3.1. Time Analysis of Post Volume
In order to summarize the research situation of distributed hydrological models, this article counted the circulation of documents related to distributed hydrological models in the core collection of Web of Science from 1986 to 2019 (Figure 1
). The total number of documents was 3079. Around the 1990s, a number of distributed hydrological models emerged in the context of the promotion of research needs such as the sustainable use of water resources, nonpoint source pollution, the impact of global changes on the hydrological cycle and the rapid development of computer technology [24
]. In 1986, three documents were published, two of which were introductions of the SHE model of the distributed water collection model system based on physics developed in Europe [25
]. No related documents were published in the core collection of Web of Science in 1988 and 1989. From 1986 to 1993, no more than 10 documents were published each year. Since then, the number of annual publications had increased significantly, from 15 in 1994 to 298 in 2019. Distributed hydrological models have shown a significant increase overall since 1994, which means that scholars had been paying more and more attention to distributed hydrological models, that research investment had gradually increased since 1994, and that the field of distributed hydrological model shows a trend of rapid development. So far, distributed hydrological models have become an indispensable application tool in related research fields.
3.2. Cooperation Network Analysis
The analysis of cooperation networks in this article includes the analysis of cooperation networks between countries/regions and between institutions. The analysis of the cooperation network can reveal the cooperation network between the issuing countries and institutions and can explore the main research force of distributed hydrological models. It can also help different research units to establish cooperative relations. Running Citespace, we obtained a country/region cooperation network map with 59 nodes and 280 links (Figure 2
) and an institution cooperation network map with 394 nodes and 775 links (Figure 3
). A node in the figure represents a country/region (Figure 2
) or research institution (Figure 3
), that is, 59 countries and 394 institutions have published research results on this topic. The size of the node represents the amount of posts. The countries/regions and institutions connected by lines indicate cooperative relations, and the thickness of the line indicates the closeness of the partnership [27
Research on distributed hydrological models was distributed in 59 countries/regions. Figure 2
shows that among 59 countries, the United States, China and some European countries (including Germany, France, Italy, England, Canada, The Netherlands, Australia, Switzerland, etc.) (top ten documents published) have more research on distributed hydrological models, which means the distributed hydrological models were widely used on a global scale. There were cooperative relations between multiple countries, among which China and France were the hubs of the cooperative network. The United States and China ranked first and second with 649 and 615 documents, respectively, accounting for 41% of the total number of documents. Therefore, the United States and China are the main research forces of distributed hydrological models. The top ten countries accounted for 96% of all publications, suggesting that these countries dominate the development of the field of distributed hydrological modeling.
The number of articles published in a country has a considerable relationship with the population base. The top 5 countries with the number of articles published are USA, China, Germany, France and Italy. The number of articles published in these five countries is related to the population (population quantity unit is one million). The ratios are 1.98, 0.44, 3.66, 3.76, 4.10, respectively, which shows that Italy has invested a lot in the field of distributed hydrological models, while the number of people active in the field of distributed hydrological models in China accounted for the total proportion is small. Figure 3
shows the changes in the number of posts issued by the top five countries from 1986 to 2019. Figure 3
shows the overall increase in the number of posts in these five countries. The annual number of articles published in the United States has accounted for a relatively large proportion for many years. China has only published a record of articles since 2003, but the growth trend has been the most obvious from 2003 to 2019.
shows that the Chinese Academy of Sciences, Beijing Normal University, Hohai University, China Institute of Water Resources and Hydropower Research and Tsinghua University have more research results. The top ten institutions in terms of publication volume are listed in Table 1
, and seven of them are Chinese institutions. It shows that China has invested more in the research of distributed hydrological models. However, the cooperation of the seven Chinese institutions is not very close. Among them, only the Chinese Academy of Sciences and Wuhan University, as well as the China Institute of Water Resources and Hydropower Research and Tsinghua University have a cooperative relationship. On the whole, the top ten institutions have few exchanges and little cooperation, so it is necessary to strengthen China’s domestic and international cooperation.
