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A method for ice concentration estimation by means of inversion techniques
0273-l
Adv.SpaceRcs. Vol. 17, No. 1. pp. (1)115_(1)11& 1996 cqyrigbt 8 1.995Cost&$ F?illkdiDGratBllthAll 0273-l I77P $930 + 0.00 177(95)00457-2
A METHOD FOR ICE CONCENTRATION ESTIMATION BY MEANS OF INVERSION TECHNIQUES K. Arai, E. Ishiyama and Y. Terayama Departmentof InformationScience, Saga University,1 Honjo, Saga 840, Japan
Methods for ice concentration estimation with passive microwave instrument data by means of inversion techniques are proposed. The experimental results with MOS-l(hlarine Observation Sate1 I i te - l)/BR(M icrowave Scanning Radiometer) data and MIS-l/VTIRfVisible and Thermal Infrared Radiometer) data as a truth of ice concentration, show that approximetely 33.5% of improvement can be achieved in terms of ice concentration estimation accuracy for the proposed methad -red with the conventional method. lNTRaWTloN Passive microwave instrument data is widely used for ice concentration estimation. For instance, EM-5 algorithm used to colnpute first year sea ice concentration in the Antarctic is given by the foIlawing expression:
C=
=‘35 & h-135
x 100(%x>
(1)
where C represents the percent ice concentration within a field of view, Ib the observed brihtness temperature, E the assunsd sea ice anissivity taken to be 0.92(nadir viewing) for first year ice having an effective physical temperature of Ts. The 135 K brightness temperature represents a combined contribution from open sea water020 K) and atmospheric emitters05 KI. The uncertainties in the assuned values are estirnsted to result in a 10 15% error in the computed ice concentrations, according to P. Gloersen et al,/l/. The other algorithms for ice concentration estimation shau aIRlost same accuracies(H. J.Zwally, et al,/?/. P. Gloersen, et al,/3/). All the factors of the above equation have not so small uncertainties so that ice concentration estimetion accuracy is not good enough. The above equation would work for the foot-printtfield of visw) without any contamination. For exssnple, briahtness temperature of 22 GHz channel might be contaminated with water vapor in the atmosphere whi le that of 37 GHz channel might be contaminated with cloud I iquid so that some corrections should be taken into accout. In order to overcome such a stuation, new methods wi I I be proposed in this paper. First the existing method wi I I be reviewed followed by intr&&ion of the proposed methods. Then ice conwntration acarr=k for the existim ad the proposed methods wi I I be assessed with Mos-lM and VTlR data.
THECCWENTICMALWHOD Since there
is a large difference
beMen
the emissivity (1)115
of ses water and that
of the
K.Ami~tal.
(1)lM
three ios types, first-year, multi-year and first-year thin ses ice, an approximate value of sea ice concentration within a field of view containing an ice-water mixture can be obtained with observations at a sinale wavelength and the use of an aver& amissivitr for the ses ice. Such a technique has besn ussd operationally by U.S.Navv on NIRWH data for ice cover map productions The proceckrre is shcwn schsmatical ly in Fig 1. Fixed values are assuned for radimces for ogen sea water and fully consol idatsd ice(lOO% sea ice concmtration). Intediate values for the ses ice mtration are then obtained by siRpIe linear interporation. It is estimated that the uncertainties in the two end points in Fig.1 result in errors of about 150 in the determination of sea ice concentration.
ICE CMENIRATION ESTIMTION By HNS
OF IMVERSIONTECHNIQUES
In order to avoid the influence due to cloud contamination, the follawing methods are grogosed. Repressnting ice concentration be C. cloud coverage be L and open sea water coverags bs 0, thsn the following expression is adecMe:
I[ Ii
&2=
C L
Slls12S13
y3
0
s31S32m
M
S21522S23
where Yl. P2 and K3 are &served bribtness tanperature of the different wavelength, Sll to S31 are spectral characteristics of the ses ice, S12 to S32 are that of the cloud and S13 to S33 are that of ouen ses water. If it is expressed with a matrix representat ion. then,
Y=
w
(3)
so that mixing ratio vector, exists inverse matrix of S.
