Automated Estimation of Coastal Bathymetry from High Resolution Multi-Spectral Satellite Images

Coastal bathymetry is the most essential tool for marine planning, monitoring and management, modelling, nautical navigation and scientific studies of marine environments. The techniques have been developed over the last decade to derive bathymetry using remote sensing technology with efficiently and low costly. Log linear bathymetric inversion model and non-linear bathymetric inversion model provides two empirical approaches for deriving bathymetry from multispectral satellite imagery, which have been refined and widely applied. This paper compares these two approaches by means of a geographical error analysis for the site Kankesanturai using WorldView-2 satellite imagery. In order to calibrate both models; Single Beam Echo Sounding (SBES) data in this study area were used as reference points. Corrections for atmospheric and sun-glint effects are applied prior to the water depth algorithm. The algorithm was tuned and both models were calibrated by performing the necessary algorithm with available single beam echo sounding data in the study area. The coefficients of standard R2 is estimated as 0.846 for log-linear and 0.692 for non-linear model. Log linear model performs better than the non-linear model. The model residuals were mapped and the spatial auto-correlation was calculated based on the bathymetric estimation model. A spatial error model was constructed to generate more reliable estimates of bathymetry by calculating the spatial autocorrelation of model error and integrating this into an improved regression model.  Finally, the spatial error model improved the bathymetric estimates of R2 up to 0.854 for log-linear and 0.704 non-linear model respectively. The Root Mean Square Error (RMSE) was calculated for the different depth ranges and also for all reference points. The overall accuracy for the log linear and the non-linear inversion model after the geographical error analysis is estimated as ±1.532 m and ±2.089 m for this study. The spatial error model improved bathymetric estimates than those derived from a conventional log-linear and non-linear technique although these methods perform very similar estimates overall.


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Abstract-Coastal bathymetry is the most essential tool for marine planning, monitoring and management, modelling, nautical navigation and scientific studies of marine environments.The techniques have been developed over the last decade to derive bathymetry using remote sensing technology with efficiently and low costly.Log linear bathymetric inversion model and non-linear bathymetric inversion model provides two empirical approaches for deriving bathymetry from multispectral satellite imagery, which have been refined and widely applied.This paper compares these two approaches by means of a geographical error analysis for the site Kankesanturai using WorldView-2 satellite imagery.In order to calibrate both models; Single Beam Echo Sounding (SBES) data in this study area were used as reference points.Corrections for atmospheric and sun-glint effects are applied prior to the water depth algorithm.The algorithm was tuned and both models were calibrated by performing the necessary algorithm with available single beam echo sounding data in the study area.The coefficients of standard R 2 is estimated as 0.846 for log-linear and 0.692 for non-linear model.Log linear model performs better than the non-linear model.The model residuals were mapped and the spatial auto-correlation was calculated based on the bathymetric estimation model.A spatial error model was constructed to generate more reliable estimates of bathymetry by calculating the spatial autocorrelation of model error and integrating this into an improved regression model.Finally, the spatial error model improved the bathymetric estimates of R 2 up to 0.854 for log-linear and 0.704 non-linear model respectively.The Root Mean Square Error (RMSE) was calculated for the different depth ranges and also for all reference points.The overall accuracy for the log linear and the non-linear inversion model after the geographical error analysis is estimated as ±1.532 m and ±2.089 m for this study.The spatial error model improved bathymetric estimates than those derived from a conventional log-linear and non-linear technique although these methods perform very similar estimates overall.Index Terms-Bathymetry, Remote Sensing, Regression Model, Spatial Error Model.

