Resolving Tropical Storm Inner Core Temperatures
with a Three-Meter Geostationary Scanning
Microwave Sounder
14th International TOVS Study Conference, Beijing | May 25, 2005
Donald Chu | Norman Grody | Michael Madden
Swales Aerospace, Inc. | 5050 Powder Mill Road | Beltsville MD 20705 USA
Three Approaches
Measuring Core Temperatures
Proposed Algorithms
1. Use visible observations …
• Inner Core
–
–
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true
3m
6m
12 m
18 m
24 m
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16
14
– 60/118 GHz temperature sounding
– maximum filled aperture ~ 3 m
– instantaneous resolution ~ 100 km
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2. Parameterize inner core profile …
–
12
10
–
8
50
in terms of location, size,
and amplitude
Choose parameters to fit
observations
3. Trade sensitivity for resolution …
4
–
–
2
– Even large antennas don’t capture
entire temperature rise from GEO
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• Method 2 – Parameter Estimation
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– Estimate Holland model parameters
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-100
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0
distance (km)
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100
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because it’s easier to improve sensitivity
Deconvolve to recover the profile
• Method 3 – Deconvolution
25
– Solve for temperature field
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Convolution
0
5
10
15
diameter(m)
20
• Actual
• HiFi Observations
full kernel
truncated
0.7
amplitude
– 1 kilometer resolution
– Truncated at 2nd null
• LoFi Predictions
• If the columns of the warm core object are
concatenated, the convolution operator is a
band diagonal matrix.
Observations
– Ground sample distance (20 km)
– Feature size (20 km)
– Antenna beamwidth (100 km)
0.4
scanned obs
a priori obs
temperature(K)
10
0
-150
-100
-50
0
50
100
150
-50
0
distance (km)
antenna pattern
Method 2 – Four Parameter Error
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100
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– Accurate to better than 1 K
– Converges even from a poor
initial guess
• Cons
– Search takes a long time
– Depends on model fidelity
Conclusions
• Simulations suggest that inner core temperature profiles
can be recovered with 3-meter antenna at GEO.
mean = 0.43764 K; std dev = 2.8216 K
14
12
10
– Model-independent
– Peak recovery:
• 75% @ 60 GHz
• 95% at 118 GHz
8
6
• Requirements
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2
0
-2
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-6
0
100
200
300
400
500
cases
600
700
800
900
1000
– Known antenna pattern
– 0.1 K temperature sensitivity
mean = -4.9909 K; std dev = 3.4061 K
10
• Cons
– Processing increases noise
– 3 K noise standard deviation
• Performance
5
– Accuracy up to 1 K
– Coverage in as little as 1 minute
0
-5
-10
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0
100
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300
400
500
cases
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800
900
1000
true
final
initial
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15
10
5
0
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Method 3 – Deconvolution
• Pros
25
• Pros
– Noise multiplied by same factor
as
observed peak temperature
– A 5 km radius error can change
the scaling by 100%
0
-100
• Result
– 0.1 K sensitivity
– 6-by-6 sample scan
– 36+ seconds
• Cons
5
-5
-150
0.1
– Scaling works if the warm core
radius is known
– Simple but more subject to error
than the later methods
15
peak error(K)
– 1 K noise
– No a priori near core
scan region
inner core
• Pros
20
Bτ
• Coverage depends on
0.5
Method 1 – Scaling
peak error(K)
• A Priori Observations
σ T = Ts
a priori region
0.6
0.2
– Resolved to ground
sample distance
– Truncated at 1st null
Warm Core
−1
G G
G G
x = x 0 + (S 0 + G T WG ) G T W ( y − g )
– System temperature (1000K)
– Bandwidth (100 MHz)
– Integration time (1 sec)
1
0.9
0.3
– 0.1 K noise
– ground sample distance
)
• Sensitivity depends on
Kernel
– 3-meter diameter (60 GHz)
– Filled aperture
• The valid convolution keeps the antenna
pattern within the bounds of the original
temperature field.
• Scanned Observations
r2
Coverage
0.8
– 20 K peak
– 10 km radius
2
25
Antenna Patterns
• The image is the 2D convolution of the
antenna pattern with the warm core
brightness temperature.
• Warm Core Profile
(
T = T0 + ∆T ⋅ 1 − e − r0
35
6
• The Problem
∆T = ∆Tobs / f
– Divide by expected fraction
55
temperature (K)
temperature (K)
• Instrument
• Method 1 – Scaling
to determine inner core location and size
Scale observed temperature peak
% expected
– temperature reflects storm strength
– measured at 250 mb (10 km)
– typically 20 km in diameter
NOAA NESDIS Office of Satellite
Operations, Hurricane Inner Core,
http://www.oso.noaa.gov/goes/
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x-axis (km)
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