Towards improved empirical isobase models of Holocene land uplift for mainland Scotland, UK

David E Smith, Peter T Fretwell, Robin A Cullingford, Callum R Firth

Abstract

A new approach to modelling patterns of glacio-isostatic land uplift during the Holocene in mainland Scotland, UK, is described. The approach is based upon altitude measurements at the inner margin or locally highest point of raised estuarine surfaces dated by radiocarbon assay supported by microfossil analyses. 2241 altitudes have been analysed by a technique new to studies of former sea-levels, Gaussian Trend Surface Analysis, and isobase models for four Holocene shorelines: the Holocene Storegga Slide tsunami shoreline, abandoned rapidly circa 7900 sidereal years BP; the Main Postglacial shoreline, abandoned during circa 6400–7700 sidereal years BP; the Blairdrummond shoreline, abandoned during circa 4500–5800 sidereal years BP, and a speculative fourth shoreline, the Wigtown shoreline, abandoned during circa 1520–3700 sidereal years BP, are shown in a series of maps. The implications of the shoreline patterns for glaicio-isostasy in the area are discussed. It is maintained that the statistical technique used enables broad estimates to be made of nearshore sea surface change.

1. Introduction

There is a long history of attempts to define patterns of land uplift which occurred during and following deglaciation of the last ice sheet in Scotland. This paper briefly reviews previous work in this field, before describing a new approach, which aims to improve definition of the pattern of uplift. The method used is based upon altitude measurements at the inner margins of comparable relict Holocene estuarine terraces in mainland Scotland, correlated on the basis of altitude, morphology, stratigraphy and radiocarbon assay supported by microfossil analyses. It takes advantage of a unique dataset, collected by the authors and colleagues over 40 years using the same methodology. These data are analysed using Gaussian Trend Surface Analysis from which isobases are derived. The Gaussian model is more appropriate than polynomial models for an area of glacio-isostatic uplift, and fits the data here somewhat better than the polynomial models. It also has the benefit of enabling broad estimates of secular sea surface changes offshore to be made, thus contributing to knowledge of regional sea surface change.

2. Previous work

The maximum extent of the Late Devensian ice sheet in Britain and Ireland is believed to have been reached around 18–22 000 radiocarbon years BP (e.g. Bowen et al. 2002). Early attempts to model glacio-isostatic land uplift in Scotland that occurred during and following deglaciation were based upon former shore features, frequently termed ‘raised beaches’, their altitudes obtained by means of comparisons with topographic maps. For the Holocene, the most prominent ‘raised beach’ was termed the ‘25-foot’, ‘Littorina’ or ‘Neolithic’ beach, and a zero isobase for this feature was produced by Wright (1937) and Movius (1942). Although these early studies gave a general indication of the likely uplift pattern, the need for models based upon altitude measurement was recognized by Donner (1959, 1963). Donner (1959, 1963) measured the altitude of some relict shore features above the UK levelling datum (Ordnance Datum Newlyn (OD)) using either instrumental levelling or barometric measurement based upon the altitude of the barnacles Balanus balanoides and Chthamalus stellatus in the present shore zone, to provide a partial isobase model. However, shortcomings in the approach used by Donner (1959, 1963) were recognized by Sissons (1962), and this led to a more systematic approach, with relict shore features mapped and their altitudes measured above OD by instrumental levelling along their lengths (Sissons 1962, 1963; Smith 1965; Sissons et al. 1966). This approach led to the publication of the first map, based upon altitude measurement and some interpolation of data from previously published work, of Holocene isobases for Scotland as a whole (Sissons 1967) and a later map produced on the same basis by Jardine (1982). In all these early studies, isobases were interpolated by eye from the data.

Recent years have seen the emergence of two contrasting approaches in the determination of patterns of Holocene glacio-isostatic land uplift in Scotland, using numerical models. Shennan et al. (1995) described these approaches as on the one hand involving the development of ‘empirically based models’, based upon the measurement of former shore features, and on the other the development of ‘glacio-hydro-isostatic models’, based upon estimates of ice loading and unloading, sea surface change, and mantle rheology. The empirically based models used trend surface (polynomial regression) analysis of spatially located altitudes on relict shore features, the altitudes correlated using detailed morphological mapping and survey, together with microfossil analysis and radiocarbon dating at key sites. These models used only altitudes on comparable shore features, rather than on a range of features, as had been the case in the earlier models of Wright (1937), Movius (1942), Donner (1959, 1963), Sissons (1967) and Jardine (1982). The first of these trend surface models (Cullingford et al. 1991) considered only eastern mainland Scotland, but later models (Firth et al. 1993; Smith et al. 2000) provided isobase maps for mainland Scotland as a whole. In the models of Smith et al. (2000), the altitude data was standardized in relation to mean high water spring tides (MHWS), thereby improving their accuracy, since MHWS can vary from OD by up to 5 m at different tidal stations around mainland Scotland (Admiralty Tide Tables 1996).

