1. AMDAR (aircraft) and Radar Data Assimilation
Scientific Conferences of WMO–RA III Meeting
AMDAR (aircraft) and Radar Data Assimilation
Ming Hu1,2, Stan Benjamin2, William Moninger1,2, Curtis Alexander1,2, Stephen Weygandt2, David Dowell2 , Eric James1,2
1CIRES, University of Colorado at Boulder, CO, USA,
2 NOAA/ESRL/GSD/AMB, Boulder, CO, USA
Thanks to Shun Liu and Jacob Carley from NCEP for contributions in radar data assimilation and process
18 September Asuncion, Paraguay

2. What is Data Assimilation
Numerical Weather Prediction (NWP) is an initial-condition problem
Given an estimate of the present state of the atmosphere (initial conditions), and appropriate surface and lateral boundary conditions, the model simulates (forecasts) the atmospheric evolution
The more accurate the estimate of the initial conditions, the better the quality of the forecasts (“accurate” doesn’t mean to fit to the observations very close)
Data Assimilation: The process of combining observations and short-range forecasts to obtain an initial condition for NWP
The purpose of data assimilation is to determine as accurately as possible the state of the atmospheric flow by using all available information for NWP

3. Data Assimilation: Variational Method (VAR)
J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x])
= Jb + Jo
J is called the cost function of the analysis (penalty function)
Jb is the background term
Jo is the observation term
The dimension of the model state is n and the dimension of the observation vector is p:
xt true model state (dimension n)
xb background model state (dimension n)
xa analysis model state (dimension n)
y vector of observations (dimension p)
H observation operator (from dimension n to p)
B covariance matrix of the background errors (xb – xt) (dimension n  n)
R covariance matrix of observation errors (y – H[xt]) (dimension p  p)
In this talk, we will use variational method to explain AMDAR and Radar data assimilation but most of steps are same for Ensemble based data analysis method

4. J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x])
VAR: Background Term
J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x])
Background (forecast field): xb
Analysis: x
Start from x=xb
Analysis increment: x-xb
Background error covariance: B
Variance: the background quality
Correlation
Horizontal and vertical relation between 2 analysis point
Balance: relation between two analysis variables

5. J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x])
VAR: Observation Term
J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x])
Observation: y
Observation operator: H[x]
Conventional observation:
T, wind, moisture, Ps
3D interpolation
Non-conventional observations:
Radiance, Radar, GPSRO, …
Complex function
Observation innovation: y-H[x]
Observation error variance: R
Assumption: No correlation between two observations x y

6. VAR: Steps of using observations
J(x) = (x-xb)TB-1(x-xb)+(y-H[x])TR-1(y-H[x]) 1 2 3 1 2
Background term are the same for all observations
Step 2:
Build observation operator:
link analysis variables x to observations H[x]
Conventional observations:
AMDAR observations
3D interpolation
Non conventional observations: Complex function
Radar Reflectivity = f(qr, qs, qh)
Radar radial wind=f(u, v, w)
Step 1:
Understand observations Y
Name
Variables observed
Geographic and time distribution
Space and time resolution
Observation errors
Quality Control and bias correction
Acceptable format (BUFR,…) …
Step 3:
Define observation error variance R

7. AMDAR data assimilation
Understand AMDAR (commercial aircraft) Data
What is AMDAR
What is observed
Data coverage and resolution
Observation errors
Quality control and bias correction
Use AMDAR data in data assimilation
The impact of the AMDAR data
Regional NWP system (Rapid Refresh for US/NCEP)
Global NWP system (ECMWF)

8. Understand AMDAR Data AMDAR: Aircraft Meteorological Data Relay
AMDAR is the automated measurement and transmission of meteorological data from an aircraft platform
The AMDAR observing system is now recognized by WMO as a critical component of the WMO Global Observing System(GOS)

