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
DOWNSCALING METHODS FOR CLIMATE
RELATED IMPACT ASSESSMENT STUDIES
Van-Thanh-Van Nguyen (and Students)
Endowed Brace Professor Chair in Civil Engineering
1
OUTLINE




INTRODUCTION
 What a hydrologic engineer needs from an
atmospheric (climate) scientist?
Extreme Precipitation Process
(Extreme Temperature Process)
 The “scale” problem
 Climate variability and climate change
OBJECTIVES
DOWNSCALING METHODS
 Spatial Downscaling Issues
APPLICATIONS



SDSM and LARS-WG
Some Current Developments
CONCLUSIONS
December 17, 2007, Singapore Climate Change Symposium
2
INTRODUCTION




Information on rainfall characteristics is essential for
planning, design, and management of various
hydraulic structures (flood protection works, urban
sewers, etc.)
Rainfall records by raingages or radar are usually
limited (< 50 years) and are not sufficient for
assessing reliability of hydraulic structure design.

Stochastic simulation of rainfall processes is
needed to generate many long rainfall series.

Several rainfall samples of adequate record
length are needed to be able to determine how
different system designs and operating policies
might perform.
 the variability and the range of future system
performance are better understood, and better
system designs and policies could be selected.
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.
Design Rainfall = maximum amount of precipitation at
a given site for a specified duration and return period.
December 17, 2007, Singapore Climate Change Symposium
3
…

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 17, 2007, Singapore Climate Change Symposium
4
Extreme Rainfall Estimation Methods

At-site Frequency Analysis of Precipitation



Current practice: Annual maximum series (AMS) using 2parameter Gumbel/Ordinary moments method, or using 3parameter GEV/ L-moments method.
Problem: Uncertainties in Data, Model and Estimation
Method
Regional Frequency Analysis of Precipitation


Current practice: GEV/Index-flood method.
Problem: How to define similarity (or homogeneity) of sites?
1
2
3
(WMO Guides to Hydrological
Practices: 1st Edition 1965 →
6th Edition: Section 5.7)
4
Geographically
contiguous fixed
regions
December 17, 2007, Singapore Climate Change Symposium
Geographically non
contiguous fixed
regions
Hydrologic
neighborhood type
regions
5
Rainfall Estimation Issues (1)
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 17, 2007, Singapore Climate Change Symposium
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What are the impacts due to the scale
problem?

On SAMPLING and MEASUREMENT
 Low resolution  High resolution
↓
Accuracy
↓
Noise
↓
Costs
 Optimum resolution?

↑
↑
↑
On DATA ANALYSIS TECHNIQUE
 Artifacts due to scale of measurement or
computation.
 Scale-invariance properties?
 New techniques?
December 17, 2007, Singapore Climate Change Symposium
7
...

On MODELLING TECHNIQUES
 Scale-invariance models?
The SCALE problem has PRACTICAL
and THEORETICAL implications.
 Scale-Invariance
(or Scaling) Methods are
developed in research ⇒ Engineering
Practice?
December 17, 2007, Singapore Climate Change Symposium
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Rainfall Estimation Issues (2)


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 17, 2007, Singapore Climate Change Symposium
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 at a Local Site
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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
(and extreme temperature) time series for
climate change impact studies.
To demonstrate the importance of scaling
consideration in the estimation of daily and
sub-daily extreme precipitations.
December 17, 2007, Singapore Climate Change Symposium
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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 17, 2007, Singapore Climate Change Symposium
high resolution
1 km
day, hour, minute
12
(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 17, 2007, Singapore Climate Change Symposium
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(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 17, 2007, Singapore Climate Change Symposium
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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 17, 2007, Singapore Climate Change Symposium
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
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 17, 2007, Singapore Climate Change Symposium
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Some Current Developments

The Markov Chain, Mixed Exponential
(MCME) Model for Daily Rainfall:

Daily rainfall occurrences (First-Order Two-State
Markov Chain)
pij ,n  P X  ,n  j | X  ,n 1  i for n  1
p00,k 

a00,k
a10,k
p10,k 
a00,k  a01,k
a10,k  a11,k
Daily rainfall amounts (Mixed exponential
distribution)
f ( x) 
p
1
e
(
x
1
)

(1  p)
December 17, 2007, Singapore Climate Change Symposium
2
e
(
x
2
)
17

AN MCME-BASED DOWNSCALING
METHOD
n
Minimize Z  w1AMPi meanMCME  w2 AMPi meandownscaledGCM  AMPi observed 
i 1



