A SPATIAL-TEMPORAL DOWNSCALING APPROACH TO A SPATIAL-TEMPORAL DOWNSCALING APPROACH TO CONSTRUCTION OF INTENSITY-DURATION-FREQUENCY CONSTRUCTION OF INTENSITY-DURATION-FREQUENCY RELATIONS IN CONSIDERATION OF GCM-BASED CLIMATE RELATIONS IN CONSIDERATION OF GCM-BASED CLIMATE CHANGE SCENARIOS CHANGE SCENARIOS Van-Thanh-Van Nguyen (and Students) Van-Thanh-Van Nguyen (and Students) Endowed Brace Professor Chair in Civil Endowed Brace Professor Chair in Civil Engineering Engineering McGill University McGill University Montreal, Quebec, Canada Montreal, Quebec, Canada Brace Centre for Water Resources Management Brace Centre for Water Resources Management Global Environmental and Climate Change Centre Global Environmental and Climate Change Centre Department of Civil Engineering and Applied Department of Civil Engineering and Applied Mechanics Mechanics School of Environment School of Environment
Transcript
Slide 1
1 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 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
Slide 2
2 December 19, 2007, Climate Change Symposium, Singapore
OUTLINE n INTRODUCTION Design Rainfall and Design Storm Concept
Current Practices Design Rainfall and Design Storm Concept Current
Practices Extreme Rainfall Estimation Issues? Extreme Rainfall
Estimation Issues? Climate Variability and Climate Change Impacts?
Climate Variability and Climate Change Impacts? n OBJECTIVES n
DOWNSCALING METHODS Spatial Downscaling Issues Spatial Downscaling
Issues Temporal Downscaling Issues Temporal Downscaling Issues
Spatial-Temporal Downscaling Method Spatial-Temporal Downscaling
Method n APPLICATIONS n CONCLUSIONS
Slide 3
3 December 19, 2007, Climate Change Symposium, Singapore
INTRODUCTION n 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. 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) Average
annual flood damages in the U.S. are US$2.1 billion dollars. (US
NRC) n Information on extreme rainfalls is essential for planning,
design, and management of various water- resource systems. n Design
Rainfall = maximum amount of precipitation at a given site for a
specified duration and return period.
Slide 4
4 December 19, 2007, Climate Change Symposium, Singapore n The
choice of an estimation method depends on the availability of
historical data: Gaged Sites Sufficient long historical records
(> 20 years?) At-site Methods. Gaged Sites Sufficient long
historical records (> 20 years?) At-site Methods.
Partially-Gaged Sites Limited data records Regionalization Methods.
Partially-Gaged Sites Limited data records Regionalization Methods.
Ungaged Sites Data are not available Regionalization Methods.
Ungaged Sites Data are not available Regionalization Methods.
Design Rainfall Estimation Methods
Slide 5
5 December 19, 2007, Climate Change Symposium, Singapore Design
Rainfall and Design Storm Estimation n At-site Frequency Analysis
of Precipitation n Regional Frequency Analysis of Precipitation
Intensity-Duration-Frequency (IDF) Relations DESIGN STORM CONCEPT
for design of hydraulic structures (WMO Guides to Hydrological
Practices: 1 st Edition 1965 6 th Edition: Section 5.7, in
press)
Slide 6
6 December 19, 2007, Climate Change Symposium, Singapore
Extreme Rainfall Estimation Issues (1) n Current practices: At-site
Estimation Methods (for gaged sites): Annual maximum series (AMS)
using 2- parameter Gumbel/Ordinary moments method, or using
3-parameter GEV/ L- moments method. Which probability distribution?
Which estimation method? How to assess model adequacy? Best-fit
distribution? Problems: Uncertainties in Data, Model and Estimation
Method
Slide 7
7 December 19, 2007, Climate Change Symposium, Singapore
Extreme Rainfall Estimation Issues (2) Regionalization methods n
GEV/Index-flood method. Index-Flood Method (Dalrymple, 1960):
Index-Flood Method (Dalrymple, 1960): Similarity (or homogeneity)
of point rainfalls? How to define groups of homogeneous gages? What
are the classification criteria? 4 3 2 1 Geographically contiguous
fixed regions Geographically non contiguous fixed regions
Hydrologic neighborhood type regions (WMO Guides to Hydrological
Practices: 1st Edition 1965 6th Edition: Section 5.7, in press)
Proposed Regional Homogeneity: 1.PCA of rainfall amounts at
different sites for different time scales. 2.PCA of rainfall
occurrences at different sites.
