Issues in estimating past climate change at local scale.
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1 14th EMS Annual Meeting, Prague Oct. 6th 2014 Issues in estimating past climate change at local scale. Case study: the recent warming ( ) over France. Lola Corre (Division de la Climatologie, Météo-France) Aurélien Ribes (CNRM-GAME, Météo-France) Anne-Laure Gibelin (Division de la Climatologie, Météo-France) Brigitte Dubuisson (Division de la Climatologie, Météo-France) 1
2 A new reference dataset Monthly homogeneous series of temperature covering the period: Mean temperature: 187 series Mean temperature over France See the poster: Production of a reference data set of homogenised series for analysis of temperature evolution in France since 1959, Gibelin et al. (MC1 session) 2
3 Background Widely used method to estimate the long term change: Linear regression model Mean temperature over France Y(t) = β. t + ε(t) Cov (ε) = σ2. Id Y: observed local temperature β: amplitude of the change ε: internal variability σ2: observed variance 3 +β
4 Method and issues Method: temporal regression model Widely used Y(t) = β. t + ε(t) Y(t) = β. X(t) + ε(t) Cov (ε) = σ2. Id Cov (ε) = σ2. Σ Y: observed local temperature β: amplitude of the change ε: internal variability σ2: observed variance Issues: 4 This study 1. Estimating the change 2. Quantifying the associated uncertainty (Ribes et al. 2010) Y: observed local temperature (known) X: temporal pattern of the change (known) β: amplitude of the change (unknown) ε: internal variability σ2: observed variance (unknown) Σ: covariance structure of ε (known)
5 1. How to estimate the change? Y(t) = β. X(t) + ε(t) Cov (ε) = σ2. Σ Simulated mean French temperature (CMIP5 multi-model ALL forcings) Which temporal pattern? - Linear X - Forced X (simulated response to external forcings) smoothing spline Time 5
6 1. How to estimate the change? Y(t) = β. X(t) + ε(t) Cov (ε) = σ2. Σ Simulated mean French temperature (CMIP5 multi-model ALL forcings) Which temporal pattern? - Linear X - Forced X (simulated response to external forcings) smoothing spline 1.2. Which estimator? ^ - OLS (Ordinary Least Square) : β = (x'x)-1x'y widely used ^ - GLS (Generalized Least Square) : β = (x'σ-1x)-1x'σy optimal when Σ Id 6 Time
7 Estimates of the recent mean French warming Observed mean French temperature evolution Forced X Various approaches lead to quite similar results 7
8 Estimates of the recent mean French warming Observed mean French temperature evolution Forced X Various approaches lead to quite similar results 8 Selected method: forced X and OLS estimator
9 Estimate of the change at local scale Observed temperature change ( ) Method: - Forced X What is the associated uncertainty? - OLS estimator
10 2. Assessing uncertainty / significance Various hypothesis to characterize the internal variability ε: - T1: independant over time (white noise) - T2: short-term memory effect estimated with an autoregressive process of order 1 in time (AR1) - T3: covariance structure deduced from CMIP5 control runs AR1: εt = α. εt-1 + noise Confidence interval (95%) calculations: C.I.up 2 cases: - α = 0.2 (Ribes et al. 2010) - α = 0.3 N.B: α = 0 white noise Estimated change (Forced X and OLS estimator) C.I.low C.I.low > 0 10 warming significantly detected
11 Confidence interval (95%) of the mean change Mean change over France ( ) I.C. width ( C) Mean 1.0 White noise 0.8 AR1(0.2) 1.0 AR1(0.3) 1.2 Models [ ] Multi-model 1.0 ~ C Hypothesis concerning ε: T T1: white noise - T2: AR1 - T3: covariance structure deduced from CMIP5 control runs T2 T1
12 Confidence interval (95%) of the local change C.I. lower margin (2.5%) Observed temperature change ( ) C.I. upper margin (97.5%) Method: - Forced X - OLS estimator - T2 ε: AR1(0.2) 12
13 Local detection result C.I. lower margin For each individual series : C.I.low > Detection of a significant warming for every locations of the French territory 13
14 Local detection result C.I. lower margin For each individual series : C.I.low > Detection of a significant warming for every locations of the French territory Not shown: same conclusion whatever is the hypothesis concerning ε 14
15 Conclusions We used a new dataset of homogeneous temperature series produced by Météo-France to estimate the recent warming over France. Different approaches have been tested: 1. To estimate the observed change results are not sensitive to the selected temporal pattern nor the estimator 2. To assess statistical signification of the change the C.I. is under-estimated by 20 % under the assumption of a white noise internal variability using an AR1 (0.2) process to characterize the internal variability leads to similar results than using control runs. On average over metropolitan France, from 1959 to 2009: 1.5 C +/- 0.5 C (95%) At local scale, for every individual series: whatever the assumption concerning the internal variability, a significant warming has been detected. 15 Selected method: - Forced signal - OLS estimator - internal variability: AR1(0.2)
16 Conclusions We used a new dataset of homogeneous temperature series produced by Météo-France to estimate the recent warming over France. Different approaches have been tested: 1. To estimate the observed change results are not sensitive to the selected temporal pattern nor the estimator 2. To assess statistical signification of the change the C.I. is under-estimated by 20 % under the assumption of a white noise internal variability using an AR1 (0.2) process to characterize the internal variability leads to similar results than using control runs. On average over metropolitan France, from 1959 to 2009: 1.5 C +/- 0.5 C (95%) At local scale, for every individual series: whatever the assumption concerning the internal variability, a significant warming has been detected. 16 Thank you for your attention! Selected method: - Forced signal - OLS estimator - internal variability: AR1(0.2)
17 17
18 Comparing methods : detection results - T1: white noise - T2: AR1 - T3: covariance structure deduced from CMIP5 control runs Lower margins of the 95% C.I. Box plots built from all individual series Whatever the hypothesis concerning ε : C.I.low> 0 Detection of a significant warming for every locations of the French territory Hypothesis concerning ε 18 T3 T2 T1
19 Comparing methods: C.I. widths C.I. width = upper margin lower margin - T1: white noise - T2: AR1 (0.2) - T3: covariance structure deduced from CMIP5 control runs Ratios of C.I. widths T3 / T1 19 Ratios around 1.2 C.I. width 20 % larger with T3 than T1 Ratios of C.I. widths T3 / T2 Ratios around 1 parametric hypothesis AR1 (0.2) acceptable
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B90.330 / C.005 NOTES for Wednesday 0.APR.7 Suppose that the model is β + ε, but ε does not have the desired variance matrix. Say that ε is normal, but Var(ε) σ W. The form of W is W w 0 0 0 0 0 0 w 0
Non-independence due to Time Correlation (Chapter 14)
Non-independence due to Time Correlation (Chapter 14) When we model the mean structure with ordinary least squares, the mean structure explains the general trends in the data with respect to our dependent