Computer models of flow and transport processes in critical or vulnerable reaches of rivers have become essential tools in assessing the long-term sustainable management of river basins. A generic long-standing source of uncertainty in the output from these models arises from the difficulty in estimating flow rates at the upstream boundary of the reach. When the process being modeled relies on an accurate description of the autocorrelation in the flow, such as in sediment transport, and predictions are required for future changed climatic conditions, this difficulty becomes acute. One currently popular solution is to combine stochastic weather generators with catchment hydrology models to simulate hydrographs. This paper offers an alternative solution, which bypasses the complexities of this approach and the extra uncertainties that arise from imposing restrictive predefined model structures. The proposed method uses an autoregressive multinomial logit model to link temperature and precipitation catchment data to flow data of the River Tees in the northeast United Kingdom. This model accounts for temporal autocorrelation by using the previous day's observation and other variables as explanatory variables. Incorporating basin area average temperature and precipitation allows climate change predictions from regional climate models to be used when predicting flows. The successful application of the method is demonstrated for the River Tees in northeast United Kingdom.