Dynamical Climate Reconstruction. Greg Hakim University of Washington. Sebastien Dirren , Helga Huntley , Angie Pendergrass David Battisti, Gerard Roe. Plan. Motivation: fusing observations & models State estimation theory Results for a simple model
University of Washington
Sebastien Dirren, Helga Huntley, Angie Pendergrass
David Battisti, Gerard Roe
IPCC Chapter 6
GRIP δ18O (temperature)
GISP2 K+ (Siberian High)
Swedish tree line limit shift
Sea surface temperature from planktonic foraminiferals
hematite-stained grains in sediment cores (ice rafting)
Varve thickness (westerlies)
Cave speleotherm isotopes (precipitation)
Mayewski et al., 2004
Mann et al. 1998
IPCC Chapter 6
Data Assimilation through Upscaling and Nudging (DATUN)Jones and Widmann 2003
The curse of dimensionality looms large in geoscience
analysis = background + weighted observations
new obs information
Kalman gain matrix
analysis error covariance ‘<’ background
Crux: use an ensembleof fully non-linear forecasts tomodel the statistics of the background (expected value and covariance matrix).
(3) Ensemble forecast to arbitrary future time.
Conventional Kalman filtering requires covariance relationships between time-averaged observations and instantaneous states.
High-frequency noise in the instantaneous states contaminates the update.
Only update the time-averaged state.
1. Time-averaged of background
2. Compute model-estimate of time-av obs
3. Perturbation from time mean
4. Update time-mean with existing EnKF
5. Add updated mean
and unmodified perturbations
6. Propagate model states
7. Recycle with the new background states
(dashed : clim)
Instantaneous states have large errors(comparable to climatology)
Due to lack of observational constraint
Ensemble used for control
Note the decreasing effect on the variance.
Avg error = 5.4484
Avg Error - Anal = 1.0427
- Fcst = 3.6403
Avg Error - Anal = 5.5644
- Fcst = 5.6279
Avg Error - Anal = 2.0545
- Fcst = 4.8808
Percent of ctr error
Assimilating just the 4 chosen locations yields a significant portion of the gain in error reduction in J achieved with 100 obs.
modeling on the sphere: SPEEDY
simulated precipitation observations