Glaciological Models in Focus

Transcription

1 Department of Probability and Statistics, University of Sheffield British Antarctic Survey, Cambridge Quantifying Uncertainty on Chronologies for Palaeoclimate Reconstruction from Ice Cores Glaciological Models in Focus Katy Klauenberg, Paul Blackwell, Caitlin Buck Department of Probability and Statistics, The University of Sheffield Regine Röthlisberger British Antarctic Survey, Cambridge / Federal Office for the Environment, Bern Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 1/17

2 Content Ice Cores as Archives Existing Dating methods Some Theory Glaciological Model and its Uncertainty Bayesian Statistics Results: Dating Uncertainty in a Toy Example Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 2/17

3 - Ice Cores The Archive - Existing Dating Methods Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 3/17

4 Ice Cores The Archive - Ice Cores The Archive - Existing Dating Methods Preserve valuable information about the climate and environment of the past Record chemical composition of snow, dust and atmospheric gases with high resolution for up to 700,000 years and longer [Parrenin et al., 2007] Source: BAS image database Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 4/17

5 Ice Cores The Archive - Ice Cores The Archive - Existing Dating Methods Preserve valuable information about the climate and environment of the past Record chemical composition of snow, dust and atmospheric gases with high resolution for up to 700,000 years and longer [Parrenin et al., 2007] Dating is essential to interpret this information Dating: relate time to depth Source: BAS image database Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 4/17

6 Existing Dating Methods layer counting using seasonality in signals - Ice Cores The Archive - Existing Dating Methods glaciological modelling model of accumulation: estimated from isotopic content of ice model of mechanical processes after accumulation: i.e. firn densification, ice flow comparison with other dated records e.g. ice cores, volcanic eruptions, insolation changes any combination of dating methods Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 5/17

7 Existing Dating Methods - Ice Cores The Archive - Existing Dating Methods layer counting using seasonality in signals sufficient annual accumulation sufficient human resources for counting error accumulates glaciological modelling model of accumulation: estimated from isotopic content of ice model of mechanical processes after accumulation: i.e. firn densification, ice flow poorly known parameters comparison with other dated records e.g. ice cores, volcanic eruptions, insolation changes uncertainty in other record uncertainty in link between records any combination of dating methods Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 5/17

8 Existing Dating Methods - Ice Cores The Archive - Existing Dating Methods layer counting using seasonality in signals sufficient annual accumulation sufficient human resources for counting error accumulates glaciological modelling model of accumulation: estimated from isotopic content of ice model of mechanical processes after accumulation: i.e. firn densification, ice flow poorly known parameters comparison with other dated records e.g. ice cores, volcanic eruptions, insolation changes uncertainty in other record uncertainty in link between records any combination of dating methods quantify uncertainty in the accumulation model and derive the dating uncertainty incorporating other dating methods Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 5/17

9 Uncertainty a Nuisance? - Ice Cores The Archive - Existing Dating Methods Comparison with other dated records Did certain climatic events occur at different locations? Were they synchronous? cooling event in record 2 cooling event in record yrBP yrBP Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 6/17

10 Uncertainty a Nuisance? Uncertainty a Nuisance the Essence! - Ice Cores The Archive - Existing Dating Methods Comparison with other dated records Did certain climatic events occur at different locations? Were they synchronous? cooling event in record 2 cooling event in record 1 Probabilty yrBP yrBP Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 7/17

11 Uncertainty a Nuisance? Uncertainty a Nuisance the Essence! - Ice Cores The Archive - Existing Dating Methods Comparison with other dated records Did certain climatic events occur at different locations? Were they synchronous? cooling event in record 2 cooling event in record 1 Probabilty yrBP yrBP Quantify uncertainty properly! Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 7/17

12 - Glaciological Model and its Uncertainty - Bayesian Statistics Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 8/17

13 Glaciological Model and its Uncertainty Accumulation Model - Glaciological Model and its Uncertainty - Bayesian Statistics chemical measurement: isotopic content of ice annual accumulation rate times covered by each slice of the core Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 9/17

