1. Radiometer channel optimization for precipitation remote sensing
Peter Bauer
Emmanuel Moreau
Sabatino di Michele
Sensitivity
Information Content
Variational Error Estimation

2. Windows vs. Sounding Channels
Moist
Dry
18.7
23.8
36.5
89.0
157.0
50.3+
118.75

3. 1-Dimensional Variational Retrieval
Linear:
Non-linear:
analysis Jacobian Observation
Error
Forward model
First guess Background Observation
R=E+F, calibration/modelling errors:
1 K window channels
0.5 K sounding channel differences
uncorrelated
unbiased
noise-free
H, HT tangent-linear/adjoint of radiative transfer model

4. Canadian Snowstorm North Atlantic Front Florida Convection
Signal vs. Noise
North Atlantic Front
Florida Convection
ECMWF 6h-3h Precipitation Forecast on 26/01/2003
[mm]

5. Land Surface Emissivity / Emissivity ‘Error’ (C. Prigent)1 1
19 GHz
37 GHz
85 GHz 4 4 2 2

6. Signal vs. Noise Radiometer noise comparably low
radiometer noise NET
geophysical noise here only TB/ 
cloud/rain/snow variability H B HT
Contributions:
NET , surface emissivity , liquid precipitation ,
solid precipitation 
Radiometer noise comparably low
Over land with weak rain and snowfall:
Only 89, 150 GHz & sounding channels
show sensitivity to snow (rain)
Over ocean:
18-37, 50 GHz are sensitive to rain,
89, 150 GHz & sounding channels
show sensitivity to snow
Over land with strong rain and snowfall:
89, 150 GHz & sounding channels
show sensitivity to snow, less to rain

7. Channel Optimization, Information Content
Signal to noise can be characterized as x/ or x / with:
x atmospheric variable
x standard deviation of x’s variability
 noise
Information content of a measurement = factor of x-knowledge improvement when
making observation(s) [often as log (factor)]
Linear Gaussian case:
Hs = S [P(x)] – S [P(x|y)] Entropy reduction
S = Analysis error covariance matrix
P = (joint) pdf of x(y)
Iterative method for channel optimization:
S-1 = B-1 + hhT Improvement of S over B with H
B = Background error covariance matrix
H = Jacobian matrix with columns h
1. calculate Hs for all channels and select highest
2. update B with S
3. calculate Hs for remaining channels and select highest

8. Channel Optimization Clear-sky absorption spectrum
and protected frequency intervals
Clear-sky absorption gradient
dk/d [km-1 GHz-1] k [km-1]
 [GHz]

9. Information Content Canadian Snowstorm #1 Canadian Snowstorm #2
Florida convection
Canadian Snowstorm #1
North Atlantic front
Canadian Snowstorm #2
Rain
Cloud
water
Snow
GHz
Averaged Entropy reduction, ER,
over profiles per case

10. 1-Dimensional Variational Retrieval Accuracy Estimation
p p
q T
p p p
wr ws wc
p p p
wr ws wc
FG-Departures
AN-Departures
p p p
wr ws wc

11. Retrieval Accuracy: Canadian Snowstorm, area #1
window
sounding
Rain
Snow
Cloud
water

12. Retrieval Accuracy: Canadian Snowstorm, area #2
window
sounding
Rain
Snow
Cloud
water

13. Retrieval Accuracy: North Atlantic Front
window
sounding
Rain
Snow
Cloud
water

14. Retrieval Accuracy: Florida Convection
window
sounding
Rain
Snow
Cloud
water

15. Retrieval Accuracy: Total
Window channels Sounding channels
Rain
Snow

16. Summary Variational framework provides an 2* simulator:
- test of modelling/calibration errors on retrievals (also biases);
- assessment of required constraints (a priori information, models);
- estimation of quantitative retrieval accuracy (systematic & random errors);
- large flexibility with respect to cases. (*end-to-end )
M. Masutani (NCEP)
NWP-analysis/forecast system (4D-Var) framework provides a simulator for
estimating the impact of existing (OSE)
and future (OSSE) observations on
NWP!