Impacts of Improved Error Analysis on the Assimilation of Polar Satellite
Passive Microwave Precipitation Estimates into the NCEP Global Data
Assimilation SystemRobert J. Kuligowski
Office of Research and Applications, NOAA/NESDIS, Camp Springs, MD, USA
Russ TreadonEnvironmental Modeling Center, NOAA/NWS/NCEP, Camp Springs, MD, USA
Wanchun ChenCaelum Research Corporation, Silver Spring, MD, USA
Presented by Arnold GruberOffice of Research and Applications, NOAA/NESDIS, Camp Springs, MD, USA
1st International Precipitation Working Group Workshop, Madrid, Spain24 September 2002
Outline
• Background and Motivation
• Data Sets
• Error Analysis
• Assimilation Scheme
• Preliminary Results
• Future Work
Background: General
• Assimilation of precipitation observations has been shown to positively impact the initialization and forecast of NWP models via improved specification of water content and latent heat release.
• One approach to assimilate precipitation data makes use of an inverted model convective parameterization.
• Another approach makes use of variational techniques in which the model precipitation physics and their adjoints are used to minimize the difference between simulated and observed precipitation.
Background: GFS Assimilation
• The Global Data Assimilation System (GDAS) of the NCEP Global Forecast System (GFS) currently assimilates rain rate estimates from:– Special Sensor Microwave/Imager (SSM/I)— since February 2001
– Tropical Rainfall Measuring Mission (TRMM) Microwave Imager – since October 2001
• Impact of data assimilation was evaluated by comparing control runs to assimilation runs and runs with a new physics package.
Background: Impact StudyRuns compared:• “Control 00”—2000 physics; no precip assimilation• “Single-cloud”—2000 physics, adjustment made to coldest
cloud in Arakawa-Schubert ensemble• “Multi-cloud”—2000 physics, adjustment made to
randomly selected cloud in Arakawa-Schubert ensemble• “Control-01”—no precip assimilation, new physics:
– Prognostic cloud water/ice, plus:• Optical path and emissivity in radiation is calculated from the cloud
water/ice• Convective detrainment as a source of cloud water/ice
– Cumulus cloud induces momentum mixing– Cumulus cloud top chosen each time step from a range of values
bounded by the sounding profile
• Likewise, SSM/I and TRMM assimilation had little impact on performance when compared to either SSM/I or TRMM as “ground truth”, while physics change had significant impact
• 2001 change in physics has much greater impact than either single-cloud or multi-cloud assimilation for most model fields at initialization time
Impact of Rain Rate AssimilationGFS guess (06 hr forecast) vs. observations (15-18 August 1999)
-15
-10
-5
0
5
ps (1.20hPa)
all T (1.38K)
all q(17.5%)
all wind(3.94 m/s)
sonde T(1.46K)
sonde q(19.47%)
sondewind
(4.48 m/s)
% d
iffer
ence
from
con
trol
00
single cloud multi-cloud control 01
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
ssmi tmi
bia
s (
mm
/hr)
control 00
single cloud
multi-cloud
control 01
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
ssmi tmi
rms
d (
mm
/hr)
Bias vs… RMSD vs…
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
anom
aly
corr
elat
ion
Forecast Impact of Rain Rate AssimilationGFS Geopotential Height Field Forecast Skill Scores (Time: 11-18 August 1999)
• Again, little impact for rain rate assimilation, especially compared to impact of 2001 physics change:
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
anom
aly
corr
elat
ion
Control 00
Single cloud
Multi-cloud
Control 01
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
anom
aly
corr
elat
ion
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
anom
aly
corr
elat
ion
NH 500 hPa
NH 1000 hPa SH 1000 hPa
SH 500 hPa
Reasons for Limited Impact:
• Nonlinearities in forward model to map analysis state to rain rates. – Nonlinearities severely limit range of validity for tangent linear
and, therefore, adjoint model used in minimization
• Lack of detailed error analysis of SSM/I and TRMM rain rates:– Uncertainty in error characteristics leads to improper weighting of
observation within analysis system
• Response: Produce a detailed error analysis of SSM/I rain rates
Error Analysis: Data Sets
Time period: April-October 2001
• SSM/I rain rate estimates using the Ferraro (1997) algorithm, aggregated onto the GFS gaussian grid (triangular truncation at total wavenumber 126 ~ 100 km at the equator)
• Stage III radar/raingauge fields over the CONUS (Fulton et al. 1998), aggregated onto the GFS gaussian grid
Error Analysis: Methodology• Objective: obtain expressions of both error and error
uncertainty as a function of SSM/I rain rate• Error is expressed as the ratio of estimated to observed
amount• Since the precipitation distribution is highly skewed, the
analysis was done on a log(n+1) scale to obtain a more Gaussian distribution – n+1 used to avoid taking log(0)
• To obtain compatible error and uncertainty expressions:– Data were sorted according to SSM/I rain rate– Data were binned into groups of 50– Ratio mean and standard deviation were computed for each bin
• Separate analyses for each SSM/I algorithm type (e.g. land scattering, ocean emission, etc.)
