NOAA High Impact Weather Working Group Workshop, Norman, OK, 24 Feb 2011

Tropical Cyclone/Hurricane Data Assimilation: An Ensemble Data Assimilation view

Milija Zupanski

Cooperative Institute for Research in the AtmosphereColorado State University

Fort Collins, Colorado, U. S. A.[ http://www.cira.colostate.edu/projects/ensemble/ ]

Acknowledgements:

- NOAA HFIP, NCEP/EMC

- JCSDA/NESDIS

- NASA PMM

Remote sensing is a major source of information- radar data- satellite data

Data assimilation has to be able to efficiently utilize these data- cloudy/precipitation-affected radiances- nonlinear transformation from model to observations (observation operators)

Localized phenomenon- dynamical impact on error covariances- relevance of microphysics

Challenges- improving intensity and position- new instruments (e.g. GOES-R GLM, ABI)- hyper-spectral (thousands of channels)- large number of observations (e.g., cloudy radiances, hyperspectral sounders)

TC/Hurricane data assimilation

Radar data are typically available only over land- coastal areas- airborne/spaceborne radars- almost continuous spatiotemporal coverage

Remote sensing data coverageRadar Reflectivity

Satellite data are available everywhere- open ocean- intermittent coverage (e.g. geostationary vs. polar-orbiting)

AMSU-A GOES-11 SNDR

Combined use of all data is best choice

Relevant components of TC data assimilation

First guess- dynamically relevant, high resolution, best forecast (easier to adjust good forecast than bad forecast) - also used for error covariance calculation (EnsDA)

Forecast error covariance- need to reflect true uncertainties of TC forecast- geographically localized in the area of storm- correlated control variables (e.g. dynamics, microphysics)

Utilize remote sensing observations- impact on intensity and position (e.g., IR, MW radiances)- cloudy radiance assimilation (TC is “defined” by clouds)- nonlinear analysis solution

Improve TC intensity and position- microphysical control variables- focus on improving the forecast after DA- include new instruments (e.g. GOES-R GLM, ABI)

Uncertainty estimation- TC forecast uncertainty important as an input for decision-making

Pf1/2 ~ xi

ens −xf

What is DA actually doing?

It projects observation increments to a subspace defined by forecast error covariance

xa - x f =PfKT (KPfK

T + R)−1(y−K (xf ))

Pf =Pf1/2Pf

T /2 =Uσ 2UT

[d =σ 2UTK T (KPfKT + R)−1(y−K (xf ))]

Recall the KF analysis equation

Pf1/2 =UσVT

The forecast error covariance is

The analysis increment becomes xa - x f =Ud

where

Analysis increment is a linear combination of Pf basis vectors (U)

(1) Analysis increment will be non-zero if

(2) This implies that the range of Pf is critical for creating good analysisσ ≠0

Forecast uncertainty(Pf)

Obs increments [y-H(x)] Obs increments

[y-H(x)]

Forecast uncertainty(Pf)

No DA impact σ =0 σ ≠0Correct DA impact Incorrect DA impact σ ≠0

Obs increments [y-H(x)]

Forecast uncertainty(Pf)

Forecast error covariance

Variational error covariance

U-wind

V-wind

t=0 h (3-d Var) t=3 h (4-d Var)

Ensemble error covariance (EnsDA, t=3 h)

Analysis response to a single U-wind obs near surface

U-wind V-wind

Rain Ice

- symmetric at initial time (3-d Var)

- changed by model at end time (4-d Var)

- only for basic model variables (p,T,u,v,q)

- similar to variational in horizontal

- strong dynamical response in vertical

- response of microphysical variables

Re-development of the TS Erin (2007): Distribution of AMSU-B radiance data in the NCEP operational data stream: (a) all observations, (b) accepted observations after cloud clearing. Data are collected during the period 15-18Z, August 18, 2007. Note that almost all observations in the area of the storm got rejected by the cloud clearing. (from Zupanski et al. 2011, J. Hydrometeorology)

TC Gustav (2008): RMS errors with respect to observed AMSU-B radiances. Time coverage indicates that only 1/3 of data assimilation cycles (6 out of 18 in this example) had available radiance observations.

