Sand, Gravel, Cobbles, and Boulders: Detrital Thermochronology Shows that One Size Does Not Tell All

Detrital thermochronology has been used to measure sediment source elevations, and thus to quantify spatial variations in sediment production and erosion in steep mountain catchments. Samples commonly include a small fraction of the sediment sizes present on mountain streambeds, which according to previous modeling may not adequately represent sediment production where hillslope sediment sizes vary or where sediment breaks down during transport. Here we explore what can be learned from multiple sizes by quantifying source elevation distributions for 12 sediment size classes collected from Inyo Creek in the eastern Sierra Nevada, California. To interpret these data, we use a new analytical framework that identifies both the elevations where sediment sources deviate from catchment hypsometry and the likelihood that observed cumulative deviations could occur by chance. We find that sediment in four gravel and cobble size classes originates preferentially from higher elevations, either because erosion rates are faster or because these sizes are disproportionately represented in the sediment from high elevations. Conversely, boulders in the stream originate mostly from low elevations near the sample point, possibly reflecting the breakdown of boulders from high elevations during transport. While source elevations of finer sediment sizes are statistically indistinguishable from hypsometry, we show that these sizes are unlikely to be consistent with uniform sediment production because they cannot be considered in isolation from the coarser sizes. Our source elevation distributions from sand, gravel, cobbles, and boulders show that no one size can tell the rich story of sediment production and evolution, and highlight opportunities for future work.

The prediction that thermochronologic age distributions vary across sediment sizes has rarely been tested in steep mountain landscapes because few studies have quantified cooling ages in multiple sediment size classes in these environments.However, when different sediment size classes have been analyzed, clear differences have emerged.For example, in the White Mountains of eastern California, boulders on an alluvial fan had fission track ages that match bedrock cooling ages on hillslopes near the catchment mouth, indicating they originated there (Vermeesch, 2007).Meanwhile, gravel in an amalgamated sample collected from across the fan had older ages than coarse sand in the same sample, indicative of higher source elevations for the gravel.Gravel also appears to have relatively high source elevations compared to finer sediment at nearby Inyo Creek in the eastern Sierra Nevada; coarse gravel and finer sediment in stream sediment have apatite (U-Th)/He cooling ages and cosmogenic nuclide concentrations consistent with enhanced production of gravel on steeper, colder, higher-elevation slopes that are eroding more rapidly (Riebe et al., 2015).This observation is corroborated by direct measurements of downvalley fining in hillslope sediment supply at Inyo Creek (Sklar et al., 2020).
Direct measurements of sediment size distributions from other mountain landscapes confirm that such spatial variations in sediment production may be common (Sklar et al., 2017) and thus should be expected in applications of detrital thermochronology.For example, size distributions of sediment produced on hillslopes have been shown to correlate with variability in lithology (Lai et al., 2021;Roda-Boluda et al., 2018), erosion rate (Riebe et al., 2015;Whittaker et al., 2010), topography (Attal et al., 2015), fracture spacing (Neely & DiBiase, 2020;Verdian et al., 2021), climate (Marshall & Sklar, 2012;Terweh et al., 2021), and geomorphic processes (Roda-Boluda et al., 2018;Sklar et al., 2017Sklar et al., , 2020)).In mountain landscapes, where many of these factors often vary across individual catchments, different sediment sizes at the outlet may reflect sediment production from different parts of the catchment, where lithologic, climatic, and topographic conditions favor different sizes.Sediment sizes at the outlet are also likely influenced by the breakdown of coarser particles during transport by abrasion, chipping, and fracturing (Attal & Lavé, 2009;Lavarini et al., 2018;Litwin Miller & Jerolmack, 2021).Breakdown rates and the size distributions of breakdown products have been shown to depend on lithology (Kodama, 1994b), degree of chemical weathering (Goodfellow et al., 2016;Heller et al., 2001), and energy of transport (Arabnia & Sklar, 2016;Attal & Lavé, 2009), and can affect grain size distributions even in durable lithologies and over short distances (Dingle et al., 2017;Kodama, 1994a).
Together, the work summarized above, which includes numerical modeling, measurements of cooling age distributions in multiple sizes in two previous studies, field measurements of variable sediment size on slopes, and both field and experimental findings of breakdown during transport, suggest that these complications are widespread and should commonly influence age distributions in stream sediment.However, the resulting complexity 10.1029/2023JF007192 3 of 20 also presents an opportunity because the age distribution in each size class of stream sediment could have a unique story to tell about where the sediment originated, thus yielding new insights into erosion, weathering, and sediment production in mountain landscapes.
Here we exploit this opportunity at Inyo Creek by quantifying apatite (U-Th)/He ages in 12 size classes ranging from sand to boulders.Inyo Creek is ideal for this analysis because inferences from the detrital age distributions across all sizes can be compared with previous measurements of size distributions on catchment slopes (Sklar et al., 2020).We evaluate the measured cooling age distributions by comparing them to numerical simulations in which erosion rates and initial sediment size distributions are both spatially uniform, and in which breakdown during transport is negligible.This null hypothesis of uniform sediment production and negligible breakdown is consistent with the analysis framework of previous studies and represents the simplest case in which any single size faithfully represents spatial patterns of sediment production without the complications described above.We interpret the apatite (U-Th)/He ages in a new analytical framework that (a) determines whether the age distributions differ from the null hypothesis and (b) locates elevations that deliver more or less of each grain size to the stream.This framework differs from previous approaches in that it considers both individual (elevation-specific) and cumulative (catchment-wide) departures from the null hypothesis.
Our results show that different size classes at the sampling location in the stream do indeed have different stories to tell.The sediment production at low elevations is dominated by boulders and fine sediment, suggestive of granular disintegration of the catchment's granodiorite bedrock.At higher elevations, where slopes are steeper and temperatures are colder, our results are consistent with a diversity of processes producing a full range of sizes including cobbles and boulders, the largest of which do not survive the journey to the outlet.Our measurements show that age distributions from multiple size classes can yield a rich portrait of sediment production in mountain landscapes.

