Generally return period T(x) of the maximum value is given as follows.
T(x)=1/(1-F(x)) (5)
F(x) is the distribution function. Fig. 4 shows the comparison of the return period values of the estimated high sea level between Kobe and Osaka based on the Frechet distribution. Estimated high sea levels with the 100 year-return period exceeds well over 2 meters above the mean sea levels in Kobe and Osaka. Since the elevation expressed in a topographic map is based on T.P., return period values of the estimated high sea levels in this figure can be represented as elevation. For example, flood-prone area can be estimated as the area under the elevation of 241cm at Kobe and of 245.5cm at Osaka.
3. MAPPING ON LANDSAT TM
Estimated high sea levels with the 100 year-return period exceeds well over 2 meters above the mean sea levels in Kobe and Osaka and they are mapped on the classified Landsat TM image. Fig.5 shows the method of mapping estimated high sea levels on Landsat TM image. First of all a subset of the image covering Kobe and Osaka is made from the TM image covering Osaka Bay. Then the sequential clustering is carried out for discriminating between land and water area. The classified water area is masked so that the boundary between land and water can be extracted. The masked image is overlaid with the contour corresponding with estimated high sea levels. The contour is provided by the elevation data of numerical map') published by Geographic Survey Institute of Japan. Plate 1 shows the estimated flood-prone area corresponding to 100 year return period values overlaid with classified Landsat TM image on April 3, 1991. Flood-prone area reaches 78 km 71% of the densely populated plain area.
4. SUMMARY
Results of the study is summarized as follows.
(1) Return period values of high sea levels for a long term such as 50 and 100 years are calculated based on the Gumbel and Frechet distributions of extreme-value statistics.
(2) The observed annual high sea levels agree better with the estimated high sea levels based on the Frechet distribution than the ones based on the Gumbel distribution for Kobe and Osaka tidal stations.
(3) Return period values of high sea levels at Kobe and Osaka for 100 years exceed 2 meters and the flood-prone area reaches 78 km 71% of the densely populated plain area between Kobe and Osaka.
References
1)Warrick, R.A, C.Le Provost, lvi. F.Meier, J.Oerlemans, and P.L.Woodworth (1996):
2)Johnson, N. L., S. Kotz, and Balakrishnan,N. (1995): Continuous Univariate Distributions, Vol.2, 2nd ed. John Wiley, New York.
3)Hosking,J.R.MI, J. RWaLlis and E. F. Wood (1985): Estimation of the Generalized Extreme-Value Distribution by the method of Probability-Weighted Moments, TECHNOMETRICS, VoL 27, No.3, pp.251-261.
4)Geographic Survey Institute (1994): Numerical Map, Japan Cartographic Center.
