# Global hydrological models continue to overestimate river discharge

Stefanie Heinicke, Jan Volkholz, Jacob Schewe, Simon N Gosling, Hannes Müller Schmied, Sandra Zimmermann, Matthias Mengel, Inga J Sauer, Peter Burek, Jinfeng Chang, et al.

► To cite this version:

Stefanie Heinicke, Jan Volkholz, Jacob Schewe, Simon N Gosling, Hannes Müller Schmied, et al. Global hydrological models continue to overestimate river discharge. Environmental Research Letters, 2024, 19 (7), pp.074005. 10.1088/1748-9326/ad52b0. hal-04624957

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# Global hydrological models continue to overestimate river discharge

Stefanie Heinicke, Jan Volkholz, Jacob Schewe, Simon N Gosling, Hannes Müller Schmied, Sandra Zimmermann, Matthias Mengel, Inga J Sauer, Peter Burek, Jinfeng Chang, et al.

► To cite this version:

Stefanie Heinicke, Jan Volkholz, Jacob Schewe, Simon N Gosling, Hannes Müller Schmied, et al. Global hydrological models continue to overestimate river discharge. Environmental Research Letters, 2024, 19 (7), pp.074005. 10.1088/1748-9326/ad52b0. hal-04624957

HAL Id: hal-04624957

https://brgm.hal.science/hal-04624957v1

Submitted on 25 Jun 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
LETTER • OPEN ACCESS

Global hydrological models continue to
overestimate river discharge

To cite this article: Stefanie Heinicke et al 2024 *Environ. Res. Lett.* 19 074005

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

You may also like

- *Intercomparison of global river discharge simulations focusing on dam operation—multiple models analysis in two case-study river basins, Missouri–Mississippi and Green–Colorado*
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- *Human impact parameterizations in global hydrological models improve estimates of monthly discharges and hydrological extremes: a multi-model validation study*
T I E Veldkamp, F Zhao, P J Ward et al.

- *Characterizing the multisectoral impacts of future global hydrologic variability*
Abigail Birnbaum, Ghazal Shabestanipour, Mengqi Zhao et al.

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

This content was downloaded from IP address 193.56.4.66 on 25/06/2024 at 16:46
LETTER • OPEN ACCESS

Global hydrological models continue to
overestimate river discharge

To cite this article: Stefanie Heinicke et al 2024 *Environ. Res. Lett.* 19 074005

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

You may also like

- *Intercomparison of global river discharge simulations focusing on dam operation—multiple models analysis in two case-study river basins, Missouri–Mississippi and Green–Colorado*
Yoshimitsu Masaki, Naota Hanasaki, Hester Biemans et al.

- *Human impact parameterizations in global hydrological models improve estimates of monthly discharges and hydrological extremes: a multi-model validation study*
T I E Veldkamp, F Zhao, P J Ward et al.

- *Characterizing the multisectoral impacts of future global hydrologic variability*
Abigail Birnbaum, Ghazal Shabestanipour, Mengqi Zhao et al.

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

This content was downloaded from IP address 193.56.4.66 on 25/06/2024 at 16:46
<figure><img src="image_3.png" /></figure>

CrossMark

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RECEIVED

15 December 2023

REVISED

21 May 2024

ACCEPTED FOR PUBLICATION

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PUBLISHED

11 June 2024

Original content from
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LETTER

# Global hydrological models continue to overestimate river discharge

Stefanie Heinicke<fnref n="1" />,<fnref n="1" />,<fnref n="4" />,* ID, Jan Volkholz<fnref n="1" />,<fnref n="1" />,<fnref n="4" />, Jacob Schewe<fnref n="1" /> ID, Simon N Gosling<fnref n="2" /> ID, Hannes Müller Schmied<fnref n="3" />,<fnref n="4" /> ID, Sandra Zimmermann<fnref n="1" /> ID, Matthias Mengel<fnref n="1" /> ID, Inga J Sauer<fnref n="1" /> ID, Peter Burek<fnref n="5" /> ID, Jinfeng Chang<fnref n="6" /> ID, Sian Kou-Giesbrecht<fnref n="7" /> ID, Manoli Grillakis<fnref n="8" /> ID, Luca Guillaumot<fnref n="5" />,<fnref n="9" />, Naota Hanasaki<fnref n="10" /> ID, Aristeidis Koutroulis<fnref n="8" /> ID, Kedar Otta<fnref n="10" /> ID, Wei Qi<fnref n="11" />, Yusuke Satoh<fnref n="12" /> ID, Tobias Stacke<fnref n="13" /> ID, Tokuta Yokohata<fnref n="10" /> and Katja Frieler<fnref n="1" /> ID

