projecting ontario’s future idf curves and associated potential … · 2017. 4. 7. · future idf...

Projecting Ontario’s future IDF curves and associated potential impacts using extrapolated and projected climate variables

Final technical report File No. CCMM-1516-008

March 14 2017

Prepared by Eric D. Soulis, Hiralben Desai, and Cameron Adams

University of Waterloo Department of Civil and Environmental Engineering

200 University Ave West Waterloo, Ontario, Canada, N2L 3G1

Tel: 519-888-4567

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Summary The Environmental Monitoring and Reporting Branch, Environmental Sciences & Standards Division of the Ontario Ministry of the Environment and Climate Change (MOECC) commissioned the University of Waterloo to improve intensity-duration-frequency (IDF) curves for Ontario by incorporating projected temperatures. This project represents the fourth installment in a series of reports documenting the results of a joint venture between the University of Waterloo, Ministry of Transportation Ontario (MTO) and MOECC. Both the MTO and MOECC have an interest in providing the best possible estimates of IDF curves over time.

Empirical data for all four phases was provided for the years 1960-2010 by the Meteorological Service of Canada (MSC), a branch of Environment Canada. In Phases I and II, a linear regression was performed using physiography as a predictor of IDF curve parameters, that resulted in an extreme precipitation interpolation model. In Phase III, the results of Phase II were extended to incorporate a linearly increasing trend previously observed in the data, which resulted in the Regional Trend Analysis (RTA) model.

Phase IV, documented in this report, extends the previous research in that it incorporated temperature into the estimate of precipitation distribution. This model is called Waterloo Interpolator – Topography, Temperature, Time (WIT3). WIT3 is more flexible than RTA, as it incorporates various hypothetical climate scenarios, such as RCP 4.5 or RCP 8.5. The model preserves a linear time trend from the RTA. This time trend dominates all other terms in the model, which results in forecasts that are similar to, but slightly lower than, those of the RTA model. The 100 y 1 h rainfall intensity values from WIT3 are, on average, 1.7 mm below those of RTA. The exception is Eastern Ontario, where intensity of short-duration rainfall projections from WIT3 was found to surpass those of the RTA after 2060.

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Contents Summary ............................................................................................................................................................. ii

List of figures ..................................................................................................................................................... iv

Definitions ........................................................................................................................................................... v

Symbols................................................................................................................................................................ v

Acronyms ........................................................................................................................................................... vi

Introduction........................................................................................................................................................ 1

Background .............................................................................................................................. 1

Project scope ........................................................................................................................... 2

IDF curves ................................................................................................................................ 2

Work completed ............................................................................................................................................... 4

1 – Comparing probabilistic precipitation estimates for historical time trends, IPCC and downscaled climate scenarios ................................................................................................. 4

2 – Relating Ontario’s historical rainfall and extreme temperatures ..................................... 5

Spatio-temporal analysis ................................................................................................................. 6

3 – Probabilistic precipitation forecast for Ontario ................................................................ 9

4 – Optimum method combination ....................................................................................... 13

Database Selection for Comparison and Results: ......................................................................... 14

5 – Risk assessment case study ............................................................................................. 18

CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 results for two sample stations ....................................... 22

6 – Incorporation into online tools ........................................................................................ 28

7 – Project findings dissemination ........................................................................................ 28

Conclusion ........................................................................................................................................................ 29

Appendix A: IDF curve projections under various climate scenarios, St. Catharines A, Ontario .......................................................................................................................................................... 30

Appendix B: Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate ...................................................................................................................................... 32

Bibliography ..................................................................................................................................................... 42

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List of figures Figure 1 : Sample MSC IDF curve for St. Catharines A (MSC 2014)......................................................... 3 Figure 2 : Probabilistic precipitation estimate comparison of PCIC data (blue) with historical MSC

extreme precipitation data (red) ............................................................................................. 5 Figure 3 : Residual analysis ...................................................................................................................... 8 Figure 4 : MSC (EC), OCCDP and PCIC extreme temperature comparisons for a) Hamilton,

Ontario, and b) Kenora, Ontario ............................................................................................ 11 Figure 5 : Empirical distribution function for historical extreme temperature and MPI-ESM-LR-

RCP 8.5 standardized by station mean, 1960-2010 ............................................................... 12 Figure 6 : Time series of annual maximum 24 h rainfall, St. Catharines A, ON .................................... 13 Figure 7 : Comparison of 24 h rainfall intensity return period estimates for eight stations across

Ontario for period, 1960-2010 for a) Armstrong, b) Cambridge Galt MOE, c) Cornwall, d) Hamilton RBG CS, e) Kenora A, f) North Bay, g) St. Catharines A, and h) Sudbury A ....... 15

Figure 8 : Geographic distribution of sample stations. .......................................................................... 16 Figure 9 : The difference in time-corrected rainfall intensity for the 100 y rainfall (99th percentile)

between the empirical MSC data and results from a) the WIT3 model, b) the RTA model, and c) the OCCDP model. A histogram d) shows the distribution of the deltas. ..... 17

Figure 10 : The difference between future 1 h extreme precipitation projections by MOECC and MTO ........................................................................................................................................ 20

Figure 11 : The difference between future 24 h extreme precipitation projections by MOECC and MTO ........................................................................................................................................ 21

Figure 12 : St. Catharines A 1 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ................................................. 22 Figure 13 : St. Catharines A 6 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ................................................. 23 Figure 14 : St. Catharines A 24 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ............................................... 24 Figure 15 : Sudbury A 1 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ........................................................... 25 Figure 16 : Sudbury A 6 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ........................................................... 26 Figure 17 : Sudbury A 24 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 ......................................................... 27

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Definitions

Base year – 2010 is the base year for this study. Time-based calculations are made relative to this date. While the study contains data for up to 2014, after 2010 the available station data decreases significantly in quantity.