Slide 8
8 December 19, 2007, Climate Change Symposium, Singapore n The
scale problem The properties of a variable depend on the scale of
measurement or observation. 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? 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 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. Existing methods cannot
take into account the properties of the physical process over
different scales. Extreme Rainfall Estimation Issues (3)
Slide 9
9 December 19, 2007, Climate Change Symposium, Singapore n
Climate Variability and Change will have important impacts on the
hydrologic cycle, and in particular the precipitation process! n
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 km 2 Temporal resolution ~ (daily),
month, seasonal Reliability of some GCM output variables (such as
cloudiness precipitation)? Extreme Rainfall Estimation Issues
(4)
Slide 10
10 December 19, 2007, Climate Change Symposium, Singapore How
to develop Climate Change scenarios for impacts studies in
hydrology? How to develop Climate Change scenarios for impacts
studies in hydrology? Spatial scale ~ a few km 2 to several 1000 km
2 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
Slide 11
11 December 19, 2007, Climate Change Symposium, Singapore IDF
Relations n At-site Frequency Analysis of Precipitation n Regional
Frequency Analysis of Precipitation Intensity-Duration-Frequency
(IDF) Relations DESIGN STORM for design of hydraulic structures. n
Traditional IDF estimation methods: Time scaling problem: no
consideration of rainfall properties at different time scales; Time
scaling problem: no consideration of rainfall properties at
different time scales; Spatial scaling problem: results limited to
data availability at a local site; Spatial scaling problem: results
limited to data availability at a local site; Climate change: no
consideration. Climate change: no consideration.
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12 December 19, 2007, Climate Change Symposium, Singapore
Summary n Recent developments: Successful applications of the scale
invariant concept in precipitation modeling to permit statistical
inference of precipitation properties between various durations.
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. 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.
Various spatial downscaling methods have been developed to provide
the linkage between (GCM) large-scale data and local scale data. n
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 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, ). GCMs produce data at daily temporal scale, while many
applications require data at sub-daily scales (hourly, 15 minutes,
).
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13 December 19, 2007, Climate Change Symposium, Singapore
OBJECTIVES n To review recent progress in downscaling methods from
both theoretical and practical viewpoints. n To assess the
performance of statistical downscaling methods to find the best
method climate change impact studies. n 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. n 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). n To assess the climate change impacts on the
extreme rainfall processes at a regional or local scale.
15 December 19, 2007, Climate Change Symposium, Singapore
(SPATIAL) DYNAMIC DOWNSCALING METHODS n Coarse GCM + High
resolution AGCM n Variable resolution GCM (high resolution over the
area of interest) n GCM + RCM or LAM (Nested Modeling Approach)
More accurate downscaled results as compared to the use of GCM
outputs alone. 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. Spatial scales for RCM
results ~ 20 to 50 km still larges for many hydrologic models.
Considerable computing resource requirement. Considerable computing
resource requirement.
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16 December 19, 2007, Climate Change Symposium, Singapore
(SPATIAL) STATISTICAL DOWNSCALING METHODS n Weather Typing or
Classification Generation daily weather series at a local site.
Generation daily weather series at a local site. Classification
schemes are somewhat subjective. Classification schemes are
somewhat subjective. n Stochastic Weather Generators Generation of
realistic statistical properties of daily weather series at a local
site. Generation of realistic statistical properties of daily
weather series at a local site. Inexpensive computing resources
Inexpensive computing resources Climate change scenarios based on
results predicted by GCM (unreliable for precipitation) Climate
change scenarios based on results predicted by GCM (unreliable for
precipitation) n Regression-Based Approaches Generation daily
weather series at a local site. Generation daily weather series at
a local site. Results limited to local climatic conditions. Results
limited to local climatic conditions. Long series of historical
data needed. Long series of historical data needed. Large-scale and
local-scale parameter relations remain valid for future climate
conditions. Large-scale and local-scale parameter relations remain
valid for future climate conditions. Simple computational
requirements. Simple computational requirements.
