Reconstructing the paleohydraulics of ancient fluvial systems has important implications when determining channel-body dimensions in the subsurface as well as aiding source-to-sink studies and quantitatively determining the impact of changing climatic conditions. We undertake a paleohydraulic analysis of the Upper Jurassic Salt Wash distributive fluvial system (DFS) of the Morrison Formation, SW USA, to determine if downstream trends such as decreasing channel size and discharge, inferred in studies of DFS, are present. Channel depth was estimated using cross-set height values and preserved bar thickness. Nine localities across the exposed part of the Salt Wash system were studied. In total, 49 bars were measured, full bar thickness was determined from 12 complete bars, and average cross-set height was calculated for 37 bars. Estimates of maximum bankfull channel depth were derived from measured bar thicknesses. Bar height was then obtained and converted to mean bankfull channel depth using a shape adjustment factor of 0.65. The bar-derived mean bankfull channel depths were then used to derive a factor for which dune cross-set heights could be converted to mean bankfull channel depth (4.6) and maximum bankfull channel depth (7.1). These factors were then applied to localities where only cross-set height data were available, thus allowing consistent comparison and extrapolation of mean bankfull channel depth over the preserved DFS area. The use of measured bar thicknesses to calibrate estimates of mean channel depth from reconstructed dune heights is considered a useful approach, with the factor of 4.6 estimated here being lower than that (6 to 10) commonly used in comparable studies.

The datasets for the Salt Wash DFS record systematic downstream trends in cross-set height, bar thickness, calculated channel depth, estimated channel width, and estimated Q, with variability and overlap between the proximal to medial, and medial to distal parts. The variability superimposed on the regional downstream trends is attributed to a combination of autocyclic processes such as variations in discharge, depth of scour, and avulsion as well as more regional-scale channel-belt switching together with allocyclic controls. The wide spatial distribution of the dataset in this study allows distinction between local autocyclic controls and regional downstream trends. Formative discharge shows no downstream trend across the entire Salt Wash DFS, with a wide range in coefficient of variation of preserved cross set thickness (CV(dst) values of 0.1 to 1.1) indicative of flashy (variable) discharge.

The spatial distribution of the Salt Wash dataset allows extrapolation of trends upstream to the unexposed part of the system that allows insights into the characteristics of the channel system in the apex area (∼ 150 km to the southwest and removed by post depositional erosion). The fluvial system would have a mean depth of 9 m, and a bankfull-depth discharge of around 1450 m3/s with mean cross-set heights of between 50 and 70 cm. These estimates are in line with those from present-day DFSs in the Himalayan and Andean foreland basins that have a scale similar to that estimated for the Salt Wash system.

Reconstructing channel dimensions in ancient fluvial deposits allows constraints to be placed on the nature of the depositing river system, providing insights into paleohydrology and discharge. Once determined, paleodischarge can be used to quantify catchment-area sizes for ancient depositional systems using scaling relationships from modern systems (e.g., Davidson and North 2009; Bhattacharya et al. 2016). Accurate estimates of the paleohydraulics and dimensions of ancient river deposits can be used to enhance paleogeographic and paleoclimatic reconstructions for specific areas and time periods and provide constraints on sandstone body dimensions. This approach is important in determining the response of fluvial systems to climate-change events such as the Paleocene–Eocene Thermal Maximum (e.g., Foreman et al. 2012) and the Carnian Pluvial Event (Dal Corso et al. 2020) or changes in catchment size and/or elevation related to tectonic events (e.g., Wernicke 2011) or drainage capture (e.g., Mather 1993). An understanding of fluvial response to climate-change events may also help in predicting and mitigating the impacts of current anthropogenically induced climate warming on fluvial systems. In addition, establishing the likely controls on dimensions of fluvial channel bodies is important for the subsurface extraction of water (e.g., Weissmann et al. 2002; MacDonald et al. 2016; van Dijk et al. 2016), heat (e.g., Willems et al. 2016) and hydrocarbons (e.g., Moscariello 2005; Keough et al. 2007) as well as the storage of greenhouse gases such as CO2 (e.g., Lu et al. 2012).