Symbols 𝐴 = coefficient for rainfall intensity in mm/h that reflects the variation in

location and return period 𝐵 = dimensionless coefficient that reflects the variation in location and

return period 𝐵0 = intercept 𝐵1,𝐵2,𝐵3,𝐵4,𝐵5,𝐵6 = coefficients 𝐷 = rainfall depth (mm) 𝑒∗(𝑡) = saturated vapour pressure in year t (kPa) 𝐼1 = longitude (°) 𝐼2 = latitude (°) 𝐼3 = barrier height to west (m) 𝐾(𝑇) = Gumbel frequency factor for the return period 𝑛 = station identification 𝑅 = rainfall intensity (mm/h) 𝑅𝑛(𝑇, 𝜏) = storm intensity for the station at a given duration and return period 𝑅𝑛(𝑇, 𝑡, 𝜏) = storm intensity 𝑅𝑛(𝜏)�� = long-term average extreme rainfall 𝑅𝑛(𝑡, 𝜏)�� = expected value of storm intensity for duration 𝜏 t, station n and year t 𝑅𝑛(𝑡|𝜏 = 24) = 24 h rainfall intensity in year t (mm/h) 𝑅𝑛(𝑇, 𝑡|𝜏 = 24) = 24 h rainfall intensity for station n in year t for a given return period, 𝑆𝑛(𝜏) = long-term standard deviation of the extreme rainfall for the period of

record 𝑆𝑛 = residual standard error of the linear regression 𝜏 = event duration in hours 𝑇 = return period in years 𝑡 = calendar year 𝑡0 = base year, 2010 ∆𝑡 = 𝑡 − 𝑡0 �̅�(𝑡) = mean temperature in year t (°C) 𝜀 = random rainfall component (reflected in the residuals of the regression)

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Acronyms AR5 IPCC Fifth Assessment Report ASCII American Standard Code for Information Interchange BCCA hybrid BCSD and CA approach BCCAQ Bias Correction/Constructed Analogues with Quantile mapping reordering BCSD Bias Correction/Spatial Disaggregation Statistical Downscaling approach CA Constructed Analogues approach CMIP5 Coupled Model Intercomparison Project Phase 5 CMOS Canadian Meteorological and Oceanographic Society GCM Global Climate Model IDF Curve Intensity-Duration-Frequency curve IPCC Intergovernmental Panel on Climate Change MOEEC Ontario Ministry of the Environment and Climate Change MSC Meteorological Service of Canada MTO Ontario Ministry of Transportation OCCDP Ontario Climate Change Data Portal PCIC Pacific Climate Impact Consortium PRECIS Providing Regional Climate for Impact Studies QMAP Quantile Mapping RCM Regional Climate Model RCP Representative Concentration Pathways RTA Regional Trend Analysis WATMAPPR Waterloo Multiple Physiographic Parameter Regression WIT3 Waterloo Interpolator – Topography, Temperature, Time

- Projecting Ontario’s future IDF curves - Page 1 of 42

Introduction

As Ontario’s climate changes over time, a more sophisticated understanding of hydrometeorological processes is required, particularly of those processes associated with severe precipitation patterns. Intensity-Duration-Frequency (IDF) curves are important statistical representations of precipitation extremes and their changes through time. The research conducted in this study was part of an ongoing research program to update the IDF curves in Ontario. This program takes advantage of improved technology, larger datasets, improved interpolation techniques, and Global Climate Model (GCM) results to update the IDF curves. This project was commissioned by the Ministry of the Environment and Climate Change (MOECC) to predict futuristic scenarios of extreme rainfall, and to update IDF curves for Ontario. The project created future forecasts for extreme precipitation, and new non-stationary values for IDF curves under the impact of climate change. The extreme precipitation forecast it provides is an effective tool for storm water management and storm water runoff forecasts that is suitable for infrastructure project design, including waste water and water treatment plants.

Background

Initial funding for this research program came from the Ontario Ministry of Transportation (MTO) to Dr. Ric Soulis of the Department of Civil and Environmental Engineering at the University of Waterloo. The MTO-funded research program used seven physiographic parameters as predictors of IDF curve values. This method is known as the Waterloo Multiple Physiographic Parameter Regression (WATMAPPR). (Seglenieks, 2009) These physiographic parameters were then used to interpolate IDF curve values across Ontario. The incorporation of a linear time trend allowed for a novel approach, the implementation of non-stationary IDF values. The presence of a time trend was taken as an indication that thermodynamic effects, associated with climate change, were impacting precipitation. The research program began in 2010 and is ongoing.

The objective of this project was to refine the future IDF curves for Ontario, and assess potential impacts of the projected IDF curves on infrastructure design through a case study. The study refined future IDF curves for Ontario with projected local climate variables, and carried out a case study to assess potential impacts of the projected IDF curves on infrastructure design.

Soulis et al. (2016), noted that the first step to refine future IDF curves is to allow the mean of the distribution to change with time. Next, an attempt must be made to quantify this time trend and the stochastic component. The authors found that a Gumbel distribution describes this best. The stochastic component is then parsed into various sub-components. A variety of atmospheric phenomena, such as temperature and dew point, explain the values of the sub-components. This creates a new paradigm that characterises rainfall series and is sensitive to environmental data.


Project scope

This present MOECC-funded project is an extension of a three-phase research project for the MTO. The various research phases are described below.