Study Site
Inyo Creek drains a steep catchment on the eastern flank of the Sierra Nevada in California.At the sampling point, the upstream catchment spans 2 km of relief with a contributing area of 3.3 km 2 .Upper elevations are dominated by exposed bedrock and steep slopes and have little-to-no vegetation (Figure 1a).Lower elevations are gentler, soil-mantled, and sparsely vegetated by sage and juniper scrub.From the base of the catchment to its top, the mean annual temperature decreases from 10.4 to −0.7°C and average precipitation increases from 277 to 654 mm/yr (PRISM, 2013).The sharp gradients in climate, topography, and vegetation correlate with variations in sediment production across the catchment (Riebe et al., 2015;Sklar et al., 2020).In contrast, many of the geologic factors that might influence sediment size are uniform across Inyo Creek.The entire catchment is underlain by granodiorite bedrock, and although feldspar crystal size is larger in the bedrock of the upper half of the catchment (Hirt, 2007;Stone et al., 2000), it does not appear to influence the size distribution of sediment produced by mineral disaggregation (Riebe et al., 2015).In addition, mean bedrock fracture spacing, another factor that could influence the initial sizes of sediment produced on hillslopes (Neely & DiBiase, 2020;Scott & Wohl, 2019), does not vary with elevation across the catchment (Sklar et al., 2020).The catchment does not show evidence of glaciation, which can preferentially produce fine sediment at high elevations (Brocklehurst & Whipple, 2004;Ehlers et al., 2015;Stock et al., 2006).The sharp contrasts in climate, topography, and vegetation, together with the lack of variation in geologic factors, make Inyo Creek well-suited for the study of links between sediment sizes and physical, chemical, and biological weathering.
Inyo Creek is also an ideal place to use apatite (U-Th)/He thermochronology to trace the origins of sediment from each of the size classes in the stream because each grain of sediment produced from bedrock carries an isotopic fingerprint of its source elevation.Apatite is abundant throughout the catchment and comprises 14%-16% by volume, on average, in each of the three granodiorite units (Hirt, 2007).Previous work shows that bedrock (U-Th)/He ages increase with elevation from 20 Ma near the detrital sampling point to 70 Ma near Lone Pine Peak (Figure 1b; House et al., 1997;Stock et al., 2006).Because the relationship is linear, spans a wide range of ages relative to analytical uncertainties in age (which are typically ∼1%) and has a high coefficient of determination (r 2 = 0.91), the distribution of catchment elevations (Figure 1c) can be readily translated into a predicted distribution of corresponding bedrock ages of catchment slopes (Figure 1d).This bedrock age distribution should match the age distribution of sediment in each size class collected from the stream only if both the erosion rate and the initial size distribution of sediment produced on slopes are spatially uniform across catchment slopes, and if the shape of the size distribution is not modified by the breakdown during transport.Hence, by measuring age distributions in multiple sediment size classes, we gain insight into both the spatial variability in sediment production on slopes and the transformation of sediment sizes during transport.

Field Work
We sampled sediment from the range of sizes present within the wetted perimeter of a ∼30-m-long reach, just above the apex of the debris fan at the base of the range front (Figure 2).Thus, our samples included sediment transported from the contributing area and excluded remobilized fan sediment.Our study reach is representative of similar reaches near the catchment outlet.We measured the grain size distribution on the bed using 16 separate  S1 in Supporting Information S2) (b) Age-elevation relationship, a = 23.3z− 24.85 (where a is age in Ma and z is elevation in km), was calculated using inverse-variance-weighted ordinary-least-squares regression, with gray band spanning ± 1 standard error of the mean on the regression.(c) Joint distribution of elevation and travel distance for Inyo Creek (after Sklar et al., 2016), plotted as the frequency of elevations from the digital elevation model using a kernel density estimator (KDE) with a bandwidth of 10 m; (d) Elevation distribution (left axis) and corresponding bedrock cooling age distribution (right axis) of Inyo Creek catchment, plotted using an adaptive KDE (Z.Botev, 2023).
All the detrital cooling age data reported here are from samples collected in 2013 with the exception of one size class (32-48 mm), which was sampled in 2012.Stream sediment was split into 12 sediment size classes ranging from sand with diameters between 1 and 2 mm to boulders with diameters >256 mm (Table 1).To sample sizes with diameters less than 8 mm, we amalgamated a ∼4 kg bulk sample from distributed locations within the wetted perimeter of the stream.For larger size classes, samples included at least 100 clasts, with the exception of the boulders (only 50 of which occurred in the reach).To obtain manageable subsamples of sizes greater than 96 mm, we measured the masses of individual clasts in the field using a spring scale and subsampled each clast after breaking them apart with a sledgehammer.Each subsampled clast was labeled for reference to its original mass (from the spring scale).Because boulders could not be weighed or readily broken with a sledgehammer in the field, we used a 4-inch diameter water-cooled rock drill to collect cores from each of the 50 boulders in the reach.All sediment clasts with diameters less than 96 mm were returned with the clasts intact for analysis in the lab.
We split the bulk sample of finer sediment into whole phi size classes (1-2, 2-4, and 4-8 mm) in the lab using a mechanical sieve.For each of the larger sizes sampled in the field (96-128, 128-192, and 192-256 mm), we cut subsampled clasts with a rock saw and combined the subsamples from the individual clasts, in proportion to their original mass, into an aggregate for crushing and mineral separation.Subsamples from each boulder core were combined in proportion to the boulder's b-axis diameter.Each size class, including the four amalgamated as described above, was crushed and pulverized to mono-mineralic grains.From these pools of grains, we isolated apatite crystals using standard magnetic and density separation techniques.We also crushed and pulverized bedrock and isolated its apatite from one sample that we collected from Lone Pine Peak to augment existing constraints on the bedrock age-elevation relationship of the catchment.

Quantifying Apatite (U-Th)/He Ages and Source Elevations
We selected euhedral apatite crystals for (U-Th)/He analysis using a Leica TL5000 microscope to hand-pick, photograph, and measure individual apatite crystals that were high quality, intact, and free of visible inclusions.The 4 He concentration of each crystal was measured via isotope dilution using a quadrupole mass spectrometer, and U and Th isotopes were measured via isotope dilution using an ICP-MS at the Noble Gas Thermochronometry Lab of Berkeley Geochronology Center following standard procedures (House et al., 2000;Tremblay et al., 2015).Raw (U-Th)/He ages were calculated assuming that all 4 He was produced from U, Th, and Sm decay, with an α-ejection correction calculated from crystal dimensions to account for direct alpha particle ejection near crystal edges (Farley et al., 1996).Four crystals were analyzed from the bedrock sample and the average age was included in the bedrock age-elevation relationship in Figure 1 (Table S1 in Supporting Information S2).Balancing the constraints of crystal abundance, quality, cost, and mass spectrometer availability, we quantified ages for between 25 and 98 crystals from each size class, for a total of 713 ages.Each of the measured cooling ages was interpreted as a source elevation plus-or-minus its uncertainty from the age-elevation relationship in Figure 1 using the inverse prediction.

