Effect of additional considerations on spatially interpolated wind hazard maps

If no additional constraints were to be considered, vAH-50 shown in Figures 2-11a or 2-11b could be adopted to represent the wind hazard and potentially used for code making. However, there were several additional considerations to assign the wind loads in the previous editions of NBCC. For example, the exposure correction factor can be less than unity due to over exposure (i.e., open water exposure at coastal regions); an open water exposure category is not currently considered in the NBCC-2010. If the open water exposure category is introduced in a future edition of NBCC, the results presented in the previous sections can be used directly. Otherwise, the exposure correction factor equal to one should be used for over exposed stations so the results to be consistent with the existing exposure categories specified in NBCC-2010. Also, a lower bound,

vLB, of 77.55 km/h which is used in the NBCC-2010. Therefore, using the value directly interpolating from vAH-50 obtained at the stations for locations specified in the NBCC-2010 may not be satisfactory. Also, the direct interpolation does not explicitly consider the proximity of a location to a meteorological station, and whether an exact or inexact interpolator is preferred. Although the exact interpolator leads to an estimated value to be the same as the observed value at a sample point, it may not be associated with the lowest root-mean-square-error (RMSE) obtained from the cross-validation analysis (Johnston et al. 2003; Ye et al. 2015). An inexact interpolator results in an estimated value differing from the known value at a sample point but could be associated with lowest RMSE obtained from the cross-validation analysis. The ordinary kriging can be an exact interpolator if the nugget equal to zero is used. Moreover, for a location tabulated in the NBCC table that is within a distance D from any meteorological stations, the use of vAH-50 for the station with the shortest distance to the location may be preferred if D is small.

Based on these considerations, maps are interpolated based on vAH-50 obtained using the ROI but considering the following additional criteria (Hong et al. 2014):

1) Use vAH-50 for the station with the shortest distance to the location if D ≤ 5 km.

2) Use the maximum of the spatially interpolated value and the estimated vAH-50 for the station with the shortest distance to the location if 5 < D ≤ 20 km.

3) Use the interpolated value for the location if 20 < D ≤ 50 km,

4) The existing value shown in NBCC-2010 is adopted, if D > 50 km to a location, 5) vLB is used if the estimate vAH-50 is less than vLB.

By considering the above requirements, sets of wind hazard maps are obtained and shown in Figure 2-13 for the case with nA ≥ 20 and Figure 2-14 for the case with nA ≥ 10. In all cases, the ROI approach was used with the Gumbel distribution. Comparison of the results shown in Figures 2-13a and 2-13b to those shown in Figures 2-13c and 2-13d, indicated that there are differences but not very large. This can be explained by noting that a degree of smoothing was already introduced in the estimated vAH-50 sine they are estimated by using the ROI approach. Similar observations can be made by comparing the results shown in Figures 2-14a and 2-14b to those shown in Figure 2-14c and 2-14d.

a) With over exposure correction & nugget ≠ 0. b) Without over exposure correction & nugget ≠0.

c) With over exposure correction & nugget = 0. d) Without over exposure correction & nugget =0.

Figure 2-13. Trends of the 50-year return period values based on the adopted criteria and applying the ordinary kriging technique without/with nugget equal to zero for the case with nA ≥ 20.

a) With over exposure correction & nugget ≠ 0. b) Without over exposure correction & nugget ≠0.

c) With over exposure correction & nugget = 0. d) Without over exposure correction & nugget =0.

Figure 2-14. Trends of the 50-year return period values based on the adopted criteria and

applying the ordinary kriging technique without/with nugget equal to zero for the case with nA ≥ 10.

To appreciate the differences between the estimated values shown in the plots presented in Figures 2-13 and 2-14 to those given in the NBCC-2005 and NBCC-2010, the ratio of the tabulated

vAH-50 in the NBCC-2005 or NBCC-2010 to that inferred from Figure 2-13d or Figure 2-14d was calculated and shown in Figure 2-15. The symbol R with subscripts represents the ratio of the 50- year return period wind speed inferred from the code to that estimated in Figure 2-13d or 2-14d, where C05 and C10 indicate that the values are inferred from NBCC-2005 and NBCC-2010, respectively, and E10 and E20 indicate that the values are estimated for the case with nA ≥ 10 and the case with with nA ≥ 20, respectively.

c) For the case with nA ≥ 20 & satisfy Criterion 1. d) For the case with nA ≥ 10 & satisfy Criterion 1.

Figure 2-15. Statistics of the estimated ratio the 50-year wind speed by considering the values inferred from the codes and the estimated values shown in Figure 2-13c and 2-14c: a) For the case with nA ≥ 20, b) For the case with nA ≥ 10, c) For the case with nA ≥ 20 & satisfy Criterion 1, and d) For the case with nA ≥ 10 & satisfy Criterion 1.

The figure showed that the ratio differs from unity for many locations. The concentration of

RC05/E10 and RC10/E10 equal to one shown in Figures 2-15a and 2-15b is a direct consequence of Criterion 4. To better appreciate the ratios of RC05/E10 and RC10/E10 for locations that are within 5 km of a considered station, these values are plotted in Figures 2-15c and 2-15d, indicating that even locations that are within 5 km from any meteorological stations, the ratios differ from unity. This again suggest that the values tabulated in NBCC need to be scrutinized and updated.