Hydrological models contain parameters whose values cannot be directly measured in many field-scale projects, hence need to be meaningfully inferred through calibration against historical records. Much progress has been made in development of efficient search algorithms in order to find optimal parameter values and their underlying uncertainty distributions. Yet, relatively little is known about the effects of calibration data (or error residual) transformations on the identifiability of model parameters and reliability of model predictions. Effects of calibration data transformations on the posterior parameter distribution and predictive capability of two parsimonious hydrological models are analyzed herein. Our results depict that calibration data transformations significantly influence parameter and predictive uncertainty estimates. Data 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 hydrological 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, than to calibrate models in a single objective framework.
This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Water Resources Management, published by Springer Netherlands. Copyright restrictions may apply. The final publication is available at link.springer.com. doi: 10.1007/s11269-018-1908-6
Sadegh, Mojtaba; Majd, Morteza Shakeri; Hernandez, Jairo; and Haghighi, Ali Torabi. (2018). "The Quest for Hydrological Signatures: Effects of Data Transformation on Bayesian Inference of Watershed Models". Water Resources Management, 32(5), 1867–1881.