The reconstruction of channel dimensions requires estimates of bankfull river depth (e.g., Bridge and Mackey 1993). This is computed from relationships between the thickness of the preserved channel fill and the depth of the depositing channel derived either from analysis of modern rivers (Allen 1965; Leeder 1973; Collinson 1978; Lorenz et al. 1985) or from data compilations (Fielding and Crane 1987; Mijnssen 1997). Estimates of bankfull channel depth of ancient channel deposits can be derived from the relationship between mean dune height and formative flow depth, although there is a large scatter (Yalin 1964; Allen 1982; Bridge and Tye 2000). Theoretical and empirical studies show a strong correspondence between the thickness of preserved cross-set strata and the height of the depositing subaqueous dunes (Leclair et al. 1997; Leclair and Bridge 2001; Leclair 2002). Studies of this kind make it possible to derive estimates of channel depth from cross-set thickness for ancient rivers that are consistent with more direct estimators such as bar thickness (Bridge and Tye 2000; Bhattacharya and Tye 2004; Adams and Bhattacharya 2005; McLaurin and Steel 2007).

This study aims to: 1) test the methodology for reconstructing bankfull depth from cross-set thickness using the approach of Leclair and Bridge (2001) by comparing channel-depth estimates with full bar thicknesses measured in the field and 2) test whether there is any spatial variability in paleohydraulic parameters across a near entire fluvial system. The Salt Wash distributive fluvial system (DFS) of the Upper Jurassic Morrison Formation, SW USA, was chosen to explore paleohydraulic relationships due to its well-established and quantified spatial context. The system was first identified and mapped by Craig et al. (1955) and Mullens and Freeman (1957) and subsequently built on and expanded by numerous authors (e.g., Tyler and Ethridge 1983; Peterson 1980 1984; Robinson and McCabe 1997; Turner and Peterson 2004; Kjemperud et al. 2008). Owen et al. (2015b) refined the extent of the system and quantified sedimentary characteristics. A downstream decrease in grain size (coarse sand to silt), amalgamated channel percentage (67–0%), channel body thickness (15–3.8 m), and geometry (from large, amalgamated complexes to isolated single story bodies) was identified with a concomitant increase in floodplain preservation (38–94%). These trends confirm the Salt Wash system to represent the deposits of a distributive fluvial system (DFS) (sensuHartley et al. 2010; Weissmann et al. 2010, 2015). The apex of the system has been statistically modeled to lie in northwestern Arizona, with the source area located around the ancient Mogollon–Sevier Highlands syntaxis (Fig. 1; Owen et al. 2015a, 2015b). The system radiates from this apex position across southern and central Utah and western Colorado and covers an area of ∼ 100,000 km2, with flow in a predominantly northeastern direction (Fig. 1; Peterson 1980, 1984; Kjemperud et al. 2008; Weissman et al. 2013; Owen et al. 2017). The Salt Wash DFS is 170 m thick in the proximal region and decreases in thickness to the northeast (downstream) to 50 m (Owen et al. 2015b). A detailed analysis of the internal stratigraphy of the unit was undertaken by Owen et al. (2017). These authors illustrated that whilst the Salt Wash system overall displays a progradational motif with a general upward increase in channel sandstone-body preservation and channel-body thickness and amalgamation, in detail there is considerable variation. For example, in most sections (61% of 23 sections) a clear progradational signature was observed, but in other areas a decrease in channel presence and thickness was observed (13%), whilst in 26% of the sections no obvious trends were present. The authors attributed this to variation in preservation potential across the system, associated with a combination of smaller-scale avulsion cycles, larger system-scale trends, and fluctuations in upstream controls such as climate and tectonics (Owen et al. 2017). In terms of the nature of the channels responsible for deposition of the Salt Wash fluvial system, early work based on grain size, dominance of cross stratification, and limited floodplain development suggested that the predominant planform type was braided (Peterson 1984; Robinson and McCabe 1998). More recent analysis, utilizing detailed outcrop studies combined with high-resolution remotely sensed imagery (Hartley et al. 2015, 2018; Swan et al. 2018), has illustrated that a meandering planform style is dominant, with most of the outcrop belt comprising an amalgamated meander belt. Only in the most proximal part of the outcrop belt (e.g., Bullfrog, Fig. 1) is a mixed braided-meandering style inferred. The climate in the basin during Morrison Formation deposition in the Late Jurassic is understood to have been semiarid with seasonal precipitation similar to that of a modern African savannah (e.g., Turner and Peterson 2004; Demko et al. 2004; Owen et al. 2015b). During Morrison deposition, the western interior seaway was regressing towards present-day Canada, with the shoreline thought to be close to the USA–Canada border by the end of the Late Jurassic (Turner and Peterson 2004). It is thus postulated that backwater effects and associated downstream base-level changes had minimal influence on the sedimentation patterns in the Salt Wash fluvial system (Owen et al. 2017). As with many fluvial deposits, a detailed chronostratigraphic framework is not available for the Salt Wash succession.

