Secondary Geomorphic Processes and Their Influence on Alluvial Fan Morphology, Channel Behavior and Flood Hazards

Alluvial fans form through primary and secondary geomorphic processes. Primary processes comprise major geomorphic events that build the fan by transporting sediment from the watershed to the fan; these events occur at decadal time scales. Secondary processes include the smaller flood events which recruit little sediment from the watershed but can re‐mobilize and rework sediment already delivered to the fan. The experiments described herein study the effects of secondary processes on alluvial fan morphology and channel behavior. We conducted four experiments, in which alluvial fans were built by alternating between primary events, with high flows and high sediment supply, and secondary events, with moderate flows and no sediment supply. In our experiments, primary events are best described as debris floods and secondary events correspond to smaller floods with much lower sediment concentrations. The duration of the secondary events varied between experiments, but the number and duration of the primary events was held constant keeping the total volume of sediment delivered to the fan the same. We monitored fan gradient, area, channel patterns and avulsions. Experiments with longer secondary events generated larger fans with gentler gradients. In addition, longer secondary events led to increased flow channelization and centralization between primary events. These morphologic changes resulted in fewer avulsions during primary events, which occurred later during the event. These results indicate that changes to the relative duration of primary and secondary events caused by climate change can affect fan morphology, wet fraction, and avulsion frequency, with implications for potential flood hazard.

2 of 16 Blair and McPherson (1994) referred to the competing forces of net deposition and net erosion on fans as "primary" and "secondary" processes, respectively. Flood events acting to transport sediment from the watershed to the fan were classified as "primary" events while those that re-mobilize and rework sediment previously deposited on the fan were classified as "secondary" events. On alluvial fans, primary and secondary events occur on vastly different temporal scales. For example, in some arid regions fan-building primary events occur at decadal to century time scales with few secondary events occurring in between the primary ones. In humid regions, primary events may occur about once a decade, with numerous secondary events occurring per year. As a result, secondary events are more important in these regions, and they can dominate the meso and micro scale morphology of alluvial fans due to the cumulative geomorphic work accomplished by these low-magnitude but high-frequency events (de Haas et al., 2014).
Primary events encompass a variety of sediment transport mechanisms, including debris floods, debris flows, hyper-concentrated flows, and mud flows, all of which act to transport material from the watershed to the fan (Pierson, 2005). These processes may be grouped by sediment concentration, velocity, water content, and typical slope gradient and may be referred to as hydrogeomorphic events (Wilford et al., 2004). Collectively, they act to construct the fan largely through aggradation, and their recurrence interval is often strongly influenced by climate, sediment availability, vegetation type and density, and weathering rates (Jakob, 1996;Webb et al., 2008). Due to variations in climate, meteorology, geology, and topography across individual fans and watersheds, each fan is subject to a unique temporal sequence of primary events of varying frequency, type, intensity, and magnitude.
The secondary events described by Blair and McPherson (1994) encompass all activity that remobilizes or modifies sediment previously deposited upon the fan. However, to assume these processes produce only net fan degradation is an over-simplification given the complex reworking that may occur during secondary events. The dominant sediment transport mechanism during secondary events is fluvial transport, with most size fractions being partially mobile (following the classification of Wilcock and McArdell, [1993]), resulting in size-selective transport and the development of localized surface armoring (Parker, 1990). In the case of debris flows, erosional processes may also be initiated by the less viscous after-flow following the initial stony and coarse surge front (Iverson, 1997;Jakob & Hungr, 2005;Takahashi, 2014). Secondary processes have a profound impact on fan morphology and bed surface sedimentology, but they remain under-represented in alluvial fan experiments.
Physical models have long been used in alluvial fan research, with experimental studies taking place as early as the 1960s (Hooke, 1967(Hooke, , 1968. Recently there have been a number of experimental studies of alluvial fan processes and forms (Clarke et al., 2010;Eaton et al., 2017;Hamilton et al., 2013;Leenman & Eaton, 2021;Leenman et al., 2022). While many of these studies focus on fluvial processes, recent work by de Haas et al. (2015de Haas et al. ( , 2016de Haas, Densmore, Stoffel, et al., 2018) has centered on debris flow fan formation. Still other recent experimental work covers deltas and fan-deltas (Esposito et al., 2018;Ganti et al., 2016;Hoyal & Sheets, 2009;Kim & Jerolmack, 2008;Kim & Paola, 2007;Miller et al., 2019;Piliouras & Kim, 2019;Reitz & Jerolmack, 2012;Reitz et al., 2010;Van Dijk et al., 2008;Van Dijk et al., 2012. Experimentation using physical models is particularly useful for alluvial fan and fan-delta systems, as it allows for observations on temporal scales consistent with fan evolution (Clarke et al., 2010;Harvey, 2010). In addition, recent work has indicated that these physical models give repeatable results (Adams et al., 2019) and have scale-independent characteristics which are especially clear in microscale modeling work (Davies et al., 2003;Malverti et al., 2008). An exhaustive history of experimental alluvial fans by Clarke (2015) concluded that the resurgence of experimental modeling has provided important insight into fan dynamics, and when paired with other techniques it can continue to provide new information.
In the past five years, a number of experiments have addressed the importance of variable discharge in determining alluvial fan and fan-delta morphology and evolution. De Haas et al.'s (2018b) debris flow experiments used flow sizes from three different magnitude-frequency distributions and showed that certain distributions resulted in more frequent avulsions. Ganti et al.'s (2016) experiments demonstrated that fan-deltas formed under constant flow had different morphology and avulsion characteristics to fan-deltas formed under variable flow. Piliouras et al. (2014) examined the effects of variable discharge on vegetated deltas and found that discharge fluctuations allowed for channel incision, reworking, and slowed plant colonization. A strong increase in channel lateral mobility and in-channel sedimentation under variable discharge were observed in the experiments of Esposito et al. (2018). The work of Miller et al. (2019) challenged the notion of representative channel-forming flood flow on deltas. Their experiments showed that changing the flood intermittency altered the timing of the equilibrium state, with low intermittency systems being in a constant state of adjustment between erosional and VINCENT ET AL.

