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.

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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: dt = G(Ψt-k. …Ψt … Ψt+m) + δt

• DATUN ansatz: use slow variables so that dt ≈ Ψt-k. ≈ Ψt

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 mean95% confidence intervals

Jones and Widmann, 2003: Instrument- and tree-ring-basedestimates of the Antarctic Oscillation. J. Climate, 16, 3511-3524

Upscaling

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Nudging of the Arctic Oscillation in ECHAM 4target field: vorticity, negative AOI, January, (7y)

vorticity target pattern

ECHAM 4vorticityNudging - Control

AO MusterSLP EOF 1

ECHAM 4SLPNudging - Control

Stormtracks (DJF) with and without nudging7y, 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 4target field: temperature, positive AOI, January, (13y)

temperature target pattern

ECHAM 4temperaturNudging - Control

AO MusterSLP EOF 1

ECHAM 4SLPNudging - Control

Stormtracks (DJF) with and without nudging13y, relaxation time 12 h, AOI = 2 std,variance of 2.5d-6d bandpass filtered Z500