**I. Z. Poonawala , S. D. Ranade, S. Selvan, C. Gnanaseelan , Anuja Rajagopalan **

Rajagopalan Central Water and Power Research Station

Pune – 411 024

Water depth is an important parameter in solving various coastal engineering problems such as erosion, accretion, shoreline stability, port and harbor construction, evaluation of tidal storage, dredging, maintenance of navigation routes etc.. The field data collection at a site is an expensive and time consuming and sometimes extremely difficult in shallow water regions. For various reasons like wide area coverage, data dependency on depth and repetivity, etc. satellite data can be used to determine shallow water depths. For calibration/validation of the bathymetric model, ground truth data at a few selected locations is essential.

The digital image data acquired by the remote sensing satellites consist of the reflectance of the surface of the earth and the atmospheric constituents. Considering the case of water bodies, there will be significant change in the reflectance due to various parameters including water depth, turbidity and bed characteristics. Assuming the other two parameters uniform, it is obvious that the intensity of reflected electromagnetic energy will vary inversely with the depth of the water column. Preliminary analysis of digital image data of IRS-1A and IRS-1B show that the band 4 data in the spectral range of 0.77 to 0.86 microns contain significant variation in intensity level for the shallow water region.

Algorithms for water depth mapping of coastal areas, using satellite data were developed by Lyzenga (1978) and Paredes and Spero (1983). This paper describes a new bathymetric model based on statistical approach, which transforms the intensity levels of the satellite data to depth values. Bathymetry of a small region is correlated with intensity levels to achieve the transformation and the transformed data contains depth information of shallow water region.

**Area of study**

The Jamnagar and Sikka region of Gujarat, in the Gulf of Kuchchh was selected as the study area. The area is about 25 sq. km. between the latitudes 22o 20′ 48″ N and 22o 28′ 48″ N and longitudes 69 o 48′ 00″ E and 69 o 56′ 24″ E.

**Satellite Imagery **

Digital satellite imagery data of 3rd Oct., 1994, covering an area of 25 sq. Km. between the latitudes 22o 20′ 48″ N and 22o 28′ 48″ N and longitudes 69 o 48′ 00″ E and 69 o 56′ 24″ E was used for the study and shown in Plate 1.

The above imagery is geocoded and contains 1024 x 1024 pixels with 25 m ground resolution. The time of satellite pass is around 1100 hours. The tidal levels before and after the time of satellite pass were determined from India Tide Tables 1994. The tidal level at the time of satellite pass was computed using sinusoidal interpolation method and was +5.12 m with respect to Chart Datum.

**Bathymetric data **

Bathymetry of the region was available covering area between latitudes 22 o 25′ 50″ N and 22 o 28′ 30″ N and longitudes 69 o 51′ 45″ N and 69 o 53′ 00″ N. The data was digitized over a grid of 100 m x 100 m. It was then resampled using two dimensional interpolation method to obtain bathymetry at a grid interval of 25 m x 25 m, which is compatible to the pixel size of satellite imagery. Then it is transformed to depth values using the transformation equation,

dij = TL – bij

where dij is depth at location ij, TL is the tidal level at the time of satellite pass and bij is bathymetry at location ij.

**Methodology**

A Domain Rippling Scheme (DRS) has been developed to estimate the depths of the shallow water region. This scheme starts with a rectangular domain D which specifies a sub area in the region of interest, where both reflectance and bathymetry are known. It estimates the depth values of the immediate neighbouring pixels of D using a transformation equation in terms of its statistical parameters like covariance, variance etc., and updates the domain by including the newly estimated pixels. The next layer is also calculated using the same principle and proceeds towards the boundary like a ripple as shown in Fig. 1. Necessary care should be taken when the domain touches the boundary of the region of interest.

Fig. 1. Domain Rippling

A linear relationship y = ax + b was assumed between the reflectance (x) and the depth (y). The rectangular domain D may be viewed as a matrix of order m x n, which is comprised of reflectance matrix Dr and depth matrix Dd . In the above relationship, a and b were calculated using the least square approximation in the domain D as

=

The depths at the 2(m+n+2) immediate neibouring pixels of the domain D were computed using the transformation equation

——————– (1)

This process is repeated by updating the domain until it merges with the full region of interest.

A model region (study area) was selected in conjunction with the satellite imagery and this can be viewed as a 1024 x 1024 pixels. In this region, the bathymetry data was available only for a small area [91×193 pixels]. A 10 x 10 matrix with significant depth variation was selected as the basic domain D, where both reflectance and depth values were available. The Digital Numbers representing reflectance and depth matrices of D are shown in Table 1 and Table 2.

Statistical analysis shows that these two matrices are correlated with a correlation coefficient of -0.99. The immediate neighbouring elements of D were computed using the transformation equation (1) and D was updated to 12 x12 matrix, including the new elements. The reflectance and depth matrices of order 12×12 corresponding to the updated domain are shown in Table 3 and Table 4 . The observed depth values of this new domain are shown in Table 5. The comparison of observed and computed depths versus reflectance is given in Fig. 2. The process was repeated with the updated domain until the whole region is covered.

