The case study refers to: 1) a 12 km section of the Aboujagane Road east of Moncton ( Figure 1 ), and 2) is supplemented with a smaller 4 km section of the Penniac Road northeast of Fredericton, and an additional location in southwestern Nova Scotia. Currently, segments along these roads are mainly used for logging access and transport. For the Aboujagane Road section, elevations vary from 20 to 200 m north to south. Its area is located on red-grey sedimentary bedrocks of Pennsylvanian to Triassic age. This partially Ca-carbonate cemented formation is covered by shallow ablation and basal tills consisting of sandy to loamy texture with a low coarse fragment content. The soil, referred to as Parry soil ( Colpitts, 1995 ), has a reddish color, compacts and ruts easily, and is prone to puddling and flooding along depressed and poorly drained road segments. For the Penniac Road section, elevations range from 70 to 180 south to north. Its area is covered by Harcourt soil that developed on a medium to coarse till on top of fine-textured basal till, all underlain by a red mudstone formation, also of Pennsylvanian to Triassic age ( Colpitts, 1995 ), and compacts and ruts easily as well. The climate for both areas is maritime, with mean monthly temperatures ranging from −13˚C to 25˚C, and annual precipitation rates of about 1200 mm, with a quarter of that being snow. These areas were selected through image-inspecting the extent incurred road damage. The Aboujagane Road segment was used for model development. The Penniac Road and Nova Scotia locations served for image-based model verification.

Inspecting high-resolution LiDAR-generated DEMs generated in 2015 and 2017 and historical Google Earth and other imageries (GeoNB, ESRI World Images) from June 2015 to August 2024 revealed considerable variations in road segment quality along the Aboujagane Road and elsewhere. The best historical Google Earth Images ( Figure 2 ) were used for marking and indexing 67 damaged locations ( Figure 3 ) and 27 additional no-damage ridge-top locations along the Aboujagane Road. Doing so produced the road damage index (RDI) as an off-road trafficability indicator, symbolized as no damage 0, rutted 1, braided 2, puddled 3, and flooded 4, and also symbolized as 0, r, b, p, f, respectively, with examples in Figure 4 . This evaluation was supplemented and confirmed: 1) by on-the-ground roadbed and culvert inspections and 2) AUV imaging in May 2020 ( Figure 3 ). The resulting RDI values for the non-upgraded road segments were averaged for further analysis.

The 2015 and 2017 LiDAR-generated Digital Elevation Model (NB DEMs; http://www.snb.ca/geonb1/e/dc/catalogue-E.asp ) and the GeoNB data layers for forest and provincial roads, waterbodies, watercourses, and wetlands ( http://www.snb.ca/geonb1/e/dc/catalogue-E.asp ) were used to produce the following data layers via ArcGIS Pro processing:

1) Depressions and related depth (D_depth, in m), determined by subtracting the original DEM from its depression-filled version.

2) Slope (in %), followed by focal 5-m radial smoothing.

3) Continuous flow direction (FD) and flow accumulation (FA, m² converted to ha), using the D8 algorithm ( Tarboton, 1997 ).

4) Log-transformed FA raster, i.e. logFA_max = log₁₀(FA_max + 1), followed by focal 5-m radial smoothing around each raster cell to serve as a flow-accumulation index across each road point of interest.

5) Flow channel lines with >0.1, >1, and >4 ha upslope FA.

6) Watershed borders for the FA > 4 ha flow lines where they cross the selected road segment.

7) Cartographically determined depth-to-water (DTW, in m; Murphy et al., 2011 ), calculated with slope as cost raster and with DTW = 0 where water can be expected to at the surface.

8) Topographic position index (TPI, in m; Weiss, 2001 ) based on the elevational difference between every DEM cell at center and its surrounding annulus 50 m away.

9) Probability of rut occurrences along single tracks, formulated as ( Snow et al., 2024 ):

${\text{PR}}_{\text{rut}}=1/\left\{1+\exp \left[-\left(-0.022-1.04{\log }_{10}\left(\text{DTW}\right)-6.4\text{TPI}\right)\right]\right\}.$ (1)

The workflow associated with establishing these layers is presented in Figure 5 . The hill-shaded version of the DEM and the FA > 0.1 ha raster layers were subsequently used: 1) to locate the hydrological centers of each of the 94 RDI locations, and 2) to extract the values for D_depth, FA, 5-m mean focal logFA_max, mean focal 5-m Slope, DTW, TPI, and PR_rut at the RDI points.

The 94 data points so generated were subject to multivariate regression analysis, with the averaged RDI numbers as dependent variable and Elevation, Slope, D_depth, DTW, logFA_max, TPI, and PR_rut as independent variables. This was done stepwise to determine which of the resulting models and associated RDI predictor variables would contribute the most to the road-incurred damage rating, from no rutting to flooding. Once established, the best-fitted results were further refined by identifying and removing model-associated RDI outliers.

