In the spring of 2020, the town of Fort McMurray, which lies on the banks of the Athabasca River, experienced an ice-jam flood event that was the most severe in approximately 60 years. In order to capture the severity of the event, a stochastic modelling approach, previously developed by the author for ice-jam flood forecasting, has been refined for ice-jam flood hazard and risk assessments and ice-jam mitigation feasibility studies, which is the subject of this paper. Scenarios of artificial breakage demonstrate the applicability of the revised modelling framework.

  • Extreme flood events require flood hazard assessments to be updated.

  • Dependency of the volume of ice to river discharge improves modelling ice-jam flood ensembles.

  • Focused ice-jam lodgements improve the calibration of the stochastic modelling framework.

  • Stochastic modelling increases the efficacy of artificial ice-cover breakage scenarios.

Data from recent extreme events and the additional data available since the last assessment was carried out will lead to adjustments in the frequency distributions of flows and water levels since such distributions are sensitive to the length of their time series and the severity of the extreme events within the series (Hu et al. 2020). This not only affects flows and water-level frequency distributions for open-water floods but also affects flow and stage frequency distributions of ice-induced flooding of northern rivers. One such example is the town of Peace River along the Peace River in western Canada which responded to the 1992 and 1997 ice-jam events, the two largest events on record, by raising dike crest elevations and inserting extra flood defense walls in keeping with the revised design flood threshold levels (although it should be noted that the dike elevations were designed to a 1:100 AEP (annual exceedance probability) open-water flood level, not to ice-jam flood levels) (Lindenschmidt et al. 2016). In the town of Peace River, ice-jams lead to more severe floods than those of open-water alone; hence, the probability of overtopping is higher from an ice-induced flood than an open-water flood. Another example where new flood hazard assessments are periodically carried out is the town of Fort McMurray along the Athabasca River, also in western Canada, where the most extreme flood levels are also induced by ice-jams.

The behaviours of ice-jams and their flooding are chaotic in nature, in which small shifts in the
  • morphology of the ice-jams (e.g. additional inflowing ice accumulating at the ice-jam front can extend the ice-jam cover upstream (top panel of Figure 1) or shove into the ice cover to shorten and thicken the ice-jam (middle panel of Figure 1)),

  • location of the ice-jams (e.g. if the toe of the jam slips a short distance downstream (bottom panel of Figure 1), where the changing fluvial geomorphology can cause changes in flow fields underneath the ice-jam and in the backwater level elevations), or

  • physical characteristics of the ice-jam cover (e.g. smoothing of the ice-cover underside due to thermal erosion (also shown in the bottom panel of Figure 1), due to the flowing water, resulting in a decrease in drag and flow resistance along the ice-jam),

Figure 1

Ice-jam with incoming ice accumulating at the ice-jam cover front to either top panel: extend the ice-jam cover in the upstream direction, middle panel: shove ice into the jam to thicken it, or bottom panel: shift the ice-jam toe to change the ice-jam's morphology and backwater staging; thermal erosion can smoothen the underside of the ice-jam cover to decrease resistance to flow and lower backwater levels.

Figure 1

Ice-jam with incoming ice accumulating at the ice-jam cover front to either top panel: extend the ice-jam cover in the upstream direction, middle panel: shove ice into the jam to thicken it, or bottom panel: shift the ice-jam toe to change the ice-jam's morphology and backwater staging; thermal erosion can smoothen the underside of the ice-jam cover to decrease resistance to flow and lower backwater levels.

Close modal
can influence the backwater flood levels along the river. Other reasons for the chaotic nature of ice-jams include variable toe and head locations from year to year, sometimes forming so far downstream as to have no backwater effect at the studied site.
Empirical relationships for water level vs. discharge can generally be established for open-water floods, for example, as a rating curve as shown for the Athabasca River gauge downstream of Fort McMurray in Figure 2. Due to their chaotic behaviours, however, this is not the case for ice-induced floods. At best, the water level vs. discharge data is scattered in an area of the plot that can be encompassed by an envelope, also shown in Figure 2. Just like for open-water flood levels, though, ice-induced floodwater level elevations can also be fit to extreme value distributions.
Figure 2

Water-level elevation vs. discharge data recorded at the Athabasca River gauge downstream of Fort McMurray (gauge # 07DA001).

Figure 2

Water-level elevation vs. discharge data recorded at the Athabasca River gauge downstream of Fort McMurray (gauge # 07DA001).

