McGill University
Montreal, Quebec, Canada
Brace Centre for Water Resources Management
Global Environmental and Climate Change Centre
Department of Civil Engineering and Applied Mechanics
School of Environment
A SPATIAL-TEMPORAL DOWNSCALING APPROACH TO
CONSTRUCTION OF INTENSITY-DURATION-FREQUENCY
RELATIONS IN CONSIDERATION OF GCM-BASED CLIMATE
CHANGE SCENARIOS
Van-Thanh-Van Nguyen (and Students)
Endowed Brace Professor Chair in Civil Engineering
1
OUTLINE





INTRODUCTION
 Design Rainfall and Design Storm Concept –
Current Practices
 Extreme Rainfall Estimation Issues?
 Climate Variability and Climate Change Impacts?
OBJECTIVES
DOWNSCALING METHODS
 Spatial Downscaling Issues
 Temporal Downscaling Issues
 Spatial-Temporal Downscaling Method
APPLICATIONS
CONCLUSIONS
December 19, 2007, Climate Change Symposium, Singapore
2
INTRODUCTION



Extreme storms (and floods) account
for more losses than any other
natural disaster (both in terms of loss
of lives and economic costs).
 Damages due to Saguenay flood
in Quebec (Canada) in 1996:
$800 million dollars.
 Average annual flood damages in
the U.S. are US$2.1 billion
dollars. (US NRC)
Information on extreme rainfalls is
essential for planning, design, and
management of various waterresource systems.
Design Rainfall = maximum amount
of precipitation at a given site for a
specified duration and return period.
December 19, 2007, Climate Change Symposium, Singapore
3
Design Rainfall Estimation Methods

The choice of an estimation method
depends on the availability of historical
data:
Sites  Sufficient long historical
records (> 20 years?)  At-site Methods.
 Partially-Gaged Sites  Limited data
records  Regionalization Methods.
 Ungaged Sites  Data are not available 
Regionalization Methods.
 Gaged
December 19, 2007, Climate Change Symposium, Singapore
4
Design Rainfall and Design Storm
Estimation


At-site Frequency Analysis of Precipitation
Regional Frequency Analysis of Precipitation
⇒ Intensity-Duration-Frequency (IDF) Relations
⇒ DESIGN STORM CONCEPT for design of
hydraulic structures
(WMO Guides to Hydrological Practices: 1st
Edition 1965 → 6th Edition: Section 5.7, in
press)
December 19, 2007, Climate Change Symposium, Singapore
5
Extreme Rainfall Estimation Issues (1)
Current practices:
At-site Estimation Methods (for gaged sites):
Annual maximum series (AMS) using 2parameter Gumbel/Ordinary moments
method, or using 3-parameter GEV/ Lmoments method.
⇒ Which probability distribution?
⇒ Which estimation method?
⇒ How to assess model adequacy? Best-fit
distribution?
Problems: Uncertainties in Data, Model and
Estimation Method

December 19, 2007, Climate Change Symposium, Singapore
6
Extreme Rainfall Estimation Issues (2)
Regionalization methods

GEV/Index-flood method.

Index-Flood Method (Dalrymple, 1960):
QT ( Ai )   ( Ai )  QT ( regional)


Similarity (or homogeneity) of point rainfalls?
How to define groups of homogeneous gages? What are the
classification criteria?
Proposed Regional Homogeneity:
1. PCA of rainfall amounts at
different sites for different time
scales.
2. PCA of rainfall occurrences at
different sites.
(WMO Guides to Hydrological
Practices: 1st Edition 1965 → 6th
Edition: Section 5.7, in press)
1
2
3
4
Geographically
contiguous fixed
regions
December 19, 2007, Climate Change Symposium, Singapore
Geographically non
contiguous fixed
regions
Hydrologic
neighborhood type
regions
7
Extreme Rainfall Estimation Issues (3)

The “scale” problem
 The
properties of a variable depend on the
scale of measurement or observation.
 Are there scale-invariance properties? And
how to determine these scaling properties?
 Existing methods are limited to the specific
time scale associated with the data used.
 Existing methods cannot take into account
the properties of the physical process over
different scales.
December 19, 2007, Climate Change Symposium, Singapore
8
Extreme Rainfall Estimation Issues (4)


Climate Variability and Change will have
important impacts on the hydrologic cycle,
and in particular the precipitation process!
How to quantify Climate Change?
General Circulation Models (GCMs):


A credible simulation of the “average” “large-scale”
seasonal distribution of atmospheric pressure,
temperature, and circulation. (AMIP 1 Project, 31
modeling groups)
Climate change simulations from GCMs are
“inadequate” for impact studies on regional scales:
 Spatial resolution ~ 50,000 km2
 Temporal resolution ~ (daily), month, seasonal
 Reliability of some GCM output variables (such as
cloudiness  precipitation)?
December 19, 2007, Climate Change Symposium, Singapore
9
…

How to develop Climate Change scenarios
for impacts studies in hydrology?


