Yoji Tanaka

Modified Lyzenga's Method for Estimating Generalized Coefficients of Satellite-Based Predictor of Shallow Water Depth

The multispectral method for the remote sensing of water depth proposed by Lyzenga has been widely applied to shallow-water bathymetry by researchers. The predictor of water depth used in this method is a linear function of image-derived variables for each visible band. The coefficients of the predictor are estimated by using a number of pixels with known depth as training data; this depth information is usually obtained by performing in situ depth measurements. Theoretically, if an appropriate set of coefficients is chosen, the predictor can be insensitive to some variations in the optical properties of the bottom material and water. However, it is sensitive to variations in atmospheric and water surface transmittance and sun and satellite elevations. Consequently, a single set of coefficients cannot always be applied to multiple images. In this letter, we propose a simple method to estimate a general set of coefficients for Lyzengas predictor that is relatively less affected by the aforementioned factors. We derive and utilize the theoretical fact that these factors affect only the intercept (constant term) of the predictor function. We demonstrate the effectiveness of the proposed method using WorldView-2 images of coral reefs. The proposed method will enable the application of a single set of coefficients (except for the intercept) to a broad range of images. This will significantly reduce the number of pixels with known depth required for the prediction of an image and thereby improve the feasibility of remote sensing of water depth.

Generalized Lyzenga's Predictor of Shallow Water Depth for Multispectral Satellite Imagery

Multispectral satellite remote sensing can predict shallow-water depth distribution inexpensively and exhaustively, but it requires many in situ measurements for calibration. To extend its feasibility, we improved a recently developed technique, for the first time, to obtain a generalized predictor of depth. We used six WorldView-2 images and obtained a predictor that yielded a 0.648 m root-mean-square error against a dataset with a 5.544 m standard deviation of depth. The predictor can be used with as few as two pixels with known depth per image, or with no depth data, if only relative depth is needed.

Which Spectral Bands of WorldView-2 Are Useful in Remote Sensing of Water Depth? A Case Study in Coral Reefs

Although visible bands of high-resolution multispectral imagery are used for bathymetry, the relative utility of different bands is poorly understood. Therefore, we evaluated the relative utility of the six visible bands of WorldView-2. We statistically selected the visible bands that gave the best accuracy under different situations, tallying how often each band was included in the best combination. The average frequency was greater than 50% for every band and differed between bands by only 17%. We conclude that all visible bands are useful for remote sensing of water depth, although the utility depends on the image and number of training pixels available.

Validation of shallow-water reflectance model for remote sensing of water depth and bottom type by radiative transfer simulation

Abstract Lyzenga proposed a shallow-water reflectance model that describes the exponential relationship between the remote-sensing reflectance ( R ) and water depth [ Appl. Opt. 17, 379 383 (1978)]. The model has been widely used in remote sensing of water depth to estimate the depth from R , and in remote sensing of bottom type to remove the effect of depth from R . Although it was derived from radiative transfer theory ignoring internal reflection at the water surface, no study has quantitatively validated it following the theory. In this study, we examine its accuracy under various conditions using Monte Carlo radiative transfer simulations. Although internal reflection contributed significantly to R in some cases, the model, if fitted to (calibrated with) data covering the entire target depth range, described the relationship between R and depth reasonably accurately ( R 2 > 0.9935 ). This was because the internally reflected component of R , as well as the other component, decreases exponentially with depth. However, because the sum of two exponentially decreasing functions is not strictly exponential, the model does not accurately estimate the depth using R when the calibration data did not cover the entire depth range of interest: the model significantly underestimated the depth when used for extrapolation.