A Stochastic Data‐Driven Ensemble Forecasting Framework for Water Resources: A Case Study Using Ensemble Members Derived From a Database of Deterministic Wavelet‐Based Models

Abstract

In water resources applications (e.g., streamflow, rainfall‐runoff, urban water demand [UWD], etc.), ensemble member selection and ensemble member weighting are two difficult yet important tasks in the development of ensemble forecasting systems. We propose and test a stochastic data‐driven ensemble forecasting framework that uses archived deterministic forecasts as input and results in probabilistic water resources forecasts. In addition to input data and (ensemble) model output uncertainty, the proposed approach integrates both ensemble member selection and weighting uncertainties, using input variable selection and data‐driven methods, respectively. Therefore, it does not require one to perform ensemble member selection and weighting separately. We applied the proposed forecasting framework to a previous real‐world case study in Montreal, Canada, to forecast daily UWD at multiple lead times. Using wavelet‐based forecasts as input data, we develop the Ensemble Wavelet‐Stochastic Data‐Driven Forecasting Framework, the first multiwavelet ensemble stochastic forecasting framework that produces probabilistic forecasts. For the considered case study, several variants of Ensemble Wavelet‐Stochastic Data‐Driven Forecasting Framework, produced using different input variable selection methods (partial correlation input selection and Edgeworth Approximations‐based conditional mutual information) and data‐driven models (multiple linear regression, extreme learning machines, and second‐order Volterra series models), are shown to outperform wavelet‐ and nonwavelet‐based benchmarks, especially during a heat wave (first time studied in the UWD forecasting literature).

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

“…For instance, if we are interested in delivering the 90% prediction interval and m = 1 000, then we simply have to pick at each time t ∊ T3 the 50 th and 950 th highest values (resulted via ranking) from the spaghetti plot of the 1 000 retained simulations. In absence of relevant information, the MK blueprint methodology can also be applied without explicitly considering input data uncertainty, i.e., by not running ensemble simulations for the hydrological model's input, without any loss of its generality (see e.g., the implementations in Quilty et al 2019).…”

“…o The error models adopted in the precursor variants, i.e., the meta-Gaussian bivariate distribution model used in simulation mode by Montanari and Koutsoyiannis (2012), and the kNN model used by Sikorska et al (2015) and Quilty et al (2019), are here replaced by a statistical learning regression model that is suitable for predicting quantiles. Some key differences from other two-stage post-processing methodologies are also summarized subsequently:…”

“…These point predictions are hereafter referred to as "sister predictions" using the terminology of Nowotarski et al (2016), Wang et al (2016), and Liu et al (2017). Different variants of the MK blueprint methodology can be found in Sikorska et al (2015) and Quilty et al (2019). The flexibility of the MK blueprint methodology is proved by the latter study, which focuses on probabilistic water demand forecasting using exogenous variables.…”

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

“…Different variants of the MK blueprint methodology can be found in Sikorska et al (2015), Quilty et al (2019) and Papacharalampous et al (2019c; companion to the present paper). The original blueprint and the variant by Sikorska et al (2015) are formulated to explicitly consider input data uncertainty, while in both related papers a large number of hydrological model parameters are obtained by using the DREAM algorithm by Vrugt et al (2009a;see also Vrugt 2016).…”

“…For benchmarking purposes, we also apply the working methodology using the linear regression model (see e.g., James et al 2013;Hastie et al 2009) as error model, and the two naïve probabilistic data-driven schemes. For the merits of using benchmarks in hydrological modelling, the reader is referred to Pappenberger et al (2015); see also benchmarking examples in Montanari and Brath (2004), Papacharalampous and Tyralis (2018), Papacharalampous et al (2018aPapacharalampous et al ( ,b,c, 2019a, Quilty et al (2019), Evin et al (2014), Sikorska et al (2015), Papacharalampous (2017, 2018), Tyralis et al ( , 2019a, and Xu et al (2018).…”