Cost-Effective Resilience - The Grey, the Green and the Ugly - WEAO Influents Article Examines Infrastructure Technology 'Bang for the Buck'

New article in the Water Environment Association of Ontario's Influents Magazine explores the cost-effectiveness on infrastructure technologies, including conventional 'grey' and emerging 'green' approaches for achieving extreme weather resiliency by reducing flood losses in existing communities.

See: article link

The article provides a brief history of Low Impact Development Best Management Practices (LID BMPs) in Ontario and the assessment of cost in infrastructure projects. New requirements for benefit-cost analysis for flood mitigation projects, such as through Infrastructure Canada's Disaster Mitigation Adaptation Fund, are also discussed. A previous post identifies some of these significant projects (

Results of a case study comparing grey, green and blended grey and green technologies are summarized. Details of this analysis are included in a previous post ( and were presented at the 2019 WEAO Annual Conference. The case study confirms the cost-effectiveness of conventional grey technologies, consisting largely of storm and sanitary sewer upgrades, and cast doubt on the cost-effectiveness of emerging green infrastructure or LID BMPs, considering full lifecycle costs. Limitations in the assessment of technical effectiveness green infrastructure in insurance industry research, as summarized in a previous post ( and in my NWWC2018 presentation Storm Warts, the Floods Awaken ( are briefly touched upon.

The move toward more rigorous assessments of project cost effectiveness is keeping with the Made-in-Ontario Environment Plan that intends to avoid the frustration of "policies and programs that don't deliver results". Such assessments are also consistent with Ontario's Long Term Infrastructure Plan 2017 that suggests that infrastructure proposals should be "supported by robust and consistent business cases".

Southern Ontario Observed Rainfall Intensities Decreasing - Annual Maximum Values Lower In Environment and Climate Change Canada's Engineering Climate Datasets (Version 3.0)

Ontario extreme rainfall annual maximum design intensity IDF trends climate change
Long term southern Ontario observed maximum rainfall trends,
according to Environment and Climate Change Canada's Version 3.0
Engineering Climate Datasets - decreasing trends in rain intensity and
more significant decreases than increases. 
Good news! Rainfall intensities have been decreasing in Ontario, Canada's most-populated province according to newly-released data. Less intense rain means lower urban flooding risk, contrary to many media reports that have confused future predictions of more extreme weather as a climate change effect with actual observed changes in the past. 

Maximum annual rainfall amounts over short durations at Ontario climate stations are used to derive engineering design intensities used in design of infrastructure such as sewers, culverts, channels, and ponds - the things that help convey rainfall runoff safety away from otherwise vulnerable people and property.

Environment and Climate Change Canada (ECCC) has recently updated its Engineering Climate Datasets that include a statistical analysis of observed trends in maximum values observed each year. The newest data are identified as Version 3.0 and are available as part of the Intensity-Duration-Frequency (IDF) Files on the ECCC website:

The previous Version 2.3 datasets showed decreasing annual maximum values at 21 southern Ontario climate stations with at least 30 years of observations - see previous post.

The updated Version 3.0 datasets continue this decreasing trend, showing that at the same 21 climate stations with an average observation period of 47 years:

  1. There are 42% more decreasing trends than increasing ones across all durations and stations (55.6% decreasing trends vs. 39.2% increasing ones).
  2. There are 75% more statistically significant decreases than increases (7 significant decreases vs. 4 significant increases).
This table shows the station name, ID, trends for each duration of 5 minutes to 24 hours, as well as the length of record and the most recent year in the Version 3.0 dataset.

Ontario Severe Rainfall Trends Climate Change Effects on Extreme Weather
Southern Ontario Observed Maximum Rainfall Trends - Environment and Climate Change Canada
Engineering Climate Datasets - Version 3.0
Trend Direction and Significance for 21 Climate Stations with Long Period Records (Greater than 30 Years)

Other observations:

  1. There are no statistically significant increases for durations less than 6 hours - that means the short duration convective storms burst that can lead to urban flooding related to most infrastructure systems do not show any appreciable increases.
  2. Overall downward trends are contrary to insurance industry statements, particularly the disproved "Telling the Weather Story" claim that there has been a one standard deviation increase in the probability of extreme rainfall according to Environment Canada data (the "Story" was only a theory/concept incorrectly cited and widely misreported as real data).
  3. Overall downward trends are contrary to many media reports citing a new normal of wild weather. Fortunately, some media, lead by the the Financial Post's Terence Corcoran are engaged in a critical review of urban flood drivers including extreme rainfall and the means to mitigate flood damages:
  4. CBC staff and the CBC Radio Canada Ombudsman have helped focus on facts Environment and Climate Change Canada data and corrected many stories on increasing storm frequency or intensity as noted here:
  5. Analysis by the School of Engineering at the University of Guelph, published in the International Journal of Environmental Research in 2015, looked at monthly trends and suggested that "The decrease in August extremes seems to have a significant impact on the annual extremes in the southwest and southeast regions":

