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Consiraints and refinement of
radiative transfer model for bathymetric mapping from satellite remotely
sensed data
Mazlan Hashim and Samsudin Ahmad
Center for Remote Sensing
University of Technology Malaysia
Locked Bag 791, 80990 Johor Bahru Malaysia
Mazlan Hashim and Samsudin Ahmad
Center for Remote Sensing
University of Technology Malaysia
Locked Bag 791, 80990 Johor Bahru Malaysia
Abstract
This paper examines the a customization of radioactive transfer model for correlating the reflectance to-depth of a typical turbid coastal water of Malaysia, hence enabling the bathymetric information be extracted from satellite remotely sensed data.
Introduction
Hence the launching of the Earth Resources Satellite Series (ERTS); (ANDSAI) 1,2,3,4,5, SPOT-1 various stations have been carried out for extracting bathymetric information from water covered area. Hammock (1977) had shown that multispectral scanner data (MSS ) within visible wavelength, band 4 00-5-0-6mm and band 5(0.6-0.7mm) are very useful for updating hydrographic charts. Misplaced or uncharted reefs and shoals could easily be detected and located. The near-infrared and infrared bands (0.7.1.1mm) are excellent for mapping the contact between land and water such as coastline. Studies by Gordon et.al. (1975) Poleyn and Lyzenga 91979) have also revealed that lands at 4 MSS data: band 4 under perfect weather condition has the capability of penetrating within the range of 24 to 40 meters while band 6 is about 2 meters. On using finer resolution data, Hallada and Lanis (1984) band that band 1 )0.45-0.52mm) and band 2 (0.52.0.60mm) of Lands at 4 Thematic Map per data were capable of penetrating 20 and 14 meters, respectively.
All the above-mentioned studies have obtained bathymetric information from satellite imagery based on radioactive transfer model which deal directly on using local in situ measurements such as water attenuation coefficient, bottom samples, sea surface state, etc. at the region being studied. Although this approach is most appropriate, a considerably large amount of effort is needed in collecting in-situ information and later much processing time is taken in reducing the field samples. Alternatively, this research will concentrate on a simplified approach of correlating the depth of a water body against its reflectance recorded by a satellite sensor. This hybrid radioactive transfer model : the single band and two reflectance models are adopted in computing the water depth from satellite digital data.
Study area and dcigital data
Four test area, located both in the eastern and western coasts of Peninsular Malaysia were distributed. The four test sites : southern waterway of Langkawi Island to Kuala perils : South port of Pelabuhan kelag; off Bandar Hilir to Fan Jung Keling, Melaka, and Tanjuna Leman to Tanjung Tenggaroh of Mersing .
The satellite digital data SPOT-1 and lands at 5 MSS were used in the study. These data were later geometrically corrected by registering to the corresponding nautical chart of the given area. A second degree polynomize transformation is employed in establishing the framework for geometric correction. This is then followed by a resembling process.
Methodology and data manipulatrion
After the satellite imagery is correctly registered to the corresponding nautical chart, the shallowest and deepest points are identified. These two points are needed to verify the correlation of the reflectance values and the depth of the water column. In formulating the correlation, the period known depth obtained from nautical chart corrected for tidal height at the time of data acquisition was used.
Radiative transfer model
The reflectance recorded over the sea or water is determined among other factors by the surface state, the optical properties of water, and in the case of shallow water as in the coast is being determined by the depth and reflectance of the sea-bottom. By radiative transfer equation, the reflectance recorded at the water surface is given by :
Lwi deep water radiance in band i
Lbi wet bottom radiance in band I,
K attenuation coefficient in band I,
K constant, f (solar irradiance, transmittance, refraction )
f secant of observation angle at nadir, and
Z water depth
This is a hybrid radiative transfer model specially simplified in this research for processing depth from single band data as an input. For a wave length in band I with depth Z, a single band reflectance model is defined by :
Lsi the average radiance over deep water,
Ki a constant which is a function of the air and water surface, and the refraction at water surface ,
RBi actual wet bottom reflectance at the location where the water depth is Z
Ki effective water attenuation coefficient 9m-1), and
f approximately ~2.0
Two band Reflectance Model
This model is tested mainly for minimizing the noises inherent in the satellite digital data. Two band data were main input to this model.
Simplifying the model for regression of the known depth, equation (3) becomes Y = a + b1X1 + b2X2.
