Water discharge and sediment flux intermittency in the fluvial Escanilla Formation, Spain: Implications for changes in stratigraphic architecture

Water discharge and sediment flux variations are important parameters controlling the morphodynamic behaviour of rivers. Although quantitative estimates for water discharge and sediment flux variability are well‐constrained for modern rivers, far fewer assessments of flow and sediment flux intermittency in ancient fluvial systems from the rock record are available. In this study, a relationship between water discharge, sediment flux variability and patterns of changing fluvial stratigraphic architecture in the Middle Eocene Escanilla Formation, Spain, is explored. Water discharge intermittency factor (IWF), calculated as a ratio of the total water discharge (over the averaging time period) to the instantaneous channel‐forming water discharge if sustained for the same period, ranges from 0.03 to 0.11 in the high amalgamation intervals and from 0.10 to 0.32 in the low amalgamation intervals. Similarly, the sediment flux intermittency factor (ISF) is estimated to be in the range of 0.008 to 0.01 in the high amalgamation intervals and of 0.01 to 0.03 in the low amalgamation intervals. Consequently, high amalgamation intervals were most probably deposited under more intermittent and short‐lived intense precipitation events while low amalgamation intervals were the result of less intermittent flows spread throughout the year. Overall, these estimates are consistent with values from modern ephemeral rivers typically found in arid to semi‐arid climate and is in agreement with available proxy data for the Middle Eocene climatic context of the studied alluvial system. This highlights an important connection between hydroclimate, river morphodynamics and landscape evolution, and has implications to predict river flow and sediment transport across the Earth's surface in the geological past.


