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         Geoplanning 
Vol 3, No. 2, 2016, 117-126                                                                                                                                                         Journal of Geomatics and Planning 

                                                                                                 E-ISSN: 2355-6544 
http://ejournal.undip.ac.id/index.php/geoplanning 

doi: 10.14710/geoplanning.3.2.117-126 

SATELLITE-DERIVED BATHYMETRY USING RANDOM FOREST ALGORITHM AND 
WORLDVIEW-2 IMAGERY 

M. D. M. Manessa a, b, A. Kanno a, M. Sekine a, M. Haidar c, K. Yamamoto a, T. Imai a, T. Higuchi a 

a Graduate School of Science and Engineering, Yamaguchi University, Ube, Japan 
b Center for Remote Sensing and Ocean Science (CReSOS), Udayana University, Indonesia 
c Center for Thematic Mapping and Integration, Geospatial Information Agency, Indonesia 

Abstract: In empirical approach, the satellite-derived bathymetry (SDB) is usually 
derived from a linear regression. However, the depth variable in surface reflectance has 
a more complex relation. In this paper, a methodology was introduced using a 
nonlinear regression of Random Forest (RF) algorithm for SDB in shallow coral reef 
water. Worldview-2 satellite images and water depth measurement samples using 
single beam echo sounder were utilized. Furthermore, the surface reflectance of six 
visible bands and their logarithms were used as an input in RF and then compared with 
conventional methods of Multiple Linear Regression (MLR) at ten times cross 
validation. Moreover, the performance of each possible pair from six visible bands was 
also tested. Then, the estimated depth from two methods and each possible pairs were 
evaluated in two sites in Indonesia: Gili Mantra Island and Panggang Island, using the 
measured bathymetry data. As a result, for the case of all bands used the RF in 
compared with MLR showed better fitting ensemble, -0.14 and -1.27m of RMSE and 
0.16 and 0.47 of R2 improvement for Gili Mantra Islands and Panggang Island, 
respectively. Therefore, the RF algorithm demonstrated better performance and 
accuracy compared with the conventional method. While for best pair identification, all 
bands pair wound did not give the best result. Surprisingly, the usage of green, yellow, 
and red bands showed good water depth estimation accuracy.  
 

Copyright © 2016 GJGP-UNDIP 
This open access article is distributed under a  

Creative Commons Attribution (CC-BY-NC-SA) 4.0 International license. 

 
How to cite (APA 6th Style): 

Manessa, M. D. M, et al. (2016). Satellite-derived bathymetry using random forest algorithm and worldview-2 imagery. Geoplanning: Journal of 

Geomatics and Planning, 3(2), 117-126. doi:10.14710/geoplanning.3.2.117-126 

 

1. INTRODUCTION  

Due to the limitation of costly and time-consuming bathymetry measurement, getting a dense or full 
coverage water depth data is difficult to achieve. Satellite derived bathymetry (SDB) is useful to efficiently 
densify (depend on image spatial resolution) the information of water depth in shallow water areas. In the 
case of a multispectral image, there are simple and applicable SDB methods such as linear regression of 
reflectance logarithm (Lyzenga, Malinas, & Tanis, 2006; Lyzenga, 1978; Paredes & Spero, 1983), the linear 
ratio (Stumpf, Holderied, & Sinclair, 2003), and Depth of Penetration Zone (Jupp, 1988). At the current 
state, the linear regression is the most common and widely used SDB (Flener et al., 2012; Kanno & Tanaka, 
2012; Liceaga-Correa & Euan-Avila, 2002; Yuzugullu & Aksoy, 2014).  

Unfortunately, Stumpf et al. (2003) showed a low accuracy estimation of SDB method using linear 
regression. The problem might be caused by the assumption of a linear relation between depth and water 
surface reflectance that sometimes does not hold. Especially when the following conditions exist: noisy 
satellite image, the dark bottom object in shallow water or vice versa, and high water attenuation. Non-
linear regression approach seems promising to improve the SDB accuracy. The non-linear regression of 
random forest (RF) algorithm shows a good performance in estimating a variable with non-linear condition 
(Knudby et al., 2013).  

