We now present results of the fully coupled model, i.e. combining GravelScape with the flexural model and considering an evolving orogen and its retro-foreland basin. Although we only plotted the basin evolution from the mountain toe (0 km) to 200 km, we also modelled the evolving orogen to calculate the flexural response of the basin dynamically. For the main focus of this paper (Fig. ), the value of the EET, Te=20 km (Table ), that we have chosen is such that the wavelength of the resulting flexural defection (≈200 km) is much greater than the size of the fan. The size of the fan (≈20 km) is set by the size of the orogen (50 km) and the relative precipitation product in the orogen (0.8) compared to the basin (1) . In our model setup, annual precipitation is incorporated into the definition of K, so relative precipitation values are dimensionless factors that determine the proportion of precipitation above or below the mean annual rate falling in the basin versus the orogen. In this situation, the surface topography is mostly controlled by surface processes and only by the subsidence at very low F values . This leads to a relatively small value for β/α=1/5 (see , for an exact definition of β), which is typical of many foreland basins, with the exception of mega fans, which could extend beyond the lithosphere flexural wavelength, or in situations where the mountain is very close to an ocean (such as in the Southern Alps of Te Waipounamu / South Island, Aotearoa / New Zealand). This choice of a low β value leads to relatively high surface slopes in the basin, which helps prevent the formation of local minima or lake depressions, which affect the grain size computations as discussed in . The choice of low β also allows for autogenic dynamics to potentially impact grain size fining as predicted in the framework (also shown in Fig. ) that were otherwise reduced in high β settings.

In Fig.  we present a series of stratigraphic sections through the foreland basin for the duration of the model. The various panels in Fig.  show (a)  the stratigraphy where colours are proportional to the value of F at the time of deposition, (b) the grain size in the main channel, (c) the grain size along a vertical section at the center of the basin, (d) deposition or erosion averaged in the y direction, and (e) the surface rugosity, at the time of deposition. The dark-blue areas (low grain size) in panel (c) correspond to regions where deposition took place along channel interfluves or what can be associated with floodplains. In two small insets, we show, in panel (a), the time evolution of the maximum topography (apex) in the orogen and in the basin and, in panel (e), the mobility frequency computed over five time intervals in the basin evolution as a function of x. Within the inset of panel (a) (a2), we also show the e-folding time towards topographic steady state in the orogen and in the basin. These times are also indicated in all stratigraphic sections of panels (a) to (e) as a blue (mountain steady state) and orange line (basin steady state). The channel mobility shown as an inset in Fig. e was calculated as the frequency of movement of the largest channel over 4 Myr time windows. These time intervals are also indicated as dashed black lines in the stratigraphic sections. In the following description of these results, we have divided the foreland basin evolution into four phases based primarily on its degree of evolution towards steady state and, in particular, the bypass parameter, F. Note that the exact value for F during each stage of the basin evolution may vary depending on the basin configuration. However, the general trend for F is independent of model parameters as is its effect on the evolution of grain size trends and autogenic dynamics.

Early in the collision, during what we shall call Phase 0 (light–blue–white section with F<1 in Fig. a), the orogen grows, and basin subsidence is fast, but little sediment is produced yet; this leads to a mostly “starved” foreland basin. During this phase, the basin is so under-filled that it becomes a large local depression. In this situation, our algorithm to solve the modified SPL cannot be used, and sediment is deposited uniformly across the basin, simulating deposition in a lacustrine environment where the self-similar grain size fining model cannot be used. In other real-life settings, this would be a marine basin in to which turbidites or marine stratigraphy might be deposited.

