Nature Does the Averaging—In-Situ Produced 10Be, 21Ne, and 26Al in a Very Young River Terrace

The concentrations of long-lived in-situ produced cosmogenic nuclides (10Be, 21Ne, 26Al) in quartz obtained from a very recent (~200 a; based on 14C data on organic material) terrace of the Swakop River in Namibia are nearly constant throughout a 322 cm-long depth profile. These findings corroborate earlier hypotheses postulating a homogeneous distribution of these nuclides in freshly deposited river terrace sediments. An averaged nuclide concentration is a crucial and generally assumed prerequisite for the determination of numerical ages of old sediments.


Introduction
Fluvial sediments are excellent archives for terrestrial environments. They record information about palaeoclimate conditions and river catchment areas at the time of their deposition (e.g., [1,2]). The depositional age of such sediments can be determined using in-situ produced cosmogenic nuclides (CN) such as 10 Be (t 1/2 = 1.387 Ma [3,4]), 21 Ne (stable), and 26 Al (t 1/2 = 0.705 Ma [5]). Large amounts of some CN, e.g., 10 Be and 14 C, originate from interactions of cosmic rays with elements in the Earth's atmosphere, particularly nitrogen and oxygen (so-called atmospheric CN). Among the studied nuclides, atmospheric 10 Be is adsorbed on aerosol particles and deposited in the sediments via precipitation [6]. In-situ production of 10 Be by interaction with minerals in surficial rocks (in-situ 10 Be) is several orders of magnitudes lower [7]. In contrast, production of 21 Ne and 26 Al in the atmosphere is negligible. In-situ production of all CN ( 10 Be, 21 Ne, 26 Al) is a function of exposure time, altitude, latitude, topographic and self-shielding, and chemical composition of the target mineral [7,8]. In general, the more short-lived CN 14 C (t 1/2~5 .7 ka [9] and references therein) from in-situ production in quartz can also be used for dating [10,11]. However, more often (and also in this study) 14 C produced in the atmosphere, incorporated in equilibrium in organic materials and buried in sediment layers, is used for indirect dating [12,13].
Ephemeral river systems like the Swakop River of Namibia occur in arid regions worldwide. Thus, these rivers play a major role in basin drainage and sediment transport [14,15]. Their siliciclastic deposits are valuable archives that are widely used to understand landscape evolution and transport processes [16][17][18].
Several studies postulate an averaged in-situ CN signal in freshly deposited riverine sediments, soils, or regolith due to mixture of mineral grains with different pre-exposure histories [19,20]. Thus, uniform CN concentrations (due to high CN concentrations from inheritance) in depth profiles from such sediments indicate very young, i.e., Mid to Late Holocene, deposition ages [21]. This is consistent with the common phrase that "nature does the averaging" [22,23], which is the inevitable prerequisite for dating river terraces of any age.
The current detection limit of accelerator mass spectrometry (AMS) and noble gas mass spectrometry methods, and the extremely low CN concentrations resulting from in-situ production, restrict the lower age limit to about one to a few hundred years [24][25][26]. Hence, dating of very young fluvial deposits can be challenging. This also applies for the depth profile from a location close to the lower Swakop River (Namibia) investigated here. As the denudation in the entire Swakop catchment is known to be remarkably low and homogeneous [27,28], consideration and discussion of potentially variable denudation rates is not a subject of great concern. Thus, the sampled ephemeral river sediments represent an ideal archive concerning the aim of this study. The sedimentological features of the studied profile resemble those of profiles upstream from the presented locality, which are only a few hundred years old (see Section 2 for details). Therefore, this study only aims to provide evidence for the yet postulated averaging of the CN signal at the time of sedimentation [19] for 10 Be, 21 Ne, and 26 Al in a very young river terrace, even for ephemeral conditions. However, accurate numerical age determination of such profiles requires more suitable dating techniques like radiocarbon age determination of organic material (if present).