10.1029/2021JF006371
3 of 16 depositional systems. Leenman et al. (2022) found that for variable discharge experiments, the shape of the flood hydrograph has important impacts on both lateral channel migration and overall morphologic change.
Our experiments evaluate the role of secondary event duration on alluvial fan morphology and channel dynamics. Previous studies that explored the effects of flow and sediment supply variations have not included experimental conditions analogous to the secondary events that frequently occur on humid region fans. Our experiments attempt to replicate the effect of secondary events by imposing periods of moderate flows and no sediment supply between primary fan-building events, and they look specifically at changes in the duration of those secondary events. Because our secondary events had no sediment feed they were strictly erosional; other experiments using variable flows maintained upstream sediment supply, thus blurring the distinction between fan-building events and fan-modifying events (e.g., Leenman et al., 2022). We add to the work of Miller et al. (2019) by exploring how longer secondary events modulate the severity of flood hazards. By varying discharge in our experiments, we examine the links between secondary geomorphic processes, fan morphology and channel dynamics in steep, gravel-cobble fan systems.
We hypothesize that longer duration secondary events act to channelize flow on fans and decrease the overall wet fraction of the fan. Moreover, we hypothesize that channelization and incision of fan channels reduces avulsions during subsequent primary events. We test our hypotheses using physical laboratory models. Our experiments generate four fans, each with a different duration of secondary events between primary fan-building events. We address the following research questions: 1. Do longer duration secondary events change fan morphology? 2. Do longer duration secondary events alter channel dynamics during subsequent primary events by changing avulsion frequency and flow dispersal over the fan surface?

Experimental Design
In this paper, we use a physical model to study fans built by a series of large, sediment-laden flood events, separated by periods of moderate flow and no sediment supply that vary in duration from experiment to experiment. The intention of this experimental design is to explore the effects of these moderate flows (representing the numerous small but frequent flood events that occur between major fan-building flood events) on the overall fan characteristics and channel dynamics that occur during fan-building flood events. The experiments are divided into two distinct phases: (a) a fan formation phase during which a fan of known volume is constructed by a series of fan-building floods having the same magnitude; and (b) a testing phase during which flood hazards are assessed, for fan-building floods of various magnitudes.

Model Setup
We conducted our experiments using the physical model of a generic gravel-cobble fan described by Leenman and Eaton (2021). The experimental setup consisted of a 2.44 × 2.44 m stream table with 0.3 m high walls, with a 0.2 m wide, 0.5 m long inlet channel at one corner ( Figure 1). The inlet channel represented a short section of a confined stream channel upstream of the fan apex which was narrowed to 0.071 m at the fan apex. The table was set to an angle of 0.0002 m m −1 (0.02%) with the inlet at the highest corner, and a vertical drain at the lowest corner. This was the minimum angle required to allow for flow from the inlet to the drain. A sediment feeder was mounted above the upstream end of the inlet channel. Water was input from a constant head tank with an adjustable outflow. Sediment was allowed to aggrade and degrade freely in the inlet channel, as in a natural system. The water used in the experiments was dyed blue to allow photos to be used for automated channel mapping.
We used a sediment mixture ranging between 0.25 and 2.8 mm to create more visually realistic channels (Hamilton et al., 2013). The mixture was truncated at 0.25 mm to maintain a hydraulically rough boundary, but otherwise reflects a scaled distribution of sediment sampled from the surface of Three Sisters Creek fan in Canmore, Alberta, Canada in July, 2018 ( Figure 2). This grain size distribution is characteristic of numerous fans in the Canmore area (BGC Engineering Inc., 2014 and is meant to reflect a scaled distribution for a generic gravel-cobble debris-flood fan. The cut-off sediment size corresponds to a size of about 32 mm on the prototype fan, which represents a significant proportion of the field GSD (approx. 42%). This truncation results in the deviation between experimental and prototype GSD for smaller grain sizes. The length scale for this generic model is 1:128, so the median size of the model bed material of 0.6 mm corresponds to a prototype value of 77 mm, and the model D 84 of 1.3 mm corresponds to a prototype value of 166 mm.