Urban flooding is certainly an important issue to be addressed. And there are many factors that affect today's flood risks as explored in a previous post. While the insurance industry has suggested a link between increasing flood damages to increasing rain extremes due to climate change, given the wealth of evidence pointing to other quantifiable factors like increasing hydrologic and hydraulic stresses - and no change in rainfall extremes! - means that there is not even a correlation much less a causation relationship between flood damage and rain extreme trends (i.e., damages are up but rain intensities are down). This was pointed out in my Financial Post OpEd

Effective flood mitigation strategies must recognize the intrinsic capacity limitations in the vast amount of legacy infrastructure built over 30 years ago, and focus on reducing risks by addressing any level of service gaps through adaptation. Cost-effective and timely methods can include increasing the conveyance capacity of grey infrastructure, as opposed to mitigating rain/weather stresses that have not appeared to change, based on official, national engineering datasets. While such infrastructure investments should consider potential future climate effects, and we have many examples of analyzing stormwater and wastewater systems for such effects, past trends do not point to an increase to date in rainfall extremes. As a result, derived intensity duration frequency values for the stations reviewed above, based on values in the Version 3.0 datasets, shows an overall decrease in design intensities for small frequent and large rare storms across southern Ontario - those results were presented in a previous post, as shown below:

Ontario extreme rain IDF trends
Ontario Intensity Duration Frequency (IDF) Trends - 2 Year to 100 Year for all Durations
Environment and Climate Change Canada Engineering Climate Datasets - Version 3.0

Recognizing trends in observed rainfall maximum values and the derived design intensities will support data-driven, evidence-based policies and programs for achieving flood resilience through strategic infrastructure investments.


The following table explores annual maximum values at Ontario climate stations with over 50 years of record:
Ontario Extreme Rainfall Severe Weather Storm Trends
Ontario Observed Maximum Rainfall Trends - Environment and Climate Change Canada
Engineering Climate Datasets - Version 3.0
Trend Direction and Significance for 11 Climate Stations with Long Period Records (Greater than 50 Years)

The table expands into higher latitude eastern Ontario communities including Kingston and Ottawa as well as to northern Ontario. The eastern Ontario climate stations show an overall consistent trend in decreasing observed rainfall maxima over the shortest durations. Another eastern Ontario station, the Ottawa Airport also shows decreasing trends over short durations, including several statistically significant decreases (i.e., lower observed rainfall intensities) for durations of 10 minutes, 15 minutes and 1 hour.

Previous analysis of the Version 2.3 datasets showed the differences in southern and northern Ontario trends. Increases in intensities in the north, beyond Ontario's largest urban centres, could reflect a shift toward more rainfall events instead of snowfall as a result of warming temperatures. 

Is Wild Weather and a New Normal for Severe Rainfall Responsible for Urban Flooding, or Urbanization and Hydrologic Stresses? Case Law Points to Urbanization Driving Runoff and Flood Effects.

Everyone has an opinion on the weather and media is saturated with stories linking extreme weather with flooding. It makes sense. Flooding happens during severe storms. The bigger the storm the bigger the flood damages in fact.

But media and groups including the insurance industry and some researchers have suggested that flooding and flood losses have increased due to changes in weather patterns characterized by increased intensity or frequency of rainfall events.

That is not true. And there is no data to support that explanation.


Because rainfall intensities have not changed according to official Engineering Climate Datasets that review and analyze trends in extreme rainfall to inform engineering design across Canada.

Some media are correcting this false explanation that new wild weather, or a new normal, is causing flooding, like the CBC.

The CBC Ombudsman has ruled that CBC News reporting violated standards of journalistic practice in reporting more 100 Year storms linked to urban flooding - see the scathing report. It begins:

"Review by the Office of the Ombudsman, French Services, CBC/RadioCanada of two complaints asserting that the articles by journalist Marc Montgomery entitled How to mitigate the effects of flood damage from climate change and Response to a climate change story, posted on September 19 and November 19, 2018, respectively by Radio Canada international (RCI), failed to comply with the CBC/Radio-Canada Journalistic Standards and Practices regarding accuracy and impartiality."

and regarding this claim in the article on changing storm patterns:

“We are experiencing storms of greater magnitude, more volume of rain coming down over short periods of time these days due to climate change. That is causing massive flooding.”

the CBC Ombudsman concludes that (my bold):

"One only had to examine the official Environment Canada data for Ontario as well as for the
entire country to acknowledge that the claim made in the article was inaccurate. Such
acknowledgement would at the same time have addressed the complainant’s criticism regarding
the lack of data to corroborate Dr. Feltmate’s claim about the increased frequency of extreme
rainfall events in Canada."