I. INTRODUCTION
Bathymetric information is of fundamental importance to coastal and marine planning and management, nautical navigation, and scientific studies of marine environments.Traditional bathymetric charts are based on individual soundings accumulated during decades of ship-borne surveying operations.Ship borne surveys with single-beam or multi-beam echo sounders can operate to depths in excess of 500 m by sensing and tracking acoustic pulses.However, mapping shallow water bathymetry from conventional methods of employing ships or boats with sonar is a quite an expensive task and comparatively inefficient.Many shallow water areas are not accessible by hydrographic ships due to rocks, coral reefs or simply the shallowness of the water.Monitoring navigation channels for shipping traffic safety and mapping underwater sand bars, rocks, shoals, reefs and other hazardous marine features relies on accurate and upto-date water depth measurements [1].
With the expansion of coastal modelling, monitoring and marine economic activities, the accurate bathymetry of near shore regions became to play a vital role to describe the physical features of the sea bottom and adjoining coastal areas [2].Then, the technology was enhanced to use active or passive remote sensing from aircraft and/or satellites.In recent decades, airborne bathymetric LiDAR (Light Detection and Ranging) systems have been developed to map shallow coastal waters.While maximum penetration of LiDAR systems is heavily dependent upon water clarity, these systems commonly achieve depth measurements of up to 30 m, with 4 m spatial resolution and 20 cm vertical accuracy.Though, these airborne bathymetric LiDAR systems provide a rapid and precise means for mapping shallow coastal waters, their use is inadequate by the high cost of operations and logistical difficulties.The feasibility of deriving bathymetric estimates from remote sensing imagery was first demonstrated using aerial photographs over clear shallow water [3].The technique has been expanded to include the use of multi-spectral satellite imagery including Land sat [4], [5], [6], IKONOS [7], and Quick Bird [8], [9] images.The main advantages over the conventional echo sounding methods are including the wide data availability, surface coverage, and high spatial resolution.Furthermore, the only requirement is that remotely sensed images need to be carefully calibrated to ensure the accuracy of extracted depth information [2].In 2009, Digital Globe launched the World View-2 (WV-2) satellite, which collects 1.84 m resolution images and includes four new color bands (coastal, yellow, red edge and NIR2) along with the four common bands.Further, the greater clear-water depth penetration of the newly The Empirical method provide two approaches for deriving bathymetry from multi spectral satellite imagery and these two bathymetric models are widely used.The method that was used to derive bathymetry from variable bottom types is an adapted version of the linear transform bathymetry algorithm originally developed by [3], [6] and nonlinear transform bathymetry algorithm developed by [10] was applied to the world view II scenes to match with the available bathymetric reference dataset.
Assuming that the ratio of bottom reflectance between two spectral bands is constant for all bottom types within a given scene, [3] derived a model (Log linear bathymetric inversion model) for two (and/or multiple) spectral bands as follows: where  0 ,   (i = 0, 1, 2, …..,N) are the constant coefficients, N is the number of spectral bands, (  ) is the remote sensing radiance after atmospheric and sun glint corrections for spectral band   , and  ∞ (  ) is the deepwater radiance for spectral band   .
Calibration of Log-linear Inversion model for 2 bands as follows; To minimize depth errors, wavelength bands with the smallest attenuation are used both in the log-linear and nonlinear bathymetric inversion models.The multiple linear regression analyses should perform to derive the coefficient.
Lately [7] proposed a non-linear bathymetric inversion model based on log-transformed band ratio: where  1 ,  and  0 are constant coefficients for the model.( 1 ) , ( 2 ) are the remote sensing radiances (after atmospheric and sun glint corrections) for spectral bands  1 and 2 .
The Non-linear Inversion Model was calibrated based on Levenberg-Marquardt Method.
Levenberg-Marquardt: elegant combination of Newton's method and the steepest descent method.The merit function is as follows; where,  -is the number of points with a known depth,   -is the known (observed) depth for point , ̂ -is the estimated depth from the inversion model based on the spectral values at point , optimal values for the model parameters minimize the merit function  2 , the value   is a measure of the error in measurement   .In this project, the high resolution satellite images (World view-2) used to derive the high quality shallow water bathymetry along the Coastal belt of Kankasanthuai area to overcome the challenges associated with estimating depths for water shallower than 20 m.Here, we apply both log linear model and non-linear inversion model for derivation of depths data.The standard least-square regression approach was used to calibrate the log-linear model and Levenburg-Marquardt algorithm was used to calibrate the non-linear bathymetric inversion model.
The objective of the study was to compare bathymetric estimates derived from above two empirical bathymetric models through a geographical analysis of the model errors for the site around Kankesanturai.The initial processing steps include the pre-processing, atmospheric correction, glint/cloud correction of the selected high resolution satellite image of world view II.In this study, Single beam echo sounding data is used for calibration the both log linear bathymetric inversion model and non-linear bathymetric inversion model.The spatial error model was constructed from the initial bathymetry estimates and the Moran's I values.The study of errors, in particular the spatial distribution and geostatistical properties of the model residuals, can reveal critical insight into model performance.Geographical or spatial analysis refers to a collection of techniques and statistical models that explicitly use the spatial referencing associated with each data value or object that is specified within the system under study [11].

