In this work, “geospatialization” is the spatial representation of a physical characteristic of the channel and its transformation into a potential ice-jamming factor. This was done using a standard geographical information system (ArcGIS software) and some specific tools developed in ArcObject through the FRAZIL project (Gauthier and al., 2008) for the support of winter hydraulic modelling and ice jam early warning systems. These tools enable the determination of the river channel centerline, its segmentation into equal length sections, calculation of the width, and calculation of channel sinuosity along the axis (Fig. 2). Calculations were integrated along segments of equal length. Sections of 250 m were found to be optimal considering the scale at which channel characteristics vary and the size of ice jams (hundreds of metres to kilometres; Beltaos, 2008). Shorter sections overestimate narrowing and underestimate sinuosity. Long sections tend to underestimate narrowing and the impact of small features (islands, bridges). A variable length based on the homogeneity of the channel morphology could be implemented in a subsequent version of the model.

The model was applied over the entire Saint-François River (861 sections) but only over the last 110 km of the Chaudière River (444 sections) and over the last 127 km of L'Assomption River (508 sections) because there, the upstream channel becomes very narrow and spatial data representation changes from a polygon to a line. Input data came from CanVec, a digital cartographic reference product of Natural Resources Canada (Natural Resources Canada, 2017), and the Québec Topographic Database (BDTQ) (Énergie et Ressources Naturelles Québec, 2008). The planimetric accuracy of these dataset is better than 2 m. Metadata do not indicate the minimal channel width represented by polygons in the dataset. For the three rivers in this study we calculated that all sections in a polygon format were over 20 m wide, which would be the limitation of the model if using this data source. Shapefile layers include river channel, watershed, vegetated islands, bridges, rapids, and elevations.

The ice jam dataset is provided by the Québec Ministry of Public Safety (MSP). The data come from digital or paper event reports provided by local authorities under the jurisdiction of MSP (Données Québec, 2016). The database contains ice jams reported in the province of Québec from 1985 to 2016, with approximate geolocation since most jams are longer than a single coordinate and because this geolocation does not refer to the toe where the jamming process is initiated. The database is not “validated” in the sense that each event has not been compared to corresponding hydrographs, a few observed ice jams could be related to anchor ice or frazil, and reported locations do not necessarily refer to the toe where the jamming process is initiated. Therefore, validation of the model from this database is not absolute. However, it is nonetheless a unique source of information in Canada. Although proceeding to a complete validation of the database was out of the scope of this study, we have discarded observations that could not be located with enough accuracy. Furthermore, the analysis will consider not only the sections directly coinciding with an ice jam observation but also neighbouring sections where the toe could have formed. In this study, we focused on 118 historical observations: 61 ice jam reports for the Chaudière River, 33 for the Saint-François River, and 24 for L'Assomption River. The 61 ice jams listed on the Chaudière River were used as test sites for calibration of the conceptual model. Then validation of the model was performed over the other two rivers.

The conceptual model proposed here integrates the NI and the sinuosity index to establish the potential predisposition of a river channel to ice jams, the “ice jam predisposition index” (IJPI).

Figure 6 shows the results of the model applied on all 250 m sections of the Chaudière River (calibration site). High predisposition is shown in red, medium predisposition in orange, and low predisposition in green. Locations of reported ice jams are indicated with thumbtacks. The symbol is blue (correct assessment) when the ice jam falls into a section with a medium or high predisposition. It is magenta (false-negative error) when the reported ice jam falls into a section with a low predisposition. Again, we have to keep in mind that there may be a difference between the initiation site (higher predisposition) and the observation site (anywhere along the jam). In contrast, a false-positive error would give a high value of predisposition in a section where no ice jam was observed. This does not mean that the model is necessarily wrong. It is possible that ice jams on some of these sections have never been reported. It is often the case in isolated or non-vulnerable areas. Or, since the model gives a “predisposition”, it does not mean that an ice jam will automatically occur or as already occurred. So the false-positive results are to be considered objectively.

In total (Table 4), the model indicates that 51 of the 444 sections (11 %) would have a high predisposition for ice jams, 69 sections (16 %) would have a medium predisposition, and 324 sections would be at low risk. Of the 61 reported ice jams on the Chaudière River, 20 (33 %) are located on sections with a high predisposition, 23 (38 %) are on a section with a moderate predisposition, and 18 (29 %) are on sections with low predisposition. These 18 sightings represent the false-negative results or where the predisposition to ice jamming was underestimated.

Table 4 also shows that of these 18 cases, 3 are related to the presence of a major tributary in the section. This could indicate that the value applied for channel width reduction underestimates the actual impact of a tributary on ice jamming.

