Residual error modelling for hourly streamflow predictions

 Statistical residual error modelling for hourly streamflow predictions

Cristina Prieto^1,2,3, Dmitri Kavetski^4,1, Fabrizio Fenicia³, James Kirchner^2,5,6, David McInerney⁴, Mark Thyer⁴, and César Álvarez¹

 

(1) IHCantabria—Instituto de Hidráulica Ambiental de la Universidad de Cantabria, Santander, Spain

(2) Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland

(3) Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland

(4) School of Civil, Environmental and Mining Engineering, University of Adelaide, Adelaide, SA, Australia

(5) Swiss Federal Research Institute WSL, Birmensdorf, Switzerland

(6) Department of Earth and Planetary Science, University of California, Berkeley, California, USA

 

Water plays a critical role in societal stability through both its excess and scarcity. Extreme hydrological events can cause substantial human and economic losses, while water scarcity affects essential services such as drinking water supply, food production, and hydropower generation. Reliable streamflow predictions are therefore fundamental for environmental assessments, flood risk management, and Integrated Water Resources Management (IWRM).

Hydrological models are central tools for understanding catchment behaviour and generating predictions to support water-resources assessment, planning, and management. However, their predictive performance strongly depends on the temporal resolution at which they are applied.

At hourly time scales, hydrological processes and associated uncertainties become markedly more complex, particularly in small and mesoscale catchments. Flood peaks may last only a few hours, so daily streamflow predictions can substantially underestimate peak magnitudes; antecedent wetness conditions can evolve rapidly; and the dominant processes controlling short-term streamflow dynamics differ from those governing longer term behavior. For example, over longer time scales, predictions are primarily constrained by mass balance, whereas short-term predictions depend more strongly on dynamics and flow routing.

In addition to classical sources of uncertainty related to data, model structure, and parameters, hourly streamflow predictions often exhibit bias, heteroscedasticity, temporal autocorrelation, and non-stationarity.

Despite their importance, hourly streamflow prediction and uncertainty characterisation have received comparatively less attention than daily-scale studies.

In this work, we use a conceptual hydrological model to generate deterministic hourly streamflow predictions and quantify predictive uncertainty using a residual error modelling framework. Case-study catchments include hydrologically diverse basins in Europe and the United States. Bias, heteroscedasticity, and temporal dependence in model residuals are addressed using Box–Cox transformations and autoregressive and moving average (ARMA) models.

Results indicate that a logarithmic transformation combined with an autoregressive model of order three (AR(3)) provides the most consistent performance across catchments. This work advances streamflow prediction by developing statistically rigorous methods for post-processing the residuals of conceptual hydrological models at the hourly time scale, supporting more reliable hourly streamflow predictions for integrated water resources management and decision-making.