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

Mathis L Messager, Chris W S Dickens, Nishadi Eriyagama, Rebecca E Tharme

► To cite this version:

Mathis L Messager, Chris W S Dickens, Nishadi Eriyagama, Rebecca E Tharme. Limited comparability of global and local estimates of environmental flow requirements to sustain river ecosystems. Environmental Research Letters, 2024, 19 (2), pp.024012. 10.1088/1748-9326/ad1cb5. hal-04592351

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LETTER • OPEN ACCESS

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

To cite this article: Mathis L Messager *et al* 2024 *Environ. Res. Lett.* **19** 024012

View the [article online](#) for updates and enhancements.

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<figure><img src="image_1.png" /></figure>
LETTER • OPEN ACCESS

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

To cite this article: Mathis L Messager *et al* 2024 *Environ. Res. Lett.* **19** 024012

View the [article online](#) for updates and enhancements.

You may also like

- Overcoming persistent challenges in putting environmental flow policy into practice: a systematic review and bibliometric analysis
Gustavo Facincani Dourado, Anna M Rallings and Joshua H Viers

- Granular and particle-laden flows: from laboratory experiments to field observations
R Delannay, A Valance, A Mangeney et al.

- Large-eddy-simulation approach in understanding flow structures of 2D turbulent density currents over sloping surfaces
M Nayamatullah, Narasimha Rao, Pillalamarri and Kiran Bhaganagar

<figure><img src="image_2.png" /></figure>
ENVIRONMENTAL RESEARCH
LETTERS

<figure><img src="image_2.png" /></figure>

CrossMark

OPEN ACCESS

RECEIVED

31 August 2023

REVISED

1 November 2023

ACCEPTED FOR PUBLICATION

9 January 2024

PUBLISHED

19 January 2024

Original content from
this work may be used
under the terms of the
Creative Commons
Attribution 4.0 licence.

Any further distribution
of this work must
maintain attribution to
the author(s) and the title
of the work, journal
citation and DOI.

<figure><img src="image_3.png" /></figure>

LETTER

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

Mathis L Messager<fnref n="1" />,<fnref n="2" />,* ID, Chris W S Dickens<fnref n="3" /> ID, Nishadi Eriyagama<fnref n="3" /> ID and Rebecca E Tharme<fnref n="1" />,<fnref n="5" />,<fnref n="6" /> ID

E-mail: mathis.messager@mail.mcgill.ca

**Keywords:** e-flows, water resource management, global hydrological modelling, river conservation, freshwater biodiversity, Sustainable Development Goals (SDGs), water scarcity

Supplementary material for this article is available online

Abstract

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 ($R^2 \le 0.31$) 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.

<footnote n="1">¹ RiverLY Research Unit, National Research Institute for Agriculture, Food and Environment (INRAE), Centre Lyon-Grenoble Auvergne-Rhône-Alpes, 5 Rue de la Doua, Villeurbanne 69625, France</footnote>

<footnote n="2">² Department of Geography, McGill University, 805 Sherbrooke St W, Montreal, QC H3A 0B9, Canada</footnote>

<footnote n="3">³ International Water Management Institute, Sunil Mawatha, Pelawatte, Colombo, Sri Lanka</footnote>

<footnote n="4">⁴ River futures, Derbyshire SK17 8SX, United Kingdom</footnote>

<footnote n="5">⁵ Australian Rivers Institute, Griffith University, Nathan, Queensland 4111, Australia</footnote>

<footnote n="6">⁶ Freshwater Conservation Committee, IUCN Species Survival Commission, Gland, Switzerland</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
ENVIRONMENTAL RESEARCH
LETTERS

<figure><img src="image_3.png" /></figure>

CrossMark

OPEN ACCESS

RECEIVED

31 August 2023

REVISED

1 November 2023

ACCEPTED FOR PUBLICATION

9 January 2024

PUBLISHED

19 January 2024

Original content from
this work may be used
under the terms of the
Creative Commons
Attribution 4.0 licence.

Any further distribution
of this work must
maintain attribution to
the author(s) and the title
of the work, journal
citation and DOI.

<figure><img src="image_4.png" /></figure>

LETTER

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

Mathis L Messager<fnref n="1" />,<fnref n="2" />,* ID, Chris W S Dickens<fnref n="3" /> ID, Nishadi Eriyagama<fnref n="3" /> ID and Rebecca E Tharme<fnref n="1" />,<fnref n="5" />,<fnref n="6" /> ID

E-mail: mathis.messager@mail.mcgill.ca

**Keywords:** e-flows, water resource management, global hydrological modelling, river conservation, freshwater biodiversity, Sustainable Development Goals (SDGs), water scarcity

Supplementary material for this article is available online

Abstract

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 ($R^2 \le 0.31$) 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.

<footnote n="1">¹ RiverLY Research Unit, National Research Institute for Agriculture, Food and Environment (INRAE), Centre Lyon-Grenoble Auvergne-Rhône-Alpes, 5 Rue de la Doua, Villeurbanne 69625, France</footnote>

<footnote n="2">² Department of Geography, McGill University, 805 Sherbrooke St W, Montreal, QC H3A 0B9, Canada</footnote>

<footnote n="3">³ International Water Management Institute, Sunil Mawatha, Pelawatte, Colombo, Sri Lanka</footnote>

<footnote n="4">⁴ River futures, Derbyshire SK17 8SX, United Kingdom</footnote>

<footnote n="5">⁵ Australian Rivers Institute, Griffith University, Nathan, Queensland 4111, Australia</footnote>

<footnote n="6">⁶ Freshwater Conservation Committee, IUCN Species Survival Commission, Gland, Switzerland</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
# 1. 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 and Matthews 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 e-flows 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 target-setting, 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 e-flows 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 trade-offs 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 e-flows 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. 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 and Matthews 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 e-flows 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 target-setting, 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 e-flows 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 trade-offs 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 e-flows 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
<figure><img src="image_4.png" /><figcaption>**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.</figcaption></figure>

how different methodological choices involved in
modelling global e-flows induce variability in the final
estimates, and which combination of data sources and
methods most closely reproduce local e-flows estim-
ates (figure 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 e-
flows (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 consist-
ent 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 result-
ing from in-depth assessments grounded in local data

and expertise assuredly surpass global estimates in
their accuracy, whereas others were of lower confid-
ence, being derived from more simplistic methods.
Therefore, local estimates are not systematically bet-
ter than global estimates at representing the needs of
ecosystems in this analysis. Additionally, most assess-
ments analysed in this study were commissioned by
government agencies for regulatory or resource man-
agement 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 imple-
mentation gap between global and local flow man-
agement of river ecosystems. Our study expands upon
our previous efforts (Eriyagama et al 2024) by com-
piling local e-flows estimates for another 661 sites and
comparing them to all common global e-flows cal-
culation methods. Considering the heterogeneity of
e-flows concepts, policy objectives and local assess-
ment methods among countries, we did not expect
<figure><img src="image_5.png" /><figcaption>**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.</figcaption></figure>

how different methodological choices involved in
modelling global e-flows induce variability in the final
estimates, and which combination of data sources and
methods most closely reproduce local e-flows estim-
ates (figure 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 e-
flows (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 consist-
ent 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 result-
ing from in-depth assessments grounded in local data

and expertise assuredly surpass global estimates in
their accuracy, whereas others were of lower confid-
ence, being derived from more simplistic methods.
Therefore, local estimates are not systematically bet-
ter than global estimates at representing the needs of
ecosystems in this analysis. Additionally, most assess-
ments analysed in this study were commissioned by
government agencies for regulatory or resource man-
agement 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 imple-
mentation gap between global and local flow man-
agement of river ecosystems. Our study expands upon
our previous efforts (Eriyagama et al 2024) by com-
piling local e-flows estimates for another 661 sites and
comparing them to all common global e-flows cal-
culation methods. Considering the heterogeneity of
e-flows concepts, policy objectives and local assess-
ment 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.