3.3. Co-Occurrence of Discipline Categories
Based on the co-occurrence analysis of discipline categories, disciplines involving distributed hydrological models can be detected, running Citespace to get 65 nodes and 255 links. A node represents a discipline category. The link linking two nodes means the co-occurrence of two discipline categories. It can be seen from Figure 5
that the research and application of distributed hydrological models involve multiple discipline categories. Figure 4
shows eleven disciplines. The top five popular research disciplines are water resources, geology, earth science, engineering and environmental science and ecology. In the field of water resources, distributed hydrological models were used to calculate snowmelt [28
], evaluate water quality [4
], observe and simulate changes in river flow [30
] and flood forecasting [31
], etc., to realize the rational allocation and sustainable use of water resources. When the research area is located in a mountainous area, it is necessary to use the knowledge of geology, earth science and engineering to explore the influence of the topography in the complex mountain on the hydrological process [28
]. This shows that there is a phenomenon of multidisciplinary integration in the field of distributed hydrological models.
3.4. Co-Citation Analysis
Co-citation analysis includes author co-citation analysis and document co-citation analysis, which means that two authors or two documents are cited by a third party at the same time. The concept of author co-citation was first proposed by White and McCain [33
]; it reflects the proximity of research directions and the importance of the author and has been widely used to assess the relevance of scientific research. High-frequency co-cited documents usually have breakthroughs and innovations in the corresponding research areas; at the same time, high-frequency co-cited references form the knowledge base of the current analyzed field, which is of great significance to the development of the field.
shows the author co-citation map created by Citespace, with a total of 582 nodes, and each node represents a cited author. The author of the largest node in the figure was BEVEN K, whose documents have been cited 1241 times, as well as NASH JE (777), ARNOLD JG (338), ABBOTT MB (269), REFSGAARD JC (261), GUPTA HV (245), MORIASI DN (230), DUAN QY (217), BERNER LT (199), BLOSCHL G (196) and others. They represent the core people in the research and development of distributed hydrological models.
Running Citespace to analyze the co-cited references, we obtained 484 nodes and 1526 links. The references co-citation map is shown in Figure 7
. The co-cited references were clustered and analyzed. The top ten major clusters in terms of size are listed in Table 2
. The size value indicates the size of the cluster. The larger the size, the greater the number of related documents published in the cluster, and large clusters usually represent the main research direction, that is, one cluster corresponds to one research hotspot. The silhouette value reflects the similarity of the clusters; the closer its value is to 1, the better the quality of the cluster. The silhouette values of the clusters in Table 2
are all close to 1, indicating that all the clusters are highly uniform. Mean year represents the average year of documents publication in the cluster. The larger the value, the newer the mean year of the publication in the cluster and the closer to the current research frontier. The most representative term in each cluster was detected and selected by Logarithmic Likelihood Ratio (LLR), which is used to mark corresponding cluster for discussion. In the top ten clusters (Table 2
), the mean years ≥ 2005 were #8 (2009) and #9 (2006). The representative terms were TRMM and ensemble Kalman filter, respectively. The full name of TRMM is Tropical Rainfall Measuring Mission, which is a meteorological satellite developed by the National Aeronautics and Space Administration (NASA) and Japan Aeronautics and Space Administration (JAXA) to quantitatively measure tropical and subtropical rainfall [34
]. Recently, ensemble Kalman filter has been used to solve in the inverse problem of water environment pollution source identification, effectively improving the efficiency of updating observations in the models [35
Highly cited documents are usually groundbreaking in the research field and are of great significance to the development of the field. The top ten most highly cited documents in the field of distributed hydrological model research are listed in Table 3
. The main content involved is as follows: (1) the proposed concepts, methods, technologies and application principles of distributed hydrological models (documents 1, 5, 6 and 8) [36
]; (2) evaluation and improvement of distributed hydrological models (documents 2, 3 and 10) [40
]. The distributed hydrological-vegetation model described in the second document considers the impact of canopy interception, evaporation and transpiration as well as snow cover and snowmelt on runoff [40
], and the tenth document solves the problem of CRR (Conceptual Rainfall-Runoff) model optimization [42
]; (3) the development and introduction of new models (documents 4, 7 and 9) [25
], including the SWAT model [43
] and the SHE model [25
3.5. Keywords Co-Occurrence and Burst
Keywords can highly condense and summarize the research content of the documents, which is an effective method to determine the overall structure and research theme of a research field. The higher the frequency of the keywords, the more representative the research hotspots in the field. Running Citespace to get the keyword co-occurrence network, with a total of 398 nodes and 1138 links, we performed cluster analysis on the co-occurring keywords and obtained 18 clusters. The result is shown in Figure 8
. The high-frequency keywords include “distributed hydrological model”, “climate change”, “SWAT”, “evapotranspiration”, “uncertainty”, “remote sensing”, “runoff”, “water balance”, “soil moisture”, “GIS”, etc., which represent the focus of research in the field. The top ten clusters of size were listed in Table 4
. Cluster #7 “CEQUEAU” in Table 4
is a distributed deterministic hydrological model that takes into account the physical characteristics of the watershed as well as their space-domain variation, which developed by the Institut National de la Recherche Scientifique, Québec, Canada [44
]. It can be seen from the average year that clusters #0 (uncertainty analysis), #3 (Great Lakes), #6 (optimization) and #9 (GRACE (Gravity Recovery and Climate Experiment)) are clusters formed in recent years, which means that the research hotspots in recent years include uncertainty analysis and optimization of the distributed hydrological model, combined with the time-varying gravity field provided by the GRACE gravity satellite to detect changes in surface water storage, and the application of the distributed hydrological model to evaluate the water storage, water quality and ecological environment of large lakes.