During Phase 1 (darker shades of blue for 1<F<4 in Fig. a), the basin and orogen are in a transient state on their way to the steady-state topographic height, and the subsidence is largely driven by flexure in response to the loading of the growing orogen. The growth of the orogen and of its mean slope results in a steadily increasing erosion rate in the mountain area and sediment flux into the basin. This leads to a progressive increase in F to values that rapidly exceed 1, as the basin fills and enters a bypass state. As F increases, grain size fining in the main channel shows coarsening upwards, i.e. less fining (Fig. b). During this transient phase towards steady state, rugosity is relatively low, except in the fan area, but channel mobility is high across most of the basin (Fig. e). Deposition rate is relatively uniform across the basin in response to the rapid subsidence (Fig. d). This generates thick stratigraphic packages (approximately 15 and 7 km deposited in the first two 4 Myr intervals). The strong fining trend that is observed during most of this phase is indicative of a system where sedimentation rate is dominated by subsidence (F<4) and the effect of autogenic processes is minimal (low rugosity) . During Phase 1, the system can be positioned in the low β vs low F (bottom left) corner of the framework of (Fig. ).

We define Phase 2 (shifting from blues to greens for 4<F<9 in Fig. a) as the period when topographic steady state in the mountain has been reached (the blue line in the stratigraphic sections) until topographic steady state in the basin has also been reached (the orange line in the stratigraphic sections). During this phase, basin subsidence transitions from being predominantly driven by the load of the mountain to the weight of the sediment itself. In this maturing phase of evolution, the system transitions into a progressive higher-bypass regime in which the value of F increases to very large values. Despite this increase in F, we see that the fining trend in the main channel remains relatively constant (Fig. b). We also see an increase in floodplain deposition (Fig. c), an increase in rugosity, and a decrease in channel mobility (Fig. e) that indicate that autogenic processes become more important. This is confirmed by an increase in variability in deposition rate (Fig. b). This strongly suggests that grain size fining is becoming progressively dominated by autogenic processes and less by subsidence. During Phase 2, the Fig.  system can therefore be positioned in the low β vs intermediate to high F region or mixed regime of the framework of (Fig. ).

Phase 3 is defined as the period after basin topographic steady state has been reached (yellow to red contours corresponding to F>10 values in Fig. a). With a constant flux from the mountain, the subsidence generated due to sediment loading continues but at a much slower pace than in Phase 2. The level of bypass increases with time (less than a few hundred metres of sediment is deposited in every 4 Myr intervals), which explains the rapidly decreasing subsidence rate (less sediment deposited cause less subsidence). During this phase, erosional unconformities can be observed that can extend across the entire basin or occur locally despite constant external conditions. These unconformities are better expressed in the model run shown in Fig.  with higher precipitation in the mountain area (and thus higher β and higher F bypass values).

During Phase 3 (high bypass), grain size in the main channel is relatively coarse but some fining still takes place (Fig. b). Channel mobility is lower than during Phases 1 and 2 (Fig. e), resulting in a larger proportion of floodplain areas (Fig. c). Channels also appear to cut into material previously deposited in floodplains (Fig. c). This and the very high rugosity (close to 100 m) (Fig. e) indicate higher reworking. Phase 3 also shows the highest variation in deposition rate in the upper reaches of the basin, i.e. near the fan (Fig. d). All these factors indicate that autogenic processes are very active and of high amplitude. With high-bypass (high F) conditions, this suggests that the observed low to moderate grain size fining has become totally autogenic-dominated. During Phase 3, the system should be position in the low-β vs high F (bottom-right) corner of the framework of (also shown in Fig. ).

In Fig. , we show the results of a model run identical to the model run shown in Fig.  except for a higher β value, obtained by increasing the precipitation rate in the mountain area to be 10 times larger than in the basin area, such that β=2.5α, and a slightly lower K (2×10-5 m^1–2 m yr⁻¹), in order to produce a more comparable response time to Fig.  despite the increasing precipitation. Consequently, the size of the fan is larger than the wavelength of the resulting flexural defection and would extend beyond the model length, similar to a megafan or confined system as described in . Note that, based on the framework of (Fig. ), a β/α=2.5 model experiment should be subsidence-dominated, regardless of the value of F.