Experimental Approach
Our experiments are mobile-bed "similarity of process" or "analog" models (Hooke, 1968;Paola et al., 2009), as are most physical models of alluvial fans and fan deltas (Bryant et al., 1995;Clarke et al., 2010;de Haas, Kruijt, & Densmore, 2018;De Haas et al., 2016;Delorme et al., 2018;Hamilton et al., 2013;Hooke, 1967Hooke, , 1968Hooke & Rohrer, 1979;Miller et al., 2019;Piliouras et al., 2017;Reitz & Jerolmack, 2012;Schumm et al., 1987;Van Dijk et al., 2009). This modeling approach is common in fan experiments as the large geometric scaling ratio required to generate conveniently small laboratory fans makes it difficult to meet the Froude scaling requirements described by Peakall et al. (1996). Furthermore, the slope of experimental fans and the width of the individual channels upon the fan surface (which together control water depth and velocity) are emergent properties of the experiment, making experimental scaling approximate at best. As a result, it was impossible to experimentally control the Froude or Reynolds numbers.
Using estimates of main channel flow width, depth, and velocity, we estimated the Froude (Fr), Reynolds (Re) and particle Reynolds (Re*) numbers for the fan-head. See Table S1 in Supporting Information S1 for the parameters used to estimate these dimensionless values. The estimated Fr was 1.1-1.3 depending on the discharge, which matches supercritical values observed during flooding on natural fans (Beaumont & Oberlander, 1971). However, flow likely became subcritical further down fan as it spread into multiple smaller channels. Re* varied between 105-143 depending on the experimental discharge and mean channel dimensions. This conforms to the minimum of 70 recommended by Yalin (1971) and exceeds the threshold of 15 proposed by Ashworth et al. (1994). Although these conditions are met at the fan apex, Re* decreases down-fan as flow disperses and velocity decreases. We estimated Re between 400-750, indicating that flow was generally laminar, which would certainly not be the case in the prototype channels. Many other physical models of fans observed flows that were not fully turbulent, but that nonetheless produced reasonable fan morphodynamics (Davies et al., 2003;Delorme et al., 2018;Guerit et al., 2014;Hamilton et al., 2013;Reitz & Jerolmack, 2012;Reitz et al., 2010;Van Dijk et al., 2012;Whipple et al., 1998).
The down-fan flow state closely approximates the conditions seen in micro-scale models (Davies et al., 2003;Malverti et al., 2008). These models typically have a small Reynolds number ( ≤ 200 ) and therefore laminar flow (Davies et al., 2003). Although the mechanics of sediment transport and flow may differ from those at the field scale, it has been shown that distinct fluvial morphologies -including those of alluvial fans-may be replicated under purely laminar flow (Malverti et al., 2008). While operating outside of Froude similarity prevents the extrapolation of experimental sediment transport volumes and rates to the field, the "similarity of process" approach preserves the broad morphologic processes present on natural fans. Similar to Schumm et al. (1987)'s small scale analog models of alluvial fans which demonstrated many of the same fundamental features and processes as natural fans, our models successfully reproduced the fan channel dynamics that were of interest to us.

