Limited comparability of global and local estimates of environmental flow requirements to sustain river ecosystems

Environmental flows (e-flows) are a central element of sustainable water resource management to mitigate the detrimental impacts of hydrological alteration on freshwater ecosystems and their benefits to people. Many nations strive to protect e-flows through policy, and thousands of local-scale e-flows assessments have been conducted globally, leveraging data and knowledge to quantify how much water must be provided to river ecosystems, and when, to keep them healthy. However, e-flows assessments and implementation are geographically uneven and cover a small fraction of rivers worldwide. This hinders globally consistent target-setting, monitoring and evaluation for international agreements to curb water scarcity and biodiversity loss. Therefore, dozens of models have been developed over the past two decades to estimate the e-flows requirements of rivers seamlessly across basins and administrative boundaries at a global scale. There has been little effort, however, to benchmark these models against locally derived e-flows estimates, which may limit confidence in the relevance of global estimates. The aim of this study was to assess whether current global methods reflect e-flows estimates used on the ground, by comparing global and local estimates for 1194 sites across 25 countries. We found that while global approaches broadly approximate the bulk volume of water that should be precautionarily provided to sustain aquatic ecosystems at the scale of large basins or countries, they explain a remarkably negligible 0%–1% of the global variability in locally derived estimates of the percentage of river flow that must be protected at a given site. Even when comparing assessments for individual countries, thus controlling for differences in local assessment methods among jurisdictions, global e-flows estimates only marginally compared (R 2 ⩽ 0.31) to local estimates. Such a disconnect between global and local assessments of e-flows requirements limits the credibility of global estimates and associated targets for water use. To accelerate the global implementation of e-flows requires further concerted effort to compile and draw from the thousands of existing local e-flows assessments worldwide for developing a new generation of global models and bridging the gap from local to global scales.


