The Quest for Hydrological Signatures: Effects of Data Transformation on Bayesian Inference of Watershed Models

Hydrological models contain parameters, values of which cannot be directly measured in the field, and hence need to be meaningfully inferred through calibration against historical records. Although much progress has been made in the model inference literature, relatively little is known about the effects of transforming calibration data (or error residual) on the identifiability of model parameters and reliability of model predictions. Such effects are analyzed herein using two hydrological models and three watersheds. Our results depict that calibration data transformations significantly influence parameter and predictive uncertainty estimates. Those transformations that distort the temporal distribution of calibration data, such as flow duration curve, normal quantile transform, and Fourier transform, considerably deteriorate the identifiability of model parameters derived in a formal Bayesian framework with a residual-based likelihood function. Other transformations, such as wavelet, BoxCox and square root, while demonstrating some merits in identifying specific model parameters, would not consistently improve predictive capability of hydrological models in a single objective inverse problem. Multi-objective optimization schemes, however, may present a more rigorous basis to extract several independent pieces of information from different data transformations. Finally, data transformations might offer a greater potential to evaluate model performance and assess specific sections of model behavior, rather than to calibrate models in a single objective framework. Findings of this study shed light on the importance and impacts of data transformations in search of hydrological signatures.