Ming Xue, Mingjing Tong, and Youngsun Jung

1
Ensemble Kalman Filter Assimilation of Radar
Data Several Aspects

• Ming Xue, Mingjing Tong, and Youngsun Jung
• School of Meteorology and
• Center for Analysis and Prediction of Storms
• University of Oklahoma
• 2006 EnKF Workshop

2
Introduction

• OSSEs with perfect models assimilating radar (Vr
  and/or Z) data using EnKF methods have shown
  near-perfect results (Snyder and Zhang 2004
  Zhang et al. 2004 Tong and Xue 2005 Caya et al
  2005 Xue et al. 2006)
• EnKF seems to be able to deal with nonlinear
  dynamics, complex physics (e.g., ice
  microphysics), and nonlinear observation
  operators (e.g., reflectivity, differential
  reflectivity)
• Successes with real radar data, however, have
  been much more limited (Dowell et al. 2004)
• Incremental impact on forecast tends to get lost
  quickly, especially in the presence of model error

3
Assimilation of Vr Z v.s. Vr onlyEnsemble Mean
RMS Errors
w error 0.5m/s
Black Vr only Red Vr Z
Blue ensemble spread as an estimate of error
Based on Tong and Xue (2005)
4
Analyses of Low level cold pool and reflectivity
v.s. Truth
Truth
Vr only
Vr Z
5
Analysis of Microphysical Fields
qh
qs
qr
qi
qc
Truth

• Vr only

Vr Z
6
Forecast starting from the ensemble mean analysis
at t80 min
Truth
Vr Z
Better!
Vr only
2h 10min forecast
7
RMSE of forecasts
w
Black Vr only Red Vr Z
?
qr
210min
80min
8
Outline

• Introduction
• Assimilation and prediction of convective storms
  using real data
• May 29, 2004 case
• May 8, 2003 case (3DVAR Cloud analysis)
• Model errors/uncertainties
• Microphysics
• Resolution
• Other sources of error
• Sensitivity of supercell storm simulation to
  microphysics and resolution
• Dual-polarization radar data assimilation
• Observation operators, nonlinearity
• Impact on analysis with perfect model
• Error modeling, non-Gaussian distribution
• DSD parameter retrieval
• Discussions and thoughts
• Multi-scale analysis
• Sensitivity to errors at convective scale and in
  the storm-environment
• Code efficiency and parallelization
• Model error problem

9
EnSRF for (Polarimetric) Radar Data Assimilation
Radar data used Vr (Zhh gt 10 dBZ) Zhh
(everywhere) KDP (KDP gt 0.3 deg./km)
Vr Vr (u, v, w) Zhh Zhh (qr, qs, qh)
KDP KDP (qr, qs)
K is the Kalman Gain, a function of background
and obs error covariances
10
Ensemble Kalman filter assimilation of Doppler
radar data

• May 29-30, 2004 OKC Tornadic Thunderstorm
• Serial EnSRF algorithm
• Single v.s. two radars
• Sounding-based v.s. 3D environment

11
May 29-30, 2004 North OKC Tornado Case
X
KVNX
1 km Analysis and Prediction Grid
F1
F3
OKC
F2
F2
F0
X
KTLX
Storm lasted gt 9 hours, producing 16 tornadoes
12
Storm positions and locations of radars
13
May 29-30, 2004 OKC Tornadic Thunderstorm00 UTC
02 UTC, May 30
Reflectivity at 1.2 elevation Assimilation in
1st hour Forecast in 2nd hour
KTLX

14
Experiment setup
1h EnKF Assimilation 40 members
1 h Forecast
00 UTC
01 UTC
02 UTC
F2 tornado 0017-0115 Z
F1 and F0 tornado 0104-0147 Z
Initial analysis background provided by a single
sounding or multi-scale 3DVAR analysis dx
1km 40 members
15
May 29-30, 2004 Central Oklahoma Tornadic
Thunderstorm Case

