Modified K-NN Model for Stochastic Streamflow Simulation

Abstract

This paper presents a lag-1 modified K-nearest neighbor (K-NN) approach for stochastic streamflow simulation. The simulation at any time t given the value at the time t−1 involves two steps: (1) obtaining the conditional mean from a local polynomial fitted to the historical values of time t and t−1, 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.