Close modal

To capture the chaotic nature of ice-jams, the author has developed a stochastic modelling approach to mimic the probabilistic nature of ice-jam flooding. In this approach, a deterministic (repeatable output for a single set of inputs) river ice hydraulics model is embedded in a Monte-Carlo framework which allows many simulations of the model to be executed automatically. Each simulation has a different set of input values for the parameters and boundary conditions, which are extracted randomly from frequency distributions. The Monte-Carlo runs yield an ensemble of backwater level profiles, from which profiles of floodwater level exceedance probabilities can be extracted. The methodology was first developed for the assessment and mapping of flood hazards and risks for the town of Peace River (Lindenschmidt et al. 2015, 2016) and was then extended to forecast ice-jam flooding along the Athabasca River (Lindenschmidt et al. 2019), lower Red River (Williams et al. 2021), and Saint John River in eastern Canada (Das et al. submitted). The method has been applied operationally to forecast ice-jam flooding along the lower Churchill River in Labrador (Lindenschmidt et al. 2020, 2021) and the Exploits River in Newfoundland (Warren et al. 2017). Applying the method for flood hazard and risk assessments proved to be useful in evaluating the best options to mitigate ice-jam floods in Fort McMurray (Das & Lindenschmidt 2021a, 2021b, 2021c).

The method required refinement so that the water-level exceedance probabilities from the modelled ensembles could attain the new and higher elevations of the return periods calculated from the gauged and surveyed data. Refinements included the following:

  • Relating the volume of ice constituting ice-jams to the river discharge; there can be much scatter in this relationship (Beltaos 2021); a confidence band of the volume rate of ice vs. discharge helps attain more extreme ensemble backscatter level profiles when the flooding effect of high flows is compounded by higher volumes of ice.

  • In the previous development, due to lack of data, the locations of the ice-jam lodgements were assumed to be uniformly distributed along the river chainage; more data has allowed lodgement locations to be concentrated in certain reaches where more ice-jams have occurred in the past.

  • Setting the water level at the downstream boundary condition of the model was made to be a function of the upstream discharge.

The three important objectives are as follows:

  • include historical data in the stage frequency analysis to capture the severity of these events in the analysis;

  • introduce refinements to the stochastic modelling approach to help attain the level of flood severity reflected in the frequency analysis of the observed data; and

  • demonstrate the refined modelling framework's applicability by simulating scenarios of artificial breakage for ice-jam flood mitigation.

Site description

Fort McMurray lies at the confluence of the Athabasca and Clearwater rivers, as indicated in Figure 3. The general flow direction is northward and when ice-jams occur downstream of the confluence, there is a tendency for the ice-jam backwater to push up into the Clearwater River and overflow the banks, thus inundating the floodplain on which downtown Fort McMurray lies.
Figure 3

Fort McMurray located at the confluence of the Athabasca and Clearwater rivers (modified from Lindenschmidt 2017).

Figure 3

Fort McMurray located at the confluence of the Athabasca and Clearwater rivers (modified from Lindenschmidt 2017).

Close modal
The mild slope of the Clearwater River allows the effect of Athabasca River water to persist farther upstream into the Clearwater River rather than the Athabasca River, as illustrated in Figure 4. Additionally, ice runs travelling downstream along the upper Athabasca River reach flow past the bridge into the lower reach which is less steep (also illustrated in Figure 4) and wider, allowing the flow to decelerate and providing greater opportunity for ice to lodge and form ice-jams. The many islands and sandbars also make the area immediately downstream of the bridge susceptible to ice lodgements.
Figure 4

Thalwegs of the Clearwater River and the upper and lower reaches of the Athabasca River.

Figure 4

Thalwegs of the Clearwater River and the upper and lower reaches of the Athabasca River.

Close modal

Ice-jamming is a regular occurrence along the Athabasca River during the spring ice-cover breakup with some of the most severe flooding having occurred in the springs of 1979, 1997, and 2020, as labelled in the water-level elevation vs. discharge plot in Figure 2. The most recent extreme event of 2020 caused insured damages amounting to over a half billion dollars (IBC 2020).

River hydraulic model RIVICE

RIVICE is a one-dimensional hydrodynamic (full dynamic wave) model with river ice processes integrated within the hydraulic processes, allowing an exchange of data between the two processes to occur after each time step (loosely coupled approach). An important river ice process in the model specific to spring breakup is the accumulation of ice floes at the ice-cover front, indicated by the incoming volume rate of ice Vice in Figure 5. The ice volume added to the ice cover can either juxtaposition to extend the ice cover in the upstream direction or shove into the ice cover, thus moving the ice-cover front downstream and thickening the ice-jam cover. Important parameters for these processes include (see Figure 5) the porosity of the ice-cover PC and the thickness of the ice-cover front FT. A roughness coefficient of the ice n8 influences the amount of drag along the ice-cover underside caused by the flowing water. The riverbed, too, contributes to the flow resistance using Manning's coefficient nb. Shoving of the accumulated ice into the ice cover due to the thrust of the flowing water against the ice-cover front, the drag of the water flow along the ice cover, and the weight of the jamming ice in the sloping direction are all resisted by friction (parameterised by K1) between the ice cover and the riverbanks and the stability of the ice-jam through its thickening (parameterised by K2). Ice can also erode from the ice cover if the mean flow velocity exceeds an erosional threshold velocity ve, to be transported further downstream. This ice-in-transit can be deposited along the ice-cover underside when the mean flow velocity drops below a depositional threshold velocity vd. Thicknesses of the intact ice cover h, against which the ice-jam abuts, and the ice floes ST are also required input to the model. Important boundary conditions include the upstream discharge and volume of ice, the downstream water-level elevation W, and the location of the ice-jam toe x.
Figure 5

Parameters and boundary conditions used to drive river ice processes in RIVICE.

