Optimum selection method of initial guess values for maximum likelihood estimation of Sea Surface Temperature and Precipitable Water
Shigeyuki Takasaki, Masao
Matsumoto, Kiyoshi Tsuchiya
Remote Sensing and Image Research Center, Chiba University
1-33,Yayoi-cho,Chiba city, Chiba, 260 Japan.
Abstract
In order to estimate the perceptible water and the sea surface temperature simultaneously as the maximum likelihood solutions of linear zed radioactive transfer equation, it si important to select the optimum initial guess values for sea surface temperature, air temperature and perceptible water.
In this study, an attempt is made to select the optimum initial guess values by using the statistical method from several atmospheric conditions and sea surface temperature which are summarized from meteorological observation data.
based on that values, the perceptible water and sea surface temperature is estimated from MOS-1/VTIR data and compared with sea surface temperature and perceptible water data.
Introduction
A method was developed by Aoki [1] to estimate the sea surface temperature and perceptible water simultaneously using the observed data from satellite in the atmospheric window region, taking a priori knowledge of statistical characteristics of meteorological data into account. As the estimation errors in this method considerably depend on the initial guess values, the optimum initial guess values must be selected. Aoki determined them from the detailed meteorological data over 1° x 1° latitudinal/longitudinal area. However, it is difficult in general to obtain such detailed meteorological data.
In this paper, atmospheric condition around Japan is divided into ten groups .Initial guess values of air temperature and perceptible water are selected from radio sounding data, and at the same time, this statistical character for each group are calculated. from that values and sea surface temperature which is selected character for each group are calculated . From that values and sea surface temperature which is selected from the mean sea surface temperature in August(summer) and February (winter),simulation data of radiance upwelling to the satellite is calculated using computer code LOWTRAN7. After comparing simulation data with the satelite observed data MOS-1/VTIR, simulation data which has minimum distance from the observed data is selected as initial guess values of that observed date based on their values, sea surface temperature and precipitable water is estimated from MOS-1/VTIR data as the maximum likelihood solutions of linearized radioactive transfer equation and discussed about estimation error of sea surface temperature and perceptible water.
Maximum Likelihood Solutions
With the assumption of local thermodynamically equilibrium and negligble scattering effect by molecules, the spectral radiance I
l and the mean effective radiance I upwelling from the cloudless area is written as
Where B
l, T, T
s,
tl and p are spectral Planck function, air temperature, sea surface temperature, spectral transmittance and pressure respectively .
F(
l) is the spectral filter response of the radiometer channel.
l1 and
l2 are the lower and upper limits of the wavelength of the filter response function T
B is the brightness temperature which is observed at the satelite. The subscript s refers to the surface. B and
tare average planck function and average transmittance defined by the following equations.
Eq. (1) can be linerarized at the neighborhood of initial guess values of sea surface temperature, air temperature and perceptible water u.Aoki[1] represented the difference between the true and initial guess value with the following equation.
The superscript 0 refers to the initial guess values.
An attempt is made to apply Eq. (4) to VTIR channel 3 and 4 data, Denoting r,
DT
B and
DT
s with x
1, x
2, x
3 and the coefficients of each term with k
ij (i=1,2,3 j=3,4) Eq. (4) can be expressed with the following equation.
y = Kx-----------------------(8)
y=(
DT
B3 DT
B4)
1, x = (x
1 x
2 x
3) (t: transpose)------------------(9)
The values of r,
T and
DT, corresponding to x
1 x
2 and x
3 are estimated as maximum likelihood solutions x
3
