1. Assessment of projected changes in seasonalprecipitation extremes in the Czech Republic with a non-stationary index-flood model Martin Hanel, Adri Buishand Technical University in Liberec (TUL) Royal Netherlands Meteorological Institute (KNMI), De Bilt Non-stationary extreme value modelling in climatology 2012/02/16 Liberec
2. OUTLINE 1. Introduction, study area & data 2. Statistical model 3. Evaluation for present climate & projected changes 4. Model diagnostics 5. Conclusions
3. INTRODUCTION Work iniciated within the ENSEMBLES project - WP5.4 Evaluation of extreme events in observational and RCM data Questions: - are the precipitation extremes properly represented in the RCM simulations? - what are the projected changes in precipitation extremes? - how large is the uncertainty associated with the estimation of precipitation extremes and their changes in the climate model data? statistical model developed to answer these questions
4. CASE STUDIES Statistical model applied to assess 1-day summer and 5-day winter precipitation extremes in the Rhine basin 54 52 5 4 50 2 3 48 1 46 4 6 8 10 12
5. CASE STUDIES Statistical model applied to assess 1-day summer and 5-day winter precipitation extremes in the Rhine basin 1-day and 1-hour annual precipitation extremes in the Netherlands
6. CASE STUDIES Statistical model applied to assess 1-day summer and 5-day winter precipitation extremes in the Rhine basin 1-day and 1-hour annual precipitation extremes in the Netherlands 1-, 3-, 5-, 7-, 10-, 15-, 20- and 30-day precipitation extremes for all seasons in the Czech Republic
7. DATA RCM DATA model acronym source period --- ECHAM5 driven --- RACMO RACMO_EH5 KNMI 1950-2100 REMO REMO_EH5 MPI 1951-2100 RCA RCA_EH5 SMHI 1951-2100 RegCM RegCM_EH5 ICTP 1951-2100 HIRHAM HIR_EH5 DMI 1951-2100 --- HadCM3Q0, HadCM3Q3, HadCM3Q16 driven --- HadRM HadRM_Q0 Hadley Centre 1951-2099 CLM CLM_Q0 ETHZ 1951-2099 ≈ 25 km × 25 km HadRM HadRM_Q3 Hadley Centre 1951-2099 RCA RCA_Q3 SMHI 1951-2099 HadRM HadRM_Q16 Hadley Centre 1951-2099 SRES A1B RCA RCA_Q16 C4I 1951-2099 transient --- ARPEGE driven --- HIRHAM HIR_ARP DMI 1951-2100 simulations CNRM-RM CNRM_ARP CNRM 1951-2100 ALADIN-CLIMATE/CZ ALA_ARP CHMI 1961-2100 --- BCM driven --- RCA RCA_BCM SMHI 1961-2100 OBSERVATIONAL DATA (≈ 25 km x 25 km) acronym source period CHMI_OBS CHMI 1950-2007
8. GEV DISTRIBUTION FUNCTION −1 x−ξ κ F(x) = exp − 1 + κ , κ 0 α x−ξ F(x) = exp − exp − , κ=0 α PROBABILITY DENSITY FUNCTION ξ ... location parameter 0.3 dgev(seq(−3, 10, 0.1), 0, 1, 0) 0.2The GEV parameters can vary over the region (spatial heterogeneity) 0.1 vary with time (climate change) 0.0 −2 0 2 4 6 8 10
9. GEV DISTRIBUTION FUNCTION −1 x−ξ κ F(x) = exp − 1 + κ , κ 0 α x−ξ F(x) = exp − exp − , κ=0 α PROBABILITY DENSITY FUNCTION ξ ... location parameter 0.3 dgev(seq(−3, 10, 0.1), 0, 1, 0) α ... scale parameter 0.2The GEV parameters can vary over the region (spatial heterogeneity) 0.1 vary with time (climate change) 0.0 −2 0 2 4 6 8 10
10. GEV DISTRIBUTION FUNCTION −1 x−ξ κ F(x) = exp − 1 + κ , κ 0 α x−ξ F(x) = exp − exp − , κ=0 α PROBABILITY DENSITY FUNCTION ξ ... location parameter 0.3 dgev(seq(−3, 10, 0.1), 0, 1, 0) α ... scale parameter κ ... shape parameter 0.2The GEV parameters can vary over the region (spatial heterogeneity) 0.1 vary with time (climate change) + − 0.0 −2 0 2 4 6 8 10
11. STATISTICAL MODEL Index flood method assumes that precipitation maxima over a region are identically distributed after scaling with a site-specific factor SPATIAL HETEROGENEITY ξ varies over the region α κ, γ = ξ are constant over the region γ is the dispersion coefficient analogous to the coefficient of variation T-year quantile at any site s can be represented as 1 −κ 1 − − log 1 − T QT (s) = µ(s) · qT , qT = 1 − γ · κ where qT is a common dimensionless quantile function (growth curve) and µ(s) is a site-specific scaling factor ("index flood") it is convenient to set µ(s) = ξ(s)
