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

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

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.

… 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.

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 1965 → 6th Edition: Section 5.7)

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.

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?

... 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?

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)?

… 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

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.

DOWNSCALING METHODS Scenarios

(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.

(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.

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.

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.

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)

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

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

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.

EVALUATION INDICES

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

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

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

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

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

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

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

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

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)

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)

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

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

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.

Mixed Exponential Model for Daily Rainfall Amounts Dorval Roxas City

Transition Probabilities Dorval Roxas City Transition Probabilities

Dorval: Mean Standard deviation Roxas City: Mean Standard deviation

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)

MCME CGCM HadCM3 Calibration: 1961-1980

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: 1981-1990

APPLICATION OF DOWNSCALING USNG PRINCIPAL COMPONENT REGRESSION

1: Annual PC; 2: Seasonal PC; 3: Stepwise; and 4: SDSM (1976-1990)

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

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

Daily AMPs estimated from GCMs versus observed daily AMPs at Dorval. Calibration period: 1961-1975 CGCMA2 HadCM3A2

Residual = Daily AMP (GCM) - Observed daily AMP (local) Calibration period: 1961-1975 CGCMA2 HadCM3A2

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

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.

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).

... Thank You!

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]

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

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