Residual uncertainty estimation using instance-based learning with applications to hydrologic forecasting

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 nearestneighbour 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.

Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models

“…o In contrast to basic two-stage post-processing methodologies using flexible quantile regression models (see e.g., Dogulu et al 2015;López López et al 2014;Solomatine and Shrestha 2009;Wani et al 2017;Papacharalampous et al 2019b), the methodology of the study is an ensemble learning methodology, as it combines multiple predictions to offer improved predictive performance.…”

“…Here the interest is on probabilistic hydrological post-processing methodologies, in which the error model is estimated conditional upon the point prediction(s) of the hydrological model by using an independent segment (with respect to the one used for estimating the parameters of the hydrological model) extracted from the historical dataset. Various methodologies of this category are currently available (see e.g., Bock et al 2018;Bourgin et al 2015;Dogulu et al 2015;Farmer and Vogel 2016;López López et al 2014;Montanari and Brath 2004;Montanari and Grossi 2008;Montanari and Koutsoyiannis 2012;Solomatine and Shrestha 2009;Papacharalampous et al 2019b;Tyralis et al 2019b;Wani et al 2017), amongst other probabilistic hydrological modelling and hydrological forecasting methodologies based on the idea of integrating process-based models and statistical approaches (see e.g., Beven and Binley 1992; Hernández- López and Francés 2017;Kavetski et al 2002;2006, Krzysztofowicz 1999, 2001, 2002Kelly 2000, Krzysztofowicz andHerr 2001;Todini 2008; see also the review of Montanari 2011). Hereafter, we use the comprehensive term "two-stage" by Evin et al (2014) to imply that the parameters of a probabilistic hydrological post-processing methodology are estimated within two subsequent stages.…”

A crash-testing framework for predictive uncertainty assessment when forecasting high flows in an extrapolation context

“…The latter approaches build a description of the predictive residuals from past error series, such as data learning-algorithms (Solomatine and Shrestha, 2009). Some related methods are the non-parametric approach of Van Steenbergen et al (2012), the empirical hydrological uncertainty processor of Bourgin et al (2014) or the k-nearest neighbours method of Wani et al (2017). The Quantile Regression (QR) framework (Weerts et al, 2011;Dogulu et al, 2015;Verkade et al, 2017) lies in between in that it 5 introduces an assumption of a linear relationship between the forecasted discharge and the quantiles of interest.…”

Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: A large-sample experiment at monthly timescale

“…Non-Bayesian post-processing methodologies that focus on the modelling of a single error term conditional on point predictions and historical information are also available in the hydrological modelling literature (see e.g., Bock et al 2018;Bourgin et al 2015;Farmer and Vogel 2016;Montanari and Brath 2004;Montanari and Grossi 2008;Dogulu et al 2015;López López et al 2014;Solomatine and Shrestha 2009;Wani et al 2017).…”

“…The quantile regression model is a balanced choice between interpretable and more flexible algorithms from the statistical learning literature. It has already been applied for post-processing hydrological predictions within hydrological modelling case studies (see e.g., Dogulu et al 2015, López López et al 2014, Solomatine and Shrestha 2009, Wani et al 2017, while its use is more common in the field of hydrological forecasting (see e.g., Tyralis et al 2019a and the references therein); see also the references in Dogulu et al (2015) for applications of this model in other geoscience concepts.…”