Sensitivity Analysis on Sea Surface Temperature Estimation Methods with Thermal Infrared Radiometer Data through Simulations

Sensitivity analysis on Sea Surface Temperature: SST estimation with Thermal Infrared Radiometer: TIR data through simulations is conducted. Also Conjugate Gradient Method: CGM based SST estimation method is proposed. SST estimation error of the proposed CGM based method is compared to the conventional Split Window Method: SWM with a variety of conditions including atmospheric models. The results show that the proposed CGM based method is superior to the SWM.


I. INTRODUCTION
Sea Surface Temperature: SST estimation with thermal infrared radiometer onboard satellites is well known and widely used in a variety of research fields, in particular climate changes, global warming, etc. SST estimation methods are proposed [1]- [4].Most of these are based on regressive analysis and use several spectral bands in Thermal Infrared: TIR wavelength region.The most dominant atmospheric factor is precipitable water.Using the different wavelength TIR bands whose influences due to water vapor are different, it is possible to reduce the influence.The most popular method is Multi Channel Sea Surface Temperature: MCSST [5].Also previously proposed SST estimation methods are summarized by I. Barton [6].In the same time, comparative study among the previously proposed methods is well reported [7].
Based on radiative transfer equation, inversion based SST estimation method is proposed [8].Nonlinear radiative transfer equation is linearized then optimum combination of wavelength regions are selected [9].Other than that, Geographic Information System: GIS based neural network is proposed for SST estimation method [10].In this paper, sensitivity analysis results are described.SST estimation accuracy, in general, depends on relative humidity, air temperature, meteorological range, wind speed, aerosol type, and so on.Sensitivity of these factors on SST estimation accuracy is clarified in order to make clear that how does component influencing to SST estimation accuracy.
The following section describes the method for sensitivity analysis together with some theoretical background followed by some experiments.Then conclusion is described together with some discussions.

A. Theoretical Background on SST Estimation with Thermal
Infrared Radiometer Data Radiation from a blackbody with physical temperature of T is expressed in equation ( 1) where The contribution from the atmosphere can be expressed as follows, (2) where and is called as optical depth of the atmosphere.

B. At Sensor Radiance of Thermal Infrared Radiometer
For sea surface observation with TIR radiometers onboard remote sensing satellites, radiance includes three components, the contribution from sea surface, the contribution from the reflected radiance at sea surface and the contribution from the atmosphere.www.ijarai.thesai.org

C. Method for Sensitivity Analysis
By using MODTRAN of radiative transfer software code with six default atmospheric models, Tropic, Mid.Latitude Summer and Winter, Sub Arctic Summer and Winter, and 1976 US standard atmosphere, brightness temperature of the assumed spectral bands in Thermal Infrared wavelength regions can be estimated.Therefore Root Mean Square Error: RMSE of SST estimation error can be estimated for the assumed SST estimation method.

D. Assumed SST Estimation Method
Assuming spectral response function in the spectral wavelength region of spectral band is 1, then the equation ( 4) and be rewritten as follows, (5) The second term of equation ( 5) can be approximated as follows, (6) Where I ai denotes representative of spectral band i of radiance.Atmospheric transparency can be rewritten as follows, (7) where u denotes perceptible water while m denotes slant length between sea surface and TIR instrument onboard satellites.In the TIR wavelength region, perceptible water is major absorbing continuants in the atmosphere.Through simulation studies with radiative transfer code of MODTRAN with six atmospheric models (Tropic, Mid.Latitude Summer, Mid.Latitude Winter, Sub Arctic Summer, Sub Arctic Winter and 1976 US Standard Atmosphere), the coefficients are obtained as shown in Table 1.Then I ai is calculated as follows, (8) The coefficients in the equation ( 8) are calculated with MODTRAN in the same manner which is mentioned above.Table 2 shows the results.Consequently, radiance of spectral band i can be expressed as follows, (9) In order to avoid divergence of the solution, the following conditional equation is introduced.

F. Simulation Conditions
The following parameters are set for the experiments with MODTRAN obtaining at sensor radiance of spectral TIR band data.
Then SST is estimated with the proposed method and the conventional split window method using the calculated at sensor radiance.

G. Evaluation of RMSE for the Proposed CGM
SST estimation error for the proposed CGM can be evaluated with RMSE which is expressed in equation (23) by using MODTRAN derived at sensor radiance of TIR bands.

H. Evaluation of RMSE for the Conventional Split Window
SST estimation error for the conventional split window can be evaluated with RMSE which is expressed in equation ( 23) by using MODTRAN derived at sensor radiance of TIR bands.Figure 4 shows RMSE of Split Window as functions of (a) relative humidity, (b) meteorological range, (c) air temperature, (d) observation zenith angle, (e) sea surface temperature, and (f) wind speed for six atmospheric models.RMSE of the conventional Split Window is much larger than that of CGM.In accordance with increasing of relative humidity, meteorological range, observation zenith angle, sea surface temperature, and wind speed, RMSE increased.RMSE is, on the other hands, decreases in accordance with increasing of air temperature.