rY can be estimated with the foIlawing
Y= s-’ Y
equation,
if
there
(4)
It is not always that there exists such inverse matrix so that a certain regularization is nsedsd for such matrix S. In such case, the least square wtcd with constraints such as IW - W’l be minimized, where J dsnotes estimstsd mixing ratio minimized and I#S+ til be minimized, where S+ denotes (St+‘S’ X= (StS)-‘S’ *
s+y
E
y
=
s+
Y= S+ Y,
Idr- #I--->
min.
vector, I I/- AVl , is aool icable.
be
Q
1-ufS+Y
ut(StS)_lu(Sf~-lu. If-W--emin. y,l-utS+
142
Y
un
IY-S+Il--->min.
where u da&es Unit matrix. Further, MaximunLike1 ihood Method to maximize the I ikel ihood function of the ovserwd vector&Lsually Multi-variate Normal Distribution) with the constraints can be aopIied(K Arai, /4/).
ExPERlENi-AL lEsllLTs MB-l/W data@3 and 37 GHz channels) of Japanese vicinity&a and Okhotsuku sea) which mre mired on 6 brch 1992 and simultaneously mired VTIR datacvisible and thermal
A
Method for Ice Concentration Ibhnation
‘“I
la
#
1oD
880
BwmmNmTMllceuTuw
Fig. 1.
The conventional
method for
ice
concentration estimation with a linear relationship between ice concentration and brightness temperature.
Fig. 3. MSR 37 @lz channel data of the study area.
SoYa
amventional method
Fig.2. VTIR image of visible channel of the study area.
Fig. 4.
Ice
concentration
through
the
i mages obtained
conventional
Proposed methods.
and the
(I)118
K.AreiCld.
infrared channels) as truth data are used. Fig2 and 3 show visible channel image of VTIR and 37GHz channel of M6R imags, respectively. IK# of VTIR is 27Km whi lo that of MSR is around 2Mm so that 8 by 8 pixels of VTIR data correspond to the one footprint(Fisld of View) of MSRdata First, classified image is ganerated for three classes, cloud, sea ice and open sea water, from VTIR imaga visually. Then VTIR and MSR data are registered by using Affine transformation then ice concentration is calculated from STIR data so that about 1.56% is accuracy of the truth data. In order to determine the parameters for the existing algorithn, maan and variance for the three classes are calculated. Then the foIlwing mtion for sea ice concentration estimation was derived: c = 4.17 DN - 220.83
03)
where DN denotes Digital N&r of 37GHz channel of MSRdata Ice concentration estimation accuracy was evaluated with Root Mean Ssuare Error between VTIR derived ice concentration and that from MSRwith the existing and proposed methods. The resultant iamges are almost sams so that only that from MaximumLikelihood Method is shown in Fig.4 while the evaluated IUSE is shc~ in Table 1.
~;ogv~an~~~t;Jrror
of ice concyt&at
Moore Penrose type of inverse matrix Least Square for observation vector Least 6ouare for mixing ratio vector MaximumLike1 ihood method
i on estimation
in unit
of %
1402 10.00 9.93 11.86
Approximately 33.5% of improvament in terms of ice concentration achieved for proposed method comparedwith the existing method.
estimation
accuracy was
1. P. Gloersen. H. J. Zwal ly, T. C. Chang, 0. K. Hal I, W.J. CampbelI and R.O. Ramseier, Tiv of sea ice concentration and muti-yaer ice fraction in the Arctic basin, Baundary-Layer Meteorology. 13, 339 - 369, Cl978I. 2. H. J. Zwally and P. Gloersen, Passive microwave images OS polar applications, Polar Record, 18, 116, 431 - 460. (1977).
regiones and resear;l
3. P. Gloersen, D. Cavalieri and W.J. CampbelI. Derivation of sea ice concentration, age and surface tanperature from multi-spectral Microwave Radia;cemoFalnad wtth the NI)?BUS-7 pace, Plenum Publ lshlng &arming Multi-ChanneI Microwave Radiometer, Dceanography Corp., 823 - 830,0961). 4. K Arai, Inversion techniques for proportion estimation of MlXELs in high resolution satellite image analysis, Proceeidngs of the 29th OXPAR symposiumA6.M.2.01.(1993).
