4th VALUE Training School Validation of Regional Climate Change Projections. Pitfalls II
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1 4th VALUE Training School Validation of Regional Climate Change Projections Pitfalls II Douglas Maraun Wegener Center for Climate and Global Change Douglas Maraun MOS ICTP, Trieste 1 / 53
2 Outline Perfect Prognosis Bias Correction Douglas Maraun MOS ICTP, Trieste 2 / 53
3 Perfect Prognosis Perfect Prognosis Bias Correction Douglas Maraun MOS ICTP, Trieste 3 / 53
4 Perfect Prognosis The Perfect Prognosis Condition Perfect Prognosis The Perfect Prognosis Condition Douglas Maraun MOS ICTP, Trieste 4 / 53
5 Perfect Prognosis The Perfect Prognosis Condition Perfect Prognosis The following notation for the horizontal spatial scales can be adapted: the minimum scale is defined as the distance between two neighboring grid points of the GCM, whereas the skillful scale is larger than N gridpoint distanes. It is likely that N 8 (Grotch and MacCracken, 1991). It is widely accepted that present-day GCMs are able to simulate the large-scale atmospheric state in a generally realistic manner, and it is believed that these models are the adequate tool to predict large-scale climate changes. Even though the GCMs produce values on the minimum scale, their implications on regional climate are questionable. (von Storch et al., J Climate, 1993) Douglas Maraun MOS ICTP, Trieste 5 / 53
6 Perfect Prognosis The Perfect Prognosis Condition Validation of predictor fields Jury et al., Clim. Dynam., 2015 Douglas Maraun MOS ICTP, Trieste 6 / 53
7 Perfect Prognosis The Perfect Prognosis Condition Validation of predictor fields Jury et al., Clim. Dynam., 2015 Douglas Maraun MOS ICTP, Trieste 7 / 53
8 Perfect Prognosis The Perfect Prognosis Condition Validation of predictor fields Brands et al., J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 8 / 53
9 Perfect Prognosis The Perfect Prognosis Condition Idea: normalise predictors As Karl et al. (1990) demonstrated, regression-based downscaling methods also benefit from the standardization of the predictor variables (by their respective means and standard deviations) so that the corresponding distributions of observed and present-day GCM predictors are in closer agreement. (Wilby et al., Env. Mod. Soft. 2002) Douglas Maraun MOS ICTP, Trieste 9 / 53
10 Perfect Prognosis The Perfect Prognosis Condition Influence of normalised predictors Karl et al., J Climate, 1990 Douglas Maraun MOS ICTP, Trieste 10 / 53
11 Perfect Prognosis The Perfect Prognosis Condition Additionally process understanding Zappa et al., J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 11 / 53
12 Perfect Prognosis The Perfect Prognosis Condition Additionally process understanding Zappa et al., J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 12 / 53
13 Perfect Prognosis Summary PP The Perfect Prognosis Condition Use large-scale free atmosphere predictors; De-biasing by substracting mean; But: substracting means hides biases and therefore potential problems; Are the relevant processes simulated? (Garbage in, garbage out) This is more than comparing means and variances! Douglas Maraun MOS ICTP, Trieste 13 / 53
14 Perfect Prognosis Variance Inflation Perfect Prognosis Variance Inflation Douglas Maraun MOS ICTP, Trieste 14 / 53
15 Perfect Prognosis Variance Inflation Variance Inflation The method of inflation, developed by Klein et al. (1958) was used, since an important goal of this analysis was to reproduce the actual variance calculated in the observations from the free-atmospheric predictors. (Karl et al., J. Climate, 1990) Douglas Maraun MOS ICTP, Trieste 15 / 53
16 Perfect Prognosis Variance Inflation Inflated regression 4 2 y x Maraun, J. Climate, 2014 Douglas Maraun MOS ICTP, Trieste 16 / 53