OPEN ACCESS 

Article Info: 
Received: 11 August 2016 
in revised form: 18 September 2016 
Accepted: 19 September 2016 
Available Online: 31 October 2016 
 

Keywords:  
Satellite-derived bathymetry, 
Worldview-2, random forest, 
multiple linear regression 
 

Corresponding Author: 
Masita Dwi Mandini Manessa 
Graduate School of Science and 
Engineering, Yamaguchi University, 
Ube, Japan 
Email: 
masita@yucivil.onmicrosoft.com 
   

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The multispectral image used in this study is the high spatial resolution image of Worldview-2 (WV-2) 
imagery. Several studies, for instances Kerr (2011), Lee et al. (2011), Doxani et al. (2012), and Eugenio, 
Marcello, & Martin (2015), have been carried out on SDB using WV-2 imagery. Since WV-2 imagery has six 
visible bands then choosing the right band combination for SDB was also important. Kerr (2011) has 
revealed the best pair of WV-2 bands for the combination of linear ratio and MLR method. However, 
identifying the best pair for the linear reflectance and Random Forest algorithm for SBD was never done 
before.  

This study examined the usage of RF algorithm for SDB. As a comparison, the confessional SDB method 
using multiple linear regression (MLR) algorithms for multiple bands were analyzed. The accuracy change 
between both algorithms shows the performance of linear and nonlinear regression for SDB. Additionally, 
63 possible pairs from six visible bands of the WV-2 image was equally tested as an input for RF algorithm 
to identify the best pair band for SDB using RF algorithm.  

 

2. DATA AND METHODS 

2.1. Study Sites  

As shown in Figure 1, the study site was a shallow coral reef environment located in Indonesia. The Gili 
Mantra Islands is off the Coast of Lombok Island, and the Panggang Island is at north part of Jakarta Coast. 
The Gili Matra Islands are a Marine Natural Park including three islands: Gili Trawangan, Gili Meno, and Gili 
Air. Both sites are coral reef environment with clear water and good visibility.  

 
Figure 1. a. Panggang Island Worldview2 true-colour image (RGB 532); and b. Gili Mantra Islands 

Worldview2 true-colour image (RGB 532) (Digital Globe, 2012) 
 
 

 
 
 
 
 
 
 
 
 
 
 

2.2. Depth measurement data  

The bathymetry data of the Gili Islands were resulted from a collaborative effort between CReSOS 
(Center for Remote Sensing and Ocean Science, Udayana University—JAXA program), Yamaguchi 
University, and the Research Institute for Marine Research and Observation (Ministry of Marine Affairs and 
Fisheries Republic of Indonesia). While for Panggang Island, the data were measured by Center for 
Thematic Mapping and Integration, Geospatial Information Agency of Indonesia, Indonesia. For both sites, 
the measurement was carried out using a single beam echo sounder and Differential Global Positioning 
System (D-GPS). Since the depth measurement data was tide affected, the measurement depth was 
necessarily referred to mean sea levels (MSL). The converter was done by subtracting the measurement 
depth with at time tide. Moreover, the tidal data were collected from nearest tidal station.  

2.3. Image acquisition and processing  

In this study, the level 2 radiometric corrected of WorldView-2 imagery with six visible bands and two 
near-infrared bands were utilized. The imagery passed three steps of image pre-processing. The first step 
was sensor calibration from digital numbers to the units of band-averaged spectral reflectance or TOA (top 
of atmosphere) reflectance. The equations and calibration coefficients applied were based on the Digital 
Globe technical note about the radiometric use of WorldView-2 imagery (Digital Globe, 2012). The physical 

a b 

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units of band-averaged spectral radiance are W∙m−2∙sr−1∙µm−1. Secondly, the atmospheric and surface noise 
then TOA reflectance were corrected by applying Lyzenga et al.’s (2006) correction. Then, the formula of 
Lyzenga et al.’s (2006) atmospheric correction is written as: 

 

[1] 

Where  is the measured TOA reflectance in NIR 1 band,  is that average over the 

deep water pixels, and  is the slope of the simple regression line between the visible reflectance and 

NIR 1 reflectance for the deep-water pixels. While  is for NIR 2.   

Lastly, the relationship between radiance and depth was linearized to create the transformed 
reflectance ( ). Based on Lyzenga et al. (2006), the transformed reflectance ( ) is a linear value of 

reflectance and depth and written as: 

 

[2] 

Where  is the mean of surface reflectance deep water area for each band i. The for six visible 

bands are used as on input for MLR and RF regression model. 
 

2.4. Prediction Models 

2.4.1. Random Forest (RF) 

Random forests for nonlinear regression are formed by growing trees depending on a random vector 
such that the tree predictor takes on numerical values as opposed to class labels (Breiman, 2001). This non-
linear regression is a machine learning approach that belongs to the family of decision tree learning 
(Breiman, 2001). The goal of decision tree learning is to create a model that predicts the value of a target 
variable based on several input variables (Diesing et al., 2014). For estimating the water depth, the 
“random forest” function from random forest package of R software was used.  