Location and Geological Setting
The Swakop River is among the largest ephemeral rivers of Namibia and drains a catchment area of 30,100 km 2 with an elevation range of zero to 2479 m a.s.l.. In contrast to perennial river systems, sediment deposition is dependent on the amount of regional precipitation, and therefore stochastic on small time scales. Beside the phases of Latest Pleistocene to Holocene sediment accumulation, the fluvial record of the Swakop River reaches back to the possibly Upper Oligocene "Langer Heinrich Formation" [29]. These sediments fill a palaeovalley, which is now used by the Tumas River. Due to the significant occurrence of uraniferous gravels, the sedimentology and stratigraphy of this succession is well-documented [30,31]. The "Langer Heinrich Formation" is unconformably overlain by fluvial facies of most likely Lower Miocene "Tsondab Sandstone Formation" [29,31]. The whole succession is discordantly covered by conglomerates of the "Karpfenkliff Formation", which is assumed to have a mid-or upper Miocene age [29,31,32]. Remnants of Pliocene strata could not yet be found in this area [29]. All of these pre-Pleistocene terrace complexes occur south of the modern Swakop River course (Figure 2b), indicating a northward migration of the river through time. The adjacent Kuiseb River valley hosts the well-studied upper Pleistocene "Homeb Silts" [33,34] and the uppermost Pleistocene "Gobabeb Gravel Formation" [29,35]. Possibly equivalent deposits are also known from the middle and upper reaches of the Swakop River and some of its tributaries [29,36].
The Swakop River and its tributaries drain large parts of the southern Damara Belt, which has a complex geology and comprises various rock types of mostly Cryogenian-Cambrian age (Figure 2a, see legend for time scale) [37]. The Palaeo-to Mesoproterozoic Abbabis Gneiss Complex forms an inlier within the central parts of the orogen [38]. However, there is also a younger cover sequence formed by siliciclastic and igneous rocks [39]. Detailed descriptions are given elsewhere [40,41] and references therein. The vast majority of the rocks in the mentioned geologic units contain quartz, which suggests an equal delivery of the latter from the entire catchment area.
Quartz-rich sediment samples were collected in January 2015 in a sporadically mined sand and gravel pit close to the ephemeral Swakop River, Namibia (22.64069 • S, 14.67411 • E, 90 m a.s.l., Figure 2c), from a 322 cm-long depth profile consisting of intercalated coarse-grained, plane bedded sand and fine to coarse gravel (Figure 1a). These sediments belong to the lowermost terrace complex of the Swakop River. According to time-resolved Google Earth satellite image series, the profile at one wall of the sand and gravel pit was exhumed after October 2013. This recent excavation has a constant depth of more than three metres and a large lateral extent of more than 80 m, which makes this profile an ideal site for sedimentological and cosmogenic nuclide depth profile studies as well as for testing the hypothesis that "nature does the averaging" sensu earlier works [22,23].
Three of the recorded gravel layers can be traced for several tens of metres, while the others are a few centimetres thin and of limited extent. This gives reason to assume that at least three flood events led to sediment deposition, matching with records of flood recurrence in the past millennium from the lower reaches of the Khan River and the middle reaches of the Swakop River [42]. There, several layers of flood deposits-from about 35 individual events-including gravel layers were dated between 240 ± 90 a and 90 ± 20 a using optically stimulated luminescence (OSL) [42]. Flood-derived coarse gravels with apparent ages between 350 and 100 years BP are also known from the Swakop River's mouth [43]. Below 300 cm depth, the sediments gradually become calcified, resulting in solidification at about 322 cm. Additionally, changing sediment colour and an older erosion surface on top of the calcified sediments (likely formed by the first of the three floods) led to the assumption that the deposits below a depth of 322 cm are a separate, older sediment complex originating from an earlier series of flood events. Older phases of extensive sediment deposition, mainly coarse sands, with OSL ages between 5100 ± 620 a and 14,900 ± 1700 a, followed by intensive calcification, have been found at other sites along the entire Swakop River catchment [42,43].