Glacio-hydro-isostatic models derive information about lithospheric thickness and mantle viscosity by estimating the loading and unloading of an ice mass; water loading and unloading in the area nearby, and the effects of far field glaciation; then validating estimates of crustal uplift from the evidence of displaced sea-levels These models were first developed for Scotland by Lambeck (1991, 1993a,b, 1995; Shennan et al. 2000b). The Lambeck models were based upon estimates of decaying Late Devensian ice masses, from the ice sheet maximum proposed by Boulton et al. (1977, 1985) to their disappearance at the end of the Younger Dryas (Loch Lomond Stadial) by 10 000 radiocarbon years BP. Values were estimated on a grid pattern at 25 km intervals around the British Isles and at 1° intervals for far field areas, and at time steps of 1000 and 500 radiocarbon years (Lambeck 1993b). Graphs of relative sea-level change were produced for sample locations and compared with sea-level index points, and isobase models produced for specific times. These models take mean sea-level, derived for the sampled locations following Thompson (1980), as their datum. Subsequently, Peltier et al. (2002) derived alternative values for lithosphere thickness and mantle viscosity from models of ice loading and far field effects, publishing graphs of relative sea-levels for the British Isles based upon MHWS at each location, but no isobase models were depicted.

3. An assessment of numerical models for Holocene land uplift in Scotland

The empirically based models and glacio-hydro-isostatic models each have different advantages. The empirically based models, based upon arrays of comparable terrace altitudes defined as shorelines, fit the available data closely, and in the analyses of Smith et al. (2000) most altitude values lie less than 2σ from the computed altitude at the location involved for each of three Holocene shorelines modelled. However, because polynomial trend surface models trend to infinity beyond the data it is difficult to view the surfaces computed in the context of likely overall patterns of uplift in this glacio-isostatically affected area. Further, displaced shorelines as inferred from arrays of terraces could in theory conceal changes in the pattern of uplift, since they may be diachronous, following Wright (1934, 1937).

The glacio-hydro-isostatic models provide estimates for land uplift well beyond the areas of measured relict shore features. In these models, shorelines are defined as synchronous levels and are, therefore, potentially more accurate in defining the patterns of uplift. However, recent work suggests that the models so far produced may be less accurate than empirical models for some areas. A comparison between the published glacio-hydro-isostatic model of Lambeck (1995) for 7000 radiocarbon years BP with measured altitudes for the synchronous Holocene Storegga Slide tsunami shoreline of circa 7100 radiocarbon years BP reveals differences of over 10 m for northern mainland Scotland (Smith et al. 2004, fig. 12), while the timing of the maximum Holocene relative sea-level indicated by the models for some W coast locations, approximately 6000 radiocarbon years BP (Shennan et al. 2000b), appears to be at variance with the timing of the observed maximum relative sea-level of younger than around 4000 radiocarbon years BP recorded at some sites. Lambeck (1993b) noted that there are distinct discrepancies between sea-level index points and his glacio-hydro-isostatic models in northern Scotland, and Lambeck et al. (1998) note that such models may require revision to take further account of the effects of the Scandinavian ice sheet. The ICE-4G (VM2) glacio-hydro-isostatic model of Peltier et al. (2002) fits most UK sea-level data well with a lithospheric thickness of 120.7 km, but a value of 90 km is required to provide a satisfactory match with the Scottish sea-level data. The Peltier et al. (2002) models assume that Loch Lomond Stadial ice cap was centrally located with respect to the Late Devensian ice sheet in Scotland, a questionable assumption given uncertainties about the extent, timing and build up of these ice masses (e.g. Sissons 1980).

It is noted here that some adjustment of the glacial loading term in glacio-hydro-isostatic models may ultimately be needed for one or more of the following reasons: firstly the extent, continuity and thickness of the Late Devensian ice sheet, both in Scotland and in Britain and Ireland generally is a matter of debate (e.g. Ballantyne et al. 1998; Bowen et al. 2002; Bowen & McCabe 2003; Hall et al. 2003); secondly there could have been temporal variations in the build up and decay of ice (Sissons 1980); thirdly, episodes of glacial loading and unloading, such as have been noted for the Perth Stage (Sissons & Smith 1965) and the Loch Lomond Advance (Sutherland 1984; Firth 1986), where field evidence for crustal redepression has been claimed, may have resulted in changes in the distribution of the ice; and finally that present models ignore topographic variation beneath the ice surface, as Shennan et al. (2000b) and Smith (2005) have observed. That there may be room for improvement in existing models is shown in recent work by Dawson et al. (2002). From work on Late Devensian lake shorelines in Glen Roy, in the Grampian Highlands, Dawson et al. (2002) have maintained that given the direction of greatest uplift indicated by these shorelines, none of the available numerical models satisfactorily locate the likely centre of land uplift during the Holocene.

