Information theory-based multi-objective design of rainfall network for streamflow simulation

doi:10.1016/j.advwatres.2019.103476

Advances in Water Resources

Volume 135, January 2020, 103476

https://doi.org/10.1016/j.advwatres.2019.103476 Get rights and content

Highlights

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Multivariate transinformation is used to measure the information transfer between rainfall and streamflow.
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Multi-objective design of a rainfall network for streamflow simulation is compared to two other methods using the ANN model.
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The combination of rainfall network design with downstream streamflow simulation is possible on a catchment scale.

Abstract

Rainfall data are needed for water resource management and decision making and are obtained from rainfall networks. These data are especially important for streamflow simulations and forecasting the occurrence of intense rainfall during the flood season. Therefore, rainfall networks should be carefully designed and evaluated. Several methods are used for rainfall network design, and information theory-based methods have recently received significant attention. This study focuses on the design of a rainfall network, especially for streamflow simulation. A multi-objective design method is proposed and applied to the Wei River basin in China. We use the total correlation as an indicator of information redundancy and multivariate transinformation as an indicator of information transfer. Information redundancy refers to the overlap of information between rainfall stations, and information transfer refers to the rainfall-runoff relationship. The outlet streamflow station (Huaxian station in the Wei River basin) is used as the target station for the streamflow simulation. A non-dominated sorting genetic algorithm (NSGA‐II) was used for the multi-objective optimization of the rainfall network design. We compared the proposed multi-objective design with two other methods using an artificial neural network (ANN) model. The optimized rainfall network from the proposed method led to reasonable outlet streamflow forecasts with a balance between network efficiency and streamflow simulation. Our results indicate that the multi-objective strategy provides an effective design by which the rainfall network can consider the rainfall-runoff process and benefit streamflow prediction on a catchment scale.

Introduction

Rainfall networks provide basic data for the study of hydrological systems, and these data are fundamental for water resource planning and management. The question of designing an optimal rainfall network has been discussed since the 1960s (Chacon-Hurtado et al., 2017), and there are different design methods, including geostatistical methods (Pardo-Igúzquiza, 1998; Cheng et al., 2008; Shafiei et al., 2013), information theory-based methods (Husain, 1989; Krstanovic and Singh, 1992; Yang and Burn, 1994; Ridolfi et al., 2011; Yeh et al., 2017), methods based on expert recommendations (Bleasdale, 1965; Laize, 2004), and other methods such as value of information and network theory (Alfonso and Price, 2012; Halverson and Fleming, 2015). The design of a network is often site-specific or case-specific and may need to consider a multitude of factors to address practical needs. Thus, it is difficult to develop a unified or “one-fits-all” methodology for rainfall network design (Behmel et al., 2016). Recently, entropy theory has been applied to different watersheds with different monitoring goals (Chen et al., 2008; Barca et al., 2008; Chebbi et al., 2011; Keum et al., 2017).

Rainfall network design usually aims at better rainfall estimations and achieving more information from the system on different spatial and temporal scales. For this purpose, some studies apply a geostatistical approach to minimize the variance in areal rainfall estimations (Chen et al., 2008; Adhikary et al., 2015). Entropy-based methods are used to obtain most information from the rainfall network system from the perspective of information theory (Yeh et al., 2017; Wang et al., 2018). Wang et al. (2019) further compared data transfer models (geostatistical approach) and information transfer models (entropy approach) for rainfall network evaluation. Recently, Abbasnezhadi et al., 2019 also mentioned the importance of hydro-geostatistical network design or assessment because the estimation of rainfall input can influence the modelled streamflow. At present, most design methods have mainly focused on a single variable, i.e., rainfall network design uses only rainfall observation data. Because network design can be case-specific and hydrological variables can differ in their characteristics, there have been few discussions on the methods to design rainfall networks for streamflow simulations. Keum and Coulibaly (2017) proposed a multi-objective optimization approach for simultaneously maximizing information, minimizing redundancy of the hydrometric network, and maximizing conditional entropy that indicates information contained in a streamflow network that cannot be obtained from the precipitation network. Previous studies have focused on different types of monitoring networks, such as precipitation networks (Ridolfi et al., 2011; Wei et al., 2014), streamflow and water-level networks (Li et al., 2012; Fahle et al., 2015), soil moisture and groundwater networks (Kornelsen and Coulibaly, 2015; Mondal and Singh, 2011), and water quality networks (Lee, 2013). However, the integrated design of networks based on entropy had not received much attention until the work by Keum and (Coulibaly 2017) was conducted. As Keum et al. (2017) also mentioned in a recent review, the practical application of a monitoring network, e.g., rainfall network, has seldom been evaluated in hydrological or other models. Since hydrological variables can be correlated and impact the environment simultaneously, many studies have been conducted on their joint behavior (Song and Singh, 2010a, Song and Singh, 2010b, Ma et al., 2013). In addition, because hydrological variables are interconnected in the water cycle and can be affected interactively (Li et al., 2014; Song et al., 2015; Zhang et al., 2015a, 2015b, 2018), it is necessary to explore network performance from a system perspective. Volkmann et al. (2010) suggested that a multi-criteria rain gage network design strategy could provide a sparse but accurate network for flash flood prediction using the Kinematic Runoff and Erosion (KINEROS2) model. Rainfall networks have also been designed for hydrological modelling using the lumped Xinanjiang model and the distributed Soil and Water Assessment Tool (SWAT) model, which is recognized as a multi-criteria network design (Xu et al., 2015). Furthermore, the effects of rainfall network density and distribution on streamflow simulations have been investigated using hydrological modeling (Bárdossy and Das, 2008; Xu et al., 2013; Zeng et al., 2018; Abbasnezhadi et al., 2019). However, these design or optimization procedures still involve only one hydrological variable (rainfall). A multivariate network design was not discussed until (Keum and Coulibaly 2017) developed an integrated design framework for streamflow and precipitation networks based on multi-objective optimization. The rainfall-runoff process was still not completely represented, as the results were not evaluated with hydrological or other models. Here, we present a multi-objective optimization approach for the design of a rainfall network to assist streamflow prediction, and the optimization involves two hydrological variables, rainfall and streamflow. The method is generally based on multi-objective optimization, which provides a framework for designing a rainfall network using hydrometric information (other than rainfall) as well. On the one hand, this approach minimizes the information redundancy in the rainfall network (Alfonso et al., 2010a; Alfonso et al., 2010b; Li et al., 2012; Fahle et al., 2015; Leach et al., 2016; Stosic et al., 2017), which has become a widely and frequently accepted principle in network design. On the other hand, the correlation between the input rainfall and the output streamflow is maximized to improve model performance. In such a case, the design of a rainfall network simultaneously reduces the redundancy among the selected set of rainfall stations and increases the relevance between rainfall input and streamflow output. Therefore, multi-objective optimization connects rainfall network design and downstream streamflow forecasting from a theoretic information viewpoint. In addition, multi-objective optimization also considers better rainfall estimations and uses another objective to achieve the minimum residual variance in the rainfall observation data. The results of the optimization method were further examined using an artificial neural network (ANN) model for streamflow simulation. The method is also compared in different aspects with two other key methods (Keum and Coulibaly, 2017; Xu et al., 2015) using multi-objective optimization.

