<s>
Ensemble	B-Application
forecasting	I-Application
is	O
a	O
method	O
used	O
in	O
or	O
within	O
numerical	B-General_Concept
weather	I-General_Concept
prediction	I-General_Concept
.	O
</s>
<s>
Ensemble	B-Application
forecasting	I-Application
is	O
a	O
form	O
of	O
Monte	B-Algorithm
Carlo	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Ideally	O
,	O
the	O
verified	O
future	O
atmospheric	O
state	O
should	O
fall	O
within	O
the	O
predicted	O
ensemble	O
spread	B-General_Concept
,	O
and	O
the	O
amount	O
of	O
spread	B-General_Concept
should	O
be	O
related	O
to	O
the	O
uncertainty	O
(	O
error	O
)	O
of	O
the	O
forecast	O
.	O
</s>
<s>
Experimental	O
ensemble	B-Application
forecasts	I-Application
are	O
made	O
at	O
a	O
number	O
of	O
universities	O
,	O
such	O
as	O
the	O
University	O
of	O
Washington	O
,	O
and	O
ensemble	B-Application
forecasts	I-Application
in	O
the	O
US	O
are	O
also	O
generated	O
by	O
the	O
US	O
Navy	O
and	O
Air	O
Force	O
.	O
</s>
<s>
There	O
are	O
various	O
ways	O
of	O
viewing	O
the	O
data	O
such	O
as	O
spaghetti	B-Application
plots	I-Application
,	O
ensemble	O
means	O
or	O
Postage	O
Stamps	O
where	O
a	O
number	O
of	O
different	O
results	O
from	O
the	O
models	O
run	O
can	O
be	O
compared	O
.	O
</s>
<s>
The	O
practical	O
importance	O
of	O
ensemble	B-Application
forecasts	I-Application
derives	O
from	O
the	O
fact	O
that	O
in	O
a	O
chaotic	O
and	O
hence	O
nonlinear	O
system	O
,	O
the	O
rate	O
of	O
growth	O
of	O
forecast	O
error	O
is	O
dependent	O
on	O
starting	O
conditions	O
.	O
</s>
<s>
An	O
ensemble	B-Application
forecast	I-Application
therefore	O
provides	O
a	O
prior	O
estimate	O
of	O
state-dependent	O
predictability	O
,	O
i.e.	O
</s>
<s>
The	O
first	O
operational	O
ensemble	B-Application
forecasts	I-Application
were	O
produced	O
for	O
sub-seasonal	O
timescales	O
in	O
1985	O
.	O
</s>
<s>
Although	O
these	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulations	I-Algorithm
showed	O
skill	O
,	O
in	O
1974	O
Cecil	O
Leith	O
revealed	O
that	O
they	O
produced	O
adequate	O
forecasts	O
only	O
when	O
the	O
ensemble	O
probability	O
distribution	O
was	O
a	O
representative	O
sample	O
of	O
the	O
probability	O
distribution	O
in	O
the	O
atmosphere	O
.	O
</s>
<s>
It	O
was	O
not	O
until	O
1992	O
that	O
ensemble	B-Application
forecasts	I-Application
began	O
being	O
prepared	O
by	O
the	O
European	O
Centre	O
for	O
Medium-Range	O
Weather	O
Forecasts	O
(	O
ECMWF	O
)	O
and	O
the	O
National	O
Centers	O
for	O
Environmental	O
Prediction	O
(	O
NCEP	O
)	O
.	O
</s>
<s>
The	O
NCEP	O
ensemble	O
,	O
the	O
Global	O
Ensemble	B-Application
Forecasting	I-Application
System	O
,	O
uses	O
a	O
technique	O
known	O
as	O
vector	O
breeding	O
.	O
</s>
<s>
The	O
process	O
of	O
representing	O
the	O
atmosphere	O
in	O
a	O
computer	O
model	O
involves	O
many	O
simplifications	O
such	O
as	O
the	O
development	O
of	O
parametrisation	B-Application
schemes	O
,	O
which	O
introduce	O
errors	O
into	O
the	O
forecast	O
.	O
</s>
<s>
When	O
developing	O
a	O
parametrisation	B-Application
scheme	O
,	O
many	O
new	O
parameters	O
are	O
introduced	O
to	O
represent	O
simplified	O
physical	O
processes	O
.	O
</s>
<s>
In	O
a	O
perturbed	O
parameter	O
approach	O
,	O
uncertain	O
parameters	O
in	O
the	O
model	O
's	O
parametrisation	B-Application
schemes	O
are	O
identified	O
and	O
their	O
value	O
changed	O
between	O
ensemble	O
members	O
.	O
</s>
<s>
While	O
in	O
probabilistic	O
climate	O
modelling	O
,	O
such	O
as	O
climateprediction.net,	O
these	O
parameters	O
are	O
often	O
held	O
constant	O
globally	O
and	O
throughout	O
the	O
integration	O
,	O
in	O
modern	O
numerical	B-General_Concept