E-mail: heinicke@pik-potsdam.de

**Keywords:** model evaluation, model intercomparison, flood, hydrological extremes, river routing

Supplementary material for this article is available [online](#)

## Abstract

Global hydrological models (GHMs) are widely used to assess the impact of climate change on streamflow, floods, and hydrological droughts. For the ‘model evaluation and impact attribution’ part of the current round of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP3a), modelling teams generated historical simulations based on observed climate and direct human forcings with updated model versions. Here we provide a comprehensive evaluation of daily and maximum annual discharge based on ISIMIP3a simulations from nine GHMs by comparing the simulations to observational data from 644 river gauge stations. We also assess low flows and the effects of different river routing schemes. We find that models can reproduce variability in daily and maximum annual discharge, but tend to overestimate both quantities, as well as low flows. Models perform better at stations in wetter areas and at lower elevations. Discharge routed with the river routing model CaMa-Flood can improve the performance of some models, but for others, variability is overestimated, leading to reduced model performance. This study indicates that areas for future model development include improving the simulation of processes in arid regions and cold dynamics at high elevations. We further suggest that studies attributing observed changes in discharge to historical climate change using the current model ensemble will be most meaningful in humid areas, at low elevations, and in places with a regular seasonal discharge as these are the regions where the underlying dynamics seem to be best represented.

## 1. Introduction

The water cycle is particularly susceptible to climate change, leading to changes in river flow with

far-reaching consequences for water availability for humans (e.g. hydrological droughts), for climatic hazards such as river floods, but also for ecosystems (Schewe et al 2014, Maxwell et al 2019, Gudmundsson

<footnote n="1">¹ Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany</footnote>

<footnote n="2">² School of Geography, Faculty of Social Sciences, University of Nottingham, Nottingham, United Kingdom</footnote>

<footnote n="3">³ Institute of Physical Geography (IPG), Goethe-University Frankfurt, Frankfurt am Main, Germany</footnote>

<footnote n="4">⁴ Senckenberg Leibniz Biodiversity and Climate Research Centre (SBiK-F), Frankfurt am Main, Germany</footnote>

<footnote n="5">⁵ International Institute for Applied Systems Analysis, Laxenburg, Austria</footnote>

<footnote n="6">⁶ College of Environmental and Resource Sciences, Zhejiang University, Zhejiang, People's Republic of China</footnote>

<footnote n="7">⁷ Department of Earth and Environmental Sciences, Dalhousie University, Halifax, Canada</footnote>

<footnote n="8">⁸ Technical University of Crete, Chania, Greece</footnote>

<footnote n="9">⁹ Water, Environment, Processes and Analyses Division, BRGM—French Geological Survey, Orléans, France</footnote>

<footnote n="10">¹⁰ National Institute for Environmental Studies, Tsukuba, Japan</footnote>

<footnote n="11">¹¹ Southern University of Science and Technology, Shenzhen, People's Republic of China</footnote>

<footnote n="12">¹² Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea</footnote>

<footnote n="13">¹³ Max Planck Institute for Meteorology, Hamburg, Germany</footnote>

<footnote n="14">¹⁴ Shared first author.</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
<figure><img src="image_3.png" /></figure>

CrossMark

OPEN ACCESS

RECEIVED

15 December 2023

REVISED

21 May 2024

ACCEPTED FOR PUBLICATION

31 May 2024

PUBLISHED

11 June 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

Global hydrological models continue to overestimate river discharge

Stefanie Heinicke<fnref n="1" />,<fnref n="1" />,<fnref n="4" />,* ID, Jan Volkholz<fnref n="1" />,<fnref n="1" />,<fnref n="4" />, Jacob Schewe<fnref n="1" /> ID, Simon N Gosling<fnref n="2" /> ID, Hannes Müller Schmied<fnref n="3" />,<fnref n="4" /> ID, Sandra Zimmermann<fnref n="1" /> ID, Matthias Mengel<fnref n="1" /> ID, Inga J Sauer<fnref n="1" /> ID, Peter Burek<fnref n="5" /> ID, Jinfeng Chang<fnref n="6" /> ID, Sian Kou-Giesbrecht<fnref n="7" /> ID, Manoli Grillakis<fnref n="8" /> ID, Luca Guillaumot<fnref n="5" />,<fnref n="9" />, Naota Hanasaki<fnref n="10" /> ID, Aristeidis Koutroulis<fnref n="8" /> ID, Kedar Otta<fnref n="10" /> ID, Wei Qi<fnref n="11" />, Yusuke Satoh<fnref n="12" /> ID, Tobias Stacke<fnref n="13" /> ID, Tokuta Yokohata<fnref n="10" /> and Katja Frieler<fnref n="1" /> ID

