Variations in tephra stratigraphy created by small-scale surface features in sub-polar landscapes

We explore the effect small-scale surface features have on influencing the morphology and grain-size distribution (GSD)oftephralayerswithintheQuaternarystratigraphyofsub-polarlandscapes.Icelandicth (cid:1) ufur,smallcryogenic earth mounds, areused to assess howandwhy the morphologyand GSDof tephra layers varyoversuch formations. Through measurement of tephra layer thickness and GSD, Hekla 1947 and Gr (cid:1) ımsv € otn 2011 tephra layers are analysed. Results indicate that such microtopographic features do indeed alter the form of tephra deposits and thereforethetephralayerthatispreservedinthestratigraphy.Tephrathicknessissignificantlygreaterinhollowsthanontheth (cid:1) ufurcrests.Thereisgreatervariationintephrathicknessmeasurementsfromth (cid:1) ufurincomparisontocontrol measurementsfromasurfacewhereth (cid:1) ufurareabsent.Th (cid:1) ufurcrestscontainlargergrainsizes thanhollows,forboth H1947 and G2011 tephras; however thiswas only statistically significant for the G2011 tephra. Such morphological patterns are thought to arise from an interplay of tephra characteristics, altered topography from the th (cid:1) ufur formations and earth surface processes operating at the sites. This study provides insight into the potential of tephra layer morphology and internal structures as indicators of Quaternary landforms and processes. Additionally, it provides important context for the appropriate sampling of tephra layers to infer volcanological processes, as the characteristics of preserved layers do not necessarily reflect those of the original fall-out.

We explore the effect small-scale surface features have on influencing the morphology and grain-size distribution (GSD) of tephra layers within the Quaternary stratigraphy of sub-polar landscapes. Icelandic th ufur, small cryogenic earth mounds, are used to assess how and why the morphology and GSD of tephra layers vary over such formations. Through measurement of tephra layer thickness and GSD, Hekla 1947 and Gr ımsv€ otn 2011 tephra layers are analysed. Results indicate that such microtopographic features do indeed alter the form of tephra deposits and therefore the tephra layer that is preserved in the stratigraphy. Tephra thickness is significantly greater in hollows than on the th ufur crests. There is greater variation in tephra thickness measurements from th ufur in comparison to control measurements from a surface where th ufur are absent. Th ufur crests contain larger grain sizes than hollows, for both H1947 and G2011 tephras; however this was only statistically significant for the G2011 tephra. Such morphological patterns are thought to arise from an interplay of tephra characteristics, altered topography from the th ufur formations and earth surface processes operating at the sites. This study provides insight into the potential of tephra layer morphology and internal structures as indicators of Quaternary landforms and processes. Additionally, it provides important context for the appropriate sampling of tephra layers to infer volcanological processes, as the characteristics of preserved layers do not necessarily reflect those of the original fall-out.
Polly Thompson (polly.thompson@ed.ac.uk), Andrew J. Dugmore and Anthony J. Newton, Institute of Geography, School of GeoSciences, University of Edinburgh, Edinburgh EH8 9XP, UK; Richard T. Streeter Tephra can undergo numerous alterations post deposition before being preserved as an enduring stratigraphical layer (Dugmore et al. 2020). The effect small-scale surface features have on the preservation of tephra has not yet been explored. Earth hummocks, known as th ufur (þ ufur) in Iceland are small, dome-shaped cryogenic earth mounds characteristic of sub-polar locations ( Fig. 1), and are used as exemplars in this pilot study, as similar topographically controlled processes will operate in different landscapes. Th ufur are features of permafrost and climatic state, providing an indication of environmental conditions (Grab 2005;Pintaldi et al. 2016). Th ufur formations result from freeze-thaw activity in high-latitude, or high-altitude, areas and are usually covered by vegetation (Van Vliet-Lano€ e & Sepp€ al€ a 2002; Grab 2005;Pintaldi et al. 2016;Fig. 1). Th ufur are a common cryogenic landform and are found globally across high-latitude areas such as Iceland, Greenland, Russia and Canada, as well as in upland areas at lower latitudes that contain enough soil for them to form, such as Dartmoor in southwestern England (Grab 2005). Such small-scale (width, height and/or length~20-250 cm) topographic features are important landforms for inferring current and past earth surface processes and land management.
It is important to understand how small-scale surface features alter tephra layers because in addition to forming chronological markers, they are also used to infer the parameters of past eruptions (Lowe 2011). Both approaches make assumptions about the tephra. For example, tephrochronology assumes that the eruption and deposition dates are simultaneous. Volcanogenic inference (using tephra deposits to infer eruption parameters such as volume) relies on the assumption that the tephra layer is representative of the material that was deposited at the time of the eruption (Bonadonna & Houghton 2005;Engwell et al. 2013;Cutler et al. 2018).