Introduction
Freshwater biodiversity is exceptionally threatened by human activities and climate change, endangering the well-being and livelihoods of people worldwide (Tickner et al 2020).To curb and recover from the ongoing loss of freshwater biodiversity, environmental flows (e-flows) have become a central tenet of sustainable water resource management (Poff andMatthews 2013, Arthington et al 2023).E-flows are defined as 'the quantity, timing, and quality of freshwater flows and levels necessary to sustain aquatic ecosystems which, in turn, support human cultures, economies, sustainable livelihoods, and well-being' (Arthington et al 2018).E-flows are now protected in principle by many governments through laws and regulations (Arthington et al 2023), and internationally through regional to global agreements, resolutions and policies (e.g.IUCN 2012, European Commission 2015, Ramsar 2015).Notably, e-flows are an integral component of indicator 6.4.2 on Water Stress under the UN Agenda 2030 on Sustainable Development (Dickens et al 2019) and contribute to achieving several other Sustainable Development Goals (SDGs;Arthington et al 2018).
Despite widespread adoption on paper, e-flows have been implemented in only a fraction of rivers worldwide, and inconsistently from one country to the next or across transboundary basins (Arthington et al 2023, Dourado et al 2023).Governance systems, technical methods and expertise, data sources, and financial resources vary widely among jurisdictions, rendering comparisons of e-flows programs across borders challenging.Additionally, the resources involved in conducting detailed, local eflows assessments make it unfeasible to assess, in time, the needs of all rivers exposed to flow alterations.Therefore, harmonised estimates of e-flows requirements across the globe are essential to progress on freshwater biodiversity recovery (Tickner et al 2020) and to accurately evaluate the health of river ecosystems (Kuehne et al 2023).Such top-down estimates must be able to complement and be informed by bottom-up aggregation of local e-flows assessments.
A global assessment of e-flows requirements can promote the sustainable management of aquatic ecosystems worldwide by allowing consistent targetsetting, monitoring and evaluation under international agreements, such as the SDGs and Global Biodiversity Framework (Convention on Biological Diversity 2021).It can also provide first-cut precautionary flow recommendations for all river reaches on Earth, constituting the initial step of a hierarchical approach to e-flows design (Opperman et al 2018).Such recommendations can help to spur dialogue among river basin stakeholders, provide a basis for planning and management in areas where detailed eflows assessment is not yet possible, identify priority rivers where further studies are needed to reduce uncertainties, provide third-party estimates to facilitate cooperative water management in transboundary basins, and more generally foster engagement and funding for more detailed assessments (Opperman et al 2018).
Since the first attempts to assess the volume of water required for the protection or restoration of freshwater-dependent ecosystems at the global scale (Smakhtin et al 2004), over 40 studies have produced global e-flows estimates (table S1).These estimates were produced either to define global e-flows targets, or to assess water stress and the associated tradeoffs with food and energy production under varying scenarios (table S1).None so far have explicitly aimed to provide a basis for e-flows management.Indeed, methods to evaluate e-flows requirements at the global level remain relatively coarse, both in terms of resolution and by relying on few hydrological criteria with little context specificity or grounding in ecology (supplementary section 1.2).These approaches differ substantially from in situ e-flows assessments used for local water management, many of which leverage ecological and sociocultural data and knowledge to quantify the flow requirements of various ecosystem components, processes and benefits to society (Tharme 2003).
Until now, three studies have benchmarked global estimates of e-flows requirements against local estimates.Two studies (Pastor et al 2014, Jägermeyr et al 2017) concluded that global estimates could be relevant as presumptive figures, based on data for 11 sites dispersed across continents and river types.By contrast, a previous assessment by the authors of this study (Eriyagama et al 2024) found little comparability between the global e-flows estimates used to compute water stress for SDG indicator 6.4.2 and local estimates for 533 sites worldwide.Furthermore, concern was expressed at an expert meeting on the e-flow component of SDG indicator 6.4.2 organized by the Food and Agriculture Organization (in October 2020, involving more than 60 representatives and researchers from 23 countries) regarding the low accuracy of these e-flows estimates and the resulting discrepancy with national statistics.While not intended to replace in situ assessments, global e-flows estimates should broadly reflect local estimates established according to best practices if they are to serve beyond theoretical global assessments of water stress.An obvious disconnect between global e-flows targets and the experience of local water practitioners risks reducing confidence in either set of outputs and limiting their uptake, both for establishing large-scale targets and for local planning and management.
The purpose of this study is to compare eflows requirements as determined by global methods with e-flows estimates calculated for local water resource management purposes in individual river reaches or basins (hereon, local e-flows estimates) from diverse methods and geographies.We assess  1).We analyse estimates of the mean amount of water which must be left instream and available for freshwater ecosystems in an average year, rather than more temporally explicit estimates of eflows (e.g. at the monthly scale).Although this focus does not encompass the multiple facets of the flow regime required to support freshwater biodiversity (i.e. the timing, frequency, duration, and rate of change of flow events; Poff et al 1997), it accounts for the information needs of SDG water stress indicator 6.4.2 (Dickens et al 2019).It also enables a consistent comparison of e-flows estimates notwithstanding the diversity of methods and levels of reporting detail in local assessments.As we analysed a heterogeneous set of local e-flows estimates, some estimates resulting from in-depth assessments grounded in local data and expertise assuredly surpass global estimates in their accuracy, whereas others were of lower confidence, being derived from more simplistic methods.Therefore, local estimates are not systematically better than global estimates at representing the needs of ecosystems in this analysis.Additionally, most assessments analysed in this study were commissioned by government agencies for regulatory or resource management purposes, rather than for academic research.Our aim was to assess the extent to which current global methods reflect e-flows estimates used on the ground, and in doing so, to further bridge the implementation gap between global and local flow management of river ecosystems.Our study expands upon our previous efforts (Eriyagama et al 2024) by compiling local e-flows estimates for another 661 sites and comparing them to all common global e-flows calculation methods.Considering the heterogeneity of e-flows concepts, policy objectives and local assessment methods among countries, we did not expect that a single global model could perform well across all local e-flow assessments.Nevertheless, we hoped to identify, for each country, the global hydrological model (GHM) and e-flow estimation method that yielded the most comparable estimate and could thus be a proxy for the local assessment approach.