E-mail: heinicke@pik-potsdam.de

**Keywords:** model evaluation, model intercomparison, flood, hydrological extremes, river routing

Supplementary material for this article is available [online](#)

**Abstract**

Global hydrological models (GHMs) are widely used to assess the impact of climate change on streamflow, floods, and hydrological droughts. For the ‘model evaluation and impact attribution’ part of the current round of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP3a), modelling teams generated historical simulations based on observed climate and direct human forcings with updated model versions. Here we provide a comprehensive evaluation of daily and maximum annual discharge based on ISIMIP3a simulations from nine GHMs by comparing the simulations to observational data from 644 river gauge stations. We also assess low flows and the effects of different river routing schemes. We find that models can reproduce variability in daily and maximum annual discharge, but tend to overestimate both quantities, as well as low flows. Models perform better at stations in wetter areas and at lower elevations. Discharge routed with the river routing model CaMa-Flood can improve the performance of some models, but for others, variability is overestimated, leading to reduced model performance. This study indicates that areas for future model development include improving the simulation of processes in arid regions and cold dynamics at high elevations. We further suggest that studies attributing observed changes in discharge to historical climate change using the current model ensemble will be most meaningful in humid areas, at low elevations, and in places with a regular seasonal discharge as these are the regions where the underlying dynamics seem to be best represented.

**1. Introduction**

The water cycle is particularly susceptible to cli-
mate change, leading to changes in river flow with

far-reaching consequences for water availability for
humans (e.g. hydrological droughts), for climatic
hazards such as river floods, but also for ecosystems
(Schewe et al 2014, Maxwell et al 2019, Gudmundsson

<footnote n="1">¹ Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany</footnote>

<footnote n="2">² School of Geography, Faculty of Social Sciences, University of Nottingham, Nottingham, United Kingdom</footnote>

<footnote n="3">³ Institute of Physical Geography (IPG), Goethe-University Frankfurt, Frankfurt am Main, Germany</footnote>

<footnote n="4">⁴ Senckenberg Leibniz Biodiversity and Climate Research Centre (SBiK-F), Frankfurt am Main, Germany</footnote>

<footnote n="5">⁵ International Institute for Applied Systems Analysis, Laxenburg, Austria</footnote>

<footnote n="6">⁶ College of Environmental and Resource Sciences, Zhejiang University, Zhejiang, People's Republic of China</footnote>

<footnote n="7">⁷ Department of Earth and Environmental Sciences, Dalhousie University, Halifax, Canada</footnote>

<footnote n="8">⁸ Technical University of Crete, Chania, Greece</footnote>

<footnote n="9">⁹ Water, Environment, Processes and Analyses Division, BRGM—French Geological Survey, Orléans, France</footnote>

<footnote n="10">¹⁰ National Institute for Environmental Studies, Tsukuba, Japan</footnote>

<footnote n="11">¹¹ Southern University of Science and Technology, Shenzhen, People's Republic of China</footnote>

<footnote n="12">¹² Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea</footnote>

<footnote n="13">¹³ Max Planck Institute for Meteorology, Hamburg, Germany</footnote>

<footnote n="14">¹⁴ Shared first author.</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
et al 2021, Thompson et al 2021, Van Vliet 2023). Fluvial floods led to the death of more than 200 000 people and incurred damages of 790 billion USD from 1980 to 2016 (Munich 2016). In addition, it has been estimated that floods and droughts resulted in 25 million people living in extreme poverty (Hallegatte et al 2017). Model-based projections show a strong increase in land area and population exposed to river floods and droughts due to increased global warming (Lange et al 2020).

Hydrological models are an important tool for decision-making in flood and drought management and preparedness and are used to make projections under different climate, land-use, and management scenarios. Global hydrological models (GHMs) in particular have been used, for example, to assess the impact of global warming on the availability of water resources (Schewe et al 2014, Liu et al 2017a, Pokhrel et al 2021), and on flood hazards (Dankers et al 2014, Hirabayashi et al 2021). In addition, GHMs can be used to attribute changes in the hydrological system to climate change. For example, Gudmundsson et al (2021) showed that observed changes in river flow are consistent with climatic changes, and Sauer et al (2021) found a climate signal in the trends in damages caused by river floods.

