Statistical Challenges in Climatology Chris Ferro Climate Analysis Group Department of Meteorology University of Reading Also featuring… David Stephenson, Abdel Hannachi, Sergio Pezzulli, Cristina Carollo (ESSC), Barbara Casati, Caio Coelho, Pascal Mailier, Tim Mosedale, Fotis Panagiotopoulos, Matt Sapiano and Neeraj Teeluk (UCL) Young Statisticians’ Meeting, Cambridge, 14-15 April 2003

Statistical Climatology? ‘primitive’ equations manual forecasts computer forecasts 1904 1922 1950 2002 Vilhelm Bjerknes Lewis Fry Richardson Jule G. Charney The Earth Simulator Speed = 40 Tflops Memory = 10Tbytes

General Issues Dependent Nonstationary Huge datasets Limited data space and time: many scales space and time: periodicities, shocks, external forcings station, satellite, simulation short record, no replication

Circulation Model Differential Equations Numerical Scheme Initial parameters errors structure Differential Equations Numerical Scheme Initial Conditions External Forcings Circulation Model deterministic sensitivity estimation

Intergovernmental Panel on Climate Change www.ipcc.ch PRUDENCE European climate 30-year control simulation, 1961-1990 30-year scenario simulation, 2071-2100 Gigatonnes of Carbon A2 = yellow, B1 = green, B2 = blue, IS92a = black, A1F1 = red dot, A1T = red dash, A1B = brown Prediction of Regional scenarios and Uncertainties for Defining European Climate change risks and Effects Intergovernmental Panel on Climate Change www.ipcc.ch

Mean Winter Precipitation mm/day mm/day

Mean Winter Precipitation mm/day Two-sample block bootstrap simultaneously at each grid point accounts for temporal dependence preserves spatial structure

Mean Winter Precipitation mm/day Two-sample block bootstrap simultaneously at each grid point accounts for temporal dependence preserves spatial structure

Observations Buoys Field Stations Ships & Aircraft Satellites Radiosondes Palaeo-records homogeneity, missing data, errors and outliers network design and adaptive observations statistical models to reconstruct past climates

Data Assimilation State Observation Solution Assumptions, approximations and choice of Prediction (3DVAR) and smoothing (4DVAR)

Forecast Calibration Caio Coelho & Sergio Pezzulli climate model Caio Coelho & Sergio Pezzulli Prior: climate-model forecast Likelihood: regression model regression model combined Wt | Ft ~ N(mean[Ft], sd[Ft]) Ft | Wt ~ N(a + bWt, cV)

Forecast ‘Verification’ Barbara Casati false wet : false dry Wavelet decomposition identifies contributions to the forecast performance measure from different spatial scales.

Other Topics Multivariate methods Stochastic models Statistical models identify climate modes investigate climate dynamics attribute climate change downscale simulated data

Conclusions Huge amount of complex data produced Frustrated by inadequate statistical methods Sophisticated techniques required Collaboration and education

Further Information Climate Analysis Group Data Assimilation Research Centre PRUDENCE 9th International Meeting on Statistical Climatology, Cape Town, May 2004 www.met.rdg.ac.uk/cag www.darc.nerc.ac.uk www.dmi.dk/f+u/klima/prudence www.csag.uct.ac.za/IMSC