状態空間法による流出予測 -kinematic wave法を中心として-

Abstract

An on-line flood runoff forecasting scheme which provides not only the estimate of runoffdischarge but also the variance of estimation error is presented on the basis of filtering and predictiontheorey developed by Kalman and others. Considering the difference in the way of observationof outputs, the meteorological system and the runoff system are supposed to be described by adiscrete-time model and a continuous-time model, respectively. Then, when the total system isconsidered, the discrete- and continuous-time random variables exist together and this makes theprediction problem somewhat complex. In this paper, we cope with this situation by consideringseparately the time instant at which the variables may change with a discrete jump and the intervalin which the variables change continuously, and by incorporating the rainfall intensity into statevariables.Though the general formulation of runoff prediction is given for the runoff system model whichis described by an ordinary vector differential equation, we can use the runoff system model which isdescribed by a partial differential equation in a similar fashion. In this context, the "stochastic"kinematic wave model which is made by introducing the noise term into the basic equation of thekinematic wave model is considered in particular and the equations which describe the evolution ofthe conditional expection and covariance of water depth are derived.