While potato crops can be grown in differently textured soil, they grow best in well drained medium-coarse soils such as sandy loams [27] [28] . Hence, medium-coarse soil textures are symbolized as M-C in Table 3 and are rated 1 (i.e., M-C = 1). In contrast, soils with dominant clay content (i.e., sandy clay loam, clay loam, and clay, symbolized by “F = 0.1” in Table 3) are rated low because fine-textured soils are easily compacted, which leads to poor soil aeration followed by potato rot when moist to wet. Across NB, soil textures vary primarily by geological surface deposition. Basal tills as well as lacustrine to marine deposits tend to be fine-textured soil whereas ablation till, riparian and glacio-fluvial deposits tend to be coarse-textured. Among these, ablation tills and basal tills are prevalent.

CF refers to gravel, cobbles, stones, and boulders from smallest (≥2 mm) to largest when present. Low CF content is rated best (L = 1), while high CF content is rated worst (H = 0.1). Large CFs need to be removed from fields to facilitate seedbed preparations and potato harvesting [29] .

Potatoes will not root well in shallow and/or firm to very firm soils. These are symbolized as “1” in Table 3 and are given a “0.1” rating. Restrictions in soil-related rooting depth are encountered on traffic compacted and/or naturally compacted soils, such as fine-textured lacustrine and marine deposits and basal tills. Moderate rooting restrictions occur on basal tills overlain by ablation till. Low to no depth restrictions as found on deep ablation tills, outwash plains, and sandy deposits along riverbanks and well-drained floodplains are symbolized by “4” in Table 3 and are rated as “1”.

Soil parent materials containing limestone and/or calcareous siltstones, sandstones, mudstones, and slates generally improve and maintain good soil qualities in terms of elevated pH (reduced soil acidity), increased exchangeable calcium (Ca) and magnesium (Mg) contents, and enhanced soil aggregation on medium- to fine-textured soils. By soil association, the calcareousness rating varies from 0 (100% siliceous) to 1 (100% calcareous) based on evaluating calcareous content from absent, minor, half-and-half, dominant, and complete.

Assuming that the coded rate entries in Table 3 capture the soil-affected variations in potato cropping responses, it was necessary to determine how these rates combine into a single potato-crop suitability factor by soil association. To do this, it was decided:

1) to multiply the ratings for topsoil and subsoil texture, rooting depth, and CF, i.e., similar to calculating the probability occurrences of random factor combinations;

2) to add the calcareousness rating to the resulting multiplication product, assuming that calcareousness is one third as important as the best combination of the other four variables;

3) to normalize the results so obtained by dividing this result with its maximum value across all the soil associations;

4) to transform the normalized values so generated to a linear 0 to 1 suitability progression across the soil associations; this was accomplished through 0.33 exponentiation; the result of so doing generated Equation (1), i.e.:

R Soil = [ R Top R Sub R Depth R CF + 0.33 R Calc max ( R Top R Sub R Depth R CF + 0.33 R Calc ) ] 0.33 ≤ 1 (1)

with R_Top and R_Sub referring to texture by topsoil and subsoil, R_Depth referring to soil compaction rating, R_CF referring to coarse fragment rating, and R_Calc referring to calcareousness rating. The results so obtained are listed in Table 4.

Applying the soil suitability ratings in Table 4 province-wide required updating of GeoNB’s catalogued forest soil shapefile to conform to GeoNB’s waterbody and wetland layers. This was done using ArcGIS Pro procedures dealing with:

1) Erasing all waterbody and organic soil features in the forest soil shapefile for NB.

2) Converting the resulting shapefile into a 1-m resolution raster with “no data” pixels for the GeoNB registered waterbody and wetland locations.

3) Systematically extending all existing soil-association identified pixels into their adjacent “no data” spaces.

4) Once completed, the resulting pixels for the GeoNB’s identified waterbody or wetland pixels were set to DTW = 0 via conditional raster calculations.

5) Converting the resulting raster into the updated soil association shapefile followed by feature smoothing to reduce pixelated appearances.

The crop suitability mapping parts by soil drainage and slope was done using the 1-m DEM for New Brunswick. For this, the slope was derived using the Slope tool in ArcGIS Pro, which determines the percent rise or descent over distance among the eight-cardinal directions adjacent to each DEM pixel. The soil drainage layer was derived using the ArcGIS Pro Cost Distance tool, with the delineated flow channels and waterbodies marking DTW = 0 reference cells, and with the slope percent raster used as cost raster. The resulting DTW > 0 cm pixels refer to the distance between the soil surface and the water table associated with the nearest waterbody and flow channel locations. The flow channels were developed using the D8 algorithm [30] that derives the flow accumulation raster from the depression-filled DEM according to the pixel-determined flow directions.