| INTRODUCTION
The response of river systems to changing hydroclimates is of increasing importance for predicting floods hazards and its impact on growing urbanisation in the context of global climate perturbations.Water discharge (hereafter referred to as 'discharge') and sediment flux (hereafter referred to as 'flux') in rivers are correlated to mean annual precipitation (MAP) which is linked to prevalent climatic conditions (Langbein & Schumm, 1958;Syvitski & Milliman, 2007;Hansford & Plink-Björklund, 2020).However, rivers in semi-arid to sub-humid tropics display a wide range of discharge variability depending on the balance between precipitation and evapotranspiration, with several rivers showing pronounced run-off seasonality and inter-annual variability (Alexander et al., 1999;Fielding et al., 2009Fielding et al., , 2011Fielding et al., , 2018)).Discharge and flux variability are further important as they can play a key role in controlling landscape evolution and the consequent sedimentary record of rivers (Allen et al., 2013;Plink-Bjorklund, 2015, 2017;Fielding et al., 2018;Hansford et al., 2019;Hansford & Plink-Björklund, 2020;Lyster et al., 2023).Seasonal discharge variability, in particular, has been found to influence preserved stratigraphy and sedimentology and thus plays a key role in the construction of fluvial bodies in both ancient and modern environments (Fielding et al., 2018;Lyster et al., 2023).Discharge variability is also crucial to bedrock rivers through its role in controlling bedrock river incision and continental erosion thereby driving the resulting flux of sediments into depositional basins (Lague et al., 2005 and references therein).
Sediment flux, depending on grain size, in rivers is typically more intermittent than discharge variation (Allemand et al., 2023).For instance, bedload sediments are typically transported only during floods when there is enough shear stress for such sediments to be entrained and transported (Phillips & Jerolmack, 2014;Phillips et al., 2018;Allemand et al., 2023).The frequency of discharge events and quantity of sediment transported is thus an important parameter to assess the efficiency of sediment transport and the ability of fluvial systems to convey environmental signals from sources to sinks in both modern and ancient systems (Castelltort & Van Driessche, 2003;Armitage et al., 2011;Simpson & Castelltort, 2012;Romans et al., 2016;Tofelde et al., 2021).
Modern river streamflow conditions are typically described in terms of the presence or duration of flow and are a fundamental metric in classifying rivers as perennial and non-perennial (intermittent and ephemeral; Poff, 1996;Bond et al., 2010;Eng et al., 2016;Sauquet et al., 2021).Further, climate plays a primary role in influencing streamflow patterns in addition to other factors such as topography and vegetation (Beaufort et al., 2019) such that the more arid the climate, the higher is the probability of a fluvial system to be non-perennial (Sauquet et al., 2021).While changes in flow patterns in modern rivers can be easily recorded using gauging stations, there exist currently few studies, such as Hayden et al. (2021), which explicitly quantify flow variability or intermittency in the rock record.
In general terms, the temporal distribution of flow and sediment transport in a river is referred to as its intermittency.Two extreme cases can be identified: a highly intermittent system is characterised by repeated or prolonged intervals of no flow or sediment transport while a non-intermittent system is characterised by continuous flow or sediment transport (Lyster et al., 2023).To study sediment fluxes and basin infilling over extended geological timescales, Paola et al. (1992) introduced a specific dimensionless intermittency factor ranging from zero to one.This factor serves as a means of scaling instantaneous sediment transport rates which for ancient rivers can be reconstructed from palaeohydrological methods applied to channel outcrops (Lyster et al., 2021(Lyster et al., , 2023;;McLeod et al., 2023;Sharma et al., 2023aSharma et al., , 2023b) ) to longer term sediment fluxes or depositional volumes which can be estimated for geological applications using mapping or from sediment thickness isopachs (Michael et al., 2013).The chosen averaging time should be considerably longer than individual channel-forming events (instantaneous conditions) yet relatively shorter than the overall geological timescale (mean conditions).The most straightforward approach is to assume that flow is intermittently characterised by a sequence of bankfull channel-forming conditions (Paola et al., 1992).Consequently, discharge or flux intermittency factor can be extrapolated to a longer timescale, such as the number of days in a year.For instance, an intermittency of 120 days yields an intermittency factor of 0.33 or 33% of a year, meaning the river could transport its entire water or sediment budget in 0.33 of the time if channelforming conditions were continuously sustained (cf.Lyster et al., 2023).This is rarely the case and hence intermittency factors do not represent the temporal distribution of individual flow events which are typically not known for ancient river systems in the geological past.As such, multiple river hydrographs could potentially have the same intermittency factor.The intermittency factor therefore corresponds to the cumulative occurrence of these channel-forming conditions and is precisely described as the proportion of a selected time interval necessary for a constant channel-forming flow to transport an equivalent amount of water or sediment as the river hydrograph accomplishes during that time period (Paola et al., 1992).The lower the intermittency factor, the more intermittent the discharge or flux is relative to annual or longer term measures of water and sediment budget.Furthermore, sediment flux intermittency factors are rarely identical to discharge intermittency factors as certain rivers might transport the entire flux in a single flood event while some transport it over the entire year.As a result, flux intermittency factor is usually less than discharge intermittency factor except for highly intermittent ephemeral rivers where all sediment and water are transported in discrete rare events (see Lyster et al., 2023).
In this study, a potential relationship between observed changes in fluvial stratigraphic architecture in the Escanilla Formation, Spain, and river discharge and flux variability reconstructed from the sedimentary record is explored for the first time.To perform such a quantitative assessment, discharge and flux intermittency and their respective intermittency factors are estimated.Further, estimated intermittency factors are compared to those from modern rivers to classify the Middle Eocene Escanilla rivers as either perennial or non-perennial.Results are then collectively discussed within the framework of the observed stratigraphic changes, the palaeo-hydroclimate context and implications for interpreting changes in fluvial stacking patterns recorded in alluvial sedimentary successions.

| GEOLOGICAL BACKGROUND
2.1 | The Escanilla sediment routing system The Escanilla sediment routing system, located in the Pyrenees, is a preserved sediment routing system of Middle to Late Eocene age (ca 41-34 Ma) that linked catchment regions of the high Pyrenees via the Sis and Gurb palaeovalleys to depositional sinks in the south Pyrenean foreland Basin (Figure 1; Bentham et al., 1993;Labourdette & Jones 2007;Labourdette 2011;Michael et al., 2013).Extensive palaeocurrent data suggest that these two palaeovalley systems sourced sediments from the axial zone of the Pyrenees with a confluence of these two systems in the Viacamp area (Figure 1).From there, sediments were transported downstream towards the west via the Ainsa Basin (Vincent 2001;Whittaker et al., 2011;Parsons et al., 2012;Michael et al., 2013; Figure 1).The entire Escanilla sediment routing system has been extensively mapped within a single source-to-sink framework through a range of provenance tools such as clast lithologies, heavy minerals, U-Pb geochronology of detrital zircons, apatite fission track analysis, palaeocurrent analysis, magneto and biostratigraphy, and has been explained in detail by Michael et al. (2013Michael et al. ( , 2014b) and references therein.

