Research papers
A water-level based calibration of rainfall-runoff models constrained by regionalized discharge indices

https://doi.org/10.1016/j.jhydrol.2021.126937Get rights and content

Highlights

  • Water-level based rainfall-runoff calibration can be improved using discharge index.

  • Efficacy of regionalized discharge index is comparable with that of observed values.

  • Water-level based calibration with discharge index works better for wet catchments.

  • Regionalized Qmean is a better choice than regionalized Q95 as discharge index.

Abstract

Rainfall-runoff models are generally calibrated by using continuous stream discharge data. However, most catchments around the globe remain ungauged due to the difficulty in installing gauges in river channels with complex morphology and due to the high costs of installation and maintenance. Recently, new calibration methods that use water level data instead of gauged discharge to calibrate rainfall-runoff models have been proposed. With emerging low-cost local water-level monitoring technologies or with satellite altimetry, these water-level based calibration methods have the potential to significantly extend runoff prediction capability. However, rainfall-runoff models calibrated from using water-level information alone may lead to biased discharge even when water-level variations are accurately reproduced. It has been shown that this bias problem can be significantly alleviated when just a few discharge measurements, especially of high flows, are available and incorporated into the model calibration. However, it is rare to have discharge measurement data when catchments are ungauged. In this study, we incorporate discharge estimates derived from regionalization into a water-level based calibration using an inverse rating curve (IRC) method. Specifically, discharge indices such as the 95th percentile of daily discharge (Q95) and the mean daily discharge (Qmean) are estimated from catchment and climate characteristics based on regionalized relationships. These estimated discharge indices are then used to constrain the IRC calibration. We evaluate both constrained and unconstrained IRC methods over 130 study catchments where observed discharge time series are available but used only for validation in this study. Modelled discharge time series from the constrained IRC methods have median Nash Sutcliffe Efficiency (NSE) values of 0.61–0.63, compared with 0.54 from the unconstrained IRC method. Improvement is seen in around 75% of the catchments, with more than 0.2 increase in NSE values in 25% of the catchments. Improvement in the modelled discharges from using regionalized discharge indices is comparable to using observed discharge indices. Using regionalized Qmean yields greater improvement than using regionalized Q95. The constrained IRC methods tend to perform better in wetter catchments than in drier ones. This method can significantly extend rainfall-runoff model calibration in a wider range of catchments, including real ungauged catchments.

Introduction

In rainfall-runoff modelling, accurate discharge time series is essential for calibrating model parameters (Beven, 2011). Commonly, continuous discharge data are derived from observed water-level data via established rating curves in each monitoring station (McMillan et al., 2012, Schmidt, 2003). However, most catchments are ungauged or sparsely gauged due to inaccessibility of remote areas and high cost of installing monitoring equipment (Alsdorf et al., 2003, Hrachowitz et al., 2013, SIVAPALAN et al., 2003). Even in catchments with continuous water-level measurements, the accuracy of discharge time series can be affected by various factors such as observation error (McMillan et al., 2012) and inaccurate rating curves (Fenton, 2015, Fenton and Keller, 2001, McMahon and Peel, 2019, McMillan et al., 2010). Therefore, a new calibration method that does not rely on continuous discharge data is highly valuable for rainfall-runoff modelling.

Instead of using discharge, water-level time series can provide an alternative and cost-effective way to calibrate rainfall-runoff models. Jian et al. (2017) and Seibert and Vis (2016) demonstrated the potentials of two water-level based calibration approaches: Spearman Rank based (SRC) (Jian et al., 2017, Seibert and Vis, 2016) and Inverse Rating-Curve based method (IRC) (Jian et al., 2017). These methods are based on a straightforward approach that does not need to establish rating curves and is not vulnerable to the biases of rating curves. Also, an increasing number of satellite altimeters could provide larger coverage of water level measurements, especially in ungauged catchments (Alsdorf et al., 2007, Biancamaria et al., 2016, Fu et al., 1994, Lambin et al., 2010, Markert et al., 2019, Ménard et al., 2003, Verron et al., 2015). Recently, a new source of citizen-based water-level measurements is developing (e.g., CrowdHydrology, CrowdWater), which trains citizens to measure water level class observations and then could extend the coverage of the water level data (Etter et al., 2020, Strobl et al., 2019). These data sources enable the application of water-level based calibration in more locations. These water-level based calibration methods may encounter large bias in the estimated discharge time series since accurate discharge information is missing. However, they can be improved significantly in their capability of reproducing flow dynamics (timing, fluctuations and trend) and prediction accuracy by incorporating a small number of discharge indices, such as the 95th percentile of discharge (Q95), the 75th percentile of discharge (Q75) and the median of discharge (Q50). Jian et al. (2017) demonstrated that incorporating the high flow data (Q95) resulted in the most significant improvement. The improvement is made by constraining the bias in discharge prediction caused by the absence of reference discharge for a given (observed) water-level dynamics.