Experiments
As briefly outlined above, our four experiments are divided into two distinct phases: fan formation (Phase 1) and flooding (Phase 2). In Phase 1, we generated alluvial fans by alternating between primary events and secondary events. The primary events were 5 min in duration, had a discharge of 100 ml/s and a sediment feed rate of 10 g/s (see Table 1). The secondary events had durations ranging from 5 to 40 min, a discharge of 50 ml/s, and no sediment feed. In total, there were 24 primary events during Phase 1, representing a total time of 120 min and a total sediment supply of 72 kg. Changes in secondary event duration resulted in four experiments with different total experiment durations (see "Total duration" in Table 1). The relatively long duration of Phase 1 allowed for multiple cycles of channel avulsion and surface reworking, and permitted observations of fan evolution processes. This phase served to create a fan with a steady state fan gradient that could be used to study channel dynamics and flood hazards during individual primary events in the next phase.
In Phase 2, the fans generated during Phase 1 were subjected to the primary flood event sequence summarized in Table 1. This phase allowed for examination of how fan morphologies resulting from Phase 1 influenced fan dynamics during a broader range of flood event magnitudes. These fan-building events were carefully documented to assess how the duration of the secondary events affected flood hazards, in detail. Each primary flood type was repeated three times, and each replicate flood was separated by a secondary event with the same discharge and duration as in Phase 1. In total, 9 separate primary flood events were studied in Phase 2, representing three sets of primary event conditions (see Table 1). Flood A, the first primary event type run during Phase 2, was identical to the primary events during Phase 1. Flood B was 50% larger than Flood A, but maintained the same sediment concentration. Flood C had the same discharge as Flood B, but had an increased sediment feed rate, resulting in a higher sediment concentration. A summary of the complete sequence of floods run for each of the experiments is shown in Figure 3.
Primary events in Phase 1 had a sediment concentration of 10% which is typical of what might be expected during a debris flood Pierson, 2005). We used a discharge of 100 ml/s to maintain Froude numbers greater than one ( 1) in fan channels near the apex. Most of the primary events during these experiments correspond to Type 1 debris floods as per Church and Jakob's (2020) definition, with the highest sediment concentration event (Flood C, Phase 2) corresponding to their Type 2 debris floods. Together, the range of primary events during Phase 2 reflect a more complete range of the debris flood types experienced by the prototype fan (Three Sisters Creek). Note. The duration of secondary events in Phase 2 equaled the duration in Phase 1 (and thus varied by experiment). Secondary events had no sediment feed, representing the end-member case in which no sediment is supplied to the fan from the watershed upstream. While this is clearly an oversimplification (i.e., sediment supply is almost never zero), halting the sediment feed during the secondary events forces a clear distinction between our primary and secondary events that is consistent with Blair and McPherson's (1994) original definition. Conceptually, the secondary events correspond to the suite of discharges in the prototype stream during which the flow is large enough to entrain sediment, but during which the sediment supply is less than the transport capacity. The ratio of discharges for our primary and secondary flows are similar to those seen in other fan-delta and river plume experiments (Chatanantavet & Lamb, 2014;Miller et al., 2019;Piliouras et al., 2017).

Data Collection and Analysis
Fan topography and flow patterns were monitored using Structure-from-Motion (SfM) photogrammetry. SfM has been used for various geoscientific approaches, and has recently been adapted for use in physical models (Kasprzak et al., 2018;Leduc et al., 2019;Morgan et al., 2017). Photographic data were collected using nine Canon EOS Rebel T6 digital single-lens reflex cameras positioned over the experimental setup ( Figure 1). Eight of the cameras were positioned at equally spaced intervals above the perimeter, and the ninth camera was mounted perpendicular, face down above the experiment at a height of 1.8 m. The cameras collected synchronous images of the experimental fans at one-minute intervals.
The images were georeferenced to a local coordinate system at each time step using eight ground control points on the stream table walls. The images were then processed in AgiSoft Photoscan (AgiSoft, 2018) to produce point clouds (∼280,000 points per m 2 ) and orthomosaics (1 mm resolution). The topographic point clouds were used to generate 1 mm resolution digital elevation models (DEMs); the point clouds were interpolated using a k-nearest neighbors approach (number of neighbors = 2), combined with inverse distance weighting (power = 2). The DEMs were cropped to 1 cm from the edges of the table to remove any edge effects. The DEM processing and analysis were completed in R (R Core Team, 2019) using functions from the lidR package (Roussel & Auty, 2020).
Using functions from the raster package (Hijmans et al., 2020), the initial (t = 0) DEM was subtracted from each subsequent DEM. This produced a surface of elevation change relative to the initial, empty table. To determine the extent of the fan at each time step, the output was thresholded at 6 mm. With the largest grains in the exper- 7 of 16 iment ranging between 5.8 and 8 mm, this threshold was used to differentiate between portions of the fan table with, and without, sediment buildup between the time step of interest and t = 0. Cells with >6 mm of elevation increase were assigned a value of 1, while those with <6 mm of increase were assigned a value of 0, to produce a map of the fan area. The DEMs were also used to characterize fan gradient from fan apex to fan toe along a series of 88 profiles at intervals of 1 degree; profiles along the table walls were excluded. Fan elevation was extracted at 1 mm intervals along each profile and a linear regression of elevation and distance values along each profile was conducted to calculate fan gradient.
Previous work by Leenman (2021) found with 90% confidence that mean elevation values for an individual cell in a topographically inactive area varied by less than −0.7, +0.8 mm, within a 30 min period. In addition, within the wetted fan area, the mean elevation difference (wet -dry) was 1.6 mm (standard deviation of 1.2 mm), while outside the wetted fan area, the mean elevation difference (wet -dry) was 1.1 mm (standard deviation of 0.9 mm). This indicates that the presence water caused a slight overestimation of elevation. As a result, measurements of channel incision in our experiments were taken on dry fan surfaces to ensure accuracy.
The orthomosaics were used to create maps showing the location of flow/channels on the fan surface. Because the water had been dyed blue to differentiate it from the fan sediment, a color threshold was used to delineate channels on the fan surface. Values greater than the color threshold were assigned a value of 1, and those less than or equal to the threshold were assigned a value of 0, resulting in a binary map of channel versus non-channel locations. These maps were smoothed with a 7 × 7 cell majority filter and wet patches smaller than 10 cm 2 were removed.
The orthomosaics and DEMs formed the primary data from which all further analysis described herein was conducted. Additional details on the experimental apparatus and data collection methods are included in Leenman and Eaton (2021).