| The Escanilla Formation at Olson- fining-upward sequences
Within the southern Ainsa Basin, the Escanilla Formation has a maximum preserved thickness of 1000 m and is divided into the Mondot and Olson members (Bentham et al., 1992(Bentham et al., , 1993;;Dreyer et al., 1992;Kjemperud et al., 2004;Labourdette & Jones 2007;Labourdette 2011).Previously, several stratigraphic sequences consisting of laterally amalgamated and vertically stacked channels have been described by Labourdette and Jones (2007) and Labourdette (2011).This study focusses on three fining-upward sequences at Olson, described by Sharma et al. (2023aSharma et al. ( , 2003b)), with each sequence having a thickness of 35 to 45 m.Each fining-upward sequence consists of a high amalgamation (HA) interval, which is defined as a 5 to 12 m thick and 600 to 2000 m wide complex of laterally and vertically amalgamated channel bodies in multiple stories, and a low amalgamation (LA) interval, which is defined as a floodplain-dominated interval consisting of isolated channel bodies (less amalgamated) that are 2 to 4 m thick and 100 to 500 m wide (Sharma et al., 2023a(Sharma et al., , 2023b)).Recent work in the Middle Eocene fluvial Escanilla Formation, Spain, has documented cyclical variations in instantaneous water discharge and bedload sediment flux relative to changes in stratigraphic architecture, that is, from HA to LA intervals within several fining-upward sequences which is indicative of an upstream climate control on fluvial stacking pattern (Sharma et al., 2023a(Sharma et al., , 2023b).

Middle Eocene
The Escanilla Formation at Olson encompasses the Middle Eocene Climatic Optimum (MECO), a global warming event at ca 40 Ma.Geochemical proxies from the Escanilla Formation suggest regional climate in the south-central Pyrenees to be dry, arid and devoid of much vegetation (Sharma et al., 2023a(Sharma et al., , 2023b)).In other localities more to the east of the Ebro Basin (northeastern Spain), other proxies such as palynological, pollen taxa and floral diversity (Cavagnetto & Anadón, 1996;Haseldonckx, 1972) suggest warm and humid climate.For instance, Middle Bartonian vegetation from the eastern Ebro Basin was characterised by a diverse mangrove swamp-type vegetation along the coast which subsequently disappeared by the Priabonian (Cavagnetto & Anadón, 1996).Such differences in regional climate could be due to a phase of climate transitioning, expressed differently in different regions, from a warm tropical Early Eocene Climatic Optimum to a colder and arid early Oligocene (López-Blanco et al., 2000;Cantalejo & Pickering, 2015).Collectively, this makes the Escanilla Formation at Olson an ideal locality to test for the link between discharge, flux intermittency and observed stratigraphic stacking patterns under greenhouse conditions of the Middle Eocene.

| METHODS
The concept of discharge intermittency can most simply be expressed through a discharge intermittency factor (I WF ) which has been defined by Paola et al. (1992) as where Q w is the total water discharge over the averaging time period, such as a year, Q w(cf) is the instantaneous channelforming water discharge and Σt is the averaging time period (e.g. 1 year).
Following Equation (1), flux intermittency factor (I SF ) can be expressed as where Q s is the total sediment flux over the period of interest and Q s(cf) is the instantaneous channel-forming sediment flux.Σt is the timespan equal to 1 year (Paola et al., 1992).
These calculations require estimates for both channelforming discharges and longer term water budgets and similarly for sediment transport capacities for channelforming conditions, compared to long-term sediment flux rates.For instantaneous discharge and flux conditions in the Escanilla Formation, the recently published palaeohydrological reconstructions for the HA and LA units of Sharma et al. (2023aSharma et al. ( , 2023b)), which are based on field measurements of channel geometries and sediment calibre (see supplementary material for full details), were used.However, drainage area, precipitation and total volumetric sediment flux estimates are required to approximately estimate the total water and sediment budget available to the Escanilla system.