The best-fitted model so generated was used to map RDI across the Aboujagane and Penniac study areas in Figure 1 . The verification involved inspecting the semitransparent RDI overlays on: 1) the hillshaded DEMs for Areas A, B, and C, and 2) the corresponding Google Earth images, all overlaid by the DEM-generated flow channels with FA > 4, >1, and >0.1 ha. Image-revealed damage locations along the road segments and powerlines so selected were circled to visually ascertain their correspondence to green (0), yellow (2) to red (4) coloration of the RDI map. This verification was further extended by checking the RDI map performance for a forest road location in southwestern Nova Scotia (Latitude 44.271; Longitude 64.872).

The image-determined RDI numbers and their averages along the non-repaired road segments are listed in Table 1 by location. image year, and associated FA, Slope, and D_depth numbers. As shown in Figure 6 for May 2017, puddling and flooding were most noticeable within depressed water-accumulating road locations, while rutting and braiding occurred along lower slopes. The corresponding post-repair RDI evaluation based on the August 2024 imagery (Locations 26 to 60) is also presented in Figure 6 , with RDI values mostly rated zero, except for rutting and puddling at Locations 45 and 46 next to the re-aligned roadbed. At Location 51, post-repair rutting also occurred but only as per the June 2022 image.

The stepwise regression analysis selected D_depth, Slope, logFA_max, and PR_rut as the

main RDI predictors. The correlation among these variables varied from −0.83 (D_depth vs. Slope) to 0.633 (logFA_max vs. PR_rut). The remaining coefficients varied from 0.158 to 0.374. The best-fitted results so obtained are listed in Table 2 from Models 1 to 6. This stepwise progression is based on and affected by the following considerations:

1) Log-transforming FA via logFA_max linearizes the FA effect along and across roads.

2) Using the 5-m focal mean Slope serves to reduce the slope variations across the DEM-profiled roads and adjacent ditches and bulldozed materials where present.

3) The DEM-assessed depression depths depend on the extent of water filling at the time of the LiDAR-based DEM scanning process, being naturally deepest when dry and equal to 0 when flooded.

4) Cells with low (0) to high (1) PR_rut values are easily spotted by overlaying the model-generated PR_rut raster on the high-resolution images and DEMs for the area of interest.

The results in Table 2 were generated after excluding outlier locations as follows: from Model 1 (Loc. 66), from Models 2, 3, 4, and 5 (Loc. 66, 67), and from Models 5 and 6 (Loc. 12, 20, 21, 49, 66).

Progressing from Model 1 to Model 6 slightly decreased the R² values and slightly increased the RMSE values while the RDI coefficients remained near the best-fitted Model 1 values. Removing logFA_max caused the least changes. Removing Slope and then also D_depth rendered the best-fitting RDI scattergram ( Figure 7 ) less uniform because PR_rut was designed to only map probable single-track off-road rut occurrences, regardless of whether rutted, braided, puddled, or flooded. Nevertheless, PR_rut still emerged as the strongest RDI predictor because removing PR_rut from Model 1 caused the largest best-fitted R² drop, i.e. from 0.819 to 0.632, with no outliers removed. The wider area-influence of PR_rut compared to the road-focused D_depth and Slope determinations is likely due to the fact that PRrut captures the soil-rutting effect in water-accumulating depressions and along permanent to ephemeral flow channels quite well, as quantified via Equation (1) and as shown in Snow et al. (2024) .

The reason that logFA_max is least significant among the RDI predictors relates to the fact that rutting, braiding, puddling, and/or sustained flooding is much reduced at culvert-protected road locations for which FA tends to be >4 ha, as was the case at Locations 20, 41, 48, 52, and 66. In contrast, 1) culvert washout had occurred at Locations 11 and 27 where FA = 65.5 and 76.7 ha, respectively, and 2) roadbeds were fully wetland-flooded at Locations 39 and 62.

