Built on the Science of Science (SoS) theory (Zeng et al., 2017), a knowledge system is understood as a dynamic system, consisting of knowledge from different disciplines and issues studied, with complex and co-evolving relationships between them; as Latour (1987) described it, it is “knitting, weaving and knotting together into an overarching scientific fabric” (Latour, 1987; Shi et al., 2015). We adopt a network-based framework to evaluate such interactions (Wei et al., 2022; Wu et al., 2021; Sayles and Baggio, 2017; Coccia, 2020). We characterize the knowledge system as a discipline–issue network, where connections are established between issues and the disciplines used to address the issues (Noyons, 2001; Callon et al., 1983). To further examine the impacts of knowledge development, the discipline–issue networks are projected into issue networks, where issues are connected if they are studied by the same discipline. We use two dimensions to capture the topological structure of a knowledge system (Wasserman and Faust, 1994; Borgatti, 2005; Zeng et al., 2017). The first is the degree of multidisciplinarity (DM), which indicates the proportion of disciplines engaged in different issues and is measured as the density of the discipline–issue network (the ratio between the actual number of connections and the maximum possible number of connections in the network) (Eq. 1). The following applies for any discipline–issue network i: 1DMi=2Cdn(n-1), where DMi is the degree of multidisciplinarity value of a discipline–issue network i, Cd is the total number of existing connections between any issue and discipline d in the network, and n is the total number of disciplines in the network. This dimension recognizes the importance of disciplinary diversity in sustainability issues (Norström et al., 2020; Cockburn, 2022; Stirling, 2007). The higher the DM, the more disciplines involved and the more multidisciplinary the knowledge system.

The second is the degree of issue connectivity (DI). It indicates how many different issues are studied in an interconnected manner and is measured as the degree centrality (Wasserman and Faust, 1994; Borgatti, 2005) of the issue network (Eq. 2). The following applies for any issue network i: 2DIi=∑nCmn, where DIi is the degree of issue connectivity of an issue network i, Cm is the number of adjacent connections to any specific issue m, and n is the total number of specific issues in the network. This dimension recognizes the increasing complexity in sustainability issues and the importance of understanding these issues in an interactive manner (Burmaoglu et al., 2019; Okamura and Nishijo, 2020). The greater the DI, the more interconnected the issues and the more centralized the knowledge system.

To compare the relative differences in DM and DI among rivers, the z scores for DM and DI (xk′) in any river k are calculated by subtracting the means (xk‾) and then dividing by the standard deviation (σk) of all rivers. Four types of knowledge structures are defined as follows (Fig. 1): (A) integrated knowledge structure (DMk′>0; DIk′>0), with diverse disciplines engaged in interconnected issues; (B) issue-driven knowledge structure (DMk′<0; DIk′>0), with limited disciplines engaged in interconnected issues; (C) fragmented knowledge structure (DMk′<0; DIk′<0), with limited disciplines engaged in isolated issues; and (D) discipline-driven knowledge structure (DMk′>0; DIk′<0), with diverse disciplines engaged in isolated issues. An integrated knowledge structure is considered ideal in studying highly interconnected issues with diverse disciplines, while a fragmented structure is at the other end of the spectrum, where both issues and disciplines are working in silos. An issue-driven knowledge structure tends to provide disciplinary-specific solutions for interconnected issues, which are often cost-effective in the short term but may lead to unintended or unexpected outcomes in the long term due to the narrow perspective of the limited number of disciplines. A discipline-driven knowledge structure tends to provide trans-disciplinary solutions for key issues of focus, which are often not cost-effective in the short term, as it often takes a long time and requires large investments to find a solution, but are more sustainable in the long term. In time, knowledge development may demonstrate different structural pathways – for example, moving from the under-developed fragmented structure to a discipline-driven structure and/or from an issue-driven structure towards an integrated one.