Spatial scale ~ a few km2 to several 1000 km2
Temporal scale ~ minutes to years
A scale mismatch between the information that
GCM can confidently provide and scales required
by impacts studies.
 “Downscaling methods” are necessary!!!

GCM Climate Simulations
Precipitation (Extremes) at a Local Site
December 19, 2007, Climate Change Symposium, Singapore
10
IDF Relations


At-site Frequency Analysis of Precipitation
Regional Frequency Analysis of Precipitation
⇒ Intensity-Duration-Frequency (IDF) Relations
⇒ DESIGN STORM for design of hydraulic structures.

Traditional IDF estimation methods:



Time scaling problem: no consideration of rainfall properties
at different time scales;
Spatial scaling problem: results limited to data availability at
a local site;
Climate change: no consideration.
December 19, 2007, Climate Change Symposium, Singapore
11
Summary


Recent developments:
 Successful applications of the scale invariant concept in
precipitation modeling to permit statistical inference of
precipitation properties between various durations.
 Global climate models (GCMs) could reasonably simulate
some climate variables for current period and could provide
various climate change scenarios for future periods.
 Various spatial downscaling methods have been developed
to provide the linkage between (GCM) large-scale data and
local scale data.
Scale Issues:
 GCMs produce data over global spatial scales (hundreds of
kilometres) which are very coarse for water resources and
hydrology applications at point or local scale.
 GCMs produce data at daily temporal scale, while many
applications require data at sub-daily scales (hourly, 15
minutes, …).
December 19, 2007, Climate Change Symposium, Singapore
12
OBJECTIVES




To review recent progress in downscaling methods
from both theoretical and practical viewpoints.
To assess the performance of statistical downscaling
methods to find the “best” method in the simulation of
daily precipitation time series for climate change
impact studies.
To develop an approach that could link daily
simulated climate variables from GCMs to sub-daily
precipitation characteristics at a regional or local
scale (a spatial-temporal downscaling method).
To assess the climate change impacts on the
extreme rainfall processes at a regional or local
scale.
December 19, 2007, Climate Change Symposium, Singapore
13
DOWNSCALING METHODS
Scenarios
RCM or LAM
(Dynamic
Downscaling)
Stochastic
Weather
Generators
GCM
Statistical
Models
(Statistical
Downscaling)
Weather Typing or
Classification
Impact
Models
(Hydrologic
Models)
Regression
Models
low resolution
~ 300 km
month, season, year
December 19, 2007, Climate Change Symposium, Singapore
high resolution
1 km
day, hour, minute
14
(SPATIAL) DYNAMIC DOWNSCALING
METHODS



Coarse GCM + High resolution AGCM
Variable resolution GCM (high resolution over
the area of interest)
GCM + RCM or LAM (Nested Modeling
Approach)
More accurate downscaled results as compared to
the use of GCM outputs alone.
 Spatial scales for RCM results ~ 20 to 50 km 
still larges for many hydrologic models.
 Considerable computing resource requirement.

December 19, 2007, Climate Change Symposium, Singapore
15
(SPATIAL) STATISTICAL DOWNSCALING
METHODS



Weather Typing or Classification
 Generation daily weather series at a local site.
 Classification schemes are somewhat subjective.
Stochastic Weather Generators
 Generation of realistic statistical properties of daily weather
series at a local site.
 Inexpensive computing resources
 Climate change scenarios based on results predicted by
GCM (unreliable for precipitation)
Regression-Based Approaches
 Generation daily weather series at a local site.
 Results limited to local climatic conditions.
 Long series of historical data needed.
 Large-scale and local-scale parameter relations remain valid
for future climate conditions.
 Simple computational requirements.
December 19, 2007, Climate Change Symposium, Singapore
16
APPLICATIONS

LARS-WG Stochastic Weather Generator
(Semenov et al., 1998)
Generation of synthetic series of daily weather data
at a local site (daily precipitation, maximum and
minimum temperature, and daily solar radiation)
 Procedure:

Use semi-empirical probability distributions to describe
the state of a day (wet or dry).
Use semi-empirical distributions for precipitation amounts
(parameters estimated for each month).
Use normal distributions for daily minimum and maximum
temperatures. These distributions are conditioned on the
wet/dry status of the day. Constant Lag-1 autocorrelation
and cross-correlation are assumed.
Use semi-empirical distribution for daily solar radiation.
This distribution is conditioned on the wet/dry status of the
day. Constant Lag-1 autocorrelation is assumed.
December 19, 2007, Climate Change Symposium, Singapore
17