We see (Fig. ) that the timing of Phases 0 to 3, as defined for the low β case, remains the same, except that the F values at steady state are much higher in Fig.  compared to Fig. . Due to the enhanced precipitation rate in the orogen, the basin more rapidly reaches a state of high bypass compared to the low β scenario, but the sediment thickness accumulated in the basin is substantially reduced. Furthermore we see, in Fig. b, that channel fining occurs early in the basin evolution, i.e. when F<10, or early in Phase 1. Once bypass is reached (F>10) in the high β scenario, i.e. during Phases 2 and 3, no further channel fining is observed (Fig. b), and channel mobility (Fig. e) is reduced. This is in contrast to results shown in Fig. , where downstream fining in the channel is observed under high-bypass F values and downstream channel mobility occurs. Around and after orogen steady state is reached, pulses of deposition and erosion result in unconformities and stratigraphic layers that are highly truncated downstream (Fig. d). In the final stages of the model simulation the main depositional depocenter migrates towards the downstream areas of the model.

The Alberta Basin formed by lithospheric flexure associated with the accretion of the Intermontane Superterrane against Western Canada in the Jurassic to form the early Rocky Mountains/Columbian Orogen . This basin should be an ideal example of a foreland system that has experienced a transition from subsidence- to autogenic-dominated control due a number of factors: (1) it is a retro-arc foreland basin , which, therefore, according to would tend to fill and reach high bypass over time; (2) it is underlain by a relatively thick elastic plate (the strong North American craton) , which results in a very long flexural wavelength and, therefore, a basin that is much wider than the orogen resulting in a small β value; (3) the basin has been evolving gradually for well over 100 Myr ; and (4) the orogen lithology consists of several erodible sedimentary terranes that are likely to generate high initial sedimentary flux. However, contrary to our synthetic example described in the previous section, the Alberta Basin has experienced periods of both subsidence and uplift and, recently, has been subject to periods of rapid glacial isostatic adjustment causing non-monotonous variations in F.

It has been well described that the collision began much earlier in southern Alberta than in northern Alberta . Consequently, at any given time in the evolution of the Alberta Basin, its northern and southern parts may have been in different states of bypass (or characterized by different F values) and, therefore, showed different level of autogenic vs subsidence grain size fining during the same time period. We have focused our comparison of model predictions to the general evolution of the system in mid-southern Alberta (between Swan Hills and Cypress Hills area) from the mid-Jurassic onwards, generally avoiding issues arising from the three-dimensional nature of the collision or pre-existing basement structures, namely the underlying Peace and Sweetgrass arches (Fig. ).

In Fig. , we show a stratigraphic cross-section across the basin, as well as paleogeographic maps for selected geological times. Within the upper Jurassic (Fig. a (dark green) or b6), central-southern Alberta exhibited subsidence in response to early mountain building and was inundated by a shallow seaway accumulating thick marine shales. This would likely represent Phase 0 in our model where the basin is under-filled (low F), its surface is below base level, coarse fluvial sediments do not propagate very far, and the grain size fining regime is largely non-fluvial and therefore not subsidence-dominated.

After an initial phase of mountain building, there is a well-defined erosional unconformity, which corresponds to a tectonic quiescence and rebound episode in the Canadian Cordillera from 140 to 125 Ma . Previous work suggests that long-wavelength uplift may have occurred due to unloading of the orogenic front . Following this unconformity is an extensive alluvial facies unit called the Cadomin Formation, made of clast-supported, subrounded, dominantly coarse conglomerates (with local sandstone occurrences). It is hundreds of kilometres in spatial extent within a fluvial system flowing northward to eastward for 12–18 Myr during roughly the Barremian–Aptian (Fig. a, above the dark green, or b). As evidenced by the erosional unconformity at the base of the Cadomin Formation and the propagation of coarse fluvial grains (gravel conglomerate with interbedded sands and occasional finer clasts ) away from the orogenic front, it is likely that during this phase, the basin had rapidly entered a state of high bypass and, thus, a highly autogenic-dominated regime (e.g. F>10). The Cadomin Formation has a thickness of 1–200 m accumulated over 12–18 Myr , implying an extraction rate of approximately 1.5×10-5 to 5.5×10-8 (m yr⁻¹), which we would consider low within our model simulations and indicative of a state of high bypass (e.g. Fig. a had a subsidence rate of 1.5×10-5 (m yr⁻¹), resulting in F≥100).