Local e-flows estimates: secondary data compilation and database structure
To compare global e-flows estimates to local assessments, we first compiled and standardized local eflows estimates from a variety of published governmental, non-governmental and academic secondary data sources (supplementary section 2).We aimed to collect data from a wide distribution across climatic zones and ecoregions.For each e-flows assessment site, the resulting database contained: basic geographic information, the name and type of the e-flows assessment method applied (table S5), the natural long-term mean annual flow (MAF, in m 3 s −1 , usually derived from local hydrological modelling conducted as part of the e-flows assessment), the e-flows requirement, and the ecological management class (EMC) associated with the site.EMCs can be used to express the current or desired future condition of the river; class A, for example, is assigned to near-natural rivers or those with a high level of protection and class D to largely modified rivers (Smakhtin and Anputhas 2006; see table S3 for descriptions).

Data from GHMs
As the hydrological basis to compute global e-flows, we used modelled time series of natural hydrology from GHMs.These GHMs take data on precipitation, evapotranspiration and other climate variables simulated by general circulation models (GCMs) as inputs to model the dynamics of soil moisture storage, the generation of runoff on land, and the discharge through the river network (Döll et al 2016).Estimates of discharge can differ strongly among models, leading to variability in subsequent e-flows calculations depending on which combination of GCM and GHM is used (Liu et al 2021, Virkki et al 2022).To assess and control for this variability, we computed eflows based on hydrological estimates from 4 distinct GHMs, each using modelled climate data from 4 GCMs for a total of 16 GCM-GHM combinations (see supplementary section 3 for information on models).We downloaded global gridded hydrological time series at a spatial resolution of 30 arc-min (i.e. each pixel spans about 55 km in width and height at the equator) for each of these combinations from the Inter-Sectoral Impact Model Intercomparison Project simulation round 2b (Frieler et al 2017).These estimates represent the water which flows out daily from each land pixel to the next pixel downstream.To represent the natural hydrology of rivers, we used model estimates from 1661 to 1860 that are based on a scenario of pre-industrial climate, CO 2 concentration, land use and human influence on water resources (for details, see Frieler et al 2017).

Global e-flows calculations
We estimated e-flows requirements based on hydrological data from each of the GCM-GHM combinations with five different hydrological e-flows calculation methods: (1) the Tennant (or Montana) method (Tennant 1976), (2) the Tessmann method (Tessmann 1980), (3) the Q90_Q50 method (Pastor et al 2014), (4) the variable monthly flow (VMF) method (Pastor et al 2014) and ( 5) the Smakhtin flow-duration curve (FDC) shift method (Smakhtin and Anputhas 2006; see supplementary section 1.2 for definitions and supplementary section 3 for calculation details).We computed four e-flows estimates using the Smakhtin FDC shift method (for EMCs A to D; Figure S1), because this method is used to calculate e-flows for SDG indicator 6.4.2.For the other four methods, we computed one e-flows estimate each, as implemented in previous global e-flows studies (supplementary section 1.2).Global e-flows estimates were first computed at monthly time steps and then averaged to a mean annual e-flows to be compared to the local e-flows assessment for every site.Altogether, we produced 8 annual e-flows estimates (5 methods, with 4 estimates for the Smakhtin FDC shift method) for each of the 16 GCM-GHM combinations, for a total of 128 e-flows estimates for every land pixel.
The coarse spatial resolution of GHMs and that of the resulting e-flows estimates limits their comparability to e-flows assessments conducted for individual river reaches.Global models can only be compared to local estimates for sites with a drainage area larger than a single pixel (∼3000 km 2 at the equator for 30 arc-min pixels; supplementary section 6; figures S5-S8 and table S7).Therefore, we derived global MAF and e-flows estimates at a spatial resolution of 0.25 arc-min (∼500 m at the equator) following Lehner and Grill (2013) before comparing them to local assessments (see supplementary section 3 for details).