While Environment and Climate Change Canada have refuted insurance industry claims on storm frequency shifts in the past (see Canadian Underwriter correction on the IBC/ICLR Telling the Weather Story theoretical shifts mistakenly reported as real data).

Yet the insurance industry has continued to promote the 'causation', with opinion pieces (not any peer-reviewed paper or analysis) saying climate-change effects on rainfall drive flood losses. See Financial Post piece

If not rainfall, what causes more flooding, more flood damages?

Canadian courts have pointed to urbanization as a driver, as in the landmark case of Scarborough Golf Country Club Ltd v City of Scarborough et al.. The decision indicates that urbanization markedly increases runoff stresses that cause runoff, erosion and flooding. Some highlights:

i) "Expert evidence confirmed the effect of the city's rapid urbanization and water control plans on the creek." 

ii) "It is important to note that the case is not presented primarily as a complaint against flooding but rather that the markedly increased flows and increased velocity of flow have caused and continue to cause damage to the creek bed and the adjacent tableland.", and 

iii) "There can be no doubt that the storm sewer facilities and urbanization of the lands to the north of the Club are the cause of the effects just described and that the difference in flow and velocity of flow is very substantial." 

So urbanization markedly increases runoff, flows and velocities, while there are no observed changes in extreme rainfall. Mapping clearly shows the significant expansion of urban areas in southern Ontario municipalities - see post and images below:

The IPCC has reviewed the size and frequency of floods at larger regional scales in their extreme events report and noted limited to medium information to assess changes, also noting the effects of changes in land use and engineering (see page 8):

"There is limited to medium evidence available to assess climate-driven observed changes in the magnitude and frequency of floods at regional scales because the available instrumental records of floods at gauge stations are limited in space and time, and because of confounding effects of changes in land use and engineering. Furthermore, there is low agreement in this evidence, and thus overall low confidence at the global scale regarding even the sign of these changes."

IPCC notes low confidence in the sign of changes at a global scale, meaning flood magnitudes could be going up or down.

Other factors driving losses? Research shows for some severe weather event types like hurricanes the driver is GDP growth, e.g., "research is robust in concluding that, for many decades into the future, the primary driver behind increasing economic losses related to hurricanes is expected to be societal growth"  

More factors? Maintenance of infrastructure affects its performance and flood risks. For example, TRCA described that flooding of the Keating Channel and lower Don River, which affects Toronto's Don Valley Parkway was due to a lack of maintenance:

"Since its construction between 1914 and 1922, the Keating Channel has been subject to heavy sediment loads, requiring regular dredging to maintain sufficient depths to allow for and maintain shipping activities at the mouth of the Don River. Between 1950 and 1970, widespread development throughout the Don Watershed and the construction of the Don Valley Parkway increased sedimentation rates by up to four times that of the pre-was era. After 1970, decreases in the number of new watershed disturbances and improved sediment control structures likely contributed to the decline in sedimentation in the Keating Channel to levels similar to the pre-war era. A reduction in shipping activities within the Keating Channel, combined with restrictions on the open water disposal of dredgate imposed by the International Joint Commission (IJC) in 1974, resulted in a cessation of dredging in the Keating Channel. In the following five to six years, the Keating channel filled with sediment and debris to the point where it became visible under all but high lake levels, resulting in increased flood risk along the lower Don."

So flood risks increase due to fluviogeomorphology (the transport and deposition of sediments in a watercourse) and hydraulics - when dredging stops, sediment builds up, hydraulic capacity is reduced and flooding is increased along the river. 