9. What is observed in AMDAR
Vertical profiles are derived as the aircraft is on ascent or descent
en-routed data are derived at cruise altitudes of around 35,000 feet (10,500 meters).
The meteorological parameters can be measured or derived:
Air temperature (static air temperature)
Wind speed and direction
Pressure altitude (barometric pressure)
Turbulence (Eddy Dissipation Rate or Derived Equivalent Vertical Gust)
Additional non-meteorological parameters include:
Latitude position
Longitude
Time
Icing indication (accreting or not accreting)
Departure and destination airport
Aircraft roll angle
Flight number
A water vapor (humidity) measurement can also be derived
Water vapor sensor: The Water Vapor Sensing System 2nd Generation (WVSS-II)
Operationally in the USA and Europe
Temperature , Wind, Pressure
Location, time, flight number
Humidity

10. List of AMDAR Participating Airlines
As of July 2013, more than 400,000 observations per day world wide
2863 aircraft are currently reporting world-wide, not including Aeromexico data (coming soon) since 1-Aug-2014

11. 24h AMDAR Data Coverage
Typically, every 5-10 minutes of regular real-time reports of meteorological variables whilst en-route at cruise level

12. AMDAR Vertical profiles
LAS Vegas
Ascent Sounding
Denver
Descent Sounding
High resolution vertical profiles:
High-reso profiles are reported every 300 feet in low level and every 1000 feet in middle and upper
Number vary a lot by airport:
Busy airport during the day : every 15 min or less
Many: couple profiles per day
Details in
Montreal
Ascent Sounding (No moisture)

13. AMDAR data coverage over US
Time in plots is US mountain time.
00 – 03 night
03 – 06 early morning
06 – 09 morning
Obs Number
Big various during day and night
09 – 12 day
12 – 15 day
15 – 18 day
18 – 21 afternoon
21 – 00 early night

14. AMDAR data coverage over S. America
17-20
20-23
23-02
02-05
05-08
Late afternoon to early night
night
Early morning
Time in plots is local time in Asuncion, Paraguay
Most of observations are during the night time
08-11
11-14
14-17
During the day time

15. Data Quality Data analysis uses tuned observation errors
The expected uncertainties for basic AMDAR data parameters (based on AMDAR Reference Manual):
Variable
Uncertainty
Temperature
+/ C
Wind Vector
+/ m/s
Pressure Altitude
+/ hPa
Data analysis uses tuned observation errors
AMDAR observation error used by GSI for US NAM and RAP applications
Pressure (hPa)
Temperature (C)
Wind (m/s)
moisture (RH %)
700
2.7272
16.605
500
2.6219
17.791
200
2.3213
19.748

16. AMDAR data quality control
GSD AMDAR Rejection list:
Week-long statistics
Used by us to generate daily aircraft reject lists for RAP and 3km HRRR (GSD/NOAA regional models)
Used actively by NWS and other centers
Statistics of aircraft obs against Rapid Refresh 1-h forecasts:
bias_T > 2 (°C), std_T > 2 (°C),
bias_S > 2 (m/s), std_S > 5 (m/s),
bias_DIR > 7°, std_DIR > 30°,
std_W > 5(m/s), rms_W > 7(m/s),
bias_RH > 10%, std_RH > 20%,
Example of GSD AMDAR rejection list:
;tail errors FSL MDCRS N bs_T Std_T bs_S std_S bs_D std_D std_W rms_W bs_RH std_RH (failures)
T W R UND_Piper ( resrch_T_W_R )
T W R UND_Piper ( resrch_T_W_R )
EU W Unknown ( std_S std_W rms_W )
N194AA - W Unknown ( bias_DIR )
N203WN T Unknown ( bias_T )
N220WN T Unknown ( bias_T )
N402WN R Unknown ( std_RH )
N407WN R Unknown ( std_RH )
N421LV T Unknown ( bias_T )
Which observed variables to reject
Aircraft tail number

17. GSD Aircraft Rejection List
Vector wind difference between
AMDAR observations and RR 1h forecasts.
Shows some obvious bad aircraft winds near Chicago.
(Used by NWS to help identify bad aircraft data.)

