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Challenges in data assimilation for ‘high resolution’ numerical
weather prediction (NWP)
Ross Bannister
Today’s observations +
uncertainty information
Today’s analysis
Today’s forecast (a-priori) +
uncertainty information
DATA ASSIMILATION
Model’s prediction of future
Thanks to: Stefano Migliorini (NCEO), Mark Dixon (MetO), Mike Cullen (MetO), Alison Fowler (Reading), Ruth Petrie (Reading)
Small-scale vs large-scale weather
Jul 7 2007
Oct 29 2008
‘Convective’ precip
‘Large scale’ precip
What is required of high-resolution NWP?
• Forecasting of ‘extreme events’ a few hours ahead.
• Weather warnings and coverage of special events.
• Probabilistic forecasting.
• Data assimilation is critical to its success.
Radar
Probability of rain (MOGREPS)
Courtesy Met Office
(c) Crown copyright
MSG visible
Friday 26th June 2009, 09 Z
What does data assimilation do?
+ a-priori
information in the
form of a forecast
‘Forward’ model:
Known ‘state vector’, x
Predicted observations, yp
‘Inverse’ model:
Yet unknown state vector, xa
New actual observations, y
How is the data assimilation problem tackled for operational
forecasting?
now
1. Four-dimensional variational data assimilation
2. Ensemble Kalman filtering
t = -T
t=0
← past
All sources of error should be accounted for:
• a-priori error
• observational error
• model errors
• unknown parameters
• positional errors
future →
What issues are especially important for high-resolution data
assimilation?
Resolution of atmospheric models
Met Office
/ 1.5km
convective scale
1-10 km
(c) MeteoFrance
1.5 km
4 km
12km
meso-scale
100 km
synoptic scale
1000 km
Balance
Geostrophic balance
Hydrostatic balance
L
L
p(z+δz)
H
ρ δz g
p(z)
What is different about processes and NWP at convective scales?
Global/synoptic/mesoscale
Error growth timescale
Features
Diagnostic relationships
Important quantities
Observations
Other
Complications
Convective scale
~ 3 days
Few hours
Cyclones, fronts
Convective storms
Hydrostatic balance, near
geostrophic balance (except in
tropics)
Near hydrostatic balance for nonconvecting regions
Vorticity, pressure, divergence,
humidity
+ vertical velocity, temperature, cloud
water and ice, surface quantities ...
Aircraft, sonde, buoys, IR sounders,
scatterometer, etc.
+ radar
Simultaneous ‘large’ and ‘small’ scale
features
Limited area model
• Lateral boundary conditions
• Inadequate representation of largescale
More scope to forecast features in the
wrong locations (phase errors)
Forecast error covariances are important in data assimilation
Forecast error covariances/correlations quantify the following information:
Pressure with pressure
E-ward wind with pressure
N-ward wind with pressure
Measured
correlations
Correlations derived
from geostrophic
balance
• the uncertainty of the forecast
• how information from observations is spread locally
• how different quantities should be adjusted together
Red: positive correlation Blue: negative correlation
Misspecification of forecast error covariance statistics
Data assimilation is suboptimal if the error covariances (uncertainty
quantification) are misspecified. E.g. If
•
•
•
•
Forecast or observation error uncertainties are misspecified
Correlation lengthscales are wrong
Balance relationships are applied inappropriately
Errors are present but not accounted for in the data assimilation (e.g. model error,
phase errors)
Phase error considerations
E.g. Positional error in the height of a temperature inversion (Alison Fowler)
I. Considering amplitude errors only
II. Amplitude and phase errors
Accurate high-resolution
forecasts (for a-priori)
Frequent high-resolution
observations with
information of relevant
quantities and accurate
observation operators
Large-scale analyses (e.g.
for lateral boundary
conditions)
How to incorporate largescale information
Less balance (etc) at convective scales:
 non-geostrophic,
 non-hydrostatic,
 non-separable,
 anisotropic …
More balance at convective scales (to minimize
spin-up problems):
 moisture balances?
 anelastic balance?
Choice of control variables in variational schemes
appropriate degree of balance,
Include lateral boundary conditions,
new small-scale variables.
Quantification of errors of all uncertain
/unknown quantities in the data assimilation
problem:
• observation error,
• a-priori error,
• model error,
• other errors
Ensemble of forecasts (for
a-priori error
characterization in
ensemble Kalman filter
schemes)
An affordable way of achieving
these requirements:
• No. of ensembles?
• Higher resolution?
• Larger domain?