The morphodynamics of ancient rivers can be reconstructed from fluvial stratigraphy using quantitative techniques to provide insights into the driving forces behind sedimentary systems. This study explores how these drivers can be evaluated from Paleozoic stratigraphy. Field measurements are taken in fluvial sediments from the Westphalian (Bolsovian and Asturian; 315.2–308 Ma) Pennant Formation of South Wales, UK, to reconstruct the hydrodynamics and morphologies of these Carboniferous rivers, which were sourced from the Variscan (Hercynian) mountain belt located south of the study area. Field data consist of cross-set heights, grain size, palaeocurrent directions and the dimensions of fluvial architectural elements. Hydrodynamic properties, including flow velocities and discharge rates, are reconstructed using a suite of numerical approaches. Results suggest median formative flow depths of 2–3 m and palaeoslopes of 4–5 × 10−4 m m−1 (0.02–0.03°). Quantitative planform prediction suggests that these rivers were probably anastomosing but with distinct single-threaded reaches. Mean single-thread width is 55 m, whereas mean channel-belt widths of 100–200 m are reconstructed, suggesting bankfull discharges of 390–560 m3 s−1. This study resolves contrasting palaeohydrological interpretations for Pennant rivers, and demonstrates how quantitative reconstructions of morphology, slope and planform can be obtained from fluvial stratigraphy.

Supplementary material: Field data, a field localities KMZ file, analysis of flow depth scaling methods and fluvial facies analysis are available at https://doi.org/10.6084/m9.figshare.c.6131975

Rivers have been among the most significant drivers of geomorphological and hydrological change on Earth's surface since the Archean (Hjellbakk 1997; Eriksson et al. 2006; Bridgland et al. 2014; Ielpi et al. 2017; Ganti et al. 2019; Gibling and Davies 2012). Their hydrodynamic and morphodynamic properties are recorded in the stratigraphic record (Whittaker 2012; Ganti et al. 2014; Bhattacharya et al. 2016), allowing researchers to reconstruct the characteristics and behaviour of ancient fluvial systems from the geological archive (e.g. Michael et al. 2014; Chamberlin and Hajek 2019; Ganti et al. 2019; Lyster et al. 2021). These reconstructions include morphological and hydrodynamic properties (Paola and Mohrig 1996; Shibata et al. 2018), sediment transport capacity (Holbrook and Wanas 2014; Lin and Bhattacharya 2017; Sharma et al. 2017; Mahon and McElroy 2018), and drainage area and shape (Bhattacharya and Tye 2004; Bhattacharya et al. 2016; Xu et al. 2017; Li et al. 2018; Lyster et al. 2020). As river development is closely linked to tectonic and climatic forcing, fluvial strata provide insights into the prevailing tectono-climatic conditions at the time of deposition (Duller et al. 2010; Castelltort et al. 2012; Whittaker 2012; Harries et al. 2021).

Although much work in the field of sedimentology has implemented qualitative techniques (e.g. facies analysis) to provide valuable insights into river characteristics from fluvial strata (e.g. Jones 1977; Miall 1985; Plink-Bjorklund 2015, amongst many others), an increasing number of quantitative approaches are beginning to present new opportunities within the discipline. Empirical and theoretical equations can be used to reconstruct the morphology and hydrology of modern rivers in terms of slope, depth and water discharge (Leopold and Maddock 1953; Hack 1957; Leopold and Wolman 1960; Williams 1984). These methods have been increasingly adapted for stratigraphic application in recent years to facilitate multifaceted reconstructions of ancient systems (Bridge and Mackey 1992; Leclair and Bridge 2001; Trampush et al. 2014; Bradley and Venditti 2017; Greenberg et al. 2021; Lyster et al. 2022), allowing fluvial morphodynamics such as channel dimensions, flow velocities and unit discharges to be quantified in a way that is not possible from qualitative facies analyses alone. Reconstruction of river behaviour within this type of palaeohydrological framework therefore adds richness to insights offered from more classical sedimentological approaches, and in some cases may even challenge pre-existing interpretations (e.g. Ganti et al. 2019). However, use of quantitative palaeohydrological techniques can be restricted by the incomplete nature of the rock record (Sadler 1981; Straub et al. 2020). Additionally, the limited number of datasets to date of ancient river deposits where important sedimentological observables (e.g. height and distributions of cross-beds) are quantified with sufficient precision means that robust reconstructions of fluvial morphodynamics are rare (see Leary and Ganti 2019; Lyster et al. 2022). Nonetheless, in principle, palaeohydrological studies offer an opportunity to assess the scale and dimensions of ancient fluvial landscapes, particularly where the corresponding geomorphological archive has been lost, and to quantify the fluxes of sediment and water across the surface of the Earth and other planets in the geological past (Ganti et al. 2019; Stack et al. 2019; Lyster et al. 2021).

This study focuses on the palaeohydrology of Late Carboniferous (Pennsylvanian) fluvial systems of the Pennant Sandstone Formation, South Wales, UK (Fig. 1). In the UK, the Upper Carboniferous succession comprises the Namurian, Westphalian, Stephanian and Autunian regional stages, with the Westphalian stage, which is the subject of this study, spanning 319–308 Ma (Davydov et al. 2012). The Westphalian stage comprises the Langsettian, Duckmantian, Bolsovian and Asturian regional substages, with the Bolsovian and Asturian substages being the focus here (315.2–308 Ma; Davydov et al. 2012).