Yet despite flooding dating back to the 1800's, as reported in the Inquiry for Premier Davis, and despite impacts on rail lines in the Don River floodplain over decades, flooding has been attributed to climate change effects. Even by the Environmental Commissioner of Ontario. The fact is there is no new normal with "wild weather", but the same old issues and extremes:

Hydraulics affect sewer system capacity and flood risks as well. Modifications to store sewage and prevent discharge to the environment can constrain capacity and contribute to higher back-up risks, as documented in approved Class Environmental Assessment Studies in Ontario. Call this "The Law of Conservation of Poop" - holding back sewage in the collection system to prevent overflows causes surcharge levels to rise, sometimes closer to basements, increasing basement flooding risks. The excerpt below from the Toronto Area 32 Municipal Class EA describes "Causes of Flooding" related to operation of the tanks installed to protect Lake Ontario and beach water quality:

And while stormwater runoff and sewage level are rising in storm and wastewater collection systems due to urbanization and hydraulic constraints, risks are being increased by lowering basements, exposing higher value finishing and contents to flood damages - in Toronto, the rate of basement lowering, tracked through Toronto Open Data building permits for foundation underpinning, has increased significantly as shown in this post. The chart below shows the data trends:

A new report "Canada’s Changing Climate Report" lead by Environment and Climate Change Canada confirms that there is no change in extreme rainfall in Canada based on observations (see Chapter 4) saying "There do not appear to be detectable trends ...":

This certainly contradicts claims made by an insurance industry-funded research group that have indicated there is 'a lot of data to show it' when it comes to bigger storms. A February, 8, 2018 presentation to the Standing Senate Committee on Energy, the Environment and Natural Resources included this statement:

"So when you see in the news and the media people talk about storms seem bigger and more intense and so forth, those perceptions are correct. And there's a lot of data to show it."

But a review in a recent presentation to the National Research Council's 2018 workshop on flooding that showed there is no data to support the statement. Concerns with insurance industry statements on frequency shifts were also expressed by Environment and Climate Change Canada staff in relation to the Telling the Weather Story 40 year to 6 year weather shift. Staff had concerns with statements that could confuse theory and actual changes. Here is an excerpt from communications regarding the Telling the Weather Story normal bell curve theory shift:

"The presentation looks to be a simple conceptual model for communicating the underlying idea – if one assumes a standard normal, then a shift in the mean implies an attendant change in extremes – which is fine as far as it goes. If this is used as the basis for statements about actual changes in extreme rainfall in Canada, then I would have concerns."

Here was the specific question posed:

Here is a graphic showing the theoretical shift in question, an arbitrary 1 standard deviation shift in a standard normal 'bell curve' (probability density function):

The Environment and Climate Change Canada report also speaks to theoretical shifts in probability density functions, like the Weather Story bell curve shift. This is the example showing a shift right in the distribution of extreme events Figure 4.2.1:

The reality is that in some regions when it comes to extreme rain intensities there is not a shift to the right but a shift to the left, meaning less extreme events, as shown in this annotated curve that reflects southern Ontario rain intensity shifts:

The 'green' shift to the left reflects an overall decrease of 0.4% in rainfall design intensities at 21 long term climate stations since 1990, considering durations related to urban flooding, i.e., 5 minutes to 24 hours. That analysis of the new Version 3.0 Engineering Climate Datasets was presented in this post.

There is often a statement that changes in means will lead to changes in extremes in a distribution of probabilities - this makes sense. This concept is reflected in IPCC reports as well:

But data shows that the means, the 2 Year storm rain intensities, the events that we have the most observations of and the most confidence in assessing trends are decreasing the most. The Version 3.0 datsets review for southern Ontario shows on average a drop of -0.8% in those rain intensities, as shown on this table in the first column:

In this region, the extremes can be expected to decrease along with the means - on average that is happening too for the 100 Year rain intensities.

The Environment and Climate Change Canada report notes 'medium confidence' in increases in annual precipitation across the country and "low confidence in quantifying regional or national total amounts of precipitation" - so medium confidence in it going up but low confidence in saying how much, especially at more local spatial scales, or regions.

Since little or no infrastructure is designed to address annual precipitation, the reports limitations on the annual precipitation statistic are irrelevant to cities facing challenges like urban flooding during extreme, short duration events. Based on CatIQ datasets, a higher number of flood claims and a higher value of claim is associated with rare storm volumes falling over duration of minutes and hours and not annual totals.

The key take-away is that extreme rainfall has not been observed to change, whether for higher frequency events like 2 Year storms, or for low frequency, rare events, like 100 Year storms.

It is easy for the media to confuse annual precipitation with rain extremes, and in the case of Canada’s Changing Climate Report, CBC News reported that urban flooding related to intense rain will increase too - CBC has since corrected that article noting the report did not find increased short-duration rainfall linked to basement flooding:

The Environment and Climate Change Canada report cites research that points to land use change having a "key role" in affecting flooding, for example for the southeast Prairies flood in 2014. Here is the excerpt on attribution of flooding to rainfall or other factors, saying "Anthropogenic influence may have influenced rainfall, but landscape modification played a key role in increased runoff":

This is consistent with reporting by the American Society of Civil Engineers who in their Adapting Infrastructure and Civil Engineering Practice to a Changing Climate document state: "It is important to point out that land-use changes (e.g., urbanization) can result in substantial flooding impacts, independent of climatic forcing functions." - see page 12.