The installed culverts were all corrugated and had a diameter of D = 500 mm. According to the Manning Pipe Flow formula ( https://en.wikipedia.org/wiki/Manning_formula ), this would accommodate even-flow stream discharge rates up to:

$q={\left(D/2000\right)}^{8/3}\pi S_{\text{culvert}}^{0.5}/\left(2^{2/3}\eta \right)=0.158{\text{m}}^{\text{3}}/\text{sec},$ (2)

and assuming that culvert roughness is represented by η = 0.022, and culvert slope (S_culvert) is set at 0.5% to allow for fish-passage. For even-flow run-off discharge resulting from a ppt = 100 mm/day storm when soils are fully saturated, this rate would be exceeded at all road-stream crossings where

$\begin{array}{c}\text{FA}>q/\text{ppt}\\ =\left[0.158{\text{m}}^{\text{3}}/\text{sec}/\left(0.1\text{m}/\text{day}\right)\right]\times 24\times 60\times 60\text{sec}/\text{day}/{10}^4\\ =4.6\text{ha}.\end{array}$ (3)

Such occurrences would lead: 1) to cumulative roadbed soil loss, as noted for Locations 48 and 52, where FA = 11.4 and 13.9 ha, and/or 2) to washouts as noted for Locations 18 and 39 where FA = 161 ha and 104 ha, respectively. Noting that the discharge-accommodating culvert radius can be estimated from:

$D=2000{\left[2^{2/3}\eta Q/\left(\pi {\text{Slope}}_{\text{culvert}}^{0.5}\right)\right]}^{3/8},$ (4)

It follows that Locations 18 and 39 would require culvert diameters amounting to 1260 and 1070 mm to prevent overflow and potential washout in response to an even-flow 100 mm/day storm event. However, single-storm discharge peaks at about three times higher than the corresponding even-flow discharge expectations ( Gray, 1962 ). Hence, Locations 18 and 39 would need culvert diameters amounting to 1900 and 1600 mm, respectively, to avoid 100 mm/day caused overflow and washout occurrences. Similarly, the corresponding diameters for Locations 48 and 52 would amount to 700 and 750 mm, respectively.

Using Model 1 in Table 2 for the RDI mapping purpose matches the image-observed and circled road-damage locations quite well. In Figure 8 , this is illustrated for the 38 to 43 Aboujagane Road Locations. At these locations, the May 2017 image-observed RDI variations revealed:

1) Channel-flow induced braiding (38, RDI = 2.8).

2) Flooding (39, RDI = 3.4).

3) Rutting on flat but slightly depressed uphill terrain (40, RDI = 1.1).

4) Rutting and puddling due to roadbed flow channeling (41, RDI = 3.4; 42, RDI = 3.1; 43, RDI = 3.3).

5) Wetland-expanded flooding at Location 39.

6) No damage (0) along nearby uphill locations.

By expressing Model 1 in equation form:

$\text{RDI}=1.72+2.12{\text{PR}}_{\text{rut}}+4.1{\text{D}}_{\text{depth}}-0.137\text{Slope}+0.5\log {\text{FA}}_{\text{max}}.$ (5)

It can be noted that RDI: 1) can take on values larger than 4, especially so with increasing values for D_depth and logFA_max, and 2) can become negative with increasing Slope values. If so, RDI > 4 would indicate a yet greater possibility of road flooding. In contrast, RDI < 0 would imply no damage, as RDI projected along an upgraded and non-upgraded Aboujagane Road segment in Figure 9 .

Extending the Model-1 RDI projections, region-wide revealed a general correspondence between image-observable and model-projected patterns regarding traffic-induced road and trail damage. Figures 10 - 14 demonstrate this not only for Sections A, B, and C in Figure 1 , but also for a similarly distant location in

southwestern Nova Scotia. In these illustrations, road damage generally occurs within the red RDI-indicated damage coloration along and/or next to adjacent non-active logging road segments, and also along powerlines. In contrast, this coloration tends to remain green where roadbeds were restored prior to LiDAR scanning, except where the red road coloration prevails at or near FA > 4 ha road-stream crossings. This suggests potential vulnerability to road rutting, braiding, puddling, flooding, and washout at these locations.

Reviewing Figures 8 - 14 indicates that the mapped RDI patterns can also be used to: 1) optimize road locations away from traffic-compromising slopes and water-accumulating areas to assess off-road rutting potentials, and 2) plan on- and off-road operations as affected by weather-, soil- and slope-anticipated conditions to avoid rutting. In this regard, rutting and flooding can be expected to occur in the lower-lying and water-accumulating sections of the red areas. As a further guide, it is recommended to overlay the DEM-projected RDI maps with officially delineated stream, wetland and waterbody maps. The advantages of

doing so include: 1) ensuring that already mapped waterbodies and wetlands become RDI > 4 entities, and 2) systematically checking and correcting for potential flow-blocking road-stream crossings.

It should be noted that the RDI mapping process as described above does not inform when newly constructed or upgraded forest roads succumb to rutting, braiding, puddling, and flooding. It does, however, inform where these roads are likely to become vulnerable due to factors such as:

1) Road washout at road-stream crossings with large upslope water-accumulating areas.

2) Culverts that are either too small, partially to completely plugged, or have incurred shape deformations ( Mai et al., 2014 ).

3) Water-logging and flooding along roads next to poorly draining depressions.