The remainder of the paper is organized as follows. In Section 2, we introduce the basic measures, multi-objective optimization and rainfall-runoff forecast models used in this study and present the proposed method framework. In Section 3, we describe the study area, including the background of the basins and dataset description. In Section 4, we discuss the results obtained from the case study. Finally, in Section 5, we provide conclusions and suggestions for rainfall network design.

Section snippets

Entropy measures

The methods based on entropy theory (Shannon, 1948) for designing hydrometric networks apply several concepts, such as marginal entropy, joint entropy, conditional entropy, mutual information, partial mutual information, total correlation and multivariate transinformation. Definitions of these measures are given as follows.

The marginal entropy (H) of a discrete variable X can be defined as: $H (X) = H (p_{1}, p_{2}, p_{3}, \dots, p_{N}) = - \sum_{i = 1}^{N} p_{i} \log p_{i}$ where p_i (0 ≤ p_i ≤ 1) is the probability of occurrence x_i (i = 1, 2, …,

Wei river basin

The Wei River is the largest tributary of the Yellow River and originates in Weiyuan County of Gansu Province, flowing through Gansu, Ningxia, Shaanxi, and other provinces from west to east. The total length of the mainstream is 818 km, and the total area of the Wei River basin is 134,800 km², accounting for 18% of the total area of the Yellow River basin. The seasonal variation in runoff is significant for the Wei River, with the largest runoff in autumn accounting for 38% ~ 40% of the annual

Spatio-temporal correlation and dependence between stations

To determine the concentration time for the hydrometric station, we compared the correlations between three hydrometric stations (S_W, S_X, S_L) and the Huaxian station (S_H) using correlation coefficients and mutual information. According to the description of the three flood processes in 2011, we found that the flood propagation time lasted no more than three days. Therefore, the time lag was chosen to vary from 0 to 3 days. The highest values of the correlation coefficient and mutual information

Conclusion

We proposed a multi-objective rainfall network design method based on information theory and applied it to the Wei River basin in China. The rainfall network design can be viewed as the input for a rainfall-runoff model, as it was intended to consider streamflow data at the outlet hydrometric station. The method adopts total correlation as an indicator of information redundancy, multivariate transinformation as an indicator of information transfer and NSC as an indicator of rainfall estimation

CRediT authorship contribution statement

Wenqi Wang: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Dong Wang: Supervision, Project administration, Funding acquisition. Vijay P. Singh: Supervision. Yuankun Wang: Supervision. Jichun Wu: Supervision. Jianyun Zhang: Project administration, Funding acquisition. Jiufu Liu: Resources. Ying Zou: Resources. Ruimin He: Resources.

Declaration of Competing Interest

No conflict of interest exits in the submission of this manuscript.

Acknowledgements

This study was supported by the National Key Research and Development Program of China (2017YFC1502704, 2016YFC0401501) and the National Natural Science Fund of China (No. 41571017, 51679118, 91647203).

We thank the National Earth System Science Data Sharing Infrastructure, National Science & Technology Infrastructure of China (http://www.geodata.cn), and Climatic Data Center, National Meteorological Information Center, China Meteorological Administration (//www.cma.gov.cn/2011qxfw/2011qsjgx/

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Information theory-based multi-objective design of rainfall network for streamflow simulation

Highlights

Abstract

Introduction

Section snippets

Entropy measures

Wei river basin

Spatio-temporal correlation and dependence between stations

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgements

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Sci. Total Environ.

Adv. Water Resour.

Environ. Model. Softw.

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J. Hydrol

Environ. Res.

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