method and the period of statistics. Then these estimated high sea levels are mapped on the Landsat Thematic Mapper image covering Osaka Bay in order to predict the flood-prone area. The flood-prone area is the area to be flooded by the estimated high sea level assuming that there are no breakwaters.
2. OBSERVED AND ESTIMATED SEA LEVEL
Annual high sea levels at Kobe and Osaka tidal stations(Fig. 1) during the period between 1952 to 1994 are collected for estimating high sea levels. These observed high sea levels are converted to the ones based on T.P.(Tokyo Peil) for comparing high sea levels at different tidal stations. The advantage using T.P.-based sea level is that the converted sea levels represent elevations at the topographic map. Fig.2 shows variations of annual high sea level from 1952 to 1994 at two tidal stations. In this figure zero centimeter at the vertical coordinate represents T.P. Variations of annual high sea levels resembles at Kobe and Osaka. So far it is possible to estimate sea levels for a short term using a deterministic method, but it is not possible to estimate sea levels for a very long term such as 100 years. It is the concept of return period based on extreme-value statistics to explain maximum appearances of sea level.
Generally speaking there are three types of extreme-value distribution for the maximum, namely the Frechet, Gumbel and Inverse Weibull distribution. These extreme-value distributions are represented as the generalized extreme-value distribution 2) follows:
F(x)=exp[-{1-k(x- μ）/σ1/k],
1-k(x-μ/σ>0. (1)
F(x) is the distribution function,μ, σ ,k are location, scale and shape parameters respectively.
When k｡絨, (1) represents the Frechet distribution and when k#), (1) represents the Gumbel distribution as follows:
F(x)=exp{-exp(-(x- μ)/ σ)} (2)
When k｡膂, (1) represents the Inverse Weibull distribution.
Three parameters μ, σ, k are estimated using PWM(Probability Weighted Moment)method3) by adapting the generalized extreme-value distribution to the observed annual high sea levels for 43 years at Kobe and Osaka tidal stations. Table 1 shows the results of parameter estimation based on PWM and MLE(Maximum Likelihood Estimation) methods for Kobe and Osaka. Since the estimated values of shape parameter k are minus, these data can be explained by the Frechet distribution. On the other hand the Gumbel distribution has been frequently used for the maximum data analysis. Therefore the Fr6chet and Gumbel distributions are compared in this study. Based on the estimated parameters estimated high sea levels X(F(x)) are given as follows.
X(F(x))= μ +(σ/ k){1-(-ｌn(F(x))k}
(Frechet distribution) (3)
X(F(x))= μ-σ ｌn(-ｌn(F(x)))
(Gumbel distribution) (4)
Fig.3 shows the estimated high sea levels versus observed annual high sea levels at Kobe and Osaka tidal stations based on the Gumbel and Frechet distributions. The observed annual high sea levels agree better with the estimated high sea levels based on the Fr6chet distribution than the ones based on the Gumbel distribution for two tidalstations around the Osaka Bay. Therefore the Fr6chet distribution is adopted as the extreme-value distribution for estimating return period value.
