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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Remotely sensed imagery is proving to be a useful tool in estimating water depths in coastal zones. On the other hand, many coastal zone studies in the southern part of the Caspian Sea are only concerned with areas of shallow water and would benefit from easily updated bathymetric estimates. In this study, we tested three different methods for extracting bathymetry information from Landsat 5 data in the southeastern Caspian Sea, Iran. The first method used was a single band algorithm (SBA), utilizing either blue or red bands. The second method was principal components analysis (PCA), and the third method was the multi-layer perceptron (back propagation) neural network between visible bands and one output neuron (bathymetry). This latter MLP-ANNs method produced the best depth estimates (r = 0.94). The single band algorithm utilizing a red band also produced reasonably accurate results (r = 0.66), while the blue band algorithm and PCA did not perform (correlation between the estimated and measured depths 0.49 and 0.21, respectively). Furthermore, the shallow waters have negative influences on the accuracy of bathymetric modeling, thus the correction of data in these shallow waters is challenged by the presence of continental aerosols, bottom reflectance, and adjacency of land.

Mapping shallow water bathymetry from ships by sonar is a quite an expensive task. Many shallow water areas are not accessible by hydrographic ships due to rocks, coral reefs or simply the shallowness of the water. Active or passive remote sensing from aircraft and/or satellites could be the tools to solve the problem [

There are different methods for retrieving water depth from remote sensing data. For example, Lyzenga [

Using of a physics-based approach that allows to map both water depth and bottom type simultaneously has been proposed by several authors [

Unfortunately, there is not much

Three different methods were tested for retrieving water depth from Landsat 5 TM data. Firstly, we used a single band algorithm calibrated against known depths. The algorithm [

The second procedure utilizes several bands of imagery and principal components analysis (PCA). This method is analogous to a multi-band algorithm that accounts for varying attenuation coefficients for different bottom types as it calculates water depth, unlike the single band algorithm [

The third procedure utilizes MLP to perform a regression analysis between input variables (visible bands) and one dependent variable with the output containing one output neuron (bathymetry) [

The different stages of methodology have been shown in

There are two very important procedures that must be undertaken prior to bathymetric analysis. First, the image must be geometrically registered so that corresponding pixels in the entire image refer to exactly the same place on the ground. Resampling was done with a set of ground control points to make the image match a base map. The second pre-analysis procedure involved removal of random noise and stripping. Both the single band algorithm and the PCA method are sensitive to random noise and striping within the raw imagery. Therefore, the image has been enhanced with a low-pass (mean) filter.

The algorithm used for depth estimation was following:

If we assume that the actual observed radiance (

By first calculating the transformed radiance values and then regressing them against control points of known depth, all of the variables in the

The transformed radiance values were calculated by taking the values from blue and red bands in SBA algorithm, subtracting

Principal components analysis (PCA) is related to factor analysis and can be used to transform a set of image bands such that the new bands (called

Because the PCA requires that input files be of a byte/binary format, transformed blue, green and red bands stretched to a value range of 0–255. Then, to make analysis more accurate, the land areas were masked for all three stretched images and use the results as the input files for the PCA. The first component has been produced using forward T-Mode PCA showing the sources of variation in the data set. PCA method assumes that change in depth explains the most variance and other factors, such as a changing bottom type, will be secondary sources of variation [

We used MLP to perform a regression analysis between input variables (visible bands) and one dependent variable with the output containing one output neuron (bathymetry). The multi-layer perceptron used in the back-propagation (BP) learning algorithm is one of the most widely used neural network models. Research indicates that a three-layered BP network can approximate any polynomial function, then the used BP network contains one input layer (three nodes), one output layer (one output neuron) and one hidden layer (six nodes). The values of the output-predicted image is the activation level of the output layer node (scaled to the original data range), _{jk}_{j}

The forward and backward passes continue until the network has “learned” the characteristics of pattern. The main training parameters consist of learning rate (the change rate of the weights) between 0.01 and 0.2, momentum factor (0.5 and 0.6) and sigmoid function constant “

There are two main assumptions in the presented methodology:

The single band algorithm (SBA) assumes that the transformed blue band corresponds directly to water depth, while PCA assumes that the first component using all three transformed bands corresponds to water depth.

Assuming that known deep water should have virtually zero radiance values in the blue band, any reflectance registered must be due to scattering.

For estimating

After regressing the transformed blue and red band

Regressing the first component of PCA and known depths (

The outputs from the neural network are obtained by fuzzying the signals into values in the range of 0–1 with the activation function and then scaled to the original data range (

Neither the true color or false color composite image nor any of the original bands can be used as an index of depth without some further processing.