4. Towards improved empirical models

This paper seeks to contribute to a more detailed description of the spatial pattern of glacio-isostatic land uplift in Scotland using high quality and comparable data based upon a larger number of sea-level index points than have hitherto been available. With the exception of two sea-level index points (from E Solway and Arcan Mains), these are primary data. It employs a surface fitting approach new to sea-level studies, Gaussian trend surface analysis. In the account below, figure 1 depicts the locations discussed, while figure 2 shows the surfaces modelled.

Figure 1

Places mentioned in the text. Inset: locations of the tidal stations from which Mean High Water Spring Tides values have been used.

Figure 2

Gaussian quadratic trend surface models of Holocene land uplift in Scotland. (a) The Holocene Storegga Slide tsunami shoreline. (b) The Main Postglacial shoreline. (c) The Blairdrummond shoreline. (d) The Wigtown shoreline. Numbered points refer to groups of measurements (see tables 3, 4, 6 and 8).

5. Methodology

(a) The data

The data analysed consist of arrays of measured altitudes on the inner margin, or locally highest point, of visible or buried estuarine surfaces. The level measured is described here as a ‘shoreline’. The widespread presence of terraces separated by low cliffs, or of buried surfaces separated by intercalated peat, is interpreted as reflecting levels reached either simultaneously or during episodes when relative sea-level fell at a consistent rate.

(i) Visible surfaces

The visible surfaces are widely known in Scotland as ‘carselands’. In the data used here from previous studies, altitudes were taken at 50 or 80 m intervals, while in the new data, a 50 m interval has been used. All altitudes are based on OD. Those obtained from previous studies are described in Smith (1965, 1968), Cullingford (1972), Smith et al. (1978, 1980, 1982, 1983, 1999, 2003a,b), Morrison et al. (1981), Firth (1984), Smith & Cullingford (1985), Firth & Haggart (1989), Cullingford et al. (1991), Smith et al. (1992), Dawson & Smith (1997), Selby (1997) and Dawson et al. (1998), many of which accounts list the data. For this paper, new altitudes were obtained by the authors from the Solway Firth and the Ayrshire coast in SW Scotland. Additionally, some altitudes in the Dunbar area, SE Scotland, were kindly provided by Dr J. B. Sissons from unpublished work. Preparation of the visible shoreline data for analysis followed Smith et al. (2000). The estimated accuracy of these altitude measurements is based upon the highest errors of Smith (1965), Gehrels et al. (1996) and Smith et al. (2003b) (table 1).

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Table 1

Error magnitudes in the visible shoreline measurements analysed.

(ii) Buried surfaces

The altitudes for buried estuarine surfaces were obtained from boreholes, in which detailed transects were employed to identify the inner margin of these surfaces, with the provenance of the sediments determined on the basis of stratigraphy and microfossil analysis. No group means are used here, only the highest altitude at each location taken. The approach is the same as used by Smith et al. (2000). However, since the surfaces measured here are often on thin minerogenic horizons within valley side peat, adjustments for peat compaction following the completion of deposition of the overlying minerogenic sediment have been made to the altitudes analysed following Smith et al. (2003b) (see table 2), with mean compaction estimates used.

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Table 2

Error magnitudes in the buried shoreline measurements analysed.

(iii) Correlation of the shorelines

The altitudes are correlated on the basis of detailed morphological mapping at a scale of 1 : 10 000 or 1 : 10 560, supported by radiocarbon dated sea-level index points (verified by microfossil analyses) at key sites. The morphological evidence consists of levelled terrace features whose altitudes have been plotted along axes orthogonal to the likely isobase trend, the arrays defined by linear regression. Radiocarbon dating followed the approach as outlined in e.g. Cullingford et al. (1991), where peat or gyttja from conformable regressive contacts overlying a surface of estuarine silt at its inland limit were dated. Occasionally, dated molluscs were used to support the likely presence of a carseland surface of particular age. This methodology, involving morphological study, survey, stratigraphic and biostratigraphic work, was employed to determine the likely number of surfaces that could be identified.

The ‘indicative meaning’ (sensu Van de Plassche 1986) of the points measured probably approximates to the former saltmarsh surfaces at the locations studied, on the basis of the widespread presence of the pollen and macrofossils of saltmarsh plants at several sites (e.g. Smith et al. 1999), and of analysis of diatoms and foraminifera (e.g. Smith et al. 2003b) and the points probably relate closely to MHWS at the time the sediment ceased accumulating. In all, the data upon which the analyses presented here are based involve over 50 pollen and diatom diagrams and over 150 radiocarbon dates supporting 2241 surveyed altitudes, many of the latter based upon transects involving in addition several hundred altitudes.