Comparison of local and global estimates of MAF
For each site in the database of local e-flows assessments, we extracted the globally estimated long-term MAF (for 1661-1860) and e-flows values of the pixel in which the site was located for all combinations of models.We then evaluated the degree of agreement between local and global estimates of MAF by computing a set of standard performance statistics.Using local estimates as the reference value, we calculated the mean absolute error (MAE; see supplementary section 4 for definitions), percent bias (%Bias), symmetric mean absolute percentage error (sMAPE), and the coefficient of determination (R 2 ) for all sites together, as well as by river size and country.For each country, we computed an ensemble multimodel weighted-mean MAF for every site whereby each GHM-GCM combination was weighed based on its skill in predicting locally estimated MAF in that country (Sanderson et al 2017, Robeson and Willmott 2023; see supplementation section 4 for details).

Comparison of local and global estimates of e-flows
We compared local e-flows estimates to global estimates by computing the same set of standard performance statistics used to compare hydrological estimates.We compared e-flows estimates both (i) as a mean annual volume (in m 3 s −1 ; from hereon, mean annual e-flows) and (ii) as a percentage of MAF, and computed separate sets of statistics for all sites, by country, and by the type of method used in the local e-flows assessment (see table S5 for definitions of method types and supplementary section 5 for calculation details).Global estimates of e-flows as a percentage of MAF were computed for each site as the ratio of the global estimate of mean annual e-flows to the global estimate of MAF (i.e.not the locally derived MAF estimate).
For all sites, we compared the local assessment results to global estimates from all methods, including the estimates with the Smakhtin FDC shift method calculated for each of the four EMCs (i.e.regardless of the site's local EMC).For sites where the EMC could be determined (about half of the database), a separate assessment was also performed using the e-flows estimate from the Smakhtin method with the site's corresponding EMC (hereafter, the 'matched EMC').
In addition to comparing local assessments to global estimates calculated with all combinations of GHMs and GCMs, we produced an ensemble e-flows estimate for each site.This estimate was a weighted average of the individual e-flows estimates computed with the various GCM-GHM combinations, using the same country-specific weights as those used in producing the ensemble MAF estimate (see supplementary section 4).This approach aimed to evaluate the performance of global e-flows methods while minimizing the effect of global hydrological modelling uncertainty.