Regarding attribution, it is also consistent with a recent report on extreme rainfall event attribution that also identifies a lack of association of extreme convective storms, those responsible for much urban flooding, with anthropogenic climate change effects. For example the National Academies of Sciences, Engineering, and Medicine. 2016 report Attribution of Extreme Weather Events in the Context of Climate Change states (see page 97):

"Studies of trends in the United States find different results depending on the time period and spatial region chosen, but there is no broad agreement on the detection of long-term trends in overall severe
convective storm activity such as might be related to anthropogenic climate change."

Regarding land use influence on runoff and flood risk, this is also consistent with analysis by the University of Guelph's Engineering Department on changes in urban 'runoff coefficients' (the fraction of rain that runs off and can contribute to flood stresses) due to urbanization like in the Don River watershed:

That analysis was intended to 'disentagle' the impacts of climate change and land use change. Green bars are pre-urbanization coefficients showing we had a small fraction of rain becoming runoff, while blue bars show significant increase in runoff potential after 50% urbanaization. Note there is uncertainty in flow monitoring too, just like in precipitation monitoring, but we see a 10 times, 1000% increase in runoff potential in summer months, when we have the highest rain intensities, due to urbanization. The urbanization effects are MASSIVE - the Scarborough Golf court case reiterated this fact over and over referring to "markedly increased flows".

Compared to urbanization effects on flows, meteorologic effects are a big "nothing burger", with no observed changes and just a lot of theory and speculation. We should design for uncertainty in the future, and incorporate cost-effective adaptation considerations or flexibility for future adaptation (ASCE's Observational Method for climate adaptation) however we should not mischaractierize past trends and risk factors driving today's infrastructure performance limitations.

The University of Guelph analysis also indicates that spring peak flow rates will decrease with climate change effects that reduce winter snowpacks and spring melt flood potential. The follow chart shows the decrease in spring peaks in the rural Moira River watershed:

The Environment and Climate Change Canada report recognizes the impacts of temperature on snow patterns in Chapter 4: "As temperatures increase, there will continue to be a shift from snow to rain in the spring and fall seasons.". The report also cites research that "The reduction in spring snow pack and the ensuing reduction in summer streamflow in British Columbia have been attributed to anthropogenic climate change". Other cited research notes "Such a change in the form of precipitation, from snow to rain, has profound impacts in other components of the physical environment, such as river flow, with the spring freshet becoming significantly earlier." - the University of Guelph research shows that the winter period flows increase from November to early March in the Moira River example, and the peaks decrease significantly from late March and April. This decrease in peaks will result in a decrease in spring flood risks in watershed affected by such events.

So there is no new wild weather, or new normal driving flood damages. Case law in Ontario defining the effects of hydrology, or urbanization, findings of inquiries into Don River flooding for Premier Davis, Municipal Class Environmental Assessment studies investigating basement flooding causes and solutions, and Environment and Climate Change Canada's Engineering Climate Datasets that examine trends in observed rainfall intensities show us that hydrology, hydraulics, fluviogeomorphology explain today's flood risks, and there is has been no shift in rainfall intensities, despite median and insurance industry 'weather stories' and claims.

Environment Canada Report Confirms No Overall Change in Extreme Rainfall - Generally Random Ups and Downs - Stated Certainty of Future Shifts Contradicts American Society of Civil Engineer's "Significant Uncertainty"

A new Environment and Climate Change Canada (ECCC) report Canada’s Changing Climate Report reviews past, observed rainfall extremes and confirms there are no observed changes in extreme rainfall across the country:

"For Canada as a whole, there is a lack of observational evidence of changes in daily and short-duration extreme precipitation."

ECCC predicts increases showing a theoretical probability density function shift (Figure 4.21) where the blue line probability density function represents today's/yesterday's eventt magnitudes and frequencies without climate effects, and red represents with effects (shift right means higher magnitude for any frequency):

Engineering Climate Datasets in some regions show trends in the magnitude of rain intensity magnitudes (reality) going the other way however: .