However, tephra deposits are rarely preserved in their original form and their transformation is often regarded as an unhelpful complication. Deposits can undergo a series of morphological alterations soon after deposition, such as compaction, reworking (by wind and/or water), bioturbation and frost action, which can indi-opportunity to extract data on past environmental conditions. For example, undulating tephra layers that define closely spaced crests and hollows can signify the presence of th ufur on the surface. If we are to extract relevant proxy environmental data from the characteristics of tephra layers, we need to be able to distinguish between those features acquired by the deposit on the surface and those acquired once the deposit becomes a stratigraphical layer. This allows us to identify features that are properties of tephra fall or features reflecting surface conditions. Assessment of tephra deposits across th ufur have indicated differences in the thicknesses of tephra on crests and in hollows, despite a uniform vegetation cover and thickness of the initial deposit. We therefore seek to determine how tephra preservation is influenced by microtopography, and what alterations in the thickness, layer morphology and grain-size distribution of tephra occur (Dugmore et al. , 2020. Surface vegetation structures are known to affect the stabilization and preservation of tephra deposits, and at scales of 10s-100s of metres vegetation cover is more critical in determining preservation than slope or location on a slope of up to 35° ( Cutler et al. 2016a, b;Dugmore et al. 2018). Examining th ufur formations will help to determine whether the presence of undulations on the surface overrides the vegetation present in terms of tephra preservation, and examines micro slope angles >35°.
Thus, this paper assesses whether tephra layers retain a signal of surface microtopography at the time of deposition and examines the transformation of the tephra during the period between its deposition and its burial. To understand these processes in greater detail, we designed a natural experiment studying two recent tephra layers that were deposited across th ufur formations to determine the impacts of such small-scale morphological features on tephra layer formation. The formation of subaerial tephra layers takes months to years and is difficult to observe directly. To allow for enough time to have passed, but ensure that surface conditions at the time of deposition were similar, our field survey in 2019 studied two Icelandic tephra layers 72 and 8 years after their respective eruptions. These tephra layers were formed by the eruption of Hekla in April 1947 and the eruption of Gr ımsv€ otn in May 2011. Ourobjectives are to measure the thickness and grain-size distribution of tephra layers deposited across areas of th ufur and our aim is to understand how small-scale surface features can create lasting morphological and sedimentological variations in the Quaternary tephrostratigraphical record. The terminology in this paper follows Dugmore et al. (2020), where the term tephra deposit is used to define tephra that has accumulated on the surface, and tephra layer describes a visible horizon of tephra bounded by sediments on its top and bottom surfaces.

Study areas
We sampled tephra thickness and grain-size distribution (GSD) over crests and hollows of th ufur from the two tephra layers at sites in southern Iceland. These samples were then analysed to determine if there is a significant difference in tephra thickness, morphology and GSD between the crests and hollows of th ufur and therefore if these geomorphological features have an effect on tephra preservation. Surveys were conducted at three sites spanning two different locations within Iceland in June and August 2019, focusing on the Hekla 1947 (H1947) and Gr ımsv€ otn 2011 (G2011) tephra layers (Figs 2, 3). Iceland has numerous volcanoes, with an eruption occurring on average every 3-4 years (Thordarson & Larsen 2007). The frequent tephra production, coupled with silty loessial soils of contrasting grain sizes and colours that have high sediment accumulation rates (SeAR), create numerous, clearly identifiable wellseparated, isochronous (age-equivalent) tephra layers. Sub-polar environmental conditions lead to extensive areas of th ufur formation, and this combination of factors makes Iceland an ideal location to investigate the impact of microtopographic variation on tephra layer preservation (Thorarinsson 1944 We measured and sampled the H1947 tephra at two sites (A and B on Fig. 2) located in the area of Hamragarður in south Iceland, on the lower western slopes of Eyjafjallaj€ okull ( Table 1). The elevation of Site A was 241 m and of Site B was 90 m a.s.l. The closest weather station with historical records to Sites A and B is located in Vatnsskarðsh olar (~40 km east). From 1949 to 2020, average yearly temperature ranged from 4 to 6.6°C, with the average temperature in 1949 (2 years after the eruption and the earliest available year in the record) 4.9°C. Average yearly precipitation varied from 882 to 2042 mm, with 1498 mm of precipitation in 1949 (Icelandic Meteorological Office 2021).
The H1947 eruption occurred in spring, beginning on 29th March and ending on 21st April. During the Plinian phase of the eruption (the first few hours) it is estimated that 180 million cubic metres of ash, pumice, bombs and scoria were erupted and dispersed in a southerly direction, covering over~3000 km 2 in tephra (Thorarinsson 1956;Rea et al. 2012;Cutler et al. 2018). H1947 is a coarse-grained dark tephra, easily identifiable in the field from its stratigraphical position close to the surface (<0.5 m deep), range of pumice colours from grey/brown to black and the occurrence of small pieces of red scoria within the layer.
We measured and sampled the G2011 tephra layer at a third site (C, Fig. 3) at K alfafell in southeast Iceland (Table 1). The elevation of Site C was 149 m a.s.l. The closest weather station to Site C with historical records is Kirkjubaejarklaustur (30 km southwest). From 1939 to 2012, average yearly temperature ranged from 3.2 to 6°C, with the average temperature in 2012 (the year following the eruption) 5.3°C. Average yearly precipitation varied from 1207 to 2442 mm, with 1990 mm of precipitation in 2012 (Icelandic Meteorological Office 2021). The G2011 tephra layer is fine-very fine grained with a uniform grey colour, although it is darker when wet. At K alfafell, the G2011 layer was found a few centimetres below the surface.