Materials and Methods
Five sediment samples of sand or sandy matrix of gravelly layers were taken in 2015 at profile depths of 0-5, 87-93, 158-162, 237-243, and 318-322 cm, respectively (NAMA031a, NAMA031b, NAMA031c, NAMA031d, NAMA031e). They were all analysed for their 10 Be, 26 Al, and-except for sample NAMA031b-21 Ne concentrations. Radiocarbon ages of driftwood and twigs (R1, R2, R3) from three accumulations of organic material in the topmost 15 cm of the profile, a piece of wood from a log found in the lower part of the sedimentary package (R4, about 60 m to the SE of the depth profile), and a snail shell (R5) from the top of the older sediment complex, all sampled in 2016, were used to bracket the age of the sediments.
The samples for 14 C analysis were prepared at the sample preparation unit for small samples for environmental research and medicine at the University of Vienna, Vienna Environmental Research Accelerator (VERA) facility [45]. Wood samples (R1-R4) were exposed to the standard acid-base-acid treatment and combusted in closed quartz vials. The snail shell sample (R5) was converted to CO 2 by hydrolysis with H 3 PO 4 . Considering the small sample size and the possible incorporation of carbonate by the living snail [46], a pre-etching step was omitted. The age obtained may thus represent an upper limit. Samples were normalised to IAEA-C3 cellulose, IAEA-C2 carbonate, and the VERA in-house-standard Vienna-CTW2 (graphite, Fraction Modern F 14 C = 1.254 ± 0.005) and blank-corrected using IAEA-C1 (carbonates) and the in-house-standard Vienna-HPG (wood samples). Calibration was performed with OxCal v4.3.2, calibration curves INTCAL 13 and BOMB 13 NH1.
Enrichment of 200-1000 µm quartz grains ( ≈ 2.65 g/cm 3 ) from the polymineral samples required a two-stage separation process: (1.) Density separation using lithiumheteropolytungstate in water at densities of 2.60 and 2.70 g/cm 3 . (2.) Hand-picking under a binocular microscope (ZEISS Stemi-2000) to exclude quartz with interior non-quartz mineral inclusions. Further steps were carried out in a dedicated CN laboratory to remove residual non-quartz-minerals. The quartz concentrate was cleaned with a 1:1 solution of H 2 SiF 6 (35%) and HCl (32%) in three (NAMA031a & NAMA031b) and five steps (NAMA031c, NAMA031d, NAMA031e), respectively [47]. Beryllium-10 from production in the atmosphere was removed by three consecutive dissolution steps of the surfaces with 48% HF, resulting in ca. 10% mass loss of the quartz grains per step. Solid aliquots for 21 Ne analysis were taken prior to total dissolution of quartz in 48% HF. Two processing blanks for radionuclide analysis were added to monitor all possible unwanted contributions such as contamination between samples in the chemistry lab and during measurement, and from all chemical products and target preparation materials used. All samples and the blanks were processed with ca. 300 µg of a 9 Be carrier ("Phenakite DD";~0.1 g solution with a 9 Be concentration of 3025 ± 9 µg/g [48]) and ca. 900 µg of a commercial 27 Al carrier (Carl Roth GmbH, Karlsruhe, Germany; ca. 0.9 g solution with a 27 Al concentration of 1000.5 ± 2.0 mg/L; = 1.011 g/cm 3 ). Further chemical separation of Be and Al followed the procedures described in [49]. Determination of natural 27 Al was done via inductively coupled plasma mass spectrometry (ICP-MS; iCAP RQ, Thermo Fisher: Waltham, MA, USA) of representative aliquots (2.6-2.9 weight % of the sample). Resulting BeO and Al 2 O 3 were mixed with Nb (ca. 4 × mass of BeO) and Ag powder (ca. 1 × mass of Al 2 O 3 ), respectively. Both mixtures were pressed into Cu cathodes.
For cosmogenic 21 Ne determination in quartz samples NAMA031a, NAMA031c, NAMA031d, and NAMA031e at GFZ Potsdam, ca. 0.7 g of cleaned quartz were degassed by stepwise heating (400, 600, 800, 1200 • C) and analysed according to procedures described in [53]. In addition, aliquots of approximately 1 g of all samples except NAMA031c were vacuum-crushed to reveal non-atmospheric and non-cosmogenic trapped 21 Ne components [54].