This image shows the difference between the theory and the local data reality - the green line is the REALITY showing for any given frequency (2, 10, 50, 100 Year events) the magnitude is going down in southern Ontario:

ECCC suggests there is insufficient data to observe the changes in extremes expected: "Estimating changes in short-duration extreme precipitation at a point location is complex because of the lack of observations in many places and the discontinuous nature of precipitation at small scales." - while that MAY be accurate for extreme events that are rare and elusive, why do 2 Year rain intensities, derived from many, many yearly observations at all long term rain gauges, show the clearest decline, across all durations from 5 minutes to 24 hours?

Surely, we have DO enough point locations and observations to see the change in these small storms. But if these small frequent storm intensities are no higher with today's temperature shifts, why do we expect the extremes to be higher either? Data we do have shows in southern Ontario these 100 year intensities are 0.2% LOWER on average. So extremes are shifting shifting along with the means.... shifting lower.

A theoretical probability density function shift has been promoted in the past by ICLR and IBC in the 2012 Telling the Weather Story report:

This has been shown to be 'made-up' and not related to real data (ECCC IDF tables and charts mistakenly cited as the source of the 40 year to 6 year frequency shift) - this chart shows the theoretical 1 standard deviation shift widely circulated by IBC and real data shifts:

See the difference between theory and data? It is pretty clear.

Given the lack of past trends, and uncertainty in future noted in the ECCC report ("It is likely that extreme precipitation will increase in Canada in the future, although the magnitude of the increase is much more uncertain"), we must follow the American Society of Civil Engineer's recommended "Observational Method" approach see 2015 report Adapting Infrastructure and Civil Engineering Practice to a Changing Climate at, and also see for the new 2018 manual on engineering practice Climate-Resilient Infrastructure, Adaptive Design and Risk Management.

The ASCE 2018 manual promotes incorporating any no-regret, now cost measures in design today considering most probable future conditions, and allowing design flexibility to adapt in the future if and when performance is shown to be inadequate or affected by future changes - this is a practical approach intended to avoid costly over-design, and over-investment in potentially unnecessary and cost-ineffective infrastructure today.

While the ASCE 2015 report notes the high degree of uncertainty "However, even though the scientific community agrees that climate is changing, there is significant uncertainty about the location, timing and magnitude of the changes over the lifetime of infrastructure."

In contrast, the ECCC report appears to asset a high degree of confidence in future changes saying "For Canada as a whole, there is a lack of observational evidence of changes in daily and short-duration extreme precipitation. This is not unexpected, as extreme precipitation response to anthropogenic climate change during the historical period would have been small relative to its natural variability, and as such, difficult to detect. However, in the future, daily extreme precipitation is projected to increase (high confidence). - how can ECCC assert high confidence when there are no observed trends? How can ECCC contradict ASCE's statement on high "signifcant uncertainty'?

ECCC reports that summer precipitation is expected to decrease: "Summer precipitation is projected to decrease over southern Canada under a high emission scenario toward the end of the 21st century, but only small changes are projected under a low emission scenario." - how can that be if the summer temperatures are going up? Does this not violate the Clausius-Clapeyron theory cited in the ECCC report states that "increased atmospheric water vapour in this part of the world should translate into more precipitation, according to our understanding of physical processes" - so that is a theory - what about the real data? What does it show? the Clausius-Clapeyron relationship does not stand up to scrutiny as shown in a previous post.

Given highest rainfall extreme are in the summer (see the work of Dr. Trevor Dickinson on seasonal extremes), a summer decrease in precipitation could potentially mean lower flood risks. The data for southern Ontario already show a decrease in the annual maximum series (reflecting lower means and typical 2 Year design intensities in derived IDF curves) and the extreme 100 Year design intensities are decreasing slightly as well.

Overall, many in the media have over-hyped concerns about changing rainfall severity. Data and ECCC's report shows there has been no change, beyond random fluctuation. Looking ahead the American Society of Civil Engineers indicates that future changes have "significant uncertainty"- this contracts the ECCC's statement on "high confidence" on future extremes.

Are Six 100 Year Storms Across the GTA Rare Over a 14 Year Period When Considering Probabilities of Observing Extremes at over 150 Rain Gauges?

Roll a 100-sided die once. That is what looking
for a 100 Year storm at a single rain gauge
in a single year is like.
A motion at the City of Toronto notes the following regarding extreme rainfall in the GTA: "According to the Insurance Bureau of Canada, the Greater Toronto Area has had six “100 Year Storms” since 2005". See Mike Layton motion here:

CBC has reported on this: link

While we are all concerned about flooding, the question on large storm frequency is "So What?". Or more specifically, from a statistical, mathematical, logical point of view, is more than five 100 Year storms over a 14 year period (2005 to 2018) rare and unexpected, or does this have a high probability of occurring? As we know the Insurance Bureau of Canada does not always rely on proper statistics to support statements on extreme weather, confusing theoretical shifts in probabilities of extreme events with real data (see IBC Telling the Weather Story where IBC ignores Environment and Climate Change Canada's Engineering Climate Datasets).