(iv) Datum

All altitudes used in the analyses here are corrected to present day MHWS using the value from the nearest tidal station in a comparable coastal setting, taken from Admiralty Tide Tables (1996). The tidal stations used are similar to those used by Smith et al. (2000), with two exceptions: the present study uses Alloa (MHWS 3.03 m OD) for Forth data rather than Rosyth (2.95 m OD); and Southerness Point (4.60 m OD) for Nith and Lochar Water data rather than Hestan Islet (4.29 m OD). No estimate has been made for possible palaeotidal changes because no information is currently available for the coastline of Scotland as a whole. Shennan et al. (2000a) estimated changes in tidal range during the Holocene for North Sea locations, maintaining that after 6000 radiocarbon years BP tidal ranges and the elevation of MHWS in that area increased by up to 1 m.

(v) Radiocarbon dates

All radiocarbon dates given here are expressed in years before present with ±1σ indicated and the CALIB 4 range from Stuiver et al. (2003) to 2σ given in parentheses, thus 3505±55 (3895–3638). Approximate ages are expressed thus: 7000 (7800). Shell dates quoted include a deduction for the marine reservoir effect of 405±40 radiocarbon years, following Harkness (1983).

(b) Analysis of the data

The data were analysed using Gaussian Trend Surface Analysis. This technique has been described by Fretwell (2001) and Fretwell et al. (2004). It involves taking the natural logarithm of the array of the data for each shoreline, corrected to MHWS, minus an arbitrary level that equates to the level that the Gaussian trends to the horizontal. This level is termed the ‘zero level’. A polynomial surface, at the required order, is then calculated from the data, and the coefficients of this calculation are taken. After this, the original data points, with the zero level added, are input into the second equation: the inverse logarithm of the same order polynomial using coefficients from the first equation. The zero level is then subtracted to recalibrate to a common datum. For each shoreline the calculations are carried out for a range of zero levels to find the best-fit level. In this paper, only quadratic (second-order) Gaussian trend surfaces have been calculated, given the distribution of the available data.

Gaussian trend surface analysis was chosen because the surfaces trend to the horizontal (the zero level), unlike polynomial regression analysis. Gaussian surfaces are thus more appropriate in a glacio-isostatic context, despite uncertainties concerning possible forebulge effects or hydro-isostasy. It is believed that any peripheral depression and forebulge effect will be slight. None is modelled for the UK in the Lambeck (1993b, 1998) or Peltier et al. (2002) solutions, and even if one exists it is likely to be small because by the time the shorelines described here were abandoned most of the uplift which followed ice sheet decay would have been achieved and any peripheral depression and forebulge reduced. The effect of hydro-isostasy on the surrounding continental shelf will have been significant, as Lambeck (1995) graphically demonstrates, but available evidence suggests that the effects of water loading on the surrounding continental shelf during the Holocene may not have reached the mainland, since individual Holocene shoreline diagrams for mainland Scotland (e.g. Smith 1968; Cullingford 1972; Firth & Haggart 1989; Smith et al. 2003b) do not disclose any consistent changes in gradient along their lengths such as might have been the result of changes on the mainland following hydro-isostasy offshore.

In the interpretation offered below, Gaussian quadratic trend surfaces for four shorelines are described: the Holocene Storegga Slide tsunami shoreline of Smith et al. (2004); the Main Postglacial shoreline of Sissons (1974); the Blairdrummond shoreline of Smith et al. (2000); and a speculative later shoreline, here termed the Wigtown shoreline. These shorelines are named rather than referred to numerically because the precise number of Holocene shorelines in mainland Scotland cannot yet be established.

6. The Holocene Storegga Slide tsunami shoreline

(a) Altitude

This shoreline is present as the inland limit of estuarine silt beneath tsunami silty sand in N, NE and SE Scotland, as detailed by Smith et al. (2004). From 20 locations, Smith et al. (2004) published a Gaussian quadratic trend surface, which they demonstrated as more accurately fitting the shoreline data than either the glacio-hydro-isostatic model for 7000 (7800) of Lambeck (1995) or the trend surface model of Smith et al. (2000). This surface is shown in figure 2a. In SE Scotland, two further tsunami sites have recently been identified, and at one of these (near Dunbar) the shoreline altitude has been measured, supporting the estimate provided by the model for the shoreline altitude there. To date, no evidence for this event has been identified on the W coast, while sites which show the tsunami on the N coast and Shetland do not also disclose the contemporary shoreline deposits, hence the data analysed remain eccentrically distributed, albeit more extensive now than in the Smith et al. (2000) model. Table 3 lists the locations where the Holocene Storegga Slide tsunami shoreline has been measured.