Statistical Downscaling Model (SDSM)
(Wilby et al., 2001)

Generation of synthetic series of daily weather
data at a local site based on empirical
relationships between local-scale predictands
(daily temperature and precipitation) and largescale predictors (atmospheric variables)
 Procedure:
Identify large-scale predictors (X) that could
control the local parameters (Y).
Find a statistical relationship between X and Y.
Validate the relationship with independent
data.
Generate Y using values of X from GCM data.
December 19, 2007, Climate Change Symposium, Singapore
18
Geographical locations of sites under study.
Geographical coordinates of the stations
Station
Dorval
Drummondville
Maniwaki
Montreal McGill
December 19, 2007, Climate Change Symposium, Singapore
Lat (o)
45o28’05”
45o52’34”
46o18’11”
45o30’00”
Long (o)
-73o44’31”
-72o28’29”
-76o00’36”
-73o34’19”
Alt (m)
35.7
76.0
192.0
56.9
19

DATA:



Observed daily precipitation and temperature extremes at
four sites in the Greater Montreal Region (Quebec, Canada)
for the 1961-1990 period.
NCEP re-analysis daily data for the 1961-1990 period.
Calibration: 1961-1975; validation: 1976-1990.
Variable
Mean sea level pressure
Airflow strength
Zonal velocity
Meridional velocity
Vorticity
Wind direction
Divergence
Specific humidity
Geopotential height
Level of measurement
surface
surface
surface
surface
surface
surface
near surface
December 19, 2007, Climate Change Symposium, Singapore
850 hPa
850 hPa
850 hPa
850 hPa
850 hPa
850 hPa
850 hPa
850 hPa
500 hPa
500 hPa
500 hPa
500 hPa
500 hPa
500 hPa
500 hPa
500 hPa
20
No
Code
Unit
Time scale
Description
1
Prcp1
%
Season
Percentage of wet days (daily precipitation  1
mm)
2
SDII
mm/r.day
Season
Daily Mean: sum of daily precipitations /
number of wet days
3
CDD
days
Season
Maximum number of consecutive dry days
(daily precipitation < 1 mm)
4
R3days
mm
Season
Maximum 3-day precipitation total
5
Prec90p
mm
Season
90th percentile of daily precipitation amount
6
Precip_mean
mm/day
Month
Sum of daily precipitation in a month /
number of days in that month
7
Precip_sd
mm
Month
Standard deviation of daily precipitation in a
month
Evaluation indices and statistics
December 19, 2007, Climate Change Symposium, Singapore
21
The mean of daily precipitation for the period of 1961-1975
(mm)
14
Dorval
12
10
8
6
Dorval
4
OBS
SDSM
LARS
2
(mm)
0
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM-GENERATED MEAN
(mm)
16
14
12
10
8
6
4
2
0
Dorval
15
10
5
0
-5
J F M A M J J A S O N D
BIAS = Mean (Obs.) – Mean (Est.)
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED MEAN
December 19, 2007, Climate Change Symposium, Singapore
22
The mean of daily precipitation for the period of 1976-1990
(mm)
14
Dorval
12
10
8
6
Dorval
4
OBS
SDSM
LARS
2
0
(mm)
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM-GENERATED MEAN
(mm)
14
Dorval
12
15
10
5
0
-5
J F M A M J J A S O N D
10
8
BIAS = Mean (Obs.) – Mean (Est.)
6
4
2
0
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED MEAN
December 19, 2007, Climate Change Symposium, Singapore
23
The 90th percentile of daily precipitation for the period of 1976-1990
(mm)
35
Dorval
30
25
20
15
Dorval
10
OBS
SDSM
LARS
5
0
(mm)
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM-GENERATED 90th PERCENTILE
(mm)
40
35
30
25
20
15
10
5
0
J
40
20
0
Dorval
-20
J F M A M J J A S O N D
BIAS = Mean (Obs.) – Mean (Est.)
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED 90th PERCENTILE
December 19, 2007, Climate Change Symposium, Singapore
24
GCM and Downscaling Results (Precipitation Extremes )
1- Observed
2- SDSM [CGCM1]
3- SDSM [HADCM3]
4- CGCM1-Raw data
5- HADCM3-Raw data
From CCAF Project Report by Gachon et al. (2005)
December 19, 2007, Climate Change Symposium, Singapore
25
SUMMARY
Downscaling is necessary!!!
 LARS-WG and SDSM models could provide
“good” but generally “biased” estimates of the
observed statistics of daily precipitation at a
local site.

