Parametric drift correction for decadal hindcasts on different spatial scales
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1 Parametric drift correction for decadal hindcasts on different spatial scales J. 1, I. Kröner 1, T. Kruschke 2, H. W. Rust 1, and U. Ulbrich 1 1 Institute for Meteorology, Freie Universität Berlin 2 GEOMAR Helmholtz Centre for Ocean Research, Kiel et al. (FU Berlin) parametric drift correction / 12
2 Introduction Parametric drift correction on different spatial scales et al. (FU Berlin) parametric drift correction / 12
3 Introduction Parametric drift correction on different spatial scales global mean temperature observation random data et al. (FU Berlin) parametric drift correction / 12
4 Introduction Parametric drift correction on different spatial scales global mean temperature observation random data linear trend et al. (FU Berlin) parametric drift correction / 12
5 Introduction Parametric drift correction on different spatial scales global mean temperature observation historical random data linear trend same model trend model run with external forcing et al. (FU Berlin) parametric drift correction / 12
6 Introduction Parametric drift correction on different spatial scales global mean temperature observation historical hindcast random data linear trend same model trend model run with external forcing initialized decadal forecast et al. (FU Berlin) parametric drift correction / 12
7 Introduction Parametric drift correction on different spatial scales bias b depends on lead time τ b/ τ 0 drift global mean temperature initialization lead year 1 lead year 2 observation historical hindcast random data linear trend same model trend model run with external forcing initialized decadal forecast et al. (FU Berlin) parametric drift correction / 12
8 Introduction Parametric drift correction on different spatial scales global mean temperature initialization lead year 1 lead year 2 observation historical hindcast bias b depends on lead time τ b/ τ 0 drift separate bias correction for each lead time: non-parametric [ICPO, 2011] random data linear trend same model trend model run with external forcing initialized decadal forecast et al. (FU Berlin) parametric drift correction / 12
9 Introduction Parametric drift correction on different spatial scales global mean temperature initialization lead year 1 lead year 2 observation historical hindcast bias b depends on lead time τ b/ τ 0 drift separate bias correction for each lead time: non-parametric [ICPO, 2011] fit curve to b (τ): parametric approach [Gangsto et al., 2013] random data linear trend same model trend curve fitted to data model run with external forcing initialized decadal forecast et al. (FU Berlin) parametric drift correction / 12
10 Introduction Parametric drift correction on different spatial scales global mean temperature random data linear trend different model trend mean drift observation historical hindcast model run with external forcing initialized decadal forecast bias b depends on lead time τ b/ τ 0 drift separate bias correction for each lead time: non-parametric [ICPO, 2011] fit curve to b (τ): parametric approach [Gangsto et al., 2013] additional term for trend correction [Kharin et al., 2012, Fučkar et al., 2014] et al. (FU Berlin) parametric drift correction / 12
11 Introduction Parametric drift correction on different spatial scales global mean temperature random data linear trend different model trend mean drift observation historical hindcast model run with external forcing initialized decadal forecast bias b depends on lead time τ b/ τ 0 drift separate bias correction for each lead time: non-parametric [ICPO, 2011] fit curve to b (τ): parametric approach [Gangsto et al., 2013] additional term for trend correction [Kharin et al., 2012, Fučkar et al., 2014] parameter depend on initialization time t [Kruschke et al., 2015] et al. (FU Berlin) parametric drift correction / 12
12 Introduction Parametric drift correction on different spatial scales global mean temperature random data linear trend different model trend mean drift observation historical hindcast model run with external forcing initialized decadal forecast bias b depends on lead time τ b/ τ 0 drift separate bias correction for each lead time: non-parametric [ICPO, 2011] fit curve to b (τ): parametric approach [Gangsto et al., 2013] additional term for trend correction [Kharin et al., 2012, Fučkar et al., 2014] parameter depend on initialization time t [Kruschke et al., 2015] D(τ, t) = a 0 (t) + a 1 (t) τ + a 2 (t) τ 2 + a 3 (t) τ 3 et al. (FU Berlin) parametric drift correction / 12
13 Introduction Parametric drift correction on different spatial scales for global mean temperature [Kharin et al., 2012] for spatially smooth variables [Kruschke et al., 2015] et al. (FU Berlin) parametric drift correction / 12