We apply our framework to evaluate the impacts of knowledge development. The commonly recognized triple-bottom-line framework is adopted to define the impacts of the knowledge system on society (Reyers and Selig, 2020), which include the social (SO), economic (EC), and environmental (EN) dimensions. We then uniquely define the impacts of the knowledge system on policy according to the whole-of-system characteristics in natural resources management, covering resource availability (RA), resource utilization (RU), and governance capacity (GC) (Wei et al., 2018; Ostrom, 2009). Resource availability refers to the supply capacity of natural resources, resource utilization reflects the extent to which a resource is used, and governance capacity indicates the government's regulation of the supply and demand of a resource (Fig. 1).

The knowledge systems of the 72 river basins were characterized by a limited increase in scientific disciplines engaged (low and stabilizing DM) but an increase in interconnections among issues studied (increasing DI). Of the river basins, 47 % had positive temporal trends for DM, but only eight were statistically significant (p<0.05), most of which are located in Asia (e.g., the Nakdong River and the Yangtze River). About 40 % had negative Sen's slopes, of which only nine were statistically significant, spreading across North America, Europe, and Oceania. Moreover, both positive and negative average significant Sen's slopes only varied between 0.02 % and 0.05 % per 5-year period, with obvious stabilization of the absolute DM values between 0 and 0.25 (i.e., no more than 25 % of the different disciplines and issues was connected) for all river basins in 2017. Multidisciplinary research for global river basin studies was highly constrained within the biophysical disciplines, with over 70 % of interactions being among the environmental sciences, water resources, ecology, multidisciplinary geosciences, and marine and freshwater biology. Only about 10 % of interactions were contributed by social sciences such as human geography, economics, and management (Fig. 2a, Table A1).

On the other hand, all river basins demonstrated statistically significant increasing trends for DI (p<0.05). The top five river basins with the greatest positive trends were the Great Lakes, the Mississippi River, the Yangtze River, the Nile River, and the Chesapeake Bay, with an average Sen's slope increase of 6 % per 5-year period, which was about 12 times greater than the bottom five river basins. The Murray–Darling River had an increasing trend of 3.8 % per 5-year period as the only river basin studied in Oceania, followed by the European river basins with an average increasing trend of 2.7 %. We found that 50 % of the river basins had absolute DI values between 20 and 40 (i.e., the average number of issue interconnections in the knowledge system), and their highest DI value reached nearly 80 (i.e., the Great Lakes) in 2017. About 40 % of issue connections were between ecological degradation and restoration and pollution and treatments, followed by similar connections between management and control, agriculture and irrigation, flood and drought management, and climate change and population, each at about 4 %–5 % (Fig. 2b, Table A2).

Classifying the knowledge structures of river basins based on their normalized DM and DI values indicates that 35 % of the river basins, located mostly in Asia, had fragmented knowledge structures with low DM and low DI. Furthermore, 25 % of the river basins had integrated knowledge systems with relatively high DM and DI values, including the Murray–Darling River, the Colorado River, the Amazon River, the Nile River, and most of the European rivers. Most of the discipline-driven rivers are located in North America, whereas there are major Asian and North American river basins (e.g., the Yellow River, the Yangtze River, the Mekong River, the Mississippi River, and the Columbia River) with issue-driven knowledge systems (Fig. 2c).