GCM-Simulated Daily Precipitation Series
Is it feasible?
Daily and Sub-Daily Extreme Precipitations
December 19, 2007, Climate Change Symposium, Singapore
26
The Scaling Concept
f (t )  C ( ). f ( t )
C ( )  

k  E{ f (t )}   (k ) t
k
December 19, 2007, Climate Change Symposium, Singapore
k
27
The Scaling Generalized Extreme-Value
(GEV) Distribution.

The scaling concept
f (t )  C (  ). f (  t )
C ( )    
k  E{ f k (t )}   ( k ) t  k

The cumulative distribution function:
1/ 
 
 (x  )  
F ( x )  exp   1 
 

 
 

The quantile:

X ( F )    1  [ ln F ] 

December 19, 2007, Climate Change Symposium, Singapore
28
The Scaling GEV Distribution
 (t )   (t )

 (t )   . (t )

 (t )   . (t )
X T (t )   . X T (t )
where


1 (t )

1 (t )
December 19, 2007, Climate Change Symposium, Singapore
29

The first three moments of GEV distribution:
 1  A  B.1
 2  A2  2 A. B. 1  B 2 . 2
 3  A3  3 A2 . B. 1  3 A. B 2 . 2  B 3 . 3
 A    / 
B   / 
 1   (  1 )
  2   ( 2  1 )
  3   ( 3  1 )
December 19, 2007, Climate Change Symposium, Singapore
30
APPLICATION: Estimation of Extreme
Rainfalls for Gaged Sites
Data used:



Raingage network:
88 stations in
Quebec (Canada).
Rainfall durations:
from 5 minutes to 1
day.
Record lengths:
from 15 yrs. to 48
yrs.
December 19, 2007, Climate Change Symposium, Singapore
31
Scaling of NCMs of extreme rainfalls with durations: 5-min to 1-hour and 1-hour to 1-day.
red: 1st NCM; blue: 2nd NCM; black: 3rd NCM; markers: observed values; lines: fitted regression
December 19, 2007, Climate Change Symposium, Singapore
32
Results on scaling regimes:

Non-central moments are scaling.
 Two scaling regimes:
 5-min. to 1-hour interval.
 1-hour to 1-day interval.
Based on these results, two estimations were
made:

5-min. extreme rainfalls from 1-hr rainfalls.
 1-hr. extreme rainfalls from 1-day rainfalls.
December 19, 2007, Climate Change Symposium, Singapore
33
5-min Extreme Rainfalls estimated from 1-hour Extreme Rainfalls
markers: observed values – lines: values estimated by scaling method
markers: observed values – lines: values estimated by scaling method
December 19, 2007, Climate Change Symposium, Singapore
34
1-hour Extreme Rainfalls estimated from 1-day Extreme Rainfalls
markers: observed values – lines: values estimated by scaling method
December 19, 2007, Climate Change Symposium, Singapore
35
The Spatial-Temporal Downscaling
Approach
GCMs: HadCM3 and CGCM2.
 NCEP Re-analysis data.
 Spatial downscaling method: the statistical
downscaling model SDSM (Wilby et al., 2002).
 Temporal downscaling method: the scaling
GEV model (Nguyen et al. 2002).

December 19, 2007, Climate Change Symposium, Singapore
36
The Spatial-Temporal Downscaling
Approach

Spatial downscaling:
calibrating and validating the SDSM in order to link
the atmospheric variables (predictors) at daily
scale (GCM outputs) with observed daily
precipitations at a local site (predictand);
 extracting AMP from the SDSM-generated daily
precipitation time series; and
 making a bias-correction adjustment to reduce the
difference in quantile estimates from SDSMgenerated AMPs and from observed AMPs at a
local site using a second-order nonlinear function.


Temporal downscaling:
investigating the scale invariant property of
observed AMPs at a local site; and
 determining the linkage between daily AMPs with
sub-daily AMPs.

December 19, 2007, Climate Change Symposium, Singapore
37
Application

Study Region


Precipitation records from a
network of 15 raingages in
Quebec (Canada).
Data

GCM outputs:
HadCM3A2, HadCM3B2,
CGMC2A2, CGCM2B2,
Periods: 1961-1990, 2020s,
2050s, 2080s.