I. Comparison of RMSE between Split Window and CGM
Overall RMSE of the conventional Split Window and the proposed CGM is shown in Table 3.
Although depending on the atmospheric model, RMSE between both are different, RMSE of the proposed CGM is lower than that of Split Window.Therefore, CGM is superior to Split Window.www.ijarai.thesai.org

J. Influence Due to Observation Noise
In order to evaluate influence due to observation noise on SST estimation accuracy, RMSE with and without of random number derived noise is evaluated.The normal distribution of random number with 10 -6 of variance and with zero mean is generated by using Messene Twister.The random number is added to the at sensor radiance of the simulated TIR bands data.Then SST is estimated based on the proposed conjugate gradient method.Table 4 shows the result.

IV. IV. CONCLUSION
Sensitivity analysis on Sea Surface Temperature: SST estimation with Thermal Infrared Radiometer: TIR data through simulations is conducted.Also Conjugate Gradient Method: CGM based SST estimation method is proposed.SST estimation error of the proposed CGM based method is compared to the conventional Split Window Method: SWM with a variety of conditions including atmospheric models.The results show that the proposed CGM based method is superior to the SWM.
means spectral sensitivity function of spectral bands of TIR onboard satellites.In general, emissivity of sea surface in TIR wavelength region is almost 1.Therefore, the second term of the equation (3) can be neglected.

( 10 )
The unknown factors are as follows, (11) Namely, sea surface temperature, perceptible water, and representative radiance.The following cost function is introduced, (12) Then iteration is stopped when the cost function is below the designated value, (13) Radiance of the spectral band i can be rewritten as follows, www.ijarai.thesai.org(14) Then the following updating equation is introduced, (15) It is rewritten in matrix and vector as follows, cost function can be rewritten as follows, or Hesse matrix.Equation (1) can be rewritten as follows, (22) where Then the unknown variables are estimated through iterations.Also Root Mean Square Error: RMSE can be evaluated.(23) The first derivatives of the cost function are expressed as follows, (24) Also the second derivatives are represented as follows, (24) The first derivatives of radiance are expressed as follows, www.ijarai.thesai.org(25) Also the second derivatives of radiance is represented as follows, (26) where E. Assumed Spectral Bands Spectral bands of ADEOS/OCTS (Advanced Earth Observing Satellite / Ocean Color and Temperature Scanner) are assumed as typical spectral bands for SST estimation which are 10300-11360nm for Band 4, and 11360-12500nm for Band 5, respectively.

Figure 1 show
Figure 1 show RMSE of CGM as functions of (a) relative humidity, (b) meteorological range, (c) air temperature, (d) observation zenith angle, (e) sea surface temperature, and (f) wind speed for six atmospheric models.In accordance with increasing of relative humidity, meteorological range, observation zenith angle, sea surface temperature, and wind speed, RMSE increased.RMSE is, on the other hands, decreases in accordance with increasing of air temperature.Meanwhile, Figure 2 (a) shows the relation between meteorological range and RMSE as parameters of different types of aerosol for the Mid.Latitude Summer of atmospheric model.RMSE for Navy Maritime shows the greatest followed by Maritime, Desert, and Troposphere aerosol.Figure2 (b)shows RMSE for the six different aerosol types, Navy Maritime, Maritime, Urban, Desert, Rural, and Troposphere aerosol types at the meteorological range of 23 km.Figure2 (c)shows RMSE as function of altitude for Desert aerosol.Figure3shows RMSE of the representative radiance from the atmosphere for the six different atmospheric models.It does not show monotonic relation between relative humidity and RMSE.Therefore, the representative radiance from the atmosphere has to be estimated precisely.

Figure 2 (
b) shows RMSE for the six different aerosol types, Navy Maritime, Maritime, Urban, Desert, Rural, and Troposphere aerosol types at the meteorological range of 23 km.

Figure 2 (
c) shows RMSE as function of altitude for Desert aerosol.

Fig. 4 .
Fig. 4. RMSE of the conventional Split Window as functions of (a) relative humidity, (b) meteorological range, (c) air temperature, (d) observation zenith angle, (e) sea surface temperature, and (f) wind speed for six atmospheric models

TABLE I .
COEFFICIENTS OF EQUATION (7) OBTAINED WITH MODTRAN OF ATMOSPHERIC SOFTWARE CODE

TABLE II .
COEFFICIENTS OF EQUATION (8) OBTAINED WITH MODTRAN OF ATMOSPHERIC SOFTWARE CODE