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17 December 19, 2007, Climate Change Symposium, Singapore
APPLICATIONS n 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) Generation of synthetic series of daily
weather data at a local site (daily precipitation, maximum and
minimum temperature, and daily solar radiation) Procedure:
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.
Slide 18
18 December 19, 2007, Climate Change Symposium, Singapore n
Statistical Downscaling Model (SDSM) (Wilby et al., 2001) (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 large- scale
predictors (atmospheric variables) 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 large- scale predictors (atmospheric
variables) Procedure: 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.
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19 December 19, 2007, Climate Change Symposium, Singapore
Geographical locations of sites under study. Geographical
coordinates of the stations
Slide 20
20 December 19, 2007, Climate Change Symposium, Singapore n
DATA: Observed daily precipitation and temperature extremes at four
sites in the Greater Montreal Region (Quebec, Canada) for the
1961-1990 period. 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. NCEP re-analysis daily data for the 1961-1990
period. Calibration: 1961-1975; validation: 1976-1990. Calibration:
1961-1975; validation: 1976-1990.
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21 December 19, 2007, Climate Change Symposium, Singapore
NoCodeUnitTime scaleDescription 1Prcp1%Season Percentage of wet
days (daily precipitation 1 mm) 2SDIImm/r.daySeasonDaily Mean: sum
of daily precipitations / number of wet days 3CDDdaysSeasonMaximum
number of consecutive dry days (daily precipitation < 1 mm)
4R3daysmmSeasonMaximum 3-day precipitation total 5Prec90pmmSeason90
th percentile of daily precipitation amount
6Precip_meanmm/dayMonthSum of daily precipitation in a month /
number of days in that month 7Precip_sdmmMonthStandard deviation of
daily precipitation in a month Evaluation indices and
statistics
Slide 22
22 December 19, 2007, Climate Change Symposium, Singapore The
mean of daily precipitation for the period of 1961-1975 BIAS = Mean
(Obs.) Mean (Est.)
Slide 23
23 December 19, 2007, Climate Change Symposium, Singapore BIAS
= Mean (Obs.) Mean (Est.) The mean of daily precipitation for the
period of 1976-1990
Slide 24
24 December 19, 2007, Climate Change Symposium, Singapore The
90 th percentile of daily precipitation for the period of 1976-1990
BIAS = Mean (Obs.) Mean (Est.)
Slide 25
25 December 19, 2007, Climate Change Symposium, Singapore 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)
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26 December 19, 2007, Climate Change Symposium, Singapore
SUMMARY Downscaling is necessary!!! LARS-WG and SDSM models could
provide good but generally biased estimates of 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 Daily and Sub-Daily
Extreme Precipitations Is it feasible?
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27 December 19, 2007, Climate Change Symposium, Singapore The
Scaling Concept
Slide 28
28 December 19, 2007, Climate Change Symposium, Singapore The
Scaling Generalized Extreme-Value (GEV) Distribution. n The scaling
concept n The cumulative distribution function: The quantile: The
quantile:
Slide 29
29 December 19, 2007, Climate Change Symposium, Singapore The
Scaling GEV Distribution
Slide 30
30 December 19, 2007, Climate Change Symposium, Singapore n The
first three moments of GEV distribution:
Slide 31
31 December 19, 2007, Climate Change Symposium, Singapore
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.
Slide 32
32 December 19, 2007, Climate Change Symposium, Singapore red :
1 st NCM; blue : 2 nd NCM; black : 3 rd NCM; markers : observed
values; lines : fitted regression Scaling of NCMs of extreme
rainfalls with durations: 5-min to 1-hour and 1-hour to 1-day.
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33 December 19, 2007, Climate Change Symposium, Singapore
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.
