INTELLIGENT DATA REDUCTION
ALGORITHMS FOR REAL

TIME DATA
ASSIMILATION
Xiang Li
, Rahul Ramachandran, Sara Graves
ITSC/University of Alabama in Huntsville
Bradley Zavodsky
ESSC/University of Alabama in Huntsville
Steven Lazarus, Mike Splitt, Mike Lueken
Florida Institute of Technology
May 5, 2009
Data Reduction
•
It is a common practice to remove a portion of or combine
high spatial and temporal resolution observations to reduce
data volume in DA process, due to
High computation resources required for large volume data set
(exponential increase with data volume)
Data redundancy in large volume high resolution observations
Local spatial correlation of satellite data
observation data resolution exceeds assimilation grid resolution
Reducing data redundancy may improve analysis quality
(Purser et al., 2000)
Little
Lot
Analysis
Technique
Data Volume
Horizontal
Resolution
Successive
Corrections
Statistical
Interpolation
4D

Var
3D

Var
Little
Lot
1km
80 km
Computational Resources Required for Data
Assimilation
Need for ‘new’ Data Reduction Techniques
•
Current data thinning approaches
Sub

sampling
Random Sampling
Super

Obing (subsampling with averaging)
•
Limitations
All data points are treated equally
Information contents that observation data contain
and their contributions to data analysis performance
may be different
•
Intelligent Data Thinning Algorithms
Reduces number of data points required for an analysis
Maintains fidelity of the analysis (keeps the most important data
points)
High Data Volume from satellite platforms
( e.g. infrared based SST, scatterometer winds) carry
redundant data. Computationally Expensive!
Analyses derived from simple subsampling of data can be inconsistent and are not
optimal in efficiency.
Same data subsampling interval, but shifted.
Simple subsampling strategies can be
susceptible to impact from
missing ‘significant’ data sample.
Example
Intelligent data thinning algorithms
•
Objective:
reserve samples in the thinned data set that
have high information content and large impact on analysis.
•
Assumption:
samples with high local variances contain
high information content
•
Approach:
Use synthetic test to determine and validate the
optimal thinning strategy and then apply to real satellite
observations
Synthetic Data Test: Truncated Gaussian
Real Data Experiment: Atmospheric Infrared Sounder (AIRS) profiles
Synthetic Data Test: Truncated Gaussian
•
Explicitly defined truth and background fields
•
Direct thinning method
35 observations sampled to find the 5 observations yielding the
best analysis (1D variational approach)
325,000+ unique spatial combinations
•
First guess: base of Gaussian function
•
Observations: created by adding white noise to truth
first guess
truth
analysis
optimal
observation
locations
Synthetic Data Test: Truncated Gaussian (cnt’d)
•
Optimal observation configuration retains data at the:
peak
gradient
anchor points (where gradient changes most sharply)
•
Dependent on key elements of the analysis itself:
length scale (L)
quality of background and observations
Lesson Learned:
Thinned data samples should
combine
homogeneous
points,
gradient
points, and
anchor
points
for optimal performance, and a
dynamic length scale
should be
applied to each thinned data set.
Intelligent Data Reduction Algorithms
•
Earlier versions of intelligent data thinning algorithms (IDT, DADT,
mDADT)
‡
Density

Balanced Data Thinning (DBDT)
Three metrics
are calculated for data samples and samples are put into priority
queues for the three metrics
Thermal Front Parameter (TFP):
High value of TFP indicates rapid change of
temperature gradient and ‘anchor’ samples
Local Variance (LV):
high values indicate gradient regions
Homogeneity:
low values indicate homogeneous regions
Data selected from the three metrics:
user determines the portions of samples
from these metrics
Radius of impact (R)
: used to control uniform spatial distribution of thinned data
set.
Distance between any two samples needs to be larger than R
Data selection process:
select top qualified samples from priority queues. Start
with TFP queue, followed by LV queue and homogeneity queue
DBDT algorithm performs best in these thinning algorithms
AIRS & ADAS: Our Real

World Testing Ground
•
Atmospheric Infrared Sounder (AIRS)
NASA hyperspectral sounder
generates temperature and moisture profiles with ≈ 50

km resolution
at nadir
each profile contains a pressure level above which quality data are
found
•
ARPS Data Assimilation System (ADAS)
version 5.2.5; Bratseth scheme
background comes from a short

term Weather Research and
Forecasting (WRF) model forecast
error covariances:
–
background: standard short

term forecast errors cited in ADAS
–
observation: from Tobin et al. (2006)
*
AIRS validation study
dynamic length scale (L) calculated from average distance of nearest
observation neighbors
*D. C. Tobin, H. E. Revercomb, R. O. Knuteson, B. M. Lesht, L. L. Strow, S. E. Hannon, W. F. Feltz, L. A. Moy, E. J. Fetzer,
and
T. S.
Cress, “ARM site atmospheric state best estimates for AIRS temperature and water vapor retrieval validation,”
J. Geophys. Res.
,
D09S14, pp. 1

18, 2006.
Thinning Strategies (11% of full)
•
Subsample:
Takes profile with most retrieved levels within a 3x3 box
•
Random:
Searches observations and ensures that retained observations
are thinned to a user

defined distance
10 permutations performed to create an ensemble
•
DBDT:
thins on 2

D pressure levels using equivalent potential
temperature; then levels are recombined to form 3

D structure
Thinning uses Equivalent Potential Temperature (θ
e
) to account for
both temperature and moisture profiles
Case Study Day: 12 March 2005
•
700 hPa temperature gradient in observations and
background over midwest and northern Gulf of Mexico
•
Observations and background show similar patterns
700 hPa AIRS temperature observations
700 hPa WRF forecast temperatures (bckgd)
Subsample
Random
DBDT
700 hPa Temperature Analysis Comparison
•
Overall analysis increments are
±
1.5
o
C over AIRS swath
•
Largest differences between analyses in upper
midwest
and over Southern Canada
Full
Subsample
Random
DBDT
# OBS
793
99
100
87
ALYS TIME (s)
244
56
56
106
L (km)
80
146
147
152
θ
e
MSE
N/A
0.60
0.56
0.36
Quantitative Results (Full vs. Thinned)
•
Computation times are 50

70% faster for the thinned data sets
•
MSEs compare analyses between full and each thinned
•
DBDT is superior analysis with least observations:
has a longer computation time (thinning algorithm more rigorous)
cuts MSE almost in half with 1/10 the observations of the full
Conclusions
•
Intelligent data thinning strategies are important to
eliminate redundant observations that may hinder
convergence of DA schemes and reduce computation times
•
Synthetic data tests have shown that observations must
be retained in gradient, anchor, and homogeneous regions
and that results are dependent on key elements of the
analysis system
•
Analyses of AIRS thermodynamic profiles using different
thinning strategies yields the DBDT as the superior thinning
technique
Future Work
•
Manuscript in review with Weather and Forecasting (AMS)
•
Testing forecasts spawned from the various thinned
analyses to see if superior DBDT analysis produces the best
forecasts
•
Demonstration of algorithm capabilities with respect to
real

time data dissemination
•
Use of gradient detecting portion of algorithm for
applications in locating cloud edges for radiance
assimilation
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