• Long-lasting tornadic thunderstorm
• More than 9 hours (2200 UTC May 29 to 0730 UTC
  May 30)
• 16 tornadoes from the same storm, all but one
  after 00 UTC May 30
• 5 F0, 8 F1, 2 F2, 1 F3 tornadoes
• The maximum single tornado damages 5M

16
Assimilation Experiments

• 180 x 120 x 16 km grid, ?x ?y 1 km, 40 layers
  with vertical stretching (?z min100m).
• Open LBC, free slip bottom and top
• No surface physics or radiation
• Initialization of ensemble using smoothed
  perturbations
• 40 ensemble members
• Vr Z from KTLX radar or from both KTLX and KVNX
  radar
• Dealiased, noise (ground clutter et al.)
  removed.
• Data interpolated to model columns, but located
  on elevation levels
• Scan volumes assimilated every 5 min, for 1 hour
• Inflation factor between 30 and 50

17
Environmental Sounding
Sounding used in assimilation experiment
OUN sounding at 0000 Z, May 30
18
Analysis Reflectivity at 1.25 Elevationfor
experiment using KTLX data onlySingle sounding
initial guess
Analysis at 01 UTC
Observation at 01 UTC
KTLX
KVNX
19
Analysis Radial Velocity at 1.25 Elevation for
experiment using KTLX data only
Analysis at 01 UTC
Observation at 01 UTC
KTLX
KVNX
20
Animation of Analysis Reflectivity at 1.2
Elevation
Analysis
Observation
0000 UTC 0100 UTC
21
RMS differences for experiment using KTLX data
only
KTLX
KVNX
EnKF, Vr prior
Vr
EnKF, Vr analysis
Homogeneous wind field (sounding)
EnKF, Z prior
EnKF, Z analysis
Z
sounding
22
RMS differences for experiment using data from
both KTLX and KVNX radar
KTLX
KVNX
EnKF, Vr prior
Vr
EnKF, Vr analysis
Homogeneous wind field (sounding)
EnKF, Z prior
EnKF, Z analysis
Z
sounding
23
Innovation statistics
Experiment using KTLX data only
for Z
for Vr
Experiment using both KTLX data and KVNX data
Spread of wind fields seem too small. Model
winds too smooth? Not enough variability?
for KTLX
for KVNX
24
Analysis ?', and Vh at 50 m AGL at 0100 UTC
Experiment using KTLX data only
?'min - 8.9 K
25
Ensemble mean analysis of w (color), Z (contour)
and Vh at 1.5 km AGL at 0100 UTC
Experiment using KTLX data only
Mesocyclone
26
Forecast Reflectivity on Radar Elevationsfor
experiment using KTLX data only
27
0100 UTC 0200 UTC
Forecast Reflectivity at 1.2 Radar
Elevationsfor experiment using KTLX data only
Observation
Forecast
28
Discussion

• The analyzed flow fields show dynamically
  consistent patterns typical of supercell storms,
  including strong mid-level rotation and hook echo
• The filter has difficulty in retrieving
  cross-beam wind component from single radar
• Predicted storm maintains supercell
  characteristics for more than 1 hour, but was
  generally weaker and propagated too fast.
• Eastward spreading echo is too weak later in the
  forecast
• Errors grow quickly in the forecast

Errors in IC, model (e.g., microphysics,
resolution), sounding, or radar data, or
insufficient data coverage????
29
EnKF analysis usingFull physics (incl. sfc
physics) ARPS model ARPS 3DVAR analysis (incl.
OK Mesonet) as initial guess Two radars (KTLX
and KVNX)
30
Dual-radar analysis at 0100UTC(storm-relative
winds, q',and Z _at_ 50 m AGL)
Hook weaker than at higher elevations
31
Dual-radar analysis at 0100UTC(storm-relative
winds, w,and Z)
1.5 km AGL
4 km AGL
Things look good
32
Forecast from dual-radar analysis
t 0 h
Verifying observation
33
Forecast from dual-radar analysis
t 0.5 h
Verifying observation
34
Forecast from dual-radar analysis
Forecast is worse!
t 1 h
Verifying observation
35
Results with real data are much less rosy!Model
and data are now imperfect!