## 2. Data and methods

### 2.1. 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 e-flows 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 m³ 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).

### 2.2. 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 e-flows 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, CO₂ concentration, land use and human influence on water resources (for details, see Frieler et al 2017).

### 2.3. 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 km² 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).

## 2.4. 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
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.

## 2. Data and methods

### 2.1. 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 e-flows 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 m³ 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).

### 2.2. 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 e-flows 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, CO₂ concentration, land use and human influence on water resources (for details, see Frieler et al 2017).

### 2.3. 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 km² 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).

## 2.4. 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 multi-model 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).

## 2.5. 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.

## 3. 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, highest-performing model across all countries (average $\pm$ SD in performance rank across all countries and statistics for ensemble model = $6.2 \pm 5.6$; for GFDL-ESM2M [GCM] + WaterGAP 2.2c [GHM] = $13.2 \pm 8.8$; 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 ($R^2 \ge 0.79$; 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 e-flows volume did (mean $R^2$ across global e-flows
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 multi-model 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).

## 2.5. 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.

## 3. 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, highest-performing model across all countries (average $\pm$ SD in performance rank across all countries and statistics for ensemble model = $6.2 \pm 5.6$; for GFDL-ESM2M [GCM] + WaterGAP 2.2c [GHM] = $13.2 \pm 8.8$; $n = 1141$). 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 ($R^2 \ge 0.79$; 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 e-flows volume did (mean $R^2$ across global e-flows
<figure><img src="image_5.png" /></figure>

calculation methods = 0.81). When comparing e-flows as a percentage of MAF, which controls for differences in river size and uncertainties in hydrological modelling, no global e-flows calculation method could predict local e-flows estimates, explaining a negligible 0%–1% of the variability in local e-flows percentage across all methods (figure 4 and table 1; see supplementary section 5.2 for an explanation). Even when comparing global and local estimates by country or by local e-flows assessment method type (i.e. controlling for cross-country or cross-method variability), global e-flows estimates offered little to no predictive ability (figure 5, table 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).

## 4. 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,
<figure><img src="image_6.png" /></figure>

calculation methods = 0.81). When comparing e-flows as a percentage of MAF, which controls for differences in river size and uncertainties in hydrological modelling, no global e-flows calculation method could predict local e-flows estimates, explaining a negligible 0%–1% of the variability in local e-flows percentage across all methods (figure 4 and table 1; see supplementary section 5.2 for an explanation). Even when comparing global and local estimates by country or by local e-flows assessment method type (i.e. controlling for cross-country or cross-method variability), global e-flows estimates offered little to no predictive ability (figure 5, table 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).

## 4. 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,
<figure><img src="image_6.png" /><figcaption>**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.</figcaption></figure>

e-flows in Brazil are defined for large basins simply as 50% of MAF at the outlet; those in the Rhône Basin (France) establish minimum flows in individual river

reaches with habitat simulation models, to ensure the survival of large-bodied fish species during low-flow months (Lamouroux et al 2017); and e-flows
<figure><img src="image_7.png" /><figcaption>**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.</figcaption></figure>

e-flows in Brazil are defined for large basins simply as 50% of MAF at the outlet; those in the Rhône Basin (France) establish minimum flows in individual river

reaches with habitat simulation models, to ensure the survival of large-bodied fish species during low-flow months (Lamouroux et al. 2017); and e-flows
<table><caption>**Table 1.** Performance statistics of e-flows estimates from global ensemble models relative to estimates from local assessments.</caption><thead><tr><th>Global e-flows calculation method</th><th>MAE<sup>a</sup></th><th>sMAPE<sup>b</sup></th><th>% Bias</th><th>R<sup>2c</sup></th><th>n<sup>d</sup></th></tr></thead><tbody><tr><td colspan="6">Comparison of mean annual e-flows (as a volume)</td></tr><tr><td>Tennant</td><td>73</td><td>74%</td><td>278%</td><td>0.83</td><td>1056</td></tr><tr><td>Tessmann</td><td>47</td><td>88%</td><td>543%</td><td>0.83</td><td>1056</td></tr><tr><td>Q90_Q50</td><td>52</td><td>83%</td><td>362%</td><td>0.79</td><td>1056</td></tr><tr><td>VMF</td><td>59</td><td>79%</td><td>404%</td><td>0.83</td><td>1056</td></tr><tr><td>Smakhtin (Ecological management class A)</td><td>91</td><td>101%</td><td>788%</td><td>0.82</td><td>1056</td></tr><tr><td>Smakhtin (EMC B)</td><td>35</td><td>88%</td><td>524%</td><td>0.81</td><td>1056</td></tr><tr><td>Smakhtin (EMC C)</td><td>51</td><td>81%</td><td>352%</td><td>0.80</td><td>1056</td></tr><tr><td>Smakhtin (EMC D)</td><td>73</td><td>82%</td><td>237%</td><td>0.79</td><td>1056</td></tr><tr><td>Smakhtin (Matched EMC<sup>e</sup>)</td><td>2</td><td>84%</td><td>322%</td><td>0.59</td><td>553</td></tr><tr><td colspan="6">Comparison of e-flows as a percentage of mean annual flow</td></tr><tr><td>Tennant</td><td>16%</td><td>—</td><td>104%</td><td>0.02</td><td>1061</td></tr><tr><td>Tessmann</td><td>24%</td><td>—</td><td>249%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Q90_Q50</td><td>21%</td><td>—</td><td>142%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>VMF</td><td>19%</td><td>—</td><td>174%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC A)</td><td>38%</td><td>—</td><td>365%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC B)</td><td>24%</td><td>—</td><td>223%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC C)</td><td>20%</td><td>—</td><td>132%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC D)</td><td>19%</td><td>—</td><td>71%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (Matched EMC<sup>e</sup>)</td><td>19%</td><td>—</td><td>117%</td><td>&lt;0.01</td><td>556</td></tr></tbody></table>

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 e-flows 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

<footnote><sup>a</sup> Mean absolute error (see supplementary section 4 for equation).</footnote>

<footnote><sup>b</sup> Symmetric mean absolute percentage error (see supplementary section 4 for equation).</footnote>

<footnote><sup>c</sup> 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.</footnote>

<footnote><sup>d</sup> *n* is smaller for mean annual e-flows (as a volume) because only e-flows as a percentage of mean annual flow were provided for some e-flows assessments without information on mean annual flow, precluding the calculation of mean annual e-flows.</footnote>

