宮古島

This system-theoretic study was carried out to analyze the variation of ground water level in the experimental ground water dam in Miyako. Miyako is an island with an area of 159km2, and a coral limestone. The surface soil is about 2m deep, then the porous limestone lies within about 40m under surface, and the bottom is impermeable mud stone. The experimental ground water dam was constructed at Minafuku in 1977. It is 16.5m high, 500m long and 1.7 km2 area of basin. The date of hydrology (daily ground water levels, rainfalls and evapotranspirations) were used to analyze from January 1 to June 30, 1979. The two-stage tank model was used to describe the recharge of water to the ground water dam, and the identification of parameters of this model was carried out by the method of minimum mean squared. In this case the estimation error was about 20%. However, the data of hydrology usually have fair errors in observation. Thus, A. E. Bryson and M. Frazier's non-linear smoothing method was used to estimate the daily variations of water storage levels in tank model more exactly. The non-linear water balance model was used for the state equation and the ground water model was used for the observation equation too. The principal idea of this analysis is to apply the system-theoretic method of data-smoothing to the above system. Thus, it was possible to describe the hydrologic cycle by the discretetime dynamical system. Finally, it was concluded that the water wtorage levels in tank model were improved by this method and random noise (estimated error of rainfall and evapotranspiration) was small comparatively. The former of estimated error was about 1.9% and the latter one was about 11%. The observation errors of ground water levels were proportionated to the variations of water levels approximately, and its value was about 4.3% on an average.