3 Results

3.1 Characteristics of publications

According to a total of 2,020 publications about uncertainties in hydrologic simulation and water resources management, they were divided into three document types for the period of 1991–2018. The dominant document type was articles, which comprise 95% of the total publications. Proceedings papers and reviews were ranked the second and the third, respectively. Fig. 1 presents the number of publication outputs for each year during the 28 years. The first publication on the uncertainty in the hydrological system was published in 1992. Over time, the publication outputs increased rapidly from 1 in 1991 to 390 in 2018, and they especially dramatically in the last five years of the study period. This result thoroughly explains why research on uncertainty in hydrological modeling and management has attracted increasing attention from scholars.
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3.2 Journal co-citation analysis

Table 1 presents the top ten frequently quoted journals in the related domain. The top-tier item was Journal of Hydrology with 1,430 publications, while Water Resources Research was in second place with a record of 1,368. These two journals contributed to the majority, making them the major source of research on uncertainty in the hydrological system. At the Impact Factor (IF) level, Water Resources Research and Hydrology & Earth System Sciences had higher IF values (4.361 and 4.256), which indicated a more substantial influence in the related areas.
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3.3 Country/territory and institution cooperation analysis

The research on the uncertainty in hydrologic simulation and water resources management has attracted global attention. Table 2 shows the top ten productive countries/territories and institutions in detail. The results demonstrated that the USA had the maximum journals for the field, subsequently were China, Canada, and Australia. China was the only developing country of these selected countries/territories. Additionally, the 590 publications from the first 10 organizations contributed to 29.2% of the total. The Chinese Academy of Sciences was the leading institution, with 113 publications, followed by Beijing Normal University (China) and the University of Regina (Canada).
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To obtain more collaboration information about countries and institutions, the first 20 co-country/territory and co-institution networks were presented in detail in Fig. 2. There existed widespread cooperation among these 20 countries/territories and institutions. The US and China played critical roles in global collaboration, especially for Canada and Australia. The relationships between China and Canada, as well as the Chinese Academy of Sciences and Beijing Normal University were notable. Additionally, some countries and institutions should improve international influence with more publications or closer collaboration in the related domain, such as India and Tsinghua University.
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3.4 Author co-citation analysis

Fig. 3 is an item density visualization showing the most influential authors in the field of uncertainty in hydrological systems. The results indicate that the most prominent scholars were Arnold (United States Department of Agriculture) in the hydrological modeling field (Arnold et al. 1998). Arnold’s researches were broadly quoted by others, with a citation frequency of 354. Beven (Lancaster University, England) was the second influential researcher, followed by Wilby (University of Derby, England), Huang (University of Regina, Canada), and Bergstrom (Karolinska Institution, Sweden). We find that these representative scholars have made significant contributions to the related domain and were closely linked.
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3.5 Reference co-citation analysis

Usually, a publication with a citation burst indicates it gained wide attention in its related scientific field. Furthermore, a new research field may be discovered by recognizing a cluster with bursts (Yu, 2015). As the top ten references were shown in Table 3, the whole length signified the time horizon from 1991 to 2018, while the red line indicates the citation burst. The first milestone paper in this field since 1991 was about model evaluation in simulations with a burst strength of 24.61 (Moriasi et al. 2007). The second item ranked by bursts was a paper on the calibration and validation of SWAT, with a burst strength of 18.6 (Arnold et al. 2012). As can be seen in this study, eight references were related to the SWAT model. This indicates that SWAT might be the most popular model for hydrological modeling and water resources management.
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3.6 Subject categories co-occurrence analysis

The dual-map overlays incorporate with more than 10,000 scientific journals from WOS (Chen and Leydesdorff, 2014). Fig. 4 shows the visualization of publications between 1991 and 2018 on the topic of uncertainty in hydrological systems, in which the coloured curves demonstrate the process from left to right. We can see that the citing and cited maps were separate for several research fields at different positions. Each color of the cluster is labelled by the corresponding field. The publications on uncertainty in hydrologic modeling and water resources management primarily appear in three domains: the blue was labelled with Ecology/Earth/Marine; while the yellow with Veterinary/Animal/Science, and the red with Mathematics/Systems/Mathematical. Publications in the discipline with blue citation links are built from at least five disciplines from the upper right corner of the map. Thus, research on the uncertainty in hydrological systems is based on broad areas, from environmental science to ecology, geology, mathematics, and chemistry.
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3.7 Keywords co-word analysis

The main function of the co-word study was to recognize hotspots and the structure of a related scientific domain ((Liu, 2015; Xiang et al., 2017). For this study, the first 20 items were chosen to construct a co-occurrence network (Fig. 5). Each cross represents one kind of keyword; the larger the size illustrates the higher frequency. From Fig. 5, we can obtain the following information that the “Uncertainty” got the highest frequency of occurrence with 932, and it was followed by “basin” with 584, “model” with 492, “management” with 447, and “climate change” with 437. Other commonly used words included system (229), simulation (228), impact (209), SWAT (191), and optimization (186). Also, the centrality represented the importance of that node in the network. Among the top 20 keywords, “water quality”, “management” and “simulation” have high centrality values, which indicate their critical positions in the field of uncertainty in hydrological systems. This result also indicates research on the uncertainties related to water quality has received more attention.
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3.8 Document co-citation analysis

3.8.1 Research cluster analysis

The reference relationship reflects the objective law of scientific development and intellectual structure (Yin et al. 2006). To further determine the distribution rule of references, the top 20 references between 1991 and 2018 were picked out. As shown in Fig. 6, the central clusters for the domain of uncertainty in hydrologic modeling and water resources management were demonstrated. The high modularity of 0.76 indicating a clear definition for the field (Chen, 2006; Chen, 2017; Yu, 2015). All of these references were separated into 96 clusters, 14 of which had labels. In general, this study field on the uncertainty in hydrologic modeling and water resources management includes many aspects, such as management objects (water resource and water quality), measures (stochastic programming and statistical learning), simulation (SWAT), technique (GIS), and study areas (China and Canada). Thus, uncertainty in hydrological modeling and integrated management has been a relatively mature study area in recent years.
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3.8.2 Timeline view of typical clusters

A timeline visualization depicts the temporal progress for each set. The top ten distinct clusters along horizontal timelines are displayed in Fig. 7. The three most cited references can be acquired under each timeline. As shown in Fig. 7, individual cluster had long period of approximately 20 years, while a short time for several clusters. The SWAT model for clusters #0 and #6 spans from 1994 to 2016 and a series of essential achievements were obtained between 2005 and 2015. Cluster #4 on uncertain management lasts 16 years and remains active. In contrast, cluster #7 on the GIS-based model ends in 2007, which indicates new specialties found in relevant research with other forms.
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