1. Radiometer retrievals of LWP
Nicolas GAUSSIAT

2. Statistical/physical retrieval
SOME BASICS:
Radiometers measure Tb at 22.2 GHz end 28.8 GHz
with
Physical retrieval : kl, kv, d are estimated using GCM model vertical information,
then
with
Statistical retrieval : a22, a28 and b are assumed to be constant and directly deduced from observations of Tb and LWP

3. Model data /radiosondes
2 years of model data
4 years of radiosondes
LWP
VWP

4. Physical retrieval d22, d28
(Kl22, kv22, d22), (Kl28, kv28, d28) are estimated using GCM model (ECMWF)
for each profiles, and a22, a28 and b are deduced.
a22
Kl22, Kl28
Kv22, Kv28
a28
d22, d28 b

5. Statistical retrieval
Use of a bi-linear regression to work out a22, a28 and b directly
We assume that LWPi depends linearly on the optical depths 22i and 28i
Ideally, we want to find a22, a28, b for all the N measurements : a22 22i + a28 28i + b =LWPi
But the best we can do is to minimize the sum : R2 = (a22 22i + a28 28i + b - LWPi)2
In matrices notations A=[…(22i 28i 1) ;…(22N 28N 1) ] X=[a22 ; a28 ; b] Y=[… LWPi ;… LWPN]
X = (AtA)-1 AtY
a22
(kg/m2xm)
a28 b
RMS error
g/m2
Using (m)
LWP<500 g/m2
6.8043
17 g/m2 cm
Using Tb instead of 
-0.009
0.029
-0.197
20 g/m2
Simpson et Al.
-0.008
0.025
-0.126
18 g/m2 cm

6. Results can look good but …
Lidar identify liquid-cloud-free regions (LWP should be 0)
statistical
physical
clear sky

7. when it comes to the details…
minutes
Fluctuations must be due to a calibration problem…

8. Cunning technique… In clear sky conditions LWP=0 so we have : then (1)
A second constrain is found by minimizing the cost fct J,
then (2)
So, from (1) and (2), we work out C22 , C28 in the clear sky regions and interpolate values in between

9. …cunning results(1)
Chilbolton offset (lens ?) … solved

10. …cunning results(2)
Palaiseau calibration problem… not a problem.

11. Further improvement
Lidar measure cloud-base and using model temperature a better estimate of Kv is obtained.