Van- Thanh -Van Nguyen (and Students) Endowed Brace Professor Chair in Civil Engineering

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

2. 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

3. 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 water-resource systems. • Design Rainfall = maximum amount of precipitation at a given site for a specified duration and return period.

4. Design Rainfall Estimation Methods • 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. 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)

6. Extreme Rainfall Estimation Issues (1) • 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

7. 1 2 3 4 Geographically contiguous fixed regions Geographically non contiguous fixed regions Hydrologic neighborhood type regions Extreme Rainfall Estimation Issues (2) Regionalization methods • GEV/Index-flood method. • Index-Flood Method (Dalrymple, 1960): • Similarity (or homogeneity) of point rainfalls? • How to define groups of homogeneous gages? What are the classification criteria? Proposed Regional Homogeneity: PCA of rainfall amounts at different sites for different time scales. PCA of rainfall occurrencesat different sites. (WMO Guides to Hydrological Practices: 1st Edition 1965 → 6th Edition: Section 5.7, in press)

8. 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.

9. 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)?

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 (Extremes) at a Local Site

11. 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.

12. 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, …).

13. 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 dailyprecipitation 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.

14. DOWNSCALING METHODS Scenarios

15. (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.

16. (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.

17. 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.

18. 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.

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

20. 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.

21. Evaluation indices and statistics

22. Themean of daily precipitationfor the period of1961-1975 BIAS = Mean (Obs.) – Mean (Est.)

23. The mean of daily precipitationfor the period of1976-1990 BIAS = Mean (Obs.) – Mean (Est.)

24. The90th percentile of daily precipitationfor the period of1976-1990 BIAS = Mean (Obs.) – Mean (Est.)

25. 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)

26. 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

27. The Scaling Concept

28. The Scaling Generalized Extreme-Value (GEV) Distribution. • The scaling concept • The cumulative distribution function: • The quantile:

29. The Scaling GEV Distribution

30. The first three moments of GEV distribution:

31. 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.

32. 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

33. Resultson 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-dayrainfalls.

34. 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

35. 1-hour Extreme Rainfalls estimated from 1-day Extreme Rainfalls markers: observed values – lines: values estimated by scaling method

36. 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).

37. 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 SDSM-generated 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.

38. 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.

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

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

41. 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

42. CGCMA2 HadCM3A2

43. 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.

44. CONCLUSIONS (2) • 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. • 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.

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49. 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) formore realistic rainfall-runoff simulation. • A design storm describes completely the distribution of rainfall intensity during thestorm durationfora givenreturn period.

50. 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 • Duration: T • Temporal pattern