Citespace’s burst terms analysis function can be used to investigate terms that appear suddenly and have a rapid increase in frequency. Burst terms often reflect the research frontiers in the field. The top 52 burst terms in strength are listed in Table 5
. According to the time axis in Table 5
, the time of the appearance and disappearance of the research front can be judged, and the time axis can intuitively reflect the historical length of the mutation word outbreak. The statistical burst terms first appeared in 1995. The earliest research front was the application of distributed hydrological models to simulate runoff and nonpoint source environmental response. The TOPMODEL [45
] was a model that scholars studied and used more in the early stage. The scale problems of distributed hydrological model modeling and the aggregation and disaggregation method in hydrological modeling have also attracted the attention of scholars [46
]. In 1999, the impact of evapotranspiration on the surface water cycle process began to receive attention [47
], and complex hydrological models for mountain basins were also developed [48
]. From 2001 to 2005, the research front shifted to the sensitivity analysis of distributed hydrological model parameters and the automatic calibration of the models. At the same time, the integration of GIS technology with distributed hydrological models provides powerful data storage, display, description and analysis capabilities for distributed hydrological models [49
]. In terms of application, distributed hydrological models have begun to be widely used to calculate snowmelt, simulate flood processes, and predict the hydrological characteristics of floods in the basin. The rainfall-runoff model was used to simulate the impact of spatial changes in rainfall on the outlet runoff of the basin [51
]. From 2006 to 2010, the water balance problem caused by climate change and its impact on wetland hydrological conditions began to attract people’s attention. Regional climate models were used to simulate climate change. Weather radar and PCRaster GIS systems were combined with hydrological models to give the model the function of spatial data analysis [53
]. In 2011, climate change became the research frontier, but the historical period as the research frontier was relatively short. The same situation of burst terms include “spatially distributed water balance model”, “spatial discretization”, “China”, “copula” and “Distributed Hydrology Soil Vegetation Model (DHSVM)”. The history of words as the research front lasted for about one year, and the “distributed model” and “hydrological model” appeared as burst terms several times in different time nodes. It can be seen that the research front is not continuous. When scholars shift their attention from one problem to another, there will be a sudden stop of frontier research and a sudden emergence of another frontier of research.
It is worth noting that as the research frontier, the burst terms lasted until 2019. They represent the current research hotspots in the field of distributed hydrological model research. The SWAT model is usually used to evaluate water volume and water quality and to simulate runoff and nonpoint source pollution. It has attracted the attention of scholars in 2015 and has been widely used until now. It shows that the SWAT model has been rapidly developed and widely used, with good simulation effects and practicality [55
]. The meteorological data provided by TRMM is used as driving data in hydrological simulations, which solves the problem of lack of precipitation data in tropical areas to a certain extent. Through continuous updating, the characteristics of the product data set have evolved from the original spatiotemporal resolution to a high spatiotemporal resolution [56
]. In order to improve the regional resolution and model simulation accuracy, the research of downscaling and bias calibration methods [57
] and their application in hydrological simulation have also attracted much attention in recent years.
Because 2020 is not over, the situation of annual published documents is not complete. Here is a phased summary of the co-occurrence of keywords in the 226 documents published in the Web of Science core collection in 2020. Figure 9
shows the co-occurrence of keywords from January to October 2020. The most frequently occurring word was “climate change”, followed by “evapotranspiration”, “SWAT”, “remote sensing”, “soil moisture”, “uncertainty”, “TRMM” etc. This shows that (1) in the context of global warming, the impact of climate change on the environment has aroused people’s attention; (2) the current SWAT model is still a distributed hydrological model favored by scholars after many updates; (3) coupling products with high-resolution data into hydrological models is currently an important means to improve simulation accuracy.