AMPs by MCME
Downscaled-GCM AMPs by SDSM method
w 1 + w2 = 1
December 17, 2007, Singapore Climate Change Symposium
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A STATISTICAL DOWNSCALING
METHOD USING PRINCIPAL
COMPONENT REGRESSION
n
n
Oi   0 
 
j ij
Ai   0 
j 1
 
j ij  
j 1
Oi = precipitation occurrence on day i
Ai = precipitation amount on day i
Pij = principal components of predictor climate variables
α , β = parameters
ε = residual
December 17, 2007, Singapore Climate Change Symposium
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
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 17, 2007, Singapore Climate Change Symposium
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
EVALUATION INDICES
December 17, 2007, Singapore Climate Change Symposium
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Geographical locations of sites under study.
Geographical coordinates of the stations
Station
Dorval
Drummondville
Maniwaki
Montreal McGill
December 17, 2007, Singapore Climate Change Symposium
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
22
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
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED MEAN
December 17, 2007, Singapore Climate Change Symposium
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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
6
4
2
0
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED MEAN
December 17, 2007, Singapore Climate Change Symposium
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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
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. LARS-WG-GENERATED 90th PERCENTILE
December 17, 2007, Singapore Climate Change Symposium
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The mean of daily tmax for the period of 1976-1990
(oC)
30
McGill
20
10
0
-10
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM- AND LARS-WG-MEAN OF TMAX
McGill
(oC)
BIAS
OBS
SDSM
LARS
30
20
10
0
-10
J
F
M
A
M
December 17, 2007, Singapore Climate Change Symposium
J
J
A
S
O
N
D
26
The 90th percentile of daily tmax for the period of 1976-1990
(oC)
35
30
25
20
15
10
5
0
McGill
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM- AND LARS-WG-90th PERCENTILE OF TMAX
McGill
(oC)
BIAS
OBS
SDSM
LARS
40
30
20
10
0
-10
J
F
M
A
M
J
December 17, 2007, Singapore Climate Change Symposium
J
A
S
O
N
D
27
The mean of daily tmin for the period of 1976-1990
(oC)
20
15
10
5
0
-5
-10
-15
-20
Drummondville
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM- AND LARS-WG-MEAN OF TMIN
Drummondville
(oC)
BIAS
OBS
SDSM
LARS
20
10
0
-10
-20
J
F
M A
M
December 17, 2007, Singapore Climate Change Symposium
J
J
A
S
O
N
D
28
The 10th percentile of daily tmin for the period of 1976-1990
(oC)
20
Drummondville
10
0
-10
-20
-30
-40
J
F
M
A
M
J
J
A
S
O
N
D
OBSERVED vs. SDSM- AND LARS-WG-10th PERCENTILE OF TMIN
Drummondville
(oC)
BIAS
OBS
SDSM
LARS
20
0
-20
-40
J
F
M A
M
December 17, 2007, Singapore Climate Change Symposium
J
J
A
S
O
N
D
29
GCM and Downscaling Results (Daily Temperature 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 17, 2007, Singapore Climate Change Symposium
30
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 17, 2007, Singapore Climate Change Symposium
31
SUMMARY


Downscaling is necessary!!!
LARS-WG and SDSM models could describe well
basic statistical properties of the daily temperature
extremes at a local site, but both models were unable
to reproduce accurately the observed statistics of
daily precipitation.
GCM-Simulated Daily Precipitation Series
Is it feasible?
Daily Extreme Precipitations
December 17, 2007, Singapore Climate Change Symposium
32
APPLICATION OF MCME-BASED
DOWNSCALING METHOD
Sooke
Reservoir
(1500 mm)
Dorval
(897 mm)
Roxas City
(2029 mm)
DATA:
• 30-year daily rainfall record at Dorval Airport (Quebec), Sooke Reservoir
(BC), and Roxas City (Philippines) for the 1961-1990 period.
• Calibration: 1961-1980
• Validation: 1981-1990
December 17, 2007, Singapore Climate Change Symposium
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Estimation of MCME Model Parameters
MCME Model Parameters:
p00 , p10 , p, 1 ,  2



Seasonal Variability: Parameters estimated for each
month.
Observed frequencies of daily rainfall occurrences for
estimation of p00 and p10
Maximum likelihood method for estimation of p, μ1, and
μ 2.