14 Glaciological Model and its Uncertainty - Glaciological Model and its Uncertainty - Bayesian Statistics Accumulation Model chemical measurement: isotopic content of ice annual logaccumulation rate times covered by each slice of the core deformation of depths Y f(y) T = g(d) e f(y) Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 9/17

15 Glaciological Model and its Uncertainty - Glaciological Model and its Uncertainty - Bayesian Statistics Accumulation Model chemical measurement: isotopic content of ice annual logaccumulation rate times covered by each slice of the core deformation of depths Y f(y) T = g(d) e f(y) Its Uncertainty true log-accumul. rates Y f(y) = A + ε T = g(d) observed log-accumul. rate f involves uncertain parameters (inverse modelling: [Parrenin et al., 2001]) model error Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 9/17 e A

16 Glaciological Model and its Uncertainty - Glaciological Model and its Uncertainty - Bayesian Statistics Accumulation Model chemical measurement: isotopic content of ice annual logaccumulation rate times covered by each slice of the core deformation of depths Y f(y) T = g(d) e f(y) Its Uncertainty Y f(y) = A + ε observed log-accumul. rate f involves uncertain parameters (inverse modelling: [Parrenin et al., 2001]) true log-accumul. rates model error T = g(d) e A Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 9/17

17 Bayesian Statistics f(y) = A + ε - Glaciological Model and its Uncertainty - Bayesian Statistics Probability The model error (likelihood) true log-accum rate A i f(y i ) A i N A i, σ 2 Observed log-accum rate f(y i ) Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 10/17

18 Bayesian Statistics - Glaciological Model and its Uncertainty - Bayesian Statistics Knowledge from elsewhere Probability (prior distribution) mean annual accum e A i Annual accumulation rate f(y) = A + ε Probability The model error (likelihood) true log-accum rate A i f(y i ) A i N A i, σ 2 Observed log-accum rate f(y i ) Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 10/17

19 Bayesian Statistics - Glaciological Model and its Uncertainty - Bayesian Statistics Knowledge from elsewhere Probability Probability (prior distribution) mean annual accum e A i Annual accumulation rate The model error (likelihood) true log-accum rate A i f(y i ) A i N A i, σ 2 Observed log-accum rate f(y i ) f(y) = A + ε The dating uncertainty (posterior distribution) depth Y 1 Y 2 Y i δ 18 O Probability Time other dating Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 10/17

20 Sources of Prior Knowledge f(y) = A + ε - Glaciological Model and its Uncertainty - Bayesian Statistics recent weather records: do not capture climate not applicable Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 11/17

21 Sources of Prior Knowledge f(y) = A + ε - Glaciological Model and its Uncertainty - Bayesian Statistics recent weather records: do not capture climate not applicable layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 11/17

22 Sources of Prior Knowledge f(y) = A + ε - Glaciological Model and its Uncertainty - Bayesian Statistics recent weather records: do not capture climate not applicable layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters use layer counting of top part as additional constraint, or use information on dated volcanic eruptions whose traces have been identified in the core Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 11/17

23 Sources of Prior Knowledge f(y) = A + ε - Glaciological Model and its Uncertainty - Bayesian Statistics recent weather records: do not capture climate not applicable layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters use layer counting of top part as additional constraint, or use information on dated volcanic eruptions whose traces have been identified in the core model and priors applicable to any Antarctic ice core with isotope measurements Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 11/17

24 - Effect of Uncertainty in Accumulation Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 12/17

25 Effect of Uncertainty in Accumulation - Effect of Uncertainty in Accumulation Toy example A shallow core from Dyer Plateau, Antarctica (70 39 S, W) Dating uncertainty x Image:Flag_of_Antarctica.svg Estimated number of years ± 5.73 years - MCMC ([Rue and Held, 2005]) (samples from posterior) Depth in m Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 13/17