<footnote><sup>e</sup> 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).</footnote>
<table><caption>**Table 1.** Performance statistics of e-flows estimates from global ensemble models relative to estimates from local assessments.</caption><thead><tr><th>Global e-flows calculation method</th><th>MAE<sup>a</sup></th><th>sMAPE<sup>b</sup></th><th>% Bias</th><th>R<sup>2c</sup></th><th>n<sup>d</sup></th></tr></thead><tbody><tr><td colspan="6">Comparison of mean annual e-flows (as a volume)</td></tr><tr><td>Tennant</td><td>73</td><td>74%</td><td>278%</td><td>0.83</td><td>1056</td></tr><tr><td>Tessmann</td><td>47</td><td>88%</td><td>543%</td><td>0.83</td><td>1056</td></tr><tr><td>Q90_Q50</td><td>52</td><td>83%</td><td>362%</td><td>0.79</td><td>1056</td></tr><tr><td>VMF</td><td>59</td><td>79%</td><td>404%</td><td>0.83</td><td>1056</td></tr><tr><td>Smakhtin (Ecological management class A)</td><td>91</td><td>101%</td><td>788%</td><td>0.82</td><td>1056</td></tr><tr><td>Smakhtin (EMC B)</td><td>35</td><td>88%</td><td>524%</td><td>0.81</td><td>1056</td></tr><tr><td>Smakhtin (EMC C)</td><td>51</td><td>81%</td><td>352%</td><td>0.80</td><td>1056</td></tr><tr><td>Smakhtin (EMC D)</td><td>73</td><td>82%</td><td>237%</td><td>0.79</td><td>1056</td></tr><tr><td>Smakhtin (Matched EMC<sup>e</sup>)</td><td>2</td><td>84%</td><td>322%</td><td>0.59</td><td>553</td></tr><tr><td colspan="6">Comparison of e-flows as a percentage of mean annual flow</td></tr><tr><td>Tennant</td><td>16%</td><td>—</td><td>104%</td><td>0.02</td><td>1061</td></tr><tr><td>Tessmann</td><td>24%</td><td>—</td><td>249%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Q90_Q50</td><td>21%</td><td>—</td><td>142%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>VMF</td><td>19%</td><td>—</td><td>174%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC A)</td><td>38%</td><td>—</td><td>365%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC B)</td><td>24%</td><td>—</td><td>223%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC C)</td><td>20%</td><td>—</td><td>132%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (EMC D)</td><td>19%</td><td>—</td><td>71%</td><td>&lt;0.01</td><td>1061</td></tr><tr><td>Smakhtin (Matched EMC<sup>e</sup>)</td><td>19%</td><td>—</td><td>117%</td><td>&lt;0.01</td><td>556</td></tr></tbody></table>

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 e-flows 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

<footnote><sup>a</sup> Mean absolute error (see supplementary section 4 for equation).</footnote>

<footnote><sup>b</sup> Symmetric mean absolute percentage error (see supplementary section 4 for equation).</footnote>

<footnote><sup>c</sup> 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.</footnote>

<footnote><sup>d</sup> *n* is smaller for mean annual e-flows (as a volume) because only e-flows as a percentage of mean annual flow were provided for some e-flows assessments without information on mean annual flow, precluding the calculation of mean annual e-flows.</footnote>

<footnote><sup>e</sup> 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).</footnote>
<figure><img src="image_7.png" /></figure>

objective of providing a precautionary e-flows estimate. However, no global method captures the context-specific 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
<figure><img src="image_8.png" /></figure>

objective of providing a precautionary e-flows estimate. However, no global method captures the context-specific 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
<figure><img src="image_8.png" /><figcaption>**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).</figcaption></figure>

levels of protection remain unusual in contexts of competing water uses.

Future comparisons between global and local e-flows estimates could improve upon this study by evaluating e-flows at the monthly scale (as done by Pastor *et al* 2014). Our focus on the mean annual volume of water deemed necessary to sustain aquatic ecosystems enabled us to compare a larger number of sites, is commonly used in water resources planning (Pedro-Monzónis *et al* 2015) and corresponds to the definition used to compute the SDG indicator 6.4.2. on water stress. Nevertheless, this mean annual volume of water is more influenced by biases and uncertainties in estimates of discharge and e-flows

during high-flow periods (which represent the bulk of annual flow) than in low-flow periods, even though our ability to sustain low-flows is key for the integrity of riverine ecosystems (Rolls *et al* 2012).

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).
<figure><img src="image_9.png" /><figcaption>**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).</figcaption></figure>

levels of protection remain unusual in contexts of competing water uses.

Future comparisons between global and local e-flows estimates could improve upon this study by evaluating e-flows at the monthly scale (as done by Pastor *et al* 2014). Our focus on the mean annual volume of water deemed necessary to sustain aquatic ecosystems enabled us to compare a larger number of sites, is commonly used in water resources planning (Pedro-Monzónis *et al* 2015) and corresponds to the definition used to compute the SDG indicator 6.4.2. on water stress. Nevertheless, this mean annual volume of water is more influenced by biases and uncertainties in estimates of discharge and e-flows

during high-flow periods (which represent the bulk of annual flow) than in low-flow periods, even though our ability to sustain low-flows is key for the integrity of riverine ecosystems (Rolls *et al* 2012).