Results
A total of 1346 local e-flows assessments were compiled and formatted for inclusion in the database, representing 1194 unique sites distributed across 25 countries (figure S2).The associated watercourses were of varying sizes and ecohydrological conditions, ranging from small streams with a MAF of 0.02 m 3 s −1 to the Amazon River.The database included at least 26 different e-flows assessment methods.In most countries where legislation requires the protection or restoration of e-flows, common practices tend to be adopted nationwide or specific e-flows assessment methods are stipulated.This explains the homogeneity of e-flows assessment methods within countries observed in the database (figure 2).The sites included in this study represent a fraction of the total number of e-flows assessments conducted globally.Their distribution reflects the extent to which secondary data could be obtained and harmonized within this study's timeframe, rather than the relative effort expended by countries on assessing e-flows.We plan further expansion of the database in the future towards full global coverage.
The comparability of global MAF estimates to local estimates varied substantially among GCM-GHM combinations (table S7 and figure S9; range sMAPE = 26%, range %BIAS = 184%).Using an ensemble model based only on the best-performing models for each country led to more uniform comparability between global and local estimates than if using the predictions from a single, highestperforming model across all countries (average ± SD in performance rank across all countries and statistics for ensemble model = 6.2 ± 5.6; for GFDL-ESM2M [GCM] + WaterGAP 2.2c [GHM] = 13.2 ± 8.8; n = 1141).Nonetheless, performance varied considerably among countries even when considering the highest-performing combination of models by country (table S8 and figure S14).
The variability in flow predictions among GCM-GHM combinations was compounded by differences among global e-flows calculation methods, producing even wider ranges in global e-flows estimates for a given site, as observed in previous studies (Liu et al 2021, Virkki et al 2022).Global estimates of mean annual e-flows (as a volume) spanned more than one order of magnitude for 47% of sites.For the rest of this section, therefore, only the results from comparing local e-flows assessments to the global e-flows estimates from the country-specific ensemble will be presented, and not all GCM-GHM combinations.
Global ensemble estimates of e-flows volume explained most of the variability in local e-flows volume estimates across multiple orders of magnitude (R 2 ⩾ 0.79; log-log linear least-square regression), regardless of the global e-flows calculation method employed (figure 3; table 1).However, a high R 2 in such log-log regressions largely reflects the ability of the model to differentiate large from small rivers.The average relative error (sMAPE = 74%-101%) and bias (%BIAS = 237%-788%) for a given site were high, and global MAF estimates alone explained as much variability in locally estimated e-flow volumes (R 2 = 0.82) than global ensemble estimates of eflows volume did (mean R 2 across global e-flows  2 and figure S17).The limited comparability of e-flows estimates as a percentage of MAF between global and local assessments is not mainly related to discrepancies in hydrological estimates between the two scales (figure S18), but to differences in e-flows estimation scale and methods.
Several e-flows calculation methods implemented at the global scale define e-flows as a fixed percentage of discharge with little variability among sites (table 3; Tennant, VMF, Tessmann).Others based on flow frequency exhibit a greater variability (Q90_Q50, Smakhtin FDC shift method; figure 6), which is more in line with the wide range of locally derived e-flows as a percentage of MAF recommended within countries (table 3; figure 5).Despite this greater comparability to local estimates in terms of range, global estimates based on the Q90_Q50 and Smakhtin methods did not perform consistently better at predicting local values (table 1).The global calculation methods also differ by design in how conservative they are.For instance, the Smakhtin FDC shift method for EMC A overestimated e-flows as a percentage by more than 10 percentage points for 87% of sites.In contrast, the Tennant method did so for only 35% of sites and underestimated e-flows as a percentage for 28% of sites.As countries also differ in how conservative they are in determining e-flows, the least biased global method, compared to local assessments, varied by country (table S9).
No environmental factor was consistently correlated with the difference between global and local estimates of e-flows as a percentage, across countries or local assessment methods.Drainage area and MAF were consistently correlated with the difference between global and local estimates within several countries, yet the direction of this relationship was inconsistent among countries (figure S19).