Results and Analysis
The measured concentrations of 4 He, U, Th, and Sm are listed in Supporting Information S2, along with α-ejection correction factors and calculated (U-Th)/He ages of each apatite crystal extracted from detrital sediment.Although crystals were carefully screened for inclusions that would bias ages toward higher values, 14 of them had cooling ages greater than 75 Ma, and thus above the upper 95% prediction interval of the bedrock age-elevation relationship at the top of the catchment.This indicates that they are too old to have originated from the population of sampled bedrock cooling ages.Moreover, five of them are older than and thus inconsistent with the 83-87 Ma range in U-Pb crystallization ages measured in the catchment's granodiorite bedrock (Chen & Moore, 1982;Mattinson, 2005).The 14 crystals with too-old cooling ages do not have higher concentrations of effective U (eU), suggesting that radiation damage does not explain these older ages.We interpret all 14 of the too-old cooling ages to reflect contamination from U-bearing microinclusions that we did not see when picking crystals (Supporting Information S1).We interpret the remaining 699 ages, which range from 20 to 75 Ma (Figure 3), to reflect erosion from source elevations within the catchment (Figure 1).
When grouped by sediment grain size (Figure 3), the ages show variability in sediment source elevations of each size class and illustrate the wealth of information that is unavailable when only measuring ages in a narrow Notable gaps in sediment production occur at low elevations for coarse gravel (16-32 mm) and high elevations for boulders (>256 mm).Horizontal spacing of points in each size class was created by jittering to show age variability despite clumping and does not represent variability in sizes.range of sizes (e.g., sand).The age distributions of the different size classes naturally overlap because they originate from the same catchment and because hillslope sediment size distributions are wide, but age distributions measured in the stream nonetheless have several notable differences.For example, sand (1-2 mm) spans the catchment's full range of cooling ages and therefore source elevations; coarse gravel (16-32 mm) has few young ages, suggesting that most of it comes instead from higher elevations; and boulders (>256 mm) have few old ages, suggesting that these largest clasts preferentially originate at lower elevations near the sample point.To determine whether these visual impressions are statistically meaningful, we developed a framework to assess the departures in each age distribution from the distribution expected for the null hypothesis of spatially uniform sediment production and negligible breakdown during transport.This framework quantifies the likelihood that a measured age distribution would arise by chance, and also pinpoints the elevation ranges where excesses and deficits in sediment production occur.Our approach detects statistically significant departures from the null hypothesis that are not readily perceived in Figure 3.

Analytical Framework
If both the erosion rate and the size distribution of sediment produced on slopes are spatially uniform (i.e., "uniform sediment production") and breakdown is negligible, the age distribution in each size class should match the catchment's bedrock cooling age distribution calculated from the elevation distribution (i.e., hypsometry) and the bedrock age-elevation relationship (Ehlers et al., 2015;Riebe et al., 2015;Ruhl & Hodges, 2005;Stock et al., 2006;Vermeesch, 2007).When this is the case, each point on the landscape has an equal chance of contributing a clast of any given size to the sample.This condition can be evaluated by comparing the measured age distributions to the distribution predicted by hypsometry.When spatially uniform sediment production is the null hypothesis, any statistically significant deviations must reflect spatial variations in erosion rates or initial sediment size distributions, the breakdown of sediment during transport, or a combination of these conditions.
To interpret measured cooling ages and corresponding elevations relative to the null hypothesis, we quantified cumulative age distributions (CADs) and kernel density estimators (KDEs, after Vermeesch, 2007Vermeesch, , 2012) ) and evaluated them using a combination of established statistical hypothesis tests and bootstrapping methods.A CAD represents the fraction of the distribution that is less than or equal to each age in the distribution and is an unbiased estimate of the cumulative distribution function of ages (Vermeesch, 2007).A KDE is similarly an unbiased estimator of the probability density function and can be generated from any set of measured ages or elevations, even when the distribution is not smooth or unimodal (Vermeesch, 2013).Here we used an adaptive KDE algorithm that optimizes the kernel bandwidth to reflect the density of measurements at each age or elevation (Z.Botev, 2023;Z. I. Botev et al., 2010).By comparing measured CADs and KDEs of age and elevation with distributions predicted from the null hypothesis of uniform sediment production, we can quantify exceedance probabilities (i.e., p values) that express the likelihood of obtaining a measured distribution by chance when both the erosion rate and the size distribution of sediment produced on slopes are spatially uniform.

K-S Tests
Perhaps the simplest way to visualize and statistically compare cooling age distributions of bedrock and stream sediment is to plot them as CADs and test for differences using a Kolmogorov-Smirnov (K-S) test.For small sample sizes commonly obtained from stream sediment (<100 ages), CADs are distinctly stepped in appearance with each step in cumulative frequency representing a discrete measurement (Figure 4).The age distribution predicted from Inyo Creek hypsometry (shown in black in Figure 4) has less-distinct steps and the CAD is comparatively smooth because there are many thousands of ages corresponding to the many thousands of 10 × 10 m digital elevation model pixels that lie within the watershed.
While a two-sample K-S test is the standard frequentist approach in statistical hypothesis testing of CADs (e.g., Vermeesch, 2007), some previous tracer thermochronology studies have also used a variant developed by Kuiper (1960) for testing cumulative distributions of circular metrics, such as the compass directions of flying birds.Similar to the more conventional K-S test described above, the Kuiper test yields the p value of the maximum vertical difference between two distributions but calculates the difference K as the sum of maximum offsets both above and below the distribution of the null hypothesis.Although sediment cooling age is not a circular metric, application of the Kuiper test in thermochronology is thought to avoid bias at the tails of the distribution-i.e., at elevations near the catchment head and mouth (Ruhl & Hodges, 2005;Stock et al., 2006).However, these elevations generally account for a small fraction of the overall area because the incremental area at each elevation approaches zero at the highest and lowest points of the catchment.Nevertheless, it has been proposed that the Kuiper test is more sensitive than a standard K-S test to differences from uniform sediment production near the catchment head and mouth because the Kuiper test is, by design, insensitive to the starting point of the distribution.To our knowledge, the Kuiper test has not been shown to be more appropriate than the standard K-S test in tracer thermochronology.For completeness, we followed previous studies and used the Kuiper test here as an additional test of each size-class CAD relative to the hypsometric age distribution.
Regardless of whether we use a K-S or a Kuiper test, we must establish an acceptable false-positive rate (typically set at 0.05).However, because our analysis involves 12 sediment size classes, and thus 12 separate statistical hypothesis tests for each type of test, the false positive rate of the collection of tests is inflated.To address this complication, we applied a Bonferroni correction of 1/12 to α = 0.05 and obtained a tolerable false-positive rate of 0.0042 or less for each of the tests.When this criterion is met, the overall (experimentwise) false-positive rate for the collection of tests will be 0.05 or less.