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).
<table><caption>**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.</caption><thead><tr><th>Country</th><th>Global e-flows method</th><th>MAE<sup>a</sup></th><th>% Bias</th><th>R<sup>2b</sup></th><th>n</th></tr></thead><tbody><tr><td rowspan="10">Australia</td><td>Tenant</td><td>17</td><td>16</td><td>0.21</td><td>33</td></tr><tr><td>Tessmann</td><td>22</td><td>85</td><td>0.19</td><td>33</td></tr><tr><td>VMF</td><td>19</td><td>54</td><td>0.05</td><td>33</td></tr><tr><td>Q90_Q50</td><td>17</td><td>55</td><td>0.23</td><td>33</td></tr><tr><td>Smakhtin—EMC A</td><td>39</td><td>182</td><td>0.06</td><td>33</td></tr><tr><td>Smakhtin—EMC B</td><td>26</td><td>112</td><td>0.26</td><td>33</td></tr><tr><td>Smakhtin—EMC C</td><td>18</td><td>60</td><td>0.22</td><td>33</td></tr><tr><td>Smakhtin—EMC D</td><td>17</td><td>25</td><td>0.17</td><td>33</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>17</td><td>28</td><td>0.12</td><td>33</td></tr><tr><td rowspan="10">Canada</td><td>Tenant</td><td>22</td><td>-4</td><td>0.17</td><td>76</td></tr><tr><td>Tessmann</td><td>21</td><td>69</td><td>0.00</td><td>76</td></tr><tr><td>VMF</td><td>20</td><td>40</td><td>0.03</td><td>76</td></tr><tr><td>Q90_Q50</td><td>22</td><td>76</td><td>0.02</td><td>76</td></tr><tr><td>Smakhtin—EMC A</td><td>37</td><td>179</td><td>0.09</td><td>76</td></tr><tr><td>Smakhtin—EMC B</td><td>28</td><td>121</td><td>0.07</td><td>76</td></tr><tr><td>Smakhtin—EMC C</td><td>23</td><td>78</td><td>0.06</td><td>76</td></tr><tr><td>Smakhtin—EMC D</td><td>22</td><td>45</td><td>0.05</td><td>76</td></tr><tr><td rowspan="10">France</td><td>Tenant</td><td>18</td><td>146</td><td>0.00</td><td>354</td></tr><tr><td>Tessmann</td><td>30</td><td>291</td><td>0.05</td><td>354</td></tr><tr><td>VMF</td><td>23</td><td>206</td><td>0.01</td><td>354</td></tr><tr><td>Q90_Q50</td><td>30</td><td>287</td><td>0.09</td><td>354</td></tr><tr><td>Smakhtin—EMC A</td><td>57</td><td>538</td><td>0.07</td><td>354</td></tr><tr><td>Smakhtin—EMC B</td><td>40</td><td>386</td><td>0.08</td><td>354</td></tr><tr><td>Smakhtin—EMC C</td><td>28</td><td>267</td><td>0.09</td><td>354</td></tr><tr><td>Smakhtin—EMC D</td><td>20</td><td>180</td><td>0.10</td><td>354</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>31</td><td>295</td><td>0.06</td><td>214</td></tr><tr><td rowspan="10">Mexico</td><td>Tenant</td><td>20</td><td>141</td><td>0.12</td><td>236</td></tr><tr><td>Tessmann</td><td>24</td><td>347</td><td>0.09</td><td>236</td></tr><tr><td>VMF</td><td>21</td><td>250</td><td>0.04</td><td>236</td></tr><tr><td>Q90_Q50</td><td>22</td><td>110</td><td>0.00</td><td>236</td></tr><tr><td>Smakhtin—EMC A</td><td>29</td><td>388</td><td>0.30</td><td>236</td></tr><tr><td>Smakhtin—EMC B</td><td>18</td><td>200</td><td>0.28</td><td>236</td></tr><tr><td>Smakhtin—EMC C</td><td>19</td><td>104</td><td>0.23</td><td>236</td></tr><tr><td>Smakhtin—EMC D</td><td>23</td><td>46</td><td>0.17</td><td>236</td></tr><tr><td rowspan="10">South Africa</td><td>Tenant</td><td>9</td><td>36</td><td>0.00</td><td>300</td></tr><tr><td>Tessmann</td><td>21</td><td>136</td><td>0.00</td><td>300</td></tr><tr><td>VMF</td><td>14</td><td>87</td><td>0.02</td><td>300</td></tr><tr><td>Q90_Q50</td><td>12</td><td>28</td><td>0.00</td><td>300</td></tr><tr><td>Smakhtin—EMC A</td><td>24</td><td>140</td><td>0.09</td><td>300</td></tr><tr><td>Smakhtin—EMC B</td><td>12</td><td>50</td><td>0.06</td><td>300</td></tr><tr><td>Smakhtin—EMC C</td><td>11</td><td>1</td><td>0.05</td><td>300</td></tr><tr><td>Smakhtin—EMC D</td><td>14</td><td>-32</td><td>0.05</td><td>300</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>10</td><td>0</td><td>0.18</td><td>300</td></tr><tr><td rowspan="10">Other countries</td><td>Tenant</td><td>16</td><td>310</td><td>0.00</td><td>50</td></tr><tr><td>Tessmann</td><td>19</td><td>610</td><td>0.01</td><td>50</td></tr><tr><td>VMF</td><td>16</td><td>443</td><td>0.01</td><td>50</td></tr><tr><td>Q90_Q50</td><td>15</td><td>159</td><td>0.13</td><td>50</td></tr><tr><td>Smakhtin—EMC A</td><td>31</td><td>865</td><td>0.08</td><td>50</td></tr><tr><td>Smakhtin—EMC B</td><td>16</td><td>493</td><td>0.12</td><td>50</td></tr><tr><td>Smakhtin—EMC C</td><td>14</td><td>265</td><td>0.20</td><td>50</td></tr><tr><td>Smakhtin—EMC D</td><td>16</td><td>133</td><td>0.22</td><td>50</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>20</td><td>104</td><td>0.31</td><td>9</td></tr></tbody></table>

<footnote><sup>a</sup> Mean absolute error (see supplementary section 4 for equation).</footnote>

<footnote><sup>b</sup> 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.</footnote>

<footnote><sup>c</sup> 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).</footnote>
<table><caption>**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.</caption><thead><tr><th>Country</th><th>Global e-flows method</th><th>MAE<sup>a</sup></th><th>% Bias</th><th>R<sup>2b</sup></th><th>n</th></tr></thead><tbody><tr><td rowspan="10">Australia</td><td>Tenant</td><td>17</td><td>16</td><td>0.21</td><td>33</td></tr><tr><td>Tessmann</td><td>22</td><td>85</td><td>0.19</td><td>33</td></tr><tr><td>VMF</td><td>19</td><td>54</td><td>0.05</td><td>33</td></tr><tr><td>Q90_Q50</td><td>17</td><td>55</td><td>0.23</td><td>33</td></tr><tr><td>Smakhtin—EMC A</td><td>39</td><td>182</td><td>0.06</td><td>33</td></tr><tr><td>Smakhtin—EMC B</td><td>26</td><td>112</td><td>0.26</td><td>33</td></tr><tr><td>Smakhtin—EMC C</td><td>18</td><td>60</td><td>0.22</td><td>33</td></tr><tr><td>Smakhtin—EMC D</td><td>17</td><td>25</td><td>0.17</td><td>33</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>17</td><td>28</td><td>0.12</td><td>33</td></tr><tr><td rowspan="10">Canada</td><td>Tenant</td><td>22</td><td>-4</td><td>0.17</td><td>76</td></tr><tr><td>Tessmann</td><td>21</td><td>69</td><td>0.00</td><td>76</td></tr><tr><td>VMF</td><td>20</td><td>40</td><td>0.03</td><td>76</td></tr><tr><td>Q90_Q50</td><td>22</td><td>76</td><td>0.02</td><td>76</td></tr><tr><td>Smakhtin—EMC A</td><td>37</td><td>179</td><td>0.09</td><td>76</td></tr><tr><td>Smakhtin—EMC B</td><td>28</td><td>121</td><td>0.07</td><td>76</td></tr><tr><td>Smakhtin—EMC C</td><td>23</td><td>78</td><td>0.06</td><td>76</td></tr><tr><td>Smakhtin—EMC D</td><td>22</td><td>45</td><td>0.05</td><td>76</td></tr><tr><td rowspan="10">France</td><td>Tenant</td><td>18</td><td>146</td><td>0.00</td><td>354</td></tr><tr><td>Tessmann</td><td>30</td><td>291</td><td>0.05</td><td>354</td></tr><tr><td>VMF</td><td>23</td><td>206</td><td>0.01</td><td>354</td></tr><tr><td>Q90_Q50</td><td>30</td><td>287</td><td>0.09</td><td>354</td></tr><tr><td>Smakhtin—EMC A</td><td>57</td><td>538</td><td>0.07</td><td>354</td></tr><tr><td>Smakhtin—EMC B</td><td>40</td><td>386</td><td>0.08</td><td>354</td></tr><tr><td>Smakhtin—EMC C</td><td>28</td><td>267</td><td>0.09</td><td>354</td></tr><tr><td>Smakhtin—EMC D</td><td>20</td><td>180</td><td>0.10</td><td>354</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>31</td><td>295</td><td>0.06</td><td>214</td></tr><tr><td rowspan="10">Mexico</td><td>Tenant</td><td>20</td><td>141</td><td>0.12</td><td>236</td></tr><tr><td>Tessmann</td><td>24</td><td>347</td><td>0.09</td><td>236</td></tr><tr><td>VMF</td><td>21</td><td>250</td><td>0.04</td><td>236</td></tr><tr><td>Q90_Q50</td><td>22</td><td>110</td><td>0.00</td><td>236</td></tr><tr><td>Smakhtin—EMC A</td><td>29</td><td>388</td><td>0.30</td><td>236</td></tr><tr><td>Smakhtin—EMC B</td><td>18</td><td>200</td><td>0.28</td><td>236</td></tr><tr><td>Smakhtin—EMC C</td><td>19</td><td>104</td><td>0.23</td><td>236</td></tr><tr><td>Smakhtin—EMC D</td><td>23</td><td>46</td><td>0.17</td><td>236</td></tr><tr><td rowspan="10">South Africa</td><td>Tenant</td><td>9</td><td>36</td><td>0.00</td><td>300</td></tr><tr><td>Tessmann</td><td>21</td><td>136</td><td>0.00</td><td>300</td></tr><tr><td>VMF</td><td>14</td><td>87</td><td>0.02</td><td>300</td></tr><tr><td>Q90_Q50</td><td>12</td><td>28</td><td>0.00</td><td>300</td></tr><tr><td>Smakhtin—EMC A</td><td>24</td><td>140</td><td>0.09</td><td>300</td></tr><tr><td>Smakhtin—EMC B</td><td>12</td><td>50</td><td>0.06</td><td>300</td></tr><tr><td>Smakhtin—EMC C</td><td>11</td><td>1</td><td>0.05</td><td>300</td></tr><tr><td>Smakhtin—EMC D</td><td>14</td><td>-32</td><td>0.05</td><td>300</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>10</td><td>0</td><td>0.18</td><td>300</td></tr><tr><td rowspan="10">Other countries</td><td>Tenant</td><td>16</td><td>310</td><td>0.00</td><td>50</td></tr><tr><td>Tessmann</td><td>19</td><td>610</td><td>0.01</td><td>50</td></tr><tr><td>VMF</td><td>16</td><td>443</td><td>0.01</td><td>50</td></tr><tr><td>Q90_Q50</td><td>15</td><td>159</td><td>0.13</td><td>50</td></tr><tr><td>Smakhtin—EMC A</td><td>31</td><td>865</td><td>0.08</td><td>50</td></tr><tr><td>Smakhtin—EMC B</td><td>16</td><td>493</td><td>0.12</td><td>50</td></tr><tr><td>Smakhtin—EMC C</td><td>14</td><td>265</td><td>0.20</td><td>50</td></tr><tr><td>Smakhtin—EMC D</td><td>16</td><td>133</td><td>0.22</td><td>50</td></tr><tr><td>Smakhtin—Matched EMC<sup>c</sup></td><td>20</td><td>104</td><td>0.31</td><td>9</td></tr></tbody></table>