Slide 34
34 December 19, 2007, Climate Change Symposium, Singapore 5-min
Extreme Rainfalls estimated from 1-hour Extreme Rainfalls markers:
observed values lines: values estimated by scaling method
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35 December 19, 2007, Climate Change Symposium, Singapore
1-hour Extreme Rainfalls estimated from 1-day Extreme Rainfalls
markers : observed values lines : values estimated by scaling
method
Slide 36
36 December 19, 2007, Climate Change Symposium, Singapore The
Spatial-Temporal Downscaling Approach n GCMs: HadCM3 and CGCM2. n
NCEP Re-analysis data. n Spatial downscaling method: the
statistical downscaling model SDSM (Wilby et al., 2002). n Temporal
downscaling method: the scaling GEV model (Nguyen et al.
2002).
Slide 37
37 December 19, 2007, Climate Change Symposium, Singapore The
Spatial-Temporal Downscaling Approach n 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);
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 extracting AMP from the SDSM-generated daily
precipitation time series; and making a bias-correction adjustment
to reduce the difference in quantile estimates from SDSM- generated
AMPs and from observed AMPs at a local site using a second-order
nonlinear function. making a bias-correction adjustment to reduce
the difference in quantile estimates from SDSM- generated AMPs and
from observed AMPs at a local site using a second-order nonlinear
function. n Temporal downscaling: investigating the scale invariant
property of observed AMPs at a local site; and investigating the
scale invariant property of observed AMPs at a local site; and
determining the linkage between daily AMPs with sub-daily AMPs.
determining the linkage between daily AMPs with sub-daily
AMPs.
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38 December 19, 2007, Climate Change Symposium, Singapore
Application n Study Region Precipitation records from a network of
15 raingages in Quebec (Canada). Precipitation records from a
network of 15 raingages in Quebec (Canada). n Data GCM outputs: GCM
outputs: HadCM3A2, HadCM3B2, CGMC2A2, CGCM2B2, Periods: 1961-1990,
2020s, 2050s, 2080s. Observed data: Observed data: Daily
precipitation data, AMP for 5 min., 15 min., 30 min., 1hr., 2 hrs.,
6 hrs., 12 hrs. Periods: 1961-1990.
Slide 39
39 December 19, 2007, Climate Change Symposium, Singapore Daily
AMPs estimated from GCMs versus observed daily AMPs at Dorval.
Calibration period: 1961-1975 CGCMA2 HadCM3A2
41 December 19, 2007, Climate Change Symposium, Singapore Daily
AMPs estimated from GCMs versus observed daily AMPs at Dorval.
Validation period: 1976-1990 CGCMA2 HadCM3A2 Adjusted Daily AMP
(GCM) = Daily AMP (GCM) + Residual
Slide 42
42 December 19, 2007, Climate Change Symposium, Singapore
CGCMA2 HadCM3A2
Slide 43
43 December 19, 2007, Climate Change Symposium, Singapore
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 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 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.
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44 December 19, 2007, Climate Change Symposium, Singapore
CONCLUSIONS (2) n It is feasible to link daily GCM-simulated
climate variables with sub-daily AMPs based on the proposed
spatial- temporal downscaling method. IDF relations for different
climate change scenarios could be constructed. n Differences
between quantile estimates from observed daily AMPs and from
GCM-based daily AMPs could be described by a second-order
non-linear function. n 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. n The proposed scaling GEV
method could provide accurate AMP quantiles for sub-daily durations
from daily AMPs. n 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.
Slide 45
45 December 19, 2007, Climate Change Symposium, Singapore Thank
you for your attention!
Slide 46
46 December 19, 2007, Climate Change Symposium, Singapore
Slides required for presentations
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47 December 19, 2007, Climate Change Symposium, Singapore
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48 December 19, 2007, Climate Change Symposium, Singapore
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49 December 19, 2007, Climate Change Symposium, Singapore
DESIGN STORM CONCEPT n Watershed as a linear system Stormwater
removal Q peak Rational Method: Q peak = CIA Uniform Design
Rainfall Stormwater removal Q peak Rational Method: Q peak = CIA
Uniform Design Rainfall n 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. Environmental control Entire Hydrograph
Q(t) More realistic temporal rainfall pattern (or Design Storm) for
more realistic rainfall-runoff simulation. n A design storm
describes completely the distribution of rainfall intensity during
the storm duration for a given return period.