| Drainage area estimates
Catchment area of ancient sediment routing systems is often hard to accurately constrain due to tectonic changes and erosion of the hinterland (Eide et al., 2018;Brewer et al., 2020).However, the Escanilla system's source area is relatively well-constrained.A total drainage area upstream of Olson, based on the mapping of the Escanilla system by Michael et al. (2014a), was estimated to be in the range of 2500 to 5500 km 2 with a probable average value of approximately 4000 km 2 .This estimate is similar to that proposed by Brewer et al. (2020) for the Escanilla system.This value includes a combined average area of approximately 2050 km 2 from the Sis and Gurb catchment areas (2088 km 2 is suggested by Michael et al., 2014a) while the downstream region until Olson constitutes an area of approximately 1950 km 2 .
3.2 | Total water budget and water discharge estimates

| Total water budget
Total water budget for the Escanilla Formation was estimated using two end members of MAP rates (ca 0.3 m year −1 and ca 1.0 m year −1 ).In the first instance, Sharma et al. (2023aSharma et al. ( , 2023b) ) estimated MAP using the chemical index of weathering (CIW; see supplementary material; Figure 2), which is based on the major elemental composition of palaeosol samples, gave values ranging between 0.25 m year −1 and 0.57 m year −1 (average value of 0.33 m year −1 ).It is important to note here that these MAP values are based only on samples from the LA interval due to the absence of floodplain in the HA intervals.Multiplying average total drainage area of 4000 km 2 by average mean rainfall results in an average total water budget of 13 × 10 8 m 3 year −1 with minimum and (1) (2) maximum values of 7 × 10 8 m 3 year −1 and 31 × 10 8 m 3 year −1 , respectively.These values are maxima because they do not include water loss due to infiltration or evapotranspiration but are reasonable first-order estimates.
In the second instance, Eocene MAP estimates for northern Spain predicted by Tardif et al. (2021), using the IPSL-CM5A2 Earth system model designed for multimillennial climate simulations, can be used to estimate the total water budget.These MAP estimates are in the range of 0.8 to 1.4 m year −1 with an average value of 1.1 m year −1 which is equivalent to an average total water budget of 4 × 10 9 m year −1 with minimum and maximum values of 2 × 10 9 m year −1 and 7 × 10 9 m year −1 , respectively.

| Water discharge estimates
Detailed water discharge estimates, in m 3 s −1 , for the three sequences at Olson was estimated by Sharma et al. (2023aSharma et al. ( , 2023b) ) using a combination of channel dimensions such as bankfull depth and width, and palaeoslope estimates (Figure 2 and supplementary material).The HA intervals have an average discharge rate of 2200 ± 550 (m 3 s −1 ) (average value ± SE, N = 45) while LA intervals have a discharge rate of 700 ± 200 (m 3 s −1 ) (N = 49) which corresponds to a threefold increase in volumetric discharge in HA intervals.However, it is important to stress that these estimates from channel outcrops in the field represent instantaneous bankfull flow conditions (channelforming conditions) and do not represent average annual flow conditions.The number of active channels can also influence water discharge estimates thereby affecting intermittency estimates.To address this, although there is no method to assess the number of active channels at any time in an ancient fluvial system, a quantitative approach to decipher fluvial style as described by Parker (1976) and Lyster et al. (2023) predicts HA and LA channels to be single threaded (see Figure S1).

| Estimating discharge intermittency factor
Discharge estimates, in m 3 s −1 , for the three sequences at Olson from both end members were first converted into m 3 day −1 .Discharge intermittency (Q WI ) was then calculated by dividing the average total available water budget by discharge estimates in m 3 day −1 to obtain the intermittency ratio as the number of days per year that channel-forming discharge would be required to equal the estimated annual water budget.Discharge intermittency factor (I WF ) was calculated relative to the number of days in a year.

| Total sediment budget and sediment flux estimates
Bankfull volumetric sediment flux and the resulting total sediment flux for the Escanilla Formation were calculated using two different approaches involving bedload and sand fraction sediment flux estimates.
F I G U R E 2 Stratigraphic log of the studied section at Olson depicting the three fining-upward sequences, each consisting of a high amalgamation (HA) and low amalgamation (LA) interval.Also shown are the mean annual precipitation (MAP) and total water discharge estimates for the Escanilla Formation.Black vertical bars denote the average value in HA intervals while grey bars denote the average value in LA intervals.