Observed data:
Daily precipitation data,
AMP for 5 min., 15 min., 30
min., 1hr., 2 hrs., 6 hrs., 12 hrs.
Periods: 1961-1990.
December 19, 2007, Climate Change Symposium, Singapore
38
Daily AMPs estimated from GCMs versus
observed daily AMPs at Dorval.
Calibration period: 1961-1975
Dist. of AM Daily Precip. before and after adjustment,1961-1975, Dorval
100
90
90
80
80
AM Daily Precipitation (mm)
AM Daily Precipitation (mm)
Dist. of AM Daily Precip. before and after adjustment,1961-1975, Dorval
100
70
60
50
Observed
40
70
60
50
Observed
40
CGCM2A2
HadCM3A2
Adj-CGCM2A2
30
0
10
1
10
Adj-HadCM3A2
2
10
Return period (years)
CGCMA2
December 19, 2007, Climate Change Symposium, Singapore
30
0
10
1
10
2
10
Return period (years)
HadCM3A2
39
Residual = Daily AMP (GCM) - Observed daily AMP (local)
Calibration period: 1961-1975
HadCM3A2 estimates vs Residuals, 1961-1975
CGCM2A2 estimates vs Residuals, 1961-1975
25
16
14
20
12
10
Residuals
Residuals
15
8
6
10
4
2
5
0
Residuals
Residuals
Fitted curve
Fitted curve
-2
30
35
40
45
50
55
60
65
70
75
80
CGCM2A2 estimates
CGCMA2
December 19, 2007, Climate Change Symposium, Singapore
0
30
35
40
45
50
55
60
65
70
75
HadCM3A2 estimates
HadCM3A2
40
Daily AMPs estimated from GCMs versus
observed daily AMPs at Dorval.
Validation period: 1976-1990
Dist. of AM Daily Precip. before and after adjustment,1961-1975, Dorval
100
90
90
80
80
AM Daily Precipitation (mm)
AM Daily Precipitation (mm)
Dist. of AM Daily Precip. before and after adjustment,1961-1975, Dorval
100
70
60
50
Observed
40
70
60
50
Observed
40
CGCM2A2
HadCM3A2
Adj-CGCM2A2
30
0
10
1
10
Adj-HadCM3A2
2
10
Return period (years)
CGCMA2
30
0
10
1
10
2
10
Return period (years)
HadCM3A2
Adjusted Daily AMP (GCM) = Daily AMP (GCM) + Residual
December 19, 2007, Climate Change Symposium, Singapore
41
Dist. of AM Daily Precip. after adjustment (CGCM2A2),Dorval
Dist. of AM Daily Precip. after adjustment (HadCM3A2),Dorval
130
110
120
100
110
90
AM Daily Precipitation (mm)
AM Daily Precipitation (mm)
100
90
80
70
60
1961-1990
50
80
70
60
50
1961-1990
2020s
40
2020s
40
2050s
2050s
2080s
30
0
10
1
2080s
30
0
10
2
10
10
Return period (years)
1
2
10
10
Return period (years)
GEV Dist. of AM 5 min Precip. after adjustment (CGCM2A2), Dorval
GEV Dist. of AM 5 min Precip. after adjustment (HadCM3A2), Dorval
20
18
18
16
16
AM 5 min Precipitation (mm)
AM 5 min Precipitation (mm)
14
14
12
10
8
12
10
8
1961-1990
6
4
0
10
CGCMA2
1
10
1961-1990
2020s
6
2050s
2080s
2
10
Return period (years)
December 19, 2007, Climate Change Symposium, Singapore
4
0
10
HadCM3A2
1
10
2020s
2050s
2080s
2
10
Return period (years)
42
CONCLUSIONS (1)




Significant advances have been achieved regarding the
global climate modeling. However, GCM outputs are still
not appropriate for assessing climate change impacts on
the hydrologic cycle.
Downscaling methods provide useful tools for this
assessment.
Calibration of the SDSM suggested that precipitation was
mainly related to zonal velocities, meridional velocities,
specific humidities, geopotential height, and vorticity.
In general, LARS-WG and SDSM models could provide
“good” but “biased” estimates of the observed statistical
properties of the daily precipitation process at a local site.
December 19, 2007, Climate Change Symposium, Singapore
43
CONCLUSIONS (2)





It is feasible to link daily GCM-simulated climate variables
with sub-daily AMPs based on the proposed spatialtemporal downscaling method. ⇒ IDF relations for
different climate change scenarios could be constructed.
Differences between quantile estimates from observed
daily AMPs and from GCM-based daily AMPs could be
described by a second-order non-linear function.
Observed AMPs in Quebec exhibit two different scaling
regimes for time scales ranging from 1 day to 1 hour, and
from 1 hour to 5 minutes.
The proposed scaling GEV method could provide
accurate AMP quantiles for sub-daily durations from daily
AMPs.
AMPs derived from CGCM2A2 outputs show a large
increasing trend for future periods, while those given by
HadCM3A2 did NOT exhibit a large (increasing or
decreasing) trend.
December 19, 2007, Climate Change Symposium, Singapore
44
Thank you
for
your attention!
December 19, 2007, Climate Change Symposium, Singapore
45
Slides required for
presentations
December 19, 2007, Climate Change Symposium, Singapore
46
I (mm/hr)
True image
time (hr)
I (mm/hr)
time (hr)
December 19, 2007, Climate Change Symposium, Singapore
47
December 19, 2007, Climate Change Symposium, Singapore
48
DESIGN STORM CONCEPT