Results
Results are summarised in Tables 1-3 and Figure 1. Carbon-14 results gave ages between 208 ± 129 a (R5) and 7562 ± 67 a (R4), while the topmost samples yielded 44 ± 3 a (R2), 37 ± 3 a (R1), and 22 ± 3 a (R3) (Table 3, Figure 1a).  Measured 10 Be concentrations for all samples overlap within 1 sigma uncertainties throughout the profile and range from 5.44 ± 0.26 × 10 5 to 6.03 ± 0.33 × 10 5 at/g. Three of the five 26 Al values (NAMA031b, NAMA031d, NAMA031e) are statistically indistinguishable within 2 sigma, ranging between 2.77 ± 0.24 × 10 6 and 3.11 ± 0.30 × 10 6 at/g. The surface sample NAMA031a contains slightly less (~30%, i.e., 2.03 ± 0.14 × 10 6 at/g) 26 Al, which further applies even more for sample NAMA031c (1.46 ± 0.07 × 10 6 at/g). Hence, the 26 Al/ 10 Be ratios for samples NAMA031b, NAMA031d and NAMA031e are the same within 2 sigma uncertainties, whereas the 26 Al/ 10 Be ratios of NAMA031a and NAMA 031c would overlap with sample NAMA031b within their 3 sigma and 7 sigma errors, respectively. The four 21 Ne samples NAMA031a, NAMA031c, NAMA031d and NAMA031e show the same trend as the 10 Be signal, although the total 21 Ne excess in the 400-800 • C heating steps, usually assumed to be cosmogenic, is 20% higher in NAMA031e. This could be a result of an increased amount of nucleogenic 21 Ne in this sample ( Figure 3); high concentrations of He with radiogenic isotopic composition (Table 3) support an important contribution of nucleogenic Ne. Figure 3. Neon three-isotope plot for stepwise heating and crushing data of NAMA031a, NAMA031c, NAMA031d and NAMA031e (grey-400 °C, yellow-600 °C, red-800 °C, green-crushing extractions). The 1200 °C data would plot out of scale far to the right (see Table 2). "Spallation line", i.e., mixing line of atmospheric and cosmogenic Ne, according to [56]. mfl: mass fractionation line. While the NAMA031a, NAMA031c and NAMA031d data are consistent with a two-component mixture of trapped Ne (as determined by the crusher extractions) and cosmogenic Ne, the 600 °C and 800 °C steps of NAMA031e may indicate the presence of some nucleogenic 21 Ne in addition. 2 sigma uncertainties are shown.

Discussion
The maximum age of the investigated terrace complex is given by a (calibrated) 14 C age of 7562 ± 67 a obtained from the snail shell (R5) on top of the calcified sands (lowermost part of the profile, Figure 2a). This age is in line with the termination of widespread calcrete formation and palaeoflood events in the Swakop catchment at 8.8 ± 1.0 ka [42,43]. The evaluation of different palaeoclimate proxies all over Namibia led to the assumption of much wetter conditions during the Early Holocene, which caused significantly higher runoff than today [57]. Just after the Early to Mid-Holocene transition, the climate of southern Africa became much drier [58], resulting in a decreased discharge and a lack of flood-derived sediments in the Swakop River [42]. Accordingly, the age of the snail shell (R5) allows the determination of the stratigraphic position of the sediments below the Swakop River's youngest terrace complex.