Figure 5

Parameters and boundary conditions used to drive river ice processes in RIVICE.

Close modal

Rubble ice describes the ice floes arriving at the ice-jam front from upriver to supplement the volume of ice in the jam and extend the length of the ice-jam cover. This ice can be thicker than the intact (thermal) ice-cover thickness h downstream of the ice-jam since it may stem from consolidated ice covers, which is often the case for ice formed along the Athabasca River upstream of Fort McMurray. Hence, the front FT of the ice-jam cover can be quite thick. The volume of ice is expressed as the rate of running ice (with voids characterised by porosity PS) that arrives at the ice-jam from upriver. This volume does become the volume of ice within the ice-jam cover. The simulation stops when the ice-jam front reaches a user-specified location, generally just downstream of the upstream boundary.

Measured and estimated values of ice-jam porosities are reported by White (1999, Table 4 and Figure 12) and can vary widely, between approximately 0.2 and 0.9. There is a tendency for higher porosities to be found in frazil-deposited ice-jams compared to breakup ice-jams and the values can vary greatly along the length and thickness of the ice-jam (White 1999). Values of porosity are generally smaller (between 0.35 and 4.5) for shoved sections of the ice-jam but can have a wider range for hanging dams (between 0.24 and 0.89) (White 1999, p. 16–17). Ice porosities for the 1977 and 2020 ice-jam events were calibrated somewhat higher when air temperatures dropped below freezing potentially allowing frazil ice to have been formed and accumulated in the ice-jams.

A river ice model from previous modelling exercises and stochastic modelling framework developments (Lindenschmidt 2017, 2020) used cross-sections from several surveys carried out in the 1970 and 1980s. The modelling was updated using new cross-sections surveyed during a recent flood hazard study of Fort McMurray (H&G 2018). Figure 6 shows the thalweg of the two model thalwegs, indicating a close resemblance in the profiles of the river bottom elevations. The newer cross-sections used for the update were surveyed with a finer spatial resolution; however, they did not span along the entire modelling domain and hence were nested into the domain of the previous model setup. This retained the long extent of the domain required to capture the entire length of ice-jams, which can extend as much as 25 to 30 km in length upstream from the area at and downstream of the confluence. Additional cross-sections were interpolated to a spacing of 50 m.
Figure 6

Comparison of profiles of thalwegs using cross-sections surveyed in the 1970 and 1980s (old) with those surveyed recently in 2015–2018 (new).

Figure 6

Comparison of profiles of thalwegs using cross-sections surveyed in the 1970 and 1980s (old) with those surveyed recently in 2015–2018 (new).

Close modal

Stochastic modelling framework

Figure 7 conceptualises the Monte-Carlo framework for the stochastic modelling approach. Flows during ice-jam events are estimated from observed data to establish a flow frequency distribution, indicated by [i] in Figure 7 and the left panel of Figure 8. The volume rate of ice is treated as a function of flow, Vice = f(Q), as shown in [ii] in Figure 7. The Vice vs. Q data was determined from calibrated models of the ice-jam events of 1977, 1978, 1979, 1997, 2015, and 2020, as shown in the middle panel of Figure 8. An exponential curve was fit to the data with a confidence band. For a certain flow chosen randomly from the flow frequency distribution ([i] in Figure 7), random values of Vice, uniformly distributed, are chosen between the upper and lower confidence bounds ([ii] in Figure 7). The downstream boundary condition of water-level elevation is also a function of flow ([iii] in Figure 7) determined from simulations with an ice cover using a range of flows in which a normal depth condition (water-level slope equals the bed slope) was maintained at the downstream boundary. The distribution of ice-jam toe locations ([iv] in Figure 7) was extracted from a stepped uniform distribution with a higher concentration of jam lodgements along the 8 km stretch immediately downstream of the Clearwater River mouth compared to the next stretch of 5 km further downstream (ratio of 6:4 ice-jam lodgements that impact water levels at the Clearwater River mouth), shown in the right panel Figure 8. Values for the parameters p1, p2, …, pn are drawn from uniform distributions ([v] in Figure 7) from ranges between the minimum and maximum values determined from the calibration of many ice-jam events (Rokaya & Lindenschmidt 2020).
Figure 7

Stochastic modelling framework.

Figure 7

Stochastic modelling framework.

Close modal
Figure 8

Input to the Monte-Carlo framework – left panel: flow frequency distribution, middle panel: volume rate of ice vs. flow relationship and right panel: distribution of ice-jam lodgements downstream of the Clearwater River mouth.

Figure 8

Input to the Monte-Carlo framework – left panel: flow frequency distribution, middle panel: volume rate of ice vs. flow relationship and right panel: distribution of ice-jam lodgements downstream of the Clearwater River mouth.