The spatial context provided by previous studies and the established downstream and along-strike characteristics of the Salt Wash system allow the DFS model proposed by Weissmann et al. (2010, 2015) to be tested. These authors consider the downstream decrease in channel size and amalgamation to result from a reduction in discharge due to a combination of channel bifurcation, infiltration into a permeable substrate, and evapotranspiration. We seek to determine the downstream changes in channel dimensions by mapping the paleohydraulic properties of the Salt Wash channels at various sites across the DFS to gain a better understanding of the spatial variability of paleodischarge as well as the nature of the formative discharge (e.g., Leary and Ganti 2019).

Channel-Depth Estimation

Channel depth and paleohydraulic parameters were calculated for each of the nine locations studied using standard methods (e.g., Bridge and Mackey 1993; Leclair and Bridge 2001). Channel depth was reconstructed using the approach outlined by Leclair and Bridge (2001), although it is noted that this provides a broad estimate and that more recent studies have highlighted that a range of relationships between dune height and flow depth are present (Bradley and Venditti 2017, 2019; Cisneros et al. 2020). Preserved trough cross-strata set height was measured in a vertical profile for 49 bars across the study area (Figs. 2, 3). Full bar thickness (Tb in Fig. 3C) was determined for 12 bars where complete preservation and exposure allowed, the remaining 37 bars are referred to as incomplete. Bars were considered complete where they graded upwards into bar-top or abandoned-channel deposits such as rippled sandstones or mudstones. Bars where cross-stratified sandstones were truncated beneath an erosion surface overlain by younger channel-fill deposits were considered incomplete. Vertical stratigraphic height was noted for all studied bars and mapped onto sedimentary logs presented by Owen et al. (2015b) to provide both vertical and spatial context (Fig. 2).

Only compound bars where the number of sets was greater than five were included in the analysis. Abnormally thick, isolated cross-sets formed by unit bars were excluded from the dataset because they would provide an overestimate of channel depth. Bars with highly truncated thalweg sets at the base were not measured. Preserved cross-set height was decompacted (factor of 10%; Leclair and Bridge 2001) and used to calculate mean dune height (Hm) using the equation
formula
mean cross-set thickness (Leclair and Bridge 2001).
With mean bankfull channel depth (D) calculated using Leclair and Bridge (2001):
formula
The wide range of factors required to determine mean bankfull channel depth is due to the large scatter in the measured relationship between mean dune height and the flow depth to form dunes (Yalin 1964; Allen 1982; Bridge and Tye 2000). To mitigate this uncertainty, we calibrated estimates of mean channel depth derived from cross-set heights against maximum channel depth determined from known bar thickness (n = 12 from all localities excluding Salt Valley, where a fully preserved bar was not observed) (Fig. 3C). This allowed the independent calculation of the correction factors used to determine depth from dune heights. Bar thickness (Tb in Fig. 3C) is taken to approximate bar height (Hb in Fig. 3C). We applied a decompaction factor of 10% to Hb. An additional factor of 20% was applied subsequently, as bar height is considered to represent approximately 80% of maximum bankflow depth (e.g., Bridge 2003):
formula
Conversion from maximum bankfull depth to mean bankfull depth utilized the shape adjustment factor of 0.65 used by Bridge and Mackey (1993):
formula
To determine the correction factor needed to ascertain depth from dune height, the bar-derived mean bankfull flow depth is divided by Hm:
formula

The range of correction factors needed to determine the mean bankfull flow depth from incomplete bar thicknesses ranged from 2.0 (227 km downstream; Caineville) to 8.23 (333 km downstream; Kane Springs) (Fig. 4; Table 1). Similarly, the range of factors needed to ascertain the measured maximum bankfull depth ranged from 3.1 (Caineville) to 12.7 (Kane Springs).

The large range in both maximum and mean bankfull flow depths may be due to variations in the stratigraphic level and lateral position in the Salt Wash system from which each bar was measured. The largest factors for mean bankfull flow depth (8.2 at 333 km downstream, Kane Springs; 6.5 at 433 km downstream, Little Park) were located towards the top of the studied sections in the most progradational (relatively proximal) part of the succession. The lowest value (2) is located towards the base of the section at Caineville (227 km downstream) in the more proximal region of the studied sections.

