情報地質 第26巻 第2号 084-085頁 2015年
Geoinformatics, vol.26, no.2, pp.084-085, 2015

Extrapolating near-shore depth using geographically weighted regression ofmulti-spectral satellite images with consideration of bottom class types
Poliyapram VINAYARAJ *, Venkatesh RAGHAVAN *Shinji MASUMOTO** and Go YONEZAWA** Graduate School for Creative Cities, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku,Osaka 558-8585, Japan. E-mail: vinay223333@gmail.com.
** Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan.

Key words ：Ggeographically weighted regression (GWR), Near-shore depth,
Multi-spectral images, Landsat 8, RapidEye.

1. Introduction
Estimation of near-shore depth from satellite
imageries have been discussed in the last two decades.
Optical remote sensing imagery offers a cost-effective
alternative to echo sounding and LiDAR surveys toderive high density bottom depth estimates for coastalwater. Multi-spectral band linear regression algorithms
are most common practiced to estimate depth fromsatellite imagery. The performance of conventional global
model is limited when the bottom type and water quality
vary spatially within the scene. Recently to address theheterogeneity of the bottom type and water quality, aGeographical Linear Regression model (GWR) model wasintroduced (Haibin et al., 2013). Further, this study
made aims to extrapolate near-shore depth using
coefficients derived by GWR model with due
consideration to bottom class types.

2. Materials and Methods
Two satellite imageries (Landsat 8 and RapidEye)and with different spatial and radiometric resolutions
are used to estimate depth from near-shore area atPuerto Rico. The in-situ depth collected from NOAA isused to calibrate the depth estimates by GWR model.
2.1 Correction and log transformation
In comparison to existing methods, we utilize
infrared band to correct the atmospheric and water
surface components from the image and assume that thecorrected bands are linearly related to the water depth.
For Landsat 8 available Short Wave Infrared band (1.57– 1.65 µm) and for RapidEye Near-infrared band (0.76 –0.85 µm) were used. The equation for correction isfollowing below (Vinayaraj et al, 2014)
X(λ)i = log (L λi α0  α1 (L λi I )) / L λiWhere, X(λ)i log transformed radiance after correction,
L λi is the radiance of the band to be corrected, α0 isintercept, α1 is slope of regression and L λi I is theradiance of the band used for correction.
2.2 Classification of the study area
The study area is classified in to different classes
according to the variation of the reflectance from bottom

types and water quality. The log-transformed bands areused to classify by maximum likelihood classification
method.
2.3 Estimating coefficients for each class from GWR
model.
For improving depth retrieval in complex andheterogeneous marine environments, the spatial
non-stationarity in the image scene was addressed bythis method. Similar to the kernel regression method,
the GWR model uses a window to define the local
neighborhood, the equation is written as follows,
hj = β0j + β1j X(λ)1j + β2j X(λ)2j + …….+ βnj X(λ)nj
Where, j is the respective pixel, therefore coefficients foreach pixel ( j) was derived by assigning a fixed bandwidth.
The bandwidth represents the size of the kernel used forregression. The points close to the centroid point wereweighted more heavily in the regression process thanthose points far away from the centroid point.
Implementation GWR model carried out by GRASS GIS
open source software (http://grass.osgeo.org/) to estimate
coefficients (intercept and slope of multiple linearregression) for each pixels. Further, the coefficients are
estimated for each class by averaging the coefficients ina particular class. These coefficients applied to
extrapolate depth for other region where in-situ dept is
not available

3. Results and discussion
The evaluation of the results derived from theproposed method carried out by correlation coefficients(R), coefficient of determination (R2) and RMSE shows thatthe estimation accuracy is good. The depth results
derived by the proposed method is compared with thedepth results derived by conventional global multiple
linear regression also show that the results are reliable
and better (Table 1).
Fig 1 and Fig 2 show that both global model andproposed model are good. Fig 3 and Fig 4 show that thehistogram of the proposed model is closer to zero,meaning that the difference is less compared to globalmodel.

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Table 1. Comparing the results between proposed method and global model.

Data

Global model

Proposed method

RR2RMSER

R2RMSE

Landsat 8

0.85

0.72

4.02

0.87

0.76

4.47

RapidEye

0.82

0.68

4.36

0.85

0.72

4.27

Figure 1. Histogram of in-situ depth, depth map derived

Figure 2. Histogram of in-situ depth, depth map derived

from proposed method (GWR model) and global

from proposed method (GWR model) and global

model from Landsat 8 data.

model from RapidEye.

Figure 3. Histogram of the difference map.
Difference calculated between in-situ depth andestimated depth respectively from Landsat 8 data.

4. Conclusion
GWR model is very efficient to estimate near-shore
depth from the optical remote sensing images. But thedensity of the in-situ depth data is potential to impact
the accuracy of the results. Therefore, this study
demonstrated a new depth extrapolation method fromclass based coefficients. In-situ depth for a small region
was used to estimate coefficients considering bottom
types and further these coefficients used to estimate
depth from where no in-situ depth available.

Figure 4. Histogram of the difference map.
Difference calculated between in-situ depth andestimated depth respectively from RapidEye data.

References
Haibin Su, Hongxing Liu, Lei Wang, Filippi A. M.,
Heyman W. D. and Beck R. A. (2013) Geographically
adaptive inversion model for improving bathymetric
retrieval from satellite multispectral imagery. IEEE

transactions on Geoscience and Remote Sensing,vol.52(1), pp.465-476.
Vinayaraj P., Raghavan V., Masumoto S., Glejin J. andManessa M. D. M. (2014) Investigation of algorithm toestimate shallow water bathymetry from Landsat-8images, Proc. Int. Symp. GIS-IDEAS 2014, pp.465-470.