The Pennant Sandstone is of key interest owing to its tectono-geographical setting in the foreland of the Variscan Orogen, temporally close to the cessation of the northward migration of the Variscan Front during the Westphalian stage (Gayer and Jones 1989; Jones 1991; Burgess and Gayer 2000; Opluštil and Cleal 2007). Hence, these strata record the behaviour, water discharges and sediment fluxes of rivers during the latter stages of the assembly of the Pangaean supercontinent. The formation crops out extensively in the South Wales and Pembrokeshire coalfields and has a well-constrained stratigraphic framework owing to geological studies during Wales’ time as a productive coal mining region (Woodland et al. 1957; Kelling 1974; Jones 1977). Previous sedimentological work on the Pennant has largely centred on qualitative facies and architectural observations to build a nuanced picture of river behaviour and environment in the late Carboniferous (De la Beche 1846; Strahan 1899; Woodland et al. 1957; Kelling 1974; Jones 1977; Jones and Hartley 1993). These classic studies provide detailed sedimentological context for our work. However, to date, the morphodynamic and hydrodynamic characteristics of these fluvial systems have not been reconstructed using a quantitative palaeohydrological framework. Here we revisit the Pennant Formation and use palaeohydrological approaches, founded in bedform analysis (see Ganti et al. 2019; Lyster et al. 2021), to exemplify how new insights into fluvial system behaviour can be obtained for classic geological formations that have received little recent study. Consequently, our field data allow us to reconstruct flow depths, palaeoslopes, water discharges and the behaviour of Carboniferous rivers draining the northern margin of the Variscan mountain belt. These results provide insight into how ancient fluvial systems responded to foreland basin evolution during a major orogenic event and demonstrate how channel planform and characteristics can now be extracted from quantitative measurements of fluvial stratigraphy.

The Pennant Sandstone Formation comprises Bolsovian and Asturian aged fluvial sediments that were deposited in the South Wales foreland basin (Fig. 1a) by rivers draining mountainous terrain built during the Variscan Orogeny (Kelling 1974; Evans 2004). Today, these sediments crop out in the South Wales and Pembrokeshire coalfields. The Variscan (Hercynian) Orogeny was the principal formative orogenic event of the supercontinent Pangaea, creating an orogenic belt that stretched east–west over 1000 km (Leveridge and Hartley 2006). Many of the north–south-oriented compressional structures and sedimentary basins of Europe today can be attributed to the Variscan Orogeny, including the South Wales and Pembrokeshire coalfields, which form the geographical focus of this study (Leveridge and Hartley 2006; Opluštil and Cleal 2007). The South Wales foreland basin, situated to the north of the northward propagating Variscan Orogenic Belt (Fig. 1c), was generated following inversion of a regional Devonian–Early Carboniferous extensional regime (Hartley and Warr 1990; Burgess and Gayer 2000; Opluštil and Cleal 2007). The northern edge of the foreland was bounded by the cratonic upland of the Wales–Brabant High (Fig. 1c; Rippon 1996).

By the end of the Carboniferous, the front of Variscan deformation had migrated northward to the location of the South Wales Coalfield, producing shortening of up to 30% and north–south compressional structures such as the major asymmetric syncline that dominates the structure of the coalfield today (Fig. 1b; Jones 1991; Gayer and Pesek 1992; Evans 2004). Subsidence curves of the South Wales basin suggest a rapid accommodation generation of 260 m Ma−1 in the west and 130 m Ma−1 in the east during the late Westphalian (Burgess and Gayer 2000). As the underlying South Wales Coal Measures consist of sediment sourced from the Wales–Brabant High (Evans 2004), the base of the Pennant Formation represents the onset of Variscan deposition in the region (Leveridge and Hartley 2006; Opluštil and Cleal 2007).

The Pennant sandstone has a maximum total thickness of 1350 m and is subdivided into five members shown in Figure 2 (Barclay 2011). These members, first described as ‘beds’ by Woodland et al. (1957) following the early classification work of De La Beche (1846) and Strahan (1899), are separated by coal horizons and form the basis for temporal differentiation in this study. Each member contains sandstone (greenish-grey, lithic arenite), mudstone, siltstone and coals of varying abundances and thicknesses (Waters et al. 2007, 2009). The Rhondda Member is the thickest and contains the highest proportion of sand (Waters et al. 2009), and is therefore the most represented member in outcrop. The Llynfi, Hughes and Swansea members have limited outcrop owing to higher proportion of muds and silts, and the Brithdir Member's lesser thickness also limits the abundance of outcrop (Waters et al. 2009). Although the exact stratigraphic boundary between the Bolsovian and Asturian substages is not formally defined in the Pennant Sandstone, it is considered to be within the Brithdir Member's depositional timespan (Waters et al. 2009; Barclay 2011).

The base of the Pennant Formation is described as the first significant ‘Pennant-type’ sandstone (greenish-grey and blueish-grey, feldspathic, micaceous, lithic arenite) of at least 3 m thickness (Waters et al. 2009), creating a diachronicity of the horizon. In the Swansea region, the base is contemporaneous with the Cambriense Marine Band at the base of the Llynfi Member (Barclay 2011) whereas the base rises as high in the stratigraphy as the Brithdir Member in the eastern coalfield (Waters et al. 2009). The top of the Pennant Sandstone is also diachronous, with the Swansea Member being absent in the east of the coalfield (Waters et al. 2009). The diachronous boundary means that the variability of thickness of the Pennant is high (Fig. 2), particularly across the Neath Disturbance, a major NE–SW-trending Caledonoid fault in the modern Vale of Neath (Barclay 2011).