Impact of cloud clearing (radiance assimilation)

Need assimilation of all-sky radiances (improve observation information value)

Transformation from forecast model variables to radiance is complex - need not only spatial interpolation but also radiative transfer- computational overhead

Nonlinearities increase for precipitation affected radiances- absorption and scattering- clouds, aerosol

Nonlinear observation operators

Most EnsDA methods use (linear) Kalman filter analysis solution (K operator assumed linear in KF)

xa =xf + P fK T (KP fK T + R)−1(y−K (xf ))

Variational DA and some EnsDA methods use an iterative nonlinear minimization of a cost function

Relevance of microphysics control variables

TC intensity- microphysical processes are fundamental for TC intensity forecast- need adjustment of microphysics control variables in DA (in addition to dynamics)

Microphysics control variables: forecast error covariance structure

Microphysics control variables: impact on DA

COV QSNOW,QRAINCOV QSNOW, QSNOW

COV QSNOW, V-wind

Physically unrealistic analysis adjustment without

microphysics control variable (cloud ice in this example)

Analysis increment of at 850 hPa

No cloud ice adjustment

> 25 K

With cloud ice adjustment5-10 K

Degrees of Freedom for Signal

C = R−1/2HPf1/2⎡⎣ ⎤⎦

TR−1/2HPf

1/2⎡⎣ ⎤⎦

where C is the observation information matrix (Rodgers, 2000; Zupanski et al. 2007, QJRMS)

DFS =λi

2

(1+ λi2 )i

∑ ; λi are eigenvalues of C

Degrees of Freedom for Signal (DFS, Rodgers 2000):

Measure of DA efficiency/value- important indicator of DA performance

Sub-optimal in both variational DA and EnsDA methods due to sub-optimal forecast error covariance

- full-rank, but static, modeled function in Var DA- situation-dependent, dynamical, but reduced-rank in EnsDA

Pa = Pf−1 + HTR−1H( )

−1=Pf

1/2 I +C( )−1 PfT /2

all-sky radiance observation information content

MW radiances: AMSR-E data assimilation (Erin, 2007)(from Zupanski et al. 2011, J. Hydrometeorology)

OBS 89v GHz Tb Wind analysis uncertainty (500 hPa) Degrees of Freedom for Signal (DFS)

IR radiances: Assimilation of synthetic GOES-R ABI (10.35 mm) all-sky radiances (Kyrill, 2007)

(from Zupanski et al. 2011, Int. J. Remote Sensing)

Cloud ice analysis uncertainy Degrees of Freedom for Signal (DFS)

METEOSAT Imagery valid at19:12 UTC 18 Jan 2007

Analysis uncertainty and DFS are flow-dependent, largest DFS in cloudy areas of the storm.

Ground-based Verification (NOAA Stage IV data)

3DVAR, WRF-GSI(no AMSR-E, TMI)

EnsDA, WRF-EDAS(with AMSR-E, TMI)

Surface precipitation short-term forecasts verification

Accumulated rain during 15-22 September 2009 in the Southeast flood region

Assimilation of precipitation-affected radiance improves short-term precipitation forecasts, in spatial pattern and intensity - implications to TC/hurricane DA

Summary

Cloudy radiance assimilation is required for improved analysis

Forecast error covariance needs to be state-dependent, and also to represent dynamical and microphysical correlations

Microphysics control variables should benefit TC analysis (e.g. intensity)

Nonlinear analysis capability required

DFS may be important for measuring progress of DA

Combination of observations from various sources is needed

(IR radiance is good for TC track, MW for TC intensity)

Observations from new instruments/platforms

(for example, GOES-R GLM is related through microphysics, impacts both track and intensity)

Analysis/forecast uncertainty estimation is required for decision-making