The variability in mean and maximum bankful flow depth is to be expected in a highly avulsive system. Due to this variation, we calculated a mean for all factors needed across the system. For our whole dataset it was found that on average a factor of 4.64 was required to accurately predict mean bankfull depth (D) and 7.14 to predict maximum bankfull depth (Table 1). D was then calculated for all localities using the factors calculated here and the minimum (6) and maximum (10) factors of Leclair and Bridge such that a comparison could be made (Fig. 5).

Paleohydraulics

To obtain paleodischarge the channel depth, cross-sectional area and flow velocities must be estimated. Mean channel depth is determined using the modified reconstructed-dune-height method of Leclair and Bridge (2001) or the thickness of preserved bars using the methodologies outlined above (Table 2). Cross-sectional area is determined by multiplying the paleochannel depth by width with an adjustment factor of 0.65 for the channel shape (Bridge and Mackey 1993):
formula
where wc is channel width. Channel width was estimated using empirical relationships reported in Crane (1982) and Bridge and Mackey (1993) (Table 3). Flow-velocity estimates are obtained from the phase diagrams of Rubin and McCulloch (1980) where the flow depth, grain size, and dominant bedform are known. Channel bodies are composed of predominantly medium sandstone (range from fine to coarse) with dunes as the dominant bedform. Discharge (Q) is calculated by multiplying cross-sectional area (A) by flow velocity (U):
formula

Nature of Formative Discharge

To investigate the nature of formative discharge in the Salt Wash channel deposits, the coefficient of variation (ratio of standard deviation to mean) of the preserved cross-set thickness (CV(dst)) was calculated. Data on preserved cross-set thickness are taken from Tables 1 and 2. CV(dst) values have been shown to vary systematically with discharge variability, and cross set thickness can therefore yield information on the relative timescales of formative flood variability and bedform adjustment (Leary and Ganti 2019).

Cross-Set Height

The mean cross-set height is shown in Figure 6 (and Tables 1 and 2) and shows a general downstream decrease for both complete and incomplete bar-height datasets; however, there is significant overlap in the data. The range in measured cross-set thickness generally decreases downstream; however, this relationship is only moderate (R2 of 0.4464) for cross-sets measured from incomplete bar thickness with R2 of 0.6392 for cross-sets taken from complete bar thicknesses. In general, the lowest values are found in the most distal part of the system; however, low cross-set heights are present across the studied sections. The largest cross-sets are generally found in the proximal and medial areas of the system. The average cross-set thickness for bars with complete thicknesses is 29.5 cm (std dev 9.9) and for incomplete bars it is 35.2 cm (std dev 11.5). The overlap between these values suggests that removal of the tops of incomplete bars through erosion has not biased the incomplete bar dataset towards the preservation of larger bedforms in the lower parts of the bars.

Channel Depth

Four channel-depth calculations were conducted on the dataset in which the bar thickness was not measured. The first set of calculations used a factor of 4.6 for mean bankfull depth and 7.1 for max bankfull depth (Fig. 5A), with the second using the minimum (6) and maximum (10) factors of Leclair and Bridge (2001) (Fig. 5B). A broad downstream decrease in channel-depth values can be observed in the dataset derived from both known bar thickness and estimated bar thickness using the mean and maximum Salt Wash factors of 4.6 and 7.1 (orange and blue lines in Fig. 5A, respectively; Tables 1, 2); however, this relationship is relatively weak given R2 values of 0.2133 (complete bars) and 0.4464 (incomplete bars for all factors). The largest range in channel depths derived from known bar thicknesses is generally found in the most proximal localities, with the smallest range in medial localities. Distal localities generally have the smallest channel depths; however, there is some variability with a mean channel depth of 5.2 m calculated at 427 km downstream (Colorado National Monument). Interestingly, fewer low values are observed in the proximal part of the system, and fewer large values in the distal part in the system when compared to the known-bar-thickness dataset. Overlap between proximal, medial, and distal channel-depth estimates is observed but is not as large as that recorded from the cross-set-height dataset. Despite the overlap, the largest channel depths are generally found in the most proximal localities and the smallest in the most distal localities. A stronger correlation exists between estimated channel depth and distance downstream (R2 of 0.4464; Fig. 5A) for the channel depths derived from cross-set thicknesses when compared to those derived from known bar thicknesses, possible reasons for which are discussed below.