Close modal

Once a set of parameter and boundary condition values has been extracted from each of their corresponding frequency distributions or functions, a simulation is carried out. The process was repeated 1680 times (Monte-Carlo analysis labelled [vi] in Figure 7) to yield an ensemble of backwater level profiles ([vii] in Figure 7). The high number of runs is deemed sufficient to provide statistics on the backwater profiles that can be summarised using 0.5, 1 and 2 percentile profiles, which correspond to the 1:50, 1:100, and 1:200 AEP profiles ([viii] in Figure 7). The elevations of the percentile profiles are compared to the return periods calculated from the instantaneous water-level maxima observed at the Clearwater River mouth and the Athabasca River (WSC) gauge ([ix] in Figure 7). If they do not coincide, the confidence level of the Vice = f(Q) relationship ([ii] in Figure 7) is adjusted and the Monte-Carlo process is repeated until the ensemble percentiles ([viii] in Figure 7) and the observed return periods ([ix] in Figure 7) coincide. To gain confidence in the results, the process is repeated several times, with each time outputting a slightly different set of percentile profiles, which are then averaged to yield the final profile. At this point, the framework is deemed calibrated.

Model calibration

Models of six ice-jam flood events were calibrated to determine a range of Vice vs. Q values and the minimum and maximum ranges of the parameter settings (see Supplementary Material). Figure 9 shows the calibrated profiles of the maximum backwater level elevations for 1977, 1978, 1979, 1997, 2015, and 2020 ice-jam events. Two objective functions were used for the calibration – highwater mark elevations and upstream extent of the ice-jam cover. Highwater marks were drawn from gauge data and reports by Doyle (1977), Andres & Doyle (1984) and Nafziger et al. (2021). Ice-cover extents were extracted from Friesenhan (2004) and Das & Lindenschmidt (2019). Satellite imagery was also available to determine the ice-cover extent of the 2020 ice-jam. Data were the sparsest for the 1997 event with only one highwater mark available. The extent of the 1978 ice-jam fell slightly short to avoid model instabilities when the ice-cover front approached the upstream boundary too closely.
Figure 9

Models of ice-jam events from 1977, 1978, 1979, 1997, 2015 and 2020.

Figure 9

Models of ice-jam events from 1977, 1978, 1979, 1997, 2015 and 2020.

Close modal

For the 2015 ice-jam event, the ice-jam toe was reported to be 12 km downstream from the bridge (chainage = 36,600 m). However, the highwater mark at the WSC gauge is more than 3 m lower than the highwater marks at the Clearwater River mouth and the bridge. With such a large difference in these highwater marks, the model could only be calibrated assuming that there was a second ice-jam toe further upstream between the mouth and the gauge. Having two lodgements within an ice-jam is not uncommon for the Athabasca River as the 16 April 1977 ice-jam event demonstrates (Doyle 1977). Much more ice accumulated at the upstream lodgement than at the downstream lodgement.

For the 2020 ice-jam event, the 2,700 m3/s flow at the upstream boundary of the model is 400 m3/s more than that used for a simulation of the ice-jam by H&G (2022) using HEC-RAS, elaborated in Nafziger et al. (2021). The modelling carried out by H&G (2022) used highwater marks to calibrate their mode; two data sets, highwater marks and the extent of the ice-jam cover were used to calibrate the modelling in my study. Because the location of the ice-jam head and toe are known, the ice-jam volume, the ice roughness, discharge, and porosity of rubble ice, and the ice-jam become important calibration variables for model calibration. The volume of ice within the ice-jam was simulated to be 31 million m3, which is in line with H&G (2022)’s estimate of the ice volume being greater than 28 million m3.

Stage frequency distributions

Maximum water-level elevations at the Clearwater River mouth and the Athabasca River gauge were provided until the early 2000s by Robichaud (2003) and Peters (2003), respectively. The time series for the 2000s, until 2021, were complemented with observations drawn from the Athabasca River gauge or from Alberta Environment and Parks (pers. comm. with Bernard Trevor). In total, there are 38 years for the recent time series, from the early 1960s to the present, with gaps in the series (see Figure 10).
Figure 10

Highwater marks recorded at the Clearwater River mouth and the Athabasca River gauge; historical observations are only available for the Clearwater River mouth.

Figure 10

Highwater marks recorded at the Clearwater River mouth and the Athabasca River gauge; historical observations are only available for the Clearwater River mouth.

Close modal

The data from the Clearwater River mouth include historical data, the largest event being from 1875, which has been estimated to have reached an elevation of 252 m a.s.l. (Hatch 2017). Figure 10 shows the observations for both recent and historical data. The programme HQ-EX 3.0 from the consulting firm DHI WASY GmbH in Berlin, Germany was used to construct the stage frequency distributions with historical data, which uses an algorithm of repeated blocks of the recent time series to fill in the gaps between the recent time series and historical events. Distributions available in the software include Gumbel, generalised extreme value, Rossi, log-normal, Pearson type 3, log-Pearson type 3 and Weibull fitted to plotting positions using the method of moments, maximum likelihood, and mixing distribution. For the analysis with historical data, gaps within the recent time series are not allowed; hence, the analysis was carried out with the recent time series of 38 consecutively years falling within two 38-year time frames, an earlier one of 1962–1999 and a later one of 1983–2000. The parameters of the distributions – location, scale, and shape – of the two analyses were averaged to obtain the resulting stage frequency distribution.

