ECMWF 10th Workshop

1
A question which does not seem relevant in this
context -Which planet in our solar system is u
s u a l l y closest to Pluto?
Mercury
2
Pluto is closer to Mercury more often (65)
than it is to Neptun
Neptun further away from Pluto than Mercury is
from Pluto
Mercury
closer to Pluto than Mercury to Pluto
Neptun
Pluto
3
The RMSE of individual EPS members The 2 m
temperature forecasts for London 2004-05
Unperturbed Control
perturbed members
1.5 days
The EPS perturbations made the forecast 1 ½ days
worse than Control!
4
2 m temperature forecast for Toulouse 2001-2005
perturbed members
Unperturbed Control
1-1.5 days
Courtesy Nicole Girardot and Serge Farges,
Météo-France
5
RMSE of 500 hPa Northern Hemisphere winter 2004-05
perturbed members
Unperturbed Control
Courtesy A Simmons, ECMWF
6
First statement The perturbed analyses have to
be up to 41 worse than the Control analysis
7
1. Discussions from Gaussian distributions
truth
truth
EMcontrol analysis
Distances from symmetrically perturbed EPS members
to the truth

Distances from the analysis to the truth
p2
p1
p3
p4
Initially members have up to 41 (v2 - 1) larger
errors than the analysis
8
2. Simplified geometrical arguments
Truth?
The analysis and the Truth are equally close to
the analysis ? The perturbations are about the
same size as the analysis error
Analysis
Truth?
Truth?
p-a
a-t
(a-t)v2
Truth?
Perturbed analysis
9
3. Full dimensional algebraic arguments
p (symmetrically) perturbed member t
truth a analysis (ensemble mean of all analyses)
Error of perturbed analyses
Perturbations
Analysis error
Covariance of perturbations and analysis errors
10
p perturbed member t truth a analysis
(ensemble mean of all analyses)
Error of perturbed analyses
Perturbations
Covariance of perturbations and analysis errors

Analysis error
The covariance term 0 because the ensemble of
perturbations comprises a set of pairs of
perturbations of opposite sign where for every
(p-a) there is a - (p-a) to cancel it out.
The remaining two terms are about equal and the
error of the perturbed analysis is therefore
about v2 times the analysis error
11
Why was this not mentioned in my ECMWF User
Guides?

• It was just a 5 ACC difference at that time
  
• The difference was expected to decrease in
  absolute terms thanks to improving analyses
• There were many other pedagogical problems with
  the EPS

12
Second statement The individually perturbed
forecasts have to be up to 41 worse than the
Control forecasts
13
The issue is if and how fast the errors of
perturbed EPS members approach the Control
forecast error?
RMSE
Slowly?
Rapidly?
T511
T255 (EPS Control)
Perturbed analysis
1.414
1.000
Forecast lead time
14
The same for the ACC (Anomaly Correlation
Coefficient)
RMSE
Rapidly?
T511
T255 (EPS Control)
Slowly?
Forecast lead time
15
1 ½ day
Courtesy Adrian Simmons
16
2 days
Courtesy Adrian Simmons
17
Figure 6.1 Probability Density Function (PDF) of
the RMS errors of the ensemble members (blue) and
control forecast (red), for the Global data set
over the time period DJF. Courtesy L. Bengtsson,
MISU
18
RMSE(pert member) 1.414 (sqrt2) RMSE (ensemble
mean)
climate
Figure 2.1 Schematic image of the RMS error of
the ensemble members, ensemble mean, and control
forecast as a function of lead-time. The
asymptotic predictability range is defined as the
average difference between two randomly chosen
atmospheric states. In a perfect ensemble system
the RMS error of the ensemble members is a factor
larger than the RMS error of the ensemble
mean.Courtesy, L. Bengtsson, MISU
19
NH diff CON and averaged pert-members - d5, d7
and d9
?
20
NH CON versus averaged perturbed members - D5
and D7ACC Control and perturbed members NH 500
hPa
Control D5
Perturbed D5
Control D7
Perturbed D7