In relatively clear waters, light penetrates the deepest in the blue part of spectrum and information in the blue band can be used for bathymetry estimation. However, in coastal and inland waters, both colored dissolved organic matter and phytoplankton absorb light strongly in the blue band. Thus, the blue band provides information about the optically active constituents in water rather than allows to estimate the water depth. This explains also the low correlation (

The single band algorithm and many other methods require extensive ground truth information. This method used a single band algorithm and assumed a constant water attenuation coefficient throughout the blue and red bands. To assume otherwise would have required more ground truth knowledge about bottom type than was available. When such data is available, there are a number of algorithms that might be used to effectively isolate changes in depth from changes in other factors. When not available, the single band method works well as a rough estimate of bathymetry, as our analysis has shown.

The second method used principal components analysis (PCA) in an attempt to adjust for varying water attenuation coefficients without additional ground truth data. This procedure is based on the assumption that the first component result of PCA, which explains most of the variance in the data set, will be a depth-dependent variable that is independent of other sources of variation such as bottom type. After producing the first component image and calibrating it to known depths, we compared the results to the algorithm method. The PCA method produces a depth-dependent variable (independent of bottom type) without ground truth data. The first component of PCA, using the three TM bands of imagery, should approximate relative water depth given the assumption that depth explains the most variance between two or more bands of information.

The third method is based on nonlinear optimization techniques and machine learning methods such as artificial neural networks (ANNs) that provide an interesting alternative to examine complex coastal waters and to handle multivariate data. Models based on these methods determine the output values (e.g., the bathymetric values) from input data (e.g., water reflectance at various wavelengths) through nonlinear multidimensional parametric functions. The determination of the model parameters, as well as the assessment of the model performance, rely on a reference data set.

From the methods tested by us, the MLP-ANNs method seems to be performing the best as it produces the highest correlation (r = −0.94) with the

Radiometric resolution of previous Landsat sensors is just eight bit. This means that the whole range between the darkest objects (usually water) and the brightest objects (clouds, snow) has to be described with only 256 gray levels. Just a few levels can be used to describe the whole variability in water leaving signal. Nevertheless, our results show that rough estimates of water depth can be produced from Landsat data. Landsat 8 was launched recently and the launch of Sentinel-2 is planned soon. Although both are again designed for land applications, they will still provide a better platform for bathymetric mapping. In fact, bathymetric retrieval from the new generation multi or hyperspectral imagery is very feasible because of the very high spatial resolution capabilities and significantly improved radiometric resolutions of the optical remote sensing images and the reliability of results due to the frequent presence of optimal clear waters. In such settings, a reduced set of measured elevation can be effectively used to derive a continuous and accurate DEM based on empirical approaches [

The complexity of coastal waters, as well as the atmosphere above, requires more complex algorithms capable of handling bathymetric modeling. The atmospheric correction process is applied to remove the effects of the atmosphere that contribute to the signal measured by a satellite sensor. The objective of this process is the discrimination, from top-of-atmosphere radiance, of the signal emerging from the sea carrying information on the materials suspended and dissolved in seawater. However, several studies focusing on water quality remote sensing using the Landsat sensors [

Also, the shallow waters have negative influences on the accuracy of bathymetric modeling. We have repeated methodology for two clusters (known depths less and greater than 5 m, which is almost 15 feet). As, the values less than 5 m are removed, the coefficient of determination increases. Therefore, the shallow waters lead to some errors in methodology. Unfortunately, there is not enough data about optically active constituents (OACs) in this region. The correction of data in these shallow waters is challenged by the presence of continental aerosols, bottom reflectance, and adjacency of land. Minimizing these perturbing effects, which generally are site specific, requires knowledge of the regional aerosol and bottom optical properties. Specifically, effects of continental aerosols are minimized by properly accounting for their scattering phase function and single scattering albedo; the increase in radiance due to bottom reflectance can be removed through iterative processes knowing the water depth and spectral reflectance of the seabed, and the adjacency effects are minimized by determining the reduction in image contrast as a function of the aerosol and of the land reflectance [

Landsat series sensors were not designed for water studies. For example, the radiometric resolution of previous Landsat sensors is merely eight bit. This means that the whole range between the darkest objects (usually water) and the brightest objects (clouds, snow) has to be described with just 256 gray levels. Only a few levels can be used to describe the entire variability of the water leaving signal. Nevertheless, our results show that rough estimates of water depth can be produced from Landsat data. Landsat 8 was launched recently and the launch of Sentinel-2 is planned in 2014. Although both are again designed for land applications, they will still provide a better platform for bathymetric mapping as their radiometric resolution, and signal-to-noise ratio and other technical parameters are more suitable for aquatic remote sensing.

In this research, we produced images of absolute bathymetry using three different but related methods. For any method, one must be aware of the possibility for error at each of the steps involved and continually question the results. While the dynamic nature of the coast makes precision in bathymetric estimation difficult (e.g., tides, waves, lack of ground truth information), it also makes such analyses essential if we are to have recent and/or time series data for the coastal zone.

