Correcting Nonstationarity in Streamflow Using Empirical Quantile Mapping

Código

I-EBHE0054

Autores

DANIEL HENRIQUE MARCO DETZEL, Victor Rodrigues Shiraishi

Tema

WG 1.08: Deep Explanation & Evaluation for Practices in Hydrological Changes (DEEPHY)

Resumo

Streamflow modeling is an essential tool in operational hydrology. For this purpose, stochastic models are employed for synthetic streamflow generation. Such scenarios should resemble the main statistical features of the observed series to be effectively applied in water resources planning activities. However, widely known models for synthetic streamflow generation are stationary (e.g., Box-Jenkins ARMA-type models). Hence, the applicability of these models has become questionable since the streamflow series of many rivers worldwide has begun to exhibit trends. In dealing with this issue, nonstationary models could be considered. For example, within the Box-Jenkins framework, the ARIMA formulation is a nonstationary approach. However, such a model is not suitable for synthetic series generation, as it relies on an unknown integration parameter for each scenario. Another solution is to correct the historical series to remove trends before subjecting them to a stationary model. This is the approach to be discussed here. Detrending techniques for time series are currently available. For streamflow series specifically, two methods are mostly known: (i) based on the trend?s slope estimation (mainly using Sen?s estimator), and (ii) based on cumulative plots of the streamflow series. In the latter, the procedure involves splitting the original series into two subsamples, plotting the cumulative streamflow series for each subsample, and estimating the respective slopes. Then, a correction coefficient is calculated by dividing the slope of the recent portion by the slope of the earlier period. Finally, the coefficient is applied to the earlier streamflow observations. It is worth mentioning that both methods assume the trend to be linear. In this study, a different correction approach is proposed. We apply Empirical Quantile Mapping (EQM), a technique frequently used for the bias removal of climate change scenarios. We first identify the splitting point of the series using Pettitt?s test. Then, we divide the series to obtain subsamples for the earlier period Qe and the recent period Qr. Each subsample is represented by its cumulative distribution function, respectively Fe(Qe) and Fr(Qr), from which empirical quantile values ? (0???1) are estimated. Then, the earlier subsample is corrected by applying cQr=Fr^(-1) [Fe(Qe)], where Fr(-1)[?] represents the quantile function. The EQM for nonstationarity correction was validated using the Foz do Areia hydropower plant's monthly streamflow series (Iguaçu River, Paraná). The data was provided by the National Electric System Operator as naturalized streamflow series ranging from January 1931 to December 2021. We identified a split point in January 1969, from which the subsamples were obtained (subsample 1: January 1931 to January 1969, with an average of 567 m³/s; subsample 2: February 1969 to December 2021, with an average of 720 m³/s). After applying the EQM, nonstationarity was successfully removed, and the long-term average equaled the recent period, resulting in 720 m³/s. It is highlighted that besides being a straightforward nonstationarity correction technique, EQM is not limited to linear trends. However, the effect of EQM correction in the presence of nonlinear trends needs to be explored in further studies.