• Analyzed surface gust front and cold pool
  appeared too strong and become even stronger
  during the forecast period.
• The gust front error appeared to be responsible
  for the propagation speed error
• The lack of near surface radar data coverage made
  it difficult to correct errors in gust front
  position and cold pool strength
• Model errors, including resolution and
  microphysics, and possible errors in the
  environmental condition are probably the main
  sources of inaccuracy
• Errors in forward operators, especially that of
  Z, can also contribute to the analysis error

36
Future Work

• Further understand the behavior and fine tune the
  EnSRF for the May 29 analysis
• Tuning EnSRF parameters concerning covariance
  localization, covariance inflation factor,
  observation error specification
• Compare covariance inflation and additive
  error for model error parameterization
• Understand why the cross-beam wind component can
  not be retrieved well
• Tuning intercept parameter and/or particle
  densities based on sensitivity experiments
  (initial trial not yielding better results)
• May test different microphysics schemes (results
  with WSM6 are worse!)

37
Are things hopeless?

• Results seem to be case dependent
• Even 3DVAR cloud analysis can be a good job for
  the May 8, 2003 OKC tornadic supercell case

38
3DVAR and Cloud Analysis Assimilation and
Prediction of the May 8, 2003 OKC Tornadic
Supercell Storm
(Hu and Xue 2006 MWR Hu 2006)
39
Configurations of 1-km experiments

• Using ARPS model
• One-way nested within a 3-km control experiment
• 280 280 km Domain and grid
• Data assimilation over 70 minutes (2030-2140
  UTC), at 5 min. intervals
• 2-hour forecast

40
May 8th, 2003 OKC tornado
OKC tornado 2210-2238 UTC 30 km long path
F4
Tornado 1 2200 UTC
2204-2210 UTC
41
ARPS 1-km-grid forecast
Reflectivity at 1.45º elevation
30-min forecast
40-min forecast
42
Observed and predicted Z and Vr at 1.45
Observation
1km Forecast
Reflectivity
Radial velocity
From 2140 to 2240 UTC every 5-min
43
100-m nested grid forecast

• 47-min forecast from 2140 to 2227 UTC
• First ever (non-realtime) model forecast of a
  real supercell tornado starting from real radar
  data

44
Hook echo at the southwestern end of the storm
from 2210 UTC
Surface Z in the northeastern part of the
forecast domain during 2105-2227 UTC
(over 22 minutes)
45
Surface Z at 30-min forecast
46
Surface fields from 2205-2215 UTCA tornado from
2210-2214 UTC
Wind
Reflectivity
Maximum over 62 m s-1
Pressure
Vorticity
Minimum 919 hPa
Maximum 0.66 s-1
47
Surface Z at 30-min forecast
48
Surface fields from 2215-2226 UTC Another tornado
from 2217-2226 UTC
Wind
Reflectivity
Maximum over 55 m s-1
Pressure
Vorticity
Minimum 933 hPa
Maximum 0.58 s-1
49
Surface Z, wind, and vertical vorticity at 30-min
forecast(valid at 2210 UTC, the beginning of OKC
tornado)
Maximum wind speed Over 50 m s-1 112 mph
tornado500 m wide
Maximum vertical vorticity 0.61 S-1
50
Ensemble Square Root Filter for Data Assimilation
Xue et al. (2006a)
51
Analysis and Prediction Domains

