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提出一个可考虑回水顶托及旁侧入流影响的线性扩散波方程水位解析解模型，并对其响应函数特性进行了研究。该模型是一个集总参数的水位预报模型。模型只包括：谢才系数Ｃ和反映河道断面不规则影响的扩散系数ＤＫ，并可由试错或优化法求出。对于给定的上、下边界条件和旁侧入流，模型可快速给出各内插断面的水位过程。选用长江荆江河段１９８１年～１９９０年３４次洪水资料进行参数率定，１９９１年～１９９３年７次洪水资料进行模型检验，结果令人满意。
An analytical solution of the linear diffusion wave equation which can consider the effect of backwater support and side inflow is proposed and its response function is studied. The model is a lumped parameter water level forecast model. The model includes only the Xiecai coefficient C and the diffusion coefficient DK that reflects the irregular effects of the river channel section, and can be determined by trial and error or by optimization. For given upper and lower boundary conditions and side inflows, the model can quickly give the water level of each interpolated section. The data of 34 floods in the Jingjiang reach of the Yangtze River from 1981 to 1990 were used for parameter calibration and the data of seven floods from 1991 to 1993 were tested with satisfactory results.