A Neural Network Approach for Wind Retrieval from the ERS1 Scatterometer Data
Part 1  Determination of the Geophysical model function of ERS1 Scatterometer
for OCEANS 94 OSATES
C. Mejia, S. Thiria, M. CrŽpon
Laboratoire d'OcŽanographie Dynamique et de Climatologie, Lodyc, UPMCCNRS, Paris
F. Badran
Conservatoire Nationale des Arts et Metiers Cedric, CNAM, Paris
Abstract
Ñ The objective of the present work is to compute a new Geophysical Model Function (GMF hereinafter) for the ERS1 scatterometer by the use of neural networks (NN hereinafter). This NNGMF is calibrated with ERS1 scatterometer sigma0 collocated with ECMWF analysed wind vectors. In order to check the validity of the NNGMF systematic comparisons with the ESA's CMOD4GMF (version 2 of 32593) and the IFREMER's CMOD2I3GMF are done. The GMF is used in many algorithms to retrieve the scatterometer wind.
RŽsumŽ
Ñ Nous proposons dans ce papier une mŽthode pour calculer la fonction du mod•le geophysique (GMF) du diffusiometre du satellite ERS1. Cette mŽthode est fondŽe sur des techniques de rŽseaux de neurones (NN). La fonction anisi obtenue, NNGMF, est ŽtalonnŽe gr‰ce ˆ la collocation des sigma0 mesurŽs par ERS1 avec les vecteurs de vent donnŽs par le mod•le ECMWF. La validitŽ de la mŽthode NNGMF est verifiŽe en la comparant avec la mŽthode CMOD4GMF (version 2 du 25393) de l'ESA et avec la mŽthode CMOD2I3GMF de l'IFREMER.
1. INTRODUCTION
The transfer function allowing to compute the wind from the scatterometer signal is very difficult to be determined. It is a non linear function which may have ambiguities on the direction. Several algorithms have been proposed to model the wind retrieval transfer function. Most of them are based on the inversion of the Geophysical Model Function (GMF) which gives the sigma0 with respect to the wind vector. The study of the GMF is then of a fundamental interest. Furthermore the GMF can give useful information on the behaviour of the scatterometer. The present study is devoted on the modelling of the GMF by the use of Neural Networks. Neural Networks have been used with success by the present team to retrieve the wind vector from the ERS1 scatterometer data. The methodology is described in [2]. In the present study we propose to determine a new GMF the Neural Networks is calibrated onto ECMWF analysed wind vectors collocated with scatterometer sigma0.
2. THE NEURAL NETWORKS GEOPHYSICAL MODEL FUNCTION (NNGMF) ALGORITHM
A. The geophysical Problem
Scatterometers are active microwave radar which accurately measure the power of transmitted and back scatter signal radiation in order to calculate the normalised radar cross section (
!
0) of the ocean surface. The
!
0
depends on the wind speed, the incidence angle (which is the angle
"
between the radar beam and the vertical at the illuminated cell, Fig. 1) and the azimuth angle (which is the horizontal angle
#
between the wind and the antenna of the radar). Empirically based relationship between
!
0 and the local wind vector can be established which leads to the determination of a geophysical model function.
antenna 1antenna 2
Satellite
trajectoriesswath
d i r e c t i o n
w i n d
w i n d
antenna 3
s a t e l l i t e t r a c k
Fig. 1. Definition of the different geophysical parameters.
Recently different GMF have been proposed for the ERS1 scatterometer. One can mention the IFREMER CMOD2I3GMF which is similar to (1) and is denoted now:
!
0
=
a + b cos(
#
) + c cos(2
#
) (1)
and the ESA CMOD4GMF which is of the form:
!
0
=
()
d + e cos(
#
) + f cos(2
#
)
1.6
(2)
where
#
is the wind direction. The coefficients a, b, c, d, e, f depend on both the wind speed V and the angle of incidence
"
.
B. Determination of the NNGMF
The ERS1 geophysical model function is modelled by using a small Neural Network (551) defined in Fig. 2.
!
Vsin( )
"
cos( )
"
sin( )
#
cos( )
#
Fig. 2. Schematic Architecture of the NN GMF.
0 30 60 90 120 150 180 210 240 270 300 330 3601110987654321012
NNGMF at Node 03
sigma0(dB)wind direction (degrees)2 m/s4 m/s6 m/s8 m/s10 m/s12 m/s14 m/s16 m/s18 m/s
0 30 60 90 120 150 180 210 240 270 300 330 36022212019181716151413121110987654
sigma0(dB)wind direction (degrees)2 m/s4 m/s6 m/s8 m/s10 m/s12 m/s14 m/s16 m/s18 m/s
NNGMF at Node 09
Fig. 3. NNGMF at node 3 and 9 as a function wind direction at different wind speeds.
The input data are the wind speed V, the wind direction
#
with respect to the antenna given by cos
#
and sin
#
and the incidence angle given by cos
"
and sin
"
.
The 5 neurones located on the input layer are connected to the 5 neurones of the hidden layer which are connected to the output neurone (Fig. 2). The learning set (or calibration set) consists in 30000 collocated sigma0analysed ECMWF wind vectors pairs for each incidence angle and the test set in 5000 independent collocated pairs. The data sets were taken on the North Atlantic ocean in 1993. The North Atlantic ocean wind is suspected to be of good quality owing to the relatively high number of observations which are assimilated in the forecasting numerical model.