<footnote><sup>a</sup> Mean absolute error (see supplementary section 4 for equation).</footnote>

<footnote><sup>b</sup> 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.</footnote>

<footnote><sup>c</sup> 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).</footnote>
<table><caption>**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).</caption><thead><tr><th rowspan="2">Global estimation method (e-flows from global models)</th><th colspan="5">Summary statistics of e-flows as percentage of mean annual flow</th></tr><tr><th>Mean</th><th>Standard deviation</th><th>Minimum</th><th>Maximum</th><th>n</th></tr></thead><tbody><tr><td>Tennant</td><td>28%</td><td>1%</td><td>25%</td><td>31%</td><td>1061</td></tr><tr><td>Tessmann</td><td>48%</td><td>1%</td><td>43%</td><td>53%</td><td>1061</td></tr><tr><td>Q90_Q50</td><td>35%</td><td>14%</td><td>11%</td><td>70%</td><td>1061</td></tr><tr><td>VMF</td><td>38%</td><td>2%</td><td>33%</td><td>44%</td><td>1061</td></tr><tr><td>Smakhtin—Ecological management class A</td><td>65%</td><td>14%</td><td>23%</td><td>86%</td><td>1061</td></tr><tr><td>Smakhtin—EMC B</td><td>46%</td><td>14%</td><td>12%</td><td>77%</td><td>1061</td></tr><tr><td>Smakhtin—EMC C</td><td>33%</td><td>13%</td><td>4%</td><td>69%</td><td>1061</td></tr><tr><td>Smakhtin—EMC D</td><td>25%</td><td>11%</td><td>1%</td><td>65%</td><td>1061</td></tr><tr><td>Smakhtin—Matched EMC<sup>a</sup></td><td>35%</td><td>17%</td><td>3%</td><td>77%</td><td>556</td></tr><tr><th colspan="6">Country (e-flows from local assessments)</th></tr><tr><td>France</td><td>21%</td><td>19%</td><td>2%</td><td>100%</td><td>354</td></tr><tr><td>South Africa</td><td>28%</td><td>12%</td><td>1%</td><td>86%</td><td>326</td></tr><tr><td>Other countries</td><td>32%</td><td>18%</td><td>1%</td><td>69%</td><td>52</td></tr><tr><td>Mexico</td><td>37%</td><td>25%</td><td>0%</td><td>100%</td><td>236</td></tr><tr><td>Australia</td><td>40%</td><td>21%</td><td>11%</td><td>96%</td><td>50</td></tr><tr><td>Canada</td><td>44%</td><td>24%</td><td>6%</td><td>98%</td><td>76</td></tr><tr><td>Brazil</td><td>50%</td><td>0%</td><td>50%</td><td>50%</td><td>12</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**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.</figcaption></figure>

<footnote><sup>a</sup> 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).</footnote>
<table><caption>**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).</caption><thead><tr><th rowspan="2">Global estimation method (e-flows from global models)</th><th colspan="5">Summary statistics of e-flows as percentage of mean annual flow</th></tr><tr><th>Mean</th><th>Standard deviation</th><th>Minimum</th><th>Maximum</th><th>n</th></tr></thead><tbody><tr><td>Tenant</td><td>28%</td><td>1%</td><td>25%</td><td>31%</td><td>1061</td></tr><tr><td>Tessmann</td><td>48%</td><td>1%</td><td>43%</td><td>53%</td><td>1061</td></tr><tr><td>Q90_Q50</td><td>35%</td><td>14%</td><td>11%</td><td>70%</td><td>1061</td></tr><tr><td>VMF</td><td>38%</td><td>2%</td><td>33%</td><td>44%</td><td>1061</td></tr><tr><td>Smakhtin—Ecological management class A</td><td>65%</td><td>14%</td><td>23%</td><td>86%</td><td>1061</td></tr><tr><td>Smakhtin—EMC B</td><td>46%</td><td>14%</td><td>12%</td><td>77%</td><td>1061</td></tr><tr><td>Smakhtin—EMC C</td><td>33%</td><td>13%</td><td>4%</td><td>69%</td><td>1061</td></tr><tr><td>Smakhtin—EMC D</td><td>25%</td><td>11%</td><td>1%</td><td>65%</td><td>1061</td></tr><tr><td>Smakhtin—Matched EMC<sup>a</sup></td><td>35%</td><td>17%</td><td>3%</td><td>77%</td><td>556</td></tr><tr><th colspan="6">Country (e-flows from local assessments)</th></tr><tr><td>France</td><td>21%</td><td>19%</td><td>2%</td><td>100%</td><td>354</td></tr><tr><td>South Africa</td><td>28%</td><td>12%</td><td>1%</td><td>86%</td><td>326</td></tr><tr><td>Other countries</td><td>32%</td><td>18%</td><td>1%</td><td>69%</td><td>52</td></tr><tr><td>Mexico</td><td>37%</td><td>25%</td><td>0%</td><td>100%</td><td>236</td></tr><tr><td>Australia</td><td>40%</td><td>21%</td><td>11%</td><td>96%</td><td>50</td></tr><tr><td>Canada</td><td>44%</td><td>24%</td><td>6%</td><td>98%</td><td>76</td></tr><tr><td>Brazil</td><td>50%</td><td>0%</td><td>50%</td><td>50%</td><td>12</td></tr></tbody></table>

<figure><img src="image_10.png" /></figure>

<footnote><sup>a</sup> 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).</footnote>
## 5. 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 e-flows 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.

### Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5683/SP3/N2SCRT.

### Acknowledgments

The authors acknowledge the support of Chandima Subasinghe (RS/GIS Analyst, IWMI) in the initial processing of spatial data. The contributions of e-flows data and reports from various countries and institutions were invaluable for the comparative analyses generated, and the willingness of practitioners to share this knowledge with the authors is gratefully acknowledged. In particular, we thank the following individuals who contributed

published local e-flows assessments and data for various countries and/or who clarified questions with site level data and studies: Tom Annear, Suresh Babu, Laureline Berthot, Anny Chaves, Louis Courseau, Shannan Crow, Christopher Estes, Ted Grantham, Thom Hardy, Avril Horne, Tim Jardine, Hilary Johnson, Nitin Kaushal, Nicolas Lamouroux, Ann Marie Larquier, Chicu Lokgariwar, Francisco Martinez Capel, Wendy Monk, Meghan Mussehl, Piotr Parasiewicz, Daniel Peters, Sébastien Ouellet-Proulx, Sergio Salinas-Rodríguez, Andrew Sharpe, Retha Stassen, Aditya Sood, André St-Hilaire, David Weedman and Åsa Widén. While it was not feasible to include all the data that were submitted during the analysis, it is our intent to include all data provided within an online version of the database, for future applications. Friends and colleagues within the global network of environmental flow practitioners are also sincerely thanked for their expertise, advice and responses to various general requests to help during this study, including Angela Arthington, Riccardo Biancalani, Bernhard Lehner, Conor Linstead, Michela Marinelli, Michael McClain, LeRoy Poff, Vladimir Smakhtin, David Tickner, Karen Villholth and William Young.

### Conflict of interest

The authors declare that they have no conflict of interest.

### Code access statement

All scripts necessary to reproduce this analysis are freely available for all purposes (and can be copied, modified and distributed) at: https://github.com/messamat/globalEF_testPy (for data-preformatting and global e-flows calculations) and https://github.com/messamat/globalEF_testR (for comparing global and local MAF and e-flows estimates).

### Funding

This project was funded by the International Water Management Institute (IWMI) as part of the CGIAR Research Initiative Nexus Gains. MLM was also supported by a Vanier Canada Graduate Scholarship (Natural Sciences and Engineering Research Council of Canada) and an H2O'Lyon Doctoral Fellowship (Université de Lyon, ANR-17-EURE-0018).

### Author contribution statement

CRediT (Contributor Roles Taxonomy): conceptualization and data curation—all authors; methodology, software, data cleaning and validation, visualization,
## 5. 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 e-flows 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.

### Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5683/SP3/N2SCRT.

### Acknowledgments

The authors acknowledge the support of Chandima Subasinghe (RS/GIS Analyst, IWMI) in the initial processing of spatial data. The contributions of e-flows data and reports from various countries and institutions were invaluable for the comparative analyses generated, and the willingness of practitioners to share this knowledge with the authors is gratefully acknowledged. In particular, we thank the following individuals who contributed

published local e-flows assessments and data for various countries and/or who clarified questions with site level data and studies: Tom Annear, Suresh Babu, Laureline Berthot, Anny Chaves, Louis Courseau, Shannan Crow, Christopher Estes, Ted Grantham, Thom Hardy, Avril Horne, Tim Jardine, Hilary Johnson, Nitin Kaushal, Nicolas Lamouroux, Ann Marie Larquier, Chicu Lokgariwar, Francisco Martinez Capel, Wendy Monk, Meghan Mussehl, Piotr Parasiewicz, Daniel Peters, Sébastien Ouellet-Proulx, Sergio Salinas-Rodríguez, Andrew Sharpe, Retha Stassen, Aditya Sood, André St-Hilaire, David Weedman and Åsa Widén. While it was not feasible to include all the data that were submitted during the analysis, it is our intent to include all data provided within an online version of the database, for future applications. Friends and colleagues within the global network of environmental flow practitioners are also sincerely thanked for their expertise, advice and responses to various general requests to help during this study, including Angela Arthington, Riccardo Biancalani, Bernhard Lehner, Conor Linstead, Michela Marinelli, Michael McClain, LeRoy Poff, Vladimir Smakhtin, David Tickner, Karen Villholth and William Young.

### Conflict of interest

The authors declare that they have no conflict of interest.

### Code access statement

All scripts necessary to reproduce this analysis are freely available for all purposes (and can be copied, modified and distributed) at: https://github.com/messamat/globalEF_testPy (for data-preformatting and global e-flows calculations) and https://github.com/messamat/globalEF_testR (for comparing global and local MAF and e-flows estimates).

### Funding

This project was funded by the International Water Management Institute (IWMI) as part of the CGIAR Research Initiative Nexus Gains. MLM was also supported by a Vanier Canada Graduate Scholarship (Natural Sciences and Engineering Research Council of Canada) and an H2O'Lyon Doctoral Fellowship (Université de Lyon, ANR-17-EURE-0018).

### Author contribution statement

CRediT (Contributor Roles Taxonomy): conceptualization and data curation—all authors; methodology, software, data cleaning and validation, visualization,
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.

## ORCID iDs

Mathis L Messager https://orcid.org/0000-0002-3051-8068

Chris W S Dickens https://orcid.org/0000-0002-4251-7767

Nishadi Eriyagama https://orcid.org/0000-0002-4493-5284

Rebecca E Tharme https://orcid.org/0000-0001-5789-1316

## References

Arthington A H et al 2018 The Brisbane declaration and global action agenda on environmental flows (2018) *Front. Environ. Sci.* **6** 45

Arthington A H et al 2023 Accelerating environmental flows implementation to bend the curve of global freshwater biodiversity loss *Environ. Rev.* **1**–**27**

Convention on Biological Diversity 2021 Proposed monitoring approach and headline component and complementary indicators for the post-2020 Global Biodiversity Framework CBD/WG2020/3/INF/2 (available at: https://www.cbd.int/doc/c/437d/a239/12a22f2eaf5e6d103ed9adad/wg2020-03-inf-02-en.pdf)

Dickens C, Smakhtin V, Biancalani R, Villholth K G, Eriyagama N and Marinelli M 2019 *Incorporating Environmental Flows into “Water Stress” Indicator 6.4.2*—Guidelines for a Minimum Standard Method for Global Reporting (Food and Agriculture Organization of the United Nations, CGIAR)

Döll P, Douville H, Güntner A, Müller Schmied H and Wada Y 2016 Modelling freshwater resources at the global scale: challenges and prospects *Surv. Geophys.* **37** 195–221

