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Figure 8. Estimated nonstationary vs. EC-generated IDFs for T = 2-, 5-, 10-, 25-, 50- and 100-year return periods for the selected urbanized locations in Southern Ontario, Canada. The updated and EC IDFs are shown using solid and dotted lines respectively.

Figure 8 Estimated nonstationary vs. EC-generated IDFs for T = 2-, 5-, 10-, 25-, 50- and 100-year return periods for the selected urbanized locations in Southern Ontario, Canada. The updated and EC IDFs are shown using solid and dotted lines respectively.

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Table 1. Selected station locations, population distribution, and hourly and daily data availability.
Table 1. Selected station locations, population distribution, and hourly and daily data availability.
Figure 1. (a) Selected urbanized sites in Southern Ontario. Southern Ontario (41-44° N, 84-76° W) is the southernmost region of Canad. and is situated on a southwest—northeast transect, bounded by lakes Huron, Erie, and Ontario. The nine locations on the map are (fron the southwestern to northeastern corner): Windsor Airport, London International Airport, Stratford Wastewater Treatment Plant (WWTP) Fergus Shand Dam, Hamilton Airport, Toronto International Airport, Oshawa Water Pollution Control Plant (WPCP), Trenton Airport, an Kingston Pumping Station. Topography map indicates the maximum slope of 670m above mean sea level. (b) The population map show six of the the sites: Windsor Airport, London International Airport, Hamilton Airport, Toronto International Airport, Oshawa WPCP, an Kingston P. Station are located either in or the vicinity of densely populated urbanized area. The remaining three sites are located in th moderately populated area. The short-duration AMP records in all locations vary between the minimum of 46 years and the maximum o 66 years. ! CMA and CA denote census metropolitan area and census agglomeration respectively. Statistics Canada defines a CMA as having a population density of at least 100000, where the urban core of that area has at least 50 000 people, whereas CA must have an urban core population density of at least 10000. A population centre (or urban area) is an area with at least a population of 1000 and a density of 400 or more people per square kilometre. All population information is collected from the Statistics Canada (https://www 12.statcan.gc.ca/) website. 2 Missing values are infilled using observations from the nearest Environment Canada station, ID 6144475 (latitude 44° and ing years or durations are obtained by disaggregating daily data to hourly and sub-hourly time steps. longitude —81.5°), located at 111.5 km geodesic distance. Annual maxima values of miss
Figure 1. (a) Selected urbanized sites in Southern Ontario. Southern Ontario (41-44° N, 84-76° W) is the southernmost region of Canad. and is situated on a southwest—northeast transect, bounded by lakes Huron, Erie, and Ontario. The nine locations on the map are (fron the southwestern to northeastern corner): Windsor Airport, London International Airport, Stratford Wastewater Treatment Plant (WWTP) Fergus Shand Dam, Hamilton Airport, Toronto International Airport, Oshawa Water Pollution Control Plant (WPCP), Trenton Airport, an Kingston Pumping Station. Topography map indicates the maximum slope of 670m above mean sea level. (b) The population map show six of the the sites: Windsor Airport, London International Airport, Hamilton Airport, Toronto International Airport, Oshawa WPCP, an Kingston P. Station are located either in or the vicinity of densely populated urbanized area. The remaining three sites are located in th moderately populated area. The short-duration AMP records in all locations vary between the minimum of 46 years and the maximum o 66 years. ! CMA and CA denote census metropolitan area and census agglomeration respectively. Statistics Canada defines a CMA as having a population density of at least 100000, where the urban core of that area has at least 50 000 people, whereas CA must have an urban core population density of at least 10000. A population centre (or urban area) is an area with at least a population of 1000 and a density of 400 or more people per square kilometre. All population information is collected from the Statistics Canada (https://www 12.statcan.gc.ca/) website. 2 Missing values are infilled using observations from the nearest Environment Canada station, ID 6144475 (latitude 44° and ing years or durations are obtained by disaggregating daily data to hourly and sub-hourly time steps. longitude —81.5°), located at 111.5 km geodesic distance. Annual maxima values of miss
Figure 2. Schematics of the process flow (blue — input steps, orange — process steps, and green — decision steps). All three tests - Mann— Kendall, Pettitt, and Mann—Whitney — check for shifts in the mean. While Mann—Kendall checks for monotonic trends, the other two tests, Pettitt and Mann—Whitney, check for a change point or regime shift in the time series. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 2. Schematics of the process flow (blue — input steps, orange — process steps, and green — decision steps). All three tests - Mann— Kendall, Pettitt, and Mann—Whitney — check for shifts in the mean. While Mann—Kendall checks for monotonic trends, the other two tests, Pettitt and Mann—Whitney, check for a change point or regime shift in the time series. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 3. Spatial distribution of trends, change points, and nonstationarities in rainfall extremes of several durations in nine urbanized locations, Southern Ontario (a—g). The up and down triangles in white indicate (statistically insignificant) upward and downward shifts; the up and down triangles in cyan and orange indicate shifts with change points only; the up and down triangles in dark blue and red show the presence of (statistically significant) trends, including change point(s). A “x” symbol in the triangle indicates nonstationarity detected through Priestley and Subbarao test statistics. All tests are performed at 10 % significance levels, i.e. p value < 0.10. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 3. Spatial distribution of trends, change points, and nonstationarities in rainfall extremes of several durations in nine urbanized locations, Southern Ontario (a—g). The up and down triangles in white indicate (statistically insignificant) upward and downward shifts; the up and down triangles in cyan and orange indicate shifts with change points only; the up and down triangles in dark blue and red show the presence of (statistically significant) trends, including change point(s). A “x” symbol in the triangle indicates nonstationarity detected through Priestley and Subbarao test statistics. All tests are performed at 10 % significance levels, i.e. p value < 0.10. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 4. DSI estimates of the median (horizontal line within the box plot) and 95 % credible intervals for 100-year return periods of stationary vs. nonstationary models across nine sites (a-i). The boxplots indicate the uncertainty in estimated DSI using Bayesian inference. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 4. DSI estimates of the median (horizontal line within the box plot) and 95 % credible intervals for 100-year return periods of stationary vs. nonstationary models across nine sites (a-i). The boxplots indicate the uncertainty in estimated DSI using Bayesian inference. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 5. Percentage changes (top panel) and Z statistics (bottom panel) of at-site T-year event estimates for T = 2-year to T = 100-year return periods (a—d) with durations between 15 min and 24h in nine urbanized locations, Southern Ontario. The Z statistic represents the statistical significance of differences in DSI obtained from the best selected nonstationary vs. stationary model. The Z statistic is statistically significant when |Z| > 1.64 at the 10 % significance level. The shades in blue and red denote decrease and increase in Z statistics, with the strength of the shading representing the magnitude of the test statistics. The durations with significant autocorrelations are excluded from the analysis. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 5. Percentage changes (top panel) and Z statistics (bottom panel) of at-site T-year event estimates for T = 2-year to T = 100-year return periods (a—d) with durations between 15 min and 24h in nine urbanized locations, Southern Ontario. The Z statistic represents the statistical significance of differences in DSI obtained from the best selected nonstationary vs. stationary model. The Z statistic is statistically significant when |Z| > 1.64 at the 10 % significance level. The shades in blue and red denote decrease and increase in Z statistics, with the strength of the shading representing the magnitude of the test statistics. The durations with significant autocorrelations are excluded from the analysis. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 6. Central tendency (median, b) and the bounds (95 % credible interval, a and c) of the updated nonstationary vs. EC-generated T =2- and 10-year event estimates for DSI at selected return periods with durations between 15 min and 24h. The DSI and associated 95 % confidence limits of EC-generated IDF are obtained from the national archive of Engineering Climate Datasets (http://climate.weather.gc.ca/). The shades in blue and red denote decrease and increase in DSI. The strength of the shading represents the magnitude of the ratio between updated and EC-generated DSI. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 6. Central tendency (median, b) and the bounds (95 % credible interval, a and c) of the updated nonstationary vs. EC-generated T =2- and 10-year event estimates for DSI at selected return periods with durations between 15 min and 24h. The DSI and associated 95 % confidence limits of EC-generated IDF are obtained from the national archive of Engineering Climate Datasets (http://climate.weather.gc.ca/). The shades in blue and red denote decrease and increase in DSI. The strength of the shading represents the magnitude of the ratio between updated and EC-generated DSI. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 7. Central tendency (median, b) and the bounds (95 % credible interval, a and c) of the updated nonstationary vs. EC-generated T =50- and 100-year event estimates for DSI at selected return periods with durations between 15 min and 24h. The DSI and associated 95 % confidence limits of EC-generated IDFs are obtained from the national archive of Engineering Climate Datasets (http://climate.weather. gc.ca/). The shades in blue and red denote decrease and increase in DSI. The strength of shading represents the magnitude of the ratio between updated and EC-generated DSI. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
Figure 7. Central tendency (median, b) and the bounds (95 % credible interval, a and c) of the updated nonstationary vs. EC-generated T =50- and 100-year event estimates for DSI at selected return periods with durations between 15 min and 24h. The DSI and associated 95 % confidence limits of EC-generated IDFs are obtained from the national archive of Engineering Climate Datasets (http://climate.weather. gc.ca/). The shades in blue and red denote decrease and increase in DSI. The strength of shading represents the magnitude of the ratio between updated and EC-generated DSI. P. Ganguli and P. Coulibaly: Does nonstationarity in rainfall require nonstationary IDF curves?
* GEV,-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, ir cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 2. Performance of stationary and nonstationary models for Toronto Pearson International Airport.
* GEV,-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, ir cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 2. Performance of stationary and nonstationary models for Toronto Pearson International Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, it cases where y > |, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 3. Performance of stationary and nonstationary models for Hamilton Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, it cases where y > |, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 3. Performance of stationary and nonstationary models for Hamilton Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, in cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 4. Performance of stationary and nonstationary models for Windsor Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, in cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DSI at a 100-year return period. Table 4. Performance of stationary and nonstationary models for Windsor Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, i cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DS] at the 100-year return period. Table 5. Performance of stationary and nonstationary models for London International Airport.
* GEV;-0 is a stationary model, whereas GEV;-I and GEV;-II are nonstationary models with a time-variant mean, and both a time-variant mean and standard deviation respectively. The selected best fitted nonstationary model is marked in bold letters. The Bayes factor, y < 1, indicates that the nonstationary model fits better than the stationary model. However, i cases where y > 1, to compare with the stationary model, the nonstationary model is selected following minimum AIC, criteria. LB and UB indicate the lower and upper bounds of DS] at the 100-year return period. Table 5. Performance of stationary and nonstationary models for London International Airport.
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