Adv.SpaceRcs. Vol. 17, No. 1. pp. (1)115_(1)11& 1996 cqyrigbt 8 1.995Cost&$ F?illkdiDGratBllthAll 0273-l I77P $930 + 0.00 177(95)00457-2
A METHOD FOR ICE CONCENTRATION ESTIMATION BY MEANS OF INVERSION TECHNIQUES K. Arai, E. Ishiyama and Y. Terayama Departmentof InformationScience, Saga University,1 Honjo, Saga 840, Japan
Methods for ice concentration estimation with passive microwave instrument data by means of inversion techniques are proposed. The experimental results with MOS-l(hlarine Observation Sate1 I i te - l)/BR(M icrowave Scanning Radiometer) data and MIS-l/VTIRfVisible and Thermal Infrared Radiometer) data as a truth of ice concentration, show that approximetely 33.5% of improvement can be achieved in terms of ice concentration estimation accuracy for the proposed methad -red with the conventional method. lNTRaWTloN Passive microwave instrument data is widely used for ice concentration estimation. For instance, EM-5 algorithm used to colnpute first year sea ice concentration in the Antarctic is given by the foIlawing expression:
C=
=‘35 & h-135
x 100(%x>
(1)
where C represents the percent ice concentration within a field of view, Ib the observed brihtness temperature, E the assunsd sea ice anissivity taken to be 0.92(nadir viewing) for first year ice having an effective physical temperature of Ts. The 135 K brightness temperature represents a combined contribution from open sea water020 K) and atmospheric emitters05 KI. The uncertainties in the assuned values are estirnsted to result in a 10 15% error in the computed ice concentrations, according to P. Gloersen et al,/l/. The other algorithms for ice concentration estimation shau aIRlost same accuracies(H. J.Zwally, et al,/?/. P. Gloersen, et al,/3/). All the factors of the above equation have not so small uncertainties so that ice concentration estimetion accuracy is not good enough. The above equation would work for the foot-printtfield of visw) without any contamination. For exssnple, briahtness temperature of 22 GHz channel might be contaminated with water vapor in the atmosphere whi le that of 37 GHz channel might be contaminated with cloud I iquid so that some corrections should be taken into accout. In order to overcome such a stuation, new methods wi I I be proposed in this paper. First the existing method wi I I be reviewed followed by intr&&ion of the proposed methods. Then ice conwntration acarr=k for the existim ad the proposed methods wi I I be assessed with Mos-lM and VTlR data.
THECCWENTICMALWHOD Since there
is a large difference
beMen
the emissivity (1)115
of ses water and that
of the
K.Ami~tal.
(1)lM
three ios types, first-year, multi-year and first-year thin ses ice, an approximate value of sea ice concentration within a field of view containing an ice-water mixture can be obtained with observations at a sinale wavelength and the use of an aver& amissivitr for the ses ice. Such a technique has besn ussd operationally by U.S.Navv on NIRWH data for ice cover map productions The proceckrre is shcwn schsmatical ly in Fig 1. Fixed values are assuned for radimces for ogen sea water and fully consol idatsd ice(lOO% sea ice concmtration). Intediate values for the ses ice mtration are then obtained by siRpIe linear interporation. It is estimated that the uncertainties in the two end points in Fig.1 result in errors of about 150 in the determination of sea ice concentration.
ICE CMENIRATION ESTIMTION By HNS
OF IMVERSIONTECHNIQUES
In order to avoid the influence due to cloud contamination, the follawing methods are grogosed. Repressnting ice concentration be C. cloud coverage be L and open sea water coverags bs 0, thsn the following expression is adecMe:
I[ Ii
&2=
C L
Slls12S13
y3
0
s31S32m
M
S21522S23
where Yl. P2 and K3 are &served bribtness tanperature of the different wavelength, Sll to S31 are spectral characteristics of the ses ice, S12 to S32 are that of the cloud and S13 to S33 are that of ouen ses water. If it is expressed with a matrix representat ion. then,
Y=
w
(3)
so that mixing ratio vector, exists inverse matrix of S.