The evaluation of hydrological models is a critical first step towards impact attribution and future projections as for both purposes we need to understand to what degree models capture the processes determining discharge at individual locations, regions or globally. To this end, GHMs have been forced by observational climate data and observational direct human forcings (e.g. land use, location of dams and reservoirs) in Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2) already. These previous ISIMIP2 simulations have been evaluated, for example, regarding the influence of river routing on simulated discharge (Zhao et al 2017), the incorporation of human impact parameterizations (Liu et al 2017b, Veldkamp et al 2018), drought characteristics (Kumar et al 2022), or the seasonality of mean and extreme runoff (Zaherpour et al 2018). It has been shown that GHMs can simulate the extent of flooded areas, but for some events, GHMs overestimate the flood extent (Mester et al 2021). In addition, studies on economic damages caused by river floods showed that interannual variability of observed damages can be captured at least in some large scale areas (Sauer et al 2021). Deviations at the damage level could be due to either the discharge simulated by GHMs or from other sources in the modelling chain (e.g. assumed river protection levels, estimated distribution of assets, local physical vulnerabilities, Sauer et al 2021).

For ISIMIP3a, the climate input data and information on direct human forcings have been updated.

For example, the data cover three additional years (2017–2019), accordingly more recent observational data has been used for bias adjustment, and an update in the bias adjustment method reduced excessively high daily maximum temperature values (Lange et al 2021, table 1 in Frieler et al 2024 shows details on data provided for daily climate, land use, irrigation, dams and reservoirs, and water abstraction). This study comprehensively evaluates the performance of nine GHMs that have contributed discharge data to ISIMIP3a so far. Five of these models were updated in terms of improving the representation of hydrological processes, and three models improved the representation of land cover (details in table 1). The effect of these improvements has been evaluated elsewhere (Müller Schmied et al 2023, Tsilimigkras et al 2023, Boulange et al 2023, Yoshida et al 2022).

The aim of this study is to intercompare model performance regarding daily and maximum annual discharge as well as low flow and compare the performance of the models' internal routing schemes to discharge generated from runoff by CaMa-Flood (Yamazaki et al 2011). We investigate which catchment properties correlate with model performance to suggest areas of model development and to identify stations that are particularly suitable for potential attribution studies or assessments of changes under future global warming as considered in ISIMIP3.

## 2. Methods

### 2.1. Simulated runoff and river discharge

We use daily runoff and river discharge provided by nine modelling groups based on the ISIMIP3a simulation round (Frieler et al 2024): CLASSIC, CWatM, H08, HydroPy, JULES-W2, MIROC-INTEG-LAND, ORCHIDEE-MICT, WaterGAP2-2e, and WEB-DHM-SG (table S1). WaterGAP2-2e is calibrated with observed discharge data (Müller Schmied et al 2023), and H08 uses parameters optimized to reproduce observed discharge in each climatic zone (Yoshida et al 2022). Simulated data are from the 'obsclim + histsoc' experiment that is designed for model evaluation and uses observation-based daily atmospheric climate forcing (GSWP3-W5 × 10⁵, Lange et al 2023) and varying direct human forcings provided by ISIMIP (Frieler et al 2024). According to ISIMIP model documentation (www.isimip.org), all GHMs use land-use data, five models use data on water-use (CWatM, H08, HydroPy, MIROC-INTEG-LAND, WaterGAP2-2e) and four models use data on dams and reservoir (CWatM, H08, MIROC-INTEG-LAND, WaterGAP2-2e). Simulations are done on a 0.5° × 0.5° grid and are available for the years 1901–2019.

It has been shown that modelled peak river discharge using the river routing model CaMa-Flood
et al 2021, Thompson et al 2021, Van Vliet 2023). Fluvial floods led to the death of more than 200 000 people and incurred damages of 790 billion USD from 1980 to 2016 (Munich 2016). In addition, it has been estimated that floods and droughts resulted in 25 million people living in extreme poverty (Hallegatte et al 2017). Model-based projections show a strong increase in land area and population exposed to river floods and droughts due to increased global warming (Lange et al 2020).