Cumulative Distributions of Ages
Of the 12 K-S tests we conducted between measured and hypsometry-based age distributions, four had p values less than 0.0042 (Table 1).Of these four, the 64-96 mm fine cobbles (Figure 4h) and >256 mm boulders (Figure 4l) have p values less than 0.000082, corresponding to an experiment-adjusted false-positive rate of at most 0.001 and thus a confidence level of at least 99.9% in rejecting the null hypothesis.The adjusted p value for the 32-48 mm coarse gravel (Figure 4e) indicates that we can reject the null hypothesis for that size class with 95.6% confidence.For the 16-32 mm intermediate gravel (Figure 4e), a sample with 24 ages, a difference as big or bigger than the maximum difference from the hypsometric age distribution would arise by chance just 3.1% of the time.Hence, we can confidently reject the null hypothesis of uniform sediment production for each of the four size classes based on the K-S test-even though the sample size is as low as 24 for one of them.The other eight size classes have maximum vertical offsets with p values that are all much greater than the 0.0042 threshold for an overall, experimentwise, false-positive rate of 0.05.Hence, we are unable to reject the null hypothesis of uniform sediment production for these sizes based on a two-sample K-S test.6).

Table 1 K-S and Kuiper Test Statistics and p-Values
In addition to determining whether differences are statistically significant, we can determine whether the differences are due to thermochronologically young or old bedrock by examining the CAD plots (Figure 4).For example, the maximum difference for the boulder plots to the left of the hypsometric age distribution (Figure 4l), indicating that they are preferentially sourced from bedrock with younger ages, and thus from lower elevations in the catchment, similar to the previously mentioned findings on detrital boulders in the nearby White Mountains, California (Vermeesch, 2007).The opposite is true for the intermediate gravel (Figure 4e), the coarse gravel (Figure 4f), and the fine cobbles (Figure 4i), with maximum differences plotting on the right side of the hypsometric age distribution, implying preferential sourcing from thermochronologically older bedrock and therefore higher elevations.
Results of the Kuiper tests are broadly consistent with the results of the two-sample K-S tests.For example, both tests yield low p values for the coarse gravel (Figure 4f), the fine cobbles (Figure 4i), and the boulders (Figure 4l), implying that the differences between the hypsometric and measured age distributions are unlikely to have arisen by chance, and thus the null hypothesis can be rejected for those sizes based on either test.However, only the K-S test yielded a difference with an experiment wise p < 0.05 for the 16-32 mm intermediate gravel (Figure 4e).This difference in test results is difficult to reconcile by inspection of the CAD plots alone, but we suspect it arises, at least in part, because the metric of interest, (U-Th)/He age, is not on a circular scale, thus violating a central assumption of the Kuiper test, whereas assumptions of the more standard K-S test are fully met.

Departure Analysis: Identifying Elevations That Differ in Sediment Production
One limitation of both the K-S and Kuiper tests is that neither provides precise information about the elevations over which the measured distributions diverge from hypsometry.Therefore, they cannot identify which elevations have excesses and deficits in sediment production (Riebe et al., 2015).To overcome this limitation, we focus on KDEs of age and elevation distributions, which reveal variations in sediment production at each elevation.