II. BATHYMETRIC MAPPING USING MULTI-SPECTRAL SATELLITE IMAGES
The physical principle of extracting the bathymetry by using multi spectral imageries is that when light passes through the water, it becomes attenuated while interacting with the water column.The Light attenuation and penetration is wave length dependent.Shallow water areas appear as bright in the image as it's less absorbed the reflected light and deep areas appear as dark since it's absorbed much more reflected lights.
The observed radiance in shallow water can be expressed as [12], [13] : Where, k() is the attenuation co-efficient, z is the depth, Lobs is the radiance observed at the sensor's detector, Lb is the radiance contribution from the bottom, and Lw is the observed radiance over optically deep water with no bottom contribution.

III. STUDY AREA
The Kankesanthurai harbor is to be developed as the third international harbor after Colombo and Ruhunu Magampura.Kankesanthurai is the main port situated in Jaffna District Northern Province of Sri Lanka and it is the nearest port for all eastern ports in India as well as for Myanmar and Bangladesh.Rapid development was started in war affected areas by government to uplift the living conditions of the civilians.Under this project provides hydrographic data to facilitate development of coastal passenger transport and fishing activities.Therefore, the understanding of the sea bottom in near shore is important for the safety of navigation and fishing activities.Hence, the study also focused to this area to accomplish the echo sounding data availability of the same time period together with the satellite data as it's a key factor to avoid the blunders when it determines the constant coefficients for deriving the depths data.The spatial resolution is 0.46m for panchromatic and 1.84m for multi-spectral bands and using 11 bit data in eight spectral bands.The wave length of the eight spectral bands is as follows.
• Coastal (400-450 nm), Blue (450-510 nm), Green (510-580 nm), Yellow (585-625 nm), Red (630-690 nm) , Red edge (705-745 nm), NIR1 (770-895 nm) m, NIR2 (860-1040 nm) V. IN SITU BATHYMETRIC DATA Depths are normally measured using "DESO 30" dual frequency Single-Beam Echo Sounder (SBES) during the period of Sep.2015-Jan.2016as per the IHO S-44 Order 1b standard.SBES was calibrated by a bar check to correct for errors in the speed of sound in the water column, and to set the correct transducer draught.The latter is to ensure that the instrument records the depth below the sea surface and not below the transducer.A bar check was conducted to ensure consistent data quality.Differential Global Positioning System (DGPS) is widely used to fix vessel position during hydrographic surveys.SxBlue II -B positioning system is used to obtain the DGPS correction to increase the precision of horizontal position.A sound velocity probe (RESON SVP 40 sound velocity prob) device is used for measuring the speed of sound, specifically in the water column of these hydrographic surveys.
Sea level (tide) measurements of height and time are required to reduce collected soundings to Lowest Astronomical Tides (LAT) as per the standards of International Hydrographic Organization.The depths obtained from the DESO 30 respect to the water level are required to reduce to the proper vertical datum.Water level was observed in 15 m interval throughout the survey period of the day.The Lowest Astronomical Tide (LAT) datum was used as vertical datum since this data use for navigation.The processing of hydrographic survey data involves the removal of erroneous data, and through the selection of valid data, the preparation of a 'cleaned' data set for further processing, or for the generation of required products (e.g.sounding sheets) for subsequent analysis.The depth profiles acquired digitally were compared with analogue echo profiles to eliminate digital signal interpretation errors.Cross lines were run appropriately across the survey lines to maintain quality of the data.Unfortunately, within the study area these data are limited to 10-13 m depth, lacking much of the depth range of interest (0-20 m) and geographical extent.These data were used as referenced data for the calibration of the log-linear inversion model and the nonlinear inversion model.Further, the performance of the both bathymetric inversion models was evaluated using the SBES data which were not used to calibrate the models.

VI. METHODOLOGY
Satellite images were geo referenced with 6 collected Ground Control points (GCPs) to Universal Transverse Mercator (UTM) Zone 44 projection referenced to the World Geodetic System 1984 (WGS84) ellipsoid.Atmospheric corrections on the images have been performed using the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) method [14] in i.atcor module GRASS GIS software.6S is a basic RT code used for calculation of lookup tables in the MODIS atmospheric correction algorithm.It can work in both scalar and vector modes.The 6S code is based on the method of successive orders of scattering (SOS) approximations and this model predicts the surface reflectance   (Top of Canopy: TOC) from the reflectance   obtained at the Top of Atmosphere (TOA), using information about the environment surface reflectance (clear water) and atmospheric conditions.Furthermore, 6S estimates the percentage of direct-diffuse-environmental normalized irradiance at ground level.This diffuse irradiance, generated mainly by the Rayleigh's scattering, has more importance in the blue spectral channels [14].
The sun glint correction was performed by using an approach proposed by the [15].
Where;   -is the regression slope,   () ′ -the sunglint corrected pixel brightness in band I,   () -the pixel value in band i , () -the pixel NIR value,   ()the ambient NIR level.
For each band, linear regression is made between the NIR radiance and the band radiance, using all the pixels in the selected regions.Deep water correction is performed to remove the subsurface volumetric radiance from total upwelling radiance recorded by remote sensor.Assuming that subsurface volumetric radiance in shallow water is the same as that of adjacent deep water, then optically deep water radiance recorded by the remote sensor can be used to correct the subsurface volumetric radiance in shallow water [3].The ENVI and GIS tool has been incorporated for preprocessing, atmospheric correction & de-glinting.