| Total sediment budget
The total volumetric sediment flux available in the Escanilla system during the 41.6 to 39.1 Ma time interval has previously been estimated by Michael et al. (2013) using an approach extrapolating the outcrop extent of the sediment routing system, where linear interpolation of cross-sectional areas in the downstream direction is used to constrain the cumulative depositional volume.The most significant uncertainty acknowledged by Michael et al. (2013) arises from the estimated cross-sectional width of the Escanilla system fairway.This mass balance framework resulted in a total depositional volume of 246,000 ± 20,000 m 3 year −1 , a value range which is used in this study.
3.4.2| Estimating bedload sediment flux and resulting total sediment flux Bedload sediment flux for the gravel grain-size fraction was estimated by Sharma et al. (2023aSharma et al. ( , 2023b; Figure 4).Since gravel fraction makes up 25% of the total sediment flux in the Ainsa area of the Escanilla system in the Ainsa Basin, as documented by Michael et al. (2013) using a modelling approach involving transformation of volumetric depositional volumes into a mass balance framework, bedload sediment flux was accordingly used to calculate the total sediment flux.
3.4.3| Estimating sand fraction sediment flux and resulting total sediment flux Total volumetric bankfull sediment flux was calculated using the model of Engelund and Hansen (1967) for sand bedded rivers and following the method described by Hayden et al. (2021).
Non-dimensional sediment flux per unit width (q t *) is related to the friction factor (C f ) and total non-dimensional shear stress * as where q * t = Q s ∕W RgD 3 50 0.5 , C f = gH bf S ∕ U 2 , g is gravitational acceleration, H bf is bankfull flow depth, S is riverbed slope, U is flow velocity, W is flow width, R is submerged specific sediment density (R = 1.65 for quartz in water) and D 50 is the median grain size.These values have been previously estimated for the Escanilla Formation by Sharma et al. (2023aSharma et al. ( , 2023b)).
Following Engelund and Hansen (1967), total nondimensional shear stress ( * ) is related to bankfull flow depth (H bf ), slope (S), submerged specific sediment density (R) and median grain size (D 50 ) as Following Equations ( 3) and ( 4), Bankfull sediment flux (Q s ) was then calculated using Equation (5) as A median grain size of 0.25 mm (fine-medium grain-size fraction) was considered while calculating the sediment flux.Channel belt widths estimated by Sharma et al. (2023aSharma et al. ( , 2023b)), using the relationship W = 8.8H bf 1.82 ± standard error (SE) (Bridge & Mackey, 1993), were used to calculate Bankfull sediment flux (Q s ).Similar to the gravel fraction, sand fraction also makes up 25% of the total sediment flux (Michael et al., 2013) and values were accordingly used to calculate the resulting total sediment flux in the Ainsa Basin.

| Estimating sediment flux intermittency factor
Total sediment flux estimates, in m 3 s −1 , from both approaches (bedload and sand fraction) were first converted into m 3 day −1 .Flux intermittency (Q SI ) for each approach was then obtained by dividing the total available annual sediment budget by the sediment flux in m 3 day −1 to obtain the flux intermittency, expressed in terms of the number of days in a year.Flux intermittency factor (I SF ) was then estimated using the same approach used to estimate discharge intermittency factor.

| Uncertainty on reported estimates
Uncertainty on all results reported in this study consists of the standard error of the mean (SE) calculated as , where SD is the standard deviation and n is sample size.Uncertainty propagation was done using the uncertainties package in Python (Spyder version 4.0.1),which is a free, cross-platform program that transparently handles calculations with numbers involving uncertainties.
Although palaeohydrological information can be extracted from ancient systems, the accuracy of such estimates is subject to limitations as noted by Lyster et al. (2021).First, there is a potential for underestimating true depths when relying on storey thickness due to incomplete preservation and erosion caused by overlying layers.Such an underestimation of flow depth could subsequently impact the estimates for slope, flow velocity, (3) discharge and flux.Second, discharge and flux estimates are based on channel belt widths.While determining individual channel widths is relatively straightforward for contemporary rivers, the challenge in assessing ancient systems lies not only in their limited preservation but also in determining the number of active channels.This could have a significant impact as a higher number of active channels would imply considerably greater discharge and sediment transport rates.These limitations directly affect water discharge and sediment flux intermittency estimates.As a result, care must be taken while interpreting these values by considering them as plausible values rather than absolute values.