Correlation of the Pennant Sandstone between the Pembrokeshire and South Wales coalfields is contentious, with an early study suggesting correlation of Pembrokeshire outcrops with the Hughes Member (Jenkins 1962). More recently, a palaeobotanical study conducted by Cleal and Thomas (1992) correlated these deposits with the Rhondda Member. Herein, the Pembrokeshire Pennant is included in the Rhondda Member.

Although there has been little recent work on the sedimentology of the Pennant Formation, previous studies in the last 50 years have generally described the depositional environment of the Pennant Sandstone as a low-sinuosity, relatively proximal braidplain, characterized by development of sheet-like or stacked sandstone bodies, a concentration of in-channel bedforms and a general absence of point bar deposits (Kelling 1969; Jones 1977; Jones and Hartley 1993). The doctoral thesis of Jones (1977), for instance, included extensive and detailed analyses of architectural features and facies within the lower Pennant, and our study makes use of this significant body of work. Jones in particular identified two major facies associations; the first is interpreted as the result of repeated incursions of small deltas, or crevasse deltas, into shallow bays, and the second, which is dominant after the Llynfi Member, is interpreted to record braided rivers characterized by a variable discharge regime, which laterally migrated through a vegetated floodplain environment. Although Jones (1977) rejected the notion of the Pennant recording classical meandering channels (sensu Allen 1963) and estimated channel widths of the order of hundreds of metres, his thesis also suggested that individual channels may have had flow depths of >15 m based on channel body thicknesses, which would have been unusually deep for braided systems. This example serves to underscore the potential discrepancies between facies-derived reconstructions presented in the historical literature and morphodynamic considerations. Consequently, our work allows for a re-evaluation of the characteristics of these Carboniferous fluvial systems that drained the growing Variscan orogen for the 21st century.

Field data collection

Field data were collected in the South Wales Coalfield (17 localities) and Pembrokeshire Coalfield (two localities) during two field campaigns in August and September 2021. All measurements were taken in channelized sandstone bodies and form the basis of the reconstruction and analysis of river morphologies in this study.

Cross-sets

Cross-sets in medium to very coarse sands were measured to reconstruct the sizes of bedforms in Pennant rivers using the method of Leclair and Bridge (2001). This approach requires mean cross-set heights, so distributions of heights in individual cross-sets (n = 268) were measured to the nearest 10 mm at 10 cm intervals along the major axis of the cross-set (7–62 measurements per cross-set; Fig. 3b). From these height distributions, mean cross-set heights, hxs, were subsequently extracted. Maximum heights were also extracted from the distributions to derive a scaling factor between mean–maximum cross-set heights for each member of the Pennant Sandstone. This method has successfully been used previously on fluvial strata in Utah, USA (Lyster et al. 2021), and NW Scotland (Ganti et al. 2019).

Cross-set height maxima were also measured at each locality (n = 1809; Fig. 3d). Using the new mean–maximum height scaling factors, mean cross-heights were estimated for each measured maximum height, expanding the total dataset from 268 to 2077 mean cross-set heights.

Palaeocurrent directions were determined at each field site by measuring the dip and dip direction of cross-set lee slopes (n = 1038). Bedding measurements were also taken at each site or from geological maps (n = 58). Palaeocurrent measurements were subsequently unfolded using Stereonet 11 (Allmendinger 2020) to correct for the dip of beds and therefore decipher true palaeocurrent directions of the rivers recorded within each member of the Pennant Formation.

Grain size

Where the height distribution of an individual cross-set was measured, the median grain size, D50, was also estimated using the Wentworth grain-size classification (Wentworth 1922; Fig. 3e) and converted to a numerical value in metres (e.g. 0.000375 m for medium sand, 0.0005 m for medium–coarse sand., etc.). Grain-size photographs were also taken at each locality to later verify the estimated grainsize using ImageJ software (Rasband 2018). Grain sizes exceeding sand grade were observed in some outcrops of the Pennant Sandstone, and typically occurred as isolated lenses at the base of channel fills (Fig. 3f; see Jones 1977; Jones and Hartley 1993). Distributions of these conglomeratic sediments were measured using the Wolman point count method (Wolman 1954) to extract D50 and were used to constrain the maximum possible, but rare, flow conditions in Pennant rivers.

Architectural fluvial elements

To validate the palaeohydrological reconstructions, the dimensions of bar-scale (1 m to tens of metres scale) architectural elements were independently measured (Fig. 4). The heights of both channel fill sandstone packages and accretion packages (downstream and lateral) were quantified using a laser range finder (Haglöf Laser Geo) to a precision of 0.1 m (n = 116). These accretion packages, representing bar-scale clinoforms, provide a maximum bankfull flow depth where the total height of the bar-clinoform is visible, or where it can be extrapolated (Mohrig et al. 2000; Hajek and Heller 2012). These estimates of bankfull flow depth were used to validate flow depths calculated from cross-set heights. Where possible, accretion package widths were measured for channel width calculations (below) and outcrop-scale photographs were taken to show the fluvial architecture of each site (Fig. 4).

