A Method for Topographical Estimation of Lake Bottoms by B-Spline Surface
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 4, July 2013, Pages: 102-109
Received: Jul. 15, 2013; Published: Aug. 10, 2013
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Authors
H. Bao, Graduate School of Environmental Science, Okayama University, Okayama, Japan
K. Fueda, Graduate School of Environmental and Life Science, Okayama University, Okayama, Japan
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Abstract
The application of B-spline (Basis spline) surface to the estimation of the lake bottom topography is described.By using the analysis of a bivariate B-spline, the shape of the lake bottom is approximated.According to the validity of the estimation by the bivariate B-spline function the method is applied to the actual data of the lake depth.Surveys over the water area have more difficulties than those on land, and the measurement data are distributed quite irregularly. The locations of the measured data donot exist regularly over the lake.Those locations were distributed along with the wake of the boat on which the sample data were collected. The density of the data is quite high in some small regions and quite low in other wide regions.Based on such irregular data, we tried a statistical estimation.The regularized term with a penalty coefficient makesa proper approximation of the parameters of the B-spline functions. There are many factors, such that the number of knots, the locations of those knots, the number of B-spline functions and the coefficient of penalized term.Appropriate information criterion which has sufficient accuracy and a small amount of computation is applied for determination of the optimal model.
Keywords
B-spline surface, Cross-validation, Influence function, Generalized cross-validation, Surface model selection, Numerical computation, Topography of lake bottom
To cite this article
H. Bao, K. Fueda, A Method for Topographical Estimation of Lake Bottoms by B-Spline Surface, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 4, 2013, pp. 102-109. doi: 10.11648/j.ajtas.20130204.12
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