Departure Analysis of the 96-128 mm Size Class
An example KDE of sediment source elevation is shown in Figure 5a for the 96-128 mm size class from our data set, along with the KDE of catchment hypsometry.The source elevation KDE of the sediment can be converted into a departure curve (Figure 5c) by subtracting catchment hypsometry from the sediment KDE, yielding the distribution of excesses and deficits in sediment production versus elevation (Riebe et al., 2015).Positive departures represent elevations with excess sediment production, whereas negative departures represent elevations with deficits.For the 96-128 mm size class (medium cobbles), deficits occur over elevations ranging from 2.0 km at the catchment mouth to 2.3 km, and from 2.6 to 3.5 km in the middle of the catchment (Figure 5c).All other elevations had positive departures.
Departures have two dimensions: height, which is the distance in frequency space between the observed KDE and the expected value at each elevation, and width, which is the range in elevations spanned by the departure.Both dimensions can represent meaningful information about spatial patterns in sediment production.For example, a high but narrow positive departure in cobbles might arise because that band of elevations is dominated by cliffs that produce rockfalls.In contrast, a low but wide negative departure in cobbles might correspond to an elevation band where enhanced granular disintegration preferentially produces finer sediment.Departures might also arise by chance because the samples do not encompass the entire population of sediment produced from catchment slopes.
To identify departures that are unlikely to arise by chance in our measurements, it is necessary to evaluate how high and wide departures can be under the condition of uniform sediment production.However, to our knowledge, there is no established analytical approach for quantifying the odds of exceeding a difference between two empirical distribution functions at every point across the range spanned by the distribution.To overcome this limitation, we used a bootstrapping approach to simulate the null hypothesis of uniform sediment production and used the results to evaluate the probability of obtaining different measured departures under that condition.
Our bootstrapping approach requires three types of data: the number of measured ages, the catchment hypsometry, and the bedrock age-elevation relationship.For each of the k = 12 size classes, we generated 10 6 random samples of n k elevations from the catchment's elevation distribution (Figure 1c), where n k is the number of ages measured in each size class.Each sample thus simulates the null hypothesis of uniform sediment production and negligible breakdown for n k particles collected from the stream.We converted the elevations into ages using the age-elevation relationship, incorporating the bedrock age uncertainty at each sampled elevation by randomly selecting an age from a Gaussian distribution with mean equal to the age predicted by the age-elevation regression and standard deviation equal to the standard error in the regression.We then used a kernel smoothing algorithm (Z.Botev, 2023; Z. I. Botev et al., 2010) to convert each simulated distribution of ages into an age KDE that represents an unbiased estimator of the probability distribution function of bedrock ages in the catchment (Vermeesch, 2012).This approach avoids the problem of double smoothing that arises when analytical errors in ages are used to convert measured detrital ages into probability distributions (Vermeesch, 2012).Because our work focuses on identifying the source elevations from ages measured in stream sediment, we converted age KDEs to elevation KDEs using the age-elevation relationship, and then calculated departures from the catchment hypsometry.
Next, we used the distribution of 10 6 randomly generated departures to quantify departure percentiles at each elevation.These percentiles serve as gauges for the exceedance probabilities of measured departures, quantifying the relative likelihood of measuring excesses or deficits in sediment production of a given magnitude at each elevation under the null condition of uniform sediment production.Collectively, across all elevations, the percentiles define confidence bands representing the fraction of the 10 6 instances that fell between the bounding percentiles at each elevation.For example, the 25th and 75th percentiles define the 50% confidence band, the 2.5th and 97.5th percentiles define the 95% confidence band, and the 0.5th and 99.5th percentiles define the 99% confidence band (Figure 5).
Focusing on the 95% confidence band for the 96-128 mm size class (Figures 5b and 5c), we find two elevation ranges, from 2.4 to 2.6 km and from 3.6 to 3.9 km, over which departures breach the upper confidence threshold.Departures also breach the lower threshold from 2.0 to 2.2 and at 3.2 km.In total, 0.72 km, or 36%, of the catchment's 2.0 km elevation range exhibits negative or positive departures from the 95% confidence band (Figure 5d).The simplest interpretation is that over a third of the catchment's elevation range is inconsistent with the null hypothesis of uniform sediment production.However, because the 95% confidence band is defined only for individual elevations, it is not a catchment-wide metric for statistically meaningful departures.The odds of exceeding the 95% confidence band anywhere in the catchment are much larger than for any specific elevation.To determine whether the observed extent of departures across the whole catchment is statistically meaningful, we used the fraction of the elevation range where departures exceed the upper and lower thresholds for the specified confidence band.We refer to this metric as the cumulative departure; for the 96-128 mm size class shown in Figure 5, the 95% confidence band has a cumulative departure of 0.36.
To determine the likelihood that this cumulative departure, or one of any magnitude, could arise by chance, we used our 10 6 simulations of uniform sediment production to quantify the probability of exceeding a given confidence band for each possible extent of cumulative departure, which ranges from 0 to 1 (Figure 5d).These probabilities, which are akin to p-values, define the exceedance probability curve of cumulative departures for that confidence band (Figure 5d).This curve can be used to gauge whether the width of an observed cumulative departure is statistically meaningful.For example, the measured 0.36 cumulative departure for the 95% confidence band (from Figure 5c) was exceeded in just 0.4% of the simulations (akin to p = 0.004), indicating that it would rarely arise by chance from uniform sediment production.This low p-value suggests that we can reject the null hypothesis that the 96-128 mm cobbles are derived from uniform sediment production over the full range of catchment elevations and therefore interpret the departures at 3.2 km and over the 2.0-2.2,2.4-2.6, and 3.6-3.9km elevation intervals to represent a non-uniform sediment production at those elevations.
So far, we have focused on the 95% confidence band, which is breached by departures that are high and thus likely to be narrow.Confidence bands closer to the median (e.g., the 50% confidence band) can be breached by shorter departures that are likely to be wide.Wide departures may extend over a large fraction of the catchment elevation and thus reflect significant deviations from the uniform sediment production.Hence, testing for non-uniform sediment production requires evaluating departures across a range of confidence bands.We used our simulations to identify elevations where departures occur, calculate cumulative departures, and evaluate the statistical likelihood (i.e., the exceedance probability) of those cumulative departures for a set of confidence bands; the 50% and 99% confidence bands are illustrated as examples in Figure 5.
For any given cumulative departure, the exceedance probability curve for the 50% band plots above the curve for the 95% band, which in turn plots above the curve for the 99% band, reflecting the greater likelihood of exceeding a cumulative departure of a given size for the narrower confidence bands.For example, a hypothetical cumulative departure of 0.3 (corresponding to 30% of the catchment's elevation range and marked by the vertical green dashed line in Figure 5d) has exceedance probabilities of 0.87, 0.01, and 0.0002 for the 50%, 95%, and 99% confidence bands, respectively, based on our simulations (corresponding to the horizontal green arrows in Figure 5d).The exceedance probabilities decrease sharply with increasing cumulative departure, except for relatively small (<0.5) cumulative departures that breach the 50% confidence band.Hence, large cumulative departures are rare, even for confidence bands closer to the median.
In the example of measurements from the 96-128 mm size class, the 50% confidence band has a large cumulative departure of 0.9, which occurred in only 0.005% of our simulations and thus is unlikely to have arisen by chance from the condition of uniform sediment production (Figure 5d).For this size class, departures do not breach the 99% confidence band, resulting in a cumulative departure of 0, which does not have an exceedance probability.
The observation that both the 50% and 95% confidence bands have cumulative departure exceedance probabilities of 0.005 or less suggests that the ages in the 96-128 mm size class are inconsistent with the null hypothesis of uniform sediment production.Furthermore, this suggests that the individual departures arise due to physically meaningful deviations in sediment production at the elevations where departures occur.

Departure Analysis of All Size Classes
To apply the departure analysis across all 12 size classes, which differ in the number of ages measured, we repeated the 10 6 simulations of uniform sediment production for each sample size.Thus, we generated confidence bands for departures for each size class, which differ in width depending on the number of ages measured (which ranges from 24 to 97 in our data set).Where the number of measured ages is smaller, confidence bands are wider (Figure 6), meaning that larger measured departures are needed to breach a given confidence band and thus contribute to the cumulative departure.Hence, we can apply the departure analysis even when the sample size is small.In addition to the 50%, 95%, and 99% confidence bands discussed above, we quantified departures from the 10%, 20%, 30%, 40%, 60%, 70%, 80%, 90%, and 98% confidence bands, representing small, moderate, and large vertical deviations from the case of uniform sediment production (Figure 6).
Unlike the 96-128 mm cobbles, the 1-2 mm sand has no statistically significant cumulative departures for any of the confidence bands (Figures 6a and 6b).The exceedance probabilities for the cumulative departures are all greater than 0.05, and most are greater than 0.2, indicating that they arise by chance in our simulations more than 20% of the time.Hence, the measured age distribution in the sand is not inconsistent with the null hypothesis of uniform sediment production and negligible breakdown across the catchment.This is also the case for fine gravel (i.e., 2-4, 4-8, and 8-16 mm in Figures 6c-6h), very coarse gravel (i.e., 48-64 mm in Figures 6m and 6n), and coarse cobbles (i.e., , with exceedance probabilities approaching 1.0 in some cases (e.g., Figure 6h), implying they commonly arose by chance in our simulations.Hence, even for grain sizes with departures that seem pronounced, as in the case of the 95% confidence band on the 2-4 mm gravel (Figure 6c), the cumulative departure is not large enough to be statistically significant (Figure 6d).
In one case-the fine cobbles (i.e., 64-96 mm size class)-some of the confidence bands have significant cumulative departures while others do not.The small-to-moderate cumulative departures from the 10%-40% confidence bands have exceedance probabilities that are greater than 0.05, indicating that they are not pervasive enough to rule out the null hypothesis.However, exceedance probabilities are less than 0.05 for all the other confidence bands and are as low as 0.001 for the 90% confidence band (Figures 6o and 6p).These moderate-to-large cumulative departures are sufficiently frequent that we can confidently rule out the null hypothesis of uniform sediment production for this size class.Rather, the 64-96 mm size class appears to originate preferentially at elevations above 3.2 km and is underrepresented in the sediment produced at lower elevations (2.0-2.6 and 2.7-3.2km).
All other size classes (i.e., 16-32, 32-48, 96-128, and >256 mm) show significant cumulative departures across all confidence bands.This means that small, moderate, and large departures are pervasive enough to rule out the null hypothesis for each size class.For instance, the 32-48 mm gravel originates preferentially at high elevations (3.3-4.0 km) and is underrepresented in sediment from low elevations, similar to the findings from Inyo Creek sediment sampled in a previous year (Riebe et al., 2015).Conversely, boulders (>256 mm diameter) in the stream originate mostly at low elevations, similar to findings in the nearby White Mountains (Vermeesch, 2007), while boulders from high elevations are largely absent in stream sediment at the catchment mouth.
On the whole, our departure analysis shows that 11 of 12 grain sizes sampled from Inyo Creek have departure curves that breach the 95% confidence band at least once, even though such high vertical departures should only occur 35% of the time for any individual grain size when sediment production is uniform and breakdown is negligible.The chance of this occurring in 11 out of 12 grain sizes is only 0.008% (i.e., a p-value of 0.0008 in a binomial test), assuming the null hypothesis is correct.Hence, even though 7 of the 12 sizes do not have significant cumulative departures across any of the confidence bands, collectively, the analysis of all grain sizes shows that either sediment production is non-uniform, breakdown is non-negligible, or both.