| Water discharge intermittency factor (I WF )
Bankfull water discharge intermittency, estimated using the first end member (ca 0.3 m year −1 MAP), in the HA intervals is 12 ± 2 days (average value ± SE, N = 35) equivalent to an intermittency factor of 0.03 or 3% of a year, while LA intervals have an intermittency of 39 ± 4 days (N = 49) equivalent to an intermittency factor of 0.10 or 10% of a year and represents a threefold increase in intermittency factor in the LA intervals over HA intervals (Figure 3), again noting that an increase in the numerical value of the intermittency factor (I WF ) implies a decrease in the temporal intermittency of water discharge-that is, water flow is relatively more constant through the year in the LA intervals.Discharge intermittency, based on the second end member (ca 1.0 m year −1 MAP), in the HA intervals is 40 ± 5 days (N = 35), equivalent to an intermittency factor of 0.11 or 11% of a year while LA intervals have an intermittency of 119 ± 13 days (N = 47) equivalent to an intermittency factor of 0.32 or 32% of a year.This represents an almost threefold increase in discharge intermittency factor.

| Sediment flux estimates
Non-dimensional unit sediment flux, q t (Equation 3), based on the model of Engelund and Hansen (1967), was estimated to be 63.5 ± 21 (average value ± SE, N = 35) for the HA intervals and 61 ± 20 (N = 49) for the LA intervals.This would imply bankfull sediment flux using the sand fraction (Equation 5) for the HA intervals to be 0.2 ± 0.06 m 3 s −1 and 0.1 ± 0.02 m 3 s −1 for the LA intervals, that is, a twofold increase in sediment flux in the HA intervals.This compares well with the one and a half fold increase in bedload sediment flux in the HA intervals documented by Sharma et al. (2023aSharma et al. ( , 2023b; Figure 4).

| Sediment flux intermittency factor (I SF )
Sediment flux intermittency, based on bedload flux, in the HA intervals is 3 ± 0.2 days (average value ± SE, N = 35) F I G U R E 3 Discharge intermittency (Q WI ) and intermittency factor (I WF ) estimates from two end members having MAP of ca 300 and ca 1000 mm year −1 .Values are strongly dependent on precipitation rate such that the more water is available the less intermittent the fluvial system becomes.Black vertical bars denote the average value in HA intervals while grey bars denote the average value in LA intervals.
equivalent to intermittency factor of 0.008 or 0.8% of a year, while the LA intervals have an intermittency of 5 ± 0.4 days (N = 49) equivalent to an intermittency factor of 0.01 or 1% of a year (Figure 5).
Intermittency based on sand fraction sediment flux, in the HA intervals is 5 ± 0.5 days (N = 35) that is, an intermittency factor of 0.01 (1% of a year), while LA intervals have an intermittency of 11 ± 0.8 days (N = 49), that is, an intermittency factor of 0.03 (3% of a year) (Figure 5).