Discussion
Our global compilation effort provided us with the largest database of e-flows assessments to date, which offers renewed evidence of the diverse concepts and methods used in evaluating the e-flows requirements of rivers.Local e-flows assessment methods vary in their degree of complexity and socio-ecohydrological grounding, but also in their objectives.For example,   for some e-flows assessments without information on mean annual flow, precluding the calculation of mean annual e-flows.e A separate assessment was performed using the e-flows estimate from the Smakhtin method with the corresponding ecological management class (EMC) of individual sites, for sites where an EMC could be determined (see supplementary section 2.2).
assessments in Victoria (Australia) rely on a combination of data and expert knowledge to identify the diverse flow events necessary to support multiple ecological and sociocultural components (Victorian Environmental Water Holder 2023).This heterogeneity reflects the varied legislative, resource and management contexts (Poff et al 2017), as well as environmental conditions, across e-flows assessments.It confirms that a single global estimate of e-flows cannot reflect e-flows practice everywhere.
Previous comparative studies have suggested that global estimates provide a good proxy for locally estimated e-flows (Pastor et al 2014, Jägermeyr et al 2017), considering the strong correlation between global and local estimates of e-flows volumes across multiple orders of magnitude.Our analysis also showed a correlation between global and local estimates in terms of mean annual e-flows, but the model error and bias are high for a given site, so this correlation mostly shows the ability of global models to capture broad differences in river size across sites rather than variations in flow requirements.Indeed, existing global methods are unable to predict the percentage of river flow deemed necessary by local e-flows assessments to sustain freshwater ecosystems.
We evaluated global e-flows estimates from 128 combinations of climate forcing models, hydrological models, and e-flows estimations methods, yet global e-flows estimates as a percentage of MAF were not meaningfully correlated to local estimates for any country, regardless of which combination of models we used.Some local assessments in this study relied on simplistic hydrological approaches that may be less defensible than current global methods.Nonetheless, a fundamental disconnect clearly exists between eflows estimates at the global scale and those used by local practitioners to protect and restore the flows needed for ecological and sociocultural purposes in rivers worldwide.
Several global e-flows methods tend to be conservative, on average, compared to local assessments (table 1 and table S9), and thus broadly meet the objective of providing a precautionary e-flows estimate.However, no global method captures the contextspecific flow requirements of rivers reflected in local e-flows assessments.Using conservative methods limits the risk of establishing e-flows targets that may still not suffice to meet river health objectives (Richter et al 2012).At the same time, we recommend that studies assessing potential trade-offs between human water uses and e-flows be cautious in drawing conclusions from such conservative methods.For instance, the safe and just Earth system boundary for freshwater (Rockström et al 2023), and several other promin-ent studies (e.g.Mekonnen and Hoekstra 2016), are based on a presumptive e-flows standard that proposes to protect 80% of mean natural monthly flows to achieve moderate ecological protection, based on a review of four case studies in the US and the UK (Richter et al 2012).However, of all local assessments in our database, including detailed holistic assessments, only 6% recommended that e-flows exceed 70% of MAF and no assessment recommended 80% or more.While we expect future iterations of our database to include such cases where flow protection of near-natural rivers is needed, it is likely that these We used simulated data from a dedicated model intercomparison project to consistently compare the variability in global estimates that results from differences among climate forcing and GHMs.These models are among the most commonly used in previous global e-flow assessments (table S1).However, we note that other global models may offer higher comparability to local assessments, if operating at higher resolutions or if already downscaled to the scale of river reaches (e.g.Lin et al 2019, Kallio et al 2021).a A separate assessment was performed using the e-flows estimate from the Smakhtin method with the corresponding ecological management class (EMC) of individual sites, for sites where an EMC could be determined (see supplementary section 2.2).

Conclusion
Current global models can broadly approximate the amount of water that should be precautionarily set aside to sustain aquatic ecosystems at the scale of large river basins or countries.However, our analysis laid bare a disconnect between global and local assessments of e-flows requirements.No amount of improvement in hydrological modelling can solve the inability of current global approaches to explain differences in local estimates of the percentage of river flow to conserve among sites, which limits the credibility of the present global e-flows estimates and associated targets for human and ecosystem water use.
In the first attempt at estimating global e-flows requirements, Smakhtin et al (2004) qualified their approach as a rule-of-thumb for determining bulk environmental water requirements in world river basins, constrained as much by uncertainties in GHMs as by a dearth of detailed e-flows assessments.This first global assessment and most subsequent ones were not intended as proxies for more detailed, site-specific methods.Since then, thousands of local e-flows assessments have been performed across diverse biogeographic regions, yet there has been little progress in compiling and leveraging this wealth of information to move beyond simple hydrological estimation methods at the global scale.Twenty years on, our study provides a first step and analytical approach to address this gap.We stress though that additional efforts are now imperative to build a more comprehensive global database of local eflows assessments, which can serve as the basis to bridge the gap between the local and global scales.Such scientifically grounded estimates could play a central role in accelerating e-flows implementation worldwide and helping to curb the global decline in freshwater biodiversity.formal analysis, writing (original draft)-M L M; results interpretation and writing (review and editing)all authors; project administration and supervision-C W S D; funding acquisition-C W S D.

Figure 1 .
Figure 1.The main methodological steps involved in computing global e-flows requirements for this study and comparing the resulting estimates to those from local e-flows assessments.

Figure 2 .
Figure 2. Distribution of the local e-flows assessment sites included in the analysis (n = 1194; from France and South Africa, with 436 and 342 sites respectively, to 5 or fewer sites from Kenya to Botswana; the 'Other' type only applies to China).

