Sensitivity of the SIMulation-EXtrapolation (SIMEX) methodology to mis-specification of the statistical properties of the measurement errors

In hydrometeorological and environmental studies, it is common to seek relations between two variables (predictand and predictor), one of which (predictor) is affected by uncertainties. These errors unavoidably affect the results of the analyses by providing erroneous estimates of the parameters of the predictor-predictand model. A possible solution is represented by the SIMulation-EXtrapolation (SIMEX) methodology. This approach follows two steps: (1) perturbation of the predictor with increasing levels of uncertainties (multiples of the known error variance); and (2) finding a relation between the model's parameters and level of uncertainty, which allows their extrapolation to the error-free case. The application of the SIMEX methodology requires a priori knowledge of the mean, variance, and distribution of the measurement errors. However, in hydrologic and climatologic studies, this is not the case, and the impact of an erroneous specification of these statistical properties on the results of the analyses has received little attention. The aim of this study is to investigate the sensitivity of the SIMEX methodology to mis-specification of the error characteristics. By using a simulation-based approach, we investigate the impact of imperfect knowledge of the characteristics of the errors associated with the predictor (mean, variance, and probability distribution). Our results suggest that SIMEX is robust against mis-specification of the moments and distribution of the measurement errors, that it performs better than standard linear regression, even when these statistical properties are erroneously specified, and that, for these reasons, it could find a useful application to seasonal forecasting of hydroclimatic variables.