INTRODUCTION
Temperature of water surfaces is the most important oceanic parameter, that
effect on climatic, atmospheric systems and aquatic life. Changes in Sea Surface
Temperature (SST) play a fundamental role in the exchange of energy, momentum
and moisture between the ocean and the atmosphere (Wentz
et al., 2000). SST is a central determinant of airsea interactions
and climate variability. SST also influences the development and evolution of
tropical storms and hurricanes (DeMaria and Kaplan, 1994;
Emanuel, 1999) is correlated with nutrient concentration
and primary productivity (Kamykowski, 1987) and impacts
the distribution of fishing grounds (Shao et al.,
2004). SST is Also, main parameter for climatic and meteorological forecasting
models and important characteristic for the modeling existing spatial and temporal
expansion data, that in the usual measures have to be accomplished by maritime
stable stations (buoy), boats and investigation ships in certain places and
spatial expansion and in some cases temporal extension of data was limited,
thus data collection is necessitate much expenses.
NOAA/AVHRR data has been especially emphasized on meteorology and oceanography
studies due to its lowspatial and hightemporal resolutions. Thus, to begin
activity of satellite search began using its data in meteorology and oceanography
studies. In some primary years Smith et al. (1970)
extracted preciseness around ±1 centigrade degree for estimate SST
via nimbus data by statistic techniques. One of the first studies was done to
produce SST via NOAA satellites by Stevenson et al.
(1972).
The SST algorithm was based on Merchant et al. (1999),
which applies the split window technique using Bands 4 and 5 (11 and 12 μm
bands, respectively) that correct atmospheric water vapour (Fig.
1).
So, In Split window method the atmospheric correction participates in the calculation.
Due to the absorption ability of energy by vapor and CO_{2 }as well
as ozone, the water surface temperature via satellites is forever less than
estimated temperature in measured field data (Cogan^{
}and Willand, 1976).

Fig. 1: 
Diagram of differences between absorption of radiation in 4 and 5 bands
AVHRR 
One widely adopted linear formula is the multichannel SST (MCSST) (McClain
et al., 1985), which applies to splitwindow observations, i.e.,
to brightness temperatures of a pair of channels within the atmospheric window
between about 10 and 13 μm, the channels typically having peak sensitivity
around 11 and 12 μm. In the MCSST, the retrieval equation is expressed
in terms of the difference of the 11 and 12 μm BTs, a formulation which
effectively imposes an additional linear constraint on the coefficients, a.
In nearly linear formulations, the coefficients are weak functions of some prior
information. One of such formulations is the NonLinear SST (NLSST) algorithm,
which is similar to the MCSST except the coefficient of the BT difference at
11 and 12 μm that is a function of a prior SST.
Coll et al. (1993), by using the splitwindow
algorithm, determine SST in midlatitudes from NOAAAVHRR data. The accuracy
achieved for SST is 0.5°K, which is the limit accuracy that can be obtained
from AVHRR measurements over midlatitudes.
The most expanded activity to accomplish via 3400 images is for a period of
8 years by Guerra et al. (1997) in the northwest
shores of Africa.
Kearns et al. (2000) show that the mean difference
between global Pathfinder SST products and SST recovered from a shipmounted
radiometer is 0.07±0.31°C for low and midlatitude data. Kilpatrick
et al. (2001) state that the global Pathfinder SST product is within
0.02°C of buoy SSTs within their database, with a standard deviation of
0.53°C. Departures from these global statistics for local high resolution
Pathfinder products which are used here may exist; however, the use of absolute
SST values in this study is restricted to seasonal differences, significantly
larger in range (>10°C) than any of the cited statistics. Other analyses
focus on relative temperature patterns within scenes.
SST values, both in situ and satellitederived, have been obtained
from the NOAA/AVHRR for assessing rates of sea temperature increase (Strong
et al., 2000).
The approximate root mean square error (RMSE) of the AVHRR SST retrievals is
near 1.15°C (Mesias et al., 2007), from buoys
located in the western North Atlantic and She et al.