Palaeohydrology

Flow depth

Cross-set heights represent a fraction of the original bedform height. Here, the scaling relation of Leclair and Bridge (2001) was used to convert mean cross-set height, hxs, to mean bedform height, hd:
hd=2.9(±0.7)hxs.
(1)
This relationship is based on the theoretical model of Paola and Borgman (1991) for bedform migration over random topography on the bed with negligible angle of climb. Here, uncertainty of the scaling factor (±0.7) represents the standard deviation of the dataset used by Leclair and Bridge (2001). To account for this uncertainty, a Monte Carlo uncertainty propagation method was used, following the method of Lyster et al. (2021); 106 random values of the model parameter were generated between the uncertainty intervals (2.9 + 0.7 and 2.9 − 0.7 for equation (1)) and were used to calculate hd. This recovered 106 values of hd,which were subsequently carried forwards; Monte Carlo uncertainty propagation was used in all subsequent equations presented here with the stated uncertainties, and the outcome of these calculations, below, are presented as box and whisker plots, which show the median and interquartile ranges for our palaeohydrological reconstructions in the results.
To estimate flow depth, H, the relationship of Bradley and Venditti (2017) was used:
H=6.7hd.
(2)
This relationship was derived following a re-evaluation of past work on dune–depth scaling relations that were deemed to be ineffective (Yalin 1964; van Rijn 1984; Julien and Klaassen 1995). The scaling factor in equation (2) (i.e. 6.7) at 50% uncertainty has a range of 4.4–10.1. A Monte Carlo propagation was again used between these values to accommodate this uncertainty. Any calculated values of H that exceeded 125% of the maximum measured package thickness at the field site were removed from the dataset at this stage (n = 89 out of more than 2000 cross-sets).

Palaeoslope

Slope, S, was reconstructed using estimates of D50 and H, and using the empirical method of Trampush et al. (2014), which is appropriate for the range of grain sizes used in this study. Here slope, S (in m m−1), is given by
logS=α0+α1logD50+α2logH
(3)
where α0, α1 and α2 are constants given as −2.08 ± 0.036, 0.254 ± 0.016 and −1.09 ± 0.044 respectively. Monte Carlo uncertainty propagation was used to accommodate uncertainty in the constants (Trampush et al. 2014). Palaeoslope values were analysed both temporally (i.e. between members) and spatially (i.e. downstream considering resolved palaeocurrent directions where we have multiple channel measurements at a similar stratigraphic level of the Pennant).

Flow velocity and unit discharge

The equation of Manning et al. (1890) was used to derive flow velocity, U, and water discharge per unit width, QU, as QU = U × H. Manning's equation is given as
U=1nH2/3S1/2
(4)
where n, Manning's Roughness Coefficient, is approximated as 0.03 following Lyster et al. (2021) based on the value for fluvial channels of the look-up table of Chow (1959). U is given in m s−1 and QU is given in m2 s−1. QU can be multiplied by an estimated width, W, to give total bankfull discharge, Q, in m3 s−1.

Fluvial style and channel widths

Determining the planform morphology of ancient river systems can be difficult as preservation of entire channels is rare in the rock record (Parker 1976; Brierley 1989; Lyster et al. 2022). Traditionally, facies analyses of architectural elements using vertical profiles and planview exposures of fluvial strata are used to classify ancient rivers as meandering, straight, anastomosing or braided (Miall 1985). However, these analyses are most effective where outcrop is complete. Therefore, quantitative techniques using the Froude number (Fr), S and aspect ratio (i.e. the ratio of channel width, W, to channel depth, H) of channels can also be implemented to determine fluvial style. Fr is calculated using
Fr=UgH
(5)
where g is gravitational acceleration.

Stability fields for braided and meandering channels can be reconstructed using plots of S/Fr against the inverse of channel aspect ratio (i.e. H/W as opposed to W/H), as the seminal work of Parker (1976) originally showed. Recently, Lyster et al. (2022) re-evaluated the stability fields of Parker (1976) using a new dataset of nearly 1700 modern rivers. They showed that H/W < 0.02 characterizes multi-thread systems and H/W > 0.02 characterizes single-thread systems, whereas S/Fr > 0.003 characterizes braided multi-thread systems and S/Fr < 0.003 characterizes anastomosing multi-thread systems. Here, these new insights were used to reconstruct channel planform for all members of the Pennant Formation.

The method of Greenberg et al. (2021) was used to quantify single-thread channel widths, WC, where lateral accretion package widths, WL, were observed at field sites (n = 23).
WC=2.34(±0.13)WL
(6)
and where lateral accretion packages were partially preserved, WL was estimated by extrapolating accretion surfaces using structural measurements of accretion surfaces relative to bedding. Monte Carlo uncertainty propagation was used with the bounds of the scalar in equation (6). Across the mapped extent of the Pennant, steeper-sided escarpments are generally composed of channel sandstones whereas rolling grass-covered slopes are typically underlain by overbank fines of the Pennant. Therefore, the width of sandstone outcrops provides a constraint on the maximum width of the channel belt and, as such, were measured as an estimate of channel belt width, W (see Jones 1977). In addition, a channel aspect ratio described in the thesis of Jones of 1:56, based on observations in the Pennant at Rhondda Fawr, was also used to estimate W from reconstructed values of H.

Palaeohydrology

Distributions of height within individual cross-sets demonstrate a linear relationship between mean and maximum cross-set height (hxs and hxsMax), where hxs is c. 62% of the maximum cross-set height (Fig. 5a). Separating these data by member resulted in similar scaling relations in the range hxs = 0.59hxsMax to hxs = 0.65hxsMax (Fig. 5b). These scaling relationships are comparable with those reported by Lyster et al. (2021) for Late Cretaceous fluvial strata in Utah, suggesting that mean cross-set heights scale predictably with cross-set maxima. Using these member-specific scaling relationships, n = 1809 cross-set height maxima were converted to mean cross-set heights, and these were used to supplement the n = 268 mean cross-set heights from measured distributions. Of these n = 2077 mean cross-set heights, the mean value is 0.12 m.