However, the unconsolidated sands that were sampled are likely much younger. An apparent 14 C age of 208 ± 129 a was calculated for the sampled tree log (R4), which times the formation of the lower part of the unconsolidated sand and gravel sequence. This age fits with the increased number of flood events between ca. 1450 and ca. 1800 AD throughout Namibia [42,43,59,60]. The latter interval is almost coeval to the Little Ice Age that is characterised by globally cooler climate conditions with wet and dry periods in southern Africa [61]. At least northeastern Namibia received significantly higher precipitation than today in the decades around 1800 AD [61]. The apparent absence of sediments from the period between ca. 7000 and 400 a shows a striking similarity to parts of the adjacent Kuiseb River [59]. This underlines the possibility of exceptionally high discharge at about 400 a [61], possibly eroding and reworking the older sediments [59]. . Neon three-isotope plot for stepwise heating and crushing data of NAMA031a, NAMA031c, NAMA031d and NAMA031e (grey-400 • C, yellow-600 • C, red-800 • C, green-crushing extractions). The 1200 • C data would plot out of scale far to the right (see Table 2). "Spallation line", i.e., mixing line of atmospheric and cosmogenic Ne, according to [56]. mfl: mass fractionation line. While the NAMA031a, NAMA031c and NAMA031d data are consistent with a two-component mixture of trapped Ne (as determined by the crusher extractions) and cosmogenic Ne, the 600 • C and 800 • C steps of NAMA031e may indicate the presence of some nucleogenic 21 Ne in addition. 2 sigma uncertainties are shown.

Discussion
The maximum age of the investigated terrace complex is given by a (calibrated) 14 C age of 7562 ± 67 a obtained from the snail shell (R5) on top of the calcified sands (lowermost part of the profile, Figure 1a). This age is in line with the termination of widespread calcrete formation and palaeoflood events in the Swakop catchment at 8.8 ± 1.0 ka [42,43]. The evaluation of different palaeoclimate proxies all over Namibia led to the assumption of much wetter conditions during the Early Holocene, which caused significantly higher runoff than today [57]. Just after the Early to Mid-Holocene transition, the climate of southern Africa became much drier [58], resulting in a decreased discharge and a lack of flood-derived sediments in the Swakop River [42]. Accordingly, the age of the snail shell (R5) allows the determination of the stratigraphic position of the sediments below the Swakop River's youngest terrace complex.
However, the unconsolidated sands that were sampled are likely much younger. An apparent 14 C age of 208 ± 129 a was calculated for the sampled tree log (R4), which times the formation of the lower part of the unconsolidated sand and gravel sequence. This age fits with the increased number of flood events between ca. 1450 and ca. 1800 AD throughout Namibia [42,43,59,60]. The latter interval is almost coeval to the Little Ice Age that is characterised by globally cooler climate conditions with wet and dry periods in southern Africa [61]. At least northeastern Namibia received significantly higher precipitation than today in the decades around 1800 AD [61]. The apparent absence of sediments from the period between ca. 7000 and 400 a shows a striking similarity to parts of the adjacent Kuiseb River [59]. This underlines the possibility of exceptionally high discharge at about 400 a [61], possibly eroding and reworking the older sediments [59].
Except for the slightly lower 26 Al concentrations of the surface sample NAMA031a and of sample NAMA031c, the entire profile exhibits a homogenous CN concentration with similar 26 Al/ 10 Be ratios. This supports the hypothesis of homogenised CN signals in very young fluvial deposits, at least for ephemeral river systems. Hence, essentially the entire production of the studied long-lived CN must have occurred during pre-exposure and/or sediment transport, while the in-situ production of CN after sediment deposition is negligible. Considering a maximum deposition age of 400 a, a Sea Level High Latitude (SLHL) production rate for 10 Be of 4.02 at/(g a) [64] scaled using [65] and no additional correction like topographic or self-shielding for "after-deposition production" yielded maximum 10 Be and 26 Al surface concentrations of ca. 1800 and 11,700 at/g, respectively, which is far lower than the measured concentrations. This is further corroborated by 26 Al/ 10 Be ratios in a range of 2.42 ± 0.13 to 5.72 ± 0.31, which are depleted with respect to the production rate of 6.61 ± 0.52 [66] and indicate that the quartz grains must have been exposed to cosmic rays at the surface a long time before their deposition in the terrace. The same applies for the 21 Ne/ 26 Al and 21 Ne/ 10 Be ratios (Figure 1c).