The same trends described for calculated bar heights using a factor of 4.6 (mean bankfull) and 7.1 (maximum bankfull) can be observed when using Leclair and Bridge minimum and maximum factors (6 and 10 respectively; Fig. 5B). However, as is to be expected, the range in estimated channel depths increases when using a factor of 10, possibly leading to an overestimation of channel depths in the system.

CV(dst)

Values for CV(dst) are illustrated in Figure 7, where they are plotted against distance downstream. Values show a wide range from 0.1 and 1.1; the majority plot between 0.2 and 0.7 with an average of 0.44 (Tables 1, 2). There is no consistent change in CV(dst) downstream. Leary and Ganti (2019) used theoretical analysis and flume experiments on steady and unsteady flows to illustrate that cross-strata with values of CV(dst) ≈ 0.88 are likely developed under broad flood hydrographs that show a gradual decline in discharge, whereas flashier flood hydrographs with rapid decreases in flood discharge tend to result in CV(dst) values lower than 0.88. The low CV(dst) values recorded here indicate significant bedform disequilibrium relative to formative flows. Deposition is considered to be associated with rapid decreases in flood discharge likely associated with flashy flood hydrographs.

Paleohydraulics

Channel depths for the Salt Wash fluvial system were calculated for two main datasets: measured bar heights and estimated depths using the Leclair and Bridge (2001) method with factors determined in this study (4.6 for mean bankfull and 7.1 for maximum bankfull). To calculate paleodischarge, channel widths were estimated using the approach of Bridge and Mackey (1993) and Crane (1982). It is noted that there can be significant variation in channel-width estimates depending on channel type (e.g., braided versus meandering). We are confident that previous work utilizing remotely sensed data and outcrop analysis (Hartley et al. 2015; Owen et al. 2015b; Swan et al. 2018) indicates that the fluvial deposits in all of the studied sections (except Bullfrog) record deposition by meandering rivers. As estimated bar heights are generally larger for the datasets in which bar height was unknown (Fig. 5), it is unsurprising that the largest width estimates are derived from this dataset, and those for the known bar heights have the lowest widths (Table 3; Fig. 8A, B). Despite the variations in absolute estimates, all estimates show a downstream decrease in channel width (Fig. 8A, B; Table 3). An average of all datasets was produced to highlight the clear downstream trend with a R2 of 0.8543 for maximum channel depth (Fig. 8A) and a R2 of 0.7929 for mean channel depth (Fig. 8B). When assessing the data as a whole it is evident there is some overlap in estimates between proximal, medial, and distal parts of the system. However, the overlap is present only when considering the different methods for estimating channel width and once average values are calculated, estimates can be clearly split into the proximal, medial, and distal regions of the system. This observation is in line with measurements of channel widths of modern DFSs from satellite imagery analysis (e.g., Weissmann et al. 2015).

To estimate discharge (Q), the average of all width estimates (Fig. 8A; Table 3) was used. Again, discharge estimates derived from known bar thicknesses are lower than those for which the bar thickness has been estimated using Leclair and Bridge (2001) (Fig. 8C). This has resulted in a low R2 value (R2 = 0.2533) because the range in bar thickness across the system is much lower with differences between most proximal and distal localities being minimal. In contrast, a much stronger correlation is present when estimating Q from the dataset in which bar thicknesses were unknown (and therefore calculated) with an R2 = 0.6877. This is due to the higher range in estimates between proximal and distal with proximal estimates being noticeably higher than the known-bar-thickness dataset (Fig. 8C). There is a degree of overlap in estimated Q between the different domains in the system (proximal, medial, and distal) for both the maximum- and mean-channel-depth datasets. For example, when considering the mean-channel-depth dataset, the upper range of estimates for Q in medial localities (e.g., 580 m3/s for Salt Valley) can fall within the range of estimates for proximal localities (e.g., 634 m3/s at Bullfrog 227 km downstream; Fig. 8C; Table 3). Similarly, estimates of Q for medial and distal localities show a general downstream decrease when considering the mean channel dataset, however, there is significant overlap between localities. For example, the lowest Q estimate for a medial locality is 161 m3/s at 352 km downstream (Slick Rock) and the highest Q estimate for a distal locality is 276 m3/s for 427 km downstream (Colorado National Monument), although this value is significantly higher than the 60 and 77 m3/s Q determined for the two other distal localities (Table 3, Fig. 8C). These datasets highlight the significant variability that is present in the system; however, a general downstream trend in Q is present, with highest Q estimates being in the most proximal localities and the lowest in the most distal localities.

