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.