Assimilating stats – the problem and experience with the DATUN approach Hans von Storch and Martin Widmann, Institute for Coastal Research, GKSS, Germany NCAR, Stats project, 9 December 2003

Mann‘s reconstruction of temperatures of the past 1000 years

Empirical reconstruction large-scale state → local state local state → proxy data (lake warves, tree rings, ice cores …) Transfer functions describe only part of the variability (typically 50%) Inversion used to reconstruct from proxy data large scale temperature distribution Only data since about 1850 available.

Simulating the effect of incomplete provision of variance by proxy data (addition of noise to grid point temp‘s)

Alternative Use of quasi-realistic climate models (GCM type) Utilization of proxy data

Hesse’s concept of models Reality and a model have attributes, some of which are consistent and others are contradicting. Other attributes are unknown whether reality and model share them. The consistent attributes are positive analogs. The contradicting attributes are negative analogs. The “unknown” attributes are neutral analogs. Validating the model means to determine the positive and negative analogs. Applying the model means to assume that specific neutral analogs are actually positive ones. The constructive part of a model is in its neutral analogs. Hesse, M.B., 1970: Models and analogies in science. University of Notre Dame Press, Notre Dame 184 pp.

Different ways of running the model

10 year low pass filtered Wagner, pers comm. Simulated temperature anomalies in “free” simulation (K)

ECHO-G simulation forced with time-variable solar radiation accounting for solar output and presence of volcanic aerosols, and presence of GHG gases.

Data driven reconstruction...

Problem „Data“ are not related to simultaneous state variables but to statistics of the state variables, in particular temporal and spatial averages. That is: d t = G(Ψ t-k. …Ψ t … Ψ t+m ) + δ t DATUN ansatz: use slow variables so that d t ≈ Ψ t-k. ≈ Ψ t

Dynamical processes in the atmosphere

Dynamical processes in the ocean

Gravest modes of atmospheric variability (200 hPa streamfunction) J. von Storch, 2000

Data Assimilation through Upscaling and Nudging (DATUN) The aim is to inter- and extrapolate in a physically consistent manner proxy data with a coupled ocean- atmosphere GCM Consists of two steps –Upscaling –Nudging (in pattern space)

The AAO pattern and the tree regression weights used to produce the AAOI Isolines in hPa, show the pressure change for AAOI +1 Black-filled circles = positive weight grey-filled circles = negative weight Upscaling

Reconstruction of the NDJ AAOI using undetrended tree-ring width chronologies 9-year running mean 95% confidence intervals Jones and Widmann, 2003: Instrument- and tree-ring-based estimates of the Antarctic Oscillation. J. Climate, 16, Upscaling

Nudging in pattern space

Forced pattern  h (related to AO index) at about 800 hPa vorticity temperature Widmann, 2001

Nudging of the Arctic Oscillation in ECHAM 4 target field: vorticity, negative AOI, January, (7y) vorticity target pattern ECHAM 4 vorticity Nudging - Control AO Muster SLP EOF 1 ECHAM 4 SLP Nudging - Control

Stormtracks (DJF) with and without nudging 7y, relaxation time 12 h, AOI = - 2 std, variance of 2.5d-6d bandpass filtered Z500

Time coefficient  h,t of prescribed pattern  h in control run (top; varies symmetrically around 0), and in two nudging runs with different nudging strength  (middle and bottom; variation ideally around 1) 1 year integration No nudging  = 12 h  = 4 h Widmann and Kirchner, 2001

Reconstruction of past temperature variations is a crucial exercise for assessing the present temperature changes Reconstruction based on proxy data and regression-like methods suffer form an underestimation of low frequency variability Attempts are needed to estimate past variations with AOGCMs, which are constrained by proxy data. DATUN is a first ansatz, but suffers from limitations (reduction of natural variability; underestimation of proxy variability) Innovations needed. Conclusions

NAO reconstruction (a) NAOI in the forced climate simulation, simulated by the ECHO-G model, and reconstructed from the simulated air- temperature field and the precipitation field in the North Atlantic sector over land grid points. (b) As (a) with a 50-year gaussian filter. (c) NAOI as in (b) but in the control simulation. Zorita and González-Rouco, 2002

Nudging of the Arctic Oscillation in ECHAM 4 target field: temperature, positive AOI, January, (13y) temperature target pattern ECHAM 4 temperatur Nudging - Control AO Muster SLP EOF 1 ECHAM 4 SLP Nudging - Control

Stormtracks (DJF) with and without nudging 13y, relaxation time 12 h, AOI = 2 std, variance of 2.5d-6d bandpass filtered Z500