In Phase I, the Recipient successfully interpolated IDF curves between stations. The Recipient developed a method to weigh station data by record length. As a result, the addition of new stations added skill to the interpolation rather than adding bias to the results.

Phase II refined the process developed in Phase I and added stations from neighbouring jurisdictions. The standard errors in results were reduced from 15 per cent to 10 per cent, and no regional bias was found in the distribution of errors after an update of the MSC dataset.

Phase III continued the refinement and validation of the model, incorporated secondary data to enhance IDF results, identified a regional time trend in the historical data, and added system enhancements to improve the functionality of the IDF Lookup tool

Phase IV, the subject of this report, uses a subset of seven physiographic parameters from previous phases for spatial interpolation. Future forecasting of precipitation extremes is achieved by considering the impacts of time and temperature-related parameters on current IDF values.

The research described in this report, with its identification and prediction of trends in extreme precipitation, refines the generation and application of local and regional IDF curves and provides objectivity and consistency for future infrastructure planning in Ontario.

IDF curves

IDF curves describe the extreme rainfall patterns of a location. They define the probability that a storm of a given intensity and duration will occur in a given year. The inverse of the likelihood is called a return period. Simply put, on average, a 2 y storm occurs every two years, a 5 y storm occurs once every five years, and so on. IDF curves summarize this annual probability of exceedance of storm intensity given a storm’s duration, 𝑃(𝑅, 𝜏), of intensity of rainfall, 𝑅, in a single event of duration, 𝜏 (h). 𝑃 is also known as the probability function. The return period, 𝑇, is defined by:

𝑇 = 1/𝑃(𝑅, 𝜏) ( 1 )

Equation (2) expresses rainfall intensity and volume:

𝑅 = 𝐴𝜏𝐵 ( 2 )

where:

𝑅 = 𝐷/𝜏 ( 3 )

and:


𝐴 = coefficient for rainfall intensity in mm/h that reflects the variation in location and return period,

𝐵 = dimensionless coefficient that reflects the variation in location and return period,

𝑅 = rainfall intensity (mm/h), 𝐷 = rainfall depth (mm), 𝜏 = event duration (h), and 𝑇 = return period (y).

Equation 2 is also known as the IDF curve. The IDF curve power-law interpolates intensity values between the common durations of 5 min, 10 min, 15 min, 30 min, 60 min, 2 h, 6 h, 12 h, and 24 h. The Regional Trend Analysis (RTA) model uses the two-parameter, 𝐴𝐵 method, which is the same method that MSC uses for the calculation of IDF curves. Figure 1 is an example of an IDF curve calculated for the St. Catharines A weather station.

Figure 1 : Sample MSC IDF curve for St. Catharines A (MSC 2014)


Work completed

The objective of this report is to provide advice to the MOECC on the appropriate selection of a scenario for Ontario and to provide a simply parameterized model that can characterize the output. The following sections reflect the Recipient responsibilities set out in the project agreement.

1 – Comparing probabilistic precipitation estimates for historical time trends, IPCC and downscaled climate scenarios

One objective of this study is the generation of a probabilistic precipitation estimate, using historical time trends from the MSC dataset, in comparison with the Intergovernmental Panel on Climate Change (IPCC) downscaled climate change scenarios for the period 1960-2010. The time trends were identified and quantified during Phase III of the MTO project, and formed the basis for the RTA. RTA provided the probabilistic precipitation estimates investigated in this section.

The IPCC Fifth Assessment Report (AR5), based on Coupled Model Intercomparison Project Phase 5 (CMIP5) was chosen as a base to select climate projections-based precipitation data based on climate models. AR5 is the most recent Assessment Report, and the data has been quality checked. Of the various sources of CMIP5 data, the Pacific Climate Impact Consortium (PCIC) is the most suitable, as the data from this source has a 10x10 km resolution, contains three climate scenarios—Representative Concentration Pathways (RCP) 2.6, 4.5 and 8.5—and is bias corrected. Further discussion about these three pathways is below in Section 3. Preliminary analyses determined the PCIC data behaviour for the historical period of 1960-2010. The empirical distribution of centered and time-adjusted PCIC data was plotted for 177 stations. The same was also done with MSC data. Figure 2 presents the comparison between the two. The PCIC data has a significantly lower standard deviation than that of the historical data, which results in upper quantiles (90 per cent, 95 per cent, etc.) that are lower than those of the observed historical data. This supports the claim that precipitation forecasts based on downscaled climate scenarios are unsuitable for IDF curve forecasts, which is the basis for this research. In contrast, the RTA model trends is generally conservative in its estimates of low-frequency, high-intensity rainfall events. For details, see Section 4 – Optimum method combination.


Figure 2 : Probabilistic precipitation estimate comparison of PCIC data (blue) with historical MSC extreme precipitation data (red)

2 – Relating Ontario’s historical rainfall and extreme temperatures

This study established a relationship between extreme precipitation and temperature, and forecasts extreme precipitation for future years with temperature as a predictor of precipitation. Downscaled GCMs under various climate change scenarios provide temperature forecasts that are used for the forecast of extreme precipitation based on the relationship between temperature and precipitation established using the historical data from 1960-2010.

Annual maximum precipitation values and physiographic parameters were taken from the MTO project database. In preparation for this study, the daily maximum, minimum, and mean temperature values were obtained from Environment Canada’s Historical Climate Data in the National Climate Data Information Archive. Of 133 stations across Ontario, 22 were filtered out as their temperature and precipitation data values did not temporally overlap with each other. The remaining 111 stations had temporally overlapped precipitation and temperature values. They were analyzed using R to filter out annual maximum and mean temperature values.

