Abstract
Abstract. A non-parametric method is applied to quantify residual uncertainty in hydrologic streamflow forecasting. This method acts as a post-processor on deterministic model forecasts and generates a residual uncertainty distribution. Based on instance-based learning, it uses a k nearest-neighbour search for similar historical hydrometeorological conditions to determine uncertainty intervals from a set of historical errors, i.e. discrepancies between past forecast and observation. The performance of this method is assessed using test cases of hydrologic forecasting in two UK rivers: the Severn and Brue. Forecasts in retrospect were made and their uncertainties were estimated using kNN resampling and two alternative uncertainty estimators: quantile regression (QR) and uncertainty estimation based on local errors and clustering (UNEEC). Results show that kNN uncertainty estimation produces accurate and narrow uncertainty intervals with good probability coverage. Analysis also shows that the performance of this technique depends on the choice of search space. Nevertheless, the accuracy and reliability of uncertainty intervals generated using kNN resampling are at least comparable to those produced by QR and UNEEC. It is concluded that kNN uncertainty estimation is an interesting alternative to other post-processors, like QR and UNEEC, for estimating forecast uncertainty. Apart from its concept being simple and well understood, an advantage of this method is that it is relatively easy to implement.
Highlights
Hydrologic forecasts for real-life systems are inevitably uncertain (Beven and Binley, 1992; Gupta et al, 1998; Refsgaard et al, 2007)
The prediction intervals generated by k nearest-neighbour (kNN) resampling are smaller, compared to the other two uncertainty estimation techniques, while the coverage probability is similar
The application of kNN resampling to two case studies shows that the forecast uncertainty intervals are relatively narrow and still capture the observations well
Summary
Hydrologic forecasts for real-life systems are inevitably uncertain (Beven and Binley, 1992; Gupta et al, 1998; Refsgaard et al, 2007). This, among other things, is due to the uncertainties in the meteorological forcing, in the modelling of the hydrologic system response and in the initial state of the system at the time of forecast. Various techniques have been developed to quantify uncertainties associated with the meteorological model input (van Andel et al, 2013), the initial state of the model (Li et al, 2009) and the hydrologic models themselves (Deletic et al, 2012; Coccia and Todini, 2011). Frameworks and guidelines have been developed to incorporate uncertainty analysis of environmental models effectively in decision making (Arnal et al, 2016; Reichert et al, 2007; Refsgaard et al, 2007). There are three basic approaches to uncertainty estimation: (i) explicitly defining a probability model for the system response, e.g. Todini (2008), (ii) estimation of statistical properties of the error time series in the post-processing phase of model forecast, e.g. Dogulu et al (2015), and (iii) methods using Monte Carlo sampling of inputs and/or parameters, aimed
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