Let's do some math to see if over five 100 Year storms is rare or not.

First, consider that a 100 Year storm has a probability of occurring of 1/100 = 1 percent per year.


Second, count up the number of rain gauges that have been proliferating across the GTA to support inflow in infiltration studies for wastewater studies and to support operational needs. Here are some counts with various sources:

i) City of Toronto ( - 46 rain gauges

ii) Region of York ( - 71 rain gauges

iii) Peel Region ( - 6 rain gauges

iv) Halton Region ( - 14 rain gauges

v) Toronto and Region Conservation Authority ( - 14 rain gauges

Total number of gauges = 151. A good first estimate - certainly there are more.


Third, assuming each rain gauge observes rainfall events independently year to year, what is the chance of getting at least one 100 Year event at a single gauge in 14 years?

Probability = 1 - (1-1/100)^14 = 13.1% chance of a 100 Year storm storm at a single gauge. That seems pretty big.

The number of 'trials' or samples equivalent to 14 rolls of a 100-sided die, meaning 14 independent observations or 'samples' from the statistical population of events.

It is reasonable to assume that a single rain gauge can record a 100 Year event but not surrounding gauges? Yes indeed. The August 2018 storm in Toronto only exceeded 100 Year rainfall totals at one gauge. So it is reasonable for smaller, spatially isolated rainfall events that do occur.


Fourth, assuming all rain gauges observe rain independently what is the chance of getting more than one 100 Year events across all 151 gauge in 14 years?

The number of trials/samples/observations = 151  x 14 = 2114

Probability = 1 - (1-1/100)^(2114) = over 99.9% chance of at least one 100 year storm at 151 independent gauges. That is almost a certainty.

(Additional comment: we know that storms exceeding 100 Year volumes can cover large areas such that observations are adjacent gauges are not completely independent, especially if they are spatially very close - so this fourth scenario is considered an upper bound on sensitivity analysis considering gauge independence - below, another bound is evaluated assuming less independence).

What about more than five 100 Year storms over 14 years? We have to then consider combinations of events (we do not care which of the 2144 samples has the events) and approach this by subtracting the probability of 1, 2, 3, and 4 events. This summarizes the approach (thanks so much FP!):

The probability of 5 or more 100 Year events is again over 99.9% (see cell F22), showing that when there are many, many trials, the probability of a multiple rare event is very high.


Fifth, assuming large storms cluster across several gauges and they do not operate independently from each other for extreme events, and that say they observe 100 Year storms in groups of 5, what is the chance of getting one 100 Year event across 151/5 = 30.2 rain gauge clusters in 14 years?

The number of trials/samples/observations = (151 x 14) / 5 = 2114 / 5 = 422.8

Probability = 1 - (1-1/100)^(422.8) = over 98.5% chance of at least one 100 year storm at 30 independent gauge clusters.  Near certainty. Not rare at all!

Let's consider over five 100 Year storms again. A keen reader has shown that the probability is 41.6% for this, as shown in cell L22 in the spreadsheet image above. Again,pretty high chance of getting 5 or more events when gauges do not observe extremes independently, but rather in clusters.

For more on this analysis, and the probability of 5 or more occurrences in 423 observations the probabilities considered in deriving the probability are as follows:
  • 4 occurrences in 423 observations (P = 0.195038119)
  • 3 occurrences in 423 observations (P = 0.183893083)
  • 2 occurrences in 423 observations (P = 0.1297298)
  • 1 occurrences in 423 observations (P = 0.060868484)
  • 0 occurrences in 423 observations (P = 0.014245815)
  • Sum = 0.583775302
So P[ X ≥ 5; 423] = 1 - 0.583775302 = 0.416224698, or 41.6% noted above. This is the common approach for deriving the probability of a scenario, i.e., by subtracting the probability of the event not occurring from 1.0 (the probability of all events). In this case the sum of the probability of zero to 4 observations occurring is the probability of the scenario of interest (5 occurrences or more) not occurring. If you are interested in testing other scenarios and assumptions for size of rain gauge clusters, use this helpful web site (also used to check the calculations in the spreadsheet shared above): Below are checks of the probability analysis:

Probability of 5 or more 100 Year Storms at Independent Rain Gauges (151 gauges x 14 years = 2114 'trials')
Probability of 5 or more 100 Year Storms at Clusters of Rain Gauges With Dependent  Observations (30.2 gauge clusters x 14 years = 422.8, say 423, 'trials')
There are more rain gauges in Durham Region and other Conservation Authorities in the GTA which means there may be more than 30 clusters to observe extreme weather in, meaning an even higher probability of observing extreme events.