Maximum daily temperature values were first used to determine monthly maximum values then the annual maximum temperature value. The highest value in that 12-month set was chosen as the annual daily maximum temperature for a station for that calendar year. To determine the annual maximum mean monthly temperature, daily values were averaged for each month. This yielded the monthly mean temperature value. The maximum of the twelve monthly mean temperature values for a given year was then calculated. For the sake of simplicity, the annual maximum mean monthly temperature will simply be referred to as the “mean” for the remainder of this report.

Through the use of annual daily maximum temperature values, the annual maximum saturated vapour pressure was calculated with the following equation (Dingman, 2002):


𝑒∗ = 0.611 ∙ 𝑒𝑒𝑒( 17.3∙𝜃𝜃+237.3

) ( 4 )

where:

𝜃 = temperature (°C), and 𝑒∗ = saturated vapour pressure (kPa).

For simplicity, this value is referred to as the “saturated vapour pressure” for the remainder of this report.

Spatio-temporal analysis

The RTA model, described above in Phases I to III in the project scope, had already established a spatial relationship between extreme precipitation and station-specific peculiarities such as physiographic factors. The physiographic factors were: longitude, latitude, barrier height to the west, slope in the north/south direction, slope in the east/west direction, elevation, and distance to nearest major body of water such as The Great Lakes, Hudson Bay, or James Bay. In addition to these factors, a temporal trend was also established for extreme precipitation across Ontario.

These physiographic parameters were combined with saturated vapour pressure, annual mean temperature values, and time for a total of ten predictor variables. Multiple linear regressions were performed, using annual maximum 24 h rainfall intensity as the dependent variable. A backward selection procedure was implemented to select an optimal linear model first by eliminating insignificant model terms. With each iteration of the selection procedure, the p-values of the various parameters were examined, and the parameter with the largest p-value (lowest significance) was dropped from the model. This process was repeated until no parameters remained with p-values greater than 0.05.

Two exceptions were made to this procedure. The mean temperature was kept as a predictor, despite being slightly above the p-value threshold, since temperature increases the model’s non-stationary potential. Temperature, unlike the other physiographic variables, is also tied to climate change, so it has the greatest potential as a predictor. The second exception to the procedure is the selection of barrier height to the west as a predictor, rather than distance to water, despite a slightly higher p-value. Barrier height to the west, relative to distance to water, has a weaker correlation with the other variables, and thus has greater use in the spatial interpolation.

The result is an expression that relates the value of the maximum precipitation with time, annual mean temperature, saturated vapour pressure, barrier height to the west, and latitude/longitude. This equation was then used to calculate the expected value of the daily maximum precipitation for a given calendar year at respective stations in Ontario. Table 1 shows values and statistics of the model coefficients.


Table 1 : Daily maximum precipitation

Coefficients Standard error t-stat P-value

Intercept 2.270 0.631 3.600 0.000325

Year-2010 (∆𝒕) 0.00551 0.00147 3.760 0.000175

Mean temperature (𝜽�)

0.0260 0.0135 1.922 0.0547

Saturated vapour pressure (𝒆∗)

-0.0705 0.0316 -2.231 0.0258

Longitude (𝑰𝟏) -0.0139 0.00612 -2.268 0.0234

Latitude (𝑰𝟐) -0.0279 0.0123 -2.274 0.0231

Barrier height to west (𝑰𝟑)

-0.000819 0.000401 -2.044 0.0411

The final equation is:

𝑅𝑛(𝑡|𝜏 = 24) = 𝐵0 + 𝐵1 ∙ ∆𝑡 + 𝐵2 ∙ �̅�(t) + 𝐵3 ∙ 𝑒∗(t) + 𝐵4 ∙ 𝐼1 + 𝐵5 ∙ 𝐼2 + 𝐵6 ∙ 𝐼3 + 𝜀 ( 5 )

where:

𝑅𝑛(𝑡|𝜏 = 24) = 24 h rainfall intensity in year t (mm/h), 𝐵0 = intercept, 𝐵1, 𝐵2, 𝐵3, 𝐵4, 𝐵5, 𝐵6 = coefficients, ∆𝑡 = (𝑡 − 𝑡0) (y), �̅�(𝑡) = mean temperature in year t (°C), 𝐼1 = longitude (decimal degree), 𝐼2 = latitude (decimal degree), 𝐼3 = barrier height to west (m), 𝑒∗(𝑡) = saturated vapour pressure in year t (kPa), 𝑡0 = base year, 2010, 𝑛 = station ID, and 𝜀 = random component (reflected in the residuals of the regression)

Residual Analysis revealed that residuals follow a Gumbel distribution, as Figure 3 shows.


Figure 3 : Residual analysis

In the classical stationary IDF curve analysis, Hogg et al. (1989) use the following equation for each duration to determine station quantiles:

𝑅𝑛(𝑇, 𝜏) = 𝑅𝑛(𝜏)�� + 𝐾(𝑇)𝑆𝑛(𝜏) ( 6 )

where:

𝑅𝑛(𝑇, 𝜏) = storm intensity for the station, 𝑅𝑛(𝜏)�� = long-term average extreme rainfall, 𝐾(𝑇) = Gumbel frequency factor for the return period, 𝑆𝑛(𝜏) = long-term standard deviation of the extreme rainfall for the period of

record, 𝑇 = return period, 𝜏 = duration, and 𝑛 = station identification.

