Modified K-NN Model for Stochastic Streamflow Simulation

This paper presents a lag-1 modified K-nearest neighbor K-NN approach for stochastic streamflow simulation. The simula- tion at any time t given the value at the time t1 involves two steps: 1 obtaining the conditional mean from a local polynomial fitted to the historical values of time t and t1, and 2 then resampling i.e., bootstrapping a residual at one of the historical observations and adding it to the conditional mean. The residuals are resampled using a probability metric that gives more weight to the nearest neighbor and less to the farthest. The "residual resampling" step is the modification to the traditional K-NN time-series bootstrap approach, which enables the generation of values not seen in the historical record. This model is applied to monthly streamflow at the Lees Ferry stream gauge on the Colorado River and is compared to both a parametric periodic autoregressive and a nonparametric index sequential method for streamflow generation, each widely used in practice. The modified K-NN approach is found to exhibit better performance in terms of capturing the features present in the data. The need to identify alternatives that will improve upon the ISM motivated the research presented in this paper. The ISM is a "nonparametric" method in that it makes no assumption of the functional form of the underlying model; instead, the method is data-driven. Keeping with the "nonparametric" spirit of ISM, we developed the proposed modified K-nearest neighbor K-NN method. The proposed approach retains all the aspects of the traditional K-NN time series bootstrap technique developed by Lall and Sharma 1996, but the "modification" enables simu- lating values not seen in the historical record. We evaluate the performance of our proposed approach by applying it to the monthly streamflow data from U.S. Geological Survey USGS stream gauge 09380000 located on the Colorado River at Lees Ferry, Arizona. We also compare the modified K-NN method with the ISM and a first-order periodic autoregressive model PAR1, each widely used in practice. The paper is organized as follows: a brief background on stochastic streamflow modeling including a description of the ISM and the PAR models is first presented, for the benefit of readers. Our proposed approach is then presented. A description of the results and summary conclude the presentation.