Estimation of Paleochannel Depth

Channel-depth reconstruction in fluvial systems is important for establishing mean and maximum bankfull flow depths and determining paleohydraulic parameters as well as predicting likely channel-body dimensions. The methodology established by Leclair and Bridge (2001) has been widely used and applied in the rock record (e.g., Bhattacharya and Tye 2004; Adams and Bhattacharya 2005; McLaurin and Steel 2007). In our analysis of the Salt Wash dataset, we suggest an approach additional to that of Leclair and Bridge to enable estimation of channel flow depth. In particular, if bar heights can be estimated from thicknesses and converted from maximum to mean bankfull flow depth, then determination of the factor to estimate mean flow depth can be used to calibrate flow depths derived from trough cross-set heights. It is interesting to note that the factor of 4.6 estimated here for mean bankfull flow depth is lower than those of Leclair and Bridge (6–10) that were derived from observations on flume experiments and present-day rivers. However, our lower value is in line with recent experimental work that established that whilst dunes developed in flow depths of > 2.5 m have a wide range of heights, they tend to be less than 1/6 of the flow depth (Bradley and Venditti 2017, 2019). If possible, we suggest that an approach that combines measured bar thickness and cross-set heights should be utilized in outcrop studies of fluvial and deltaic channel deposits (e.g., Bhattacharya and Tye 2004) to determine mean and maximum channel flow depth.

Paleohydraulics

Downstream changes in channel presence and grain size have been demonstrated on a number of distributive fluvial systems, such as the Salt Wash (Mullens and Freeman 1957; Owen et al. 2015b), the Miocene Huesca system, Spain (Hirst 1991; Martin et al. 2021), and the Sunnyside Member of the Eocene-age Green River Formation, USA (Wang and Plink-Björklund 2019). In addition, downstream changes in discharge on the modern Pilcomayo River have been documented by Martin-Vide et al. (2014) and active channel width on the modern Bermejo DFS by Weissmann et al. (2015). Yet, systematic changes in paleohydraulic properties have yet to be documented on any ancient DFS deposit, despite the assumption that these trends are present (e.g., Weissmann et al. 2015). The paleohydraulic properties of the Salt Wash DFS show systematic downstream trends in cross-set height (Fig. 6), bar height, and channel depth (Fig. 5), and estimated channel width and estimated Q (Fig. 8). Downstream loss of discharge is considered to occur on DFSs due to channel bifurcation, infiltration into a sandy substrate, or evapotranspiration (dependent on basin climate), or a combination of these processes (Weissmann et al. 2010, 2013, 2015). The progressive loss of discharge due to a lack of tributary input means that flow competence and volume decrease downstream, resulting in a decrease in the bedload grain size and progressively smaller channels (as documented by Mullens and Freeman 1957; Hirst 1991; Owen et al. 2015b). Additionally, reduced discharge restricts the ability of the channel to erode underlying deposits, which, coupled with an increase in the area available for avulsion, results in a downstream reduction in channel-deposit amalgamation and increasing isolation of channel bodies in floodplain sediment (e.g., Hirst 1991; Owen et al. 2015; Martin et al. 2021).