The resulting flow-channel raster was classified to have no-data pixels with < 4 ha upslope flow accumulation. This threshold refers to mapping the extent of permanent streams consistent with end-of-summer water flow. The end-of-summer conditions for soil drainage, ranging from very poor to poor, imperfect, moderate, well, and excessive generally corresponds to DTW ≤ 0.1, 0.1 to ≤0.25 m, 0.25 to ≤0.5 m, 0.5 ≤ 1 m, 1 to, e.g., ≤20 m and >20 m, respectively. In turn, the 0 to 1 crop suitability rating function for DTW was formulated such that:

R DTW = a [ 1 − exp ( − b   DTW ) ] c [ exp ( − d   DTW ) ] ≤ 1 (2)

with a = 1.065, b = 2.5, d = 0.03, c = 4.8. As illustrated in Figure 2, R_DTW starts from 0 when DTW = 0 (too wet), reaches 1 at 2 m (sufficiently moist most of the time), and trails downward from there to about 0.6 and further as DTW approaches 20 m and beyond due to decreasing uphill soil and subsoil water availability.

The 0 to 1 crop suitability rating function for slope (%) was estimated by setting:

R Slope = 1 − 1 / { 1 + exp [ − 3 ( Slope − 10 ) ] } ≤ 1 (3)

This equation uses Slope = 10% as the DEM-derived slope threshold for ensuring that if Slope < 10%, then 1) field operations pertaining to, e.g., seedbed preparation, seeding, and harvesting remain safe and 2) soil erosion remains minimal. This threshold was modified by gradually approaching the slope = 10% threshold from 8% upwards, and by gradually moving away from this threshold towards 12% (Figure 2).

Potatoes require about nine weeks (63 days) for full canopy development, and 18 weeks (126 days) to initiate senescence and thereby completing tuber growth (Figure 3, [31] ). Late frost in spring delays crop preparations and foliage development. Early frost in fall affects tuber quality by tissue damaging (black spots). Formally, the FFD-related potato cropping restriction was formulated and represented in Figure 4(A) as follows:

R FFD = 1 / [ 1 + exp ( − 0.06 ( FFD − 100 ) ) ] ≤ 1 . (4)

Since FFD exceeds 100 days across NB except for the elevated areas in the northwest (Figure 5), the FFD rating can be set at 1 for most of NB, but 0 where FFD << 100 days.

Potatoes require about 1000 and 1500 GDDs from emergence to tuber initiation and harvesting (Figure 6). Across NB, GDDs range from 1300 to 1800 (Figure 5), therefore potato cropping across NB is not GDD restricted except for the high elevation location in the northwest. Where conditions are suitable, GDDs > 1500 lead to additional tuber growth, particular for Russet potatoes (Figure 6). The effect of increasing GDD on tuber numbers and tuber length is represented in Figure 4(B) by setting:

R GDD ( tubernumbers ) = 1 − 1 / [ 1 + exp ( − 0.006 ( GDD − 800 ) ) ] ≤ 1 , (5)

and

R GDD ( tuberlength ) = 1 − 1 / [ 1 + exp ( − 0.006 ( GDD − 13 00 ) ) ] ≤ 1 . (6)

The combined equation for crop suitability rating is therefore given by

R CS = R Soil × R DTW × R Slope × R FFD × R GDD ≤ 1 . (7)

Note that R_Soil is set to 0 for waterbodies and wetlands. Otherwise, R_Soil varies from 0.3 to 1. In contrast, R_DTW, R_Slope, R_FFD and R_GDD are set to vary from 0 to 1 because of crop curtailing conditions where too wet (DTW = 0), too steep (Slope > 12%), and insufficient frost-free days (R_FFD < 100 days) and/or growing degree day (R_GDD < 500).

The data layers used to evaluate the extent to which the above crop suitability process for R_CS reflects the GeoNB-registered property taxation values per Property Account Number (PAN) and building footprint layers (PAN data file [19] ). This property-by-property evaluation was limited to partially farmed POC and AOI areas in Figure 1. PAN areas not associated with farming, farms < 5 ha, and forestry properties (assessed at $100/ha, [33] ) were removed from this analysis.

Also removed were all PAN areas intersected by the POC and AOI borders. The information for the remaining properties compiled included 1) mean PAN taxation value per property and per hectare, 2) mean PAN R_CS value, 3) PAN area, 4) PAN building footprint, and 5) a PAN binary “0” code for Farm and “1” for a Farm/Woodlot combination. The resulting PAN values were:

1) summarized by property type and AOI and POC area, and

2) regression analyzed with taxation values per property and per hectare as dependent variables, and PAN area, building footprint, property type and mean R_CS value as independent variables.

For best results, it was necessary to log-transform the PAN taxation, area and building footprint numbers. In addition, building footprint numbers needed to be transformed to (Building footprint, m²)^0.33 for the best-fitted PAN $/ha assessment evaluations.