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Table 3

Altitude data for the Holocene Storegga Slide tsunami shoreline (20 values) with Gaussian surface residual values.

(b) Age

The age of this shoreline has been discussed in Smith et al. (2004), where an overall estimate of circa 7100 (7900) is maintained, based the pooled mean of 20 regressive contact dates along the eastern UK coastline, the age of the regressive contact ranging from 6580±55 (7341–7572) to 7490±70 (8171–8406). Subsequent to the paper by Smith et al. (2004), Tooley & Smith (2005) provided an age of later than circa 7215 (8000) from a specimen of Cerastoderma edule in a sequence of sands in which the tsunami deposits occur in SE Scotland, though this deposit is not at the shoreline in the area. Given the short time over which the tsunami occurred, this shoreline is considered to be synchronous.

7. The Main Postglacial shoreline

(a) Altitude

Above the deposits associated with the Holocene Storegga Slide tsunami shoreline, the carseland surface forms the main evidence for later relative sea-levels. The inner margin of this surface has been regarded as a single shoreline, termed the Main Postglacial shoreline (e.g. Sissons et al. 1966), and altitudes on this feature formed most of the evidence for the isobase model of Sissons (1967) and the trend surface-based isobase model of Cullingford et al. (1991). However, Smith et al. (2000) later showed that only the higher areas of this surface belong to this shoreline. A Gaussian quadratic trend surface for the shoreline is shown in figure 2b and the altitudes upon which this surface is based are summarized in table 4.

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Table 4

Altitude data for the Main Postglacial shoreline (990 values) and Gaussian surface residual values.

The altitude data are the same as that used by Smith et al. (2000), but with additional data from the Montrose Basin, East Fife, the Nith and Lochar valleys, Ayrshire coast and Skye. The Islay data of Dawson et al. (1998), originally included by Smith et al. (2000) are excluded because the existence of the Main Postglacial shoreline there was based upon shell dates from nearby Colonsay obtained by Jardine (1978, 1987), which are uncertain as indicating a specific relative sea-level (Jardine 1978). Data from regressive contacts beneath surface peat at the heads of gulleys at Montrose and in E Fife, and dated at a similar age to other Main Postglacial shoreline regressive contacts (shown in the dates from Fullerton and E Fife, table 5) are included. New data from the Nith valley follow Smith et al. (2003a). For both the Ayrshire coast and Skye, the values are from the inland margins of transects of boreholes on radiocarbon dated horizons (the Skye data are taken from Selby (1997)). The Main Postglacial shoreline dataset is larger, better distributed and based upon more comparable data than that used by Smith et al. (2003a).

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Table 5

Index point ages and altitudes from conformable regressive contacts along the Main Postglacial shoreline.

(b) Age

Radiocarbon dates from organic sediment directly overlying transitional horizons at the regressive contact and supported by microfossil analyses are listed in table 5. They range from 5700±90 (6717–6306) to 6850±50 (7788–7589). On the available evidence, therefore, a generalized range of 5600–6900 (6400–7700) is indicated.

The samples are all less than 3 cm thick, with the exception of the sample from Arcan Mains, Inner Moray Firth, which was from peat 5 cm thick. They give a pooled mean of 6366.1±19.8 (7408–7311). Smith et al. (2002) reported that regression analysis of dates for the Main Postglacial shoreline compared with their distance from the centre of uplift as defined by a polynomial surface indicated that the shoreline is diachronous, but with additional dates here neither linear nor second-order curvilinear regression analyses for dates against altitude are statistically significant. Consequently, diachroneity cannot be proven with the present data.

8. The Blairdrummond shoreline

(a) Altitude

The Blairdrummond shoreline was first proposed by Smith et al. (2000). This shoreline lies below the Main Postglacial shoreline close to the area of maximum uplift, but towards the periphery is found stratigraphically above it. A Gaussian quadratic trend surface for this shoreline is shown in figure 2c. Altitudes for the Blairdrummond shoreline are summarized in table 6. The altitude data are the same as those used by Smith et al. (2000) with the exception of those from Wick and Islay. For the Inner Moray Firth, shoreline IF2A of Firth & Haggart (1989) is used, since this gives a stronger correlation than IF3, which Smith et al. (2000) used. Additionally, new data from E Solway, Luce Bay, the Ayrshire coast and Skye are added.

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Table 6

Altitude data for the Blairdrummond shoreline (789 values) and Gaussian surface residual values.