We may thus conclude that the artificial neural network method and the single band method using red Landsat band can produce reasonably good depth estimates in shallow coastal waters even with a relatively small amount of

In summation, this study provides the empirical algorithm as the first step for the development and validation of bathymetric algorithms in the southeastern Caspian Sea. It is quite evident that in shallow waters and in spectral regions where the upwelling light is influenced by multiple parameters, the signal from the bottom can only be separated from the signal from the water column by more detailed optical modeling. The collection of IOP and reflectance measurements and the set-up of such models and inversion schemes for developing bathymetric algorithms specific to the Caspian Sea are thus recommended for further study.

The study presented here is part of the dissertation in partial fulfillment of the requirements for the degree of Ph.D. in Tarbiat Modarres University (T.M.U.) of Iran. The authors extend their appreciation for the support provided by the authorities of the Tarbiat Modares University in funding the study. First and foremost, the first author would like to thank Nemat Mahmoudi for continuing encouragement and support in the preparation of the field data. Also, thanks to Ghasem Ghorbanzadeh, Bagher Teimouri, Vahid Kheirabadi, Asghar Alizadeh and Mohammad Abbasi for a great deal of help concerning sampling affairs. We also thank the anonymous reviewers for their constructive suggestions and comments.

The author declares no conflict of interest.

Stages of the presented methodology.

False color composite of the study area (FCC 234) with the sampling stations. FCC 234 shows a 24-bit color composite image from three bands (green, red and near-infrared bands) of byte binary imagery for display and visual analysis.

The original blue band of Landsat TM imagery.

The transformed blue band (ln(

Regression of transformed blue band against known depths.

The map of water depth (m) produced by the blue single band algorithm (SBA). The green part is the land and masked from analysis.

Regression of transformed red band against known depths.

The map of water depth (m) produced by the red single band algorithm (SBA). The green part is the land and masked from analysis.

Regression of first component of PCA against known water depths.

The map of water depth (m) produced by principal components analysis (PCA). The green part is the land and masked from analysis.

The map of water depth produced by MLP ANNs. The green part is the land and masked from analysis.

Comparison of known and estimated depths in sampling stations.

1 | 6 | 10.19 | 6.76 | 8.08 | 3.56 |

2 | 10.5 | 10.29 | 9.87 | 9.62 | 13.44 |

3 | 15 | 10.62 | 11.75 | 10.81 | 14.82 |

4 | 19 | 10.95 | 14.28 | 12.28 | 20.92 |

5 | 24 | 11.32 | 15.79 | 13.33 | 20.75 |

6 | 28 | 13.06 | 22 | 17.95 | 28.1 |

7 | 45 | 16.54 | 31.61 | 25.84 | 44.61 |

8 | 32 | 13.93 | 25.66 | 20.44 | 35.94 |

9 | 24 | 11.02 | 14.85 | 12.62 | 22.51 |

10 | 19 | 10.68 | 11.85 | 10.86 | 14.12 |

11 | 14 | 10.57 | 10.57 | 10.07 | 13.53 |

12 | 10 | 9.99 | 7.44 | 8.14 | 8.4 |

13 | 5 | 10.09 | 8.04 | 8.54 | 8.07 |

14 | 10 | 10.51 | 11.14 | 10.41 | 13.82 |

15 | 15 | 10.85 | 12.51 | 11.31 | 13.28 |

16 | 5 | 8.82 | 3.22 | 5.09 | 8.51 |

17 | 10 | 10.72 | 11.14 | 10.63 | 9.74 |

18 | 15 | 9.98 | 8.39 | 8.62 | 13.03 |

19 | 5 | 7.66 | 0 | 1.97 | 5.91 |

20 | 10 | 9.62 | 6.64 | 7.38 | 11.33 |

21 | 15 | 9.13 | 4.93 | 6.12 | 13.55 |

22 | 0.6 | 12.33 | 8.53 | 11.02 | 0.83 |

23 | 0.9 | 17.17 | 19.67 | 21.04 | 1.92 |

24 | 0.7 | 17.17 | 24.26 | 23.15 | 3.88 |

25 | 2.8 | 11.26 | 8.11 | 9.74 | 1.49 |

26 | 0.8 | 10.66 | 4.93 | 7.71 | 0.99 |

27 | 2.5 | 11.48 | 8.18 | 10.05 | 1.29 |

28 | 1.1 | 12.85 | 11.75 | 13.04 | 1.35 |

29 | 3 | 11.28 | 7.57 | 9.55 | 1.28 |

30 | 2.8 | 11.83 | 8.53 | 10.48 | 1.05 |

31 | 1.3 | 10.4 | 3.88 | 6.96 | 0.86 |