Whilst the downstream reduction in cross-set height and bar height, and subsequent derivations of channel width, depth, and estimated discharge in the Salt Wash DFS are clear, there is however, important variability in these parameters. Cross-set height values show significant variability and overlap in the data and relatively high standard deviations, particularly at the most proximal sites in the system (Fig. 6; Table 1). Variability of cross-set height may be due to variation in formative flow depth and/or preservation potential. The latter is deemed to be of particular importance in the most proximal part of the system where the greatest degree of reworking by subsequent channels is expected and is supported by the greater degree of channel-deposit amalgamation (Owen et al. 2015b). Variability in flow conditions related to formative channel processes may also account for the range in cross-set-height values. For example, cross-set heights recorded in channel deposits that form due to neck cutoff and progressive channel abandonment will reflect lower formative discharge values than equivalent main-stem-channel deposits. Fluctuations in formative discharge are also indicated by the CV(dst) values (Fig. 7), which range from 0.1 to 1.1 and show no downstream trend. If the measured bedforms were generated at or shortly after peak flood events, then values close to 0.88 would be expected (Leary and Ganti 2019). The wide range in CV(dst) reported here is indicative of more flashy discharge across the entire Salt Wash DFS; as such, it would not be unusual to record a wide range of cross-set and bar-height values leading to significant variability in subsequent derivations of channel width, depth, and discharge. This is in line with the interpretation of the prevailing climate during Salt Wash deposition as semiarid with seasonal precipitation, similar to the African savannah of today (e.g., Demko et al. 2004; Turner and Peterson 2004; Owen et al. 2015b). Flashy (variable) discharge associated with a semiarid climate regime is also supported by the dominance of trough cross-strata as the prevailing bedform (Owen et al. 2015b), although upper-flow-regime structures and large-scale low-angle bedforms suggestive of more flashy dry subtropical systems (e.g., Fielding et al. 2009) are noted but are not prevalent.

Variability in cross-set and bar-height values may also be related to stratigraphic position in the Salt Wash succession, particularly because the system is known to be overall prograding in response to climatic and/or tectonic controls in the catchment area (e.g., Kjemperud et al. 2008; Owen et al. 2017). In a progradational succession, at any given point it would be expected that the hydraulic geometry and discharge of a channel will increase up-section. The distribution of the data collected is shown in Figure 2 with measurements across the entire stratigraphic range from base to top. No significant variability with stratigraphic position was recorded. The lack of correspondence between cross-set and/or bar height and stratigraphic position could be due to a number of reasons. At the small scale, autocyclic switching of avulsive channel belts will lead to significant variability in channel size, as shown by the fact that measurements taken from nearly equal stratigraphic positions (e.g., at the base or top of the succession: Fig. 2), show a wide range in values that cover much of the dataset. At a larger scale, the migration and/or avulsion of active channel belts across a DFS will produce significant temporal variations in channel dimensions, as documented in the Tista megafan in the Himalayan foreland of India (Chakraborty and Ghosh 2010; Abrahami et al. 2018). Large-scale channel-belt switching across the Salt Wash DFS is also considered to be responsible for sections that deviate from the norm of progradation, with aggradational or retrogradational successions locally developed (Owen et al. 2017). Autocyclic variability is therefore expected and evident at a range of scales in the Salt Wash system and likely accounts for the lack of a coherent up-section change in cross-set and bar-height values. The inherent variability that results from combined autocyclic (channel avulsion and channel-belt switching) and allocyclic (progradation caused by tectonic–climatic changes in the catchment) controls is evident in a number of studies of fluvial systems e.g., Rittersbacher et al., (2014); Kukulski et al. (2013), Owen et al. (2017), Hajek and Straub (2017), Wang and Plink-Bjorkland (2019), and Lyster et al. (2021).

The data presented here highlight the significant spatial and temporal variation in paleohydraulic characteristics recorded in the Salt Wash DFS, including both autocyclic controls related to discharge, channel abandonment, and depth of scour and more regional allocyclic controls such as progradation. To capture this inherent variability, a system-wide study with a significant number of measurements is required and is particularly important in medial deposits. Despite this variability, though, it is clear that meaningful regional trends can be identified in the data, but that a wide spatial and temporal distribution is required, such that studies with more limited datasets may not necessarily identify regional trends.

Paleodischarge and Drainage-Basin Area

The methods utilized here to calculate paleodischarge and to derive drainage-basin size are widely used in the literature (e.g., Bhattacharya and Tye 2004; Davidson and North 2009; Bhattacharya et al. 2016). It is important to note that for a true estimate of drainage-basin area, paleodischarge values must be derived from channel deposits that record the discharge from the whole of the catchment area. For example, in their study of the Ferron delta Bhattacharya and Tye (2004) identified and estimated the discharge for the trunk channel system using a number of approaches. In nondeltaic systems it is important therefore to understand the context of the fluvial system being studied and to consider whether the calculated discharge from studied channel deposits is likely to be representative of the whole of the drainage-basin area. For example, calculations from channels deposited as part of axial or valley-fill fluvial system (Hartley et al. 2018), as with the trunk channels supplying deltas, are likely to encompass all the upstream discharge of a drainage basin and be representative of the whole catchment area. In contrast, as discharge is known to decrease downstream on DFS deposits (Davidson et al. 2013) then unless the studied deposits occur at the apex of the DFS then drainage-basin area will be underestimated. The discrepancy between drainage-basin area and paleodischarge estimates will increase with increasing distance downstream of the apex.