Equation (6) was used in Soulis et al. (2015), to estimate 𝑅𝑛(𝑇, 𝜏), which varies yearly. Thus, in non-stationary form, the design rainfall intensity for a given return period and year is given by Equation (7):

𝑅𝑛(𝑇, 𝑡, 𝜏) = 𝑅𝑛(𝑡, 𝜏)��+ 𝐾(𝑇)𝑆𝑛(𝜏) ( 7 )

where, 𝑅𝑛(𝑡, 𝜏)�� is the expected value from the precipitation-temperature model for station 𝑛 and year 𝑡.

Thus, the final equation, which estimates the design rainfall intensity of a 24 h storm for a given return period is:

𝑅𝑛(𝑇, 𝑡|𝜏 = 24) = 𝐵0 + 𝐵1 ∙ ∆𝑡 + 𝐵2 ∙ �̅�(𝑡) + 𝐵3 ∙ 𝑒∗(𝑡) + 𝐵4 ∙ 𝐼1 + 𝐵5 ∙ 𝐼2 + 𝐵6 ∙ 𝐼3 + 𝐾(𝑇) ∙ 𝑆𝑛 ( 8 )

where:

00.10.20.30.40.50.60.70.80.9

1

-2 3 8

Cum

ulat

ive

prob

abili

ty

Residuals

Gumbel Fit

EmpiricalDistribution

Gumbel distribution parameters: Alpha = -0.353 Beta = 0.612


𝑅(𝑇, 𝑡|𝜏 = 24) = estimated 24 h rainfall intensity for station 𝑛 in year 𝑡 for given return period,

𝐵0 = intercept, 𝐵1, 𝐵2, 𝐵3, 𝐵4, 𝐵5, 𝐵6 = coefficients, ∆𝑡 = (𝑡 − 𝑡0) (y), �̅�(𝑡) = mean temperature in year t (°C), 𝐼1 = longitude (decimal degree), 𝐼2 = latitude (decimal degree), 𝐼3 = barrier height to west (m), 𝑒∗(𝑡) = saturated vapour pressure in year t (kPa), 𝐾(𝑇) = Gumbel frequency factor for the return period, 𝑛 = station ID, 𝛵 = return period (y), and 𝑆𝑛 = residual standard error of the linear regression.

The difference between Equation 5 and Equation 8 is that 𝜀 is replaced by 𝐾(𝑇) ∙ 𝑆𝑛. To calculate return period rainfall intensities for durations other than 24 h, Equation 2 can be rearranged into the following form:

𝑅𝑛(𝑇, 𝑡, 𝜏) = 𝑒𝑙𝑛[𝑅𝑛(𝑇,𝑡|𝜏=24)]+𝐵(𝑙𝑛 𝜏−𝑙𝑛24) ( 9 )

where:

𝑅𝑛(𝑇, 𝑡, 𝜏 = 24) = 24 h storm intensity for a given year and return period 𝐵 = slope of the IDF curve, determined during previous research to be equal

to −1√2

τ = storm duration

3 – Probabilistic precipitation forecast for Ontario

To project the expected value of precipitation for future events, and using the year 2010 as a base, the input parameters required were annual daily maximum temperature and annual mean temperature. Various options were considered for future temperature data, such as GCM-based outputs, Regional Climate Model (RCM)-based temperature data, and different ensemble based temperature data. GCM output is coarse as it has large gridded climate data, and needs to be downscaled using either dynamic or statistical methods for its output to be used in the temperature-precipitation model. Downscaling methods have different biases that affect the end data. RCM outputs are finer than GCM outputs, which mean their grid sizes are much smaller than GCM outputs, but RCM methods also have biases which affect output. Often, an ensemble approach is adopted to compensate for these different biases and to compensate for systematic errors. The IPCC used an ensemble approach to develop the best possible climate impact studies for future years. The IPCC’s AR5, released in 2014, uses the data from CMIP5 that was also released in 2014. CMIP5 is the source of a quality assessed, reliable database used for scientific studies.


As per the objectives in Section 3, two sources were used to consider temperature inputs for future years: Ontario Climate Change Data Portal (OCCDP) and PCIC. OCCDP uses the Providing Regional Climate for Impact Studies (PRECIS) model, under the A1B emissions scenario and the RCM, under the RCP 8.5 emissions scenario. For this study, PRECIS data was selected for analysis. PRECIS is an ensemble of five GCMs, developed by the Hadley Centre for Meteorological Studies, in the United Kingdom. The GCMs use the A1B climate change scenario for future projections. The output from the OCCDP is downscaled to a 25 km resolution without bias correction, and is not continuous. The output is grouped into the 30 y periods of 1960-1990, 2015-2045, 2035-2065, and 2065-2095. PCIC output is historical daily gridded climate data based on an ensemble of 12 GCMs. PCIC contains historical data as well as future projections based on the IPCC’s RCP 2.6, 4.5 and 8.5. The data are quality checked as they are based on CMIP5. The data are bias corrected and statistically downscaled to a 10 km resolution using two methods: Bias Correction Spatial Disaggregation (BCSD), and Bias Correction/Constructed Analogues with Quantile mapping reordering (BCCAQ). BCCAQ is a hybrid method that combines results from BCCA (Maurer et al. 2010) and quantile mapping (QMAP) (Gudmundsson et al. 2012).

Observed historical data from ten randomly selected Environment Canada stations were used to compare the historical maximum temperature data from OCCDP and PCIC outputs from 1960-1990. Figure 4 shows the output for two stations, Hamilton and Kenora.


