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
Total state variable
Averaging time of state variable
Constrains signal at higher freq.than the obs themselves!
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