| DISCUSSION
The above results provide new insights into how water discharge and sediment transport evolved relative to alluvial channel stratal architecture in the Middle Eocene Escanilla Formation.Overall, discharge intermittency values from both the end members suggest that flow in the HA intervals was more intermittent (probably concentrated within a few days in a year) while flow during the LA intervals was less intermittent and more probably to be characterised by non-bankfull perennial flow.Any increase in precipitation in the source area would result in a higher water budget translating overall into a higher discharge intermittency factor (I WF ), that is, less intermittent flow.The Escanilla system is consistent with lower discharge intermittency in a temporal sense under increased precipitation and supports evidence from modern rivers that climatic conditions such as the amount and timing of precipitation have a first-order control on flow variability (Buttle et al., 2012;Eng et al., 2016).In contrast, higher flow intermittencies (i.e. a few days a year) in the HA intervals are more characteristic of ephemeral (intermittent) streams where flows are typically short, intense and associated with periods of intense rainfall (Picard & High, 1973;Mabbutt, 1977).
Flux intermittency data suggest that events moving sediment through the Escanilla system happened more intermittently than water transport and probably occurred in just a few days in a year.Again, the HA intervals are reconstructed to have lower sediment flux intermittency factor (i.e. more intermittent sediment transport) than the LA intervals.Collectively, discharge and flux intermittency factor is systematically lower in the HA intervals and higher in the LA intervals (Figures 3 and 5).Given that there is no evidence for very large changes in mean annual rainfall during this period (e.g. Figure 2), it is hypothesised that this could be due to changes in the distribution of rainfall and storminess at these timescales.
According to palaeogeographical reconstructions from Hay et al. (1999), the Pyrenees were situated at approximately 35°N during the Eocene period.This particular latitude is recognised to be sensitive to climate changes induced by astronomical factors with some studies suggesting that orbital variations could impact precipitation and evaporation patterns at such latitudes (Cantalejo & Pickering, 2014).For instance, in the Middle Eocene (Late Lutetian) Ainsa System submarine fan deposits, F I G U R E 4 Bedload sediment flux calculated by Sharma et al. (2023aSharma et al. ( , 2023b)), using the Meyer-Peter and Muller equation, and sand fraction sediment flux calculated using the Engelund and Hansen (1967) model.Black vertical bars denote the average value in HA intervals while grey bars denote the average value in LA intervals.cyclical variations relatively coarser and finer-grained reflect a strong relationship to the 400 kyr eccentricity cycles (Cantalejo & Pickering, 2014;Cantalejo et al., 2021).In the continental Escanilla Formation, 400 kyr eccentricity cycles have recently been proposed to influence sediment depositional patterns from the HA to LA intervals due to cyclical variations in sediment flux and water discharge (Sharma et al., 2023a(Sharma et al., , 2023b)).
These new intermittency results indicate that sediments during the deposition of the HA intervals were on average transported within 4 ± 0.3 days most probably suggesting that the HA intervals were deposited under concentrated 'bursts' of sediment flux potentially under high-frequency convective storms over the Pyrenees during summertime (Callado & Pascual, 2005;Llasat et al., 2021) while sediment transport in the LA intervals took on average 8 ± 0.65 days but represents a much larger spread in the number of days over which sediments were transported (Figure 5).While differences in intermittency, although small, are observed relative to the HA and LA intervals, they do not fully explain the differences in stratigraphy between these intervals.
Collectively, this suggests a strong link between eccentricity cycles, discharge and flux rates and their respective intermittencies in the Escanilla Formation such that eccentricity maxima most probably corresponds to higher flux and discharge and potentially more stormy conditions that resulted in concentrated flow events (more intermittent flow) during the deposition of the HA intervals.Contrary to this, eccentricity minima most probably corresponds to lower discharge and flux in the Escanilla system under calm climatic conditions with less intermittent flow conditions.

| Sediment flux intermittency (I SF ) to water discharge intermittency (I WF ) ratio
For an MAP value of ca 0.3 m year −1 , the ratio of sediment flux intermittency factors (from bedload flux) to water discharge intermittency is 0.33 and 0.17 for the HA and LA intervals, respectively, that is, 33% and 17% of the water discharge intermittency factor (Figure 6).For the same MAP, the ratio of sediment flux intermittency factor (from sand fraction sediment flux) to water discharge intermittency factor is 0.52 and 0.43 for the HA and LA intervals, respectively, that is, 52% and 43% of the water discharge intermittency factor (Figure 6).
For an MAP value of ca 1.0 m year −1 , similar trends are obtained: 10% and 5% of the water discharge intermittency factor for the HA and LA intervals (Figure 6), and 16% and 13% of sediment flux intermittency for the HA and LA intervals, respectively (Figure 6).This implies that sediment transport intermittencies vary in proportion to the assumed rainfall such that during lower rainfall rates, discharge and flux intermittency are similar in value since the infrequent discharge and sediment transport events happen together.However, as rainfall increases, there is a marked increase in the proportion of water transport below channel-forming conditions during which sediment is not transported.This results in flux intermittency to be lower than discharge intermittency and constitutes a proportion of the discharge intermittency factor.
These results also demonstrate how upstream environmental drivers (precipitation) can be a predominant factor that determines how sediments are transported in fluvial systems and reinforces the idea that upstream climate plays an important role in how sediments are mobilised, and how they influence the resulting depositional architecture (cf.Sharma et al., 2023aSharma et al., , 2023b).

