Optimal perturbations and observations for decadal climate predictions

Ed Hawkins, Rowan Sutton

THOR annual meeting

Motivation – reducing uncertainty

after Hawkins & Sutton, 2009

CMIP3 projections of UK decadal mean temperature

Motivation

Decadal climate predictions are now being made (e.g. THOR CT4)

— initialised from ocean state to try and predict the climate response to radiative forcings and internal variability

But, large uncertainties exist in ocean analyses

— need to sample this initial condition uncertainty efficiently

— need to identify regions where additional observations are most valuable for improving climate predictions

Perturbation methods developed for NWP can be exended and adapted for decadal climate predictions to address these needs

Example decadal predictions

June 1995

Observations

DePreSys hindcasts

June 2001

Atlantic sub-polar gyre heat content

Jon Robson, Rowan Sutton, Doug Smith

Predictions from UK Met Office Decadal Prediction System (DePreSys)

Motivation – reliability of hindcasts

Reliability diagrams from Smith et al. (2007) showing that for global temperature, DePreSys is slightly overconfident in it’s hindcasts, suggesting the need for greater spread in the predictions.

Also found in ENSEMBLES decadal predictions.

1 yr lead 9 yr lead

init

ial unce

rtain

ty

fore

cast

unce

rtain

ty

reference forecast

Optimal perturbations (or ‘singular vectors’)

reality

ensemble forecasts

Optimal perturbations for decadal predictions are:

perturbations which grow most rapidly, averaged over weather ‘noise’

consistent with the observational uncertainties

useful as efficient perturbations in ensemble forecasts

suitable for identifying regions where additional observations would be most valuable to improve predictions

We have been using two different methods:

1. Linear Inverse Modelling (LIM) e.g. Penland & Sardeshmukh 1995

• computationally cheap

• initial condition independent

• multi-model analysis as part of THOR

2. Climatic Singular Vectors (CSVs) e.g. Kleeman et al. 2003

• expensive to estimate

• calculated for each initial condition separately

• just HadCM3 considered so far

Optimal perturbations

Multi-model LIM optimal perturbations

Models considered so far

Models planned

Other models welcome! e.g. IPSL, …

Only requirement is a long (>500 year) control integration

Detailed analyses already published:

HadCM3: Hawkins & Sutton (2009) GFDL CM2.1: Tziperman et. al. (2008)

LIM optimal perturbations

Linear Inverse Modelling:

• fit a statistical model to the evolution of the ocean state

• reduce dimensionality by representing ocean variability using leading 3d joint EOFs of temperature and salinity

• using control run data, and a focus on Atlantic/Arctic domain )F(y

y

dt

dGCM: Bx

x

dt

dLIM:

y represents ocean data

x represents leading PCs

)()( tt xPx

• From P, the optimal perturbations can be found

Multi-model amplification

HadCM3 decadal amplification

Temperature

GFDL CM2.1 decadal amplification

Temperature

Bergen CM2 decadal amplification

Temperature

Climatic singular vectors (CSVs)

Climatic Singular Vectors (CSVs) - are estimated for specific initial conditions rather than an average state

Approximate propagator matrix (P) constructed from a series of ensemble runs from a single initial condition

Optimal perturbation

Note changed colour scales!

Predicted state 10 years later

Computationally very expensive

HadCM3

Does the CSV work?

Predicted:

Actual:

State after 10 years

Summary

Demonstrated two methods for estimating optimal perturbations for decadal climate predictions

In HadCM3, both methods show significant amplification

largest growing perturbations located in far North Atlantic

some other models show similar growth

Multi-model analysis shows diverse range of variability and amplification to be explored further

Plan to test these perturbations in THOR decadal predictions, and to consider other regions, e.g. Southern Ocean

These approaches have potential to aid development of:

efficient decadal ensemble forecasting systems

optimal ocean observing systems for improving climate predictions

Does the CSV work?

HadCM3 version

GFDL CM2.1 version