Following this tectonic quiescence, mountain building reactivated in the Cretaceous when the Insular Superterrane collided with North America and reactivated the eastward thrusting of the Intermontane Superterrane. Subsidence resumed as well. Throughout the Albian, there are varying occurrences of brackish bay, delta, and shallow marine shelf deposits, while any fluvial propagation of coarse grains that was observed in the Cadomin Fm is significantly reduced (e.g. Fig. a (light green) or b4). The foreland trough, parallel to the Rocky Mountain front, substantially broadened and deepened during the Cretaceous such that the stratigraphic preservation is much higher than in the underlying upper Jurassic interval. Based on the lack of fluvial propagation and high marine inundation, we are likely back in a Phase 0 to 1 of basin filling. One could argue that a Phase 1, early-filled basin (where F approaches and even briefly exceeds 1) occurred during select pulses throughout the Cretaceous where the fluvial and delta facies propagated further (Fig. b3) due to variations in uplift in time and space. But any grain size fining would likely still be subsidence-dominated on account of the low F associated with active mountain building. argue for high variability in the fluvial front and the extent of marine inundation events throughout the Cretaceous, which is likely linked to sea-level oscillations.

By the end of the Cretaceous (i.e. above the Bearpaw Formation in Fig. a (gold)), the marine seaway retreated due to the increased sediment flux and reduced subsidence resulting both from the effective erosion of the mountain belt that limited its height and thus the resulting flexure. However, the sediment flux from the mountain continued to be high and comparable to the flexure-driven subsidence . Thus, in the Uppermost Cretaceous and into the Tertiary (Fig. a gold and b2), the basin entered Phase 1–2, with the majority of the basin consistently above sea level and fluvial (dark green-mainly sandstone) sediments transported over very long distances. Subsidence generally continued at a reduced pace during most of the Mesozoic and Cenozoic (see Fig. a), most likely in response to the load of the sediment, and allowing for the preservation of strata and, thus, with F values comprised between 1 and 10, indicating a potential combination of subsidence and autogenic/transient control on fining.

Finally, during the Quaternary period the system entered what can be considered Phase 3 in the foreland basin evolution with strong bypass (F>10) or erosion (Fig. a). Quaternary deposition is limited to the outer basin in Saskatchewan . The modern topography of the central-southern Alberta Basin is high near the orogenic front (700–1000 m) with ample slope (promoting channel mobility and a thick active layer), which, with the small β value, promotes a high autogenic influence on grain size fining. The modern fans developing at the surface of the Alberta Basin have been described as being dominated by internal processes and are therefore likely to be in a autogenic-dominated fining regime.

To examine a range of foreland basin evolution spanning low- to high-bypass regimes (F>100), we implemented a compressed (200 km), time-accelerated (20 Myr) basin evolution in our model simulations in which scaling K and U produced orogen elevations from 1000 to 10 000 m. While this approach offers an idealized overview of foreland basin evolution, it differs from the Alberta Basin in a number of ways. Some of these include, changes in base level over time , spatial and temporal variations in erodibility in the mountain area due to localized igneous and metamorphic lithologies , and the N–S diachronous evolution of the collision . Thus, simulation time (1 Myr) should not be directly equated to Alberta Basin stratigraphy in terms of timing or thickness.

Keeping these complexities in mind, we can further estimate key model inputs (G, K, and flexure wavelength/α) and parameters (β) for the Alberta Basin that have not already been as fully discussed as F. A global compilation by suggests that systems tend to favour a slight transport limitation (laboratory median of G=0.7), with common values of G ranging from 0 to 3.1. The response time and K are also difficult to constrain due to lateral growth of the mountain by terrane accretion of varied lithologies over the basin's long lifespan, exceeding 100 Myr . Episodic high uplift events, such as during the 100–99 Ma Viking Formation, show spatially variable sedimentary responses across the basin, with downstream sediment infilling in some areas but not others , indicating that the system's response time exceeds 1 Myr. The parameter 1/K is one of the dominant controls on response time (see equations in ), resulting in estimates of K on the order of 10-7 to 10-8 m^1–2 m yr⁻¹ with response time estimates of 10–100 Myr (based on the above descriptions). Elastic plate thickness in the Alberta foreland basin is estimated at 20–60 km, yielding a flexural wavelength λ of 274–739 km, assuming a lithosphere–asthenosphere density contrast (Δp) of 500 kg m⁻³ . The adjacent craton, 60–150 km e-thickness, produces longer flexural wavelengths >739 km . Early in basin evolution, limited sediment cover and a thick cratonic basement likely led to a rigid, long-wavelength system , suggesting a potential rigid-end α range (e.g. 0.2–0.5).