So about 423 rolls of a 100-sided die may result in more than five occurrences of a single number with a relatively high probability. If the clusters are bigger, the probability is a bit less, but as we have seen, sometimes only one gauge 'sees' the 100 Year extreme rain. If gauges observe events in clusters of 10, which is an extreme end of the range as we have examples of storms affecting only one gauge (August 2018 in Toronto), there is still a probability for 5 events of over 5% (see below):

Probability of 5 or more 100 Year Storms at Large Clusters of Rain Gauges With Dependent  Observations (15.1 gauge clusters x 14 years = 211.4, say 211, 'trials')
Past flood events in Toronto reveal that between 1 and 13 rain gauges observe 100 Year rainfall depth, as shown in this Toronto Water presentation:
It shows:

  • May 12, 2000 - 1 rain gauge over 100 Year (see slide 9)
  • August 19, 2005 - 12 rain gauges over 100 Year (see slide 11)
  • July 13, 2018 - 6 rain gauges over 100 Year (see slide 19)
The August 7, 2018 flood in Toronto was due to only one Toronto rain gauge in the Open Data dataset exceeding 100 Year volumes. Therefore, assuming a cluster size of 5 dependent rain gauges within independent clusters that observe extreme events seems quite reasonable.

Conclusion - is it not rare to get more than five 100 Year rainfall observations at over 151 GTA gauges, over 14 years. The chances range from near certainty (over 99.9%) for independent events at each rain gauge to relatively high probability (over 40%) if gauges are independent clusters of 5 or more.


So what else does that tell us? There is a tendency to exercise an 'availability bias' in the words of Daniel Kahneman, and ignore statistics when making quick observations about extreme events. A description of this and other "Thinking Fast" heuristic biases surrounding flooding and extreme weather is in this paper.

Most media reports seldom "do math" and echo sources without question many times - that was the finding of the CBC Ombudsman on this topic of more frequent or severe extreme rainfall recently - see Ombudsman ruling.

Its one thing for a reporter to echo IBC statements on extreme weather for a news story, but Toronto should be careful in taking on a court case with limited data - it would be great to see any IBC statistics or analysis (unlike in the Telling the Weather Story communications). Toronto should also be aware that its flood problems are due mainly to its own design standards in the original size municipalities dating back before the 1980's. Spatial analysis shows that is where the risks are and where the flood reports are being made to the City of Toronto - see slide 36 in this review of flood risk factors which clearly do not include more extreme weather - partially separated systems have the highest risk and Toronto has allowed development to occur without mitigating risks in the past (hence the famous Scarborough Golf court case decision against municipalities for gaps in their stormwater management practices (Scarborough Golf Country Club Ltd v City of Scarborough et al)). Same thing on other GTA cities - see slide 7 in this presentation to the National Research Council's national workshop on urban flooding February 2018 for flood vulnerabilities in the City of Markham - see where Mississauga flood calls occur in this previous post (more than half of flood calls are in pre-1980 areas designed with limited resiliency for extreme weather).

So there has always been flooding:

And the most extreme rainfall intensities in Toronto over short durations happened in in the 1960's:

And now extreme rainfall statistics from Environment and Climate Change Canada show decreasing short duration intensities since 1990 in and around Toronto:

.. as shown in a previous post. These 5 minute 100 Year intensities have dropped between 4.0 % and 8.1% between 1990 and 2016-2017 depending on the location.

Such decreases in short duration intensities are happening across southern Ontario as well, based on the newest Engineering Climate Datasets as shown here. Toronto should be careful in preparing for a legal challenge and any claims on flood causes.

As noted in my recent Financial Post OpEd, making a big deal about irrelevant risk facts distracts us from addressing the root cause of flood problems. The City of Toronto should try to not get distracted. And Councilor Mike Layton is probably in the running for a Milli Vanilli "Blame it on the Rain" award this year :)


Terence Corcoran covers this all very well in today's column, referencing analysis on this blog.

Note: probabilities for 5 or more events corrected/updated April 1, 2019. Thanks to keen readers for helping define the probabilities of combination events and for the nostalgic references to University of Toronto's Professor Emeritus Dr. Barry Adams' CIV340 course notes that outline the analysis approach.