Historical data for the Athabasca River gauge were not available. However, to make the stage frequency distributions comparable, historical data needed to be generated. Hence, for the recent time period, an empirical relationship was determined between the highwater marks recorded at the gauge and those observed at the Clearwater River mouth, as shown in Figure 11. The equation was then used to derive estimated historical water-level elevations at the gauge using the correlation with the elevations that were reached historically at the mouth. Although uncertainties exist in extrapolating historical water levels from one gauge location to another, such estimates are deemed necessary to provide more reliable frequency distributions. Without the consideration of historical flood information, return periods of flood events can be grossly underestimated. This can lead to grave consequences for flood management, as was the case for the catastrophic flood event of the Ahr River catchment in Germany in the summer of 2021 (Vorogushyn et al. submitted). The best three fitted distributions were used to provide a range of the return periods, 1:50, 1:100, and 1:200 AEP, which are plotted in Figure 12 along the reach spanning from just upstream of the Clearwater River mouth to immediately downstream of the Athabasca River gauge. These are compared with the results from the ensemble runs, which are described next.
Figure 11

Relationship between the highwater marks recorded at the Clearwater River mouth and the Athabasca River gauge.

Figure 11

Relationship between the highwater marks recorded at the Clearwater River mouth and the Athabasca River gauge.

Close modal
Figure 12

Percentile profiles of the ensemble runs coinciding with the return periods calculated from the observed data from the Clearwater River mouth and the Athabasca River gauge.

Figure 12

Percentile profiles of the ensemble runs coinciding with the return periods calculated from the observed data from the Clearwater River mouth and the Athabasca River gauge.

Close modal

A total of 1,680 model runs were carried out using the Monte-Carlo framework, to yield an ensemble of 1,680 backwater level profiles. The 0.5, 1, and 2 percentile profiles, respectively corresponding to the 1:200, 1:100, and 1:50 AEP, are plotted in Figure 12 for a short reach of the model domain extending from the Clearwater River mouth to the Athabasca River gauge. The profiles overlay the return periods from the observed data, indicating a well-calibrated stochastic modelling framework and represent the flood hazard status quo for Fort McMurray. For reference, the 2020 ice-jam profile is also included and lies somewhat higher than the 1:50 AEP level at the Clearwater River mouth, which coincides with what is reported in Nafziger et al. (2021), that ‘the 2020 ice-jam produced water levels between the 1:50 and 1:100 AEP ice-jam water levels at Fort McMurray’. An important variable in the modelling framework that was fine-tuned to improve the calibration was the confidence level of the confidence band of the volume rate of ice vs. flow data (Vice vs. Q), indicated by [ii] in Figure 7, which was set from 95% initially, to a final setting of 85%. The narrower confidence band was required to constrain the scatter between Vice and Q. Also, concentrating more ice-jam toe locations in the stretch immediately downstream of the Clearwater River mouth helped to obtain more extreme backwater level profiles to raise the percentile profiles to the corresponding observed return period elevations.

Due to the flatness of the lower reach of the Clearwater River, the backwater flooding mechanism and the floodwater level elevation at the river's mouth can be extended horizontally over the floodplain on which downtown Fort McMurray is built, to map flood depths and extents throughout the town, a practice which was applied and justified in Lindenschmidt (2020) and Lindenschmidt et al. (2022). The hazard map for the 1:100 AEP ice-jam flood is provided in Figure 13.
Figure 13

Flood hazard map of downtown Fort McMurray for a 1:100 AEP ice-jam flood event (from Lindenschmidt et al. 2022).

Figure 13

Flood hazard map of downtown Fort McMurray for a 1:100 AEP ice-jam flood event (from Lindenschmidt et al. 2022).

Close modal
To demonstrate the applicability of the stochastic modelling framework beyond calculating the status quo of the ice-jam flood hazard for the town of Fort McMurray, scenarios were carried out to determine the effectiveness of reducing the flood hazard by artificially breaking the ice cover downstream of the Clearwater River mouth just before spring breakup. Artificial breakage is carried out to reduce the effect of ice-jams by breaking an area of ice where ice-jam lodgements are to be hindered, which, for the Athabasca River, would be a reach extending downstream from the Clearwater River mouth. This can be achieved using various mechanical methods such as ice breakers or amphibex machines, which have been used extensively along the Red River in Manitoba, Canada, one of which is shown in Figure 14. The amphibex has an excavation claw on its front to help pull the machine up onto an intact ice cover. The weight of the machine then cracks and breaks through the ice cover. For very thick ice, slots are precut into the ice cover to weaken it, making it easier for the amphibex to break through.
Figure 14

Amphibex machine used to artificially break up ice on rivers (from ECO Technologies 2021; used with permission).

