Soil rutting due to off-road forest harvest and post-harvest operations is a widespread problem [1] - [5] . Rutting would primarily occur when operating on wet and non-frozen soil conditions, as these would exist temporarily to permanently on drainage-challenged soils, i.e., in depressed areas, on flat to slightly sloping land, and adjacent to temporary to permanent stream channels, wetlands, water bodies, and shores [6] - [9] . In general, soils are limited in resisting soil compaction as soil moisture approaches the plastic limit and decreases further towards water saturation ( [10] - [13] . Where rutting cannot be avoided, soil compaction and displacement:

Since off-road soil trafficability can now be related to per-tire machine loads, tire/track footprints, number of machine passes along the same track, and soil type [20] - [22] , it is now possible to determine when and where machines likely induce soil rutting, and how deep these ruts will be. Specifically, this can be done through [6] [23] :

Briefly, TWI, which indexes the D8-derived upslope flow accumulation for each DEM cell [28] in relation to the slope of that cell, increases towards flat and low-lying areas with increasing upslope watershed areas. TPI relates the elevation of any cell within the DEM raster to the mean elevation of its surrounding annulus at a specified radius [29] . The resulting numbers are, respectively, positive, zero, or negative where the cells lie above, at, or below their mean annulus elevations. The cartographic depth-to-water index (DTW) is determined by assessing the minimum (“least-cost”) rise of the land away from weather-dependent open-water areas including temporal to permanent flow channels for which DTW is set to 0. This being so, soils along permanent open waters are considered to be:

This article reports on developing practical and easy-to-use techniques that led to 1) marking where off-road traffic rutting has (1) or has not (0) occurred within forested cutblocks, and 2) to use this information to project where else such rutting is likely to occur in wet and unfrozen soils. This was done in three stages involving three areas of interest ( Figure 1 ) dealing with an initial methodology exploration (AOE). This was followed by checking (AOM) and verifying (AOV) the approach. The process of doing so was facilitated using:

The analytical processing involved logistically analyzing the binary rut and no-rut marks as the to-be-predicted variable, and the associated soil- and location-indexed Slope, Curvature, DTW, TPI, and TWI numbers as independent rut-predictor variables.

The best-fitted logistic regression analysis results for the individual and combined study areas are summarized in Table 2A . As shown, the AOE and AOV results so obtained are nearly identical individually and combined, with TPI and DTW_FA>4ha as the only significant rut occurrence predictor variables. In this, the similarity of the AOV to AOE results indicates that the AOE-generated rut occurrence predictions are, in principle, equally applicable to the much wider AOV area, and are therefore likely applicable across New Brunswick. The AOM results, however, differ from the AOE and AOV results by way of the AOM-enhanced and mostly TPI-based rut occurrence results. This suggests that using the AOM-derived model is based on guiding the image-based rut marking process deeper into the low-lying TPI locations. To that effect, a considerable number of ruts occurred within the DTW< 1 m zonations along and next to the DEM-derived flow channels with >4 and >1 ha upslope flow accumulations.

Using TPI ( Table 2B ) as the only rut occurrence predictor variable slightly increased the number of false positives and negatives while lowering the overall correctness classification by 1.2%. In contrast, using only the DTW_FA>4ha raster drastically reduced the correctness classification to 63.4% ( Table 2C ), therefore implicating TPI as the most significant rut occurrence predictor variable. In comparison, the Sink depth, Slope, TWI, and soil type data for the rut and no-rut locations were all found to be insignificant when used in combination with TPI and DTW_FA>4ha as rut probability predictor variables.

Based on the Table 2A entries, the resulting rut occurrence probability function takes on the following form

P_rut(y) = 1/{1 + exp[−(−0.022 − 6.14 TPI − 1.08 log₁₀(DTW))]}

with TPI and DTW = DTW_FA>4ha or DTW_FA>1ha all in m. This equation was subsequently applied across New Brunswick based on the provincial DEM-generated DTW_FA>4ha and TPI data layers. The result of so doing is illustrated in Figure 6 by way of the traffic-light P_rut(y) overlay on the six images in Figure 2 underneath the marked rut (red) and no-rut (green) locations.

Figure 6. Overlay of the 0 (green) to 1 (red) rut occurrence probability pattern underneath the marked rut (red) and no-rut (green) locations on the image panels in Figure 2 , with yellow-colored P_rut(y) ≈ 0.5 transition zones.