We then examined the development of the society and policy indicators in the 72 river basins by investigating the change trends in absolute values and their relative proportions among the three society indicators and among the three policy indicators, respectively. The impacts of SO (i.e., increasing populations) dominated among the society indicators (over 60 % of the relative proportions) of the African and South American river basins. These basins also had the greatest increases in the absolute SO values on average (an average Sen's slope of 25 % per 5-year period, same thereafter), and the South American river basins also had the greatest increase in the EN values on average (13.7 %) (i.e., increasing water stress). For Asian river basins, SO contributed to over 50 % of proportions among the society indicators and less than 20 % was contributed by EC (i.e., increasing water productivity), yet, mostly by the Yangtze River, the Pearl River, and the Yellow River (average 100 % increase), they had the greatest absolute EC increase at over 60 % per 5-year period on average, whereas other basins like the Ganges–Brahmaputra–Meghna Basin, the Mekong River, and the Jordan River only increased by 10 % on average. Most of the European and North American river basins had relatively stable development of their society indicators, characterized by low SO (0 %–40 %) and balanced EC (30 %–60 %) and EN (50 %–70 %). European river basins demonstrated the lowest absolute increase in SO at less than 3 %, and all European and North American river basins studied had decreasing trends (-2.4 % and -1.2 % on average) in EN (i.e., reducing waster stress) (Figs. 3a and B1).

Lake Tana in Africa demonstrated the greatest relative proportions in RA (i.e., area of cultivated area to indicate reduced water availability) among the three policy indicators, whereas the greatest absolute increases in RA were observed for the South American (9.1 %) river basins. Most river basins studied (African, European, North American, South American, and the Murray–Darling Basin in Oceania) had similarly lower RU (i.e., freshwater withdrawal amount) (0 %–40 % of relative proportions) and higher GC (i.e., governance effectiveness) (50 %–100 %). Among them, the African river basins had the greatest absolute RU increase at 43 % on average, whereas non-significant change trends in GC were observed for over 60 % of the rivers. Although the Asian river basins had comparatively lower GC (20 %–50 %), a significant increase of 2.4 % per 5-year period on average was identified (Figs. 3b and B2).

The structural characteristics of the knowledge systems have been strongly linked to the society indicators with over 90 % river basins had acceptable regression model fits, but the link with the policy indicators is much weaker as only 41 river basins had two or more linear models that validated the relationships between their knowledge systems and the policy indicators (adjusted R2>0.3; statistical significance p<0.05).

Additionally, 69 % river basins mostly in North America, Europe, and the Murray–Darling River in Oceania were identified to have a pattern of knowledge for environment (KFE), of which increases in DM and DI corresponded to decreases in the EN (an inverse indicator of water stress). For river basins with this pattern, relationships with the SO were generally positive (median DM=0.10 and DI=0.74 and the same thereafter), and trade-off relationships between the DM (-0.02) and DI (0.92) with the EC were also identified. Also, 21 river basins, located mostly in Asia, Africa and South America, were identified to have a pattern of knowledge against environment (KAE). These river basins had strong positive relationships of DM (0.12) and DI (0.93) with EN, SO (DM=0.28; DI=0.72), and EC (DM=0.02; DI=0.90). Only the DM and DI of Lake Kinneret had insignificant correlations with the EN and EC indicators, and the lake was grouped into a separate group identified as “unclear knowledge–society interaction” (Figs. 4a and b and B3).

In total, 25 river basins spreading across North America, Asia, South America, and Oceania had a pattern of knowledge for resource availability (KFR). These rivers demonstrated negative relationships of DM (-0.04) and DI (-0.80) with RA (an inverse indicator of cultivated land). There were also trade-off relationships of DM and DI with RU (DM=0.19; DI=-0.58) and with GC (DM=-0.01; DI=0.16). However, 16 rivers in Asia and Africa had a pattern of knowledge against resource availability (KAR), which tended to have strong positive relationships of DM and DI with RA (DM=0.40; DI=0.72) and RU (DM=0.32; DI=0.63) and trade-off relationships (DM=-0.03; DI=0.91) with GC. The remaining 31 river basins, located mostly in North America, were identified to have “unclear knowledge–policy interaction”. Further, the impacts of DI were generally stronger and statistically significant, whereas the impacts of DM were much weaker and tended to be insignificant (Figs. 4c and d and B4).

