ESSAY: Model interpretation of climate signals: an application to the Asian monsoon climate - The Global Climate System: Patterns, Processes, and Teleconnections - page 296

experiments. The control consists of at least 5 to 10 members subject to
identical climate forcings, e.g. SST, sea ice, or present-day CO 2 composition,
etc., but different initial conditions, to ensure that the model results span the
range of possible realizations of the model climate.
In the anomaly experiments, the ensemble integrations are repeated as in
the control, but the forcing function is varied in some specified but identical
manner, but with different initial conditions. The sensitivity of the forcing
function on the climate system can then be evaluated based on the variance of
the ensemble mean and the spread of the ensemble members about the mean.
For a climate variable X ij , where the index i ( ¼ 1, 2 ...N ) is the time index,
say at yearly in te rvals, and the ensemble num be r is j ( ¼ 1, 2 ... n), the
ensemble mean X i and the climatological mean X are defined by:

n X

n

nN X

N

X

n

X i ¼ 1 X ¼ 1 X ij ; X ij

j ¼ 1 i ¼ 1 j ¼ 1

An unbiased estimator of the variance of the noise and of the ensemble is
given respectively by:

N ð n 1 Þ X

X

N n

1

ð X ij X j Þ 2 noise ¼

i ¼ 1 j ¼ 1

N 1 X

N

1

E ¼ ð X i X Þ 2

i ¼ 1

The climate forced variance and the total variance are obtained respectively as:

signal ¼ E 1

n noise

total ¼ noise þ signal

The climate signal-to-noise ratio is then defined as S ¼ signal = total . The
statistical significance of the signal for a given ensemble climate experiment
can then be tested using the F-test (Von Storch and Zwiers 1999 ). The larger
the ratio, the more likely it is that the signal is detectable in the real world.
In most applications, the ensemble mean is computed with equal weights
for each ensemble member. In more recent applications, when the ensemble
comprises not only outputs from the same models with different initial
conditions, but also different models, it may be necessary to assign a different
weight to each model ensemble member. In the so-called multi-ensemble super-
ensemble approach, weights for each model variable and for each model grid
are assigned based on past model performance (Krishnamurti et al. 2000 ;
Stefanova et al. 2002 ). In this way, models with strong bias tend to be
weighted less than those with weak bias. The super-ensemble approach has