 
2.4.2. Multiple Linear Regression (MLR) 

The multiple linear regression is (Lyzenga et al., 2006). The MLR analysis was conducted to depth as 
the dependent variable and the as the independent variables. Then depth estimation formula for 

WorldView-2 imagery with six visible bands is as follows:  

 

[3] 

where β0 is offset, βi is determined by a linear regression analysis using a set of depths measured with the 
linearized surface reflectance and n is a number of the band. In the case of MLR analysis, the water depth 
estimation is predicted using the “lm” function from basic package in R software.  
 

2.5. Band Pair or Combination 

Since WV2 have six visible bands, 63 different pairs (= 6 combinations one band + 15 combinations of 
two bands + 20 combinations of three bands + 15 combinations of four bands + 6 combinations of five 
bands + 1 combination six bands) could be used as an input for Eq. 3. We tested the performance of each 
pair to estimate the water depth using RF formula (see Figure 2).  

 

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Figure 2. Worldview-2 Image: a. Panggang Islands Image before correction, b. Panggang Islands Image after 
correction, c. Gili Mantra Islands Image before correction, d. Gili Mantra Islands Image after correction. 

(Analysis, 2016) 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 

a 

b 

c 

d 

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2.6. Cross Validation  

In order to further test the efficiency of each model, a cross-validation experiment was performed. In 
each round, the depth measured points were randomly selected, with 10% used as training data and 90% 
as test data. This cross-validation procedure was repeated 100 times. For each run, the model prediction 
accuracy were evaluated using two statistical key that explain in subsection 2.7. 

2.7. Model Validation  

The depth estimation accuracy of each model is measured by: 
 

 
[4] 

 

[5] 

Where h is measurement depth,  is estimated depth,  is the mean of depth measurement value, and n is 
the number of input data. 
 

3. RESULTS AND DISCUSSION 

3.1. Image Correction  

Lyzenga et al.’s (2006) image correction was applied to the evaluated Worldview-2 images of Gili 
Mantra Islands and Panggang Island. The NIR band was used to remove the noise from sea surface and 
atmospheric. Since the Worldview-2 have two NIR bands, both of them bands was used in this study as 
shown in Equation 1. Figure 2 shows the image of before and after correction. Besides correcting the image 
noise, this method also masks the depth and land areas, as shown in Figure 2b for Panggang Island and 
Figure 2d for Gili Mantra Islands.  

 
Figure 3.  Scatterplot of estimate depth versus actual depth for RF and MLR algorithm in Gili Mantra Island 

and Panggang Island. The red line axis is line of y = x. (Analysis, 2016) 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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Figure 4. Graph of Statistic value of RMSE and R2 for RF and MLR algorithm  
in Gili Mantra Island and Panggang Island (Analysis, 2016) 

 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

3.2. Random forest (RF) algorithm for SDB 

Figure 3 shows the result of the SDB performance for the RF compared with MLR algorithm in Gili 
Mantra Islands and Panggang Islands. In general, the estimation of depth shows better fitting in the shallow 
area with depth less than ± 7 m then gradually increase following the increse water depth. The higher error 
in deeper depth mainly occurred because of high noise in the deeper water generated by the high 
absorption and scattering of light, and as explain by Stumpf et al. (2003). 

In Figure 4, a statistical evaluation was carried out to qualitatively measure the performance of RF in 
compared with MLR algorithm. As a result, the error created from RF algorithm is smaller than MLR 
algorithm for the both evaluated sites. The RF algorithm for depth estimation accuracy is more accurate 
with less error with -0.14 and -1.27 m of lower RMSE and better fitting of 0.16 and 0.47 of R2 improvement 
for Gili Mantra Islands and Panggang Island, respectively. This result has further strengthened our 
conviction that in some case the depth had a complex’s relation with reflectance. 

Theoretically, the relation between depths and linearize surface reflectance should be linear but a 
noise could cause a non-linear condition (Lyzenga, 1978). Referring to the Gili Mantra Islands and Panggang 
Islands Site, the plotted value (Figure 5) between depths and linearize surface reflectance shows un-
linearity relations, where the relationship became scatter following the increases depth. The scatters 
relation in the deeper water areas because of reflectance or radiance received by multispectral satellite 
contain higher percentage of noise than bottom reflectance information due to high absorption and 
scattering. Then, it has limited the maximum detected depth of multispectral SDB.  This un-linear relation 
factor is potentially responsible for this different performance in both sites. Moreover, in Panggang Island, 
the pixels in different depth had almost the same value that might be caused by dark object in shallow 
depth or bright object in deeper depth. This fact became the main reason of poor estimation in Panggang 
Island.  