In this analysis, the data from Wick are excluded because uncertainties exist about the surface of the minerogenic horizon concerned. Dawson & Smith (1997) found that the transgressive horizon was conformable, and their dates of 4400±50 (5250–4850) and 4420±80 (5300–4840) are close to the range of ages given by Smith et al. (2000) for the Blairdrummond shoreline. However, the horizon is less than 10 cm thick at the borehole where both the transgressive and regressive contacts dated are in stratigraphic succession and thus the regressive contact dates of 2160±80 (2340–1935) and 2130±100 (2340–1865), although mutually supportive, imply an unusually long period of deposition at the boreholes involved for such a thin layer, raising the possibility that a hiatus, though not proven, might be present. The Islay data are also excluded because there is no date from a conformable horizon. The inclusion of the latter data in the analyses of Smith et al. (2000) relied upon a date of 4120±50 (4826–4452) from nearby Colonsay, which was not thought conformable by Jardine (1987).

New data provide a wider coverage of this shoreline than in Smith et al. (2000). In E Solway, extensive carseland areas are correlated with the Blairdrummond shoreline following Dawson et al. (1999), who dated a conformable regressive contact for the base of peat overlying the highest carseland surface there, of 4795±50 (5636–5330). The Girvan data comes from a transect of boreholes at the inland limit of the carselands there, from which a date of 3680±40 (4140–3900) for the regressive contact supports Blairdrummond age. The Skye altitude is from the inland limit of the deposit from a transect of boreholes from Selby (1997), conformably dated as of Blairdrummond age. At both the Girvan and Skye locations, Blairdrummond shoreline deposits overlie Main Postglacial shoreline deposits, as was also observed for the Cree valley carselands by Smith et al. (2003b).

Smith et al. (2000) included altitudes from the Montrose Basin, E Fife and Dunbar. Recent work supports this. At Cocklemill Burn, in Fife, Tooley & Smith (2005) found Blairdrummond shoreline deposits, dated from a specimen of the mollusc Cerastoderma edule at 4685±80 (5596–5071), overlying Main Postglacial shoreline deposits, thus indicating that in this area the carselands at a similar altitude to the north (E Fife) and slightly lower to the south (Dunbar) probably belong to the Blairdrummond shoreline (excluding the gully deposits referred to in table 3). This is, probably, also true for the Montrose Basin carselands, farther to the north, where it is believed that although remnants of the Main Postglacial shoreline lie at the heads of gulleys, as observed above, the majority of the carseland, generally slightly lower, is of Blairdrummond age. A date of 3653±135 (4406–3639) (the mean of the outer, middle and inner fractions) on a museum specimen of Cyprina islandica from Dryleas, towards the seaward margin of the Montrose carselands offers some support for this, but stronger support is obtained from comparison with the Cree valley, where carseland of a similar MHWS altitude discloses the Main Postglacial shoreline and Blairdrummond shoreline almost at the same altitude. At Creich, in the Dornoch Firth, the date of 3505±50 (3895–3638) broadly supports a Blairdrummond age (see below).

(b) Age

Dates from the carseland surface associated with the Blairdrummond shoreline are summarized in table 7. The dates indicate a range of 5030±110 (6164–5491)–3505±50 (3895–3638). However, a more narrow range is suspected, as outlined below.

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Table 7

Index point ages and altitudes from conformable regressive contacts along the Blairdrummond shoreline.

The date from Creich, in the Dornoch Firth, may be slightly too young, since Smith et al. (1992) reported that the condition of the pollen in the minerogenic sediment at the regressive contact dated suggested a hiatus. The date at Ochtertyre Moss, in the Forth valley, was originally thought to be from a hiatus (Sissons & Brooks 1971), but Brooks (2004, personal communication) subsequently believed it to reflect a transitional horizon, and this date is supported by dates from nearby sites on Ochtertyre Moss and Lecropt Moss in unpublished work by Smith, Dawson, Brooks and Holloway. The dates from the Solway Firth are the shoreline dates only from that sequence. Excluding the possibly rather young date from Creich (see above), the conformable dates for the Blairdrummond shoreline provide a pooled mean of 4150.4±29.3 (4552–4824) and a range of 4000–5000 (4500–5800) is suggested here. This range is older than the range suggested from fewer dates, including the dates from Wick, by Smith et al. (2000). Linear and second-order curvilinear regression analysis of the dates (excluding that from Creich) according to their altitude does not present a statistically significant solution. Diachroneity of this shoreline is, therefore, unproven with the present data.