• CAPS Advanced Regional Prediction System
• Dx Dy 1.5 km
• 40-member ensemble

52
Simulated CASA Data
53
(No Transcript)
54
Ensemble Mean RMS Error in Precipitation Regions
During Assimilation
KTLX (NEXRAD) Only
NEXRADCyril
Pressure Deviation
Potential Temperature Deviation
North/South Wind
East/West Wind
Vertical Wind
Cloud Water
Water Vapor Cloud Ice
Snow
Rain Water
Hail
55
So

• Explicit prediction of convective storms, or even
  tornadoes, is hopeful.
• But, both prediction models and data assimilation
  need to be improved.
• Model uncertainties can seriously impact
  prediction, as well as data assimilation.
• E.g., microphysics.

56
Sensitivity to Microphysics Schemes
2 hour simulation of May 20th supercell storm
surface fields
Lin et al. (1983) GSFC implementation Default in
ARPS
Lin (LFO) scheme Gilmore et al (2004)
WRF WSM6 Based on WSM5 of Hong et al. (2004)
57
Sensitivity to Microphysics Schemes
t5400s
Milbrantdt and Yau Multi-moment double-moment
option
Milbrandt and Yau Multi-moment single-moment
option - Lin like
Lin et al (1983) GSFC Implementation Default in
ARPS
58
Sensitivity to Resolution
dx 1 km
dx 250m
what about dx25 meter?
Lin scheme t5400s
59
Sensitivity to Resolution
dx 1000 m
dx 250 m
Lin scheme t7200s What if dx 25m ??
60
EnSRF Assimilation and Microphysical DSD
Parameter Retrieval with Polarimetric Radar Data

• Youngsun Jung and Ming Xue
• with input from Jerry M. Straka and Guifu Zhang
• School of Meteorology and Center for Analysis and
  Prediction of Storms
• University of Oklahoma

61
Background

• The use of a differential reflectivity for rain
  estimation was originally proposed by Seliga and
  Bringi in 1976.
• Polarimetric measurements can help improve
  precipitation classification (Straka et al. 2000
  Vivekanandan et al. 1999 Zrnic et al. 2001) and
  QPE (Brandes et al. 2003, 2004 Straka et al.
  2000 Zhang et al. 2001).
• The national WSR-88D radar network will be
  upgraded to include polarimetric capabilities
  with data now available from a prototype system
  (KOUN)
• CASA radars have polarimetric capabilities
• Radar data are essential for initializing
  storm-scale NWP models.
• Direct assimilation of polarimetric parameters
  has never been done before.

62
Background

• The use of a differential reflectivity for rain
  estimation was originally proposed by Seliga and
  Bringi in 1976.
• Polarimetric measurements can help improve
  precipitation classification (Straka et al. 2000
  Vivekanandan et al. 1999 Zrnic et al. 2001) and
  QPE (Brandes et al. 2003, 2004 Straka et al.
  2000 Zhang et al. 2001).
• The national WSR-88D radar network will be
  upgraded to include polarimetric capabilities
  with data now available from a prototype system
  (KOUN)
• CASA radars have polarimetric capabilities
• Radar data are essential for initializing
  storm-scale NWP models.

63
Background

• Polarimetric measurements can help improve QPE
• The WSR-88D network will be upgraded to include
  polarimetric capabilities. Data from a prototype
  KOUN radar currently available.
• CASA (ERC for Collaborative Adaptive Sensing of
  Atmosphere which supported this work) radars
  have polarimetric capabilities
• Direct assimilation of polarimetric parameters
  may improve estimation of microphysical species
  and parameters

64
Advanced Data Assimilation Methods for Radars

• Snyder and Zhang (2003) have shown that both
  directly observed and unobserved model variables
  can be retrieved successfully using Ensemble
  Kalman Filter (EnKF).
• Tong and Xue (2005) and Xue et al. (2005) show
  that the cloud fields, including microphysical
  species associated with a 3-ice microphysics
  scheme, can be accurately retrieved using the
  EnKF method from simulated radial velocity and
  reflectivity data.
• Wu et al. (2000) indirectly assimilated ZDR in a
  4DVAR system for microphysical retrievals by
  first deriving rain and hail mixing ratios from
  the radar reflectivity the only existing work
  assimilating ZDR.