14 Introduction Parametric drift correction on different spatial scales for global mean temperature [Kharin et al., 2012] for spatially smooth variables [Kruschke et al., 2015] potential problems on small scale are: data on small scale can be noisy: parameter estimation can be difficult data on small scale can have wrong trend: correction approach can lead to artificial skill et al. (FU Berlin) parametric drift correction / 12
15 Introduction Parametric drift correction on different spatial scales for global mean temperature [Kharin et al., 2012] for spatially smooth variables [Kruschke et al., 2015] potential problems on small scale are: data on small scale can be noisy: parameter estimation can be difficult data on small scale can have wrong trend: correction approach can lead to artificial skill does the best choice of the parametric model depend on the spatial scale? et al. (FU Berlin) parametric drift correction / 12
16 Data yearly mean near surface temperature (tas) et al. (FU Berlin) parametric drift correction / 12
17 Data yearly mean near surface temperature (tas) observation HadCRUT4 [Jones et al., 2012] 5 5 grid et al. (FU Berlin) parametric drift correction / 12
18 Data yearly mean near surface temperature (tas) observation HadCRUT4 [Jones et al., 2012] 5 5 grid model simulations decadal hindcasts with MPI-ESM, 10 ensemble members full-field initialized with ERA in the atmosphere and ORA S4 [Balmaseda et al., 2013] in the ocean integrated at T63: 1.85 grid et al. (FU Berlin) parametric drift correction / 12
19 Method: bias adjustment correction is done for yearly mean values leave one out for the adjustment et al. (FU Berlin) parametric drift correction / 12
20 Method: bias adjustment correction is done for yearly mean values leave one out for the adjustment non-parametric drift correction [ICPO, 2011] separate bias correction for each lead time et al. (FU Berlin) parametric drift correction / 12
21 Method: bias adjustment correction is done for yearly mean values leave one out for the adjustment non-parametric drift correction [ICPO, 2011] separate bias correction for each lead time parametric drift correction [Kruschke et al., 2015] D(τ, t) = a 0 (t) + a 1 (t) τ + a 2 (t) τ 2 + a 3 (t) τ 3 D(τ, t) = (b 0 + b 1 t) + (b 2 + b 3 t)τ + (b 4 + b 5 t)τ 2 + (b 6 + b 7 t)τ 3 et al. (FU Berlin) parametric drift correction / 12
22 Method: verification verification [Illing et al., 2014] using mean square error skill score (MSESS) comparing forecast (FC) and reference (REF) MSE = 1 (H t O t ) 2 n MSESS = 1 MSE FC MSE REF t et al. (FU Berlin) parametric drift correction / 12
23 Method: verification verification [Illing et al., 2014] using mean square error skill score (MSESS) comparing forecast (FC) and reference (REF) MSE = 1 (H t O t ) 2 n for example: MSESS = 1 MSE FC MSE REF FC: non-parametric, REF: climatology t et al. (FU Berlin) parametric drift correction / 12
24 Method: verification verification [Illing et al., 2014] using mean square error skill score (MSESS) comparing forecast (FC) and reference (REF) MSE = 1 (H t O t ) 2 n for example: MSESS = 1 MSE FC MSE REF FC: non-parametric, REF: climatology FC: parametric, REF: climatology t et al. (FU Berlin) parametric drift correction / 12
25 Method: verification verification [Illing et al., 2014] using mean square error skill score (MSESS) comparing forecast (FC) and reference (REF) MSE = 1 (H t O t ) 2 n for example: MSESS = 1 MSE FC MSE REF FC: non-parametric, REF: climatology FC: parametric, REF: climatology FC: parametric, REF: non-parametric t et al. (FU Berlin) parametric drift correction / 12
26 Results: global mean MSESS leadyears 2-5 FC: non-parametric, REF: climatology leadtime et al. (FU Berlin) parametric drift correction / 12
27 Results: global mean MSESS leadyears 2-5 FC: non-parametric, REF: climatology FC: parametric, REF: climatology leadtime poly3 et al. (FU Berlin) parametric drift correction / 12
28 Results: 20 grid 2_5_tas_user-b324056_tas_leadtime_loo_r18x9.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ 90 N N N 0 30 S 60 S MurCSS 90 S 0 60 E 120 E W 60 W leadyears 2-5 FC: non-parametric, REF: climatology et al. (FU Berlin) parametric drift correction / 12
29 Results: 20 grid 2_5_tas_user-b324056_tas_leadtime_loo_r18x9.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ 90 N N N 0 30 S 60 S MurCSS 90 S 0 2_5_tas_user-b324056_tas_poly3_loo_r18x9.output_mpi-esm-lr_dffs4e_vs_ 60 E 120 E W 60 W user-b324056_tas_leadtime_loo_r18x9.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ 90 N 60 N 30 N 0 30 S leadyears 2-5 FC: non-parametric, REF: climatology FC: parametric, REF: non-parametric 60 S MurCSS S 0 60 E 120 E W 60 W 1.0 et al. (FU Berlin) parametric drift correction / 12
30 Results: 20 grid Can parameters estimated on small scales? 2_5_tas_user-b324056_tas_poly3_loo_r72x36.output_mpi-esm-lr_dffs4e_vs_ user-b324056_tas_leadtime_loo_r72x36.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ 90 N 60 N 30 N 0 30 S 60 S MurCSS 90 S 0 60 E 120 E W 60 W 1.0 leadyears FC: parametric, REF: non-parametric parameters are estimated on 5 grid Parameter estimation on different grids makes no difference et al. (FU Berlin) parametric drift correction / 12