 
 

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Figure 5. The relation between depth and linearize surface reflectance for each band  
in Gili Mantra Island and Panggang Island (Analysis, 2016) 

 

 

3.3. Best combination bands of Random Forest (RF) algorithm for SDB 

Figure 6 shows the performance of RF algorithm under 63 possible combinations of Worldview-2 
bands for both sites. As a result, the rank of the best pair is varied between Gili Mantra Islands and 
Panggang Island. Thus, this result needs to be interpreted with caution as a following. Firstly, the SDB 
accuracy ranges between 0.746 – 1.779 m and 0.350 – 0.874 for RMSE and R2, respectively, in the case of 
Gili Mantra Island. While for Panggang Islands, the accuracy varies between 1.747 – 3.712 and 0.354 – 
0.858 for RMSE and R2, respectively. Secondly, in contrast with the previous study (Kerr, 2011), the best 
performance of RF was not given by the usage of all the visible bands. In the case of Gili Mantra Island, the 
best accuracy was achieved when four bands of coral, green, yellow and red (14.CGYR) were used. While 
Panggang Island site shows the best accuracy using three bands of green, yellow and red (39.GYR). 
Although six visible bands of WV-2 were expected to estimate the depth accurately, it was not predicted 
that the six bands would also give the best accuracy compared with less number of bands as an input. This 
is not particularly unexpected considering that some bands contain more noise or less bottom reflectance 
information than other, such as Red Edge bands having less bottom reflection information especially in the 
deeper depth due to high absorption value.  

Interestingly, for both evaluated sites the usage of band green, yellow, and red shows better 
estimation accuracy. Meanwhile, the other bands namely coastal, blue, and rededge had a tendency to give 
the adverse effect of poor estimation accuracy. As shown in Figure 5, even though the short wavelength 
namely coastal and blue band are sensitive to water depth and penetrate into the deeper water, the high 
noise is also included. This problem is an issue of WV-2 coastal band that claims to be useful for shallow-
water mapping.  

 

 

 

 

 

 

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Figure 6.  Graph of SDB estimation accuracy of RF algorithm of 63 combination bands.  
(Left) Gili Mantra Island and (right) Panggang Islands (Analysis, 2016) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The color bar is the RMSR in meter, and black dot is R2. Example: 01.CBYGRRed is 

combination number 1 consisting of Coral, Blue, Yellow, Green, Red, and Red Edge 

bands, for Gili Islands the RMSR is 0.8 m and R2 is 0.9.

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It is worth noting that this study has a few limitations. The first is a time gap between measurement and 
image recording dates; some morphological change might appear in the shallow water areas. The second is 
error created from measurement instrument; the single beam echo sounder generates error caused by 
inaccurate of average sound speed measurement, especially due to rapid movement of the boat or 
extreme morphological changes. Then, the measurement data on deeper depth will tend to have a high 
error. Thirdly, in the application of random forest algorithm, three hyper-parameters, i.e., mtry, sampling 
size, and node size should be optimized. Moreover, the random forest function (Random Forest package of 
R software) used in this study has an auto-tuning capability for mtry, but it does not consistently work well. 
Further works need to be performed to do the manual optimization.  

4. CONCLUSION 

In this study, non-linear model of Random Forest (RF) regression was tested to estimate the water depth 
of shallow coral reef. Also, the linear model of Multiple Linear Regression (MLR) was used for comparison. 
A cross-validation test comparing the accuracy of the both algorithms was performed for two coral reef 
sites of Gili Mantra Islands and Panggang Island using WorldView-2 (WV-2) imagery and corresponding in-
situ depth measurements. Considering the six visible bands of WV-2 images, 63 possible pairs were 
evaluated to identify the best pair as an input in estimating the water depth using Random Forest algorithm.  

The result of this study indicates that the nonlinear regression (RF) performed better than linear 
regression (MLR) in estimating the water depth. The RF regression is suitable for multispectral-based SDB, 
especially, when the relation between depth and linearized reflectance was far from linear due to the noisy 
image. Moreover, the best RF model for SDB was set when Green, Yellow, and Red bands have been 
utilized. This study only tested two sites with water in clear visibility. Subsequently, the RF performance for 
the different type of water might show a different result. Further studies, which take more sites into 
account, are suggested.  

5. ACKNOWLEDGMENTS 

The authors acknowledge support from the Indonesia Endowment Fund for Education (LPDP) by the 
Ministry of Finance. We would like to thank the Geospatial Information Agency of Indonesia for providing 
the Gili Mantra Islands’ as well as Panggang Island’s bathymetry and tidal data. This research was partially 
supported by a research grant of Kurita Water and Environment Foundation (No. 15B013). 

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