Figure 3 .
Figure 3.Comparison of mean annual e-flows as a volume estimated by local assessments to global model estimates from different global estimation methods.Each panel shows values generated by a global e-flows calculation method, with each dot representing the global (y-axis) and local (x-axis) mean annual e-flows estimates for a river site with a local e-flows assessment.The black diagonal line represents the 1:1 line along which local and global estimates are equal; the light blue-shaded ribbon shows one order of magnitude around the 1:1 line; the dark blue curved line shows model fits from general additive models.Global e-flows estimates were computed as a multi-model weighted-mean estimate for each site whereby the e-flow estimate from each GHM-GCM combination was weighed based on this combination's performance in predicting locally estimated MAF in the country where the site was located (see supplementation section 4 for details).VMF: variable monthly flow.

c
Coefficient of determination from a log-log linear least-square regression for mean annual e-flows (as a volume), and from a standard linear least-square regression for e-flows as a percentage of mean annual flow.d n is smaller for mean annual e-flows (as a volume) because only e-flows as a percentage of mean annual flow were provided

Figure 4 .
Figure 4. Comparison of e-flows as a percentage of mean annual flow estimated by local assessments to global model estimates from different global estimation methods.Each panel shows values for a global e-flows calculation method, with each dot representing the global (y-axis) and local (x-axis) e-flows estimates as percentages of long-term natural MAF for a river site with a local e-flows assessment.The black diagonal line represents the 1:1 line along which local and global estimates are equal.Global e-flows estimates were computed as a multi-model weighted-mean estimate for each site whereby the e-flow estimate from each GHM-GCM combination was weighed based on this combination's performance in predicting locally estimated MAF in the country where the site was located (see supplementation section 4 for details).

Figure 5 .
Figure 5.Comparison of e-flows as a percentage of mean annual flow estimated by local e-flows assessments to global model estimates from different global e-flows calculation methods, by country.Each panel shows values for a global e-flows calculation method (columns) in a specific country (rows), with each dot representing the global (y-axis) and local (x-axis) e-flows estimates as percentages of long-term natural MAF for a river site with a local e-flows assessment.The thin black diagonal line represents the 1:1 line along which local and global estimates are equal; the thick black lines show model fits from least-square regressions.Global e-flows estimates were computed as a multi-model weighted-mean estimate for each site whereby the e-flow estimate from each GHM-GCM combination was weighed based on this combination's performance in predicting locally estimated MAF in the country where the site was located (see supplementation section 4 for details).

Figure 6 .
Figure 6.Example estimates of mean annual flow and e-flows as a percentage of mean annual flow from a global model.Both MAF and e-flows were estimated based on discharge data simulated by the WaterGAP 2.2c GHM (Müller Schmied et al 2016) forced with climate data from the GFDL-ESM2M global circulation model (Dunne et al 2012); e-flows were calculated with the Q90-Q50 method (Pastor et al 2014); 127 other sets of estimates were produced as part of this study with different combinations of GHM, global circulation model, and e-flows calculation method.See supplementary sections 1 and 3 for details on these methods.

Table 1 .
Performance statistics of e-flows estimates from global ensemble models relative to estimates from local assessments.
a Mean absolute error (see supplementary section 4 for equation).b Symmetric mean absolute percentage error (see supplementary section 4 for equation).

Table 2 .
Performance statistics of e-flows estimates as a percentage of mean annual flow from global ensemble models relative to estimates from local assessments, by country and global estimation method.
a Mean absolute error (see supplementary section 4 for equation).b Coefficient of determination from a log-log regression for mean annual e-flows (as a volume) and from a standard linear regression for e-flows as a percentage of mean annual flow.c A separate assessment was performed using the e-flows estimate from the Smakhtin method with the corresponding ecological management class (EMC) of individual sites, for sites where an EMC could be determined (see supplementary section 2.2).

Table 3 .
Summary statistics of e-flows as a percentage of mean annual flow estimated by global models (top section; by estimation method) and local assessments (bottom section; by country).
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