17 Perfect Prognosis Variance Inflation Inflated regression x y prediction underrepresents total variance Douglas Maraun MOS ICTP, Trieste 16 / 53 Maraun, J. Climate, 2014
18 Perfect Prognosis Variance Inflation Inflated regression x y prediction underrepresents total variance inflate regression (Klein et al., 1958; Karl et al., 1990; Bürger, 1996 Douglas Maraun MOS ICTP, Trieste 16 / 53 Maraun, J. Climate, 2014
19 Perfect Prognosis Variance Inflation Inflated regression y x prediction underrepresents total variance inflate regression (Klein et al., 1958; Karl et al., 1990; Bürger, 1996 flawed concept (Glahn and Allen, 1966; von Storch, 1999; Maraun, 2013) Maraun, J. Climate, 2014 Douglas Maraun MOS ICTP, Trieste 16 / 53
20 Perfect Prognosis Variance Inflation Inflated time series Simulated example: black: observed series; Temperature [arb. units] Time [arb. units] Douglas Maraun MOS ICTP, Trieste 17 / 53
21 Perfect Prognosis Variance Inflation Inflated time series Simulated example: black: observed series; blue: predicted mean of series; Temperature [arb. units] Time [arb. units] Douglas Maraun MOS ICTP, Trieste 17 / 53
22 Perfect Prognosis Variance Inflation Inflated time series Simulated example: black: observed series; blue: predicted mean of series; green: inflated result. Temperature [arb. units] Time [arb. units] Douglas Maraun MOS ICTP, Trieste 17 / 53
23 Perfect Prognosis Variance Inflation Inflated time series Simulated example: black: observed series; blue: predicted mean of series; green: inflated result. CORR(obs,pred)=0.60 CORR(obs,inflate)=0.60 Temperature [arb. units] Time [arb. units] Douglas Maraun MOS ICTP, Trieste 17 / 53
24 Perfect Prognosis Variance Inflation Inflated time series Simulated example: black: observed series; blue: predicted mean of series; green: inflated result. CORR(obs,pred)=0.60 CORR(obs,inflate)=0.60 Temperature [arb. units] RMSE(obs,pred)=2.02 RMSE(obs,inflate)= Time [arb. units] Douglas Maraun MOS ICTP, Trieste 17 / 53
25 Perfect Prognosis Variance Inflation Skill for inflated regression Maraun, J Climate, 2014 Douglas Maraun MOS ICTP, Trieste 18 / 53
26 Perfect Prognosis Variance Inflation Summary inflated regression Inflated regression is flawed and should not be used. Douglas Maraun MOS ICTP, Trieste 19 / 53
27 Perfect Prognosis Bias Correction Douglas Maraun MOS ICTP, Trieste 20 / 53
28 Validation problem Bias Correction Validation problem Douglas Maraun MOS ICTP, Trieste 21 / 53
29 Validation problem Problem: naive validation does not help Map Buenos Aires daily temperature on Cambridge daily precipitation (DJF) Calibration: ; validation: Prediction: Temperature [ C]/Precipitation[mm] calibration, uncorrected validation, uncorrected calibration, corrected validation, corrected Observation: Precipitation[mm] Douglas Maraun MOS ICTP, Trieste 22 / 53
30 Validation problem Summary validation Cross validation and qq plots (etc) is not suffient to assess whether a bias correction is meaningful. Douglas Maraun MOS ICTP, Trieste 23 / 53
31 Representativeness Bias Correction Representativeness Douglas Maraun MOS ICTP, Trieste 24 / 53
32 Representativeness Bias correction only if the model represents what we are interested in! Wilke et al., Clim. Change, 2013 Douglas Maraun MOS ICTP, Trieste 25 / 53
33 Representativeness Bias correction only if the model represents what we are interested in! Maraun et al., Clim. Dynam., 2012 Douglas Maraun MOS ICTP, Trieste 26 / 53
34 Representativeness Summary representativeness Bias correction should only be carried out if the dynamical model represents the local variable. Assessment, e.g., by means of correlation analysis. Maraun and Widmann, Hydrol. Earth Syst. Sci., 2015 Douglas Maraun MOS ICTP, Trieste 27 / 53
35 Bias Correction and Inflation Bias Correction Bias Correction and Inflation Douglas Maraun MOS ICTP, Trieste 28 / 53