Mapping the river basins' knowledge system classifications with their society and policy impact patterns, it was found that river basins with integrated knowledge structures tended to have KFE (83 % of rivers with integrated structures, same thereafter) and KFR (50 %) patterns. The issue-driven river basins tended to have KFE (61 %) and KAR (38 %) patterns, whereas the discipline-driven river basins were dominated by the KFE (94 %) and unclear knowledge–policy (75 %) patterns. River basins with fragmented knowledge structures were prone to the KAE (36 %) and KAR (48 %) patterns (Fig. 5a).

We further identified the optimal DM and DI values for river basins with each of the KFE, KAE, KFR, and KAR patterns, with the objective to maximize their positive and minimize their negative society and policy impacts (see Table C1 in Appendix C for criteria of optimization). For the KFE river basins, an integrated knowledge structure (DM=1; DI=1) should be targeted, which maximizes the SO (normalized value of 1) and EC (0.94) indicators while minimizing the negative EN indicators (0.13) (Fig. 5a and b). On the other hand, there exist trade-offs for the KAE river basins to select the optimal knowledge structure. While the integrated knowledge structure (DM=1; DI=1) could maximize the SC (1) and EC (0.93), it also maximizes the negative EN (1). A fragmented knowledge structure is optimal for minimizing the negative EN impact (0.13) but reduces positive SC (0.33) and EC (0.13) impacts (Fig. 5a and c).

For river basins with the KFR pattern, an integrated structure is optimal for minimizing the negative RA (0.14) and maintaining a balanced RU (0.41) and GC (0.43) (Fig. 5a and d). For the river basins with the KAR patterns, an integrated knowledge structure could maximize RA (1), RU (1), and GC (0.89). A fragmented knowledge structure minimizes the negative RA (0.32) and yet trades off low RU (0.36) and GC (0.10). It should also be noted that the knowledge systems for rivers with unclear knowledge–society interaction (1) and unclear knowledge–policy interaction (31) could not be optimized (Fig. 5a and e).

Current knowledge structures in the 72 main river basins in the world were characterized by increasing degree of issue connectivity (DI), whereas the degree of multidisciplinarity (DM) was low and had limited growth (Fig. 2). We identified that even for river basins with discipline-driven knowledge structures, they had low values of DM and their interconnections were concentrated among biophysical disciplines, indicating the domination of natural sciences in multidisciplinary research for most river basins across the world. Additionally, the impacts of DM tended to be statistically insignificant with both society and policy indicators (Figs. 4, B3, and B4), coupled with booming populations (SO) for resource demand (i.e., large RA indicating low water availability) and low economic and resource productivity (EC and RU), along with deteriorating environment (EN) (Fig. 3). This implies that current practices of multidisciplinary research were not sufficient to solve the complex sustainability issues. Addressing many sustainability issues requires more knowledge from the human perspective to comprehend the human–nature interactions (Krausmann and Fischer-Kowalski, 2013; Jerneck et al., 2011). Drawing knowledge from social sciences (e.g., political science, sociology, management, and psychology) is the key to improving multidisciplinary research to transform the current knowledge systems of river basins. Knowledge systems for river basins could benefit from strengthening these governance-related disciplines to reconcile the relationship between individual behaviors and collective management decisions for water and coordinate the interactive relationships between socio-economic development and environmental sustainability.

Over 90 % of the river basins had knowledge structures that are strongly linked to the society indicators, but only 57 % of rivers had statistically significant relationships with the policy indicators (Fig. 4). This is closely related to the challenge knowledge transfer imposes on decision-making at the science–policy interface (Nguyen et al., 2017; Louder et al., 2021). Such a challenge has been widely recognized as policy and practice decisions are informed by diverse values and beliefs and multiple sources of knowledge and are shaped by cognitive factors and power dynamics beyond the direct influence of research activities (Hakkarainen et al., 2020; Pitt et al., 2018; Posner and Cvitanovic, 2019). We propose developing “boundary spanners” as a potential solution (Edwards and Meagher, 2020). These spanners could be creditable academic organizations for the policy community, individual or groups of scientists, or professional consultants who facilitate knowledge and information across otherwise disconnected communities and synthesize different values and insights to facilitate collective sense-making (Stovel and Shaw, 2012; Bodin, 2017). They can not only bridge disciplinary silos of natural and social scientists but are also, more importantly, able to coordinate scientists with local stakeholders and policy-makers with different levels of management power and contexts. Additionally, although beyond the scope of this study, we recognize the interactions between society and policy. In particular, the SO in society indicators and the RU in policy indicators were most strongly positively correlated (r=0.81; p<0.05) (Fig. B5), which indicates a need to recognize the connections between policy and society development and their spillover effects on knowledge in future study.

