Simultaneous Calibration of Hydrologic Model Structure and Parameters Using a Blended Model

Abstract

Hydrologic models have been used for numerous applications in the last number of decades. These applications include streamflow prediction, flood forecasting, or reservoir level forecasting, or in a scientific capacity to advance our understanding of hydrologic systems. Whether used in a predictive or scientific capacity, models are an abstraction of the complex natural system being simulated, and necessarily simplify the treatment of hydrological processes occurring in a watershed, either to facilitate computational expediency or in recognition of the large degree of uncertainty regarding how the watershed functions. In most practical cases, model calibration is required in order to reconcile model output with historical observation; conventionally, this calibration process focuses on tuning only model parameters. However, hydrologic models are typically considered to have four main components that contribute to model uncertainty (e.g., Beven, 2005;Butts et al., 2004;Gupta, Clark, et al., 2012): (1) input forcing data, such as precipitation and temperature, (2) model structure, which includes the algorithmic functions used to simulate the hydrologic cycle, (3) model parameters related to the selected hydrologic process algorithms (often the only degree of freedom used to tune model performance), and (4) an error term, which represents any uncertainty or deviation from reality not captured in the other three components of model uncertainty.This study focuses upon the simultaneous calibration of model structure and model parameters. We refer to model structure here as a combination of (a) the number and type of stores represented in the model and (b) the collection of algorithms used to describe the relationships between fluxes and storage in each hydrological response unit (HRU). Model structure can be further extended to other modeling decisions such as spatial discretization, but this extended definition is not evaluated here. Historically, most hydrologic models have been designed with a fixed model structure while the input data and model parameters may vary from watershed to watershed. These fixed model structures were typically chosen because they (1) adequately represented the hydrologic response of one or more watersheds, (2) generally respected the physics of water flow and storage, (3) were consistent with conceptual models of the water cycle garnered from field investigation, and/or (4) convention (Addor & Melsen, 2019). In many cases, trial and error was used to determine final model structure (e.g., Perrin et al., 2003). However, there are many such model structures that can generally meet these criteria, and as such, there exist dozens of fixed structure models which used different algorithms to represent various components of the water cycle. The fixed model structure concept

Time to Update the Split‐Sample Approach in Hydrological Model Calibration

“…Raven is a robust and highly generalized object‐oriented flexible modeling framework platform. It supports flexible customization in terms of a wide range of model structures, watershed discretization, process representations, forcing function estimation and interpolation methods and other numerical algorithms, which provides a standardized modeling platform and allows various types of hydrological modeling investigations, such as model structure sensitivity/uncertainty analysis (Chlumsky et al., 2021; Mai et al., 2022) and model inter‐comparison (Mai et al., 2021). Raven conveniently unifies the format for both models' input and output files.…”

“…In the proposed SST experiment, GR4J and HMETS are both calibrated in each of the 463 CAMELS catchments over the 50 CSPs introduced in Section 2.1. The dynamically dimensioned search (DDS) algorithm (Tolson & Shoemaker, 2007), which has been widely applied in hydrological model calibration studies (Chlumsky et al., 2021; Dembélé et al., 2020; Lahmers et al., 2019; Sharma et al., 2019; Spieler et al., 2020), is used to automatically calibrate model parameters. We utilize DDS as implemented in the optimization and calibration software toolkit OSTRICH (Matott, 2017).…”

“…The HMETS introduced by Martel et al ( 2017) is a more complex lumped model than GR4J, which considers more complicated hydrological processes and has up to 21 parameters for calibration, all of which are calibrated in our study. This model has been used in many hydrological modeling studies and has shown robust performance in previous studies (Arsenault et al, 2018;Chlumsky et al, 2021;Shen et al, 2018). HMETS employs two Unit Hydrographs to route the surface and delayed runoff.…”

Leveraging ensemble meteorological forcing data to improve parameter estimation of hydrologic models

“…Calibration approach 1 uses the deterministic forcing as model input and calibrates the hydrologic model by minimizing RMSE using the dynamically dimensioned search (DDS) global optimization algorithm (Tolson & Shoemaker, 2007). DDS is widely used in hydrology and operates on a pre‐specified computational budget (Arsenault et al, 2014; Bárdossy & Singh, 2008; Chlumsky et al, 2021; Kumar et al, 2013; White et al, 2011; Yen et al, 2015). The computational budget here is measured by the maximum allowable model evaluations and is set to 500.…”

“…The objective function to be minimized is the RMSE between the simulated flow and the synthetic true flow expressed as: where and are the simulated and the synthetic true flows at time . Calibration approach 1Calibration approach 1 uses the deterministic forcing as model input and calibrates the hydrologic model by minimizing RMSE using the dynamically dimensioned search (DDS) global optimization algorithm (Tolson & Shoemaker, 2007). DDS is widely used in hydrology and operates on a pre‐specified computational budget (Arsenault et al, 2014; Bárdossy & Singh, 2008; Chlumsky et al, 2021; Kumar et al, 2013; White et al, 2011; Yen et al, 2015). The computational budget here is measured by the maximum allowable model evaluations and is set to 500.…”