Mean cross-set heights correspond to median flow depths, H, in the Pennant Sandstone of 2.3 m using equations (1) and (2), whereas taking channel or accretion package heights as a proxy for H gives a median of 2.45 m (Fig. 6a). This suggests that the results are robust, with only 4% of calculated flow depths exceeding 125% of the maximum measured package height at the corresponding locality (Supplementary material 3). Figure 6 further summarizes the hydrodynamic properties (H, S, U and QU) reconstructed for the Pennant Formation and its constituent members. As each measured cross-set has been used within our Monte Carlo uncertainty propagation approach, the median and interquartile ranges of reconstructed fluvial morphodynamcs of Pennant rivers can be extracted and shown as box and whisker plots, grouped by member. This grouping aims to maximize the potential to isolate any temporal trends in the data. Flow depths reconstructed for all members are similar to the mean for the Pennant Sandstone as a whole (2.3 m), with interquartile depth ranges of c. 2 to 3 m. Only the Llynfi has marginally more shallow channels than the succeeding members, but its interquartile range shows significant overlap with the overlying succession (Fig. 6a). Palaeoslopes show limited temporal variation with all members returning median slopes of 4.5 × 10−4 and interquartile ranges of c. 4–6 × 10−4 (m m−1; 0.02–0.03°), values that are consistent with sand-bedded lowland rivers today (Fig. 6b; Trampush et al. 2014). No statistically significant up-section change in S was observed following Kolmogorov–Smirnov tests between each member (Supplementary material 5). Values of U and QU similarly show limited temporal variation with median values in the range of 1.2–1.3 m s−1 and 2–3 m2 s−1 respectively, and interquartile ranges that also overlap (Fig. 6c and d). In the few outcrops in which conglomerates were observed, representing the coarsest fraction of the Pennant Formation, reconstructed flow velocities are greater (>1.9 m s−1) and show greater variation (1.9–2.3 m s−1), and QU is a factor of 1.5–2 greater than in the sand fraction (blue crosses, Fig. 6).

Palaeocurrent rose diagrams were produced for each locality using structural measurements of cross-set lee faces, unfolded to account for the dip of beds (Fig. 7). A range of palaeocurrent directions were recovered, with flow directions to the west more common (11/18 sites) than flow directions to the east. It is important to stress, however, that outcrops belonging to each member would not have necessarily formed part of a single fluvial system, as deposition in the Pennant clearly involved more than one river system in both temporal and spatial senses.

Spatial variation of S between outcrops of the same member shows more marked trends, despite the fact that the interquartile ranges of predictions overlap (Fig. 8). The clearest of these trends can be seen in the Brithdir Member's three field sites, which show a westward decline in channel gradient from c. 6 × 10−4 in the east to c. 4 × 10−4 in the west. Two sample Kolmogorov–Smirnov tests on the distributions of palaeoslopes resolved at each of the field sites of the Brithdir confirm that the sites produce distributions that are significantly different from one another (Supplementary material 5). It is noted that the Pembrokeshire Pennant, which is here correlated with the Rhondda Member, has significantly steeper palaeoslopes of 5–6 × 10−4 than the Rhondda outcrops in the west of the South Wales Coalfield. Consequently, the palaeogeographical relationship of these outcrops to the main part of the Pennant remains unclear, as previous researchers have noted (e.g. Jones 1977; Jones and Hartley 1993).

Planform morphologies

Plausible estimates of the channel width of single threads in the Pennant Formation, WC, and the channel belt width, W, are shown in Figure 9a. Mean WC is 55 m and ranges from 12 to 106 m. In contrast, values of W using the channel body aspect ratio of Jones (1977) have a mean value of 137 m, whereas outcrop widths measured in this study have a mean value of c. 210 m. Bankfull water discharges, Qbf, calculated using WC, have an interquartile range of 80–200 m3 s−1 and a median of 140 m3 s−1 (Fig. 9b). Considering the entire channel belt, bankfull discharges using the outcrop width give an interquartile range of 440–760 m3 s−1 and a median of 560 m3 s−1 (Fig. 9c), whereas using the ratio of Jones (1977) gives an interquartile range of 320–490 m3 s−1 and a median bankfull discharge of 400 m3 s−1 (Fig. 9d).

A key question is whether Pennant rivers were single-thread or multi-thread. Figure 10 shows the inverse of channel aspect ratio (i.e. H/W as opposed to W/H) plotted against S/Fr for n = 1227 measured cross-sets with corresponding single-thread widths, and for n = 1569 cross-sets with corresponding outcrop widths. For all data points combined (n = 2820), only 0.3% of data points fall outside the single-thread field of Parker (1976); however, this method has been recently recognized to disfavour multi-thread classification for geological examples (see Lyster et al. 2022).