weather	I-General_Concept
prediction	I-General_Concept
it	O
is	O
more	O
common	O
to	O
stochastically	O
vary	O
the	O
value	O
of	O
the	O
parameters	O
in	O
time	O
and	O
space	O
.	O
</s>
<s>
A	O
traditional	O
parametrisation	B-Application
scheme	O
seeks	O
to	O
represent	O
the	O
average	O
effect	O
of	O
the	O
sub	O
grid-scale	O
motion	O
(	O
e.g.	O
</s>
<s>
A	O
stochastic	O
parametrisation	B-Application
scheme	O
recognises	O
that	O
there	O
may	O
be	O
many	O
sub-grid	O
scale	O
states	O
consistent	O
with	O
a	O
particular	O
resolved	O
scale	O
state	O
.	O
</s>
<s>
Instead	O
of	O
predicting	O
the	O
most	O
likely	O
sub-grid	O
scale	O
motion	O
,	O
a	O
stochastic	O
parametrisation	B-Application
scheme	O
represents	O
one	O
possible	O
realisation	O
of	O
the	O
sub-grid	O
.	O
</s>
<s>
When	O
many	O
different	O
forecast	O
models	O
are	O
used	O
to	O
try	O
to	O
generate	O
a	O
forecast	O
,	O
the	O
approach	O
is	O
termed	O
multi-model	O
ensemble	B-Application
forecasting	I-Application
.	O
</s>
<s>
The	O
ensemble	B-Application
forecast	I-Application
is	O
usually	O
evaluated	O
by	O
comparing	O
the	O
ensemble	O
average	O
of	O
the	O
individual	O
forecasts	O
for	O
one	O
forecast	O
variable	O
to	O
the	O
observed	O
value	O
of	O
that	O
variable	O
(	O
the	O
"	O
error	O
"	O
)	O
.	O
</s>
<s>
This	O
is	O
combined	O
with	O
consideration	O
of	O
the	O
degree	O
of	O
agreement	O
between	O
various	O
forecasts	O
within	O
the	O
ensemble	O
system	O
,	O
as	O
represented	O
by	O
their	O
overall	O
standard	B-General_Concept
deviation	I-General_Concept
or	O
"	O
spread	B-General_Concept
"	O
.	O
</s>
<s>
Ensemble	O
spread	B-General_Concept
can	O
be	O
visualised	O
through	O
tools	O
such	O
as	O
spaghetti	B-Application
diagrams	I-Application
,	O
which	O
show	O
the	O
dispersion	O
of	O
one	O
quantity	O
on	O
prognostic	O
charts	O
for	O
specific	O
time	O
steps	O
in	O
the	O
future	O
.	O
</s>
<s>
Another	O
tool	O
where	O
ensemble	O
spread	B-General_Concept
is	O
used	O
is	O
a	O
meteogram	B-Application
,	O
which	O
shows	O
the	O
dispersion	O
in	O
the	O
forecast	O
of	O
one	O
quantity	O
for	O
one	O
specific	O
location	O
.	O
</s>
<s>
It	O
is	O
common	O
for	O
the	O
ensemble	O
spread	B-General_Concept
to	O
be	O
too	O
small	O
,	O
such	O
that	O
the	O
observed	O
atmospheric	O
state	O
falls	O
outside	O
of	O
the	O
ensemble	B-Application
forecast	I-Application
.	O
</s>
<s>
The	O
spread	B-General_Concept
of	O
the	O
ensemble	B-Application
forecast	I-Application
indicates	O
how	O
confident	O
the	O
forecaster	O
can	O
be	O
in	O
his	O
or	O
her	O
prediction	O
.	O
</s>
<s>
When	O
ensemble	O
spread	B-General_Concept
is	O
small	O
and	O
the	O
forecast	O
solutions	O
are	O
consistent	O
within	O
multiple	O
model	O
runs	O
,	O
forecasters	O
perceive	O
more	O
confidence	O
in	O
the	O
forecast	O
in	O
general	O
.	O
</s>
<s>
When	O
the	O
spread	B-General_Concept
is	O
large	O
,	O
this	O
indicates	O
more	O
uncertainty	O
in	O
the	O
prediction	O
.	O
</s>
<s>
Ideally	O
,	O
a	O
spread-skill	O
relationship	O
should	O
exist	O
,	O
whereby	O
the	O
spread	B-General_Concept
of	O
the	O
ensemble	O
is	O
a	O
good	O
predictor	O
of	O
the	O
expected	O
error	O
in	O
the	O
ensemble	O
mean	O
.	O
</s>
<s>
Reliability	O
(	O
or	O
calibration	O
)	O
can	O
be	O
evaluated	O
by	O
comparing	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
error	O
in	O
the	O
ensemble	O
mean	O
with	O
the	O
forecast	O
spread	B-General_Concept
:	O
for	O
a	O
reliable	O
forecast	O
,	O
the	O
two	O
should	O
match	O
,	O
both	O
at	O
different	O
forecast	O
lead	O
times	O
and	O
for	O
different	O
locations	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
probabilities	O