Figure 4 : MSC (EC), OCCDP and PCIC extreme temperature comparisons for a) Hamilton, Ontario, and b) Kenora, Ontario

The comparison of these ten sites revealed that PCIC data more closely matches the historical observed data. This is likely because the projections under AR4 at OCCDP were not bias-corrected.

Figure 5 shows the results of an empirical distribution fitting exercise performed on observed data and PCIC data from 1960-2010. As in Figure 2, the data for each station were adjusted to equivalent 2010 values with a fitted linear trendline, and subsequently standardized by subtracting the station mean. This exercise revealed that the PCIC temperature database matches the distribution of observed data. It was determined that downscaled GCM temperature projections from the PCIC database are suitable for use as input into a precipitation forecast model.

05

101520253035404550

1960 1965 1970 1975 1980 1985 1990

a)

ExtremeHighTemp(EC) ExtremeHigh Temp(OCCDP) ExtremeHigh Temp(PCIC)

0

10

20

30

40

50

1960 1965 1970 1975 1980 1985 1990

b)

ExtremeHighTemp(EC) ExtremeHigh Temp(OCCDP) ExtremeHigh Temp(PCIC)


Figure 5 : Empirical distribution function for historical extreme temperature and MPI-ESM-LR-RCP 8.5 standardized by station mean, 1960-2010

As discussed above, PCIC uses an ensemble of 12 GCMs. The authors adopted Cannon’s (2015) approach, a method that orders GCM scenarios to provide the widest spread of projected climate scenarios for smaller subsets of the full ensemble. Table 2 shows the top five GCMs by region.

Table 2 : Model ensembles and Giorgi-Francisco regions

Order Western North America (WNA)

Alaska (ALA) Central North America (CAN)

Eastern North America (ENA)

Greenland (GRL)

1 CNRM-CM5-r1 CSIRO-Mk3-6-0-r1 CanESM2-r1 MPI-ESM-LR-r3 MPI-ESM-LR-r3

2 CanESM2-r1 HadGEM2-ES-r1 ACCESS1-0-r1 INMCM 4-r1 INMCM 4-r1

3 ACCESS1-0-r1 INMCM 4-r1 INMCM 4-r1 CNRM-CM5-r1 CanESM2-r1

4 INMCM4-r1 CanESM2-r1 CSIRO-Mk3-6-0-r1 CSIRO-Mk3-6-0-r1 CNRM-CM5-r1

5 CSIRO-Mk3-6-0-r1 ACCESS1-0-r1 MIROC5-r3 HadGEM2-ES-r1 ACCESS1-0-r1

As Giorgi and Francisco (2000) defined, Ontario falls into three subcontinental regions: Central North America (CNA), Greenland (GRL), and Eastern North America (ENA). The top models for Ontario were determined to be CanESM and MPI-ESM. Consequently, downscaled temperature projections were downloaded for both GCMs. Each GCM output had three RCPs to choose from: RCP 2.6, RCP 4.5, and RCP 8.5. The authors downloaded all three RCPs for both GCMs, resulting in a total of six climate scenarios. The temperature values were used as input into Equation (8), as described in Section 2, to generate extreme precipitation values. Equation (9) was then used to determine the corresponding return period rainfall intensity for arbitrary storm durations.


Figure 6 : Time series of annual maximum 24 h rainfall, St. Catharines A, ON

Figure 6, above, shows a time series of expected annual maximum 24 h rainfall, the 100 y return period value, and the values produced by six different downscaled GCMs for St. Catharines, Ontario. In the legend, WIT3 refers to the temperature-precipitation model, the coefficients of which are presented in Table 1. The relatively small standard deviations of the red and black series are attributed to the fact that these series represent precipitation quantiles, whereas the green data series represents an actual model run.

Figure 6 shows that time is the main driver of change in precipitation intensity in the WIT3, with temperature contributing to mild fluctuations on top of the main linear trend. Note that these temperature-related fluctuations lead to a slightly variable design rainfall value, which occasionally decreases slightly from one year to the next.

In addition to the time series described above, IDF curve projections were produced for St. Catharines for the years 2010, 2060 and 2099. See Appendix A for the complete set of projections.

4 – Optimum method combination

One of this project’s objectives is to determine the optimum combination of the three different methods for infrastructure design. As noted earlier, the three methods include: WIT3, described in Section 4; the RTA model, developed in Phase III of the MTO project and active on the MTO website; and the OCCDP model, another GCM-based model.


The advantage of the OCCDP model is its consideration of atmospheric physics. Unfortunately, it is not bias-corrected. The RTA model has the advantage of being sensitive to physiography. WIT3 combines the OCCDP model’s sensitivity to atmospheric conditions with the physiographic sensitivity of the RTA. A comparison of the three methods, described in the following section, has shown WIT3 to match empirical observations most closely.

Database Selection for Comparison and Results:

As Section 2 outlines, the WIT3 model uses the historic relationship between temperature and precipitation in Ontario to refine extreme precipitation projections. For the historical comparison, 56 stations were selected that have a minimum of 20 years of records in total. The stations were also required to have historic temperature and precipitation records that overlap each other by 10 or more years. The average record year for each station was then identified. The results from WIT3 and the RTA model were then time corrected to the average years for each station for accurate comparisons. The stationary OCCDP data was also considered for comparison as outlined by objectives under Sections 3 and 4 of the project agreement. Figure 7 shows the results of a comparison of eight selected stations across Ontario. Note that, due to the nature of the data available for the OCCDP, the results cannot be time-adjusted, as they are given as a stationary value for the years 1960 to 1990.

Figure 7 shows the results of the comparison for eight stations across Ontario. The geographic distribution of these eight stations is shown in Figure 8.