12. STATISTICAL MODEL NON-STATIONARITY location parameter varies over the region, but with common trend ξ(s, t) = ξ0 (s) · exp [ξ1 · I(t)] where I(t) is the time indicator dispersion coefficient and shape parameter are constant over the region, but vary with time γ(t) = exp [γ0 + γ1 · I(t)] κ(t) = κ0 + κ1 · I(t) UNCERTAINTY assessed by a bootstrap procedure (1000 samples for each RCM simulation, season and duration)
13. RELATIVE CHANGES T-year quantile in time t and location s: QT (s, t) = ξ(s, t) · qT (t) Relative change between t2 and t1 (t2 > t1 ) is: QT (s, t2 ) ξ(s, t2 ) qT (t2 ) = · QT (s, t1 ) ξ(s, t1 ) qT (t1 ) ξ(s, t2 ) ξ(s, t) = ξ0 (s) · exp [ξ1 · I(t)] ⇒ = exp ξ1 · [I(t2 ) − I(t1 )] ξ(s, t1 )
14. RELATIVE CHANGES T-year quantile in time t and location s: QT (s, t) = ξ(s, t) · qT (t) Relative change between t2 and t1 (t2 > t1 ) is: QT (s, t2 ) ξ(s, t2 ) qT (t2 ) = · QT (s, t1 ) ξ(s, t1 ) qT (t1 ) ξ(s, t2 ) ξ(s, t) = ξ0 (s) · exp [ξ1 · I(t)] ⇒ = exp ξ1 · [I(t2 ) − I(t1 )] ξ(s, t1 ) ⇒ the relative change in quantiles can be written as QT (s, t2 ) qT (t2 ) = exp ξ1 · [I(t2 ) − I(t1 )] · QT (s, t1 ) qT (t1 ) which does not depend on s.
15. TIME INDICATORVarious choices for I(t) are possible: year t CHANGE IN PRECIPITATION e.g., I(t) = t, but more complicated functions are needed temperature/ temperature anomalyWe use: seasonal global temperature anomaly of the driving GCM
16. TIME INDICATORVarious choices for I(t) are possible: SEASONAL GLOBAL TEMPERATURE ANOMALY JJA year t 3 ECHAM5 HadCM3Q0 temperature anomaly HadCM3Q3 2 HadCM3Q16 e.g., I(t) = t, but more complicated functions ARPEGE 1 BCM CGCM are needed 0 −1 temperature/ temperature anomaly −2 1950 2000 2050 2100 DJF Index 3 temperature anomaly 2 1 ECHAM5 0We use: HadCM3Q0 −1 HadCM3Q3 HadCM3Q16 ARPEGE −2 BCM seasonal global temperature anomaly CGCM −3 1950 2000 2050 2100 of the driving GCM
17. IDENTIFICATION OF HOMOGENEOUS REGIONS For each RCM simulation and season we assessed the grid box estimates of the GEV parameters for the period 1961-1990 and 2070-2099 their changes between these two periods focus mainly on the dispersion coefficient and changes in location parameter and dispersion coefficient formation of homogeneous regions common for all RCM simulations and seasons is challenging
18. IDENTIFICATION OF HOMOGENEOUS REGIONS For each RCM simulation and season we assessed the grid box estimates of the GEV parameters for the period 1961-1990 and 2070-2099 their changes between these two periods focus mainly on the dispersion coefficient and changes in location parameter and dispersion coefficient formation of homogeneous regions common for all RCM simulations and seasons is challenging JJA SON DJF MAM
19. IDENTIFICATION OF HOMOGENEOUS REGIONS For each RCM simulation and season we assessed the grid box estimates of the GEV parameters for the period 1961-1990 and 2070-2099 their changes between these two periods focus mainly on the dispersion coefficient and changes in location parameter and dispersion coefficient formation of homogeneous regions common for all RCM simulations and seasons is challenging
20. IDENTIFICATION OF HOMOGENEOUS REGIONS obviously it is not possible to identify strictly homogeneous regions common for all RCM simulations and seasons - however, regional frequency analysis is more accurate than the at-site analysis even in not strictly homogeneous regions - allowing more heterogeneity of precipitation maxima in the statistical model improves goodness-of-fit, however, the estimated changes are not much different when compared to the standard model it turned out that the regions could be acceptably based on the areas of the eight river basin districts in the Czech Republic different groupings of the river basin districts were examined with respect to the lack-of-fit of the statistical model
