate periods of different positions, could lead to false model flip ages. We consider this scenario very unlikely, as once a boulder is imbricated and stacked, a far greater hydraulic power would be required to dislodge the stack and cause a subsequent repeat flip event (Wende, 1999). The ejection of successive slabs from channel bedrock at the same location in a single event (e.g., Jansen et al., 2013) does not affect the model calculation. This scenario is also considered to be unlikely, as typical relief of our bedrock channel is about one boulder thickness (i.e., 0.5–1 m) and there is no evidence of deep exhumation in our study site. However, for events causing deep excavation and/or producing very thick imbricated slabs (multiple meters in depth/thickness), contributions to the measured nuclide inventory from muon production prior to flipping (i.e., inherited nuclides) become more relevant as the total integrated thickness of slab removal increases (see the Data Repository). Further complex scenarios in inheritance, post-flipping, and its influence on 10Be-26Al isotope systems are beyond the scope of the present paper and offer opportunities for future study.

CONCLUDING REMARKS

We present a numerical model for determining the timing of boulder-flipping events, and apply it to flood-generated massive boulders in the Durack River, the Kimberley, northern Australia. Our model calculation provides four finite flip ages; while the older ages (ca. 150 ka and ca. 260 ka) are strongly sensitive to the erosion rate correction, the younger, early to mid-Holocene ages 10.3 ± 1.9 ka and 5.6 ± 1.0 ka are robust against such correction. The younger flip ages correspond to a period of relatively warmer and wetter Holocene conditions in northern Australia (e.g., Kershaw and Nanson, 1993; Nott and Price, 1999). The early to mid-Holocene flip ages may correspond to large flood events suggested by plunge pool sediment records, located further to the east in the Northern Territory, that indicate extreme pluvial events 4–5 times present discharge values (Nott and Price, 1999). We suggest that such extreme floods may have been widespread in northern Australia during the early to mid-Holocene. The boulder flip model established in this study can also be applicable to similar deposits related to other extreme events such as paleo-tsunamis.

We thank editor J. Spotila for his advice during the review process. We acknowledge the contributions of John Gosse and five other anonymous reviewers for their constructive comments that improved the manuscript.

1GSA Data Repository item 2015030, analytical methods, boulder flip model, sample information (Table DR1), platform sample data (Table DR2), site map (Fig. DR1), field photos (Fig. DR2), and satellite image of the site (Fig. DR3), is available online at www.geosociety.org/pubs/ft2015.htm, or on request from editing@geosociety.org or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA.