*4.6. Storm Intensity as Function of Estimated Wave Height*

Average clast sizes and maximum boulder sizes from the three field samples are summarized in Table 1, allowing for direct comparison of mean values for all clasts, as well as values for the largest clasts in each sample based on Equations (1) and (2) derived from the work of Nott [17] and Pepe et al. [19]. The Nott formula [17] shown in Equation (1) yields an average wave height of 3.6 m for the extraction of joint-bound blocks from chromite sea cliffs and their subsequent transfer as beach cobbles and boulders in samples 1–3. According to these results, the mean wave height that impacted shores along the midpoint of Støypet valley and led to the boulder beach on the saddle between Steinstind and Hagafjellet was greatest at 4.1 m. The formula influenced by Pepe et al. [19] showed in Equation (2) yields higher values across all categories with the mean wave height also at the valley's midpoint reaching a value of 4.8 m. Taking into consideration the largest individual boulders from the three samples (Tables A1–A3), Equation (2) differs from Equation (1) in showing a decline in wave heights from the SW end to the NE end of the valley with the most dramatic reduction to 5.2 m (Table 1).

**Table 1.** Summary data from Appendix A (Tables A1–A3) showing maximum bolder size and estimated weight compared to the average values for sampled boulders from each of the transects together with calculated values for wave heights estimated as necessary for boulder-beach mobility. Abbreviations: Max. = maximum, EAWH = estimated average wave height, EMWH = estimated maximum wave height.


#### **5. Discussion**

#### *5.1. Physiographic Changes in Island Size*

In the context of Leka Island's general physiography, the midpoint of Støypet valley reflects postglacial uplift of the surface from earliest Holocene sea level to nearly 100 m above contemporary sea level mid-valley. This amount of rebound is commensurate with uplift of the sea stack at the SE end of the island said by legend to embody the Leka troll maiden (Figures 1 and 2a). In terms of physical geography prior to uplift, Støypet valley evolved from an open channel that isolated the adjacent heights of Steinstind and Nerskard as a separate entity from the rest of Leka Island. The core of the smaller island would have stood about 80 m above earliest Holocene sea level. The high point of Hagafjellet on the opposite side of the channel was 220 m above earliest Holocene sea level. Cobbles and boulders of chromite and dunite eroded from the facing sea cliffs along the channel began to accumulate as a beach deposit mid-channel, eventually forming a dry connection between the main island and Steinstind. Three archaeological sites are marked on the northwest (NW) embankment overlooking the Støypet channel [16] that were occupied by immigrants who arrived sometime after the local retreat of ice at the end of the Younger Dryas about 11,500 years ago. Cave paintings at nearby Solsem on Leka

Island are dated to the earliest Bronze Age, although Stone Age finds have been excavated from the cave floor [20]. Precise dating for the onset of human occupation in North Trondelag (including Leka Island) is poorly documented, but data from carbon-14 testing in neighboring Nordland and farther north in Troms and Finnmark indicate a pattern of first settlements spanning 9000 to 6000 years ago [21]. Erosion by ice scour along the inner passage between Leka Island and the Norwegian mainland left a distinctive trace correlated with the Main Line now found at a higher elevation between 106 and 112 m above today's sea level [11]. Amalgamation of beach deposits during Holocene time added to the base of the mid-channel connection between Steinstind and Hagafjellet as the land on both sides continued to rebound after ice retreat. The loose "rolling stones" deposited in Støypet valley formed a 50-m wide and 300 m in length plug (Figure 4). In some respects, the deposit on the SW flank may be compared to beach ridges commonly formed in more tropical latitudes as a result of cyclonic storms [22], some of which can be dated by radiometric analysis drawn from coral heads incorporated within distinct ridges. No such method of absolute dating for the testing of storm frequency is possible in Støypet valley, but the centrality of the deposit far from present-day shores at opposite ends of the valley makes it clear that channel erosion ceased long ago.

#### *5.2. Direction of Holocene Storms*

Application of Equation (1) from Nott [17] and Equation (2) influenced by Pepe et al. [19] differs in results estimating the magnitude of waves impacting sea cliffs along the Holocene Støypet channel, but agrees in the relative ranking of wave energy responsible for transferal of chromite clasts to the three sample sites. Maximum wave energy appears to have focused on the SW part of the channel relative to field sample 1, followed by a reduction in wave energy mid-channel relative to field sample 2, with registration of the lowest wave energy in regard to field sample 3 in the NE part of the channel. From these data (Table 1), it may be argued that initiation of the beach deposit occurred in the vicinity of field sample 1, but that beach ridges pushed farther into the channel as typified by field sample 2. The same amount of surface rebound should have resulted along the entire length of Støypet valley, but the nearly 25 m difference in elevation comparing the altitude of the deposit's axial midpoint (field sample 2) to the its SW and NE extensions is likely due to the formation of a central storm ridge at the same time when uplift began to occur throughout the rest of the island consistent with that around the Leka maiden's Holocene sea stack (Figure 1). The wider mouth of Støypet channel and its emergent valley at one end (Figure 4) also may have influenced the funneling of storm waves that entered from the SW. The smaller clast sizes evident from field sample 3 (Table A3 and Figure 9e,f) can be interpreted as a result of waves that overtopped the central storm ridge and sent lesser clasts down the apparent lee side of the beach to accumulate on a smooth 5◦ slope. Such a hypothesis posits that early Holocene storms in the Norwegian Sea were more likely to have arrived from the SW, trending to the NE against the adjacent Norwegian mainland. The downward shift in clast sizes from sample 3 (Figure 9e,f) compared to samples 1 (Figure 9a,b) and 2 (Figure 9c,d) implies that a different wave regime may have been in place on the NE end of the valley compared to the SW end.

#### *5.3. Inference from Historical Storms*

Observations on the steering winds in Norway's Arctic Vestifjord district north of Leka Island are summarized by Jones et al. (1997), based on information derived from weather stations on small islands in the Norwegian Sea as well as the Norwegian mainland [10]. Cod fishing in this district has a long history as a major industry dating back centuries [23], and the difference between winter and summer weather is well known. During the winter months when the fishing season is in play, the dominant winds arrive from the southwest commonly interpreted as fresh breezes between 4 and 5 on the Beaufort scale. However, there is a 10% chance that gale-force winds (8 on the Beaufort scale) will occur with wind speeds reach 20.7 m/s. During the summer months, lighter winds generally arrive from the NE and gale-force winds are rare, comprising less than 1% of station observations [10]. Hurricanes are a seasonal feature of tropical and subtropical settings uncharacteristic for Boreal Seas. Technically, they are a tropical to subtropical phenomenon that depends on high ocean-surface water temperatures and excessive air moisture [22]. During the last decade (2011 to 2020), four storms assigned to the category of "orkan" by the Norwegian Meteorological Institute [24–27] struck the Norwegian coast including the vicinity of Leka Island (Table 2). These specific storms share a general history of duration lasting 48 h, or more, with a frequency of arrival every second year. Clearly, these factors play a role in beach dynamics related to clast size.

**Table 2.** Impact of superstorms in the North Trondelag and Nordland districts of coastal Norway summarized from reports issued by the Norwegian Meteorological Institute.


The direct translation of the Norwegian word "orkan" to English is hurricane, and the NMI's basis for such storms is defined by a minimum wind speed of 32.7 m/s. Major storms in high latitudes express a cyclonic circulation similar to hurricanes, but originate independently of water vapor arising from excessively high ocean-surface water temperatures. Instead, they rely on the acceleration of weather fronts with extreme contrasts in air temperature on opposite sides of the line [28]. Based on the Saffir–Simpson hurricane wind scale, a wind speed of 32.7 m/s falls below the range of a Category 1 hurricane with wind speeds between 33 and 42 m/s. During the last decade, at least two major storms reached the North Trondelag and Nordland districts of Norway packing maximum wind speeds of 50 m/s or higher that according to the Saffir–Simpson scale qualify as Category 3 disturbances. Based on standard energy calculations in mega joules, a high-latitude storm of the kind reaching the mid-section of Norway in recent years expends roughly 50% of the energy of a large tropical hurricane [28], but such a release is sufficient to do extensive damage to coastal infrastructure and erode coastal shores. It is notable that all four superstorms reaching North Trondelag and Nordland including Leka Island arrived from the southwest (Table 2). The local climate in this area following the retreat of glaciers 10,000 years ago was sure to have been more extreme than today, but the arrival pattern of today's major storms fits with the physical characteristics of Holocene boulder deposits filling Støypet valley. Moreover, it is notable that even the lower range of storm-wave heights reported for Hilde and Tor [25,26] exceed the storm-wave heights estimated to have entered the Holocene channel.5.4. Contrast with Coastal Deposits Elsewhere

Holocene deposits formed by unconsolidated cobbles and boulders are widely distributed all around the world, but studies in coastal geomorphology seldom take into account rock density as related to variability in parent rock types when investigating the range of wave heights necessary for their development. Equation (1) as derived from Nott [17] has been applied to coastal boulder deposits throughout Mexico's Gulf of California, including those formed by limestone, rhyolite, and andesite clasts [6–8]. Extension of this work to include Equation (2) as influenced by Pepe et al. [19] also has been applied to coastal basalt deposits in the Azores [9]. The variation in density among these rock types ranges from 1.86 g/cm3 for limestone, 2.16 g/cm3 for the rhyolite, 2.55 g/cm3 for andesite, and 3.0 g/cm3 for basalt. Cobbles and boulders of low-grade chromite ore that are the subject of the present study register a higher density measured as 3.32 g/cm3 and high-grade chromite ore is known to yield an even greater value. Limestone differs from the others as a marine product derived mostly from organic materials, whereas the rest are igneous rocks some of which like rhyolite and andesite typically form under subaerial conditions as volcanic flows. The limestone, rhyolite, and andesite all produce stratified bodies that sooner or later become subject to joints that break perpendicular to the bedding plane. Basalt may issue under subaerial conditions subject to jointing in the same way, but also

forms under submarine conditions that entail a different style of accumulation as pillow-shaped bodies, typical on Santa Maria Island in the Azores [9]. Dunite and chromite as found exposed on Norway's Leka Island are igneous rocks that originated deep within the Earth's crust but also under conditions that allowed for stratified bodies associated with serial injections of magma that cooled slowly one after the other. The key similarity among all these rock types is the appearance of horizontal partings cut by joints and fractures. In sea cliffs subject to wave erosion, it is the configuration of layering dissected by joints common to all such rocks that determines the effectiveness of storms to detach blocks subsequently incorporated in coastal boulder deposits.

Rock density is an important factor in coastal erosion, because a storm wave of any given height will behave differently depending on the degree of stratification and jointing in the parent sea cliff. The same wave will have the capacity to dislodge a larger, less dense block of limestone compared to a smaller, denser block of basalt or chromite. Another factor to be considered is the difference between tropical hurricanes limited to lower latitudes and Boreal storms characteristic of higher, more poleward latitudes. The largest block detached from a limestone sea cliff by Holocene hurricanes in the Gulf of California is estimated to weigh 28 metric tons [6], whereas limestone blocks between 100 and 200 metric tons are attributed to detachment from sea cliffs in the Philippines during Super Typhoon Haiyan in 2013 [29]. However, the erosional effectiveness of tropical hurricanes compared to Boreal storms is not to be underestimated on account of movements in blocks weighing as much as 620 metric tons during the winter storms of 2013–2014 against limestone sea cliffs in western Ireland [30]. By comparison, the chromite cobbles and boulders entrained as a Holocene beach deposit in Støypet valley are exceedingly small, but with a much greater density than limestone. Studies on the geomorphology of boulder deposits composed of other rock types such as granite and gabbro are to be encouraged.

### **6. Conclusions**

Study of the cobble-boulder beach entrained in Støypet valley on Norway's Leka Island offers insights based on mathematical equations for estimation of Holocene wave heights and wave heights from recent superstorms in the same region:


Pepe et al. [19]. In this study, the latter yielded estimates from 12% to 24% higher depending on analysis of mean clast size or maximum clast size. Holocene wave heights estimated by both equations are within the range of observed wave heights during major storms in the same region.

The Norwegian National Geological Monument within the Trollfjell (Troll Mountain) Geopark already provides an outstanding resource for visitors of all ages and educational backgrounds to learn about earth processes and achieve a better appreciation for our common geoheritage. Its significance can be expected to grow with visitors offering fresh input from different perspectives.

**Funding:** The research project received no external funding.

**Acknowledgments:** B. Gudveig Baarli organized the logistics for a visit to Leka Island and assisted in the collection of field data in Støypet valley in July 2019. Sérgio P. Ávila (University of the Azores) provided the calculations for wave heights based on the mathematical model influenced by Pepe et al. (2018). The author is grateful for recommendations offered by three anonymous reviewers that helped him to improve the final product, as well as crucial comments provided by the scientific advisor.

**Conflicts of Interest:** The author declares no conflict of interest.