Multi-start (MSX) procedure using the local simplex technique
(Nelder and Mead, 1965): A good guess of initial value;
otherwise, no convergence to optimal solution.
Shuffled Complex Evolution (SCE) method (Duan et al., 1993):
Random search + local search, more accurate and more robust.
December 17, 2007, Singapore Climate Change Symposium
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Mixed Exponential Model for Daily Rainfall Amounts
Dorval
Roxas
City
December 17, 2007, Singapore Climate Change Symposium
35
Dorval
Roxas
City
Transition Probabilities
December 17, 2007, Singapore Climate Change Symposium
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Dorval: Mean
Standard deviation
Roxas City: Mean
Standard deviation
December 17, 2007, Singapore Climate Change Symposium
37
Dorval
Physical Properties
1: Observed
2: MCME Model
(100 simulations for
June-July-August)
Roxas City
PRECIPITATION
CHARACTERISTIC
INDEX
DEFINITION
UNIT
Frequency
Prcp1
Percentage of wet days
(Threshold of 1 mm)
%
Intensity
SDII
Simple daily intensity index: sum
of daily precipitation divided by
the number of wet days
mm/number of wet
days
CDD
Maximum number of consecutive
dry days (<1mm)
days
R3days
Maximum 3-day precipitation
total
mm
Prec90p
90th percentile of rainy amount
mm/day
R90N
Number of days precipitation
exceeds the 90th percentile
days
Extremes: Magnitude and
Occurrence
December 17, 2007, Singapore Climate Change Symposium
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MCME
CGCM
HadCM3
December 17, 2007, Singapore Climate Change Symposium
Calibration: 1961-1980
39
CGCM
HadCM3
Model 1
Validation: 1981-1990
Calibration ('61-'80)
Validation ('81-'90)
MAE
RMSE
MAE
RMSE
MCME
3.00
3.77
4.35
4.08
HadCM3
3.52
4.94
5.66
4.69
MCME+HadCM3
2.83
3.40
4.23
3.56
Model 2
Calibration ('61-'80)
Validation ('81-'90)
MAE
RMSE
MAE
RMSE
MCME
3.00
3.77
4.35
4.08
CGCM
3.16
3.71
3.72
3.01
MCME+CGCM
3.09
3.63
3.81
3.23
December 17, 2007, Singapore Climate Change Symposium
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APPLICATION OF DOWNSCALING USNG
PRINCIPAL COMPONENT REGRESSION
December 17, 2007, Singapore Climate Change Symposium
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1: Annual PC; 2: Seasonal PC; 3: Stepwise; and 4: SDSM
December 17, 2007, Singapore Climate Change Symposium
(1976-1990)
42
1: Annual PC; 2: Seasonal PC; 3 Stepwise; and 4: SDSM
December 17, 2007, Singapore Climate Change Symposium
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1: Annual PC; 2: Seasonal PC; 3 Stepwise; and 4: SDSM
December 17, 2007, Singapore Climate Change Symposium
44
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 17, 2007, Singapore Climate Change Symposium
30
0
10
1
10
2
10
Return period (years)
HadCM3A2
45
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 17, 2007, Singapore Climate Change Symposium
0
30
35
40
45
50
55
60
65
70
75
HadCM3A2 estimates
HadCM3A2
46
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 17, 2007, Singapore Climate Change Symposium
47
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;
 tmax and tmin were strongly related to geopotential heights and
specific humidities at all levels.
LARS-WG and SDSM models could describe well basic statistical
properties of the daily temperature extremes at a local site, but both
models could provide “good” but “biased” estimates of the observed
statistical properties of the daily precipitation process.
The MCME model could describe from good to excellent many
important (statistical and physical) properties of daily rainfall time
series.
It is feasible to link local-scale MCME rainfall extreme simulations
with large-scale climate variable simulations.
December 17, 2007, Singapore Climate Change Symposium
48
CONCLUSIONS (2)





The proposed PC regression models outperform the SDSM and
the stepwise model in the prediction of the mean and standard
deviation of the observed series.
The PC regression models are more accurate than the SDSM in
reproducing the SDII, R3days and Prec90p for the winter, spring
and autumn seasons, and has comparable performance for the
summer season and for other indices.
The principal component analysis created statistically and
physically meaningful groupings of the NCEP predictor
variables.
It is feasible to link daily GCM-simulated AMPs with observed
daily AMPs at a local site using a second-order nonlinear biascorrection function. Hence, the impacts of climate change for
different scenarios on daily AMPs could be described.
Choice of the “best” downscaling method requires rigorous
evaluation (study objectives and region of interest).
December 17, 2007, Singapore Climate Change Symposium
49
...
Thank You!
December 17, 2007, Singapore Climate Change Symposium
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Validation of GCMs for Current Period (1961-1990)
Winter Temperature (°C)
Model mean =all flux & non-flux corrected results (vs NCEP/NCAR dataset)
December 17, 2007, Singapore Climate Change Symposium
[Source: IPCC TAR, 2001, chap. 8]
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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 17, 2007, Singapore Climate Change Symposium
Point
GCMs or RCMs supply...
1m
10km
50km
300km
Impact models require ...
P. Gachon
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I (mm/hr)
True image
time (hr)
I (mm/hr)
time (hr)
December 17, 2007, Singapore Climate Change Symposium
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December 17, 2007, Singapore Climate Change Symposium
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UNKNOWN TRUE
IMAGE
A
A1
A2
Α1  Α2  Α
December 17, 2007, Singapore Climate Change Symposium
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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 17, 2007, Singapore Climate Change Symposium
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