18. Bias of AMDAR obs and bias correction
Comparing with RAOBs, AMDAR temperature observations are biased:
At flight levels, AMDAR have a warm bias. (BUT RAOBs have a cold bias at the same level (ref 1). So exactly how to balance these two biases to move the model temperature toward the truth is a difficult --and somewhat philosophical--question)
Bias can be dependent to fly phase (ref 2):
Descent: a strong cool bias
Ascent: a slight warm bias
Bias correction (BC) to the AMDAR observations
ECMWF: variational aircraft temperature BC
NCEP: testing similar method as ECMWF with GSI
NASA/GMAO: bias calculated after analysis and var method
Bomin Sun, Anthony Reale, Steven Schroeder, Dian J. Seidel and Bradley Ballish  (2013) Toward improved corrections for
radiation-induced biases in radiosonde temperature observations. JGR 118,
Barry Schwartz and Stanley G. Benjamin, 1995: A Comparison of Temperature and Wind Measurements from ACARS-
Equipped Aircraft and Rawinsondes. Wea. Forecasting, 10, 528–544.

19. Use AMDAR data in analysis
Observation operator for AMDAR data:
Conventional observations: T, Q, U, V
3D interpolation from grid analysis field to observation location
Same as other conventional observation, such as sounding and surface observations
Better to define a data type for AMDAR, for example, in NCEP PrepBUFR:

20. Use AMDAR data in analysis
Convert data to the values and format analysis system accepts. Use GSI as an example:
Convert AMDAR data into temperature, U and V component of wind observation, specific humidity
Encode the observations into PrepBUFR file with all other conventional observations.
Let analysis system run …
After analysis, must check the analysis impact:
How many observations are used in the analysis
The distribution of the analysis increment over analysis domain in one analysis
Data impact from OSE, …

21. AMDAR data impact: RAP
The Rapid Refresh (RAP) is a US operational hourly updated regional numerical weather prediction system for aviation and severe weather forecasting.
Configuration:
13 km horizontal North American grid
Twice daily partial cycles from GFS atmospheric fields
Hourly continue cycled land-surface fields
Model:
WRF-ARW dynamic core
Data Assimilation:
GSI 3D-VAR/GFS-ensemble hybrid data assimilation
GSI non-variational cloud/precipitation hydrometeor (HM) analysis
Diabatic Digital Filter Initialization (DDFI) using hourly radar reflectivity observation
RAP version 1 operational implementation: 01 May 2012
RAP version 2 operational implementation: 24 February 2014

22. Observations used in RAP
Hourly Observations (2012)
Rawinsonde (T,V,RH)
Profiler – NOAA Network (V)
Profiler – 915 MHz (V, Tv)
Radar – VAD (V)
Radar reflectivity - CONUS
Lightning (proxy reflectivity)
Aircraft (V,T)
Aircraft - WVSS (RH)
Surface/METAR
(T,Td,V,ps,cloud, vis, wx)
Buoys/ships (V, ps)
Mesonet (T, Td, V, ps)
GOES AMVs (V)
AMSU/HIRS/MHS radiances
GOES cloud-top pressure/temp
GPS – Precipitable water
WindSat scatterometer

23. Impact of AMDAR moisture in RAP
Valid 00z - daytime
RAP 2013
RH –
national – hPa
#1 obs type = aircraft
Distant #2 tie –
Surface, GPS, raobs
Valid 12z - nighttime
12z and 00z combined

24. Impact of AMDAR Temp in RAP
national hPa
flight levels hPa
Valid 00z - daytime
Valid 12z - nighttime
12z and 00z combined
#1 = Aircraft
#2 = RAOBs, surface
Aircraft more impact at 3h, more at flight levels