31 Results: 5 grid Adjustment and verification on small scale 90 N 2_5_tas_user-b324056_tas_poly3_loo_r72x36.output_mpi-esm-lr_dffs4e_vs_ user-b324056_tas_leadtime_loo_r72x36.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ N 30 N 0 30 S 60 S MurCSS 90 S 0 60 E 120 E W 60 W leadyears 2-5 FC: parametric, REF: non-parametric data quality? does the forecast system has skill on the 5 grid boxes? et al. (FU Berlin) parametric drift correction / 12
32 Results: different parametric models which parametric model? D 1 (τ, t) = (b 0 + b 1 t) + (b 2 + b 3 t)τ + (b 4 + b 5 t)τ 2 + (b 6 + b 7 t)τ 3 D 2 (τ, t) = (c 0 + c 1 t) et al. (FU Berlin) parametric drift correction / 12
33 Results: different parametric models which parametric model? D 1 (τ, t) = (b 0 + b 1 t) + (b 2 + b 3 t)τ + (b 4 + b 5 t)τ 2 + (b 6 + b 7 t)τ 3 D 2 (τ, t) = (c 0 + c 1 t) 1_1_tas_user-b324056_tas_poly3_loo_r72x36.output_mpi-esm-lr_dffs4e_vs_ user-b324056_tas_poly0_loo_r72x36.output_mpi-esm-lr_dffs4e_ _ msss.nc_masked_ 90 N 60 N 30 N 0 30 S 60 S MurCSS 90 S 0 60 E 120 E W 60 W leadyear 1 FC: parametric D 1 REF: parametric D 2 and non-parametric no difference on global scale small improvement on local scale et al. (FU Berlin) parametric drift correction / 12
34 Summary parametric drift correction shows higher skill than non-parametric method et al. (FU Berlin) parametric drift correction / 12
35 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale et al. (FU Berlin) parametric drift correction / 12
36 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale improvement on e.g. 20 grid et al. (FU Berlin) parametric drift correction / 12
37 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale improvement on e.g. 20 grid improvement does not depend on the grid where parameter estimation is done et al. (FU Berlin) parametric drift correction / 12
38 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale improvement on e.g. 20 grid improvement does not depend on the grid where parameter estimation is done skill enhancement on 5 grid is this skill of the forecast system true? et al. (FU Berlin) parametric drift correction / 12
39 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale improvement on e.g. 20 grid improvement does not depend on the grid where parameter estimation is done skill enhancement on 5 grid is this skill of the forecast system true? third order polynomial shows slight benefits only on small scales et al. (FU Berlin) parametric drift correction / 12
40 Summary parametric drift correction shows higher skill than non-parametric method non-significant on global scale improvement on e.g. 20 grid improvement does not depend on the grid where parameter estimation is done skill enhancement on 5 grid is this skill of the forecast system true? third order polynomial shows slight benefits only on small scales Thank you et al. (FU Berlin) parametric drift correction / 12
41 References Magdalena Alonso Balmaseda, Kristian Mogensen, and Anthony T. Weaver. Evaluation of the ecmwf ocean reanalysis system oras4. Quarterly Journal of the Royal Meteorological Society, 139(674): , ISSN X. doi: /qj URL Neven S. Fučkar, Danila Volpi, Virginie Guemas, and Francisco J. Doblas-Reyes. A posteriori adjustment of near-term climate predictions: Accounting for the drift dependence on the initial conditions. Geophysical Research Letters, 41(14): , ISSN doi: /2014GL URL R Gangsto, AP Weigel, MA Liniger, and C Appenzeller. Methodological aspects of the validation of decadal predictions. Clim Res, 55(3): , URL ICPO. Data and bias correction for decadal climate predictions. CLIVAR Publication Series, No. 150, January Sebastian Illing, Christopher Kadow, Kunst Oliver, and Ulrich Cubasch. Murcss: A tool for standardized evaluation of decadal hindcast systems. Journal of Open Research Software; Vol 2, No 1 (2014), pages, September URL P. D. Jones, D. H. Lister, T. J. Osborn, C. Harpham, M. Salmon, and C. P. Morice. Hemispheric and large-scale land-surface air temperature variations: An extensive revision and an update to Journal of Geophysical Research: Atmospheres, 117 (D5):n/a n/a, ISSN doi: /2011JD URL D V. V. Kharin, G. J. Boer, W. J. Merryfield, J. F. Scinocca, and W.-S. Lee. Statistical adjustment of decadal predictions in a changing climate. Geophysical Research Letters, 39(19):n/a n/a, ISSN doi: /2012GL URL L Tim Kruschke, Henning W. Rust, Christopher Kadow, Wolfgang A. Müller, Holger Pohlmann, Gregor C. Leckebusch, and Uwe Ulbrich. Probabilistic evaluation of decadal prediction skill regarding northern hemisphere winter storms. Meteorologische Zeitschrift, pages, URL et al. (FU Berlin) parametric drift correction / 12
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