**Results and Conclusions**

The Domain Rippling Scheme is a useful technique for the estimation of water depths over shallow water region. The digital satellite image with reflectance values is successfully transformed to depth image using this technique and is shown in Plate 2. A rigorous correlation analysis was done for the observed and computed depth values with various matrix sizes. The correlation analysis results are briefed in Table 6. It is found that the computed and observed depth values have good correlation, particularly in the shallow water region (Fig. 2). It can be seen that for the area under study, the intensity variation with depth is proportionate in shallow water region upto -3m depth contour. Hence it can be concluded that the present method can be restricted to shallow water depths. The analysis can be improved by assuming a nonlinear relationship between the reflectance and the water depth for deeper water region. Also it is important to consider the parameters like suspended sediment concentration and bed characteristics in the model which influence the reflectance.

**Acknowledgement**

The authors are grateful to Shri. R. Jeyaseelan, Director, Central Water and Power Research Station, Pune for his kind consent for presenting this paper

**References**

- Jain A.K. (1989). Fundamentals of Digital Image Processing, Pentice Hall, London
- Katiyar S.K., Rampal K.K. (1991). Bathymetric Mapping Over Coastal Andhra Pradesh Using Landsat – MSS Data, Journal of Indian Remote Sensing, No.19
- Lyzenga D.R. (1978). Passive Remote Sensing Techniques for Mapping Water Depth and Bottom Features, Applied Optics, No. 17
- Paredes J.M., Spero I.E. (1983). Water Depth Mapping from Passive Remote Sensing Data Under a Generalized Ratio Assumption, Applied Optics, No.22

13 | 13 | 13 | 14 | 13 | 14 | 14 | 14 | 14 | 14 |

13 | 13 | 13 | 13 | 13 | 14 | 14 | 13 | 13 | 14 |

13 | 14 | 13 | 13 | 13 | 14 | 14 | 13 | 13 | 13 |

13 | 13 | 13 | 13 | 13 | 14 | 14 | 14 | 14 | 14 |

13 | 13 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 |

14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 |

14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 14 |

14 | 14 | 13 | 13 | 14 | 14 | 14 | 14 | 14 | 14 |

14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 15 |

14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 15 |

Table 1: Reflectance matrix

3.11 | 3.09 | 3.08 | 3.07 | 3.04 | 2.97 | 2.89 | 2.81 | 2.76 | 2.77 |

3.06 | 3.03 | 3.03 | 3.03 | 3.00 | 2.93 | 2.84 | 2.75 | 2.70 | 2.71 |

3.01 | 2.99 | 2.99 | 2.98 | 2.96 | 2.89 | 2.80 | 2.72 | 2.68 | 2.70 |

2.95 | 2.93 | 2.92 | 2.90 | 2.88 | 2.82 | 2.75 | 2.69 | 2.66 | 2.68 |

2.88 | 2.85 | 2.83 | 2.81 | 2.78 | 2.74 | 2.70 | 2.66 | 2.64 | 2.67 |

2.82 | 2.79 | 2.75 | 2.72 | 2.69 | 2.66 | 2.63 | 2.62 | 2.61 | 2.64 |

2.78 | 2.74 | 2.68 | 2.63 | 2.60 | 2.58 | 2.57 | 2.57 | 2.58 | 2.60 |

2.75 | 2.69 | 2.61 | 2.54 | 2.49 | 2.48 | 2.49 | 2.51 | 2.52 | 2.55 |

2.73 | 2.65 | 2.55 | 2.45 | 2.39 | 2.38 | 2.41 | 2.44 | 2.47 | 2.48 |

2.73 | 2.63 | 2.51 | 2.39 | 2.32 | 2.31 | 2.35 | 2.39 | 2.42 | 2.43 |

Table 2 : Depth matrix

14 | 13 | 13 | 13 | 14 | 13 | 13 | 13 | 14 | 14 | 14 | 14 |

14 | 13 | 13 | 13 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 14 |

14 | 13 | 13 | 13 | 13 | 13 | 14 | 14 | 13 | 13 | 14 | 14 |

13 | 13 | 14 | 13 | 13 | 13 | 14 | 14 | 13 | 13 | 13 | 15 |

13 | 13 | 13 | 13 | 13 | 13 | 14 | 14 | 14 | 14 | 14 | 15 |

13 | 13 | 13 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 14 |

14 | 14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 14 |

14 | 14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 14 | 14 |

14 | 14 | 14 | 13 | 13 | 14 | 14 | 14 | 14 | 14 | 14 | 14 |

14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 15 |

14 | 14 | 14 | 13 | 14 | 14 | 14 | 14 | 14 | 15 | 15 | 15 |

14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 14 | 15 | 14 |

Table 3: Reflectance matrix

2.66 | 2.88 | 2.88 | 2.66 | 2.88 | 2.88 | 2.88 | 2.66 | 2.66 | 2.66 | 2.66 | 2.66 |

