Data Assimilation for High Impact Weather Forecast. Yuanfu Xie NOAA/OAR/ESRL. Outline. Review data assimilation techniques; Improving variational data assimilation; Limitations of ensemble Kalman filter (EnKF); Highly nonlinear and non-Gaussian data assimilation;
Major reason for the recent interests in EnKF is due to the unsatisfactory variational analysis even it is so successful at ECMWF.
Of course, the easy implementation of EnKF or any Monte Carlo methods is another reason.
Variational analysis, particularly, 4DVAR, is too complicated and difficult to maintain.
Xie et al 2002 has studied the analysis impact by selecting different control variables for wind, ψ-χ, u-v, or ζ-δ VARS.
type of integral of
u-v. A correction to
the background toward the obs changes the integral of u. The background term adds opposite increment to the analysis for keeping the same integral as the background.
For a single obs of u, e.g., ψ-χ, u-v, or ζ-δ VARS have different responses as shown here. A ψ-χ VAR may not show this clearly as many filters applied.
Ensemble DA is relatively easy to implement and It has been considered to improve VARs.
At ESRL, STMAS uses a multigrid technique to combine EnKF or particle filter with a sequence of variational analysis; at coarse grids, it can use any estimated error covariance matrix, e.g. EnKF…
Using the number of gridpoints to control the base functions. For irresolvable scales, EnKF or particle filter is used.
Space and Time Multiscale Analysis System (STMAS) is a 4-DVAR generalization of LAPS and modified LAPS is running at terminal scale for FAA for wind analysis.
STMAS real time runs with 15 minute latency due to the observation data:
STMAS surface analysis with 5 minute latency with (MPI/SMS) and targeting at
over CONUS domain;
assimilating 1-minute ASOS;
using HRRR as background.
NOAA HFIP is a major effort for improving hurricane forecast (both tracks and intensity);
NOAA 5 year plan:
Overview of 2008 hurricane season:
8 hurricanes (5 major)
Damage: $42 billions
— 48-Hour Hurricane Track Forecast Error
— 48 hr Hurricane Intensity Forecast Error Trend
Pre-balanced 950-mb wind speed
Balanced 950-mb wind speed
every 6 hours
72 hour fcst w/
every 3 hours
Intensity: WRF Katrina forecast by STMAS
Wind Barb, Windspeed image,
Pressure contour at 950mb
OAR/ESRL/GSD/Forecast Applications Branch
NOAA long term goal (20 years) is on tornado forecasts, for longer lead time forecasts (1-3 hour forecast)
ESRL/GSD/FAB is investigating the possibility of tornado forecast, what is needed and how to improve.
Radar data assimilation is critical to severe storms and tornado forecasts.
LAPS hot-start & WRF-ARW Forecast (2km with Lin Micro-physics ): IHOP cases
LAPS Forecast: Jun. 13, 2002
LAPS Forecast: Jun. 16, 2002
(Steve Albers and Isidora will talk these cases in more details at their presentations
A well-balanced initial condition is the key for improving very short range
forecast for tornados.
A simplified version:
Pa(x) P(x=xt | x=xo) = P(x=xo | x=xt) P(x=xt);
P(x=xo | x=xt) = P(xo=xt) = Po(x-xo), i.e., observational error probability.
Assumption II.P(x=xt) = Pb(x-xb), as this prior probability can depend our knowledge of the background on the true atmosphere, see Lorenc 86.
Then we have: Pa(x)= Po(x-xo) Pb(x-xb).
The background and observation error probabilities follow a Gaussian distribution:
Covariances O and B are known!
To maximize the probability for estimation of the To best approximate the true atmosphere xt , we maximize
This is equivalent to minimize:
the standard 3DVAR cost function.
Optimality = maximized probability
It is derived from a statistical analysis assuming the error’s distribution is Gaussian. It solves a variational problem:
subject to a model constraint for 4DVAR
a Given Observation Network
Difference on longer wave
Difference on shorter wave
STMAS is implemented in two steps.
With long waves retrieved, STMAS deals with a localized error covariance, a banded matrix, at its last phase of analysis.