In practice, however, these discharge indices are rarely available in ungauged catchments, limiting the application of the bias-constrained water-level based calibrations. Currently, there exist various methods of regionalization to derive discharge indices without the actual discharge observations, such as spatial interpolation (Zhang et al., 2014), multiple linear regression (MLR) and log-transformed multiple linear regression (Zhang et al., 2014), and hydrological similarity based approach (Westerberg et al., 2016). Among them, MLR is widely adopted due to its simplicity and effectiveness (Lima et al., 2015, Yadav et al., 2007). For example, Joshi et al. (2013) estimated low-flow indices in three rivers in Eastern Canada using Bayesian Learning and Multiple Linear Regression. Zhang et al. (2018) estimated 13 runoff indices (including low-flow, mean flows and high-flow data) in 605 Australian catchments via linear regression and regression ensemble. All these applications indicate that direct data-driven method can be used as a practical tool in estimating discharge indices.

In this work, we examine the efficacy of the water-level based calibration scheme constrained by regionalized discharge indices. Two discharge indices, the 95th percentile of daily discharge (Q95) and the mean daily discharge (Qmean), are derived using MLR with a set of fourteen easily accessible predictors that represent climatic, geologic, topographic and land cover properties (details in section 3.2). Our novel approach is applied to a large number of catchments (130 catchments with Hydrological Reference Stations of the Australian Bureau of Meteorology) to evaluate its performance and robustness. In addition, catchment properties that influence the calibration performance are also explored.

This method can significantly enhance our capability to calibrate rainfall-runoff models in the ungauged catchments.

Section snippets

Study catchments and datasets

In this study, Hydrological Reference Stations (HRS) of the Bureau of Meteorology of Australia (http://www.bom.gov.au/water/hrs/about.shtml) are selected as study catchments. They are unregulated catchments that are not affected by human activities, and discharge data in these catchments are quality-checked (Zhang et al., 2016). The catchment locations are spread widely covering major climate zones in Australia (Peel et al., 2007). Additional quality assurance is taken based on the quality of

Rainfall-runoff model

A conceptual daily rainfall-runoff model GR4J (Perrin et al., 2003) is employed in this work. GR4J is one of the operational streamflow forecast models used by the Bureau of Meteorology of Australia. The model outperforms other commonly used hydrological models in the study catchments in capturing the flow behavior (Pagano et al., 2010). Besides, GR4J is a simple and effective model that involves only four parameters representing store capacity (x1), groundwater exchange coefficient (x2), and

Regionalization of discharge indices

Through regionalization, the following regression models are found for estimating the discharge indices:Qmeanreg=-0.57+0.54meanArain+0.25Tmean-0.15Area+0.19meanSlope-0.07meanClay%+0.13meanPAWC_1mQ95reg=0.75+0.79meanArain+0.30Tmean+0.15meanSlope-0.16meanClay%+0.18MeanPAWC_1m

The estimation accuracy quantified via the NSE are 0.83 for regionalized Qmean (Qmeanreg) and 0.77 for regionalized Q95 (Q95reg), indicating that the regionalized Qmean is more accurate than the regionalized Q95.

Performance of water-level based calibration schemes

Comparison of evaluation results in Fig. 4 indicates that the overall improvement of median NSE and reduced IQR for Schemes 3–4 over Scheme 2 is largely contributed by the pronounced improvements over catchments where Scheme 2 calibration struggles. Reduced IQR of Schemes 3–4 also indicates improved robustness of IRC calibration when observed or regionalized discharge indices are introduced as a constraint.

In order to examine whether the water-level based calibration would provide similar

Conclusion

The inverse rating-curve based method (IRC) enables water-level based calibration of rainfall-runoff models in ungauged catchments. Although the IRC method provides calibration efficacy weaker than the conventional discharge-based calibration, the efficacy improves when a small number of discharge indices derived from observations are integrated as constraints. In real ungauged catchments, however, observed constraints are not available. We showed that discharge indices derived from a method of

CRediT authorship contribution statement

Jie Jian: Methodology, Formal analysis, Writing– original draft. Dongryeol Ryu: Methodology, Formal analysis, Writing – review & editing. Q.J. Wang: Methodology, Formal analysis, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

We thank Dr. Justin Costelloe (University of Melbourne) who inspired the authors with his extensive experience in arid zone hydrology and provided fundamental ideas to this study.

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