2.66 | 3.11 | 3.09 | 3.08 | 3.07 | 3.04 | 2.97 | 2.89 | 2.81 | 2.76 | 2.77 | 2.66 |

2.66 | 3.06 | 3.03 | 3.03 | 3.03 | 3.00 | 2.93 | 2.84 | 2.75 | 2.7 | 2.71 | 2.66 |

2.88 | 3.01 | 2.99 | 2.99 | 2.98 | 2.96 | 2.89 | 2.8 | 2.72 | 2.68 | 2.7 | 2.66 |

2.88 | 2.95 | 2.93 | 2.92 | 2.9 | 2.88 | 2.82 | 2.75 | 2.69 | 2.66 | 2.68 | 2.44 |

2.88 | 2.88 | 2.85 | 2.83 | 2.81 | 2.78 | 2.74 | 2.7 | 2.66 | 2.64 | 2.67 | 2.44 |

2.66 | 2.82 | 2.79 | 2.75 | 2.72 | 2.69 | 2.66 | 2.63 | 2.62 | 2.61 | 2.64 | 2.66 |

2.66 | 2.78 | 2.74 | 2.68 | 2.63 | 2.6 | 2.58 | 2.57 | 2.57 | 2.58 | 2.6 | 2.66 |

2.66 | 2.75 | 2.69 | 2.61 | 2.54 | 2.49 | 2.48 | 2.49 | 2.51 | 2.52 | 2.55 | 2.66 |

2.66 | 2.73 | 2.65 | 2.55 | 2.45 | 2.39 | 2.38 | 2.41 | 2.44 | 2.47 | 2.48 | 2.66 |

2.66 | 2.73 | 2.63 | 2.51 | 2.39 | 2.32 | 2.31 | 2.35 | 2.39 | 2.42 | 2.43 | 2.44 |

2.66 | 2.66 | 2.66 | 2.66 | 2.66 | 2.66 | 2.66 | 2.66 | 2.66 | 2.44 | 2.44 | 2.44 |

Table 4: Depth matrix (computed)

3.19 | 3.15 | 3.10 | 3.00 | 2.98 | 2.90 | 2.83 | 2.80 | 2.78 | 2.77 | 2.78 | 2.78 |

3.16 | 3.11 | 3.09 | 3.08 | 3.07 | 3.04 | 2.97 | 2.89 | 2.81 | 2.76 | 2.77 | 2.72 |

3.14 | 3.06 | 3.03 | 3.03 | 3.03 | 3.00 | 2.93 | 2.84 | 2.75 | 2.7 | 2.71 | 2.62 |

3.11 | 3.01 | 2.99 | 2.99 | 2.98 | 2.96 | 2.89 | 2.8 | 2.72 | 2.68 | 2.7 | 2.49 |

3.09 | 2.95 | 2.93 | 2.92 | 2.9 | 2.88 | 2.82 | 2.75 | 2.69 | 2.66 | 2.68 | 2.37 |

3.05 | 2.88 | 2.85 | 2.83 | 2.81 | 2.78 | 2.74 | 2.7 | 2.66 | 2.64 | 2.67 | 2.29 |

3.00 | 2.82 | 2.79 | 2.75 | 2.72 | 2.69 | 2.66 | 2.63 | 2.62 | 2.61 | 2.64 | 2.32 |

2.94 | 2.78 | 2.74 | 2.68 | 2.63 | 2.6 | 2.58 | 2.57 | 2.57 | 2.58 | 2.6 | 2.37 |

2.88 | 2.75 | 2.69 | 2.61 | 2.54 | 2.49 | 2.48 | 2.49 | 2.51 | 2.52 | 2.55 | 2.39 |

2.84 | 2.73 | 2.65 | 2.55 | 2.45 | 2.39 | 2.38 | 2.41 | 2.44 | 2.47 | 2.48 | 2.40 |

2.83 | 2.73 | 2.63 | 2.51 | 2.39 | 2.32 | 2.31 | 2.35 | 2.39 | 2.42 | 2.43 | 2.40 |

2.85 | 2.80 | 2.76 | 2.75 | 2.66 | 2.71 | 2.68 | 2.64 | 2.57 | 2.50 | 2.43 | 2.40 |

Table 5 : Observed Depth matrix

Matrix order of Domain D | Correlation between reflectance and observed depth | Correlation between reflectance and computed depth | Correlation between observed and computed depth |

12 x 12 | – 0.9937 | – 0.9950 | 0.9910 |

14 x 14 | – 0.9937 | – 0.9932 | 0.9981 |

16 x 16 | – 0.9936 | – 0.9955 | 0.9978 |

18 x 18 | – 0.9933 | – 0.9955 | 0.9977 |

20 x 20 | – 0.9916 | – 0.9952 | 0.9964 |

Table 6 : Correlation analysis