Figure 14

Amphibex machine used to artificially break up ice on rivers (from ECO Technologies 2021; used with permission).

Close modal
Conceptually, the same Monte-Carlo framework that was set up for the status quo flood hazard simulations is applied with one difference in the variable setting. As indicated in Figure 15, the ice-jam toe locations along the chainage where artificial breakage is to be carried out are removed from the boundary condition setting (see [IV] in Figure 15). Random numbers are chosen only from locations where the ice cover remains intact, not where the ice is broken up. Two scenarios were carried out, each with 1,680 runs: Scenario 1 with breakage along a 4-km stretch and Scenario 2 with breakage along an 8-km stretch, both stretches starting at and extending downstream from the Clearwater River mouth. Ice-jam lodgements were not set in the part of the model domain where the ice cover was to be artificially broken up. A change in the elevations of the AEP profiles is expected (see [VIII] in Figure 15). Again, the process is repeated several times to obtain slightly different sets of AEP profiles, due to the randomisation of different sets of numbers. These are then averaged to yield the final profiles.
Figure 15

Adjustments (shown in grey) in the stochastic modelling framework to accommodate scenarios of artificially breakage.

Figure 15

Adjustments (shown in grey) in the stochastic modelling framework to accommodate scenarios of artificially breakage.

Close modal

An important assumption for these artificial breakage scenarios is that there is no possibility of ice-jamming occurring within broken-up stretches. This is not always the case, however, and experience on the Red River has shown that ice-jams do occur even in stretches of the river which were previously broken up, as described in Lindenschmidt (2020). Another assumption is that the volume rate of ice distribution remains the same as for the status quo. This may not be the case, however, for it is not known (i) how much of the extra water exposed to the freezing air temperatures, after the ice is broken up, freezes to create additional ice that can accumulate in ice-jams, or (ii) how much melting of the ice rubble occurs when more ice surfaces from the broken-up pieces come in contact with the water during artificial breakage. Hence, no change in Vice is assumed for the scenario simulations.

For the 4-km ice-cover breakage scenario (see top panel of Figure 16) all AEP profiles dropped at the Clearwater River mouth, which helped to reduce the flood hazard in Fort McMurray, particularly for the more extreme 1:200 AEP event (1.33 m drop). At the gauge location, however, there is an increase in the AEP profiles, with higher elevation changes for the less extreme event. This is due to the fact that within the simulations, ice-jam lodgements are not occurring upstream of the gauge any longer, but now only downstream of the gauge. The artificial breakage has shifted the flood hazard downstream, away from the Clearwater River mouth to the gauge location. This often happens in flood hazard mitigation in which a reduction of hazard in one area can increase the hazard in another. Since ice-jam lodgements were not included in the model scenario for the 4-km breakage stretch, the ice-jam toe locations are further downstream with more ice-jam toes concentrated in the reach downstream of the gauge. However, the focus of the mitigation strategy is to reduce flood water levels at the Clearwater River mouth, which this scenario appears to do. Although increased flood hazard at the gauge may not have a large flood impact in the vicinity of the gauge, further study is required to confirm this. Figure 17 summarises the elevation changes of each of the AEP profiles for the 4- and 8-km scenarios.
Figure 16

AEP profiles for artificial breakage of a 4 km stretch (top panel) and an 8 km stretch (bottom panel) starting at and extending from the Clearwater River mouth.

Figure 16

AEP profiles for artificial breakage of a 4 km stretch (top panel) and an 8 km stretch (bottom panel) starting at and extending from the Clearwater River mouth.

Close modal
Figure 17

Changes in the elevations (negative values indicate a drop, positive values a raising of the elevation) of the annual exceedance probabilities due to 4 and 8 km artificial breakage of the ice cover downstream of the Clearwater River mouth.

Figure 17

Changes in the elevations (negative values indicate a drop, positive values a raising of the elevation) of the annual exceedance probabilities due to 4 and 8 km artificial breakage of the ice cover downstream of the Clearwater River mouth.

Close modal

For the 8-km breakage scenario, additional drops in backwater levels were simulated at the Clearwater River mouth (see bottom panel of Figure 16). The additional drops are not as substantial as the initial drop incurred by the 4-km-only breakage scenario (see Figure 17). Again, there are elevation increases at the gauge but not as high for the 8-km breakage scenario as they were for the 4-km breakage scenario. This again reveals the shifting of more extreme flood hazard further downstream as artificial breakage is carried out further downstream. It appears that longer stretches of breakage downstream of the Clearwater River mouth move the toe location and the extreme ice-jam backwater levels further downstream.

An amphibex machine has difficulty breaking ice thicker than ∼0.6 m, as is the case near Fort McMurray; moreover, the Athabasca River is much wider than the Red River. Depending on how many machines are deployed, it might require several weeks to break 4 or 8 km of ice. During this time, below-zero air temperatures may cause ice fragments to freeze together again. Altogether, it is not clear that ice breaking is a feasible mitigation measure near Fort McMurray, an important point from this study is that the updated MOCA model is capable of quantifying the benefits of ice breaking in situations where ice breaking would be feasible.