Fan Morphology
Fan gradient is a crucial indicator of how fans self-adjust in response to their supply of water and sediment. Figure 4 shows the mean fan gradient, averaged over each of the 88 fan profiles, at each time step of the experiments. The mean standard deviation for fan gradient measurements throughout the four experiments was 0.016 m m −1 . Because the four experiments had different total durations, the results were normalized by the total experiment duration giving normalized time, t*, on the x-axis.

of 16
Throughout our experiments, fan gradient decreased over time before asymptotically approaching a dynamic equilibrium. This dynamic equilibrium was characterized by fan gradient oscillating around a relatively constant value, where the oscillations were a result of alternating primary and secondary events. The peaks (i.e., higher gradients) in this pattern corresponded approximately to primary events when sediment was being added to the fan, while the lower gradients corresponded to secondary events. Although this 'sawtooths pattern was visible in all experiments, the pattern was most regular and most consistently linked with primary events in Experiment 4 (Figures 4 and S1 in Supporting Information S1). Changes in mean fan gradient were observed over periods as short as 5 minutes. These rapid changes are an indicator of the profound topographic effects of secondary processes and point to the importance of secondary event duration as an allogenic forcing on fan morphology.
Fan gradient achieved a lower equilibrium value with longer secondary events; on average approximately 0.1 m m −1 for Experiment 1 and 0.06 m m −1 for Experiment 4. Because the same quantity of sediment was discharged onto each fan, fans with shallower gradients had correspondingly larger areas. In other words, longer secondary events generated larger, gentler-gradient fans.
The results also appear to be grouped, in that fan area and gradient were similar for Experiments 1 & 2 and for Experiments 3 & 4. There is a clear shift between Experiments 2 and 3 which may indicate the presence of a threshold between the two. Further experiments with secondary event durations between 10 and 20 min would be needed to evaluate the presence of a threshold. The abrupt decrease in fan gradient at t* ≈ 0.58 seen in Experiment 1 was related to a temporary sediment blockage. Results for a repeat of Experiment 1 are included in the Figure S2 in Supporting Information S1.
Mean fan gradient was also plotted by fan azimuth to assess differences in gradient across the fan surface. In Figure 5 the gradient along a given fan axis-to-toe profile was averaged over the complete duration of the experiment. In our experiments, fan gradient was highest near the flanks of the fan and gentlest along the fan axis. This pattern was particularly pronounced for Experiments 3 and 4, with the longest secondary events. Hooke and Rohrer (1979) and Zarn and Davies (1994) found similar fan topography in their experiments and attributed their findings to flow partitioning, whereby higher discharges build the fan axis and are less readily diverted to the fan flanks. While some of the variation in cross-fan gradient in our experiments may be attributed to flow partitioning, generally lower discharges (during secondary events) were responsible for much of the flow on the central fan, resulting in reworking and flattening along the fan axis (see Figures S3 and S4 in Supporting Information S1). This channel behavior was likely due to reduced sediment concentration rather than flow partitioning; Zarn and Davies (1994) observed that slope along the fan axis decreased with a reduction in the sediment-water ratio. This reworking of the central fan by secondary events is thought to explain the increased variation in crossfan gradient for Experiments 3 and 4.