The G2011 eruption occurred in late spring, beginning on 21st May and ending on 28th May 2011 (Liu et al. 2014). The interaction between glacial meltwater and magma initiated a phreatomagmatic style eruption. The eruption was short-lived, but intense, with a Volcanic Explosivity Index Magnitude of 4 (Guðmundsson et al. 2012;Cabr e et al. 2016). The eruption generated a total (bulk) volume of tephra of 0.7 km 3 (Guðmundsson et al. 2012) and had a plume height of <20 km . The axis of tephra dispersal during the 2011 eruption was in a (generally) southerly direction from the volcano .
We assumed that in terms of its influence on tephra deposition, the vegetation cover in 2019 was broadly the same as during the deposition of H1947 and G2011. Examining aerial photographs from 2 years before the eruptionin1947confirmsthatthelandcoverwassimilarto today's (NCAP 2021). Site C where the G2011 tephrawas sampledwas alsovisited in 2012 and the vegetation in 2019 was comparable. These sites were chosen as they had numerous,well-developedth ufur.SitesAandBhadhigher plant diversity than Site C. As well as grass and moss, thyme (Thymus vulgaris), blueberry (Vaccinium sp.), crowberry (Empetrum nigrum) and patches of dwarf birch (Betula nana) were all present. Species cover at Site C in K alfafell was limited to moss and grass species. The initial H1947 deposit thickness at Hamragarður was~50 mm (Thorarinsson1956).Approximately10-20 mmofG2011 tephra was deposited at Kirkjubaejarklaustur (Stevenson et al. 2013

Field sampling
The ways in which small-scale topographic features affect tephra layer morphology and grain-size distribution (GSD) were assessed with a combination of field observations and laboratory experiments. We assessed differences in tephra preservation by taking paired measurements of tephra layer thickness from th ufur crests and adjacent hollows. Samples of tephra were collected from sampling locations within Sites B and C to measure differences in GSD between crests and hollows. Prior to data collection, a power analysis on pilot data was conducted to determine the optimum number of measurements required. The power analysis was based on 11 pairs of H1947 thickness measurements collected from th ufur crests and hollows (n = 22). In this data set, the mean tephra thickness was lower on the crests (11.3 mm) than in the hollows (18.5 mm), but the difference was not significant (paired t-test: t (10) = 1.624, p = 0.13). Power analysis was conducted using the function power.t.test in R (R Core Team 2019), with the following parameters: mean tephra thickness = 15 mm; standard deviation = 9 mm, effect size = 25% (4 mm) and power = 0.8. The results indicated that a minimum of 42 th ufur (n = 41.70) should be surveyed (paired measurements). At each site, a suitable cluster of th ufur formations was identified by inspection. The size of the survey area reflected the density of earth hummocks, but in all cases was comparable in terms of vegetation, slope and elevation; Site A was 224 m 2 , Site B was 100 m 2 and Site C was 56 m 2 . Each cluster had well-developed th ufur, with a relative relief of at least~20 cm and diameter~50 cm. A small block of surface vegetation and the underlying soil 20925930 cm deep was then removed intact from each selected th ufur crest and the adjoining hollow to allow the tephra to be measured. Three representative measurements of the overlying soil thickness and the tephra layer thickness were taken from three sides of the excavated block at a resolution of AE1 mm. The measurements were taken directly from the middle of the block extracted from the crest and the hollow so that they were systematic and taken from the same place on each th ufur formation. Samples for GSD were also taken in this way. These measurements were averaged to give a mean soil thickness and tephra layer thickness for each th ufur crest and hollow. This process was repeated at each site for every th ufur sampling location surveyed within the cluster. The number of samples collected for grain-size analysis is summarized in Table 1. A sample of the entire layer was collected from every crest and hollow (where there was a tephra layer present) on each th ufur.
Control sets of measurements were collected to obtain tephra layer thickness from a site with no th ufur. The control site in Hamragarður was located <1 km from Sites A and B on a moss heath area with no notable gradient or undulations. The thickness of the H1947 tephra layer was measured every centimetre along a 4.8m-long transect (Fig. 2). Three control sets of measurements from K alfafell were also used (Fig. 3); Control 1 was collected in Bl omsturvellier from a rofabard (an Icelandic erosion feature, see Arnalds 2000) with measurements obtained 5-15 m from the edge of the escarpment (100 measurements in total, measured every 5 cm). Controls 2 and 3 were both collected in K alfafell and presented in Cutler et al. (2016a) as sites K alfafell (moss, K m ) and K alfafell (grass, K g ). Control 2 consisted of 200 measurements, collected every 12.5 cm and Control Site 3 consisted of 120 measurements, collected from 24 pits at 5-m intervals along a transect. Further details about the control data sets used are provided in Data S1.

Grain-size analysis
GSD of samples was measured by laser diffraction granulometry, using a Beckmann Coulter LS230 with a PIDS detector. Samples of tephra were prepared and the grain-size distribution analysed following the steps outlined in Data S2. H1947 is a coarse-grained tephra with lithic and pumice clasts; thus each sample was sieved so that clasts larger than 2000 lm were not processed through the grain-size analyser, as this is the maximum size fraction that can be measured. This coarser fraction was sieved using half phi sizes allowing it to be easily combined with the laser diffraction derived measurements. G2011 is a fine-grained tephra with all grains in the samples <2000 lm; therefore the samples were not sieved. The cone and quartering technique was used to subsample the tephra to be measured in the grain-size analyser. The sample was passed through a cone so that a representative distribution of grain sizes was subsampled for measurement (Blott et al. 2004). Raw outputs were converted from increments in lm to half Φ units for analysis and plotting. The results of the ultrasonic bath test (Data S3) indicated that using the ultrasonic bath for a 5-min period prior to analysis did not damage or alter the grainsize distribution significantly (Fig. S1, Table S1) and therefore all samples were run through the ultrasonic bath prior to analysis. Trials to remove soil from the tephras (Data S4, Figs S2, S3, Table S2) confirmed that this method worked and all samples were cleaned of soil prior to analysis.
Statistical techniqueswere used to analyse the data sets collected on tephra layer thickness and GSD to determine if there is a significant difference between tephra layers preserved in crests and hollows of th ufur. Key grain-size statistics (mean, median, standard deviation, etc.) were obtained using the Excel plugin GRADISTAT (version 9.1; Blott & Pye 2001). Median tephra grain size and thickness of the layer are correlated as a function of the distance from the volcanic vent and distance from axis of fall-out, with thinner tephra layers containing finer grain sizes at a landscape scale (Pyle 2016). As data for both parameters were collected in this study, the relationship was tested to examine if this association holds true when tephra layers are deposited across th ufur.

Layer thickness
Variabilityof tephra and soil thickness in all sites (A-C) is summarized in Fig. 4. At each site the layer thicknesswas variable: Site A crests ranged 3-29 mm, hollows 0-64 mm, Site B crests 6-14 mm, hollows 11-33 mm (both H1947) and Site C crests 17-98 mm, hollows 30-141 mm (G2011). The results of the paired t-test showed that there was a statistically significant difference in tephra thickness between th ufur crests and the hollows at all sites. At all three sites the tephra layers were thicker in the hollows than in the crests (Fig. 4). Soil thickness had a smaller difference between crests and hollows than the tephra layer thickness, particularly in Sites A and C, with mean and standard deviationvalues similar in both crests and hollows. Site B has a significant difference in soil thickness between crests and hollows, with a thicker soil layer in the crests. Many crests at Site B had little or no tephra layer present. At Site B, only four th ufur crests contained a measurable layer of H1947; however, overlying soil was measured on every crest where sufficient tephra grains were present to define the surface in 1947. Sites A and C had a measurable tephra layer on all crests and hollows.
Tephra thickness measurements from the control sites compared to measurements from th ufur crests and hollows at Sites A-C are also presented in Fig. 4. Both crest and hollow measurements are largelyout of range of the control site thicknesses for H1947, although the crests at Site A are very similar to the control thicknesses. G2011 values largely fall within the control ranges, apart from hollow measurements at Site C, which have a much larger range.

Grain-size distribution patterns
Site A did not have samples collected for grain-size analysis (Table 1). Samples for GSD were collected from each region (Hamragarður and K alfafell) rather than each site. This streamlined the number of samples analysed for GSD. Tephra layer thickness is measured at every site as this is the primary variable investigated, and is able to be tracked across a landscape more easily than GSD. Variation in GSD gives an indication of the processes taking place to redistribute the tephra layer and therefore selective sampling is sufficient. GSD patterns for Sites B and C are presented.
Site B: H1947 tephra. -The overall mean GSD is displayed in Fig. 5A. The GSD on crests and in hollows follow a similar pattern, with a mode of 0 Φ for both crests and hollows, although crests have a slightly higher proportion of large grains than the hollows. Both have a distribution of grains between À2.5 and 5.5 Φ. The GSD for H1947 tephra was unimodal, with a mode centred around 0 Φ in both crests and hollows. Figure 5B shows boxplots of the distribution of median grain-size values for Site B. These indicate that crests have a larger median grain size than hollows, with hollows having a greater variability in grain size than crests. There was no significant difference in mean grain size between the th ufur crests and hollows (Welch two sampled t-test: t (3.6) = 2.44, p = 0.078). There was also no significant difference in median grain size between th ufur crests and hollows (Kruskal-Wallis test: (46) p = 0.47). The grain sizes came from different distributions (two sample Kolmogorov-Smirnov test: D = 0.66, p = 0.046), indicating that populations may differ in median, variability or the shape of the distribution.
Site C: G2011 tephra. -Site C has a complete set of crest and hollow samples, measured from 43 pairs of th ufur, with the overall mean distribution displayed in Fig. 6A. Crests peak at 2 Φ and hollows at 4 Φ. Crests have a distribution between 0.5 and 7.5 Φ and hollows have a distribution between 1.5 and 7.5 Φ. Boxplots in Fig. 6B show the distribution of median grain-size values for Site C and indicate that crests have a larger median grain size than hollows; however, the crests show a greater variance.
There was a significant difference in mean grain size between the th ufur crests and hollows (paired t-test: t (42) = 9.18, p < 0.001). Unlike mean grain size, there was no significant difference between median grain size of crests and hollows (Kruskal-Wallis test: (85), p = 0.48). The grain sizes came from different distributions (two sample Kolmogorov-Smirnov test: D = 0.60, p < 0.001). Thus, the tephra layer is thicker in the hollows, but has a finer grain size than the crests.

Relationship between tephra thickness and grain size
At both Sites B and C median grain size was negatively correlated with tephra layer thickness, for crests and hollows combined (Spearmanrank; Site B: r s [48] = À0.34, p = 0.02; Site C: r s [87] = À0.50, p < 0.001). Therefore, as tephra layer thickness increases, median grain size decreases (Fig. 7). The data were also separated into crests and hollows for each site to examine if this relationship holdswhen looking at specific locations on the th ufur; Spearman rank  In summary, tephra thickness varied with location on the th ufur and on average was thicker in hollows than crests. Overlying soil thickness only varied in this way at Site B. In comparison to the control tephra thickness measurements, measurements from th ufur have greater variability in thickness for both H1947 and G2011. Crests contained larger grains than the hollows at both sites, where grain size was measured.

Discussion
Our results show that the characteristics of the tephra layers formed by H1947 and G2011 tephra deposits are influenced by microtopographic variations created by th ufur formations. Across th ufur, hollows develop a thicker tephra layer than crests. GSD show a complex interplay between surface conditions at the time of tephra deposition and the nature of that surface.

Processes controlling tephra thickness and grain-size distribution on th ufur
Our analysis indicates that thicker tephra layers are found in th ufur hollows. For both H1947 and G2011, the tephra layer is consistently~50% thicker in the hollows than on the crests. The lack of tephra on the crests at Site B in comparison to Site A, 1 km away, could be due to a number of factors. Reworking of the tephra from the crests by Earth surface processes could have occurred as they are more prominent than the hollows. Alternatively, land management practices (such as actively clearing the tephra or grazing livestock) at the time of deposition could have cleared the tephra from the surface. The area is used for sheep and occasional horse grazing today and this is very likely to have been the case at the time of the eruption in 1947, which could have resulted in tephra being cleared so that grazing could continue. The action of grazing in itself could also effectively remove tephra  from th ufur crests preferentially. The thickness of the soil overlaying the H1947 tephra did not exhibit the same pattern of greater accumulation in the hollows (in locations where it was possible to measure this properly). This highlights a fundamental contrast between the gradual, incremental accumulation of aeolian soils across th ufur in particular (and probably variable vegetated microtopography in general), and the episodic deposition of tephra.
At all sites, thickness measurements collected from th ufur show greater variation than the control sites, which have smaller ranges. Therefore, not all measurements from th ufur fall within the range of the controls. This, coupled with the significant difference in tephra thickness between crests and hollows, indicates that the processes operating on th ufur, such as wind, water and movement on slopes, are very effective at redistributing the original fall-out of tephra, compared to a deposit on a surface with few undulations.
Given that the tephra thickness measured in the control sites is more similar to the crests than the hollows, and that the control is considered a reasonable approximation of the original fall-out of both H1947 and G2011 (Cutler et al. 2016a, th ufur crests are more likely to reflect the original fall-out than the hollows. This is not to say that tephra on th ufur crests is exempt from reworking, as is demonstrated by Site B, but overall the formations appear to modify thickness more in the hollows. Similarly, the control measurements are also likely to contain some aeolian reworking as this is difficult to mitigate, but they are still representative as controls given that they were taken from an unth ufured surface. This helps us to separate features that are characteristics of the primary tephra fall-out from those that are acquired due to surface modification, although separating the two is not without its challenges and assumptions.
Crests contain larger grains than hollows, but the significance of this difference varies by site. Mean grain size varies, but medians do not. This indicates the influence of outliers, which skew mean values, but not the medians and is confirmed by KS test results. Although it is difficult to separate the role of the th ufur formations in determining GSD from the other factors, the difference in the grain sizes found in the crests and hollows is important evidence that tephra layers could preserve a record of these formations within their internal structures and GSD. Given these results, we present a number of processes that we believe could be responsible for controlling tephra thickness and grain-size distribution on th ufur.
Surface movements of tephra can occur through the interplay of numerous factors (Arnalds et al. 2016). We propose that the differences in preservation observed in this study are the result of slope processes (driven by gravity, water and/or wind movement) and to a lesser extent, vegetation cover. On slopes below 35°, the physical structure of surface vegetation present when tephra is deposited is important in determining the volume of tephra that is incorporated into the stratigraphy at a landscape scale (Antos & Zobel 2006;Cutler et al. 2016b;Dugmore et al. 2018). Depending upon vegetation height, stem form and packing density, tephra grains are trapped and retained to differing degrees (Shao 2008;Arnalds et al. 2016;Dominguez et al. 2020). Given the scales at which this operates, the structural variations in the vegetation recorded between crests and hollows surveyed here are too small to drive any significant difference in relation to the aim of this study.
Th ufur form micro-slopes, often >35°, which is at or above the angle of repose of tephra. Thus, down-slope movement driven by gravity may begin to override the stabilizing effect of surface vegetation. As mean grain size increases, the angle of repose will decrease, as large grains are less cohesive, with grains below 50 lm (4.3 Φ) having greater cohesion and a greater angle of repose (Lu et al. 2015;Beakawi Al-Hashemi & Baghabra Al-Amoudi 2018). Thus, one explanation for the thickening of tephra layers in hollows across all sites is that slope angles on th ufur exceed the critical angle of repose. As the slope angles on the th ufur were not measured in detail in this study, but inferred from the vertical and horizontal displacements of crests and hollows, this explanation is speculative and highlights a need to both quantify slope angles on th ufur in greater detail and collect measurements from avariety of slope angles above and below 35°. The potential role of slope in tephra layer formation is summarized in a conceptual model (Fig. 8).
Rainfall and snow-melt increase surface moisture and saturation, which will alter shear stresses operating on the slope and can initiate movement of poorly consolidated surface material, such as tephra (Horton 1933;Major & Yamakoshi 2005). Vegetation cover and the characteristics of soils underlying tephra will affect infiltration and rainfall interception, runoff and erosion rates (Major & Yamakoshi 2005;Cerd a & Doerr 2008;Woods & Balfour 2010;Jones et al. 2017). Rainfall simulation studies conducted using freshly fallen tephra deposits by Jones et al. (2017) reported that tephra grain movement was dominated by rainsplash detachment of coarse individual grains, with no rill formation or overland flow. They concluded that tephra transport depends on the grain size, with rainsplash the dominant detachment and transport mechanism for coarser (D90: 852.2 lm 0.2 Φ) grained tephra (Jones et al. 2017). Finer grained tephra demonstrate more airborne mobilization, pellet formation and increased overland flow due to surface sealing.
Given the evidence that rainsplash detachment of larger grains will be enhanced by steeper slope angles, the patterns in our GSD indicate that water is a key driver of grain movement over the small-scale topography such as th ufur formations. All three sites are similar in terms of past climate data (temperature and precipitation), with both exhibiting cool average temperatures and >1000 mm of rainfall on average most years since records began (Icelandic Meteorological Office 2021). Sites A and B receive greater fluctuations in average rainfall than Site C, but overall all three sites received a substantial volume of rainfall over the year(s) post deposition of the respective tephra. Thus, it is likely that the precipitation coupled with the th ufur formations on each site contributed to the GSD measured and the changing morphology and thickness of the tephra layer.
Freshly deposited tephra is also vulnerable to reworking via wind. Dominguez et al. (2020) identified a size range for wind remobilization based on field observations and airborne and ground material samples; 0.4-500 lm. However, Del Bello et al. (2021) found that the threshold velocity for entrainment via wind (U* th ) for tephra in real world conditions is much lower than the theoretical value, as theoretical calculations assume grains are spherical, which volcanic ash shards are not. The mean and median grain sizes of G2011 tephra at Site C fall within the range identified by Dominguez et al. (2020) in both crests and hollows (mean crests: 129.2 lm (3 Φ) and hollows: 99.3 lm (3.3 Φ)). This indicates that the G2011 deposit was more vulnerable than H1947 to remobilization from wind, although hollows have less of this vulnerable size fraction than crests. The interplay of different factors mean that it is the intermediate fractions of the G2011 deposit, rather than the finest (<3.5 Φ), that are most vulnerable to remobilization from wind (Etyemezian et al. 2019;Dominguez et al. 2020).
H1947 is a much coarser grained tephra and therefore the most likely transport mechanism for much of this tephravia wind is by creep. Thus, while the bulk of H1947 tephra is less susceptible to remobilization by wind than G2011, other processes are operating to produce similar grain-size patterns. The presence of th ufur will increase surface roughness (Essery & Pomeroy 2004;Wever 2012), with crests and hollows having different, potentially significant, levels of exposure to surface windspeeds. However, this has not yet been tested on small-scale changes in surface roughness created by th ufur, which would provide greater insight into the differences. A summary of the main drivers of the variations in the tephra layers is presented in Table 2.
Implications for the interpretation of landscapes using tephra layers As highlighted above, tephra sedimentology (tephra layer thickness and GSD) can be used as a tool to help interpret palaeo-landscapes and landscape formations. This work has shown that the morphology of preserved tephra layers and the GSD will be altered by small-scale surface features and by a number of processes operating in conjunction with each other on the surface. Thus, in addition to being used as a chronological tool in palaeoresearch, interpreting these alterations will provide additional insight into past landscapes.
Slope angle is clearly important for determining tephra layer thickness. Coarser grained tephra such as H1947 will move on shallower slope angles than a finegrained tephra, as highlighted in Fig. 8. If a fine-grained tephra, such as G2011 is found to exhibit thickening at certain points in the layer, it can be interpreted as being deposited on a steep (above the critical angle of movement) slope of a greater angle than would be required to move a coarse tephra. When examining tephra layers across, for example, an archaeological site, finding pockets of thicker tephra can therefore provide information about the angle of slope. A preserved tephra layer with few areas of thickening can be interpreted as being deposited across an area of (relatively) flat land below the critical angle of movement for that tephra, as opposed to a layer that has areas of thickening, thinning and a layer morphology that reflects the ground surface. The presence of small-scale surface features such as th ufur can also be used as a proxy for past climate conditions and/or fluctuations, as the climate must have included freezethaw cycles for such features to form and be preserved in the tephra record (Grab 2005;Dugmore et al. 2020). Thus, by recording the presence of slope angles above the critical angle of movement, tephra layers can be used to interpret the presence (or absence) of such surface features, which can lead to further interpretations about prevailing climate at the time.
As with slope, tephra size fractions will be moved differently by wind. Both Del Bello et al. (2021) and Dominguez et al. (2020) concluded that fractions between 50 and 500 lm were most vulnerable to reworking by wind. Some reworking will occur below 50 lm, but very small particles are more cohesive, reducing their mobility (Del Bello et al. 2021). The proportion of the H1947 layer <50 lm was 3% on crests and 1% in hollows. In contrast, the figures for G2011 were 24 and 34%, respectively. Finer grained tephras will have a larger portion of grain sizes that are susceptible to aeolian reworking. For very fine grained tephras this will be the intermediate size fraction of the overall GSD, whereas for coarser grained tephras it will be the very smallest fraction or none at all. This is an important consideration when interpreting tephra layers in a landscape, as the preserved layer will partly be the result of reworking, particularly for finer tephras. As we have Fig. 8. Conceptual model illustrating the potential movement of a fresh tephra deposit on th ufur formations and the preservation of an enduring tephra layer. We show a range of increasingly well-developed th ufur formations with progressively steeper sides. A. H1947 has a lower critical angle than G2011 and therefore movement is more likely to occur on shallower slopes on the left, with the greatest movement on fully developed th ufur. B. G2011 has a higher angle of repose so more movement is only likely to occur on fully developed th ufur. demonstrated, wind, combined with slope redistributing GSD (crests containing larger particles than hollows), creates a tephra layer with distinctive characteristics that reflect these processes.
Thus, when interpreting the GSD and thickness of a tephra layer, the nature of that tephra layer will to some extent reflect the landscape that it was deposited onto. There are a number of processes occurring at once and it can be challenging to separate out a single environmental signal from a tephra layer. However, by considering the pattern of thickness and GSD changes measured, novel insights (mostly unavailable from other proxies) can be gained. This highlights the utility of tephra layers in palaeoenvironmental research beyond chronology and dating but as a useful tool aiding environmental reconstruction.

Implications for volcanological reconstruction
At a landscape scale, median tephra grain size and thickness of the tephra layer are partly a function of both the distance from the volcanic vent and axis of fall-out (Pyle 2016). In general, thicker tephra layers with larger grain sizes are located close to the vent, thinning and reducing in grain size as one moves further from the volcanic vent (Pyle 1989;Gudnason et al. 2018). This pattern is not observed here (Fig. 7) as for both the H1947 and G2011 tephras, thicker layers contain smaller grains, with these thicker layers present in hollows. This is an issue of scale, as the overall pattern will be maintained on the scale of fall-out, but the variation in individual measurements is at a scale of centimetres rather than metres or kilometres. As larger grains were measured in the crests, which have thinner tephra layers, this relationship is not surprising in the context of this study. However, this finding has important implications in terms of volcanological reconstruction.
If we were to reconstruct the eruptions of H1947 and G2011 using the thickness and GSD measurements from this study, the resulting values would be different to those presented in published work. For example, thickness measurements taken by Thorarinsson (1956) to reconstruct the fall-out from H1947 show that Sites A and B are within the 1-cm isopach (Fig. 2). Taking the median thickness measurements from both sites, all apart from crest measurements at Site B show a thickening of tephra, in some cases more than twice as thick (A: crests -1.1 cm, hollows -2.5 cm, B: crests -0 cm, hollows -2.4 cm). This reinforces the idea that crest values are more representative of the original fall-out than hollows, as discussed above. Sites measured by Cutler et al. (2018) to identify how the H1947 layer had been altered since Thorarinsson's original work also showed that in some areas the tephra had increased in thickness. Given the distance from the vent, the grain sizes measured at both Sites A and B are as expected (Pyle 1989). However, the relationship between layer thickness and grain size on the crests is not what would be expected, so sampling from crests only would alter the volcanological reconstruction of the H1947 eruption.
At Site C, the GSD shows a similar pattern to the H1947 sites, with crests containing larger grains than hollows. Whilst the size of the grains is not surprising given the transport distance from the vent, as with the H1947 sites sampling from only crests or hollows would give a skewed GSD, unrepresentative of the original deposit. A detailed isopach map of the G2011 fall-out has not yet been produced, apart from the 1-cm isopach produced by Thordarson & H€ oskuldsson (2014). More than 1 cm of tephra could therefore have been deposited at Site C and our thickness values suggest this. However, as tephra can become thickened in hollows, thickness from hollows (6.2 cm) is likely to be an exaggeration of the thickness of the original deposit, which may lie closer to the thickness found in the crests (3.5 cm).
