Preprints
https://doi.org/10.5194/egusphere-2022-857
https://doi.org/10.5194/egusphere-2022-857
01 Sep 2022
 | 01 Sep 2022

Bayesian parameter inference in hydrological modelling using a Hamiltonian Monte Carlo approach with a stochastic rain model

Simone Ulzega and Carlo Albert

Abstract. Conceptual models of the rainfall-runoff behaviour of hydrological catchments have proven to be useful tools for making probabilistic predictions. However, model parameters need to be calibrated to measured data and their uncertainty quantified. Bayesian statistics is a consistent framework for learning from observed data, in which knowledge about model parameters is described through probability distributions. One of the dominant sources of uncertainty in rainfall-runoff modelling is the true rainfall over the catchment, which often needs to be inferred from a few rain-gauge and runoff measurements. modelling this uncertainty naturally leads to stochastic differential equation models, which render traditional inference algorithms such as the Metropolis algorithm infeasible due to their expensive likelihood functions. Therefore, in hydrology and other applied fields of research, error models are traditionally oversimplified for ease of inference as additive errors on the output, leading to biased parameter estimates and unreliable predictions. However, thanks to recent advancements in algorithms and computing power, full-fledged Bayesian inference with stochastic models is no longer off-limits for hydrological applications. We demonstrate this with a case study from urban hydrology, for which we employ a highly efficient Hamiltonian Monte Carlo inference algorithm with a time-scale separation.

Simone Ulzega and Carlo Albert

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2022-857', Anonymous Referee #1, 05 Oct 2022
    • AC1: 'Reply on RC1', Simone Ulzega, 28 Nov 2022
      • RC2: 'Reply on AC1', Anonymous Referee #1, 30 Nov 2022
        • AC3: 'Reply on RC2', Simone Ulzega, 20 Feb 2023
  • RC3: 'Comment on egusphere-2022-857', Anonymous Referee #2, 12 Jan 2023
    • AC2: 'Reply on RC3', Simone Ulzega, 20 Feb 2023
  • RC4: 'Comment on egusphere-2022-857', Anonymous Referee #3, 06 Feb 2023
    • AC4: 'Reply on RC4', Simone Ulzega, 24 Feb 2023

Simone Ulzega and Carlo Albert

Simone Ulzega and Carlo Albert

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Short summary
Embedding input uncertainties in hydrological modelling naturally leads to stochastic models, which render parameter calibration an often computationally intractable problem. We use a case study from urban hydrology based on a stochastic rain model, and we employ a highly efficient Hamiltonian Monte Carlo inference algorithm with a time-scale separation, to demonstrate that full-fledged Bayesian inference with stochastic models is no longer off-limits for hydrological applications.