It seems likely that this shoreline is the most extensive Holocene raised marine shoreline in mainland Scotland. On the east coast, the association of much of the extensive carseland of the Forth with the shoreline is supported by the work of Robinson (1993), who from a widespread level on the south side of the river, obtained a date from an in situ specimen of Littorina sp. of 4225±64 (4532–4954) from the mean of the inner and outer fractions. Most of the carselands in the Dornoch Firth, part of the carseland in Munlochy Bay and the Beauly Firth, probably much of the carselands around the Montrose Basin, at Arbroath and in E Fife, and in the Tyne valley near Dunbar are associated with the shoreline. On the W coast, most of the carselands in the Solway Firth and at Girvan are also deposits of this shoreline. Interestingly, the isolation basin studies of Shennan et al. (1995, 2000b) record a final marine transgressive episode which may correlate with the Blairdrummond shoreline. Thus, at Arisaig, Shennan et al. (1995) record marine influence withdrawing after 6630±50 (7578–7430), then a final inundation ending after 4010±50 (4788–4299), while at Dubh Lochan, near Ullapool, Shennan et al. (2000b) record a withdrawal of marine influence after 5265±60 (61287–5914) before a return of marine conditions, ending after 4250±60 (4966–4573).

9. The Wigtown shoreline

(a) Altitude

Below the carseland surface associated with the Blairdrummond shoreline, up to four levels have been identified in the carselands (e.g. Smith 1965, 1968; Cullingford 1972; Firth 1984; Firth & Haggart 1989; Smith et al. 1992, 1999, 2003a,b). While some of these levels may be related to local hydrological effects, it seems very likely, given the presence of such levels widely around the E and SW coasts, that at least some reflect relative sea-level change. Several studies report one particularly well developed level, and others only one level. These surfaces have not been dated, although ages can be estimated from shell dates and age ranges obtained from dates on higher shorelines and lower deposits. In the analysis presented in figure 2d, a Gaussian quadratic trend surface is computed from altitudes on the highest and most extensive surface below the Blairdrummond shoreline for the data listed in table 8. This shoreline is speculative, since the dates are less sure and the distribution of the evidence less widespread. It is termed the Wigtown shoreline from the location on the Cree estuary where it is best developed.

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Table 8

Altitude data for the Wigtown shoreline (441 values) and Gaussian surface residual values.

Altitude values for this shoreline in the Forth valley occur in an area near Alloa where there is extensive mining subsidence. Here, all heights were based upon two or more bench marks (Smith 1965, 1968), but in addition the Gaussian surface shown here was computed with and without the Forth data, showing no significant change in the surface and on this basis it is shown here with all the data included. In the Tay valley, Cullingford (1972) identified a prominent level below the Main Postglacial shoreline, which he believed was an equivalent of PG3 of Smith (1968) in the Forth, the latter correlated here with the Wigtown shoreline; these values are thus included. The remaining values listed in table 8 are from the next terrace below that correlated with the Blairdrummond shoreline.

(b) Age

This shoreline was probably abandoned sometime between circa 3400 (3700) and circa 1800 (1700). In the Cree valley, shells of Cerastoderma sp., obtained from deposits associated with this shoreline, have been dated at 2290±95 (2209–2062) and 2027±108 (2311–1714) (Smith et al. 2003b), while the youngest index point age from Blairdrummond shoreline carselands (seaward of the shoreline) there is 3380±70 (3829–3467) (Smith et al. 2003b). At the mouth of the Nith valley in the Solway Firth, the ‘merse’, or saltings, are dated as having begun to form before 1760±70 (1870–1520) (Smith et al. 2003a), so the Wigtown shoreline must be at least as old in that area. At Creich, in the Dornoch Firth, the shoreline is younger than circa 3505±55 (3895–3638) (the minimum age of the Blairdrummond shoreline there, see above) but probably older than at least 1890±50, the age of peat resting unconformably upon the saltings surface there (Smith et al. 1992). On Islay, Dawson et al. (1998) report peat resting conformably upon an estuarine surface at Gruinart Flats, at 4.5 m OD (2.9 m MHWS), which they maintain was only abandoned after circa 2000 (2000), and thus may have been occupied at the time of the Wigtown shoreline elsewhere.

10. Implications for isostasy in mainland Scotland

(a) Fit of the Gaussian surfaces

The surfaces described above fit the data more closely than polynomial surfaces for the same data, as can be seen from the statistics provided in table 9. For every shoreline, the Gaussian surface is an improvement on the polynomial. However, the improvement is slight, most residuals lying within the error ranges in tables 1 and 2, above. Although the Gaussian surfaces fit the data closely, in view of the lack of data on the W and N coasts, there remain uncertainties as to the general orientation of the quadratic surfaces, although the close fit to the Wick, Skye and Girvan data is encouraging. The possibility of variations on the W coast, reflecting variations in ice load or more widely of neotectonics, following increasing evidence for fault reactivation (e.g. Sissons 1972; Gray 1974; Sissons & Cornish 1982; Firth & Stewart 2000) cannot be excluded. There is no indication from the distribution of residuals that a forebulge effect is registered on mainland Scotland.

View this table:
Table 9

Statistics for Gaussian and polynomial quadratic trend surfaces for the shoreline data in this paper.