Here, using the revised stability fields of Lyster et al. (2022), 94% of points calculated using the width scaling method of Greenberg et al. (2021) plot in the revised single-thread stability field of Lyster et al. (2022; Fig. 9), which is expected as this method (equation 6) recovers estimates of single-thread channel widths. Given that single-thread widths appear to have been of the order 50 m and that outcrop widths have mean values of c. 200 m but maximum values up to 300 m, it is reasonable to anticipate that multiple threads could have coexisted within channel belts. This is consistent with the observation that 90% of data points using our measured outcrop width, which give an upper limit on maximum channel active width, plot in the multi-thread stability field of Lyster et al. (2022). Ultimately, we do not know whether multiple threads were present. However, if present, it is likely that a few active threads existed rather than many active threads, given the relative magnitudes of bar clinoform widths, thread widths and outcrop widths (e.g. Greenberg et al. 2021). Further, if multiple threads coexisted then, using the y-axis of the multi-thread stability field proposed by Lyster et al. (2022), Pennant rivers were more likely to have been anastomosing multi-thread rivers than braided multi-thread rivers (Fig. 9).

These results underline that reconstruction of channel planform depends on effective evaluation of channel width estimates alongside facies-based interpretations. Nevertheless, the results presented here suggest that both single-thread and anastomosing multi-thread planforms may have prevailed during Pennant deposition. Therefore, these results do not support the notion that the Pennant Formation preserves predominantly braided multi-thread systems (Kelling 1974; Jones and Hartley 1993).

What did the rivers of the Pennant Sandstone look like?

This study provides the first application of a quantitative palaeohydrological framework to the late Carboniferous rivers of the Pennant Formation, based on a combination of bedform scale measurements, grain size and channel architectural elements. Rivers of the Pennant had individual threads with bankfull widths of c. 50 m and channel belts spanned 100–300 m. Median flow depths were 2–3 m, implying median bankfull discharges of 390–560 m3 s−1 across the channel belt. Channel morphodynamics and hydrodynamics remain similar up-section, within the propagated uncertainties, although channels were probably steeper in the Pennant of Pembrokeshire where conglomerates are more abundant and Variscan deformation is more pronounced. Channels with depths of 10–15 m were not reconstructed and no measured cross-sets that might suggest such large depths were observed.

This study finds that, although the ancient rivers of the Pennant Sandstone drained northwards from the Variscan Mountains in the south (Jones and Hartley 1993; Evans 2004), field results from most localities (11/18) suggest west-directed palaeoflow, matching the study of Jones (1977). Axial drainage is common in foreland basins and can be seen in the modern Ganges Basin, at the foot of the Himalayas, or the rivers of the upper Amazon Basin (Garcia-Castellanos 2002). Flow to the north would have been limited spatially by the presence of the Wales–Brabant High at the northern margin of the foreland basin (Opluštil and Cleal 2007). The landscape was relatively flat in the foreland with river gradients of 4–5 × 10−4 (0.02–0.03°), comparable with upper reaches of the continental Guadalquivir River, southern Spain (S = 3.9 × 10−4; Baena-Escudero et al. 2016) and of the Ebro River, northern Spain (S = 6.7 × 10−4; Ollero Ojeda 1990).

Whereas previous work on the Pennant produced estimates for channel depths of 10–15 m (Jones 1977), our analyses suggest that rivers of the Rhondda Member were probably five times shallower than this. Our data also suggest that planform channel belt widths were 3–8 times narrower than those resolved by Jones (1977). Architectural elements unambiguously related to individual channels and large enough to reflect rivers of the previously reconstructed size were not observed in our field study but amalgamated sandstone packages were observed to reach scales comparable with those previously reported. As such, our results provide constraints between insights that can be drawn from the bedform scale compared with the channel body scale. The study by Jones and Hartley (1993) on the reservoir characteristics of the Pennant Sandstone presents a channel depth to width ratio of 1:5–15 based on channel fill deposits whereas we find a single-thread depth to width ratio of 1:15–30, greater by a factor of about two, again based on depths derived from cross-set analysis.

Within the channel sandstones of the Pennant, distinct horizons of wood (Lepidodendron and Calamites) debris are observed. These packages resemble clast-supported deposits in places, with wood fossils up to 1 m in length found in outcrops of the Llynfi Member (Fig. 11). This, along with the presence of coal seams at all stratigraphic intervals of the Pennant, provides evidence of a heavily vegetated region. This is in agreement with the palaeofloral work of Opluštil and Cleal (2007), in which an ever-wet, tropical palaeoclimate is proposed. The presence of these wood debris dominated beds in the Pennant indicates that rivers displayed marked discharge variability, as was also hypothesized in the thesis of Jones (1977). Conglomeratic lags in several outcrops of the Pennant, where reconstructed flow velocities are 1.5–2 times greater than in sands, probably reflect flow dynamics of the largest discharge events that would have occurred in rivers of the late Carboniferous South Wales foreland basin. In the Westphalian, Britain was palaeogeographically sub-equatorial (Scotese 2001), meaning that tectono-climatic conditions may have been analogous to the modern Amazon and Congo basins. Given water discharges of 300–600 m3 s−1 it is estimated that the ancient rivers had drainage areas of 4500–9500 km2, based on an average precipitation rate of 2 m a−1 from modern equatorial rainforests (e.g. Amazon rainforest; Sombroek 2001), and assuming that water discharge scales with drainage area.