VII. MODEL CALIBRATION
To estimate the absolute depths, the both bathymetric inversion models need to be calibrated using the known true depths as reference points.Then, the calibrated inversion models are applied for the multi-spectral images to compute the depth at each pixel.The coastal blue, blue, green and red bands of the worldview-2 images and 1000 single beam echo sounder points which are reduced to Lowest Astronomical Tide (LAT) were used as reference depths points for calibration both log linear and non-linear inversion bathymetric models to derive bathymetric grids of the entire study area.Firstly, a log-linear model was calibrated using the standard multiple regression approach.
[3], [5], [6], [12] log linear algorithm facilitate for deriving bathymetry from a single spectral band as follows; =1 (7) where, Z=water depth, N=number of spectral bands L(λ i ) =observed radiance for band I after atmospheric and sun glint correction, L ∞ (λ i )= deep water radiance of optically deep water for band I, a 0 , a 1 , … … .a N =empirically determined coefficients This equation is re-arranged for coastal blue and blue spectral bands of Worldview-2 multi-spectral images to perform a log-linear bathymetry inversion model as follows; a 0 , a 1, , a 2 Co-efficients were derived by performing the multiple linear regression analysis for calibration.Parameters of log liner model fine-tuned in calibrations were used to derive bathymetry.
The non-linear inversion model proposed by [7] used for determine the three model parameters of m0, m1 and n.Then, calibrated the non-linear inversion model using the Levenberg-Marquardt algorithm.
Model residuals were mapped as a simple way to visually examine the spatial distribution of the performance of the both log linear and non-linear bathymetric estimations.Residuals were calculated as the difference between the derived depth values and the validation echo sounder bathymetry data.A point shapefile was produced to depict the model residuals of the study area and interpolated with kriging method.Spatial autocorrelation of the model residuals was measured via the Morans I static using the GeoDa software.A scatter plots were constructed to investigate the univariate Moran's I, with the spatially lagged residuals on the vertical axis and the residuals on the horizontal axis.Then a spatial error model was constructed from the initial bathymetry estimates and the Moran's I values.
u i = ρ ∑ w i,j u j + e i (10) where;  0 and  1 are empirically-defined coefficients,  is the Moran's I,  , is spatial weight matrix,   is sum error and   is error term [11].
The performance of the both bathymetric inversion model was evaluated using the independent 4167 Single Beam Echo Sounder (SBES) measurements that were not used to calibrate the model parameters.Final bathymetric estimates were derived by applying the regression equation and beta coefficients to the initial estimates of bathymetry and locally-calculated estimates of Moran's I for the model residuals.

VIII. RESULTS AND DISCUSSION
The procedure evolved to estimate the coastal bathymetry from high resolution multi-spectral satellite images using log linear inversion model.The coefficients were derived by performing the multiple regression analysis and the estimated coefficients are shown in Table I.The parameters of the non-linear inversion model were obtained by applying the Levenburg Marquardt method are shown in Table II.The performance of the log-linear inversion model and the non-linear inversion model is evaluated by comparison with each other.The model predicted depths were plotted verses the ground truth depths and the scatter plots shows that both log linear and non-linear inversion models produce acceptable depth estimates up to 20m.The coefficient of determination value  2 of bathymetry estimates derived from a standard error model when compared to the validation echo sounder data.Coefficient of determination values   of bathymetry estimates derived from a standard error model when compared to the validation echo sounder data.In this study, the standard model  2 for log-linear model is calculated as 0.846 and for non-linear model is calculated as 0.692.The log linear inversion model offers the good correlation between the derived depths and the sounding data than the non-linear inversion model as per their performances.where n is the number of depth points used.
The prediction residuals were calculated as the difference between the derived depth values and the validation echo sounder bathymetry data.The prediction residuals of both models are displayed in figure in histograms as follows.The spatial autocorrelation plots for the residual datasets as follows.Model residuals were mapped and Moran's I value was calculated for both log-linear and non-linear inversion models by separately in this study area.where, n= number of depth points used for validation.The statistical analysis is performed to check the quality assurance of the data and to assess the absolute accuracy of the results.The depth uncertainties were estimated for finally derived bathymetric data for both log-linear and nonlinear inversion model.The Root Mean Square Error (RMSE) was calculated for the different depth ranges and also for all reference points.The magnitude of the prediction error increases with depth for both the log-linear and the non-linear inversion models.Overall RMSE for log-linear and the non-linear inversion models were ±1.532 m and ±2.089 m respectively.

