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The Ontario Ministry of the Environment Conservation and Parks, and other regulatory agencies perform much more rigorous statistical analyses than the example presented, and their resultant stormwater management targets vary accordingly.
The Ontario Ministry of the Environment Conservation and Parks, and other regulatory agencies perform much more rigorous statistical analyses than the example presented, and their resultant stormwater management targets vary accordingly.
==Example: City of Barrie, using years 2015 to 2017==
===Example: City of Barrie, using only years 2015 to 2017===
Daily rainfall records from ''BARRIE LANDFILL'' weather station were obtained for the years 2015 - 2017, from the [http://climate.weather.gc.ca/historical_data/search_historic_data_e.html Environment Canada historical data record].
Daily rainfall records from ''BARRIE LANDFILL'' weather station were obtained for the years 2015 - 2017, from the [http://climate.weather.gc.ca/historical_data/search_historic_data_e.html Environment Canada historical data record].
This graph shows the data as a ''time series'':
This graph shows the data as a ''time series'':
[[File:Barrie time series.jpg|border|700 px]]
[[File:Barrie time series.jpg|border|600 px]]
The number of times each depth of storm occured can be counted and grouped like this:
The number of times each depth of storm occured can be counted and grouped like this:
[[File:Picture1.jpg|border|700 px]]
[[File:Picture1.jpg|border|600 px]]
These same data can be fitted to a single equation which would then allow predictions to be made. In this example an exponential distribution function has been selected and an [https://www.wessa.net/rwasp_fitdistrexp.wasp online tool] used to find the fitting parameter 'λ'.
These same data can be fitted to a single equation which would then allow predictions to be made. In this example an exponential distribution function has been selected and an [https://www.wessa.net/rwasp_fitdistrexp.wasp online tool] used to find the fitting parameter 'λ'.
<math>f\left(x,\lambda\right)=\lambda e^{-\lambda x}</math>
<math>f\left(x,\lambda\right)=\lambda e^{-\lambda x}</math>
The fitting found λ to be 0.11. When the equation is plotted, the graph looks like this:
[[File:Barrie prob.jpg|border|600 px]]
But the frequencies of the different rainstorms aren't very easy to understand like this.
The cumulative distribution function uses the same λ and is a more useful way to read the data.
<math>F\left(x,\lambda\right)=1- e^{-\lambda x}</math>
Plotted, it looks like this:
[[File:Barrie cumulative.jpg|border|600 px]]
The 90th percentile event is the rainstorm for which 90% of all rainstorms are this depth or less. In this example, using a very limited data set it was found to be 20 mm.
i.e. 90% of all storms ≤ 20 mm.
Storms of ≤ 5 mm represent 40% of the total in this example.
==See also==
[[Drainage time]]