However, we also have to look at these results in the context of the uncertainty related to the geolocation and length of the ice jam reported in the historical database. Considering that an ice jam may have a length of a few hundred metres to a few kilometres, one could have reported the sighting upstream from the toe of the jam, where it was initiated. The geolocation of the point in the database would then lie upstream of the predisposed section. This could be the case for 10 of the 18 false-negative errors on the Chaudière River, where the ice jam is reported less than 1 km upstream from a section with a high or medium predisposition. This would mean that the performance of the simplified model could be underestimated.

Table 4 finally shows that 32 sections (7 %) were classified with a high predisposition to ice jams but without any event reported. For moderate predisposition, it concerns 46 sections (10 %). These cases are the false-positive results. As mentioned earlier, these are not necessarily errors but it could still mean that the model is overestimating predisposition in some areas. For example, when looking at the false-positive cases (32 sections of high predisposition), we can determine that in each case the class of the narrowing index is greater than the class of the SI. This would indicate that we may overestimate the impact of the narrowing of the channel. The false positives can be caused by all types of narrowing but we found that five of the “faulty” sections have a bridge. Considering that there are only a dozen of bridges in the study area, this number tends to confirm that all bridges are not equal and that the model could be easily improved at the local level with specific information about bridge characteristics.

As mentioned earlier, the Saint-François River is comparable to the Chaudière River. Both flow mostly northward, through the same geological region, and have similar channel lengths and drainage areas. Results for the IJPI on the Saint-François River are shown in Fig. 7. As can be seen in Table 5, the percentage of sections classified as high, moderate, or low predisposition to ice jams are similar to the Chaudière River. Of the 33 reported ice jams on the Saint-François River, 11 (33 %) are located on sections with a high predisposition, 13 (40 %) are on a section with a moderate predisposition, and 9 (27 %) are on sections with low predisposition (false negatives). Here we notice that three false-negative errors occurred on sections with at least one island.

The number of sections with false-positive results is similar to the Chaudière River also (17 % vs. 20 %). However, when looking at the false-positive errors with a high predisposition index (79 sections), only 46 show that the NI is greater than the class of the SI. But again, the number of “faulty” sections with the presence of a bridge (12) is quite high since there are around 20 bridges on the Saint-François River.

In Fig. 8, we take a closer look at some false-negative errors because not foreseeing an area at risk is more significant in terms of public safety. These errors could be caused by a parameter not considered in the model (e.g. slope break), by the simplification approach, or by an inaccurate geolocation of the observation. In site A (Fig. 8) the shape of the channel and the presence of islands are probably enough to trigger an ice jam. But the islands are small (may even be bars) and do not seem to impact on the mean narrowing calculated over the sections. The problem is then related to generalization and scale. In A, we can see that the area has shallow waters (not considered in the model), which could also support ice jamming. In site B, the model sees the bends upstream and downstream but again, misses the islands. Here they are located in a wider section of the channel, cancelling the narrowing effect. In site C, the first island causes a sudden narrowing well detected by the model. But the main channel width remains stable over the next sections, again cancelling the potential narrowing impact of the islands. However, the changes in direction of the main channel should have increase predisposition. In site D, the land strip going into the channel could have caused the ice jam. But the feature is so localized compared to the section's length that it may not sufficiently affect the mean width to register as a narrowing. Thus, the error here could be related to scale. Finally, let us note that if we cannot identify with certainty the cause of a false-negative error, either from channel characteristics, model generalization or scale, there is still the possibility that the ice jam was initiated by the presence of an intact ice cover. According to Lindenschmidt and Das (2015), wider and mild slope sections of the river are more susceptible to have a persistent ice cover until the end of breakup. Again, this is a time-dependent parameter, which is not directly considered by the model. Also, there is the possibility that the observation point did not correspond to the ice jam toe.

We could expect to get different results from L'Assomption River, as it flows southward in a different geological area and has a much higher sinuosity in its lower portion. Figure 9 shows the results of IJPI on L'Assomption River. According to Table 6 the percentage of sections classified as having a high or moderate predisposition to ice jams is higher by about 20 % compared to the two other rivers. Of the 24 reported ice jams on L'Assomption River, 14 (58 %) are located on sections with a high predisposition and 10 (42 %) are on a section with a moderate predisposition. There are no false negatives. However, with more sections at risk (meandering channel) and a smaller ice jam dataset, false-positive errors are naturally higher (31 %). As expected, more false-positive errors are on sections where the SI is greater than the NI. Finally, as for the other rivers, the bridges seem to create some overestimation of the risk as eight false positives are at sections where a bridge is present (on a total of 14 bridges over the study area).