As the water requirement for food production and other human needs grows, quantification of environmental flow requirements (EFRs) is necessary to assess the amount of water needed to sustain freshwater ecosystems. EFRs are the result of the quantification of water necessary to sustain the riverine ecosystem, which is calculated from the mean of an environmental flow (EF) method. In this study, five EF methods for calculating EFRs were compared with 11 case studies of locally assessed EFRs. We used three existing methods (Smakhtin, Tennant, and Tessmann) and two newly developed methods (the variable monthly flow method (VMF) and the Q₉₀_Q₅₀ method). All methods were compared globally and validated at local scales while mimicking the natural flow regime. The VMF and the Tessmann methods use algorithms to classify the flow regime into high, intermediate, and low-flow months and they take into account intra-annual variability by allocating EFRs with a percentage of mean monthly flow (MMF). The Q₉₀_Q₅₀ method allocates annual flow quantiles (Q₉₀ and Q₅₀) depending on the flow season. The results showed that, on average, 37% of annual discharge was required to sustain environmental flow requirement. More water is needed for environmental flows during low-flow periods (46–71% of average low-flows) compared to high-flow periods (17–45% of average high-flows). Environmental flow requirements estimates from the Tennant, Q₉₀_Q₅₀, and Smakhtin methods were higher than the locally calculated EFRs for river systems with relatively stable flows and were lower than the locally calculated EFRs for rivers with variable flows. The VMF and Tessmann methods showed the highest correlation with the locally calculated EFRs (R²=0.91). The main difference between the Tessmann and VMF methods is that the Tessmann method allocates all water to EFRs in low-flow periods while the VMF method allocates 60% of the flow in low-flow periods. Thus, other water sectors such as irrigation can withdraw up to 40% of the flow during the low-flow season and freshwater ecosystems can still be kept in reasonable ecological condition. The global applicability of the five methods was tested using the global vegetation and the Lund-Potsdam-Jena managed land (LPJmL) hydrological model. The calculated global annual EFRs for fair ecological conditions represent between 25 and 46% of mean annual flow (MAF). Variable flow regimes, such as the Nile, have lower EFRs (ranging from 12 to 48% of MAF) than stable tropical regimes such as the Amazon (which has EFRs ranging from 30 to 67% of MAF).

Several safe boundaries of critical Earth system processes have already been crossed due to human perturbations; not accounting for their interactions may further narrow the safe operating space for humanity. Using expert knowledge elicitation, we explored interactions among seven variables representing Earth system processes relevant to food production, identifying many interactions little explored in Earth system literature. We found that green water and land system change affect other Earth system processes strongly, while land, freshwater and ocean components of biosphere integrity are the most impacted by other Earth system processes, most notably blue water and biogeochemical flows. We also mapped a complex network of mechanisms mediating these interactions and created a future research prioritization scheme based on interaction strengths and existing knowledge gaps. Our study improves the understanding of Earth system interactions, with sustainability implications including improved Earth system modelling and more explicit biophysical limits for future food production.