Evidence suggests a value of β/α<1 for the Western Canada foreland basin, more consistent with Fig.  than Fig. , due to the rain shadow effect and the large downstream basin relative to the orogen. Recall the relationship β/α=vMLMvBLB , where β can be derived from a ratio of orogen vs basin precipitation and length. Satellite imagery and paleogeographic maps show the Canadian Rockies as a series of ranges approximately 50–200 km wide, while the foreland basin spans on the order of +1000 km, bounded to the east by the Canadian Shield. Precipitation data (1971–2000) indicate 300–1500 mm yr⁻¹ over the orogen and 300–500 mm yr⁻¹ across the basin , resulting in an orogen that is ∼2–3 times wetter. Keep in mind that Cretaceous seaways (e.g. Fig. ) may have increased basin moisture and reduced the rain shadow effect, while aridification may have enhanced precipitation gradients. Using modern averages, β/α can be estimated around 0.2 to 0.4.

The early Cretaceous Cadomin Formation is described in areas as a megafan similar to the Kosi Fan, India, but with coarser grain sizes (e.g. on average 1–3 cm gravels clasts that reach up to a maximum of 40 cm, ) and with some preserved evidence of autogenic dynamics . Amalgamation, frequent shifting, and bank cutting of channels that have been described within the stratigraphy match our stratigraphic results of an autogenic-dominated fining system under very high bypass with reworking (Fig. ). However, recent work has identified terraces in the upper basin that are preserved in the stratigraphy and are indicative of aggrading and incision pulses (similar to our depositional divergence) during this period, which have been interpreted as related to climate cyclicity. This alternation of well-sorted and poorly sorted episodes within the conglomerate has been described as a potential series of inter-flood episodes characterized by reworking and flood episodes without time for sorting . Banded argillic horizons within the soil deposits are also evidence of climate seasonality around this time that may impact the grain size signal.

We propose that the Cadomin Fm would be located in the lower-right corner of the framework (Fig. ) in the region with a low β and high F, where autogenic dynamics dominate the grain size record. We reiterate that the Cadomin Fm was deposited during a period of tectonic quiescence in the orogen collision and rebound in the basin , indicative of a high bypass F. We can also infer a generally low β value for the Cadomin Fm from (1) the extent of the basin (i.e. the orogen existed several hundreds of kilometres from the shoreline, ), which is likely to be larger than the size of the orogen resulting in a lower β value; and (2) a generally semi-arid climate for Western Canada around the Jurassic–early Cretaceous transition, as indicated by the presence of silcrete in the paleosols , which is the modern environments where steep fan to plain topography is observed (e.g. Mongolia). Furthermore, the system during the Cadomin clearly exhibits some reworking and variations in grain size typical of the autogenic dominated regime described in and shown in Fig. a.

Seasonality could also have impacted climatic gradients between the newly formed orogen and basin. It is possible that the efficiency of the autogenic dominated grain size fining during the Cadomin Formation may have fluctuated under a cyclic climate, with periods of enhanced precipitation in the mountain causing variations in β. Periods of enhanced precipitation in the mountain would have caused an increase in β and a decrease in surface slope, rugosity, and magnitude of autogenic processes . This, in turn, would have decreased the grain size fining and caused the propagation of the coarse grain front further into the basin, as observed by and previously interpreted as periods of intense flooding. We have shown that our approach to modelling and interpreting foreland basin evolution, including identifying when such basins may record autogenic dynamics based on spatial gradients and sediment bypass, can be applied to real mountain belts. We suggest that this framework could be useful for analyzing other foreland basins at different stages of evolution.