Various planforms probably existed over the course of these ancient rivers. Using outcrop widths as a proxy for channel belt widths, many of these rivers may have been multi-threaded. Of these multi-thread rivers, quantitative analysis using estimates of slope and Froude number (equations 3 and 5) and the stability fields of Lyster et al. (2022) suggest that multi-thread Pennant rivers were likely to have been anastomosing. There is, however, both facies-based and quantitative evidence for single-thread reaches in Pennant rivers. Facies evidence includes laterally dipping accretion surfaces representing meander growth, and the correspondence between estimates of single-thread widths and outcrop widths for some localities of the Hughes and Llynfi Members also suggests that some outcrops preserve rivers with a single-thread planform. In addition, the variability in resolved palaeocurrent between field sites of similar spatio-temporal setting in the Pennant may suggest that the sinuosity of the rivers was higher than previously reported.

The anastomosing river planform morphologies implied by the results in this study suggest that Pennant rivers were probably more stable than previous interpretations of relatively proximal braided systems. Anastomosing rivers are often characterized by large, typically vegetated, mid-channel bars or islands, in contrast to the highly mobile barforms that are typically observed in braided systems (e.g. Makaske 2001). The abundant vegetation in the Variscan foreland in the Westphalian (Opluštil and Cleal 2007) would have acted as a stabilizing agent for the river systems, generating the large but spatially limited sandstone bodies that occur between the extensive mudstone-dominated landscapes in the valleys of South Wales. Overall, results suggest that the hydrodynamics of fluvial systems in the Variscan foreland were remarkably similar throughout Pennant deposition, despite the 10 km Ma−1 northward advancement of the Variscan Mountains (Burgess and Gayer 2000) with rivers showing limited temporal trends up-section.

Upstream to downstream trends, however, are more visible in the data, particularly for slope; in the Brithdir Member, slope decreases from c. 6 × 10−4 to 4 × 10−4 across the >10 km planview distance between three field sites. Considering these trends in palaeoslopes, it is hypothesized here that the three field sites visited in the Brithdir Member formed part of the same fluvial system, based on slope, palaeocurrent and the authors’ observations of similar facies. The three westernmost localities in the Rhondda Member in the South Wales Coalfield also show decreasing S downstream, although the facies evidence is less convincing that they form the same system here. The Llynfi and Hughes members do not have field sites showing evidence of being part of the same system and, given the spatial scale (>100 km), are interpreted as outcrops representing spatially separated but temporally equivalent river systems.

The mean hydrodynamic parameters and morphologies of Pennant rivers are summarized in Figure 12. This figure represents the morphology of a hypothetical modern fluvial system, using the parameters reconstructed in this study, which suggest that anastomosing morphologies of c. 200 m width and c. 2.5 m flow depths were most common in the rivers of the Pennant.

Overall, results of this study suggest that Pennant rivers exhibited both anastomosing and single-threaded planforms with bankfull discharges up to 560 m3 s−1. To a first order, the rivers were similar in scale and tectonic setting to the modern Guadalquivir and Ebro rivers of Spain, and the upper Kuban River, Russia.

Tectonic implications

The ancient river deposits preserved in the stratigraphy of the Pennant Sandstone provide an opportunity to explore the evolution of the northern foreland basin margin of the Variscan mountain belt. Our data analysis shows that there is no statistical temporal change in the morphodynamic parameters resolved in the Pennant rivers over the c. 7 myr depositional interval of the formation, despite a reconstructed northward migration of the Variscan Front of greater than 50 km in the same period (Burgess and Gayer 2000). In contrast, recent quantitative palaeohydrological studies of ancient rivers draining the Late Cretaceous Sevier fold-and-thrust belt of Utah, which flowed in a broadly similar orogenic setting to the Pennant rivers, show marked steepening temporal trends in palaeoslope over a 9 myr period related to the migration of the thrust front (Lyster et al. 2021, 2022). Rivers of the Pennant Formation appear to be remarkably insensitive to tectonic forcing by comparison.

Various mechanisms could be responsible for this stability in reconstructed palaeoslopes. First, subsidence rates of c. 130–260 m Ma−1 in the centre of the South Wales basin (Burgess and Gayer 2000) may have been neatly balanced by sediment supply from Pennant rivers, maintaining the fluvial topography of the depocentre despite the advancing thrust front, which continued to migrate until 305 Ma, after the end of Pennant deposition. In this explanation our sample sites are hypothesized to be sufficiently downstream within the basin that we do not capture any steepening palaeoslopes of feeder rivers located to the south. Instead, our data capture, in relative terms, a topographic steady-state within the fluvial fill of the basin despite the evolving tectonic context. One potentially important influence on the slopes of the foreland that has not as yet been explored is the presence of the Wales–Brabant High bounding the north of the basin (Fig. 1c), which would act as a secondary source of the sediment for the rivers of the Pennant. This contribution from the north is consistent with the spread in palaeoflow directions presented above (Fig. 7). This palaeogeography creates a pronounced contrast in tectonic setting to the Late Cretaceous rivers of the Sevier fold-and-thrust belt, which drained directly into the Western Interior Seaway (Lyster et al. 2021), and additional sediment supply from the Wales–Brabant High thus would also have helped to offset any slope increases. Finally, we must acknowledge that climatic forcing can also influence the morphodyamics of rivers, with slope and sediment supply variations also being coupled directly to river discharge. The presence of abundant vegetation on the banks of the rivers could have acted as a stabilizing agent against tectonic forcing. Palaeoclimatic reconstructions (e.g. Opluštil and Cleal 2007), however, do not propose significant local climatic variations in the Westphalian and as our data analyses do not show a unidirectional change in palaeohydrological variables or in water discharge, we therefore suggest that the morphodynamics of the Pennant rivers reflect an equilibrium between accommodation generation and sediment supply within the foreland basin setting.