21. EVALUATION FOR CONTROL CLIMATE Relative bias in quantiles 0.4 0.4 0.4 0.4 areal mean JJA areal mean DJF areal mean MAM areal mean SON 50 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 40 relative bias [% x 100] relative bias [% x 100] relative bias [% x 100] relative bias [% x 100] return period [years] 30 20 10 5 −0.2 −0.2 −0.2 −0.2 2 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 duration [days] duration [days] duration [days] duration [days] Relative (ξ, γ) and absolute (κ) bias in parameters relative [% x 100] or absolute [−] bias relative [% x 100] or absolute [−] bias relative [% x 100] or absolute [−] bias relative [% x 100] or absolute [−] bias areal mean JJA areal mean DJF areal mean MAM areal mean SON ξ 0.4 0.4 0.4 0.4 γ κ 0.2 0.2 0.2 0.2 −0.4 −0.2 0.0 −0.4 −0.2 0.0 −0.4 −0.2 0.0 −0.4 −0.2 0.0 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 duration [days] duration [days] duration [days] duration [days]
22. CHANGES BETWEEN 1961-1990 AND 2070-2099 Relative changes in quantiles 0.4 0.4 0.4 0.4 areal mean JJA areal mean DJF areal mean MAM areal mean SON 50 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 relative change [% x 100] relative change [% x 100] relative change [% x 100] relative change [% x 100] 40 return period [years] 30 20 10 5 −0.2 −0.2 −0.2 −0.2 2 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 duration [days] duration [days] duration [days] duration [days] Relative (ξ, γ) and absolute (κ) changes in parameters relative [% x 100] or absolute [−] change relative [% x 100] or absolute [−] change relative [% x 100] or absolute [−] change relative [% x 100] or absolute [−] change 0.3 0.3 0.3 0.3 areal mean JJA areal mean DJF areal mean MAM areal mean SON ξ γ κ 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 −0.1 −0.1 −0.1 −0.1 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 1 5 10 20 30 duration [days] duration [days] duration [days] duration [days]
23. MODEL DIAGNOSTICS For each grid box we calculate the residuals: we transform the seasonal maxima Xt to: ˆ 1 ξ(t) Xt Xt = · log 1 + · −1 , ˆ ˆ(t) ˆ(t) ξ(t) γ µ which should have a standard Gumbel distribution; Pr{Xt ≤ x} = exp [− exp(−x)] if the model is true. these residuals can be inspected visually and/or e.g. by the Anderson-Darling statistics: ∞ [FN (x) − F(x)]2 A2 = N dF(x), −∞ F(x)[1 − F(x)] where FN (x) is the empirical distribution function of Xt and F(x) standard Gumble distribution function. critical values can be derived using simulation Xt can be further transformed to have a standard normal distribution: normal residuals: Φ−1 exp[− exp(Xt )] ∼ N(0, 1)
25. MODEL DIAGNOSTICS Switzerland average autocorrelation of normal residuals 1.0 0.05 critical values 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 lag
26. MODEL DIAGNOSTICS 2.5 2.0 Switzerland Anderson−Darling statistic global 0.1 critical value ≈ pointwise 0.0017 critical value 1.5 pointwise 0.1 critical value gridbox value 1.0 0.5 0 10 20 30 40 50 60 gridbox
27. CONCLUSIONS Regional GEV modelling provides an informative summary of changes in parameters and various quantiles (rather than a single quantile only). Taking ξ and γ constant over a region strongly reduces standard errors. A negative ensemble mean bias decreasing (in absolute value) with duration is found in summer (6–17%) The bias is mostly small for short duration precipitation extremes in the other seasons (-5–2%), however, as the duration gets longer, the bias is increasing, especially in winter (more than 20%) The average relative changes in the quantiles of the distribution are positive for all seasons and durations. The magnitude of the changes depends on duration only for summer precipitation extremes and large quantiles in autumn
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