Channel Pattern and Incision
Using the binary channel maps described in Section 3, we calculated the wet fraction (fraction of the total fan area occupied by flow) for each time step, following Hamilton et al. (2013), Kim and Jerolmack (2008), and Reitz et al. (2010). The wet fraction in our experiments ranged from 14% to 32%. Abrupt changes to wet fraction were used as a proxy for changes in channel pattern ( Figure S5 in Supporting Information S1). In general, more channelized flow resulted in lower wet fractions while more dispersed channels resulted in higher wet fractions. This relationship between wet fraction and characteristic fan channel patterns allowed for characterization of flow patterns across primary and secondary events in our experiments.
To visualize the differences between Phase 2 wet fractions for our four experiments, the data were grouped by experiment and separated into flood and pre-flood values. "Pre-flood" values were taken from the minute prior to the onset of a primary flood event. "During flood" values were averaged over the five-minute duration for each of the primary events in Phase 2. Floods A, B, and C were considered together to highlight differences across the four experiments. Flood and pre-flood wet fraction values are summarized in Figure 6a. Although the "during As an additional metric for channel patterns, we monitored the number of channels intersecting a transect at 0.25 m down-fan over Phase 2; these data are summarized in Figure 6b. All of our experiments averaged approximately two channels during flooding. The number of fan channels increased throughout each flood, with a maximum of four and three distinct channels during and prior to flooding, respectively. The number of channels at the onset of flooding decreased with increasing secondary event duration, so that Experiment 4 generally had only one channel at the start of each flood. This increase in channelization explains the notable decrease in pre-flood wet fraction across Experiments 1-4 ( Figure 6a). These results highlight the power of secondary events in governing pre-flood conditions. Throughout our experiments, fan channels diverted toward the fan edges at the onset of flooding, and gradually re-centralized during secondary events, leading to the characteristic channel patterns exemplified in Figures S4  and S5 in Supporting Information S1. Channel re-centralization occurred most frequently and completely during Experiment 4 (Figure 6b). Due to the gradual nature of flow centralization under constant discharge (during a single secondary event), this process of channel centralization is not fully attributed to a decrease in discharge. As channels centralized they also incised into the fan surface ( Figure S5a in Supporting Information S1). This channel incision differed from autogenic periods of incision and sheetflow observed in other fan and fan-delta experiments (Hamilton et al., 2013;Hoyal & Sheets, 2009;Kim & Jerolmack, 2008;Kim & Paola, 2007;Van Dijk et al., 2009. In our experiments, incision increased progressively over the course of secondary events until being halted by allogenic forcing; incision did not resolve into aggrading sheetflow under constant discharge.