The Gaussian surfaces, even with more and better distributed data, support the polynomial surfaces of Smith et al. (2000) in placing the main centre of uplift in the southern Grampian Highlands, and thus contrast with the view of Dawson et al. (2002) on the location of the centre. It is possible that since the findings of Dawson et al. (2002) relate to earlier, Late Devensian, shorelines, there could have been a change in the pattern of uplift later and early in the Holocene, perhaps because an uplift pattern resulting from the development of an ice cap during the Loch Lomond Stadial was superimposed upon the pattern of uplift following decay of the main ice sheet and that the latter pattern continued after the effect of unloading had either ended or become minor compared with the pattern related to the main ice sheet. Equally, the difference between the centre of uplift indicated by the work of Dawson et al. (2002) and the centre indicated by the Holocene shorelines in this paper could be due to a migration of the centre towards the S or SE, which had commenced before Loch Lomond Stadial ice developed.

(b) A comparison with previously published surfaces

In table 10, a comparison is made between the Gaussian surfaces here and published polynomial models of Smith et al. (2000) and glacio-hydro-isostatic models of Lambeck (1993b, 1995). The sample locations are chosen from broadly N–S and E–W transects. It should be noted that this comparison is generalized because the altitude values from the glacio-hydro-isostatic surfaces are only estimated from published maps.

View this table:
Table 10

A comparison of observed shoreline altitudes with altitudes predicted from Gaussian, polynomial and glacio-hydro-isostatic isobase models at sample locations.

The figures in table 10 show that, while the surfaces defined in the Gaussian and polynomial models fit the shoreline data relatively closely, the surfaces for the 6000 and 7000 BP glacio-hydro-isostatic isobase models are noticeably discrepant, these surfaces being generally below the empirical shoreline data, particularly for N Scotland. In closely matching the empirical shoreline data and differing from the glacio-hydro-isostatic isobase models in N Scotland, the Gaussian and polynomial models support the view of Lambeck (1993b) that the ice sheet model upon which the glacio-hydro-isostatic models are based may require revision.

11. Sea surface changes

Table 11 gives the age and altitude ranges for the zero level of each Gaussian surface. The age range is given to 2σ and the altitude range incorporates the errors considered inherent in the altitude data in tables 1 and 2, above. The values compare relatively closely with the published graphs of sea surface change offshore NW Europe of Mőrner (1969).

View this table:
Table 11

Predicted altitudes of the shorelines for the zero level, with possible ages.

12. Conclusions

The following conclusions are drawn from this work:

  1. Gaussian trend surface models based upon the altitudes of three displaced shorelines interpreted from comparable estuarine deposits, the Holocene Storegga Slide tsunami shoreline, Main Postglacial shoreline and Blairdrummond shoreline, indicate that the main centre of uplift in Scotland during the Holocene lay in the SE Grampians, supporting previous work. The model for a fourth shoreline, the speculative Wigtown shoreline, discloses a broadly similar pattern. These models fit the shoreline data somewhat better than the polynomial models, and better than glacio-hydro-isostatic isobase models.

  2. Although more shoreline data are needed from the W and N coasts, the Gaussian models support the views of Lambeck (1993b) and Peltier et al. (2002) that further consideration needs to be given to ice sheet extent (and/or thickness) at the Late Devensian maximum. They also indicate that there may have been changes in the location of the main centre of isostatic uplift in Scotland during the Loch Lomond Stadial and Holocene.

  3. Gaussian trend surface analysis constitutes a more appropriate approach to describing trends in empirical shoreline data than polynomial regression analysis. Additionally, with well distributed and high quality data the technique may ultimately enable graphs of Holocene nearshore sea surface change to be produced from glacio-isostatically affected areas.

Acknowledgments

The authors would like to acknowledge the award of a Coventry University research grant (2000–2002) and a Leverhulme Trust Emeritus Fellowship (2003–2005), to DES. They are grateful for the advice of Professor Ian Petersen on the development of Gaussian trend surfaces and Dr Phil Woodworth on tidal factors. The advice and assistance many people, notably Dr C. L. Brooks, Professor A. G. Dawson, Dr S. Dawson, Dr L. K. Holloway, Dr J. Jordan, Dr T. Mighall, Dr S. Shi, Dr S. C. Turbayne and Dr J. M. Wells is greatly appreciated. Dr K. Selby is thanked for her permission to refer to unpublished data from Skye. The illustrations were drawn by Stuart Gill, of SGC Cartographics. The referees are thanked for their most helpful comments. This paper is a contribution to IGCP Project 495 ‘Quaternary Land-Ocean Interactions: Driving Mechanisms and Coastal Responses’. The data used in the shoreline models described in this paper may be viewed in the website: http://www.scottishsealevels.net.

Footnotes

  • One contribution of 20 to a Theme Issue ‘Sea level science’.

    References

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