Figure 7 : Comparison of 24 h rainfall intensity return period estimates for eight stations across Ontario for period, 1960-2010 for a) Armstrong, b) Cambridge Galt MOE, c) Cornwall, d) Hamilton RBG CS, e) Kenora A, f) North Bay, g) St. Catharines A, and h) Sudbury A

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Figure 8 : Geographic distribution of sample stations.

For the comparison, model quantiles were compared to the quantiles of the “MSC Gumbel” distribution, which was selected as the best estimate of the true distribution of station data. This is a Gumbel distribution which has been parameterized for each station using the station mean and the standard deviation of the overall MSC dataset. This overall standard deviation was used under the assumption of a constant standard deviation across Ontario.

The same procedure was carried out for the remaining 48 stations, for a total of 56. The comparison was made on the 2, 5, 10, 25, 50 and 100 y return period rainfall intensity values for the 24 h storm. Statistics on the differences (deltas) in these return period values, in mm/h, between the MSC Gumbel and the three models are presented in Table 3. Figure 9 (a) to (c) shows the difference between the MSC Gumbel and modeled results for the 24 h annual maximum rainfall intensity at the 99th percentile (100 y return period). Since, for ease of communication, the scales are not consistent between comparisons, the histogram Figure 9 (d) illustrates the distribution of the deltas on a common scale.


Figure 9 : The difference in time-corrected rainfall intensity for the 100 y rainfall (99th percentile) between the empirical MSC data and results from a) the WIT3 model, b) the RTA model, and c) the OCCDP model. A histogram d) shows the distribution of the deltas.

As the histogram shows, the WIT3 model has the largest number of observations near zero. This indicates that the WIT3 model represents the historical data with the least discrepancy between actual observations and WIT3 generated model output. Although the WIT3 quantiles tend to slightly underestimate those of the MSC Gumbel for higher return period values, as Table 3 shows, the difference is negligible.

The RTA quantiles were also found to match those of the MSC Gumbel quite closely, but show potential for refinement as they, on average, tend to overestimate the historical quantiles. The OCCDP values, which represent the median IDF curve estimate from the AR4:A1B scenario, generally significantly overestimate the historical quantiles.

When compared, the WIT3 model has the closest match with the quantiles of historic data, and is therefore assumed to be the most likely to accurately represent future extreme precipitation scenarios.

0

5

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30

-0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25

Freq

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WIT3 RTA OCCDP

d) Distribution of the deltas on a single scale


Table 3 : Mean differences between empirical MSC results and the modeled results for the 24 h storm, compared over 56 Ontario MSC station locations

5 – Risk assessment case study

To determine the risk associated with currently unanticipated increases in extreme precipitation, IDF curve projections of the WIT3 model were compared with those of the RTA model. In this assessment, the RTA was taken as the base projection. Any instances in which the WIT3 model projected IDF curve values are higher than those in the RTA model were taken to indicate risks which are presently unaccounted for.

Starting with base year 2010, future 1 h, and 24 h rainfall intensity projections were made for years 2060 and 2090, using both the RTA model and the WIT3 model. As described in the Project Scope, the RTA model was based on the temporal variation of extreme precipitation with consideration of physiographic factors, while the WIT3 model, described in Section 2, forecasts extreme precipitation based on physiography, temperature and time. Figure 10 and Figure 11 show the difference between 100 y return period rainfall intensity values for the 1 h and 24 h storms, as predicted by WIT3 and RTA, for two GCMs: CanESM and MPI-ESM. The RCP 8.5 scenario was chosen for comparison, as this is the most severe climate change scenario considered in this study.

Statistics on the difference in 1 h and 24 h extreme precipitation projections between RTA and WIT3 models for 55 weather stations are presented in Table 4. From Figure 12 to Figure 17 shows the difference between the RTA and WIT3 models over time for two MSC weather stations.

Mean difference from MSC

Standard deviation of difference from MSC

Return period (y)

WIT3 RTA OCCDP WIT3 RTA OCCDP

2 0.03 0.20 0.58 0.15 0.37 0.37

5 0.01 0.26 0.77 0.15 0.47 0.47

10 0.00 0.30 0.89 0.15 0.53 0.53

25 -0.01 0.34 1.05 0.15 0.62 0.62

50 -0.02 0.37 1.17 0.15 0.69 0.69

100 -0.03 0.40 1.29 0.15 0.76 0.76


Table 4 : Mean differences between WIT3 and RTA precipitation projections for the 100 y return period rainfall events

1h storm 24h storm

GCM scenario Year Mean

(mm/h)

Standard deviation

(mm/h)

Mean (mm/h)

Standard deviation

(mm/h)

CanESM RCP 8.5

2010 -2.84 1.70 -0.43 0.19

2060 -1.72 1.69 -0.45 0.19

2090 -0.96 1.96 -0.46 0.22

MPI-ESM-LR RCP 8.5

2010 -2.48 1.73 -0.39 0.20

2060 -1.37 1.72 -0.42 0.19

2090 -0.73 1.96 -0.44 0.22

Incorporating projected temperature into the forecast resulted in an overall decrease in projected precipitation over the next 70 years, with the difference decreasing with time for the 1 h storm. WIT3 design rainfall values for the 100 y 1 h storm fall, on average, 1.7 mm below those of RTA. For the foreseeable future, and given existing RTA safety margins, the precipitation projections of the MTO IDF lookup tool appear to be conservative enough that there is little risk in ignoring warming effects. The one exception is in Eastern Ontario, as Figure 10 shows, where 1 h storm intensities from the WIT3 model can be seen to surpass those of the RTA model. While the risk in these areas appears minor, it does warrant further investigation. These differences could have significant implications for climate change related risk and vulnerability assessments depending on the types of facilities and infrastructure.