The integrated knowledge structure was identified to be most desirable, which links with the patterns of knowledge for environment (KFE) and the knowledge for resource availability (KFA). Issue-driven knowledge structures were identified to have similar optimized society and policy impacts to the integrated knowledge structure, whereas discipline-driven knowledge structure was not effective in optimizing multiple society and policy indicators at the same time (Figs. 5 and C1). About 15 % of the river basins studied in America, Europe and Oceania (e.g., the Amazon River, the Colorado River, the Danube River, and the Murray–Darling Basin) with integrated knowledge structures demonstrated more balanced impacts on society and policy (Fig. 5). They provide good examples for other river basins in achieving a holistic integration of science, society, and policy. On the other hand, river basins with the patterns of knowledge against environment (KAE) and the knowledge against resource availability (KAR) are considered less desirable, as optimizing the current knowledge structure to reduce the negative environmental impacts or improving resource availabilities would be traded off for socio-economic development and governance capacities (Fig. 5). Rivers with fragmented knowledge structures comprising 35 % of the river basins studied, mostly in Asia, Africa, and South America, were most prone to these impact patterns (Fig. 3). It reflects the inevitable concerns and interests of these river basins with greater development pressures and inequalities. A more balanced and integrated knowledge development approach could be supported by raising awareness of human impacts on river basins and targeted research funding that facilitate bridging the gap between science and policy (Matsumoto et al., 2020; Jabbour, 2022).

Our network-based framework contributes to advancing the Science of Science theory (Zeng et al., 2017) and transforming knowledge for more sustainable river basin development. It provides a method of explicitly measuring the structure of knowledge as a discipline–issue network system, which guides future knowledge development by identifying explicitly where and what to change or connect between disciplinary knowledge and issues at hand, therefore assisting in more suitable, more precise, and more predictable knowledge development. Moreover, our framework links the structural configurations of knowledge systems with developments in society and policy, thus contributing to better evaluation of research outcomes and action-oriented research for specifying “credible, legitimate, and relevant” criteria in good governance (Kim, 2019; Cash et al., 2003). Finally, this framework will contribute to river basin management by enabling comparisons of knowledge development for river basins with varying management issues regarding focus and context and thus also enabling the design of tailored management strategies and co-learning according to different patterns of connections among river basin knowledge, society, and policy development.

The limitations in this study and future research directions are also recognized. Regarding the data source, only scientific publications indexed in the WoS that were written in English were studied. While the WoS provides a consistent, systematic documentation of scientific knowledge development across a broad range of disciplines for a long time frame, gray literature focusing on practice-driven knowledge (e.g., conference paper, government reports) also contributes to the river basin knowledge development and can be included in future studies (Ramírez-Castañeda, 2020). Selecting case river basins based on scientific publications also led to potential bias towards large river basins with societal and natural significance, and selections of the indicators to represent the society and policy of the river basins were also bounded by the temporal and spatial data availability. Additionally, classifications of disciplines in this study were conducted based on journal assignments. It should be recognized that boundaries between disciplines are becoming increasingly blurred when used in the context of research evaluation. Most importantly, further research efforts should be made to reveal the mechanisms behind the interactive dynamics between the knowledge system and its impacts on society and policy.