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50 December 19, 2007, Climate Change Symposium, Singapore
DESIGN STORM CONCEPT n Two main types of synthetic design storms:
Design Storms derived from the IDF relationships. Design Storms
derived from the IDF relationships. Design Storms resulted from
analysing and synthesising the characteristics of historical storm
data. Design Storms resulted from analysing and synthesising the
characteristics of historical storm data. n A typical design storm:
Maximum Intensity: I MAX Maximum Intensity: I MAX Time to peak: T b
Time to peak: T b Duration: T Duration: T Temporal pattern Temporal
pattern
Slide 51
51 December 19, 2007, Climate Change Symposium, Singapore n
Different synthetic design storm models available in various
countries: US Chicago storm model (Keifer and Chu, 1957) US Chicago
storm model (Keifer and Chu, 1957) US Normalized storm pattern by
Huff (1967) US Normalized storm pattern by Huff (1967)
Czechoslovakian storm pattern by Sifalda (1973) Czechoslovakian
storm pattern by Sifalda (1973) Australian design storm by Pilgrim
and Cordery (1975) Australian design storm by Pilgrim and Cordery
(1975) UK Mean symmetric pattern (Flood Studies Report, 1975) UK
Mean symmetric pattern (Flood Studies Report, 1975) French storm
model by Desbordes (1978) French storm model by Desbordes (1978) US
storm pattern by Yen and Chow (1980) US storm pattern by Yen and
Chow (1980) Canadian Atmospheric Environment Service (1980)
Canadian Atmospheric Environment Service (1980) US balanced storm
model (Army Corps of Engineer, 1982) US balanced storm model (Army
Corps of Engineer, 1982) Canadian temporal rainfall patterns
(Nguyen, 1981,1984) Canadian temporal rainfall patterns (Nguyen,
1981,1984) Canadian storm model by Watt et al. (1986) 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? No general agreement as to which temporal
storm pattern should be used for a particular site How to choose?
How to compare? Design Storm Estimation Issues
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52 December 19, 2007, Climate Change Symposium, Singapore
Intensity-Duration-Frequency curves for Montreal area.
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53 December 19, 2007, Climate Change Symposium, Singapore
Chicago IDF Design Storm
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54 December 19, 2007, Climate Change Symposium, Singapore
Design Storm Patterns for southern Quebec (Canada)
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55 December 19, 2007, Climate Change Symposium, Singapore
Design Storm Patterns for southern Quebec (Canada)
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56 December 19, 2007, Climate Change Symposium, Singapore
SUMMARY n Results indicated: For runoff peak flows: For runoff peak
flows: the Canadian AES design storm the Desbordes model (with a
peak intensity duration of 30 minutes) For runoff volumes: 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. None of the eight design storms was able
to provide accurate estimation of both runoff parameters.
Slide 57
57 December 19, 2007, Climate Change Symposium, Singapore The
1-hr optimal storm pattern for southern Quebec (Canada)
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58 December 19, 2007, Climate Change Symposium, Singapore
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.
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59 December 19, 2007, Climate Change Symposium, Singapore
Assessment of the Proposed Optimal Storm Pattern
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60 December 19, 2007, Climate Change Symposium, Singapore
Climate Trends and Variability 1950-1998 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 Fall Mean
Temp (C / 49 years) Trends in Spring Mean Temp (C / 49 years)
Trends in Winter Mean Temp (C / 49 years) Trends in Summer Mean
Temp (C / 49 years) From X. Zhang, L. Vincent, B. Hogg and A.
Niitsoo, Atmosphere-Ocean, 2000
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61 December 19, 2007, Climate Change Symposium, Singapore
Validation of GCMs for Current Period (1961-1990) Winter
Temperature (C) Model mean =all flux & non-flux corrected
results (vs NCEP/NCAR dataset) [Source: IPCC TAR, 2001, chap.
8]
Slide 62
62 December 19, 2007, Climate Change Symposium, Singapore 300km
50km 10km 1m Point GCMs or RCMs supply... Impact models require...