Future perspectives and challenges

Dominantly qualitative approaches have produced valuable insights into the hydrodynamics of the ancient rivers of the Pennant (e.g. Kelling 1974; Jones 1977; Jones and Hartley 1993) but the methods presented in this study show that a well-constrained quantitative framework can be used to determine hydrodynamic and morphological parameters using easily measurable field data (e.g. cross-set heights). This is particularly pertinent where poor outcrop preservation limits architectural mapping but cross-sets and grain sizes can be measured. However, it remains critical to consider qualitative and facies-based evidence together where available to validate quantitative reconstructions (e.g. Supplementary material 3). The combination of methods used in this study demonstrates how to tackle this issue in the rock record. Here, reconstructions of hydrodynamics using cross-set and grain-size measurements (Leclair and Bridge 2001; Trampush et al. 2014; Bradley and Venditti 2017) are found to provide results in agreement with evidence and observations of, for instance, the heights of accretion packages. The reconstruction of anastomosing and single-thread planforms is consistent with facies associations and bedforms previously documented in the Pennant Sandstone (Kelling 1969, 1974; Jones and Hartley 1993) but the data in this work also allow us to rule out some reconstructions such as channel depths as great as 15 m (see Jones 1977), which are inconsistent with the scale of the dune-scale cross-set heights, and the implied original bedform heights, documented here. Recent theoretical work has continued to improve extraction of quantitative information from fluvial strata (e.g. Greenberg et al. 2021; Lyster et al. 2022) and further refinements will facilitate reconstructions in a broader number of ancient fluvial systems to greater resolution than previously possible.

As all the equations used in this study carry forward calculated parameters (e.g. slope calculations implement the previously calculated flow depths), errors and uncertainties are compounded in this type of analysis. This must be addressed carefully, and here we use a Monte Carlo uncertainty approach to propagate error throughout. Despite this, the greatest confidence remains in parameters calculated early in this approach, owing to the potential for architectural validation (i.e. H), whereas uncertainty is greater in parameters calculated later in the workflow, which require more assumptions to be made (i.e. Qbf).

Moving beyond the scope of this study, further detailed work is required to identify and trace individual fluvial systems in the Pennant Sandstone, which will serve to better constrain upstream to downstream trends in these rivers and to constrain the pathways of sediment dispersal from the Variscan highlands in the south. Additionally, previous interpretations of wet climatic conditions throughout Pennant deposition, as well as the presence of conglomeratic channel fills and woody debris pointing to the occurrence of floods, could be used to better constrain potential palaeohydrological variability in these systems and the climate drivers behind this (Fielding et al. 2018; Leary and Ganti 2020). Assuming that uncertainties are appropriately acknowledged, there is clear potential to apply the method used in this study to many more ancient fluvial systems on Earth, but also increasingly on other planetary surfaces including Mars, where high-resolution imagery increasingly allows grain sizes, bedforms and larger scale architectures to be quantified (e.g. Edgar et al. 2018; Davis et al. 2019; Stack et al. 2019; Balme et al. 2020; Mangold et al. 2021).

During the Westphalian stage of the Late Carboniferous, the Variscan foreland in South Wales was characterized by large fluvial systems with median bankfull discharges of 390–560 m3 s−1, which deposited over 1300 m of sediment over a period of c. 4 myr. The reconstruction of the ancient fluvial systems of the Pennant Formation presented in this study suggests that these rivers had median flow depths of 2–3 m, median slopes of 4–5 × 10−4 (m m−1), individual channel thread widths of a few tens of metres, and channel belt widths of 100–200 m; these ancient rivers probably possessed both anastomosing and single-thread reaches. The reconstructed depositional setting is consistent with modern rivers in similar tectonic regimes such as the Ebro and Guadalquivir rivers, Spain, and in climatically similar regions such as the upper Amazon Basin. There is little variation in these key palaeohydrological and morphodynamic variables up-section through the five members of the Pennant.

This study provides new insights into river behaviour during the latter stages of supercontinent assembly. Despite rapid subsidence rates in the South Wales foreland basin, little temporal variation is observed in key hydrodynamics and morphodynamics up-section, which implies that these ancient fluvial systems were relatively stable in a time of intense compressional tectonism. This study of Carboniferous rivers in the UK adds to the growing body of recent work applying quantitative techniques to fluvial strata (e.g. Ganti et al. 2019; Lyster et al. 2021) and builds on the qualitative and facies-based fluvial sedimentological studies undertaken on the Pennant Sandstone. This work demonstrates the utility of reconstructing hydrodynamics and styles of ancient fluvial systems from quantitative field data and could be applied even where facies-based reconstructions are equivocal or where outcrop is limited.

The authors acknowledge research support from Imperial College London. We thank G. Hampson and C. John for useful feedback on an early version of the paper, and the reviewers and editor for their comments on the paper. This feedback has resulted in a much improved study.

JW: data curation (lead), formal analysis (lead), investigation (lead), methodology (lead), visualization (lead), writing – original draft (lead), writing – review & editing (equal); JSM: data curation (supporting), investigation (supporting), writing – review & editing (supporting); SJL: data curation (supporting), formal analysis (supporting), investigation (supporting), methodology (supporting), supervision (equal), writing – review & editing (equal); ACW: data curation (supporting), formal analysis (supporting), investigation (supporting), methodology (supporting), supervision (equal), writing – review & editing (equal)

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

All data generated or analysed during this study are included in this published article (and its supplementary information files).

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0/)