C. Analyse of the NNGMF
In order to investigate the pertinence of the NNGMF we systematically compared it against the ESA's CMOD4GMF (version 2 of 3251993) and the IFREMER's CMOD2I3GMF. For these comparisons we used the above test set (5000 collocated sigma0ECMWF wind vectors pairs taken on the North Atlantic ocean in 1993). Figure 3 display the NNGMF at different nodes as a function wind direction at different wind speeds. First it is found that the NNGMF exhibits the periodic structure with respect to the wind direction as found on the CMOD2I3GMF and CMOD4GMF. A realistic small upwind downwind modulation with an upwind component larger than the downwind one is observed as found on the CMOD2I3GMF and CMOD4GMF. At node 3 (Fig. 3) the NNGMF still presents an upwind component larger than the downwind one while the CMOD4GMF and the CMOD2I3GMF present a downwind component larger than the upwind one. Furthermore the minimum at constant wind speed of the NNGMF does not correspond exactly to the crosswind direction. The dynamic range of the NNGMF is smaller than CMOD4GMF and CMOD2I3GMF. The NNGMF gives smaller sigma0 values at high wind speed than the CMOD4GMF and the CMOD2I3GMF (Fig. 4) and larger values at small wind speed. This is in agreement of the observations of Etcheto
et al
(1994 in preparation) who finds that high winds are underestimated by ERS1. Statistical estimators have been computed. The bias and the RMS values of the three GMF are presented in Table I and II at different wind speeds and for three different incidence angles. In every case the NNGMF RMS performs better than the CMOD4GMF and the CMOD2I3GMF. The bias is defined as
_____
BIAS
=
$
()
!
comp

!
real
N
(3)
where:
¥
!
comp
is the sigma0 computed by the GMF.
¥
!
real
is the sigma0 observed by ERS1.
¥
N
is the number of observations. The RMS is defined as:
RMS
=
$
()
!
comp

!
real
N
(4)
TABLE I RMS OF NNGMF, CMOD4GMF AND CMOD2I3GMF
Node 03  (Inner node) N RMS
NN
 GMF (dB) RMS
CMOD4
GMF (dB) RMS
CMOD2 I3
GMF (dB) Learning set 25919 1.44 1.65 1.64 Test set 4514 1.45 1.65 1.69 Subset test 26 m/s 781 1.87 1.99 2.09 Subset test 610 m/s 2219 0.94 1.23 1.19 Subset test 1018 m/s 436 0.74 1.07 1.19 Node 09  (Central node)  N RMS
NN
 GMF (dB) RMS
CMOD4
GMF (dB) RMS
CMOD2 I3
GMF (dB) Learning set 25919 1.65 1.95 1.78 Test set 4514 1.65 1.97 1.79 Subset test 26 m/s 781 1.89 2.19 2.00 Subset test 610 m/s 2219 1.48 1.81 1.63 Subset test 1018 m/s 436 1.41 1.83 1.65 Node 17  (External node)  N RMS
NN
 GMF (dB) RMS
CMOD4
GMF (dB) RMS
CMOD2 I3
GMF (dB) Learning set 25919 2.07 2.62 2.17 Test set 4514 2.02 2.55 2.12 Subset test 26 m/s 781 2.37 2.70 2.39 Subset test 610 m/s 2219 1.69 2.03 1.82 Subset test 1018 m/s 436 1.70 2.19 1.94
CONCLUSION
The NNGMF is a good candidate to model the ERS1 scatterometer transfer function. The NNGMF RMS is better than the CMOD4 and CMOD2I3 RMS. The dynamic range of the NNGMF is smaller than the CMOD4GMF and the CMOD2I3GMF. The NNGMF gives smaller sigma0 values at high wind speed than CMOD4 and CMOD2I3 and larger values at small wind speed.
ACKNOWLEDGEMENTS
This work has been supported by the PNTS (Programme National de TŽlŽdŽtection Satellitaire), the CNES (Centre National d'Etudes Spatiales) and the CNRS (Centre National de la Recherche Scientifique).
TABLE II BIAS FOR THE DIFFERENT GMF
Node 03  (Inner node) N BIAS
NN
 GMF (dB) BIAS
CMOD4
GMF (dB) BIAS
CMOD2 I3
GMF (dB) Learning set 25919 0.04 0.53 0.75 Test set 4514 0.01 0.55 0.76 Subset test 26 m/s 781 0.02 0.35 0.75 Subset test 610 m/s 2219 0.04 0.74 0.71 Subset test 1018 m/s 436 0.10 0.71 0.90 Node 09  (Central node)  N BIAS
NN
 GMF (dB) BIAS
CMOD4
GMF (dB) BIAS
CMOD2 I3
GMF (dB) Learning set 25919 0.31 0.66 0.61 Test set 4514 0.31 0.66 0.61 Subset test 26 m/s 781 0.29 0.00 0.40 Subset test 610 m/s 2219 0.34 1.08 0.73 Subset test 1018 m/s 436 0.26 1.12 0.82 Node 17  (External node)  N BIAS
NN
 GMF (dB) BIAS
CMOD4
GMF (dB) BIAS
CMOD2 I3
GMF (dB) Learning set 25919 0.21 0.64 0.52 Test set 4514 0.17 0.56 0.46 Subset test 26 m/s 781 0.31 0.05 0.21 Subset test 610 m/s 2219 0.09 1.15 0.68 Subset test 1018 m/s 436 0.04 1.25 0.73
REFERENCES
[1] F. Badran, S. Thiria, and M. Crepon, ÒWind ambiguity removal by the use of neural network techniques,Ó
J. Geophys. Res., 96, 2052120529,
1991. [2] S. Thiria, F. Badran, C. Mejia and M. Crepon, ÒA Neural Network Approach for modelling Non Linear Transfer functions: Application for Wind Retrieval from Spaceborne Scatterometer Data,Ó
J. Geophys. Res. 98, 2282722841,
1993.