Dynamical climate reconstruction
Download
1 / 57

Dynamical Climate Reconstruction - PowerPoint PPT Presentation


  • 92 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Dynamical Climate Reconstruction' - indra


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Dynamical climate reconstruction l.jpg

Dynamical Climate Reconstruction

Greg Hakim

University of Washington

Sebastien Dirren, Helga Huntley, Angie Pendergrass

David Battisti, Gerard Roe


Slide2 l.jpg
Plan

  • Motivation: fusing observations & models

  • State estimation theory

  • Results for a simple model

  • Results for a less simple model

  • Optimal networks

  • Plans for the future


Motivation l.jpg
Motivation

  • Range of approaches to climate reconstruction.

  • Observations:

    • time-series analysis; multivariate regression

    • no link to dynamics

  • Models

    • spatial and temporal consistency

    • no link to observations

  • State estimation (this talk)

    • few attempts thus far

    • stationary statistics


Goals l.jpg
Goals

  • Test new method

  • Reconstruct last 1-2K years

    • Unique dataset for climate variability?

    • E.g. hurricane variability.

    • E.g. rational regional downscaling (hydro).

  • Test network design ideas

    • Where to take highest impact new obs?



Climate variability a qualitative approach l.jpg
Climate variability: a qualitative approach

GRIP δ18O (temperature)

GISP2 K+ (Siberian High)

North

Swedish tree line limit shift

Sea surface temperature from planktonic foraminiferals

hematite-stained grains in sediment cores (ice rafting)

Varve thickness (westerlies)

foraminifera

Cave speleotherm isotopes (precipitation)

Mayewski et al., 2004


Statistical reconstructions l.jpg
Statistical reconstructions

  • “Multivariate statistical calibration of multiproxy network” (Mann et al. 1998)

  • Requires stationary spatial patterns of variability

Mann et al. 1998


Paleoclimate modeling l.jpg
Paleoclimate modeling

IPCC Chapter 6


An attempt at fusion l.jpg
An attempt at fusion

Multivariate regression

Data Assimilation through Upscaling and Nudging (DATUN)Jones and Widmann 2003


Fusion hierarchy l.jpg
Fusion Hierarchy

  • Nudging: no error estimates

  • Statistical interpolation

  • 3DVAR

  • 4DVAR

  • Kalman filters

  • Kalman smoothers

}

}

oper

NWP

fixed stats

}

Today’s talk

The curse of dimensionality looms large in geoscience



Gaussian update l.jpg
Gaussian Update

analysis = background + weighted observations

new obs information

Kalman gain matrix

analysis error covariance ‘<’ background



Ensemble kalman filter l.jpg
Ensemble Kalman Filter

Crux: use an ensembleof fully non-linear forecasts tomodel the statistics of the background (expected value and covariance matrix).

Advantages

  • No à priori assumption about covariance; state-dependent corrections.

  • Ensemble forecasts proceed immediately without perturbations.


Summary of ensemble kalman filter enkf algorithm l.jpg
Summary of Ensemble Kalman Filter (EnKF) Algorithm

  • Ensemble forecast provides background estimate & statistics (B) for new analyses.

  • Ensemble analysis with new observations.

(3) Ensemble forecast to arbitrary future time.


Paleo assimilation dynamical climate reconstruction l.jpg
Paleo-assimilation dynamical climate reconstruction

  • Observations often time-averaged.

    • e.g. gauge precip; wind; ice cores.

  • Sparse networks.

  • Issue:

    • How to combine averaged observations with instantaneous model states?


Issue with traditional approach l.jpg
Issue with Traditional Approach

Problem:

Conventional Kalman filtering requires covariance relationships between time-averaged observations and instantaneous states.

High-frequency noise in the instantaneous states contaminates the update.

Solution:

Only update the time-averaged state.


Algorithm l.jpg
Algorithm

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


Illustrative example dirren hakim 2005 l.jpg
Illustrative ExampleDirren & Hakim (2005)

  • Model (adapted from Lorenz & Emanuel (1998)):

  • Linear combination of fast & slow processes

“low-freq.”

“high-freq.”

  • LE ~ a scalar discretized around a latitude circle.

  • - LE has elements of atmos. dynamics:

  • chaotic behavior, linear waves, damping, forcing


Rms instantaneous l.jpg
RMS instantaneous

(dashed : clim)

Instantaneous states have large errors(comparable to climatology)

Due to lack of observational constraint


Rms all means l.jpg

Improvement Percentage of RMS errors

RMS all means

Obs uncertainty

Climatology uncertainty

Total state variable

Averaging time of state variable

Constrains signal at higher freq.than the obs themselves!