36 Bias Correction and Inflation Popular approach: quantile mapping (QM) adjust intensities; adjust number of wetdays. e.g., Piani et al., T.A.C., 2010; Maraun, J. Climate, 2013 Douglas Maraun MOS ICTP, Trieste 29 / 53
37 Bias Correction and Inflation Popular approach: quantile mapping (QM) adjust intensities; adjust number of wetdays. e.g., Piani et al., T.A.C., 2010; Maraun, J. Climate, 2013 Douglas Maraun MOS ICTP, Trieste 29 / 53
38 Bias Correction and Inflation Bias Correction Settings Pure bias correction vs. bias correction plus downscaling Douglas Maraun MOS ICTP, Trieste 30 / 53
39 Bias Correction and Inflation Bias Correction Settings Pure bias correction vs. bias correction plus downscaling Douglas Maraun MOS ICTP, Trieste 30 / 53
40 Bias Correction and Inflation Bias Correction Settings Pure bias correction vs. bias correction plus downscaling Douglas Maraun MOS ICTP, Trieste 30 / 53
41 Bias Correction and Inflation One Grid Box State Several Local States Grid box variability does not explain all local variability Douglas Maraun MOS ICTP, Trieste 31 / 53
42 Bias Correction and Inflation QM does not add Random Variability Quantile Mapping is deterministic Douglas Maraun MOS ICTP, Trieste 32 / 53
43 Bias Correction and Inflation Local variability not explained by grid-box EOBS gridded data rain gauge data; Hasselfelde, Harz mountains; summer Local Precipitation [mm/day] Gridded Precipitation [mm/day] raw data quantiles corrected with quantile mapping Douglas Maraun MOS ICTP, Trieste 33 / 53 after Maraun, J Climate, 2013
44 Bias Correction and Inflation Example Study 20 rain gauges within one grid box in Harz mountains 51.9 Latitude Longitude gauge density: white: low, green: high Maraun, J. Climate, 2013 Douglas Maraun MOS ICTP, Trieste 34 / 53
45 Bias Correction and Inflation Quantile mapping applied to RACMO2 and 20 gauges within one gridbox in Harz mountains DJF JJA 25 Simulated Precipitation [mm/day] Simulated Precipitation [mm/day] Observed Precipitation [mm/day] Observed Precipitation [mm/day] red: uncorrected, blue: corrected Maraun, J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 35 / 53
46 Bias Correction and Inflation Illustrating the Problem REMO grid box precipitation mapped onto 20 rain gauges Precipitation [mm] Maraun, J. Climate, 2013 Douglas Maraun MOS ICTP, Trieste 36 / 53
47 Bias Correction and Inflation QM Effect at Grid Scale QM overcorrects the area drizzle effect and inflates area extremes DJF JJA Simulated Precipitation [mm/day] Simulated Precipitation [mm/day] Observed Precipitation [mm/day] Observed Precipitation [mm/day] Maraun, J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 37 / 53
48 Bias Correction and Inflation QM Effect at Grid Scale QM overcorrects the area drizzle effect and inflates area extremes DJF JJA Simulated Precipitation [mm/day] Simulated Precipitation [mm/day] Observed Precipitation [mm/day] Observed Precipitation [mm/day] Maraun, J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 37 / 53
49 Bias Correction and Inflation A Spectral Perspective Downscaling requires adding small scale variability Douglas Maraun MOS ICTP, Trieste 38 / 53
50 Bias Correction and Inflation A Spectral Perspective Downscaling requires adding small scale variability Douglas Maraun MOS ICTP, Trieste 38 / 53
51 Bias Correction and Inflation Quantile Mapping Inflates Trends value time Maraun, J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 39 / 53
52 Bias Correction and Inflation Quantile Mapping Inflates Trends value time Maraun, J Climate, 2013 Douglas Maraun MOS ICTP, Trieste 39 / 53
53 Bias Correction and Inflation Quantile Mapping Inflates Trends time value Douglas Maraun MOS ICTP, Trieste 39 / 53 Maraun, J Climate, 2013
54 Bias Correction and Inflation Quantile Mapping Inflates Trends time value Douglas Maraun MOS ICTP, Trieste 39 / 53 Maraun, J Climate, 2013