An explanation of what can be observed in this restricted outcrop can be deduced from earlier published data of the Swakop River's catchment area and the adjacent regions. This allows a better documentation of average CN concentrations that can be found in this part of Namibia. To do so, we have taken benefit of the work of Bierman and Caffee [27], where 66 samples were prepared for both 10 Be and 26 Al measurements. Ignoring the ten northern samples (samples NAM-52 to NAM-62) due to their remote distance to the studied area, there is a good agreement between the CN concentrations of this study and those of [27] (Figure 4). Additionally, no correlation to altitude can be observed. As mentioned in [27], our study confirms that small streams are eroding more rapidly than surrounding outcrops.
Although only five samples were taken at the site discussed here, at least the 10 Be signal is completely averaged throughout the profile. This also holds for 21 Ne and 26 Al (except for NAMA031c 26 Al) when considering the weighted mean of all samples ± 2 sigma. This applies for four (out of five) of the 26 Al, as well as for all four investigated 21 Ne samples (Figure 1b), which excludes different provenances of quartz grains from NAMA031a to NAMA031e.
The lower 26 Al values of the surface sample NAMA031a and sample NAMA031c might be partially explained by erroneous 27 Al data, likely caused by the formation of "aluminium-magnesium-fluorides (xH 2 O)", which have been produced as secondary reaction products during the sample digestion [67]. Total destruction of these compounds is challenging for some sample compositions (high in Mg) and sometimes does not allow quantitative redissolution of aluminium for accurate 27 Al determination in liquid aliquots. Regrettably, we have not analysed the aliquots for Mg concentrations to have final proof, however, the measured 27 Al concentration, being two to three times higher in NAMA031a than in the other two samples (Table 1), is usually a well-accepted proxy also for a high Mg concentration [47].  26 Al concentrations versus altitude of the sample location in samples of [27] and from this study (the five rightmost samples of panels a and b, i.e., NAMA031 ab-c-d-and e).

Conclusions
Radiocarbon ages of organic materials time the terminal deposition of an older terrace complex at 7562 ± 67 a, while the deposition of the studied part of the profile is about 200 years old or even younger. These ages are in line with the increased flood frequency at the terminal phase of calcrete formation in the Early Holocene and during the Little Ice Age.
The studied profile gives evidence for a complete averaging of long-lived and stable CN concentrations in young, i.e., Latest Holocene fluvial sediments. Negligible in-situ production of those CN since deposition indicates that the measured signal is mostly inherited from previous exposure. These data strongly support the hypothesis that "nature does the averaging" by complete and homogeneous mixing of the sediments before and during deposition. Additional proof for sediment supply representative of the entire catchment area of the Swakop River and not biased by a single dominant source is given by detrital zircon data, which indicate the presence of material from all major lithological units [68].    26 Al concentrations versus altitude of the sample location in samples of [27] and from this study (the five rightmost samples of panels a and b, i.e., NAMA031 a-b-c-d-and e).

Conclusions
Radiocarbon ages of organic materials time the terminal deposition of an older terrace complex at 7562 ± 67 a, while the deposition of the studied part of the profile is about 200 years old or even younger. These ages are in line with the increased flood frequency at the terminal phase of calcrete formation in the Early Holocene and during the Little Ice Age.
The studied profile gives evidence for a complete averaging of long-lived and stable CN concentrations in young, i.e., Latest Holocene fluvial sediments. Negligible in-situ production of those CN since deposition indicates that the measured signal is mostly inherited from previous exposure. These data strongly support the hypothesis that "nature does the averaging" by complete and homogeneous mixing of the sediments before and during deposition. Additional proof for sediment supply representative of the entire catchment area of the Swakop River and not biased by a single dominant source is given by detrital zircon data, which indicate the presence of material from all major lithological units [68]. team for their assistance with AMS measurements. The ASTER AMS national facility (CEREGE, Aix-en-Provence) is supported by the INSU/CNRS, the ANR through the "Projets thématiques d'excellence" program for the "Equipements d'excellence" ASTER-CEREGE action and IRD. Furthermore, the authors like to thank R. Krause, M. Hofmann, J. Zieger, M. Stutzriemer, J. Harazim, and J. Rothe for field assistance and help during quartz picking, E. Schnabel for performing the noble gas analyses and S. Beutner for 27 Al analysis by ICP-MS.

Conflicts of Interest:
The authors declare no conflict of interest.