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The linear form of the Muskingum model has been widely applied to river flood routing. I iowever, a nonlinear relationship between storage and discharge cxists in most actual river systems, making the use of the linear model irinppropriale. 111 t tiis paper, a nonlinear Muskingum model is solved using the state variable modeling tecliniclue. Various curve fitting techniques are ernployrd for the cdibra[ion of modc4 pranteters, and their performances within the model are compared. thth linear atid nonlincar niodels are applied to an cxaniple with pronounced nonliiwarity between storage and discliarge. The results show that the nonlinear Muskingum modcl is superior to the linear one. I ' s, = K [ x l , + (1x) O f ] .

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In the design of flood levee systems there are many parameters and variables with associated uncertainties. This paper presents models which systematically analyze the various types of uncertainties in the hydrologic aspect as well as hydraulic aspect of design and analysis to define the risk and reliability of overtopping. Both static and time dependent risk models are developed. Results show that risk evaluated by the simple return period method can be underestimated by 10% to 50%, depending on the loading distribution model used. The risk‐safety factor relationships are shown to be very sensitive to the hydrologic loading probability model adopted, so that composite models are suggested for risk analysis.

Occurrence of rainstorm events can be characterized by the number of events, storm duration, rainfall depth, inter-event time and temporal variation of rainfall within a rainstorm event. This paper presents a Monte-Carlo based stochastic hourly rainfall generation model considering correlated non-normal random rainstorm characteristics, as well as dependence of various rainstorm patterns on rainfall depth, duration, and season. The proposed model was verified by comparing the derived rainfall depth-duration-frequency relations from the simulated rainfall sequences with those from observed annual maximum rainfalls based on the hourly rainfall data at the Hong Kong Observatory over the period of 1884-1990. Through numerical experiments, the proposed model was found to be capable of capturing the essential statistical features of rainstorm characteristics and those of annual extreme rainstorm events according to the available data.

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