1. DOWNSCALING METHODS FOR CLIMATE RELATED IMPACT ASSESSMENT STUDIES
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

2. 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

3. 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.

4. …
The choice of an estimation method depends on the availability of historical data:
Gaged 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.

5. Extreme Rainfall Estimation Methods
At-site Frequency Analysis of Precipitation
Current practice: Annual maximum series (AMS) using 2-parameter Gumbel/Ordinary moments method, or using 3-parameter 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? 4 3 2 1
Geographically contiguous fixed regions
Geographically non contiguous fixed regions
Hydrologic neighborhood type regions
(WMO Guides to Hydrological Practices: 1st Edition → 6th Edition: Section 5.7)

6. THE “SCALE” PROBLEM Rainfall Estimation Issues (1)
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.

7. 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?

8. ... 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?

9. 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)?

10. …
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

11. 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.

12. DOWNSCALING METHODS
Scenarios

13. (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.

14. (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
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.

15. 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.

16. 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 large-scale 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.

17. Some Current Developments
The Markov Chain, Mixed Exponential (MCME) Model for Daily Rainfall:
Daily rainfall occurrences (First-Order Two-State Markov Chain)
Daily rainfall amounts (Mixed exponential distribution)

18. AN MCME-BASED DOWNSCALING METHOD
AMPs by MCME
Downscaled-GCM AMPs by SDSM method
w1 + w2 = 1

19. A STATISTICAL DOWNSCALING METHOD USING PRINCIPAL COMPONENT REGRESSION
Oi = precipitation occurrence on day i
Ai = precipitation amount on day i
Pij = principal components of predictor climate variables
α , β = parameters
ε = residual

20. DATA:
Observed daily precipitation and temperature extremes at four sites in the Greater Montreal Region (Quebec, Canada) for the period.
NCEP re-analysis daily data for the period.
Calibration: ; validation:

21. EVALUATION INDICES

22. Geographical locations of sites under study.
Geographical coordinates of the stations

23. The mean of daily precipitation for the period of 1961-1975
BIAS

24. The mean of daily precipitation for the period of 1976-1990
BIAS

25. The 90th percentile of daily precipitation for the period of 1976-1990
BIAS

26. The mean of daily tmax for the period of 1976-1990
BIAS

27. The 90th percentile of daily tmax for the period of 1976-1990
BIAS

28. The mean of daily tmin for the period of 1976-1990
BIAS

29. The 10th percentile of daily tmin for the period of 1976-1990
BIAS

30. 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)

31. From CCAF Project Report by Gachon et al. (2005)
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)

32. 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

33. 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 period.
Calibration:
Validation:

34. Estimation of MCME Model Parameters
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 μ2.
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.

35. Mixed Exponential Model for Daily Rainfall Amounts
Dorval
Roxas
City

36. Transition Probabilities
Dorval
Roxas
City
Transition Probabilities

37. Dorval: Mean Standard deviation
Roxas City: Mean Standard deviation

38. Dorval Roxas City Physical Properties 1: Observed 2: MCME Model
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
Extremes: Magnitude and Occurrence
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
Physical Properties
1: Observed
2: MCME Model
(100 simulations for
June-July-August)

39. MCME
CGCM
HadCM3
Calibration:

40. HadCM3 CGCM Validation: 1981-1990
Model 1
Calibration ('61-'80)
Validation ('81-'90)
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
CGCM
3.16
3.71
3.72
3.01
MCME+CGCM
3.09
3.63
3.81
3.23
Validation:

41. APPLICATION OF DOWNSCALING USNG PRINCIPAL COMPONENT REGRESSION

42. 1: Annual PC; 2: Seasonal PC; 3: Stepwise; and 4: SDSM
( )

43. 1: Annual PC; 2: Seasonal PC; 3 Stepwise; and 4: SDSM

44. 1: Annual PC; 2: Seasonal PC; 3 Stepwise; and 4: SDSM

45. Daily AMPs estimated from GCMs versus observed daily AMPs at Dorval.
Calibration period:
CGCMA2
HadCM3A2

46. Residual = Daily AMP (GCM) - Observed daily AMP (local)
Calibration period:
CGCMA2
HadCM3A2

47. Daily AMPs estimated from GCMs versus observed daily AMPs at Dorval.
Validation period:
CGCMA2
HadCM3A2
Adjusted Daily AMP (GCM) = Daily AMP (GCM) + Residual

48. 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.

49. 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 bias-correction 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).

50. ...
Thank You!

51. 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]

52. Impact models require ... GCMs or RCMs supply...
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.
300km
Impact models require ...
50km
10km 1m
Point
GCMs or RCMs supply...
P. Gachon

56. 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