Extrapolating discharge upstream to the apex area would suggest mean bankfull depth discharge values of 1450 m3/s with a maximum bankfull discharge around 4600 m3/s (Fig. 8C), which is in line with present-day DFS of similar sizes such as the Pilcomayo in the Andean foreland (discharge values between 3.2 and 5500 m3/s, Martin-Vide et al. 2014) and Tista (up to 2000 m3/s, Chakraborty and Ghosh 2010). To accurately reconstruct the drainage-basin area of an entire DFS it is necessary to either have a wide spatial range of data from channels of approximately the same age and demonstrably from the same DFS or be able to reconstruct downstream trends to extrapolate likely discharge values at the apex of the system. Without the spatial context of the studied system being well understood, drainage-basin-area calculations of DFS/megafans based on paleodischarge reconstructions are likely to be significantly underestimated.

A useful predictive aspect of the Salt Wash paleohydrological study is that the spatial distribution of the dataset allows extrapolation of trends that permit the characteristics of the proximal apical area of the DFS to be inferred. The estimated location of the apex area is shown in Figure 1, and approximately 150 km of strata are either unexposed or removed by erosion between the inferred apex point and the closest outcrop of Salt Wash strata (Owen et al. 2015a). Our data indicate that the fluvial system in the apex area would have had an approximate mean and maximum bankfull depth of 9 and 14 m, respectively (Fig. 5A) and a mean bankfull depth discharge of around 1450 m3/s (Fig. 8), and would have produced mean cross-set heights of between 50 and 70 cm (Fig. 6). Whilst it is noted that there is significant uncertainty associated with these estimates, they do provide a useful approach to predicting likely characteristics of fluvial systems in areas with limited or no data.

A paleohydraulic analysis has been undertaken on fluvial channel deposits of the Upper Jurassic Salt Wash DFS of the Morrison Formation, SW USA. Channel depth was estimated using two independent methods: 1) cross-set-height values following the methodology of Leclair and Bridge (2001) and 2) preserved bar thickness. Nine localities distributed across the exposed part of the Salt Wash system were studied. Average cross-set height was calculated from 49 bars and compared to measured bar thickness determined from 12 of the studied bars. Calibration of estimates of mean channel depth derived from cross-set heights against maximum channel depth determined from known bar thickness allowed the independent calculation of a factor of 4.6 required to ascertain mean channel depth from bar thickness and 7.1 for maximum channel depth. Calibration against known bar height is useful, because the application of the factors of 6 to 10 identified by Leclair and Bridge (2001) where bar thickness is not known results in a significant range in channel-depth estimates.

Systematic downstream trends in cross-set thickness, bar thickness, and channel depth (mean and maximum), estimated channel width, and estimated Q are recorded with variability and overlap between the proximal to medial, and the medial to distal parts of the DFS. The variability superimposed on the regional downstream trends is attributed to a combination of autocyclic processes such as local variations in discharge, channel abandonment, depth of scour, and channel avulsion as well as more regional-scale channel-belt switching on the DFS together with allocyclic controls such as the overall progradation of the Salt Wash system. An important aspect of this study is the recognition that without the wide spatial distribution of the datasets in this study, regional trends would be difficult to identify and the variability inherent in large scale fluvial systems would predominate.

Formative discharge shows no downstream trend with a wide range in coefficient of variation of preserved cross set thickness indicative of flashy discharge across the entire Salt Wash DFS.

The spatial distribution of the Salt Wash dataset allows extrapolation of trends that permit the characteristics of the proximal apical area of the DFS which is considered to lie ∼ 150 km to the southwest of the closest outcrop of Salt Wash strata (Owen et al. 2015a). Our data indicate that the fluvial system in the apex area would have had a mean bankfull depth of 9 m and a bankfull depth discharge of around 1450 m3/s with mean cross-set heights of between 50 and 70 cm. These estimates are in line with those from modern DFSs of similar scales in the Himalayan and Andean forelands.

We would like to thank AE Janok Bhattacharya and Journal reviewers John Holbrook and W. Lin for their insightful and helpful reviews.

Open Access CC-BY 4.0.