Avulsion
For our experiments, a channel was defined as any continuous wet portion of the fan surface whose source was traceable to the fan apex. We followed the Bryant et al. (1995) definition of avulsion: the formation of a new channel carrying over 50% of the discharge from the previous channel, and occurring near the fan apex. Channel changes which met these criteria within the one-minute time interval between photographs were considered avulsions.
We conducted a manual analysis of avulsion frequency over Phase 2 of the experiments wherein avulsions were characterized visually at one-minute intervals using the orthomosaics. The characterization of avulsion frequency was limited to Phase 2 to compare avulsion characteristics across the different Phase 2 flood events. Avulsions occurring within 0.25 m of the fan apex, that is, the top 35%-50% of the fan by radius, were included. Avulsions occurring on more distal, minor fan channels were excluded from this analysis. To eliminate bias, the results of 10 of 16 the manual avulsion assessment were validated with an automated analysis which used the binary channel maps to chart abrupt changes in channel patterns. Although the automated method was more sensitive to channel shifting than the manual method, the two methods identified many of the same avulsion events to within 5 min ( Figure  S6 in Supporting Information S1).
Avulsion became less frequent with increasing secondary event duration (Figure 7). Our manual avulsion count indicated that in Phase 2, 20 avulsions occurred in Experiment 1 (5 min secondary events), while only 12 avulsions occurred during Experiment 4 (40 min secondary events). In general, avulsions were reflected in the number of channels observed 0.25 m from the fan apex, plotted in gray on Figure 7. Of the 65 avulsions observed during Phase 2 of the four experiments, 50 avulsions (77%) were associated with a change in the number of fan channels. In addition, the time at which the avulsions first occurred was earliest for Experiment 1 and latest for Experiment 4. That is, avulsion occurred both sooner after the onset of flooding and more frequently in experiments with shorter secondary events. On natural fans, this implies that high-frequency debris-flow or debris-flood creeks are more likely to avulse than in low flood-frequency systems. Reitz et al. (2010) suggested that avulsion follows a predictable frequency set by the conservation of mass. Their experiments indicated that avulsion frequency is tied to fan radius and may be predicted by estimating the time required to fill a channel of a certain width and depth under a given sediment feed rate. They estimated ( ) , the characteristic avulsion timescale: where is the typical channel depth, is the average wetted width, ( ) is the mean fan radius at time and is the sediment feed rate (or sediment transport rate in natural streams).
We calculated the expected avulsion timescale for each experiment using Equation 1 and an estimated channel width and depth of 20 and 0.33 cm, respectively. The channel width of 20 cm was based on measurements of 11 of 16 typical fan channel dimensions from the orthomosaics. The channel depth was an average value taken from channel incision measurements throughout Phase 2. It should be noted that measurements of channel incision from the DEMs were considered underestimates due to refraction occurring on wetted portions of the fan (see Section 3). As a result, channel incision measurements were limited to measurements taken on dry fan surfaces (and corroborated by manual measurements of the fan surface). However, these measurements are sparse relative to wetted fan data, and the following estimates of predicted avulsion frequency could be improved by real-time monitoring of channel depth.
We estimated the avulsion timescale for Phase 2; due to the data limitations described above, we estimated the average timescale across all three flood types (A-C). Expected avulsion timescales ranged from approximately 150 s for Experiments 1 and 2 to 170 s for Experiments 3 and 4, and increased progressively as fan area increased. From these timescales, the Reitz et al. (2010) equation predicted ∼18 avulsions during Phase 2 for Experiments 1 and 2 and ∼16 avulsions during Phase 2 for Experiments 3 and 4. These projected values for avulsion predicted within 10% the observed avulsions throughout Phase 2 for Experiments 1 through 3 (Figure 7). The over-prediction of avulsion events for Experiment 4 indicates that the decrease in avulsion frequency for this experiment cannot be explained entirely by increased fan area.
While avulsions occurred during each of the three flood sequences, in Experiments 1 and 2 the avulsion count was highest for Flood C which had the greatest input sediment concentration (∼13%). This aligns with previous work suggesting that avulsion frequency is proportional to sediment concentration (Ashworth et al., 2004;Bryant et al., 1995;De Haas et al., 2016;Reitz et al., 2010). It is also intuitive as higher sediment concentrations both increase flood stage because of the flow bulking but also encourage differential channel bed aggradation which further minimizes freeboard, or the vertical distance between the water's surface and the channel banks .
While Experiments 1 and 2 had the greatest number of avulsions during Flood C, Experiment 3 experienced the most avulsions during Flood B and Experiment 4's avulsions were equally distributed across all three flood types.
Although it is difficult to extract definite conclusions from these limited data, it is plausible that longer secondary events in Experiments 3 and 4 countered avulsion tendency during periods of increased sediment concentration. This may be attributed to fan channel incision, achieved by the reworking of erodible sediments which are subsequently transported toward distal portions of the fan. Fan channel incision during secondary events ( Figure S4a in Supporting Information S1) increases channel freeboard and thereby reduces avulsion potential.

Summary
Figure 8 summarizes the differences in fan and channel morphology under differing secondary event durations. Fan A was formed under shorter secondary events (Experiment 1) while Fan B was formed under longer secondary events (Experiment 4). Fan A is smaller and steeper. Numerous braided channels are present on the surface of Fan A and there is negligible channel incision. The intersection point (where an incised channel reaches the fan surface) is located approximately half way down-fan from the apex. Conversely, Fan B is larger and has a shallower gradient. It has a single channel which is incised, and the intersection point is located further from the fan apex, in the bottom third of the fan.