rY can be estimated with the foIlawing
Y= s-’ Y
equation,
if
there
(4)
It is not always that there exists such inverse matrix so that a certain regularization is nsedsd for such matrix S. In such case, the least square wtcd with constraints such as IW - W’l be minimized, where J dsnotes estimstsd mixing ratio minimized and I#S+ til be minimized, where S+ denotes (St+‘S’ X= (StS)-‘S’ *
s+y
E
y
=
s+
Y= S+ Y,
Idr- #I--->
min.
vector, I I/- AVl , is aool icable.
be
Q
1-ufS+Y
ut(StS)_lu(Sf~-lu. If-W--emin. y,l-utS+
142
Y
un
IY-S+Il--->min.
where u da&es Unit matrix. Further, MaximunLike1 ihood Method to maximize the I ikel ihood function of the ovserwd vector&Lsually Multi-variate Normal Distribution) with the constraints can be aopIied(K Arai, /4/).
ExPERlENi-AL lEsllLTs MB-l/W data@3 and 37 GHz channels) of Japanese vicinity&a and Okhotsuku sea) which mre mired on 6 brch 1992 and simultaneously mired VTIR datacvisible and thermal
A
Method for Ice Concentration Ibhnation
‘“I
la
#
1oD
880
BwmmNmTMllceuTuw
Fig. 1.
The conventional
method for
ice
concentration estimation with a linear relationship between ice concentration and brightness temperature.
Fig. 3. MSR 37 @lz channel data of the study area.
SoYa
amventional method
Fig.2. VTIR image of visible channel of the study area.
Fig. 4.
Ice
concentration
through
the
i mages obtained
conventional
Proposed methods.
and the
(I)118
K.AreiCld.
infrared channels) as truth data are used. Fig2 and 3 show visible channel image of VTIR and 37GHz channel of M6R imags, respectively. IK# of VTIR is 27Km whi lo that of MSR is around 2Mm so that 8 by 8 pixels of VTIR data correspond to the one footprint(Fisld of View) of MSRdata First, classified image is ganerated for three classes, cloud, sea ice and open sea water, from VTIR imaga visually. Then VTIR and MSR data are registered by using Affine transformation then ice concentration is calculated from STIR data so that about 1.56% is accuracy of the truth data. In order to determine the parameters for the existing algorithn, maan and variance for the three classes are calculated. Then the foIlwing mtion for sea ice concentration estimation was derived: c = 4.17 DN - 220.83
03)
where DN denotes Digital N&r of 37GHz channel of MSRdata Ice concentration estimation accuracy was evaluated with Root Mean Ssuare Error between VTIR derived ice concentration and that from MSRwith the existing and proposed methods. The resultant iamges are almost sams so that only that from MaximumLikelihood Method is shown in Fig.4 while the evaluated IUSE is shc~ in Table 1.
~;ogv~an~~~t;Jrror
of ice concyt&at
Moore Penrose type of inverse matrix Least Square for observation vector Least 6ouare for mixing ratio vector MaximumLike1 ihood method
i on estimation
in unit
of %
1402 10.00 9.93 11.86
Approximately 33.5% of improvament in terms of ice concentration achieved for proposed method comparedwith the existing method.
estimation
accuracy was
1. P. Gloersen. H. J. Zwal ly, T. C. Chang, 0. K. Hal I, W.J. CampbelI and R.O. Ramseier, Tiv of sea ice concentration and muti-yaer ice fraction in the Arctic basin, Baundary-Layer Meteorology. 13, 339 - 369, Cl978I. 2. H. J. Zwally and P. Gloersen, Passive microwave images OS polar applications, Polar Record, 18, 116, 431 - 460. (1977).
regiones and resear;l
3. P. Gloersen, D. Cavalieri and W.J. CampbelI. Derivation of sea ice concentration, age and surface tanperature from multi-spectral Microwave Radia;cemoFalnad wtth the NI)?BUS-7 pace, Plenum Publ lshlng &arming Multi-ChanneI Microwave Radiometer, Dceanography Corp., 823 - 830,0961). 4. K Arai, Inversion techniques for proportion estimation of MlXELs in high resolution satellite image analysis, Proceeidngs of the 29th OXPAR symposiumA6.M.2.01.(1993).