| How do these results compare to modern rivers?
To contextualise these findings, the flux intermittency factor of 94 gravel-bedded modern rivers, having grain size ranging from 0.003 to 0.08 m, is compared to the flux intermittency factors deduced in this study (Figure 6).Modern rivers from climatic environments with MAP ranging from 0.4 to 1.2 m year −1 were selected from the Sediment flux intermittency factors of the HA and LA intervals from the Escanilla Formation range from 0.008 to 0.03 with an average value of 0.02 (N = 82) while those from modern rivers have intermittency values ranging from 0.0026 to 0.8 with an average value of 0.14 (N = 94).These results are therefore plausible and similar to the sediment flux intermittency values of modern ephemeral rivers dominated by warm and humid summer climates, such as the Little Shenango River in Pennsylvania, Bluestone River in west Virginia or the Jemez River in New Mexico (Hayden et al., 2021).

| CONCLUSIONS
A quantitative approach to estimating discharge and flux variability relative to changes in fluvial stratigraphic architecture provides new insights into how channel stacking patterns in ancient sedimentary successions can be interpreted.Cyclical variations in discharge and flux intermittency correspond to changes in architectural styles such that the HA intervals are deposited under more intermittent flow conditions (discharge intermittency of 12-40 days per year) which are interpreted to be influenced by short and intense precipitation events while the LA intervals are deposited under less intermittent flow conditions (discharge intermittency of 39-119 days per year).Overall, the sediment flux intermittency factor of the Escanilla Formation has values ranging from 0.008 to 0.03 (3-11 days per year), which are within the same range of values from modern ephemeral rivers (0.0026-0.954).These values are typical of rivers found in arid and semi-arid climatic conditions and are consistent with the regional climate at Olson during the Middle Eocene.This further demonstrates the ability of palaeohydraulic reconstructions to predict, within acceptable error limits, estimates that are consistent with values from modern rivers.Importantly, data presented in this study suggest that changes in depositional architecture are the result of relatively infrequent sediment transport events and indicate that changing rainfall distributions (including magnitudes) significantly influenced sediment routing systems on the Earth's surface in the past.
Map of the Escanilla palaeo-sediment routing system in the southern Pyrenees, Spain, and showing the main tectonic structures.Figure modified afterMichael et al. (2014a).Red arrows mark the water discharge and sediment transport direction of the Escanilla system away from the source regions of Sis and Gurb palaeovalleys.(B) Lithostratigraphic framework of the Escanilla Formation at Olson consists of two main members-the Mondot and the Olson members with the Olson Conglomerate (OC; red line) at the transition between the two members.(C) Geological map of the southern Ainsa Basin encompassing the Escanilla Formation around the village of Olson.The 'OC' is marked in red as a basin wide, laterally extensive amalgamated channel body lying in between the Mondot and Olson members of the Escanilla Formation.This map was prepared using QGIS Desktop 3.22.8(https:// qgis.org/ en/ site/ ).(D) Studied composite section of the Escanilla Formation with the local magnetostratigraphic interpretation byVinyoles et al. (2020) correlated to the Geomagnetic Polarity Time Scale, GPTS 2020(Ogg, 2020).The thickest normal magnetozone C18n in the local magnetostratigraphic interpretation includes C18n.1n,C18n.1r and C18n.2n.(E) Panorama of the studied sequences two and three (sequence one lies below).At the base of the panorama lies a thick floodplain-dominated interval terminating the LA interval of sequence one and above which lies the HA interval corresponding to the OC.Above the HA interval lies the floodplain-dominated LA interval.

F
Sediment flux intermittency (Q SI ) and intermittency factor (I SF ) based on total flux estimated from bedload fraction and sand fraction sediment flux.Black vertical bars denote the average value in HA intervals while grey bars denote the average value in LA intervals.

F
Ratio of sediment flux intermittency, based on bedload and sand fraction flux estimates, and water discharge intermittency.dataset of et al. (2021; see supplementary rial) (Figure 7).