A mismatch of scales between what climate models can supply and
what environmental impact models require. Climate Scenario
development need: from coarse to high resolution P. Gachon
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63 December 19, 2007, Climate Change Symposium, Singapore
Choice of distribution model for fitting annual extreme rainfalls n
Common probability distributions: Two-parameter distribution:
Two-parameter distribution: Gumbel distribution Normal Log-normal
(2 parameters) Three-parameter distributions: 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
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64 December 19, 2007, Climate Change Symposium, Singapore
Generalized Gamma distribution Generalized Gamma distribution
Generalized Normal distribution Generalized Normal distribution
Generalized Pareto distribution Generalized Pareto distribution n
Four-parameter distribution Two-component extreme value
distribution Two-component extreme value distribution n
Five-parameter distribution: Wakeby distribution Wakeby
distribution No general agreement on the choice of distribution for
extreme rainfalls!!! Choice of distribution model for fitting
annual extreme rainfalls
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65 December 19, 2007, Climate Change Symposium, Singapore n A
three-parameter distribution can provide sufficient flexibility for
describing extreme hydrologic data. n A two-parameter distribution
could be adequate for prediction. n 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). Choice of distribution model for
fitting annual extreme rainfalls
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66 December 19, 2007, Climate Change Symposium, Singapore
Estimation of model parameters n Graphical method (Probability
plots) Different plotting-position formulas Different
plotting-position formulas n Frequency factor method n Method of
moments Sample mean, variance, and skewness. Sample mean, variance,
and skewness. Sample mean, variance, 1st and/or 2nd moments in
log-space (method of mixed moments) 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) Sample mean, variance, and geometric and/or
harmonic mean (generalized method of moments) Should we use
higher-order moments?
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67 December 19, 2007, Climate Change Symposium, Singapore n
Method of maximum likelihood Optimal estimators (unbiased, minimum
variance) of the parameters. Optimal estimators (unbiased, minimum
variance) of the parameters. Iterative numerical methods. Iterative
numerical methods. It could give bad estimators for small samples.
It could give bad estimators for small samples. n Method of
L-moments Linear combination of order statistics Linear combination
of order statistics Sample L-moments are found less biased than
traditional moment estimators better suited for use with small
samples? Sample L-moments are found less biased than traditional
moment estimators better suited for use with small samples? n Other
methods Maximum entropy method Maximum entropy method Etc. Etc.
Estimation of model parameters
Slide 68
68 December 19, 2007, Climate Change Symposium, Singapore MODEL
ASSESSMENT n Descriptive Ability Graphical Display:
Quantile-Quantile Plots Graphical Display: Quantile-Quantile Plots
Numerical Comparison Criteria Numerical Comparison Criteria n
Predictive Ability Bootstrap Method Bootstrap Method
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69 December 19, 2007, Climate Change Symposium, Singapore
Numerical Comparison Criteria n Root Mean Square Error Relative
Root Mean Square Error Maximum Absolute Error Correlation
Coefficient
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70 December 19, 2007, Climate Change Symposium, Singapore
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.
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71 December 19, 2007, Climate Change Symposium, Singapore
Location of the 20 Climatological Stations Record Length Max: 52
yrs Min: 24 yrs
Slide 72
72 December 19, 2007, Climate Change Symposium, Singapore
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) Observed
Precipitation (mm)
Slide 73
73 December 19, 2007, Climate Change Symposium, Singapore
Extrapolated Right-Tail Quantiles Box Plots of Extrapolated
Right-Tail Bootstrap Data for 5-Minute Annual Precipitation Maxima
at McGill Station
Slide 74
74 December 19, 2007, Climate Change Symposium, Singapore
Results for At-site Frequency Analysis of Extreme Rainfalls in
Quebec n Comparable performance for all distributions in terms of
Descriptive and Predictive abilities. n Top three distributions
WAK,GEV and GNO n Computational simplicity
GUM>GPA>BEP>BEK>GEV>GNO>PE3>WAK>LP3
GUM>GPA>BEP>BEK>GEV>GNO>PE3>WAK>LP3 n
Theoretical basis of GEV GEV is recommended as the most suitable
for representing annual maximum precipitation in Southern
Quebec