55 Bias Correction and Inflation Stochastic model output statistics New research avenue in climate science Idea: Regression Model observed precipitation = corrected RCM precipitation + noise Requirement for any regression model: a day to day correspondence between predictor and predictand. Ensured by ERA40 boundary conditions and spectral nudging Wong et al., J. Climate, 2014 Douglas Maraun MOS ICTP, Trieste 40 / 53
56 Bias Correction and Inflation Summary QM-Downscaling QM (and variance correcting BC) cannot be used to downscale processes, that exhibit large random variability at local scales; Idea: use stochastic bias correction approaches. Douglas Maraun MOS ICTP, Trieste 41 / 53
57 Large-Scale Errors Bias Correction Large-Scale Errors Douglas Maraun MOS ICTP, Trieste 42 / 53
58 Large-Scale Errors Temperature and precipitation biases CMIP5, multi-model mean Impact modellers often desire to correct these biases. Flato et al., IPCC AR5, 2013 Douglas Maraun MOS ICTP, Trieste 43 / 53
59 Bias Correction Large-Scale Errors Cause: too little meridional heat transport Temperature at 50m depth east of Newfoundland left: observations; right: typical resolution ocean model eddies not resolved; Douglas Maraun MOS Eden et al., J. Phys. Oceanography ICTP, Trieste 44 / 53
60 Large-Scale Errors Impacts of GCM biases on large-scale circulation left: imposed SST anomaly; right: DJF SLP response Keeley et al., QJRMS, 2012 Douglas Maraun MOS ICTP, Trieste 45 / 53
61 Large-Scale Errors Displaced storm tracks black: ERA40; green: CMIP3 models; red, blue: two high resolution models Woollings, Phil Trans R. Soc, 2010 Douglas Maraun MOS ICTP, Trieste 46 / 53
62 Large-Scale Errors Typical impact modeller statement We just need a reference state that agrees with observations. But how do we get a correct reference state if the model simulates the wrong dynamics? Douglas Maraun MOS ICTP, Trieste 47 / 53
63 Large-Scale Errors A step back: Gedankenexperiment Bias correction attempts to correct model misspecifications Increase misspecifications as far as possible energy balance model Bias correcting an energy balance model to infer regional changes obviously doesn t make sense. So, where are the limits? Douglas Maraun MOS ICTP, Trieste 48 / 53
64 Large-Scale Errors Origins of BC in weather forecasting Douglas Maraun MOS ICTP, Trieste 49 / 53
65 Large-Scale Errors Origins of BC in weather forecasting Douglas Maraun MOS ICTP, Trieste 49 / 53
66 Large-Scale Errors Origins of BC in weather forecasting Douglas Maraun MOS ICTP, Trieste 49 / 53
67 Large-Scale Errors In climate modelling, things are different Douglas Maraun MOS ICTP, Trieste 50 / 53
68 Large-Scale Errors In climate modelling, things are different Douglas Maraun MOS ICTP, Trieste 50 / 53
69 Large-Scale Errors In climate modelling, things are different Douglas Maraun MOS ICTP, Trieste 50 / 53
70 Large-Scale Errors In climate modelling, things are different Douglas Maraun MOS ICTP, Trieste 50 / 53
71 Large-Scale Errors In climate modelling, things are different We get rain without storms and vice versa Douglas Maraun MOS ICTP, Trieste 50 / 53
72 Large-Scale Errors Bias Correction under storm track bias Maraun et al., in prep. Douglas Maraun MOS ICTP, Trieste 51 / 53
73 Large-Scale Errors Quantile mapping under blocking bias frequency spell length [days] Maraun et al., in prep. Douglas Maraun MOS ICTP, Trieste 52 / 53
74 Large-Scale Errors Summary large-scale errors GCMs have substantial large-scale circulation errors; these errors cannot sensibly be corrected by current methods; prior to any bias correction, a pre-selection of suitable GCMs is required. If key processes are not simulated, a GCM should not be downscaled. How to mitigate GCM biases? Douglas Maraun MOS ICTP, Trieste 53 / 53
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