Departure Analysis
The departure analysis reveals two types of information about the production of different sediment sizes on hillslopes: where excesses and deficits occur; and whether they are likely to arise by chance from uniform sediment production with negligible breakdown.The departure plots identify the elevations where the elevation distribution of each grain size differs from catchment hypsometry.These differences may arise because either (a) sediment is produced at higher or lower rates at those elevations or (b) breakdown of sediment shifts ages from coarse to finer size classes, creating apparent deficits and excesses in the production of coarse and fine sediment, respectively.However, departure plots alone are insufficient to determine whether excesses and deficits of a given sediment size are statistically significant at the catchment scale.Cumulative departure plots overcome this limitation by quantifying the likelihood that the observed departures would arise by chance, irrespective of location in the catchment, when sediment production is spatially uniform and breakdown is negligible.Thus, it avoids overstating the significance of departures over any single narrow range of elevations, which are common in the simulations of uniform erosion.In addition, the cumulative departure plots identify statistically significant cumulative departures spanning a range of scales, from small but frequent to large but infrequent.Thus, it provides a more comprehensive analysis of sediment production than studies that have focused only on breaches of the 95% confidence band.

Comparison With K-S and Kuiper Tests
The departure analysis confirms the findings of the K-S and Kuiper tests, showing that the 32-48, 64-96, and >256 mm size classes are inconsistent with the null hypothesis of uniform sediment production and negligible breakdown (Table 1).It also confirms the K-S test and differs from the Kuiper test in identifying departures from the null hypothesis for the 16-32 mm size class.In addition, the departure analysis identifies one additional size class, the 96-128 mm cobbles, which has cumulative departures that are significant across all but one of the confidence bands.For the seven other size classes, we are unable to reject the null hypothesis of uniform sediment production based on any of the tests, raising the question of whether the analysis is powerful enough to detect sizable departures from a uniform sediment production.In this case, we can be reasonably confident in the power of the departure analysis given that we reject the null hypothesis in five out of the 12 size classes.
Together, our results show that the departure analysis is broadly consistent with and more sensitive than both the K-S and Kuiper tests in detecting differences between distributions.However, whereas the K-S and Kuiper tests only identify differences in cumulative distributions of elevations, and thus cannot specify elevations over which departures occur, the departure analysis can pinpoint the departures because it is based on the probability density function.Hence, a departure analysis such as the one detailed here provides a more complete picture of deviations from the uniform sediment production in thermochronological studies of sediment source elevations.

One Size Does Not Tell All
Of the 12 sediment size classes in which we measured (U-Th)/He ages, five relatively coarse sizes are inconsistent with the null hypothesis.While we are unable to reject the null hypothesis for the other seven generally finer sizes, this does not prove that the null hypothesis is true for those sizes because frequentist statistical inference does not work that way.Hence, we cannot conclude that the finer (and therefore any of the) sediment size classes represent spatially uniform sediment production across the catchment.Moreover, as we show next, the ages from the finer sizes are also consistent with another hypothesis about sediment production that also explains direct observations of sediment size distributions from catchment slopes (Sklar et al., 2020).It involves modification by breakdown during transport downstream.While this evidence is specific to Inyo Creek, similar conditions control sediment 10.1029/2023JF007192 16 of 20 production in mountain landscapes around the world, implying that the lack of representativeness of any one size class may be widespread in studies of tracer thermochronology.

