Bluecat: A Local Uncertainty Estimator for Deterministic Simulations and Predictions

Abstract

We present a new method for simulating and predicting hydrologic variables with uncertainty assessment and provide example applications to river flows. The method is identified with the acronym “Bluecat” and is based on the use of a deterministic model which is subsequently converted to a stochastic formulation. The latter provides an adjustment on statistical basis of the deterministic prediction along with its confidence limits. The distinguishing features of the proposed approach are the ability to infer the probability distribution of the prediction without requiring strong hypotheses on the statistical characterization of the prediction error (e.g., normality, homoscedasticity), and its transparent and intuitive use of the observations. Bluecat makes use of a rigorous theory to estimate the probability distribution of the predictand conditioned by the deterministic model output, by inferring the conditional statistics of observations. Therefore Bluecat bridges the gaps between deterministic (possibly physically based, or deep learning‐based) and stochastic models, as well as between rigorous theory and transparent use of data with an innovative and user oriented approach. We present two examples of application to the case studies of the Arno river at Subbiano and Sieve river at Fornacina. The results confirm the distinguishing features of the method along with its technical soundness. We provide an open software working in the R environment, along with help facilities and detailed instructions to reproduce the case studies presented here.

Revisiting causality using stochastics: 2. Applications

“…However, the modelling of the entire system cannot be reliably made without data and without moving from a deterministic to a stochastic description (cf. [12,13]). Therefore, induction is absolutely necessary.…”

“…It is true that some of the mechanisms of the transformation are described by differential equations as dynamical systems. However, the modelling of the entire system cannot be reliably made without data and without moving from a deterministic to a stochastic description (cf [12,13]…”

A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecasting

“…et al (2019, 2020b), Tyralis et al (2019a, Sikorska-Senoner and Quilty (2021), Koutsoyiannis and Montanari (2022), Quilty et al (2022), Romero-Cuellar et al (2022)]. Notably, reviews, overviews and popularizations that focus on the above-referred to as existing and useful machine learning concepts and methods are currently missing from the probabilistic hydrological post-processing and forecasting literatures.…”

Application of hybrid machine learning models and data pre-processing to predict water level of watersheds: Recent trends and future perspective

“…Hybridisation has emerged as a promising technique for overcoming numerous drawbacks of standalone methods while also improving prediction accuracy (Hajirahimi & Khashei, 2022). There are several types of hybrid models, e.g., the hybrid model that combines a physical model and a machine learning model (Nualtong et al, 2021;Xu et al, 2019), and the hybrid stochastic-ML model proposed by Koutsoyiannis and Montanari (Koutsoyiannis & Montanari, 2022). Papacharalampous (Papacharalampous et al, 2019) showed that the hybrid stochastic-ML model is better than single stochastic or ML models.…”