IX. DISCUSSION
Recently, the large number of studies have been done for deriving the bathymetry from the multi-spectral satellite images based on the spatial resolution of the image.Several techniques have been developed from time to time period for converting pixel values into depth estimates.The loglinear inversion model developed by [3] and the non-linear model developed by [7] is commonly used for deriving bathymetry from the satellite images.We have applied the multiple linear regression analysis with necessary algorithms for automatic calibration of log-linear inversion model and the Levenberg-Marquardt method for non-linear model for deriving bathymetry.The results show the log linear model is performing better for the study area than the non-linear inversion model.The non-linear model produces slightly more accurate depths for the areas deeper than 10-15 m.Then modelled the spatially structured error component and the spatial error models improved the final estimate bathymetry of both log-linear and non-linear inversion model and the prominent improvement can be seen in the non-linear inversion model.Further, it seems that the derived depths are significantly match with the nautical information of BA chart 1584 for both inversion models.In this study in Kankesanturai area, the results illustrated that depths can be derived from the 2m spatial resolution World View II images for log linear model with the vertical accuracy of ±1.532 m and for non-linear inversion model with the vertical accuracy of ±2.089 m up to 20m depths.These accuracy does not match with the standards of International Hydrographic Organization for the purpose of safety of navigation.But, the bathymetric information retrieval from the satellite images are vital important for identifying the morphology of the sea bottom specially in unsurvey areas and remote areas where shipborne surveys are difficult to carry out.

X. CONCLUSION
The comparison of the empirical log linear and non-linear inversion model reveals that both methods are having overall a similar bathymetric estimation.Further, the empirical method provides a better estimation for deriving bathymetric information from the multi spectral satellite images.In this study, although the log linear model appeared to perform better than the non-linear method, both were subject to the same depth limitations.The mapping of model residuals and the calculation of spatial autocorrelation, emerged as useful tools for the exploration of error in bathymetry estimation models and the spatial error models improved bathymetric estimates derived from both methods.The results specified that this technique provide a quick and reliable estimation for deriving shallow water bathymetry up to 15m depths.This technique can be applied to national hydrographic offices for the purpose of chart adequacy to evaluate the bathymetry of available nautical charts.Further, the environmental conditions of the image such as water clarity, cloud cover and sun glint are needed to be considered as it's directly affect to degrade the accuracy of the retrieval depths.This method can be applied for the applications of habitat mapping, Mari-culture, chart adequacy, coastal research, modelling and marine spatial planning etc.Also the bathymetric retrieval from the high resolution multispectral satellite images adore the advantages of low-cost, high spatial resolution and large area coverage.Finally, Satellite derived bathymetry using remote sensing techniques is a valuable tool for coastal monitoring and research in shallow areas.Also this technique can be used as a reconnaissance tool to get the shallow water bottom information efficiently and at low costly especially for the remote areas where the acoustic surveys are limited.

Fig. 3 .
Fig. 3. Spatial Distribution of independent depth Points used in Models Evaluation

Fig. 4 .Fig. 5 .
Fig. 4. Scatter plots of estimated depths from log-linear inversion model versus the ground truth depths

Fig. 14 .Fig. 15 .
Fig. 14.Scatter plots of estimated depths derived from log-linear inversion and spatial error model versus the ground truth depths

TABLE I :
ESTIMATED COEFFICIENTS FOR LOG-LINEAR INVERSION MODEL

TABLE II :
BEST FIT PARAMETERS FOR NON-LINEAR INVERSION MODEL

TABLE III :
COMPARISON OF STANDARD MODEL R 2 FOR LOG-LINEAR AND NON-LINEAR INVERSION MODELS

TABLE IV :
COEFFICIENT OF DETERMINATION VALUES   OF BATHYMETRIC ESTIMATES DERIVED FROM A STANDARD AND A SPATIAL ERROR MODEL WHEN COMPARED TO THE VALIDATION ECHO SOUNDER DATA