Evidence for Breakdown During Transport at Inyo Creek
Compared to previous direct measurements of sediment size distributions on slopes, our (U-Th)/He data are consistent with substantial sediment size reduction during transport at Inyo Creek.Direct measurements of size from point counts, transects, and sieved sediment masses (Sklar et al., 2020), show that, from the outlet to the mid-elevations of the catchment, the proportion of fine sediment decreases while the proportions of gravel and cobbles both increase in the sediment size distribution (Figures 7a-7c).Boulders, in contrast, show no clear trend with elevation and make up 24% on average of the grain size distribution (dashed horizontal line in Figure 7d).In comparison, our (U-Th)/He results from stream sediment at the catchment mouth suggest that finer sizes (<16 mm) originate from the full range of elevations in the catchment; some size classes of coarse gravel and cobbles originate preferentially from higher elevations; and boulders originate preferentially from low elevations.While these comparisons are somewhat limited by the fact that the hillslope sediment (Figure 7) is grouped into fewer size classes and spans only the lower half of the catchment's elevation range, the spatial patterns in results from finer sediment and boulders do not agree across the (U-Th)/He and direct sediment size measurements.Thus, spatial variability in sediment size distributions on slopes is not sufficient to explain the observed patterns in detrital (U-Th)/He age distributions, and breakdown or variable erosion rates (or both) must also be important in this landscape.
One possibility is that erosion rates are faster at higher elevations, providing sand to the stream from elevations where direct measurements indicate that sand makes up a smaller fraction of the total sediment production.However, this would not explain why bed sediment at the outlet has no boulders sourced from high elevations.Another possibility that would explain the patterns in both the boulders and the sand is that the boulders from high elevations break down into sand either by weathering in place or by fracturing and abrasion during transport by rock falls and debris flows.Thus, the high elevation signal from the boulders is transferred to finer size classes, including sand.This would explain both the deficit of boulders and excess of sand from high elevations in the detrital data relative to the direct measurements of sediment size from catchment hillslopes.
If the breakdown is driving the differences between the hillslope-based measurements and the thermochronology data presented here, we might expect the departure plots to match the hillslope-based measurements more closely at lower elevations, where sediment does not travel as far to reach the outlet.And they do: the departure plots suggest that sediment production is dominated by boulders and fine sediment at low elevations, while the hillslope data are consistent with a bimodal size distribution consisting mostly of fine sediment (∼60%) and coarse boulders (∼24%) according to Figure 7. Bimodality in granitic sediment has commonly been attributed to granular disintegration caused by biotite weathering (Buss et al., 2008;Shen et al., 2019;Wahrhaftig, 1965), which would tend to be enhanced at lower elevations in the catchment, where temperatures are warmer and vegetation is denser.Conversely, at higher elevations, where slopes are steeper and frost cracking is more common (Riebe et al., 2015), a diversity of processes produce a range of sizes, including abundant gravel and cobbles (Sklar et al., 2020), from a latent size distribution that is set by the fracture spacing of the underlying bedrock (Verdian et al., 2021).This sediment is then abraded and fractured as it travels downstream to the outlet, and thus the source elevations inferred from ages in stream sediment fail to match the observations of sediment size from hillslopes at higher elevations.(Sklar et al., 2020) show that slopes at low elevations have more fine sediment (a) and less gravel and cobbles (b, c) than slopes at higher elevations.Linear regressions (red lines with 95% confidence intervals) shown for (a)-(c) have p values < 0.02.The relative abundance of boulders on slopes (d) shows no significant trend with elevation (p = 0.18), and the mean value (23.6 ± 2.3%, ±std.err.) is plotted for reference (black dashed line).
Because the breakdown is substantial in this landscape, we cannot consider any one sediment size class in isolation.Rather, finer sediment sizes at the outlet are a mix of particles produced on hillslopes and fragments produced by physical wear of coarser sizes, which are generated in proportion to travel to distances.This means that sand or any single size may misrepresent spatial patterns of erosion across the catchment.At Inyo Creek, breakdown may mask spatial patterns of erosion, consistent with a modeled scenario in which ages in sand mirror hypsometry when in fact there is a strong elevational gradient in the erosion rate (Lukens et al., 2020).Independent evidence at Inyo Creek suggests an elevational gradient in both erosion rate (Riebe et al., 2015) and sediment size (Sklar et al., 2020), which are also consistent with modeled scenarios.

Implications for Detrital Thermochronology
The comparison between the (U-Th)/He ages and hillslope sediment sizes provides strong evidence that the breakdown during transport modifies signals of sediment production at Inyo Creek, despite the catchment's small area (3 km 2 ) and durable granitic bedrock.Both factors should tend to limit the effects of breakdown.Hence, while our results are site specific, the effects of breakdown on (U-Th)/He signals of sediment production are likely common and may be especially pronounced in larger catchments with less durable bedrock.Larger catchments are also likely to encompass diverse lithologies and weathering conditions, which should promote spatial variation in the sediment size distributions produced on hillslopes.It may therefore also be common that no single sediment size is representative of spatial patterns in sediment production in studies of detrital thermochronology.Indeed, there are few conditions under which a single size class might be representative of sediment production when it is complicated by spatially variable hillslope sediment size distributions, breakdown during transport, or both of these factors.For example, a representative sample could be obtained if the sampled size were produced on slopes in the same proportion of the sediment size distribution everywhere in the catchment, even if the proportions of other sizes vary.This would also require negligible breakdown or that size reduction only occurs by abrasion that produces silt, not by fracturing, such that the remaining sediment mass is shifted to smaller size classes without changing the shape of the size distribution.Field data indicate that sand fractions vary widely on hillslopes (e.g., Attal et al., 2015;Sklar et al., 2020;Terweh et al., 2021), and both field and laboratory data suggest that fracturing is common, especially in high-energy mountain rivers (Arabnia & Sklar, 2016;Kodama, 1994aKodama, , 1994b;;Le Bouteiller et al., 2011;Scott & Wohl, 2019).Together, these considerations suggest that conditions under which ages from a single, narrow size class will tell all about sediment production in a catchment should be rare.
These considerations have important implications for studies in which the shape of the age distribution is central to the interpretations, such as in tracer thermochronology studies of spatial patterns of erosion.In these studies, it will be important to obtain additional independent information, such as measurements of sediment size on slopes, erosion rates from cosmogenic nuclides in multiple sediment sizes, and realistic modeling of the effects of breakdown.
If the shape of the age distribution is not important, the complications described here are less likely to affect study outcomes.For example, determining a maximum depositional age requires only the youngest ages present, and inferring thermal histories may require only the range of ages present in the landscape, rather than their relative abundance.In catchments where breakdown effectively destroys sediment from distal parts of the landscape, previous modeling results suggest that detrital ages do not capture the entire range of ages present in bedrock (e.g., Lukens et al., 2020), but we do not see evidence for this at Inyo Creek.

From a Thermochronological Portrait to a Sediment-Production Portrait
The breakdown of sediment after it is produced on slopes adds a complication to interpreting initial sediment size distributions from the thermochronological portrait of sediment presented here.However, abrasion and fracturing, the two main modes of sediment breakdown in streams, can be modeled mechanistically using theory and data from experiments and field observations (e.g., Attal & Lavé, 2009;Le Bouteiller et al., 2011;Litwin Miller & Jerolmack, 2021;Szabó et al., 2015).It should be possible to combine these models with (U-Th)/He ages in stream sediment to better resolve and explain the spatial variation in size distributions of sediment produced on slopes.
Such efforts should also account for the spatial variability in erosion rates that is common in steep mountain catchments, for example, by measuring cosmogenic nuclide concentrations in each size class and possibly at multiple locations along the stream bed.This would provide constraints on how rates of sediment production vary with elevation across the sediment source area.We argue that it may be necessary to measure not only age distributions but also cosmogenic nuclide concentrations in multiple sizes (Riebe et al., 2015).Even then, it will be crucial to account for the breakdown by both abrasion and fracturing to obtain a comprehensive portrait of both the rate and size distribution of sediment production in steep mountain landscapes.