(2007) investigated SST in the Baltic Sea and North Sea, they concluded
that the best available fullcoverage SST product is generated by assimilating
the SST observations to obtain a yearly mean model bias of 0.07°C and RMSE
of 0.64°C.
The aim of this study is to investigate accuracy of SST retrievals algorithms in the Persian Gulf, using AVHRR data. Finally, we present a modified algorithm by using the regression analysis.
MATERIALS AND METHODS
In order to achieve the objects of the study, water (sea) surface temperature of Boushehr buoy over the Persian Gulf during 19962000 periods were obtained from Iranian Meteorological Organization (IRIMO) and for these periods images of AVHRR sensor of NOAA 14 satellite were obtained. The selected study area is located between 48° E to 56° E and 24° N to 30° N. This inland sea of some 251,000 km^{2} is connected to the Gulf of Oman in the east by the Strait of Hormuz.
First, geometric correction was done in two ways: systematic and terrestrial
point control and then, equivalent blackbody temperature computed from Eq.
1.
where, T_{E}* is equivalent blackbody temperature (^{°}K),
V_{c} is value of central wave, where in 4 and 5 bands in turn are 929.3323
and 835.1647, C_{1} and C_{2} are constant coefficients, that
in turn are 1.4387863 and 0.0000191062, N_{E} computed from Eq.
2.
where, N_{E} is Earth radiance value in units of mW/(m^{2}srcm^{1}), A and B are constant coefficients, where A in 4 and 5 bands in turn are 0.165526 and 0.18382 and B in 4 and 5 bands in turn are 160.22 and 179.598, DN = Digital Number in pixel.
Then, Brightness Temperature (BT) computed from Eq. 3. Where
A and B are constant coefficients A in 4 and 5 band in turn is 0.338243 and
0.304856, B in 4 and 5 bands in turn are 1.001989 and 1.005977, T_{E}
= BT.
Because emissivity of water is approximately equal 1, thus BT is assumed to be equal to water surface temperature. Then, performance of the atmospheric corrections was computed from differences of absorption between 4 and 5 bands. These techniques are called split window algorithms.
In this study, SST was computed using MCSST. Several algorithms by researchers
were presented for calculation of SST. In this study, the algorithms Murty
et al. (1998), Eq. 4, Gowda
et al. (1993) Eq. 6 and national center of remote
sensing Australia Eq. 7 were used for calculation of SST
(Downing and Williams, 1975):
where, T_{11} and T_{12} are the brightness temperatures corresponding to channel 4 and channel 5, respectively and the SECsza is the secant of satellite zenith angle. The difference between the brightness temperatures of channel 4 and channel 5 in the SST retrieval algorithm has been incorporated for correcting the effect of atmospheric water vapour absorption. Pixels are considered to be contaminated when the brightness temperature difference between the channel 4 and channel 5 is greater than the threshold value (2.5°K).
The satellite zenith angle (θ_{i}) is computed from:
where R = radius of the earth (= 6378.388 km), h = height of the satellite
(= 833 km), φ = look angle of the satellite = 55.4+(55.4i/1024) and i
is the pixel number. The SST computations are performed only when the satellite
zenith angle is less than 53° (Murty et al., 1998):
RESULTS AND DISCUSSION
At first, we assessed Murty et al. (1998), Gowda
et al. (1993) and national center of remote sensing Australia (Downing
and Williams, 1975) algorithms for estimating SST of Persian Gulf. Later, by
using linear regression analysis (LRA) was modified Murty
et al. (1998) algorithm with best accuracy in Table
1 (column 6). Finally SST was computed with modified algorithm for two months
in Table 1 (column 12).
Algorithms test: Accuracy assessment of algorithms for estimating SST
of Persian Gulf comparison with Boushehr buoy has been shown in Table
1. According to this table Murty et al. (1998)
algorithm has the best accuracy in rate of SST.
