Vector and raster models were created using network analysis and spatial analysis, respectively. Distance (km) and yield (t) values obtained for each data type were used to calculate the annual aggregated supply and delivery costs for each distance at each city for each type of biofuel residue. Consequently, supply-cost and supply-distance curves were generated for both models to be compared. The comparison shows a significant difference between the two supply-cost modelling methodologies.The determination of the significant difference was based on the strengths and weaknesses of both models,visual assessments of Figures 11 and 12, as well as simple paired t-tests performed on the data.

## Supply-Distance Curves

Figure 11 shows the difference in yield obtained per distance between network analysis and raster analysis. Both datasets (Figure 11) illustrate how biomass yield increases as distance increases, based on the assumption that trucks would increasingly collect residues as they approach the bio-refineries from far distances. It is worth pointing out that network analysis has greater collecting rates than raster analysis. In other words, network analysis generates higher yields as distance increases. Also, slightly greater distances were seen with the raster data (maximum distance = 202 km; minimum distance = 40km) than with the vector data (maximum distance = 200km; minimum distance = 30) in Figure 11.This was due to the applied tortuosity factor (1.35) and because raster- based road estimations lack topological features that exist within vector data (Moller & Nielsen, 2007). This is in a slight overestimation of the general area for raster, which was reflected in the overestimation of distances from refineries to supply sources. Raster data uses 625m^{2} pixels (25m * 25m) to calculate the areas of the biofuel residues as well as the distance from supply sources to refineries. In the case of network analysis, the vector data considered the preferred driving routes with fewer errors for least cost routing (Moller & Nielsen, 2007). Furthermore, vector modelling made use of the topological features in the road network, which has been shown to improve locational accuracy (Moller & Nielsen, 2007; Yoshioka et al., 2011).

Figure 11: Distance-supply curves modelled with raster and network analysis for annual aggregated supply for four types of biofuel residues in three southeastern Ontario cities.

## Cost-Supply Curves

Based on a visual assessment of Figure 12, it seems that derived supply-cost curves from network analysis, provide greater annual aggregate supply values at each of the seven considered delivered costs, overall. The differences are clearly noticed in the case of Smith's Falls. For instance, at $75/t, vector modelling determines a total annual aggregate supply of 200,000 tonnes, which would results in a delivery cost of 15 million dollars for one year. In contrast, raster estimates a total annual aggregate supply of 100,000 tonnes, half as much as the one estimated by network analysis.This results in 7.5 million dollars for the delivery cost in a year. Based on this comparison, it is clear that there is a noticeable difference between these modelling methodologies. To confirm that a difference existed between the vector and raster data, a paired t-test was performed on the sum of annual aggregated supply data for all the cities. In order to confirm a significant difference the result from the t-test has to be greater than 2.086.

Figure 12: Cost-supply curves modelled with raster and network analysis for three cities in southeastern Ontario for four different biofuel residues.

Table 4 : Paired T-test results for differences between modelling cost-supply curves with spatial analyst and network analyst.All tests showed significant differences.

Residue Type (n=21) |
Paired T-test (95% Confidence Level) |

Aggregated Overall Results |
4.0568 |

Hardwood Overall |
2.5992 |

Softwood Overall |
2.6353 |

Stover Overall |
2.4461 |

Straw Overall |
4.0408 |

The results show that there is a significant (t=4.06; p<0.05; n=21) statistical difference overall in modelling cost-supply curves with network analysis and raster analysis. The same was done for each type of biofuel residue. The results are illustrated in Table 4.It is clear that the same significant difference is noticed with each type of biofuel individually, thus providing enough evidence to affirm that there is a significant difference between the two methodologies of modeling supply-cost curves. It was expected that network analysis would provide a more detailed analysis at 10 km increments from 30 to 200km distances due to its topological analysis capabilities, accurate calculation of geometry for areas, and implementation of real-world distance based on the road networks. Additionally, it is observed that the curves for each city reflect the most common type of biofuel residue produced in their respective regions. Figure 12 illustrates how Cornwall has a greater tendency to produces stover and straw than wood residues, in comparison to Bancroft, which is located in a forestry region. Moreover, Smith’s Falls shows a brief balance between the production of agricultural and forestry biofuel residues. There cannot be an assertion on which model is overestimating or underestimating yield and cost values since actual field data is needed to compare to the model output. However, this research project demonstrates that there is a significant difference between network analysis and raster analysis when modelling supply-cost curves.