Conclusions
Here we presented detrital (U-Th)/He age distributions of 12 sediment size classes and used them to quantify sediment source elevations and constrain the downstream evolution of sediment size across a steep mountain catchment in the eastern Sierra Nevada.Our analysis builds on previous work that evaluated spatial variations in sediment production by testing the null hypothesis that the sediment production is uniform across the catchment using a bootstrapping approach.Here, we expanded this framework by considering all sediment sizes present in the stream, and explicitly included negligible breakdown during transport in the null hypothesis.We also expanded our analytical approach to simultaneously identify the range of elevations over which sediment production departs from the null hypothesis and quantified the likelihood that the sum of all departures across the catchment would occur by chance when sediment production and size distributions are spatially uniform and when the breakdown is negligible.
The inferred source elevation distributions of the finer sediment sizes (up to intermediate gravel) are statistically indistinguishable from hypsometry.However, they are not consistent with uniform erosion and sediment size distributions across the catchment.Ages from coarser sizes and comparisons to direct measurements of sediment size on hillslopes suggest that breakdown plays an important role in transforming sediment, and therefore that finer sediment sizes likely do not adequately represent the sediment production across the catchment.Two of the coarser gravel sizes and two of the cobble sizes have statistically significant departures from uniform sediment production that imply faster production at higher elevations, either because erosion rates are faster or because the sizes are disproportionately represented in the sediment size distribution at high elevations.Conversely, boulders in the stream are preferentially sourced from low elevations near the sample point, potentially reflecting the breakdown of boulders that originate from higher in the catchment.
Together, our analyses of multiple sediment sizes yield perhaps the most comprehensive thermochronological portrait to-date of the origins of sediment in a steep mountain catchment.Additional information on the spatial variability in erosion rates from cosmogenic nuclides in multiple sediment sizes should improve our understanding of how sediment production rates vary with elevation.We propose that this information can be used with detrital age data in a comprehensive model that accounts for sediment breakdown by abrasion and fracturing to obtain a complete portrait of sediment production and evolution across steep mountain landscapes.

Figure 1 .
Figure 1.Study site and age-elevation relationship.(a) Oblique Google Earth image of the eastern Sierra Nevada showing the Inyo Creek study area.Yellow and orange circles are bedrock sampling locations from previous work and this study, respectively (TableS1in Supporting Information S2) (b) Age-elevation relationship, a = 23.3z− 24.85 (where a is age in Ma and z is elevation in km), was calculated using inverse-variance-weighted ordinary-least-squares regression, with gray band spanning ± 1 standard error of the mean on the regression.(c) Joint distribution of elevation and travel distance for Inyo Creek (afterSklar et al., 2016), plotted as the frequency of elevations from the digital elevation model using a kernel density estimator (KDE) with a bandwidth of 10 m; (d) Elevation distribution (left axis) and corresponding bedrock cooling age distribution (right axis) of Inyo Creek catchment, plotted using an adaptive KDE (Z.Botev, 2023).

Figure 2 .
Figure 2. Inyo Creek has steep bedrock slopes (a, upper elevations), weathered granodiorite bedrock (b, lower elevations), and a range of sediment sizes from sand to boulders in the stream (c, d).Panel (d) shows the average grain size distribution from 16 separate Wolman-style pebble counts across the sample reach.Sampling efforts included measuring (e), weighing, and sub-sampling (f) clasts from 12 different size classes that span the full range of sizes present on the stream bed.

Figure 3 .
Figure3.Distributions of apatite-helium ((U-Th)/He) ages by sediment size class.The right axis shows elevations predicted from the bedrock age-elevation relationship in Figure1.Across 12 size classes, 699 individual crystal ages provide information about altitudinal patterns in sediment production within the catchment.An additional 14 grains were excluded (see Supporting Information S1).Age distributions in different size classes overlap and also clump at different elevations.Notable gaps in sediment production occur at low elevations for coarse gravel (16-32 mm) and high elevations for boulders (>256 mm).Horizontal spacing of points in each size class was created by jittering to show age variability despite clumping and does not represent variability in sizes.

Figure 4 .
Figure 4. Cumulative age distributions (CADs) for apatite (U-Th)/He ages from the 12 sediment size classes from Inyo Creek (colored lines).Black lines represent CAD of catchment bedrock calculated from the elevation distribution (i.e., hypsometry) using the age-elevation relationship.

Figure 5 .
Figure 5. Guide for interpreting the age distribution of each size class.(a) kernel density estimators (KDEs) of catchment elevations from 30-m digital elevation model (black dashed line) and sediment source elevations (violet), inferred from the age distribution of 96-128 mm size class using age-elevation relationship (Figure1).Gray lines in a and c define upper and lower limits of the 50%, 95%, and 99% confidence bands from 10 6 simulations of spatially uniform sediment production and negligible breakdown.(b) Oblique aerial view of elevations where excesses (orange) and deficits (blue) occur in the production of the measured sediment size relative to predictions from hypsometry for the 50% (lighter shading) and 95% (darker shading) confidence bands from the simulations.(c) The difference between the measured age and hypsometry KDEs in (a) yields a departure plot.(d) The simulations also yielded exceedance probabilities (y-axis) of cumulative departures for each of the confidence bands (gray lines).Violet circles are observed cumulative departures for the 96-128 mm age distribution.Orange and blue bars above (d) show the fraction of the catchment where observed ages represent positive and negative departures from the simulated 50% and 95% confidence bands.The vertical green dashed line and corresponding horizontal arrows mark the probability of cumulative departures of 0.3 or more for each of the confidence bands in (a) and (c) (see text).

Figure 6 .
Figure6.Departure (e.g., panel a) and cumulative departure (e.g., panel b) plots for 12 grain size sampled from Inyo Creek.Departure plots show differences between kernel density estimators of measured age distributions (colored lines) and catchment hypsometry (black horizontal line), with gray lines showing confidence bands from 10 6 simulations of uniform sediment production for each size class.Confidence band width increases with decreasing number of ages measured, reflecting greater chance of gaps and corresponding clumps in sampled elevations with smaller sample sizes.Exceedance probabilities of observed cumulative departures (colored circles) for each of the confidence bands (gray lines) are plotted for each grain size.The dashed black lines in cumulative departure plots correspond to exceedance probability of 0.05 or 5% of the total simulations.

Figure 7 .
Figure 7. Direct measurements of sediment size on hillslopes in the Inyo Creek catchment(Sklar et al., 2020) show that slopes at low elevations have more fine sediment (a) and less gravel and cobbles (b, c) than slopes at higher elevations.Linear regressions (red lines with 95% confidence intervals) shown for (a)-(c) have p values < 0.02.The relative abundance of boulders on slopes (d) shows no significant trend with elevation (p = 0.18), and the mean value (23.6 ± 2.3%, ±std.err.) is plotted for reference (black dashed line).