Conditional resampling of hydrologic time series using multiple predictor variables: A K-nearest neighbour approach

Unlike parametric alternatives for time series generation, non-parametric approaches generate new values by conditionally resampling past observations using a probability rationale. Observations lying ‘close’ to the conditioning vector are resampled with higher probability, ‘closeness’ is defined using a Euclidean or Mahalanobis distance formulation. A common problem with these approaches is the difficulty in distinguishing the importance of each predictor in the estimation of the distance. As a consequence, the conditional probability and hence the resampled series, can offer a biased representation of the true population it aims to simulate. This paper presents a variation of the K-nearest neighbour resampler designed for use with multiple predictor variables. In the modification proposed, an influence weight is assigned to each predictor in the conditioning set with the aim of identifying nearest neighbours that represent the conditional dependence in an improved manner. The workability of the proposed modification is tested using synthetic data from known linear and non-linear models and its applicability is illustrated through an example where daily rainfall is downscaled over 15 stations near Sydney, Australia using a predictor set consisting of selected large-scale atmospheric circulation variables.