65
Goals

• Development of atmospheric state variables and a
  microphysical parameters retrieval and DA system
  based on ensemble square-root Kalman filter
  (EnSRF) method for dual-polarization radar data
• To develop methodology for utilizing CASA X-band
  dual-polarization radar data
• Determine the impact of the data on convective
  storm analysis and forecasting

66
Goals

• Assimilate dual-pol data into NWP models using
  EnSRF
• Estimate uncertain parameters in microphysics
  schemes

67
Configurations of Experiments

• OSSE using EnSRF assimilation method.
• ARPS is used in both simulation and analysis.
• 20 May 1977 Del City, Oklahoma supercell sounding
• Physical domain is 66x66x16 km3 and centered at
  34.8ºN and 98.1ºW.
• Methods as in Tong and Xue (2005) and Xue et al.
  (2005) except for ?x ?y 2 km

Simulation Radar
Analysis Domain
68
Configurations of Experiments

• 20 May 1977 Del City, Oklahoma supercell sounding
• Physical domain is 66x66x16 km3 and centered at
  34.8ºN and 98.1ºW.
• Methods as in Tong and Xue (2005) and Xue et al.
  (2005) except for ?x ?y 2 km

69
EnSRF for Radar Data Assimilation
Radar data used Vr (Zhh gt 10 dBZ) Zhh
(everywhere) KDP (KDP gt 0.3 deg./km)
Vr Vr (u, v, w) Zhh Zhh (qr, qs, qh)
KDP KDP (qr, qs)
K is the Kalman Gain, a function of background
and obs error covariances
70
Forward operators

• Reflectivity
• Specific Differential Phase (KDP,rain/dry snow)
• Differential Reflectivity (ZDR) and Reflectivity
  Difference (ZDP)

71
Forward operators (each components)

• Reflectivity (rain, dry snow)
• Wet snow
• Dry and Wet Hail

72
RMSEs of forecast and analysis ZHH ZDR sZ 2
dBZ, sZDR 0.2 dB
Black ZHH Blue ZHHZDR
73
RMSEs of forecast and analysis ZHH ZDP sZ 2
dBZ, sZDP 1 (dB)0.2
Black ZHH Blue ZHHZDP
74
Evolution of Analyzed Storms (3.5 km)
T40 min T60 min
T80 min
T100 min
qr
Truth
ZHH ZDR
ZHH
Slight improvement in qr analysis
75
Evolution of Analyzed Storms (0.5 km)
T40 min T60 min
T80 min
T100 min
Truth
ZHH ZDR
ZHH
Improvement hardly discernable from reflectivity
field
76
RMSEs of forecast and analysis ZHH KDP sZ 2
dBZ, sKDP 0.3 deg/km
Black ZHH Blue ZHHKDP
77
Summary on Assimilation of Polarimetric data with
a Perfect Model

• Polarimetric data have positive impact on the
  analysis when they are directly assimilated with
  ZHH without Vr.
• When both Vr and ZHH are assimilated, the impact
  of polarimetric data are rather small.
• It is believed that most of the value of
  polarimetric data lies with their information
  content on DSDs and hydrometeor types.
• The use of a perfect model in OSSE with fixed
  DSDs limits the impact of polarimetric data.
• More accurate observation operators may help.
• More general microphysics may give the data more
  freedom to adjust model state, but can also
  introduce too many degrees of freedom.

