The relationship between Root Mean Square (RMS) error and probable error was investigated under the condition of normal distribution with independent x, y and z error components. In the ideal case of no bias and equal standard deviations (in the case of two or three dimensions), the ratios of 90% probable error to RMS error are 1.645 (one dimensional normal distribution), 2.144 (two dimension) and 2.333 (three dimension) . Similarly the ratios for 50% probable error are 0.674 (one dimension), 1.177 (two dimension) and 1.500 (three dimension) . The bias within one standard deviation causes the variation of the ratio of 90% probable error to RMS error by the value of 0.0295 (2% of the above ratio) in one dimensional case, 0.0433 (2%) in two dimensional case, and 0.1771 (8%) in three dimensional case. Similarly, the different values of standard deviation within 2 times each other causes the variation of the ratios of 90% probable error to RMS error by the value within 0.3104 (14% of the above ratio) in two dimensional case and 0.2404 (10%) in three dimensional case.
A new model to extract coral reef area was proposed and applied to an estimation model of bottom depth. Image density on 1540 pixels of LANDSAT/5-TM and provided data on depth and bottom condition from JODC (Japan Oceanographic Data Center) were used for mapping coral reef area and for estimating bottom depth. Both models were adopted to Okinawa Main Island and Yaeyama Islands and discussed on its practical use. Moreover, limitations of applied model were also discussed and an errors analysis was performed. Depths from surface to 34m were measured with RMS residuals of 3.38m and 4.23 against the data obtained at fine atmospheric and the fine plus cloudy atmospheric conditions, respectively. Two and four bottom features models were compared each other on its application. Finally, using two bottom features model described above, a three-dimensional image and a isodepth image were obtained by a personal computer at an area of Yaeyama Islands.