A less simple model helga huntley u delaware l.jpg
A less simple modelHelga Huntley (U. Delaware)

  • QG “climate model”

    • Radiative relaxation to assumed temperature field

    • Mountain in center of domain

  • Truth simulation

    • Rigorous error calculations

    • 100 observations (50 surface & 50 tropopause)

    • Gaussian errors

    • Range of time averages






Average spatial rms error32 l.jpg
Average Spatial RMS Error

Ensemble used for control


Implications l.jpg
Implications

  • State is well constrained by few, noisy, obs.

  • Forecast error saturates at climatology for tau ~ 30.

  • For longer averaging times, the model adds little.

    • Equally good results can be obtained by assimilating the observations with an ensemble drawn from climatology (no model runs required)!



Changing o observation error l.jpg
Changing o (Observation Error)

  • Previously:

    • o = 0.27 for all .

  • Now:

    • o ≈ c/3

    • (a third of control error).


Observing network design helga huntley u delaware l.jpg
Observing Network DesignHelga Huntley (U. Delaware)


Optimal observation locations l.jpg
Optimal Observation Locations

  • Rather than use random networks, can we devise a strategy to optimally site new observations?

    • Yes: choose locations with the largest impact on a metric of interest.

    • New theory based on ensemble sensitivity (Hakim & Torn 2005; Ancell & Hakim 2007; Torn and Hakim 2007)

    • Here, metric = projection coefficient for first EOF.


Ensemble sensitivity l.jpg
Ensemble Sensitivity

  • Given metric J, find the observation that reduces uncertainy most (ensemble variance).

  • Find a second observation conditional on first.

  • Sketch of theory (let x denote the state).

    • Analysis covariance

    • Changes in metric given changes in state

      + O(x2)

    • Metric variance


Sensitivity state estimation l.jpg
Sensitivity + State Estimation

  • Estimate variance change for the i’th observation

  • Kalman filter theory gives Ai:

    where

  • Given  at each point, find largest value.


Ensemble sensitivity cont d l.jpg
Ensemble Sensitivity (cont’d)

  • If H chooses a specific location xi, this all simplifies very nicely:

    • For the first observation:

    • For the second observation, given assimilation of the first observation:

    • Etc.


Ensemble sensitivity cont d41 l.jpg
Ensemble Sensitivity (cont’d)

  • In fact, with some more calculations, one can find a nice recursive formula, which requires the evaluation of just k+3 lines (1 covariance vector + (k+6) entry-wise mults/divs/adds/subs) for the k’th point.



Results for tau 2043 l.jpg
Results for tau = 20

  • The ten most sensitive locations (without accounting for prior assimilations)

  • o = 0.10


Results for tau 2044 l.jpg
Results for tau = 20

  • The four most sensitive locations, accounting for previously found pts.


Results for tau 20 o 0 10 l.jpg
Results for tau = 20; o = 0.10

Note the decreasing effect on the variance.


Control case no assimilation l.jpg
Control Case: No Assimilation

Avg error = 5.4484


100 random observation locations l.jpg
100 Random Observation Locations

Avg Error - Anal = 1.0427

- Fcst = 3.6403


4 random observation locations l.jpg
4 Random Observation Locations

Avg Error - Anal = 5.5644

- Fcst = 5.6279


4 optimal observation locations l.jpg
4 Optimal Observation Locations

Avg Error - Anal = 2.0545

- Fcst = 4.8808


Summary l.jpg
Summary

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.


Experiment 15 chosen observations l.jpg
Experiment: 15 Chosen Observations

  • For this experiment, take

    • 4 best obs to reduce variability in 1st EOF

    • 4 best obs to reduce variability in 2nd EOF

    • 2 best obs to reduce variability in 3rd EOF

    • 2best obs to reduce variability in 4th EOF

    • 3 best obs to reduce variability in 5th EOF

  • The cut-off for each EOF was chosen as the observation with .

  • All obs conditioal on assimilation of previous obs.





Current future plans angie pendergrass uw l.jpg

Current & Future PlansAngie Pendergrass (UW)

modeling on the sphere: SPEEDY

simplified physics

slab ocean

simulated precipitation observations

ice-core assimilation

annual accumulation

oxygen isotopes


Summary56 l.jpg
Summary

  • State estimation = fusion of obs & models

    • Lower errors than obs and model.

    • Provides best estimate & error estimate

  • Idealized experiments: proof of concept

    • Averaged obs constrain state estimates.

    • Optimal observing networks

  • Moving toward real observations

    • Opportunity for regional downscaling.