Measures of Estimating Uncertainty of Seasonal Climate Prediction

Information-based vs signal-to-noise based metrics

Youmin Tang

University of Northern British Columbia, Canada

State Key Laboratory of Satellite Ocean Environment Dynamics, The second Institute of Oceanography, China

Potential Predictability

Rowell, D. P. (1998), Assessing potential seasonal predictability with an ensemble of multidecadal GCM simulations, J. Clim., 11, 109–120.

Peng, P., A. Kumar, W. Wang (2009), An analysis of seasonal predictability in coupled model forecasts, Clim. Dyn., 36, 637-648.

Information Entropy--- Uncertainty measure

dxxpxpxH )(ln)()(

dvvpvpdvvpvpPI )]|(ln[)|()](ln[)(

dv

vp

vpvpRE

)(

)|(ln)|(

Relative Entropy （ RE), Predictable Information(PI),

Climatology Distribution , Initial (Boundary) condition

)(p

.

Mutual Info. MI

.

])()(

),(ln[),(

pvp

vpvpMI

Relative Entropy （ Gaussian)

.

Yang, D. Tang, Y and Zhang, Y and Yang X, 2012: JGR-Atmosphere, doi:10.1029/2011JD016775

)2exp(1 MIACMI

t)coefficien ( ncorrelatioperfectSTRACMI

Also equivalent to the correlation of the signal component to the prediction target itself 。

Principal prediction component analysis (PrCA) and Maximum SNR

Denoting by S and N signal and noise, PrCA, or maximum of SNR, looks for a vector q, which can maximize the ratio of the variance of signal and noise that are projected onto the vector, namely,

2

2

;* ;*

N

s

r

r

TN

Ts

SNR

NqrSqr

Maximum

qq

qqSNR

NT

ST

Multiple Model Ensemble

ENSEMBLES project stream-2 Hindcasts (1-tier forecast) http://ensembles.ecmwf.int/thredds/ensembles/stream2/seasonal/atmospheric/monthly.html

UKMO, ECMWF, MF, CMCC_INGV, IFM_GEOMAR

Time Period: January, 1969 to December, 2001.

Domain: 210E-300E; 20N-80N (NA: Northern America)

Ensemble size: 9

Multiple ensemble: 5*9=45

Prediction target: seasonal mean temperature of NA for MAM, JJA, SON and DJF 。

Yan, X , Tang, Y., 2012: An analysis of multi-model ensemble for seasonal climate predictions, Quarterly Journal of the Royal Meteorological Society, 15 OCT 2012 | DOI: 10.1002/qj.2019

MI-based potential predictability and its difference from SNR-based measure

Signal and Noise

For 2-seasons prediction (the calendar season is the target time of prediction, such as MAM meaning the prediction starting from Nov.

The most predictable pattern of the NA TAS at the lead of one season for different seasons (prediction target)

Predictable Component Analysis （ PrCA)

PI Maximum ; SNR Maximum

The time series of PrCA mode 1 and mode 2

The SST patterns associated with the PrCA mode 1 and mode 2 of TAS.

The 500mb height pattern associated with the PrCA TAS mode 1

The PrCA mode 1 (left) and mode 2 (right) for SSTA

Schematic diagram of teleconnection of ENSO to NA SAT Predictability

Correlation RMSE

The predicted time series of the first PrCA mode against the observation counterpart.

Same as above but for the prediction of the first principal component.

Conclusions

Signal-to-noise ratio (SNR) is a special case of information-based predictability measure. When the ensemble spread changes with initial condition, SNR often underestimates the potential predictability.

The most predicable component (PrCA) of the Northern America climate (temperature) is the interannual mode and a long-term trend (the global warming). The most predicable interannual variability, characterized by a dipole structure, is highly related to the ENSO and PNA. When El Nino occurs, a strong positive phase of PNA prevails in the middle-high latitude in spring and winter via the tele-connection, leading to warming in the northwestern Canada and cooling in the southeastern US.

The PrCA has potential benefits to the improvement of seasonal climate prediction.

Thank You

http://web.unbc.ca/~ytang

ytang@unbc.ca