Dourado G F, Rallings A M and Viers J H 2023 Overcoming persistent challenges in putting environmental flow policy into practice: a systematic review and bibliometric analysis *Environ. Res. Lett.* **18** 043002

Dunne J P et al 2012 GFDL’s ESM2 global coupled climate-carbon Earth System Models Part I: Physical formulation and baseline simulation characteristics *J. Clim.* **25** 6646–65

Eriyagama N, Messager M L, Dickens C, Tharme R E and Stassen R 2024 *Towards the Harmonization of Global Environmental Flow Data* IWMI Research Report 186 International Water Management Institute (IWMI) (https://doi.org/10.5337/2023.224)

European Commission 2015 Ecological flows in the implementation of the water framework directive *Guidance Document* No. 31

Frieler K et al 2017 Assessing the impacts of 1.5 °C global warming—simulation protocol of the inter-sectoral impact model intercomparison project (ISIMIP2b) *Geosci. Model Dev.* **10** 4321–45

IUCN 2012 *The importance of assessing the water needs of wetlands in order to preserve their ecological functions* Motion M087, Congress Document WCC-2012-9.6 World Conservation Congress (available at: www.iucn.org/sites/dev/files/import/downloads/2012_congress__all_motions_en.pdf) (Accessed 6–15 September 2012)

Jägermeyr J, Pastor A, Biemans H and Gerten D 2017 Reconciling irrigated food production with environmental flows for sustainable development goals implementation *Nat. Commun.* **8** 15900

Kallio M, Guillaume J H A, Virkki V, Kummu M and Virrantaus K 2021 Hydrostreamer v1.0—improved streamflow

predictions for local applications from an ensemble of downscaled global runoff products *Geosci. Model Dev.* **14** 5155–81

Kuehne L M, Dickens C, Tickner D, Messager M L, Olden J D, O’Brien G, Lehner B and Eriyagama N 2023 The future of global river health monitoring *PLOS Water* **2** e0000101

Lamouroux N, Hauer C, Stewardson M J and N L P 2017 Physical habitat modeling and ecohydrological tools *Water for the Environment: From Policy and Science to Implementation and Management* (Academic) pp 265–85

Lehner B and Grill G 2013 Global river hydrography and network routing: baseline data and new approaches to study the world’s large river systems *Hydrol. Process.* **27** 2171–86

Lin P et al 2019 Global reconstruction of naturalized river flows at 2.94 million reaches *Water Resour. Res.* **55** 6499–516

Liu X, Liu W, Liu L, Tang Q, Liu J and Yang H 2021 Environmental flow requirements largely reshape global surface water scarcity assessment *Environ. Res. Lett.* **16** 104029

Mekonnen M M and Hoekstra A Y 2016 Four billion people facing severe water scarcity *Sci. Adv.* **2** e1500323

Müller Schmied H et al 2016 Variations of global and continental water balance components as impacted by climate forcing uncertainty and human water use *Hydrol. Earth Syst. Sci.* **20** 2877–98

Opperman J J, Kendy E, Tharme R E, Warner A T, Barrios E and Richter B D 2018 A three-level framework for assessing and implementing environmental flows *Front. Environ. Sci.* **6** 76

Pastor A V, Ludwig F, Biemans H, Hoff H and Kabat P 2014 Accounting for environmental flow requirements in global water assessments *Hydrol. Earth Syst. Sci.* **18** 5041–59

Pedro-Monzónis M, Solera A, Ferrer J, Estrela T and Paredes-Arquiola J 2015 A review of water scarcity and drought indexes in water resources planning and management *J. Hydrol.* **527** 482–93

Poff N L, Allan J D, Bain M B, Karr J R, Prestegaard K L, Richter B D, Sparks R E and Stromberg J C 1997 The natural flow regime *BioScience* **47** 769–84

Poff N L and Matthews J H 2013 Environmental flows in the Anthropocene: past progress and future prospects *Curr. Opin. Environ. Sustain.* **5** 667–75

Poff N L, Tharme R E and Arthington A H 2017 Evolution of Environmental Flows Assessment Science, Principles, and Methodologies *Water for the Environment: From Policy and Science to Implementation and Management* (Academic) pp 203–36

Ramsar 2015 Resolution XII.12: Call to action to ensure and protect the water requirements of wetlands for the present and the future (available at: www.ramsar.org/sites/default/files/documents/library/cop12_res12_waterrequirements_e.pdf)

Richter B D, Davis M M, Apse C and Konrad C 2012 A presumptive standard for environmental flow protection *River Res. Appl.* **28** 1312–21

Robeson S M and Willmott C J 2023 Decomposition of the mean absolute error (MAE) into systematic and unsystematic components *PLoS One* **18** e0279774

Rockström J et al 2023 Safe and just Earth system boundaries *Nature* **619** 1–10

Rolls R J, Leigh C and Sheldon F 2012 Mechanistic effects of low-flow hydrology on riverine ecosystems: ecological principles and consequences of alteration *Freshwater Sci.* **31** 1163–86

Sanderson B M, Wehner M and Knutti R 2017 Skill and independence weighting for multi-model assessments *Geosci. Model Dev.* **10** 2379–95

Smakhtin V and Anputhas M 2006 *An assessment of environmental flow requirements of Indian river basins* IWMI Research Report 107 International Water Management Institute (IWMI) (https://doi.org/10.3910/2009.106)
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.

## ORCID iDs

Mathis L Messager https://orcid.org/0000-0002-3051-8068

Chris W S Dickens https://orcid.org/0000-0002-4251-7767

Nishadi Eriyagama https://orcid.org/0000-0002-4493-5284

Rebecca E Tharme https://orcid.org/0000-0001-5789-1316

## References

Arthington A H et al 2018 The Brisbane declaration and global action agenda on environmental flows (2018) *Front. Environ. Sci.* **6** 45

Arthington A H et al 2023 Accelerating environmental flows implementation to bend the curve of global freshwater biodiversity loss *Environ. Rev.* **1**–**27**

Convention on Biological Diversity 2021 Proposed monitoring approach and headline component and complementary indicators for the post-2020 Global Biodiversity Framework CBD/WG2020/3/INF/2 (available at: https://www.cbd.int/doc/c/437d/a239/12a22f2eaf5e6d103ed9adad/wg2020-03-inf-02-en.pdf)

Dickens C, Smakhtin V, Biancalani R, Villholth K G, Eriyagama N and Marinelli M 2019 Incorporating Environmental Flows into “Water Stress” Indicator 6.4.2—Guidelines for a Minimum Standard Method for Global Reporting (Food and Agriculture Organization of the United Nations, CGIAR)

Döll P, Douville H, Güntner A, Müller Schmied H and Wada Y 2016 Modelling freshwater resources at the global scale: challenges and prospects *Surv. Geophys.* **37** 195–221

Dourado G F, Rallings A M and Viers J H 2023 Overcoming persistent challenges in putting environmental flow policy into practice: a systematic review and bibliometric analysis *Environ. Res. Lett.* **18** 043002

Dunne J P et al 2012 GFDL’s ESM2 global coupled climate-carbon Earth System Models Part I: Physical formulation and baseline simulation characteristics *J. Clim.* **25** 6646–65

Eriyagama N, Messager M L, Dickens C, Tharme R E and Stassen R 2024 *Towards the Harmonization of Global Environmental Flow Data* IWMI Research Report 186 International Water Management Institute (IWMI) (https://doi.org/10.5337/2023.224)