Watershed as a linear system
 Stormwater removal  Qpeak  Rational
Method: Qpeak = CIA  Uniform Design
Rainfall
Watershed as a nonlinear system.
 Environmental control  Entire
Hydrograph Q(t)  More realistic temporal
rainfall pattern (or Design Storm) for more
realistic rainfall-runoff simulation.
A design storm describes completely the
distribution of rainfall intensity during the
storm duration for a given return period.
December 19, 2007, Climate Change Symposium, Singapore
49
DESIGN STORM CONCEPT


Two main types of “synthetic” design storms:
 Design Storms derived from the IDF relationships.
 Design Storms resulted from analysing and
synthesising the characteristics of historical storm
data.
A typical design storm:




Maximum Intensity: IMAX
Time to peak: Tb
Intensity
Duration: T
I
Temporal pattern
max
Tp
T
December 19, 2007, Climate Change Symposium, Singapore
Time
50
Design Storm Estimation Issues

Different synthetic design storm models available in
various countries:












US Chicago storm model (Keifer and Chu, 1957)
US Normalized storm pattern by Huff (1967)
Czechoslovakian storm pattern by Sifalda (1973)
Australian design storm by Pilgrim and Cordery (1975)
UK Mean symmetric pattern (Flood Studies Report, 1975)
French storm model by Desbordes (1978)
US storm pattern by Yen and Chow (1980)
Canadian Atmospheric Environment Service (1980)
US balanced storm model (Army Corps of Engineer, 1982)
Canadian temporal rainfall patterns (Nguyen, 1981,1984)
Canadian storm model by Watt et al. (1986)
No general agreement as to which temporal storm
pattern should be used for a particular site ⇒ How to
choose? How to compare?
December 19, 2007, Climate Change Symposium, Singapore
51
Intensity-Duration-Frequency curves for Montreal area.
December 19, 2007, Climate Change Symposium, Singapore
52
700
600
t
 i( ) d  I (t )  t
Intensity (mm/hr)
500
0
400
⇓
300
200
a t
0 i( ) d  (b  t )c
t
100
0
5
10
15
20
25
30
35
40
45
50
55
Time (min)
Return Period:
2 years
5 years
10 years
50 years
Chicago
a
I (t ) 
c
(b  t )
IDF
⇒
60
⇓
100 years
a[(1  c)( /  )  b]
i
[( /  )  b] c 1
  t p  t and   r  tb / D for t  t p
  t  t p and   1  r for t  t p
Design Storm
December 19, 2007, Climate Change Symposium, Singapore
53
Design Storm Patterns for southern
Quebec (Canada)
DESBORDES MODEL (peak duration of 15 minutes)
DESBORDES MODEL (peak duration of 30 minutes)
300
300
200
150
100
50
200
150
100
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
5
10
15
20
25
Time (min)
30
35
40
45
50
55
60
Time (min)
SIFALDA MODEL
CHICAGO MODIFIED MODEL
300
300
250
200
Return Period:
2 years
5 years
10 yeas
50 years
100 years
2 years
5 years
10 years
50 years
100 years
250
Intensity (mm/hr)
Return period:
Intensity (mm/hr)
2 years
5 years
10 years
50 years
100 years
250
Intensity (mm/hr)
250
Intensity (mm/hr)
Return period:
2 years
5 years
10 years
50 years
100 years
Return period:
150
100
200
150
100
50
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
Time (min)
December 19, 2007, Climate Change Symposium, Singapore
5
10
15
20
25
30
35
40
45
50
55
60
Time (min)
54
Design Storm Patterns for southern
Quebec (Canada)
AES MODEL
BALANCED MODEL
300
300
Return period:
200
150
100
200
150
100
50
50
0
0
5
10
15
20
25
30
35
40
45
50
55
5
60
10
15
20
25
30
35
40
45
50
55
60
Time (min)
Time (min)
YEN MODEL
WATT MODEL
300
300
Return period:
2 years
5 years
10 years
50 years
100 years
200
Return period:
2 years
5 years
10 years
50 years
100 years
250
Intensity (mm/hr)
250
Intensity (mm/hr)
2 years
5 years
10 years
50 years
100 years
250
Intensity (mm/hr)
250
Intensity (mm/hr)
Return Period:
2 years
5 years
10 years
50 years
100 years
150
100
50
200
150
100
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
Time (min)
December 19, 2007, Climate Change Symposium, Singapore
5
10
15
20
25
30
35
40
45
50
55
60
Time (min)
55
SUMMARY

Results indicated:

For runoff peak flows:
the Canadian AES design storm
the Desbordes model (with a peak intensity duration of
30 minutes)

For runoff volumes:
the Canadian pattern proposed by Watt et al.

