Radiometer retrievals of LWP
Nicolas GAUSSIAT
Statistical/physical retrieval
SOME BASICS:Radiometers measure Tb at 22.2 GHz end 28.8 GHz
with
bm
skym
TT
TTlog
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
28,28,28,28
22,22,22,22
dvl
dvl
VWPkLWPk
VWPkLWPk
bTaTaLWP bb 28,2822,22
),,,,,(,, 28,22,28,22,28,22,2822 ddvvll kkkkfbaa
Model data /radiosondes4 years of radiosondes2 years of model data
LWP
VWP
Physical retrieval (Kl22, kv22, d22), (Kl28, kv28, d28) are estimated using GCM model (ECMWF)
for each profiles, and a22, a28 and b are deduced.
Kl22, Kl28
Kv22, Kv28
d22, d28
a22
a28
b
Statistical retrieval
a22
(kg/m2xm)
a28
(kg/m2xm)
b (kg/m2xm)
RMS errorg/m2
Using (m)LWP<500 g/m2 -1.9962 6.8043 -0.1530 17 g/m2
0.0017 cm
Using Tb instead of LWP<500 g/m2
-0.009 0.029 -0.197 20 g/m2
0.0017 cm
Using Tb instead of Simpson et Al.
-0.008 0.025 -0.126 18 g/m2
0.0018 cm
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 = (AtA)-1 AtY
Lidar identify liquid-cloud-free regions (LWP should be 0)
Results can look good but …
statisticalphysicalclear sky
when it comes to the details…
minutes
Fluctuations must be due to a calibration problem…
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
28,
2828,28
22,
2222,22
v
d
v
d
k
C
k
C
28,28,28
22,22,22
dv
dv
VWPk
VWPk
228
222 CCJ
2822,
28,22 C
k
kC
v
v
…cunning results(1)Chilbolton offset (lens ?) … solved
Palaiseau calibration problem… not a problem.
…cunning results(2)
Further improvement Lidar measure cloud-base and using model temperature a better estimate of Kv is obtained.