Refinements to a stochastic modelling framework were successfully applied to capture the severity of the 2020 ice-jam flood in Fort McMurray. The refinements included establishing a dependency between the volume of ice accumulating in ice-jams and upstream discharge. Concentrating the ice-jam toe locations in areas where more ice-jams have occurred in the past helped to attain the extreme exceedance flood levels reflected in the return periods of the observed water-level elevations. Including historical data in the frequency analyses provided a better description of the return periods. The framework allowed scenarios to be run for mitigating ice-jam flooding by artificial breakage of the ice cover downstream of the Clearwater River mouth. There is a substantial drop in the flood hazard at the Clearwater River mouth when 4 km of the reach's ice cover broke up. Further breakage of the cover seems to have only marginal additional impact in reducing the flood hazard in Fort McMurray. At the gauge, however, the flood hazard increases, with the increase becoming less as more ice is broken up further downstream. This shows the shift of flood hazard further downstream along the Athabasca River as more of its ice is artificially broken downstream.

The stochastic framework is a means to evaluate ice-jam flood risk reductions due to the artificial breakage mitigation option. However, there is no guarantee that ice-jams will not lodge within the broken-up areas and a probability of lodgements occurring within those areas could be integrated within the modelling framework, a topic of future work. The cost should also include the likelihood of ice-jams still occurring in the broken-up areas of the ice cover.