25. Impact of AMDAR wind in RAP
RAP Domain
US CONUS region
Valid 00z - daytime
Valid 12z - nighttime
12z and 00z combined
Wind - national –
#1 = Aircraft
#2 = RAOBs,
Some impact from sfc, GPS-Met, AMVs

26. AMDAR data impact (ECMWF)
From The Benefits of AMDAR to Meteorology and Aviation (WIGOS Technical Report , Version 1, Jan 2014)
Available one line:

27. Radar data assimilation
Understand Radar Data
What is weather Radar
What is observed
Data coverage and resolution from single radar
Observation errors
Radar data Quality Control
Radar observation operator
Assimilate radar reflectivity data with DDFI and the data impact in RAP

28. What is weather radar
Weather radar, also called weather surveillance radar (WSR) and Doppler weather radar, is a type of radar used to locate precipitation, calculate its motion, and estimate it type (rain, snow, hail etc.)
Modern weather radars are mostly pulse-Doppler radar, capable of detecting the motion of rain droplets (radial velocity) in addition to the intensity of the precipitation (reflectivity)
Both types of the data can be analyzed to determine the structure of storms and their potential to cause the severe weather

29. Radar Coordinate and Resolution
The radar is located at the origin of the coordinate system; the Earth’s surface lies in the x-y plane:
Azimuth angle Θ ; Elevation angle α; Range R.
WSR88D data resolution:
Beam width: 1 degree
Scan levels (tilt): 14 scans
Maximum range: 230 km
Gate resolution:
250 m for Radial wind
1 km for reflectivity
Products update every 6 minutes α

30. Understand 3D radar coverage
The approximate height and width of the radar beam with distance from the radar site.
Values in red represent the different elevation angles in this VCP
3 dimensional radar coverage from ground level
Maury Markowitz - Own work

31. US Radar Coverage reflectivity
One of the only networks of fairly comprehensive, storm-scale data
Radial velocity
Courtesy of Jacob Carley from NCEP

32. Radar Data Quality Control at NCEP
To meet the high standard required by data assimilation, it is necessary to develop simple and efficient QC technique for operational applications.
Radar data quality control is a necessary and initial step for operational applications of radar data.
Develop statistically reliable QC techniques for automated detection of QC problems in operational environments
Among various of radar data quality problems, radar measured velocities can be very different (≥10 m/s) from the air velocities in the presence of migrating birds.
Courtesy of Shun Liu from NCEP

33. Composite reflectivity
Radar data QC at NCEP
Composite reflectivity
Scatter plots of radial wind
Before QC
Before QC
after QC
after QC
composite dual-pol variable CC
Courtesy of Shun Liu; more details see Shun Liu’s talk at GSI tutorial 2010: Or
Shun Liu, et al: WRS-88D Radar Data Processing at NCEP. Submitted to Wea. Forecasting.

34. Radial Velocity Operator
Vr(θ, α)=u cosα cosθ + v cosα sinθ +[w sinα]
Elevation angle α
90° - azimuth angle θ
Wind components from background
No term for the vertical velocity (w) in GSI
Suggest only radial velocity observations from lower elevations should be considered
Avoid contamination of the horizontal wind field, especially due to hydrometeor sedimentation
Courtesy of Shun Liu and Jacob Carley from NCEP

35. Reflectivity Operator (example)
From model forecast rain, snow, hail mixing ratio: qr, qh, qs
rain
hail
snow
T <= 0 °C (dry snow)
T > 0 °C (wet snow) To
David C. Dowell, Louis J. Wicker, and Chris Snyder, 2011: Ensemble Kalman Filter Assimilation of Radar Observations of the 8 May 2003 Oklahoma City Supercell: Influences of Reflectivity Observations on Storm-Scale Analyses. Mon. Wea. Rev., 139, 272–294.