European Commission 2015 Ecological flows in the implementation of the water framework directive *Guidance Document* No. 31

Frieler K et al 2017 Assessing the impacts of 1.5 °C global warming—simulation protocol of the inter-sectoral impact model intercomparison project (ISIMIP2b) *Geosci. Model Dev.* **10** 4321–45

IUCN 2012 *The importance of assessing the water needs of wetlands in order to preserve their ecological functions* Motion M087, Congress Document WCC-2012-9.6 World Conservation Congress (available at: www.iucn.org/sites/dev/files/import/downloads/2012_congress__all_motions_en.pdf) (Accessed 6–15 September 2012)

Jägermeyr J, Pastor A, Biemans H and Gerten D 2017 Reconciling irrigated food production with environmental flows for sustainable development goals implementation *Nat. Commun.* **8** 15900

Kallio M, Guillaume J H A, Virkki V, Kummu M and Virrantaus K 2021 Hydrostreamer v1.0—improved streamflow

predictions for local applications from an ensemble of downscaled global runoff products *Geosci. Model Dev.* **14** 5155–81

Kuehne L M, Dickens C, Tickner D, Messager M L, Olden J D, O’Brien G, Lehner B and Eriyagama N 2023 The future of global river health monitoring *PLOS Water* **2** e0000101

Lamouroux N, Hauer C, Stewardson M J and N L P 2017 Physical habitat modeling and ecohydrological tools *Water for the Environment: From Policy and Science to Implementation and Management* (Academic) pp 265–85

Lehner B and Grill G 2013 Global river hydrography and network routing: baseline data and new approaches to study the world’s large river systems *Hydrol. Process.* **27** 2171–86

Lin P et al 2019 Global reconstruction of naturalized river flows at 2.94 million reaches *Water Resour. Res.* **55** 6499–516

Liu X, Liu W, Liu L, Tang Q, Liu J and Yang H 2021 Environmental flow requirements largely reshape global surface water scarcity assessment *Environ. Res. Lett.* **16** 104029

Mekonnen M M and Hoekstra A Y 2016 Four billion people facing severe water scarcity *Sci. Adv.* **2** e1500323

Müller Schmied H et al 2016 Variations of global and continental water balance components as impacted by climate forcing uncertainty and human water use *Hydrol. Earth Syst. Sci.* **20** 2877–98

Opperman J J, Kendy E, Tharme R E, Warner A T, Barrios E and Richter B D 2018 A three-level framework for assessing and implementing environmental flows *Front. Environ. Sci.* **6** 76

Pastor A V, Ludwig F, Biemans H, Hoff H and Kabat P 2014 Accounting for environmental flow requirements in global water assessments *Hydrol. Earth Syst. Sci.* **18** 5041–59

Pedro-Monzónis M, Solera A, Ferrer J, Estrela T and Paredes-Arquiola J 2015 A review of water scarcity and drought indexes in water resources planning and management *J. Hydrol.* **527** 482–93

Poff N L, Allan J D, Bain M B, Karr J R, Prestegaard K L, Richter B D, Sparks R E and Stromberg J C 1997 The natural flow regime *BioScience* **47** 769–84

Poff N L and Matthews J H 2013 Environmental flows in the Anthropocene: past progress and future prospects *Curr. Opin. Environ. Sustain.* **5** 667–75

Poff N L, Tharme R E and Arthington A H 2017 Evolution of Environmental Flows Assessment Science, Principles, and Methodologies *Water for the Environment: From Policy and Science to Implementation and Management* (Academic) pp 203–36

Ramsar 2015 Resolution XII.12: Call to action to ensure and protect the water requirements of wetlands for the present and the future (available at: www.ramsar.org/sites/default/files/documents/library/cop12_res12_waterrequirements_e.pdf)

Richter B D, Davis M M, Apse C and Konrad C 2012 A presumptive standard for environmental flow protection *River Res. Appl.* **28** 1312–21

Robeson S M and Willmott C J 2023 Decomposition of the mean absolute error (MAE) into systematic and unsystematic components *PLoS One* **18** e0279774

Rockström J et al 2023 Safe and just Earth system boundaries *Nature* **619** 1–10

Rolls R J, Leigh C and Sheldon F 2012 Mechanistic effects of low-flow hydrology on riverine ecosystems: ecological principles and consequences of alteration *Freshwater Sci.* **31** 1163–86

Sanderson B M, Wehner M and Knutti R 2017 Skill and independence weighting for multi-model assessments *Geosci. Model Dev.* **10** 2379–95

Smakhtin V and Anputhas M 2006 *An assessment of environmental flow requirements of Indian river basins* IWMI Research Report 107 International Water Management Institute (IWMI) (https://doi.org/10.3910/2009.106)
Smakhtin V, Revenga C and Döll P 2004 Taking into account environmental water requirements in global-scale water resources assessments Comprehensive Assessment Research Report 2 Comprehensive Assessment of Water Management in Agriculture (available at: https://hdl.handle.net/10535/4649)

Tennant D L 1976 Instream flow regimens for fish, wildlife, recreation and related environmental resources *Fisheries* 16–10

Tessmann S 1980 *Environmental Assessment, Technical Appendix E in Environmental Use Sector Reconnaissance Elements of the Western Dakotas Region of South Dakota Study* (Water Resources Research Institute, South Dakota State University)

Tharme R E 2003 A global perspective on environmental flow assessment: emerging trends in the development and application of environmental flow methodologies for rivers *River Res. Appl.* 19 397–441

Tickner D et al 2020 Bending the curve of global freshwater biodiversity loss: an emergency recovery plan *BioScience* 70 330–42

Victorian Environmental Water Holder 2023 VEHW 10-year strategy 2023-2033 (available at: https://www.vewh.vic.gov.au/__data/assets/pdf_file/0004/547438/VWH27-10-Year-Strategy_FA_4.0.pdf)

Virkki V et al 2022 Globally widespread and increasing violations of environmental flow envelopes *Hydrol. Earth Syst. Sci.* 26 3315–36
Smakhtin V, Revenga C and Döll P 2004 Taking into account environmental water requirements in global-scale water resources assessments Comprehensive Assessment Research Report 2 Comprehensive Assessment of Water Management in Agriculture (available at: https://hdl.handle.net/10535/4649)

Tennant D L 1976 Instream flow regimens for fish, wildlife, recreation and related environmental resources *Fisheries* 16–10

Tessmann S 1980 *Environmental Assessment, Technical Appendix E in Environmental Use Sector Reconnaissance Elements of the Western Dakotas Region of South Dakota Study* (Water Resources Research Institute, South Dakota State University)

Tharme R E 2003 A global perspective on environmental flow assessment: emerging trends in the development and application of environmental flow methodologies for rivers *River Res. Appl.* 19 397–441

Tickner D et al 2020 Bending the curve of global freshwater biodiversity loss: an emergency recovery plan *BioScience* 70 330–42

Victorian Environmental Water Holder 2023 VEHW 10-year strategy 2023-2033 (available at: https://www.vewh.vic.gov.au/__data/assets/pdf_file/0004/547438/VWH27-10-Year-Strategy_FA_4.0.pdf)

Virkki V et al 2022 Globally widespread and increasing violations of environmental flow envelopes *Hydrol. Earth Syst. Sci.* 26 3315–36