26 Effect of Uncertainty in Accumulation - Effect of Uncertainty in Accumulation Toy example A shallow core from Dyer Plateau, Antarctica (70 39 S, W) Dating uncertainty x Image:Flag_of_Antarctica.svg Estimated number of years Depth in m Depth in m Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 13/17

27 - Current and Future Research - Thank you! Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 14/17

28 Current and Future Research current research gain better prior knowledge include mechanical model - Current and Future Research - Thank you! Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 15/17

29 Current and Future Research - Current and Future Research - Thank you! current research gain better prior knowledge include mechanical model future research more complex accumulation models f multicore, multiproxy analysis statistical approach for layer counting (pilot: XY441 J. Wheatley) combine Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 15/17

30 Current and Future Research - Current and Future Research - Thank you! current research gain better prior knowledge include mechanical model future research more complex accumulation models f multicore, multiproxy analysis statistical approach for layer counting (pilot: XY441 J. Wheatley) combine problems hard to quantify uncertainty further back in time hiatus: summer melting, ice flow disturbances Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 15/17

31 Thank you! - Current and Future Research - Thank you! Thank you! Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 16/17

32 Sources of Prior Knowledge - Current and Future Research - Thank you! recent weather records: do not capture climate not applicable f(y) = A + ε layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters Accumulation model priors (f linear [Johnsen et al., 1995]) P(A 0 ) A 0 ~N( 0.79, 0.27) Evidence from 11 cores P(b) b~n(0.027, ) Evidence from 11 cores Intercept A 0 Slope b Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 17/17

33 Sources of Prior Knowledge - Current and Future Research - Thank you! recent weather records: do not capture climate not applicable f(y) = A + ε layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters Accumulation model priors (f linear [Johnsen et al., 1995]) Model error prior P(A 0 ) A 0 ~N( 0.79, 0.27) Evidence from 11 cores P(b) b~n(0.027, ) Evidence from 11 cores P(σ) σ~γ(7355, 3.5e 05) Evidence from 11 cores Intercept A 0 Slope b Stand Deviation of Model Error σ Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 17/17

34 Sources of Prior Knowledge - Current and Future Research - Thank you! recent weather records: do not capture climate not applicable f(y) = A + ε layer counted ice cores assume accumulation model f holds globally : fit a hierarchical linear model to 11 layer counted ice cores use results as priors for parameters use layer counting of top part as additional constraint Layer counting likelihood P(L i A i A i ) N(0, ) N(log(1.8), ) N(log(0.6), ) Layer counted minus true accum. L i A i Uncertainty in Ice Core Chronologies: Glaciological Models in Focus European Geosciences Union, General Assembly, Vienna April 21, p. 17/17

35 [Johnsen et al., 1995] Johnsen, S. J., Dahl-Jensen, D., Dansgaard, W., and Gundestrup, N. (1995). Greenland palaeotemperatures derived from GRIP bore hole temperature and ice core isotope profiles. Tellus B, 47(5): [Parrenin et al., 2007] Parrenin, F., Dreyfus, G., Durand, G., Fujita, S., Gagliardini, O., Gillet, F., Jouzel, J., Kawamura, K., Lhomme, N., Masson-Delmotte, V., Ritz, C., Schwander, J., Shoji, H., Uemura, R., Watanabe, O., and Yoshida, N. (2007). 1-d-ice flow modelling at EPICA Dome C and Dome Fuji, East Antarctica. Climate of the Past, 3(Special Issue: The EPICA (EDC and EDML) ice cores age scales):1961. [Parrenin et al., 2001] Parrenin, F., Jouzel, J., Waelbroeck, C., Ritz, C., and Barnola, J.-M. (2001). Dating the Vostok ice core by an inverse method. Journal of Geophysical Research Atmospheres, 106(D23): doi: /2001jd [Rue and Held, 2005] Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Number 104 in Monographs in Statistics and Applied Probability. Chapman & Hall/CRC Press, Boca Raton. 17-1