generated	O
from	O
operational	O
weather	O
ensemble	B-Application
forecasts	I-Application
are	O
not	O
highly	O
reliable	O
,	O
though	O
with	O
a	O
set	O
of	O
past	O
forecasts	O
(	O
reforecasts	O
or	O
hindcasts	O
)	O
and	O
observations	O
,	O
the	O
probability	O
estimates	O
from	O
the	O
ensemble	O
can	O
be	O
adjusted	O
to	O
ensure	O
greater	O
reliability	O
.	O
</s>
<s>
Another	O
desirable	O
property	O
of	O
ensemble	B-Application
forecasts	I-Application
is	O
resolution	O
.	O
</s>
<s>
This	O
forecast	O
quality	O
can	O
also	O
be	O
considered	O
in	O
terms	O
of	O
sharpness	O
,	O
or	O
how	O
small	O
the	O
spread	B-General_Concept
of	O
the	O
forecast	O
is	O
.	O
</s>
<s>
If	O
ensemble	B-Application
forecasts	I-Application
are	O
to	O
be	O
used	O
for	O
predicting	O
probabilities	O
of	O
observed	O
weather	O
variables	O
they	O
typically	O
need	O
calibration	O
in	O
order	O
to	O
create	O
unbiased	O
and	O
reliable	O
forecasts	O
.	O
</s>
<s>
For	O
forecasts	O
of	O
temperature	O
one	O
simple	O
and	O
effective	O
method	O
of	O
calibration	O
is	O
linear	B-General_Concept
regression	I-General_Concept
,	O
often	O
known	O
in	O
this	O
context	O
as	O
Model	O
output	O
statistics	O
.	O
</s>
<s>
The	O
linear	B-General_Concept
regression	I-General_Concept
model	I-General_Concept
takes	O
the	O
ensemble	O
mean	O
as	O
a	O
predictor	O
for	O
the	O
real	O
temperature	O
,	O
ignores	O
the	O
distribution	O
of	O
ensemble	O
members	O
around	O
the	O
mean	O
,	O
and	O
predicts	O
probabilities	O
using	O
the	O
distribution	O
of	O
residuals	O
from	O
the	O
regression	O
.	O
</s>
<s>
However	O
,	O
in	O
2004	O
,	O
a	O
generalisation	O
of	O
linear	B-General_Concept
regression	I-General_Concept
(	O
now	O
known	O
as	O
Nonhomogeneous	O
Gaussian	O
regression	O
)	O
was	O
introduced	O
that	O
uses	O
a	O
linear	O
transformation	O
of	O
the	O
ensemble	O
spread	B-General_Concept
to	O
give	O
the	O
width	O
of	O
the	O
predictive	O
distribution	O
,	O
and	O
it	O
was	O
shown	O
that	O
this	O
can	O
lead	O
to	O
forecasts	O
with	O
higher	O
skill	O
than	O
those	O
based	O
on	O
linear	B-General_Concept
regression	I-General_Concept
alone	O
.	O
</s>
<s>
This	O
proved	O
for	O
the	O
first	O
time	O
that	O
information	O
in	O
the	O
shape	O
of	O
the	O
distribution	O
of	O
the	O
members	O
of	O
an	O
ensemble	O
around	O
the	O
mean	O
,	O
in	O
this	O
case	O
summarized	O
by	O
the	O
ensemble	O
spread	B-General_Concept
,	O
can	O
be	O
used	O
to	O
improve	O
forecasts	O
relative	O
to	O
linear	B-General_Concept
regression	I-General_Concept
.	O
</s>
<s>
Whether	O
or	O
not	O
linear	B-General_Concept
regression	I-General_Concept
can	O
be	O
beaten	O
by	O
using	O
the	O
ensemble	O
spread	B-General_Concept
in	O
this	O
way	O
varies	O
,	O
depending	O
on	O
the	O
forecast	O
system	O
,	O
forecast	O
variable	O
and	O
lead	O
time	O
.	O
</s>
<s>
In	O
addition	O
to	O
being	O
used	O
to	O
improve	O
predictions	O
of	O
uncertainty	O
,	O
the	O
ensemble	O
spread	B-General_Concept
can	O
also	O
be	O
used	O
as	O
a	O
predictor	O
for	O
the	O
likely	O
size	O
of	O
changes	O
in	O
the	O
mean	O
forecast	O
from	O
one	O
forecast	O
to	O
the	O
next	O
.	O
</s>
<s>
This	O
works	O
because	O
,	O
in	O
some	O
ensemble	B-Application
forecast	I-Application
systems	O
,	O
narrow	O
ensembles	O
tend	O
to	O
precede	O
small	O
changes	O
in	O
the	O
mean	O
,	O
while	O
wide	O
ensembles	O
tend	O
to	O
precede	O
larger	O
changes	O
in	O
the	O
mean	O
.	O
</s>
<s>
Centralized	O
archives	O
of	O
ensemble	O
model	O
forecast	O
data	O
,	O
from	O
many	O
international	O
centers	O
,	O
are	O
used	O
to	O
enable	O
extensive	O
data	B-Application
sharing	I-Application
and	O
research	O
.	O
</s>