I would like to thank Jennifer Nafziger from Alberta Environment and Parks for providing the new cross-sections of the Athabasca River and corrected gauge data.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Andres
D. D.
&
Doyle
P. F.
1984
Analysis of breakup and ice-jams on the Athabasca River at Fort McMurray, Alberta
.
Canadian Journal of Civil Engineering
11
,
444
458
.
Beltaos
S.
2021
Assessing the frequency of floods in ice-covered rivers under a changing climate: review of methodology
.
Geosciences
2021
(
11
),
514
.
https://doi.org/10.3390/geosciences11120514
.
Das
A.
&
Lindenschmidt
K.-E.
2019
Predicting rates of water-level rise for ice-jam flood hazard assessment. CGU HS Committee on River Ice Processes and the Environment
. In:
20th Workshop on the Hydraulics of Ice Covered Rivers
,
May 14–16, 2019
,
Ottawa, Ontario, Canada
. .
Das
A.
&
Lindenschmidt
K.-E.
2021a
Evaluation of the implications of ice-jam flood mitigation measures
.
Journal of Flood Risk Management
14
,
e12697
.
https://doi.org/10.1111/jfr3.12697
.
Das
A.
&
Lindenschmidt
K.-E.
2021b
Corrigendum to ‘Evaluation of the implications of ice-jam flood mitigation measures’
.
Journal of Flood Risk Management
2021
,
e12697
.
https://doi.org/10.1111/jfr3.12759
.
Das
A.
,
Budhathoki
S.
&
Lindenschmidt
K.-E.
submitted
A stochastic modelling approach to forecast real-time ice-jam flood severity along the transborder (New Brunswick/Maine) Saint John River of North America
.
Stochastic Environmental Research and Risk Assessment
.
Doyle
P. F.
1977
Breakup and Subsequent ice-jam at Fort McMurray
.
Report SWE-77/01
.
Report by the Alberta Research Council, Transportation and Surface Water Engineering Division
.
Friesenhan
E. C.
2004
Modeling of Historic ice Jams on the Athabasca River at Fort McMurray
.
Master of Engineering report, University of Alberta
. .
H&G
2018
Ice-jam Modelling and Flood Hazard Identification Report (From the Fort McMurray River Hazard Study)
.
November 2018
.
Prepared by Hatch and Golder Associates for Alberta Environment and Parks
.
H&G
2022
Ice-jam Modelling and Flood Hazard Identification Report (From the Fort McMurray Flood Hazard Study)
.
Prepared by Hatch and Golder Associates for Alberta Environment and Parks
.
Hatch
2017
Fort McMurray River Hazard Study – Report on 1875 ice-jam Flood Assessment
.
Report 1662603_R0061_Rev.D_1875 Ice-jam Flood
.
Prepared by Hatch for Golder Associates Ltd. 2017
.
Hu
L.
,
Nikolopoulos
E. I.
,
Marra
F.
&
Anagnostou
E. N.
2020
Sensitivity of flood frequency analysis to data record, statistical model, and parameter estimation methods: an evaluation over the contiguous United States
.
Journal of Flood Risk Management
2020
(
13
),
e12580
.
https://doi.org/10.1111/jfr3.12580
.
IBC
2020
Insured Damage for Fort McMurray Flood Rises to $522 Million
.
Insurance Bureau of Canada
. .
Lindenschmidt
K.-E.
2017
Using stage frequency distributions as objective functions for model calibration and global sensitivity analyses
.
Environmental Modelling and Software
92
,
169
175
.
http://dx.doi.org/10.1016/j.envsoft.2017.02.027
.
Lindenschmidt
K.-E.
2020
River ice Processes and ice Flood Forecasting – A Guide for Practitioners and Students
.
Springer Nature Switzerland AG
, p.
267
.
https://doi.org/10.1007/978-3-030-28679-8
.
Lindenschmidt
K.-E.
,
Das
A.
,
Rokaya
P.
,
Chun
K. P.
&
Chu
T.
2015
Ice-jam flood hazard assessment and mapping of the Peace River at the Town of Peace River
. In:
CRIPE 18th Workshop on the Hydraulics of Ice Covered Rivers
,
August 18–20, 2015
,
Quebec City, QC, Canada
. .
Lindenschmidt
K.-E.
,
Das
A.
,
Rokaya
P.
&
Chu
T.
2016
Ice-jam flood risk assessment and mapping
.
Hydrological Processes
30
,
3754
3769
.
http://dx.doi.org/10.1002/hyp.10853
.
Lindenschmidt
K.-E.
,
Rokaya
P.
,
Das
A.
,
Li
Z.
&
Richard
D.
2019
A novel stochastic modelling approach for operational real-time ice-jam flood forecasting
.
Journal of Hydrology
575
,
381
394
.
https://dx.doi.org/10.1016/j.jhydrol.2019.05.048
.
Lindenschmidt
K.-E.
,
Brown
D.
,
Khan
A. A.
,
Khan
H.
,
Khayer
M.
,
McArdle
S.
,
Mostofi
S.
,
Naumov
A.
,
Pham
T.
&
Weiss
A.
2020
A novel fully-operational fully-automated real-time ice-jam flood forecasting system
. In:
25th IAHR International Symposium on Ice
,
23–25 November 2020
,
Trondheim
. .
Lindenschmidt
K.-E.
,
Brown
D.
,
Khan
A. A.
,
Khan
H.
,
Khayer
M.
,
McArdle
S.
,
Mostofi
S.
,
Naumov
A.
,
Pham
T.
&
Weiss
A.
2021
Modelling freeze-up of the lower Churchill River (Labrador) as input to an operational ice-jam flood forecasting system
. In:
CGU HS CRIPE 21st Workshop on the Hydraulics of Ice Covered Rivers
,
29 Aug.–1 Sep. 2021
,
Saskatoon, Saskatchewan
. .
Lindenschmidt
K.-E.
,
Das
A.
,
Trudell
J.
&
Russell
K.
2022
Flood hazard and risk mapping to assess ice-jam flood mitigation measures
. In:
26th IAHR International Symposium on Ice
,
19–23 June 2022
,
Montréal, Canada
.
Nafziger
J.
,
Kovachis
N.
&
Emmer
S.
2021
A tale of two basins: the 2020 river ice breakup in northern Alberta, Part 1: the Athabascsa river
. In:
CGU HS Committee on River Ice Processes and the Environment, 21st Workshop on the Hydraulics of Ice Covered Rivers
,
29 August - 1 September 2021
,
Saskatoon, Saskatchewan, Canada
. .
Peters
C.
2003
Controls on the Persistence of Water in Perched Basins of the Peace-Athabasca Delta, Northern Canada
.
PhD thesis
,
Trent University, Peterborough
,
Ontario, Canada
. .
Robichaud
C.
2003
Hydrometeorological Factors Influencing Breakup ice-jam Occurrence at Fort McMurray, Alberta
.
Master of Science thesis
,
University of Alberta
. .
Rokaya
P.
&
Lindenschmidt
K.-E.
2020
Correlation among parameters and boundary conditions in river ice models
.
Modeling Earth Systems and Environment
6
,
499
512
.
https://dx.doi.org/10.1007/s40808-019-00696-7
.
Vorogushyn
S.
,
Apel
H.
,
Kemter
M.
&
Thieken
A. H.
submitted
Analysis of Flood Hazard in the Ahr Valley Considering Historical Floods
.
Warren
S.
,
Puestow
T.
,
Richard
M.
,
Khan
A. A.
,
Khayer
M.
&
Lindenschmidt
K.-E.
2017
Near Real-time ice-related flood hazard assessment of the Exploits River in Newfoundland, Canada
. In:
CGU HS Committee on River Ice Processes and the Environment, 19th Workshop on the Hydraulics of Ice Covered Rivers
,
July 9–12, 2017
,
Whitehorse, Yukon, Canada
. .
White
K. D.
1999
Hydraulic and Physical Properties Affecting ice Jams
.
US Army Corps of Engineers, Cold Regions Research & Engineering Laboratory
,
Report 99-11, December 1999. https://apps.dtic.mil/sti/pdfs/ADA375289.pdf.
Williams
B. S.
,
Das
A.
,
Johnston
P.
,
Luo
B.
&
Lindenschmidt
K.-E.
2021
Measuring the skill of an operational ice-jam flood forecasting system
.
International Journal of Disaster Risk Reduction
52
,
102001
.
https://doi.org/10.1016/j.ijdrr.2020.102001
.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).

Supplementary data