By using measured temperature data in Boushehr buoy and estimated temperature for 4 and 5 bands of AVHRR/2 sensor, Linear Regression Analysis (LRA) has been done to produce an equation, so that it can estimate SST via BT. In this study, the fit Linear method for production of an equation was Enter, that the temperature data in Boushehr buoy was as Dependant variable and 4 bands temperature and difference of temperature in 4 and 5 bands was as Independent variable.
Results of LRA are as follows: Correlation coefficient between variables (bands 4 and 5) was 0.977, R^{2} = 0.994, constant was 1.331, coefficient of BT_{4} was 0.987 and correlation difference between temperature in 4 and 5 bands was 0.183.
As a result the LRA produced an equation to assess the value of SST in the
Persian Gulf. This equation was computed by using BT in 4 and 5 bands of AVHRR/NOAA
14 sensor. The equation is as follows:
In Eq. 8, the maximum of estimated error for SST in the
Persian Gulf was 0.77, its minimum 0.09 and mean of error was ±0.43,
it is an acceptable amount.
Finally, this equation was tested in 2 months (September and December 1999)
of NOAA14 AVHRR images and SST was computed in the Persian Gulf. For example,
two images show SST in September and December 1999. Figure 2
shows the SST image in 4/09/1999 for the Persian Gulf, in this image SST differs
from 32°C in the southern shore to 38°C in the southwestern shore.
Table 1: 
Sample of images selected and results of calculation of algorithms 

1: Measured temperature in Boushehr buoy, 2: Brightness temperature
In 4 band, 3: Brightness temperature In 5 band, 4: Difference between 4
and 5 bands (BT4BT5), 5: SST of calculated algorithm Murty
et al. (1998), 6: Difference between column 1 and column 5, 7:
SST of calculated algorithm Gowda et al. (1993),
8: Difference between column 1 and column 7, 9: SST of calculated algorithm
national center of remote sensing Australia, 10: Difference between column
1 and column 9. 11: SST of produced algorithm, 12: Difference between column
11 and column 1 

Fig. 2: 
Map of sea surface temperature the Persian Gulf in date 4/09/1999(°C) 

Fig. 3: 
Map of sea surface temperature the Persian Gulf in date 4/12/1999(°C). 
Mean
of SST is 34.79°C in Table 1 (Column 11). In general the
temperature is high in summer, because it is located near the tropic of cancer.
So, the deserts are located around the Persian Gulf, which is high SST.
Figure 3 shows the SST image in 4/12/1999 for the Persian
Gulf, in this image SST differs from 15°C in the northwestern shore to 28°C
in the northern shore. Mean of SST is 22.26°C in Table 1
(Column 11). The temperature lowers in the northwestern shore because of the
entrance of the water of the Shatt alArab (Arvand Rood) river to the Persian
Gulf.
CONCLUSIONS
The presents study, firstly assessed the accuracy of SST retrievals algorithms
with the NOAAAVHRR satellite over the Persian Gulf. Secondly, SST an equation
by using linear regression analysis (LRA) was produced.
Thirdly, this equation was tested on AVHRR images and SST computed in the Persian
Gulf. The important findings of the study are:
• 
The AVHRR/ NOAA14 images are suitable for generating the time series
SST in the Persian Gulf 
• 
Mean of error in formula was ±0.43, which is an acceptable amount 
• 
In summer, the highest temperature was in the southwestern shore and the
lowest temperature was in the southern shore and the difference between
the highest and lowest was 6°C 
• 
In the last autumn, the highest temperature was in the northern shore
and the lowest temperature was in the northwestern shore and the difference
between the highest and lowest was 13°C 
• 
Different temperature in the summer was lower as compared with the last
autumn, because it is located near the tropic of cancer 
This study is an introductory work and we hope that it will be helpful in economical
planning over the Persian Gulf and its surrounding countries.
ACKNOWLEDGMENTS
The researchers appreciate Iranian Meteorological Organization (IRIMO), for presented data and appreciate Spatial Organization of Iran, for present satellite images.