Measurements used for volcanological reconstruction are usually collected in a systematic way, often from transects along the axis of fall-out (Bonadonna &  However, our results highlight that sampling strategy will influence the interpretation of sedimentological records in areas of microtopographic variation, like th ufur fields. Strategic and thorough sampling is therefore desirable, but in palaeo-research it is often not possible to sample as intensively as we have here, for example reconstructions are often conducted from a limited number of cores. Instead, studies should attempt to capture the uncertainty attached to any interpretations made from tephra layers, where possible. In the case of volcanological reconstructions, researchers may consider undertaking a set of calculations using an assumed maximum and minimum range of layer thicknesses, centred on the actual measured thickness of a tephra layer taken from a core. This should then provide a reconstruction that takes into account the alterations that can occur to tephra layers post deposition.
Overall, the findings of this study have clear implications for the interpretation of tephra layers. Alterations that tephra deposits undergo as they are preserved in the stratigraphy can clearly be used to infer environmental processes. We have presented evidence that the presence of th ufur on the surface at the time of tephra deposition is preserved in buried tephra layers. This ability to infer the presence or absence of th ufur has implications in establishing palaeoenvironmental conditions, as freeze-thaw cycles must have existed for th ufur to form, and the soil must have contained enough moisture for this to happen.

Conclusions
There is a thickening of all tephra layers in the hollows of th ufur, regardless of tephra type, and the morphology of the layer follows the shape of the feature. The tephra layers were coarser on the crests. This study has shown that features such as th ufur do indeed drive variations in tephra layer preservation. Differences in thickness are primarily driven by the shape of the formations and the critical slope angle for movement of the tephra.
The G2011 tephra layer at Site C shows a statistically significant difference in grain size, with crests having a larger mean and median grain size than hollows. The H1947 tephra follows a similar pattern, with larger grains in the crests than hollows. As the G2011 and H1947 tephras differ in mean grain size, it is likely that different drivers are relatively more or less important depending on the tephra. But small topographic variations on the land surface result in similar patterns of variation in grain-size distribution, regardless of the mean grain size.
These findings show that variations in the thickness and grain-size distribution of recent tephra layers may be influenced by small-scale topographic variation. Given that this difference is visible in recent layers, we propose that this should also be preserved in older tephra layers, and similar variations may give an indication of land surface features at the time of tephra deposition. Thus, this study adds to a growing body of work that highlights the potential of tephra layer morphology and internal structures as indicators of palaeolandscape conditions, as well as tephra layers' utility as high-quality chrono-lithostratigraphical marker horizons. In addition, it provides important context for the appropriate sampling of tephra layers to infer volcanological processes.
Acknowledgements. -Financial support for this work was provided by NERC Doctoral Training Partnership Ph.D. studentship NE/L002558/ 1 to Polly I. J. Thompson. We are very grateful to the landowners in Iceland who allowed the fieldwork to take place. Many thanks to our field assistants in August 2019: Martin Dugmore and Connor Morrison. Dr Gavin Sim was most helpful and provided valuable guidance with lab work and particle size analysis of tephra samples. Authors have no conflicts of interest. We are grateful to the reviewers for their comments on the initial manuscript.
Author contributions. -The study was conceived and designed by PIJT, AJD and AJN. Fieldwork and data collection was carried out in 2019 by PIJT, AJD and AJN. Fieldwork to collect control data sets used was carried out by AJD, RTS, NAC and PIJT in 2014/2015. All laboratory work, particle size analysis and statistical analysis was conducted by PIJT. The initial draft of the manuscript was written by PIJT, with subsequent comments and edits made by all other co-authors.
Data availability statement. -All data used in this manuscript are freely available on the University of Edinburgh DataShare facility, which can be accessed via: https://doi.org/10.7488/ds/3104.

Supporting Information
Additional Supporting Information may be found in the online version of this article at http://www.boreas.dk.
Data S2. Grain-size distribution sample preparation.
Data S3. Use of ultrasonic bath prior to running samples.
Data S4. Cleaning of samples.   S2. Plots of GSD of the same sample that has been cleaned and not cleaned using an ultrasonic bath. Fig. S3. Results of method to remove soil contamination from tephra samples. The image shows a sample of G2011 tephra that was split so that half has had the ultrasonic process to remove soils performed (right) and the other has not (left). The left sample has a clear layer of pale grey silt on top of the tephra, whereas this layer is not observed in the sample on the right. Table S1. Summary statistics of samples treated with the ultrasonic bath (blue) and without (red). Values in lm were converted to phi using the equation ø = Àlog 2 (D/ D 0 ), where D is the diameter of the grain in mm and D 0 is the reference diameter equal to 1 mm. Table S2. Summary statistics of samples that have been cleaned using an ultrasonic bath (purple) and samples that have not been cleaned (teal). Values in lm were converted to phi using the equation ø = Àlog 2 (D/D 0 ), where D is the diameter of the grain in mm and D 0 is the reference diameter equal to 1 mm.