Mesoscale Predictability

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Mesoscale Atmospheric Predictability
Martin Ehrendorfer Institut für Meteorologie und
Geophysik Universität Innsbruck
Presentation at 14th ALADIN Workshop 1-4 June
2004 Innsbruck, Austria 3 June 2004
http//www2.uibk.ac.at/meteo http//www.zamg.ac.at
/workshop2004/
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Mesoscale Atmospheric Predictability
Outline
1 Predictability error growth 2 Global Models
doubling times 3 Singular Vectors assessing
growth 4 Mesoscale Studies moist physics 5
Ensemble Prediction sampling 6 Conclusions
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T36 02/06/2004/00
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T12 T24
T36 T48
02/06/2004/12
01/06/2004/12
T24 T36
T48 T60
02/06/2004/00
03/06/2004/00
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- intrinsic error growth - chaotic to extent to
which model and atmosphere correspond
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reduced D1 error better consistency reduced
gap between error and difference
amplification of 1-day forecast error, 1.5 days
A. Simmons, ECMWF
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nonlinearity of dynamics and instability with
respect to small perturbations ? sensitive
dependence on present condition chaos irregulari
ty and nonperiodicity unpredictability and error
growth
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Tribbia/Baumhefner 2004
all scales
DAY 0
55 m
25m
large scales
small scales
10 m
45m
10m
15m
10m
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Tribbia/Baumhefner 2004
all scales
DAY 1
85m
large scales
85m
small scales
10 m
10m
75m
75m
10m
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all scales
Tribbia/Baumhefner 2004
DAY 3
small scales
large scales
20 m
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similarity of spectra at day 3 ? spectrally
local error reduction will not help
only small- scale error
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error growth to due resolution differences
(against T170) D1 error T42 10 x D1 error
T63 10 x D1 error T106
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even at T42 the D1 truncation error growth has
not exceeded D1 IC T106 growth T106
truncation error growth is one order
of magnitude smaller than D1 T106 IC error
growth need IC/10 before going beyond T106
IC analysis error growth exponential
T106
Tribbia Baumhefner 2004
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- sensitive dependence on i.c. - preferred
directions of growth
Lorenz 1984 model
Ehrendorfer 1997
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R.M. Errico
SVs / HSVs -gt fastest growing directions account
for in initial condition stability of the flow
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psi at 500 hPa
Optimized TL error growth
data assimilation, stability, error dynamics
French storm
tau_d 4.9 h
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lambda 56.6 tau_d 4.1 h
Ehrendorfer/Errico 1995
MAMS - DRY
TE-Norm
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Mesoscale Adjoint Modeling System MAMS2 PE with
water vapor (B grid) Bulk PBL (Deardorff) Stabilit
y-dependent vertical diffusion (CCM3) RAS scheme
(Moorthi and Suarez) Stable-layer
precipitation Dx80 km 20-level configuration (d
sigma0.05) Relaxation to lateral boundary
condition 12-hour optimization for SVs 4
synoptic cases moist TLM (Errico and Raeder 1999
QJ)
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Lorenz 1969
Tribbia/Baumhefner 2004
errors in small scales propagate upscale in
spectral space small-scale errors grow and
contaminate larger scale
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grad_x J MT grad_y J
M
R.M. Errico
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Example Sensitivity Field
36-h sensitivity of surface pressure at P to
Z-perturb. 10m at M ? 1 Pa at P
Errico and Vukicevic 1992 MWR
Contour interval 0.02 Pa/m M0.1 Pa/m
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4 MOIST PHYSICS initial- and final-time norms E
-gt E E_m -gt E V_d -gt E V_d -gt P V_m -gt E V_m
-gt P A larger value of E can be produced with
an initial constraint V_m1 compared with V_d1.
(hypothetical norm comparison larger E with
E_m1 compared with V_d1)
Errico et al. 2004 QJ
MAMS - MOIST
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t_d 2.5 h
t_d 2 h
moisture perturbations more effective than
dry perturbations to maximize E
larger than E_m-gt E and V_d-gtE
Doubling time t_d OTI ln 2 / ln l
has no vertical scaling
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r 0.81
-gt E
-gt P
initial time case S2
V_d -gt
v
SV2
SV1
?
r0.76
q
V_m -gt
SV2
SV1
?
large r similar structures are optimal for
maximizing both E and P
highly correlated with T of SV2 for V_d -gt E
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Perturbations in Different Fields Can Produce the
Same Result
12-hour v TLM forecasts
Initial u, v, T, ps Perturbation
Initial q Perturbation
?
?
Errico et al. QJRMS 2004
Hc_p T L q condensational heating
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summarizing comments on moist-norm SV-study -
moisture perturbations alone may achieve larger
E than dry perturbations - given same initial
constraint, similar structures can be optimal
for maximizing E and P in most cases however
structures are different - dry-only and
moist-only SVs may lead to nearly identical
final-time fields (inferred dependence on H)
q converts to T (diabatic heating) through
nonconvective precipitation - nonlinear
relevance TLD vs NLD may match closely (2 g/kg)
- sensitivity of non-convective precipitation
not universally dominant
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5 Ensemble Prediction
- generate perturbations from (partial) knowledge
of analysis error covariance Pa -
methodology on the basis of SV - SV-based
sampling technique
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QG TE SV spectrum
1642 13
lambda_133.47
T45/L6
lambda 0.0212
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169 SVs growing out of 4830 (dry balanced norm)
i.e. 3.5 of phase space
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TD and TM curves 169 (dry) and 175 (wet) growing
SVs
included for reference
(Errico et al. 2001)
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height correlations 500 hPa derived from ensemble
Integrations (D4)
operational EPS (N25)
sampling, N25, M50
sampling, N50, M100
(Beck 2003)
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Mesoscale Atmospheric Predictability
Summary
Intrinsic Error Growth limited predictability
(nonlinearity) presence of analysis
error Predictability rapid doubling of
analysis error account for fastest error growth
SV dynamics importance of lower
troposphere insight into growth
mechanisms initial moisture perturbations Ensemb
le Prediction generation of perturbations
sampling SV relation to analysis error
nonmodal IC growth
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