In the open channel, the water stage is connected closely to its discharge and the discharge is obtained by the observation of stage. But, almost every river in a cold climate such as Hokkaido freezes at the surface in winter. Therefore, the results of studies about the open channel can not be applied directly to the closed river with the whole frozen surface. The stage-discharge curve of the above mentioned closed river is obtained by the same method in the open channel, if the water stage of the closed ice-covered river is defined as the water level in the hole of ice drilled for measurement. But, it is indicated theoretically that the curve is not invariable and varies with the changes of the accumulated snow weight on the whole frozen surface and the other conditions. The lower limit level of the surface ice of river was introduced as the parameter of the discharge in the closed river with the whole frozen surface. It is the theoretical and suitable parameter and is not affected by the accumulated snow weight and the other coditions. The vertical distribution of the suspended material in the closed river with the whole frozen surface was explained by the constant apparent viscosity all over the depth. The total suspended material is corresponded to the lower limit level of the surface ice of river.