Error Analysis: Sample Results
SSM/I estimates exhibit a dry bias for very low rates, then a wet bias that increases with SSM/I rain rate
Similar results for other algorithms
Assimilation Scheme• Intermittent assimilation system with a 6-hourly ingest cycle (00, 06, 12, 18
UTC) using observations within ±3 hours of the analysis time• Approximately 7600 SSM/I 1 superob rain rates are used in each analysis
cycle in the 60° S - 60° N latitude band• 3-D variational technique to minimize the cost function
2 J(xa) = (xb – xa)T B-1 (xb – xa) + (yobs – R(xa))
T O-1 (yobs – R(xa)) + (Jdiv + Jq)
where
xa the analysis
xb best estimate (background) of the current state of the atmosphere
yobs assimilated observations
R(xa) forward model - operator that transforms analysis state to type, location,
and time of observation. The forward model for rain rate is built around the GFS precipitation physics. The adjoint of the physics provides gradient information used by the minimization algorithm.
B error covariance matrix for the background stateO error covariance matrix for the observations and the forward model
Jdiv and Jq additional constraints placed on analysis state
O-1 and B-1 Errors
• “Observation” error, O– SSM/I error, Ossmi, from error analysis
– representativeness error, Orep, is set to constant, 0.1
– forward model error, Omod is estimated by comparing model rain rates computed from background at location of SSM/I observations.
– Total O = Orep + max[Ossmi , Ossmi + (1- )Omod], where =0.5
• “Background” error, B– statistics for analysis variables are computed from set of 24
and 48 hour GFS forecasts verifying at the same time
Preliminary Results• SSM/I assimilation reduces excessive precipitation both in
tropics and extratropics
• Less success in enhancing light rainfall rates. Most likely due to non-linearities in model physics.
Control
Assimilation-Control
SSM/I
Impact of Rain Rate AssimilationGFS guess (06 hr forecast) vs. observations (27 July - 05 August 2002)
-0.4%
-0.3%
-0.2%
-0.1%
0.0%
0.1%
0.2%
all ps (1.26hPa)
all T (1.3 K) all q (15.5%) all wind (3.88m/s)
sonde T(1.55 K)
sonde q(17.4%)
sonde wind(4.22 m/s)
SSM/I TPW(3.24 mm)
% d
iffe
ren
ce
fro
m c
on
tro
l
-20%
-15%
-10%
-5%
0%
5%
all ps (0.4 hPa) all T (0.07K) all q (0.22%) sonde T (0.14 K) sonde q (-1.92%) SSM/I TPW (0.53 mm)
% d
iffe
ren
ce
fro
m c
on
tro
l
(observation-guess) bias
(observation-guess) rmsd
• Largest impact on moisture field; other impacts are slight
Forecast Impact of Rain Rate AssimilationGFS Geopotential Height Field Forecast Skill Scores (Time: 27 July -05 August 2002)
• Very slight positive impact in Northern (summer) Hemisphere• Neutral impact in Southern (winter) Hemisphere
NH 500 hPa
NH 1000 hPa SH 1000 hPa
SH 500 hPa
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
an
om
aly
co
rre
lati
on cntrl
ssmi
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
ano
mal
y co
rre
lati
on cntrl
ssmi
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
an
om
aly
co
rre
lati
on cntrl
ssmi
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 1 2 3 4 5
forecast day
ano
mal
y co
rre
lati
on
cntrl
ssmi
Summary of Results
• Even with improved error analysis, SSM/I assimilation has had only a slightly positive impact, mainly on moisture variables and in the longer-range performance of the model
• Most significant impact appears to be reduction of excessive moisture/ precipitation in summer hemisphere tropical regions
• Improvements in assimilation techniques may permit greater impact of assimilated precipitation in the future
Future Work• Error analysis of AMSU data has been performed over the
CONUS in preparation for AMSU-B assimilation experiments
• Results are similar to SSM/I, but apparently larger differences exist in the tropics—will need to be resolved.
SSM/I AMSU-B
Future Work
• Forward model development– minimize negative impact of non-linearities in GFS precipitation
physics (simplify physics to retain essential features) permits larger iterations in applying adjoints
– extend radiative transfer model (OPTRAN) used to assimilate radiances to include cloud and precipitation effects consider assimilation of radiances from cloudy/precipitating FOVS
• Analysis variable– current moisture analysis is univariate multivariate?– consideration of issues associated with analysis moisture variable:
• large dynamic range (several orders of magnitude from surface to TOA)
• phase changes—need to express errors as a function of phase instead of looking at total water