Discussion
In our experiments, the duration of secondary events had a profound impact on both fan morphology and behavior during floods. Each of the four fans was created with the same volume of sediment; the only difference was the duration of secondary events between each fan-building flood. Secondary events were run for periods of 5, 10, 20, and 40 min for Experiments 1, 2, 3, and 4, respectively.
The results of this study indicate that pre-flood conditions are important determinants of fan flood hazards during primary events. In our analysis, avulsion frequency and fan wet fraction were used as proxies for flood hazard. The fan wet fraction decreased notably over longer secondary event durations as flow was confined to a single centralized channel. Single-thread channels are thought to allow for greater containment of flood events and may serve to delay avulsion onset and decrease avulsion frequency in our experiments. This aligns with the findings 12 of 16 of Wasklewicz and Scheinert (2016) who demonstrated that increased channelization and incision of flow on fans can contain aggradational events and shift flood hazards down-fan.
However, while avulsion frequency decreased, no significant change in the fan wet fraction during flooding was observed across the four experiments ( Figure 6a). This indicates that while flood hazard related to avulsion may be reduced under longer secondary events, a similar area of the fan may be exposed to flow during flooding. In addition, it should be noted that while the incised channels generated by secondary events resulted in delayed avulsion, they did not prevent avulsion altogether. The conveyance of flood events through a single straightened channel results in higher shear stresses which may lead to channel bank erosion, bed infilling, and eventually avulsion.
In addition to channel characteristics, the overall fan morphology played a role in pre-flood conditions affecting flood hazard. The larger areas of fans in Experiments 3 and 4 likely provided greater potential for energy dissipation during floods. Further, these larger fans may have contributed to the increased channelization observed throughout Experiments 3 and 4. Re-centralization and straightening of fan channels increases channel efficiency (Graf & Blanckaert, 2002;Pacheco-Ceballos, 1984), allowing for the transport of additional sediment, and thereby increasing fan area. Clarke et al. (2010) hypothesized that flow channelization is related to a decrease in fan aggradation rate as fans prograde. The same positive feedback may exist in our experiments whereby increases in fan area due to channelization in turn decrease aggradation rates and further encourage channelization.
Climate and sediment availability strongly influence the recurrence interval of primary events (Bovis & Jakob, 1999;Jakob, 1996;Webb et al., 2008). In many places, changes in precipitation are predicted to increase the frequency and magnitude of extreme geomorphic events in the coming century (Jakob & Lambert, 2009;Jakob & Owen, 2021;Turkington et al., 2016). The decreased recurrence interval of these events may decrease the time over which secondary processes are able to act on alluvial fans, thereby shifting the balance of material deposition and erosion on fans. In addition, increased precipitation will both mobilize in-channel sediment and increase the frequency of mass movement events within the watershed, such as shallow landslides (Jakob & Owen, 2021); potentially contributing to primary fan-building events. For fans with supply unlimited (Jakob, 1996(Jakob, , 2021 source basins, climate change will likely result in a greater frequency of primary fan-building events arriving at the fan apex. Such an increase in primary events would be expected to shift the fan morphology and behavior towards that of Fan A (Figure 8), producing fans with greater avulsion potential. For sediment supply limited watersheds, the frequency of debris floods (primary event) will likely increase but with decreasing sediment volumes attributable to the lesser time available for channel sediment recharge. This would result in a shift towards the fan morphology and behavior typical of Fan B (Figure 8).
In addition to climate change, other variables such as land use change, forest fires, or increased landslide activity in the watershed may alter the balance of primary and secondary events acting on the fan. The impacts of these changes on fan morphology will need to be investigated through further experimentation and field studies.
While the boundaries between primary and secondary events were clear in the controlled environment of our experiments, flood events on natural fans exist upon a spectrum between these two theoretical end-members. As mentioned previously, in the case of debris flows, vertical scour and channel degradation may be initiated during the primary event by the less viscous tail, or afterflow (Iverson, 1997;Jakob et al., 2013;Takahashi, 2014), producing effects normally associated with secondary processes. This was the case at Neff Creek, southern British Columbia, where channel erosion was thought to have begun during the debris flow itself. Ultimately, the afterflows of the primary event resulted in vertical erosion of the channel to depths of 14 m (Lau, 2017) indicating that channel incision does not exclusively occur as a secondary process. A precise separation of primary and secondary geomorphic processes on natural fans is not possible nor commensurate with observed fan behavior. While our results provide general conclusions on the impacts of primary and secondary events (broadly defined), this complexity should be considered when interpreting results at the event scale.

Conclusion
Despite several decades of alluvial fan experimentation and research, the focus has remained on primary (fan-building) events. The influence of secondary (fan-reworking) events on fan evolution, morphology, and flood hazard has largely been neglected. The objective of this study was to advance our understanding of secondary events on steep alluvial fans. This was achieved through four experiments that isolated the impacts of secondary event duration. The results yield insight into the emergent properties of the fan system under different secondary event durations.
Our results suggest that: 1. Fan morphology may be strongly influenced by secondary event duration. In our experiments, fans formed during longer secondary events were larger and had gentler gradients. 2. The morphologic features produced during secondary events -including channel incision and centralization of flow paths -act to contain primary fan-building events by channelizing floods and decreasing the overall fan wet fraction. The fan reworking that occurs during secondary events is therefore an important determinant of fan flood hazards associated with the more destructive fan-building primary events. 3. Decreased secondary event durations result in increased avulsion frequency and earlier avulsions during fan-building primary events. Conversely, increasing length of secondary events delays avulsions and reduces their frequency.
These findings highlight the importance of understanding antecedent morphologic fan conditions in estimating the overall flood hazard. While our results hold true in an experimental setting, much work remains to support these data with detailed long-term observations on fan adjustments during and after primary and secondary fan events. Scaling limitations must be considered when interpreting our results; in particular, extrapolations of rates and volumes of sediment transport measured in our model should be validated against field data from the fan of interest.