None of the eight design storms was able to
provide accurate estimation of both runoff
parameters.
December 19, 2007, Climate Change Symposium, Singapore
56
The 1-hr optimal storm pattern for
southern Quebec (Canada)
PROPOSEDDESIGN STORM
Intensity
200
2 years
5 years
10 years
50 years
100 years
Return Period:
Total Volume = 1.3 V1hr
1.4 I15min
Intensity (mm/hr)
150
0.8 I15min
100
50
5 min
25 min
0
Time
15 min
5
10
15
20
25
30
35
40
45
50
55
60
Time (min)
60 min
December 19, 2007, Climate Change Symposium, Singapore
57
Assessment of the Proposed
Optimal Storm Pattern
Probability distributions of runoff peak flows and volumes for a
square basin of 1 ha
Similar results of probability distributions for all tested basins.
December 19, 2007, Climate Change Symposium, Singapore
58
Assessment of the Proposed Optimal Storm
Pattern
Runoff peak flows
Imperviousness
Basin shape
(%)
100
Square
65
100
Rectangular
L/W=2
65
100
Rectangular
L/W=4
65
Rectangular
65
(Residential)
35
Runoff volumes
Imperviousness
Basin shape
(%)
100
Square
65
100
Rectangular
L/W=2
65
100
Rectangular
L/W=4
65
Rectangular
65
(Residential)
35
AES
+1.0
+0.9
+1.9
+0.8
+1.1
+0.6
-0.2
-1.8
AES
-27.2
-24.0
-27.1
-24.0
-27.1
-24.1
-24.0
-20.3
December 19, 2007, Climate Change Symposium, Singapore
Desbordes
(30 min)
+4.5
+4.7
+5.7
+5.5
+8.8
+6.6
+4.2
+5.6
Desbordes
(30 min)
+8.9
+21.8
+9.0
+21.8
+9.0
+21.9
+21.4
+40.7
Watt
Proposed
+23.4
+26.3
+25.0
+27.2
+29.2
+30.0
+21.3
+31.9
+1.4
-0.6
+1.2
-0.5
+1.3
-0.1
-1.6
-2.4
Watt
Proposed
-8.3
+0.5
-8.2
+0.5
-8.2
+0.4
+0.7
+13.4
-0.2
+3.7
-0.2
+3.8
-0.2
+3.8
+3.6
+5.0
59
Climate Trends and Variability
1950-1998


Maximum and minimum temperatures have increased at similar rate
Warming in the south and west, and cooling in the northeast (winter & spring)
Trends in
Winter
Mean Temp
(°C / 49 years)
Trends in
Spring
Mean Temp
(°C / 49
years)
Trends in
Summer
Mean Temp
(°C / 49 years)
Trends in
Fall
Mean Temp
(°C / 49
years)
From X. Zhang, L. Vincent, B. Hogg and A. Niitsoo, Atmosphere-Ocean, 2000
December 19, 2007, Climate Change Symposium, Singapore
60
Validation of GCMs for Current Period (1961-1990)
Winter Temperature (°C)
Model mean =all flux & non-flux corrected results (vs NCEP/NCAR dataset)
December 19, 2007, Climate Change Symposium, Singapore
[Source: IPCC TAR, 2001, chap. 8]
61
Climate Scenario development need: from coarse to high resolution
A mismatch of scales between what climate models can supply and what
environmental impact models require.
December 19, 2007, Climate Change Symposium, Singapore
Point
GCMs or RCMs supply...
1m
10km
50km
300km
Impact models require ...
P. Gachon
62
Choice of distribution model for fitting
annual extreme rainfalls

Common probability distributions:

Two-parameter distribution:
Gumbel distribution
Normal
Log-normal (2 parameters)

Three-parameter distributions:
Beta-K distribution
Beta-P distribution
Generalized Extreme Value distribution
Pearson Type 3 distribution
Log-Normal (3 parameters)
Log-Pearson Type 3 distribution
December 19, 2007, Climate Change Symposium, Singapore
63
Choice of distribution model for fitting
annual extreme rainfalls
Generalized Gamma distribution
 Generalized Normal distribution
 Generalized Pareto distribution


Four-parameter distribution


Two-component extreme value distribution
Five-parameter distribution:

