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This paper is concerned with the hydrologic cycle, from rainfall to evaporation, in the basin of Lake Biwa. The four-stage tank model is used for describing the runoff in the basin. The variables of water storage level in the model play an important role for calculating the amount of runoff and evapotranspiration. From the system-theoretic viewpoint, the fourstage tank model can be regarded as a piecewise linear dynamical system with four dimensions and the water storage levels as state-variables. In addition, the water balance equation can be regarded as an observation process in the dynamical system. Thus it is possible to describe the hydrologic cycle by the discrete-time dynamical system. The principal idea of this paper is to apply the system-theoretic method of data-smoothing to the system described above and to estimate the daily variations of water storage levels. Based on their estimated values, it is possible to evaluate the amount in each stage of the cycle such as rainfall, evapotranspiration, and observation noise. Finally, it is concluded that the system-theoretic method applied to the water balance model discloses internal states of the hydrologic cycle.

A System-Theoretic Study of the Hydrologic Cycle in the Basin of Lake Biwa