KNN-based local linear regression for the analysis and simulation of low flow extremes under climatic influence

Abstract

Climate change frequently causes highly nonlinear and irregular behaviors in hydroclimatic systems. The stochastic simulation of hydroclimatic variables reproduces such irregular behaviors and is beneficial for assessing their impact on other regimes. The objective of the current study is to propose a novel method, a k-nearest neighbor (KNN) based on the local linear regression method (KLR), to reproduce nonlinear and heteroscedastic relations in hydroclimatic variables. The proposed model was validated with a nonlinear, heteroscedastic, lag-1 time dependent test function. The validation results of the test function show that the key statistics, nonlinear dependence, and heteroscedascity of the test data are reproduced well by the KLR model. In contrast, a traditional resampling technique, KNN resampling (KNNR), shows some biases with respect to key statistics, such as the variance and lag-1 correlation. Furthermore, the proposed KLR model was used to simulate the annual minimum of the consecutive 7-day average daily mean flow (Min7D) of the Romaine River, Quebec. The observed and extended North Atlantic Oscillation (NAO) index is incorporated into the model. The case study results of the observed period illustrate that the KLR model sufficiently reproduced key statistics and the nonlinear heteroscedasticity relation. For the future period, a lower mean is observed, which indicates that drier conditions other than normal might be expected in the next decade in the Romaine River. Overall, it is concluded that the KLR model can be a good alternative for simulating irregular and nonlinear behaviors in hydroclimatic variables.