The following can be observed from Figure 6 :

Figure 7 illustrates how the P_rut(y) projected red-to-yellow and green zones (Panels E, F) relate to 1) Google Earth images for August 2021 and May 2023 for a select location (Panels A and B), 2) the corresponding change in elevation (Panel C), and 3) the resulting DTW_A>4ha pattern (Panel D). Note that the area at the and of the logging road in Panel A transits from dark to yellow and green in June 2021, but not so in May 2023. These changes reflect the re-foliation extent in June, and the lack thereof in May. The dark area is due to the presence of water-filled ruts due to the road-blocked west-to-east flow pattern.

The overlay of the P_rut(y) projection on the hillshaded canopy height Panel F may provide insights in terms of (e.g.):

Figure 8 presents another example of the P_rut(y)-generated red to green zonation with the DEM-derived FA > 1 ha flow channels and associated DTW_FA>1ha < 1 m overlaid. Also included are the DEM and DEM-DTW_FA>1ha profile lines which connect 10 individually dug soil pits. The observed soil drainage conditions, judged by depth of mottle appearances, varied from poor at Location 8, to imperfect at Locations 6, 9, and 10, moderate at Locations 1 and 2, and well at Locations 3, 4, 5 and 7.

Figure 9 confirms that ruts—where they occur—are generally found within the lower-lying stream-supporting parts of the P_rut(y)-projected high rut-occurrence zones. In addition, these zones connect smoothly across the land from one stream to the next. The two examples in Figure 9 show that this remains so as the terrain changes from gently sloping (left side) to being highly irregular (right side) while the elevational variations for these examples remain within 20 m across their areal extent.

Figure 10 provides an example where the P_rut(y) projection fails to project actual rut occurrences. This is seen to occur along an up to 5-m incised train track along its adjacent flat terrain. This caused the derivation of the TPI index to remain positive across this terrain therefore rendering the P_rut(y) projections to be near 0%, and therefore no-rut predictive up to about 30 m on either side of the track. Similar situations would occur along other deeply incised landscape-affecting features such as flat terrains incised by highways, steep shores, and/or river channels.

Elsewhere on nearly flat ground such as table tops and wetlands, TPI projections vary around zero by definition, thereby rendering the resulting P_rut(y) projections transitional and to be rut and no-rut predictive at 50% - 50%. Where this occurs, overlaying the DEM-derived 10-m smoothed slope layer on ortho images reveals that image-recognized ruts become increasingly more visible as the slopes decrease from 6% to 0% ( Figure 11 ).

Note that the P_rut(y) projections do not only apply to the rut versus no-rut marking extent as portrayed in Figure 1 , but also apply to locating rut-prone cutblock operations across New Brunswick and elsewhere. This is demonstrated in Figure 12 , showing two Google-Earth located cutblock examples in Nova Scotia, with corresponding P_rut(y) rut probability projections, but with the TPI and DTW_FA>1ha combination as the y-predictor variables. The reason for selecting DTW_FA>1ha instead of DTW_FA>4ha relates to the fact that mean annual precipitation levels generally increase from 1000 mm/ha across New Brunswick to 1500 mm/ha across southwestern Nova Scotia, thereby enhancing the intensity of operation-induced soil rutting along ephemeral flow channels.

In addition to rut occurrences in cutblocks, P_rut(y) projections reveal where roads, trails, powerlines, and pipelines also incur rutting. This is demonstrated in Figure 13 , showing corridor-centered rut occurrences within the P_rut(y)-projected rutting zones. As can be verified, the same pattern recurs when and where the corridor-locating images are bare, wet, and unfrozen. This being so, the above methodology can be used to map and address matters pertaining to, e.g., corridor access and related on- and off-road trafficability and maintenance requirements.

It appears that the P_rut(y) projections, apart from delineating single-pass rut versus no-rut occurrence zones, can also be interpreted as a DEM-generated way to delineate discharge versus recharge zonation. As such, the P_rut(y)-projected rut-occurrence zones represent downslope water-accumulating areas where machine-incurred ruts become prevalent while operating on wet and unfrozen soils.

The above rut-marking approach provides no information on the depth of the ruts. Rut depths would generally be shallowest in upslope positions and deepest in downhill water-saturated areas. As reported elsewhere (e.g., [5] [6] [31] - [34] ), rut depths depend on machine load, number of passes, tire or track footprint pressure, the timing of the operations, and the resistance of the soil to compaction as affected by upslope to downslope changes in soil density, texture, presence of coarse fragments, and soil moisture content. Additional rut deepening would be incurred along uphill tracks due to increased tire traction [35] . Further research is required to determine which soil types prove to be more conducive to rutting specifically. Doing so would require marking and evaluating rut and no-rut locations when incurred across varying soil types during same or similar weather and machine-operating conditions.