Fig.1. Location of the study area
Results
In solving for all the parameters in both models, with known depth obtained from nautical chart, the water attenuation coefficient is `then estimated. Table 1 tabulates the results of the regression analysis. To evaluate the depth computed using the models in comparison with the known depth, a graphical plot of the residual vectors obtained in the computation is drawn. Figure 2 (a) and 2(b) show residuals of depth computed using single band reflectance model with band 1 and 2 as input data, while figure 3 (c) illustrates the residual of depth computed with double band reflectance model of band 1 and 2 as input. From the result of the regression analysis, this study indicates :
- With single band reflectance model, at 95 % confidence level for a
depth range of 0.5-1.6 and 8-14 meters an error of 5-10 meters is
observed. The residual vector, however, is at lower magnitude for
1.7-7.9 meters depth range, with an average residual of 0.25 meters.
- With two band reflectance model, the residuals seem to be optimal level. At depth shallower than 1 meter, a deviation of 3 to 110 meters is recorded. This suggests that the model des not apply to a very shallow water. For a depth of 1.1 to 14 meters, however, an average of 1.5 meters deviation is recorded.
reflectance model, and (b) two band reflectance model.
(a) Y = a + bx
| Site | Data | ----------------- R E S U S LT -------------- | ||||
| a | s(Y est.) | R squa. | b | s(b) | ||
| 1 1 2 2 3 3 4 4 5 5 |
1 2 1 2 1 2 4 5 4 5 |
78.34 69.30 75.24 45.32 26.09 18.71 24.52 11.70 47.79 19.32 |
3.81 3.95 4.44 5.69 2.67 2.83 0.73 0.95 1.64 1.89 |
0.85 0.84 0.62 0.34 0.36 0.28 0.80 0.67 0.72 0.63 |
-0.82 -1.11 -0.81 -0.81 -0.26 -0.26 -0.65 -0.37 -0.54 -0.24 |
0.14 0.20 0.15 0.29 0.10 0.12 0.05 0.04 0.06 0.03 |
(b) Y =ax1 + bx2
| Site | Date | ----------------- R E S U L T -------------------- | ||||||
| C | s(Y est) | R. squa | a | s (a) | b | s(b) | ||
| 1 2 3 4 5 |
1 & 2 1 & 2 1 & 2 4 & 5 4 & 5 |
77.46 62.72 28.22 22.18 41.51 |
4.18 3.50 2.61 0.61 1.62 |
0.85 0.76 0.44 0.85 0.74 |
-0.73 -1.64 -0.19 -0.47 -0.40 |
1.22 0.31 0.11 0.07 0.12 |
-0.12 1.40 -0.16 -0.15 -0.08 |
1.67 0.44 0.12 0.04 0.06 |
1=mersing, 2=perlis, 3=langkawi, 4= melaka, dan 5=kelang.
Fig.2. (a) Residual vectors of single band reflectance model using band 1,
(b) Residual vectors of single band reflectance model using band 2,
(c) Residual vectors of two band reflectance model using band 1 and band 2.
Fig.3.
Conclusions
The simplified approach of radioactive transfer model devised in this study has shown its potential for including quick bathymetric information. The results show that in-situ information at the time of satellite overpass are still needed if finer results are to be expected. Not only true samples are needed for the depth determination from satellite data, a knowledge of the possible 'error contributors' like bottom type, current flow, suspended sediments and etc., are also essential for accurate analysis.
For both models employing band 1 and 2 of SPOT-1 data, the difference between the computed and true depths are minimally observed for depth range of 1.7 to 7.9 meters in the single band models, and 1.1 to 14 meters for the two band model. In the former range, an average of 2.5 meter deviation is obtained and in later range an average of 111.5 meter depth deviation is observed. The tested models, however, exhibit a negative aspect for depth below or higher than the mentioned range; suggesting that the model does not comprehensively capable of modeling of deeper depth than the mentioned range.
References
- Gordon, H.R. and W.R.Mc Cluney (1985). Estimation of Sunlight Penetration in the sea for Remote Sensing. Applied Optics 14. pp. 413-416.
- Hammack, J.C. (1977). Lands at Goes to Sea. Photo grammar Engineering and Remote Sensing 43. 43. pp 683-691.
- Hallada, W.A. and Tanis (1984). Evaluation of Lands at TM for Shallow Water Bathymetry. Proceedings of 18th International Symposium of Remote Sensing on Environments, Paris, France.
- Polcyn, F.C. and D.R. Lyzenga (1979). Land sat Bathymetric Multi temporal Processing. Proceedings of 13th. Symposium on Remote Sensing on of Environment. Ann Arbor, MI. pp.1269-1279.