36. Example of Radial Velocity Data analysis with GSI
Radar reflectivity at 0900 UTC on 23 May 2005
Wind analysis Increment
Full wind vectors
Upper row:
Analysis using default decorrelation length
Low row:
Analysis using a 1/4th of the default decorrelation length
Need to modify Background Error Matrix to improve Rv
Courtesy of Shun Liu from NCEP

37. Reflectivity data assimilation in RAP/HRRR
Radar reflectivity data are assimilated through Diabatic digital filter initialization (DDFI)
-20 min min Initial min min
Backwards integration,
no physics
Forward integration,full physics with radar-based latent heating
Initial fields with improved balance, storm-scale circulation
RUC / RAP/ HRRR model forecast
+ RUC/RAP Convection suppression

38. Impact of DDFI with reflectivity
Low-level
Convergence
Upper-level
Divergence
NSSL radar
reflectivity (dBZ)
14z 22 Oct 2008
Z = 3 km
K=4 U-comp. diff
(radar - norad)
K=17 U-comp. diff
(radar - norad)

39. Radar Reflectivity Verification Eastern US, Reflectivity > 25 dBZ
11-21 August 2011
CSI 13 km
CSI 40 km
HRRR radar
RAP radar
HRRR radar
RAP radar
HRRR no radar
RAP no radar
HRRR no radar
RAP no radar
You NEED the high resolution model to get the neighborhood skill!
3km HRRR forecasts improve upon RAP 13km forecasts, especially at coarser scales much better upscaled skill
Radar DDFI adds skill at both 13km and 3km

40. HRRR Radar Reflectivity Assimilation
3 km
HRRR
Run
13z
14z
15z
Digital
Filter
Digital
Filter
Digital
Filter
3-km Interp
3-km Interp
3-km Interp
15 hr fcst
15 hr fcst
15 hr fcst
HRRR 2013 introduction of
3-km data assimilation (DA)
On 10 April 2013
Latency reduced 45 min to 1-2 hrs
Digital
Filter
2013
1 hr pre-fcst
Obs
3-km Interp
GSI
3D-VAR HM
Obs
GSI HM Anx
15 hr fcst
Refl Obs

41. HRRR 2013 Pre-forecast Hour
Temperature Tendency (i.e. Latent Heating) = f(Observed Reflectivity)
LH specified from reflectivity observations applied in four 15-min periods
NO digital filtering at 3-km
Reflectivity observations used to specify latent heating in previous 15-min period as follows:
Positive heating rate where obs reflectivity ≥ 35 dBZ over depth ≥ 200 mb (avoids bright banding)
Zero heating rate where obs reflectivity ≤ 0 dBZ
Model microphysics heating rate preserved elsewhere
-45
-30
-15
LH = Latent Heating Rate (K/s)
p = Pressure
Lv = Latent heat of vaporization
Lf = Latent heat of fusion
Rd = Dry gas constant
cp = Specific heat of dry air at constant p
f[Ze] = Reflectivity factor converted to
rain/snow condensate
t = Time period of condensate formation
(300s i.e. 5 min)
Model Pre-Forecast Time (min)

42. HRRR 3-km Reflectivity Assimilation
3-km radar DA
NO 3-km radar DA
Radar Obs
05z 18 May 2013
0-hr fcst
0-hr fcst
05z + 45min
45 min fcst
45 min fcst

43. HRRR Retrospective Statistical Verification
Statistical Retrospective Comparison
30 May - 04 June 2012 (55 matched runs)
3-km grid ≥ 35 dBZ
Eastern US
With 3-km DA
Without 3-km DA
With 3-km DA
Without 3-km DA
Optimal
Bias = 1.0
Improved 0-2 hr convection

44. Real-time HRRR case study
Moore, OK 20 May 2013
20 – 21 UTC Tornadic Supercell
HRRR 13 UTC run 8 hr forecast valid 21 UTC
HRRR Composite
Reflectivity
Observed
Reflectivity