Wakeby distribution
No general agreement on the choice of
distribution for extreme rainfalls!!!
December 19, 2007, Climate Change Symposium, Singapore
64
Choice of distribution model for fitting
annual extreme rainfalls



A three-parameter distribution can provide
sufficient flexibility for describing extreme
hydrologic data.
A two-parameter distribution could be
adequate for prediction.
The choice of a distribution is not as crucial
as an adequate data sample. Discrepancies
increase for extrapolation beyond the length
of record (model error is more important than
sampling error).
December 19, 2007, Climate Change Symposium, Singapore
65
Estimation of model parameters

Graphical method (Probability plots)



Different plotting-position formulas
Frequency factor method
Method of moments
Sample mean, variance, and skewness.
 Sample mean, variance, 1st and/or 2nd moments
in log-space (method of mixed moments)
 Sample mean, variance, and geometric and/or
harmonic mean (generalized method of moments)


Should we use higher-order moments?
December 19, 2007, Climate Change Symposium, Singapore
66
Estimation of model parameters

Method of maximum likelihood




Method of L-moments



Optimal estimators (unbiased, minimum variance) of the
parameters.
Iterative numerical methods.
It could give bad estimators for small samples.
Linear combination of order statistics
Sample L-moments are found less biased than traditional
moment estimators  better suited for use with small
samples?
Other methods


Maximum entropy method
Etc.
December 19, 2007, Climate Change Symposium, Singapore
67
MODEL ASSESSMENT

Descriptive Ability
 Graphical
Display: Quantile-Quantile Plots
 Numerical Comparison Criteria

Predictive Ability
 Bootstrap
Method
December 19, 2007, Climate Change Symposium, Singapore
68
Numerical Comparison Criteria

Root Mean Square Error
RMSE  [ ( x  y ) /( n  m)]
Relative Root Mean Square Error
2
i
RRMSE 
1/ 2
i
 ( x  y ) / x 
2
i
i
i

/( n  m)
1/ 2
Maximum Absolute Error
MAE  max( x i  y i )
Correlation Coefficient
CC   ( xi  x )( y i  y )
 ( x
December 19, 2007, Climate Change Symposium, Singapore
i
 x)
2
(y
i
 y)

2 1/ 2
69
BOOTSTRAP METHOD
A nonparametric approach that repeatedly draws, with replacement,
n observations from the available data set of size N (N >n) and yields
multiple synthetic samples of the same sizes as the original observations.
GEV
74
66
58
50
42
34
26
18
December 19, 2007, Climate Change Symposium, Singapore
70
Location of the 20 Climatological Stations
Record Length
Max: 52 yrs
Min: 24 yrs
Daily Precipitation (mm)
5-Minute Data 1-Hour Data
Maximum
18.5
84.0
Minimum
0.3
1.5
Mean
7.3
21.0
December 19, 2007, Climate Change Symposium, Singapore
71
Goodness-of-fit on the Right Tail
Quantile-Quantile Plots for the Distributions Fitted to
5-Minute Annual Precipitation Maxima at St-Georges Station
Fitted Precipitations (mm)
BEK
GEV
BEP
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
0
5
10
15
20
25
0
0
5
GNO
10
15
20
25
0
GPA
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
5
10
15
20
25
5
LP3
10
15
20
25
0
20
20
20
15
15
15
10
10
10
5
5
5
0
0
15
20
25
20
25
10
15
20
25
15
20
25
WAK
25
10
5
PE3
25
5
15
0
0
25
0
10
GUM
25
0
5
0
0
5
10
15
20
25
0
5
10
Observed Precipitation (mm)
December 19, 2007, Climate Change Symposium, Singapore
72
Extrapolated Right-Tail Quantiles
Box Plots of Extrapolated Right-Tail Bootstrap Data for
5-Minute Annual Precipitation Maxima at McGill Station
24
24
20
20
20
16
16
16
12
12
12
8
8
8
24
Precipitation (mm)
GEV
BEP
BEK
(32.5)
GUM
GPA
GNO
24
24
24
20
20
20
16
16
16
12
12
12
8
8
8
WAK
PE3
LP3
24
24
24
20
20
20
16
16
16
12
12
12
8
8
8
December 19, 2007, Climate Change Symposium, Singapore
73
Results for At-site Frequency Analysis of
Extreme Rainfalls in Quebec



Comparable performance for all distributions in
terms of Descriptive and Predictive abilities.
Top three distributions – WAK,GEV and GNO
Computational simplicity

GUM>GPA>BEP>BEK>GEV>GNO>PE3>WAK>LP3
Theoretical basis of GEV
⇒ GEV is recommended as the most suitable for
representing annual maximum precipitation in
Southern Quebec

December 19, 2007, Climate Change Symposium, Singapore
74