78
Observation Error Modeling

• Gaussian errors in log scale
• Positive errors are overestimated and negative
  errors underestimated.
• Gaussian errors in linear scale (Non-Gaussian in
  log scale)
• More realistic
• Sharp decrease in the positive side of error with
  long tail in the negative side

ZHH Reflectivity factor, Zhh Equivalent
reflectivity
79
Observation Error Distribution
80
Simulated Observations
Gaussian error s 3dBZ
Gaussian error s 5dBZ
Non-Gaussian error s 3.5dBZ (75)
81
error in obs/error assumed in DA (added dBZ/used
dBZ) Black 1.2/1.2 SKY 3/3 Blue
3/1.2 Orange 5/5 Red 5/1.2
RMSEs of forecast and analysis (Gaus.) s(ZHH)
1.2, 3, 5 dBZ
82
error in obs/error assumed in DA (added / used
dBZ) Black 25/1.2 SKY 50/2.6 Blue
50/1.2 Orange 75/3.5 Red 75/1.2
RMSEs of forecast and analysis (N-Gaus.) s(Zhh)
25, 50, 75 of Zhh
83
Summary on Observation Error Model

• The magnitude of the Gaussian errors added in the
  log domain does not reflect the effective error
  of the observation a symptom of the
  non-linearity of the observation operator
• The filter is better behaved when errors are
  correctly modeled from the error source, even
  though the error distribution of the assimilated
  data is non-Gaussian.

84
Summary on Assimilation of Polarimetric data with
a Perfect Model

• Forward operators to convert model variables into
  polarimetric measurements has been incorporated
  in EnSRF system. They include ZDR, ZDP and KDP
  for rain and dry snow.
• Polarimetric data have positive impact on the
  analysis when they are directly assimilated with
  ZHH without Vr. When both Vr and ZHH are
  assimilated, the impact of polarimetric data are
  rather small.
• It is believed that most of the value of
  polarimetric data lies with their information
  content on DSDs and hydrometeor types.

85
Can dual-pol data improve DSD definition and/or
remove model error?

• Microphysical parameter estimation experiments
• Simultaneous estimation of state variables and
  intercept parameters of rain, snow and hail DSDs,
  and the densities of snow and hail.

86
DSD Parameter Retrieval

• Experiment design

• Different realization are used in SET1 and 2 and
  SET3 and 4.
• Each set of experiments consists of 4
  experiments, ZHH, ZHHZDR, ZHHKDP, and
  ZHHZDRKDP.
• 30 observations are used in ZHH-only case and 15
  observations for each of Zhh, Zdr and Kdp in the
  rest of experiments.

87
Parameter retrieval results (SET2) Retrieved
parameter values v.s. cycles
ZHH
ZHHZDRKDP
N0r
N0s
N0r
N0s
?s
?s
N0h
N0h
?h
?h
88
RMSEs of forecast and analysis
Gray ZHH Blue ZHHZDR Orange ZHHKDP Green
ZHHZDRKDP
89
SET2 (z3.5 km)
T40 min T60 min
T80 min
T100 min
qr
Truth
Parameter Retrieval (ZHHZDRKDP)
No parameter retrieval
90
Summary on DSD Parameter Retrieval

• Parameters retrieval experiments show that ZDR
  and KDP can help multiple DSD parameter retrieval
  when ZHH alone is not successful.
• Generally, polarimetric data improve parameter
  retrieval. However, they can give negative impact
  on the analysis when parameters can be retrieved
  fairly accurately using ZHH alone.

91
Research Needs for Convective-scale DA

• Much better understanding of the error sources
  and the sensitivity of error covariance
  estimation to ensemble forecast accuracy
• Better ways for accounting for model errors
• Better physics, especially microphysics
• Effectively analysis of data representing
  structures at different scales
• Better understanding of the sensitivity of
  convection storm prediction to errors at the
  convective scale and in the storm-environment
• Better radar data quality control and observation
  error characterization
• Scalable (parallel) analysis codes/algorithms for
  high-resolution applications
• Capabilities to assimilate future observations,
  including polarimetric measurements, radar
  refractivity, clear air winds.

92
Thanks you!