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CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5 results for two sample stations

Figure 12 : St. Catharines A 1 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5

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Figure 15 : Sudbury A 1 h, CanESM-RCP 8.5 vs MPI-ESM-RCP 8.5

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6 – Incorporation into online tools

The results of this study can be integrated into the MTO IDF Curve Lookup Tool subject to discussions between the MOECC and the MTO and the approval of the MTO. The Recipient has started discussion with MTO and MOECC for the incorporation of the MOECC model into the MTO online tool. The changes to the current tool are not expected to include any interface changes. The updates and additions are limited to:

I. A new interpolation formula – the new formula will take temperature into account and is shown above as Equation (8).

II. A new time-change formula – Equation (8) the new formula which will replace the existing linear trend currently in use on the MTO website. This formula accounts for temperature change.

III. Two new independent variable files – these American Standard Code for Information Interchange (ASCII) files will be integrated with the seven other independent variables (latitude, longitude, elevation, etc.) and will be used for the interpolation of extreme rainfall projections.

IV. An update to the MTO IDF Curve Lookup Tool About page – the update will summarize the changes made to the site for user reference.

The changes will be implemented by the former MASc student, Daniel Princz, who built the original tool. He estimates the update will take 36 hours over the course of 3 weeks, with a further 3 weeks for testing, revisions, corrections, or changes, as required. MTO will take part in and support the testing and final upload.

7 – Project findings dissemination

This technical report fulfills part of this project responsibility. The Recipient intends to present this research at the forthcoming Canadian Meteorological and Oceanographic Society (CMOS) conference in June 2017. This work will also be presented at the 4th Water Research Conference in September 2017. Some of this work was discussed in Sarhadi and Soulis, “Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate”, Geophysical Research Letters, 44, 2017. (see Appendix B).


Conclusion

A new stochastic method of forecasting extreme precipitation, dubbed WIT3, has been developed that uses temperature, time and location/physiography to estimate the distribution of extreme rainfall events for Ontario locations. WIT3 is compared with the previous RTA method, as well as the median IDF curve estimates from the OCCDP under the AR4:A1B scenario, and downscaled GCM data from the Pacific Climate Impacts Consortium. When comparisons were made during the historical period of 1960-2010, it was determined that WIT3 has the closest match of the empirical distribution of Ontario weather stations.

Forecasts of IDF curves were created until 2099, using temperature projections from two GCM models under three different RCP scenarios. When these forecasts were compared with the RTA model, which is the MTO’s current standard, it was found that WIT3 tends to predict lower-intensity precipitation events than RTA. The 100 y 1 h rainfall intensity values from WIT3 are, on average, 1.7 mm below those of RTA. However, the difference between the projections of the two models was found to decrease over time, and the WIT3 projections eventually surpassed those of RTA in Eastern Ontario.

WIT3 will be incorporated into an online lookup tool, and should be tested for possible incorporation into the design standards of Ontario’s infrastructure.


Appendix A: IDF curve projections under various climate scenarios, St. Catharines A, Ontario

(a) CanESM RCP 2.6

(b) CanESM RCP 4.5


(c) CanESM RCP 8.5

(d) MPI-ESM RCP 2.6

(e) MPI-ESM RCP 4.5

(f) MPI-ESM RCP 8.5


Appendix B: Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate


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ensemble: application to CMIP5 climate extremes indices. Journal of Climate, 28(3): 1260-1267, doi:10.1175/JCLI-D-14-00636.1

2. Dingman S.L. (2002). Physical Hydrology, Long Grove,IL: Waveland Press Inc. 3. Giorgi, F. and R. Francisco, 2000. Evaluating Uncertainties in the Prediction of Regional

Climate Change. Geophysical Research Letters, 27(9): 1295-1298. 4. Gudmundsson, L., J. B. Bremnes, J. E. Haugen, and T. Engen-Skaugen, 2012. Technical Note:

Downscaling RCM precipitation to the station scale using statistical transformations - a comparison of methods. Hydrology and Earth System Sciences, 16: 3383–3390, doi:10.5194/hess-16-3383-2012.

5. Hogg W.D., Carr D.A., Routledge B. 1989. Rainfall Intensity–Duration–Frequency Values for Canadian Locations. Environment Canada, Atmospheric Environment Service: Ottawa.

6. Maurer, E., H. Hidalgo, T. Das, M. Dettinger, and D. Cayan, 2010. The utility of daily large-scale climate data in the assessment of climate change impacts on daily streamflow in California. Hydrology and Earth System Sciences, 14(6): 1125–1138, doi:10.5194/hess-14-1125-2010.

7. Pacific Climate Impacts Consortium (2017). Statistically downscaled climate scenarios”, https://pacificclimate.org/data/statistically-downscaled-climate-scenarios.

8. Sarhadi, A. and E.D. Soulis, 2017. Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate. Geophysical Research Letters, 44. doi:10.1002/2016GL072201

9. Seglenieks, F. (2009). Creation of a Gridded Time Series of Hydrological Variables for Canada. Waterloo, Ontario: University of Waterloo. PhD Thesis.

10. Soulis, E.D., A. Sarhadi, M. Tinel, M. Suthar, 2016. Extreme precipitation time trends in Ontario, 1960–2010. Hydrological Processes. 30(22): 4090-4100, doi: 10.1002/hyp.10969

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projecting ontario’s future idf curves and associated potential … · 2017. 4. 7. · future idf...

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