Hydrological models are an important tool for decision-making in flood and drought management and preparedness and are used to make projections under different climate, land-use, and management scenarios. Global hydrological models (GHMs) in particular have been used, for example, to assess the impact of global warming on the availability of water resources (Schewe et al 2014, Liu et al 2017a, Pokhrel et al 2021), and on flood hazards (Dankers et al 2014, Hirabayashi et al 2021). In addition, GHMs can be used to attribute changes in the hydrological system to climate change. For example, Gudmundsson et al (2021) showed that observed changes in river flow are consistent with climatic changes, and Sauer et al (2021) found a climate signal in the trends in damages caused by river floods.

The evaluation of hydrological models is a critical first step towards impact attribution and future projections as for both purposes we need to understand to what degree models capture the processes determining discharge at individual locations, regions or globally. To this end, GHMs have been forced by observational climate data and observational direct human forcings (e.g. land use, location of dams and reservoirs) in Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2) already. These previous ISIMIP2 simulations have been evaluated, for example, regarding the influence of river routing on simulated discharge (Zhao et al 2017), the incorporation of human impact parameterizations (Liu et al 2017b, Veldkamp et al 2018), drought characteristics (Kumar et al 2022), or the seasonality of mean and extreme runoff (Zaherpour et al 2018). It has been shown that GHMs can simulate the extent of flooded areas, but for some events, GHMs overestimate the flood extent (Mester et al 2021). In addition, studies on economic damages caused by river floods showed that interannual variability of observed damages can be captured at least in some large scale areas (Sauer et al 2021). Deviations at the damage level could be due to either the discharge simulated by GHMs or from other sources in the modelling chain (e.g. assumed river protection levels, estimated distribution of assets, local physical vulnerabilities, Sauer et al 2021).

For ISIMIP3a, the climate input data and information on direct human forcings have been updated.

For example, the data cover three additional years (2017–2019), accordingly more recent observational data has been used for bias adjustment, and an update in the bias adjustment method reduced excessively high daily maximum temperature values (Lange et al 2021, table 1 in Frieler et al 2024 shows details on data provided for daily climate, land use, irrigation, dams and reservoirs, and water abstraction). This study comprehensively evaluates the performance of nine GHMs that have contributed discharge data to ISIMIP3a so far. Five of these models were updated in terms of improving the representation of hydrological processes, and three models improved the representation of land cover (details in table 1). The effect of these improvements has been evaluated elsewhere (Müller Schmied et al 2023, Tsilimigkras et al 2023, Boulange et al 2023, Yoshida et al 2022).

The aim of this study is to intercompare model performance regarding daily and maximum annual discharge as well as low flow and compare the performance of the models' internal routing schemes to discharge generated from runoff by CaMa-Flood (Yamazaki et al 2011). We investigate which catchment properties correlate with model performance to suggest areas of model development and to identify stations that are particularly suitable for potential attribution studies or assessments of changes under future global warming as considered in ISIMIP3.

## 2. Methods

### 2.1. Simulated runoff and river discharge

We use daily runoff and river discharge provided by nine modelling groups based on the ISIMIP3a simulation round (Frieler et al 2024): CLASSIC, CWatM, H08, HydroPy, JULES-W2, MIROC-INTEG-LAND, ORCHIDEE-MICT, WaterGAP2-2e, and WEB-DHM-SG (table S1). WaterGAP2-2e is calibrated with observed discharge data (Müller Schmied et al 2023), and H08 uses parameters optimized to reproduce observed discharge in each climatic zone (Yoshida et al 2022). Simulated data are from the 'obsclim + histsoc' experiment that is designed for model evaluation and uses observation-based daily atmospheric climate forcing (GSWP3-W5 × 10⁵, Lange et al 2023) and varying direct human forcings provided by ISIMIP (Frieler et al 2024). According to ISIMIP model documentation (www.isimip.org), all GHMs use land-use data, five models use data on water-use (CWatM, H08, HydroPy, MIROC-INTEG-LAND, WaterGAP2-2e) and four models use data on dams and reservoir (CWatM, H08, MIROC-INTEG-LAND, WaterGAP2-2e). Simulations are done on a 0.5° × 0.5° grid and are available for the years 1901–2019.

It has been shown that modelled peak river discharge using the river routing model CaMa-Flood
<table><caption>**Table 1.** Model improvements implemented since ISIMIP2a for models evaluated in this study. More details on models in table S1.</caption><thead><tr><th>Model</th><th>Hydrological processes</th><th>Land-cover representation</th><th>Comment</th><th>Reference</th></tr></thead><tbody><tr><td>CLASSIC</td><td></td><td></td><td>Did not participate in ISIMIP2a</td><td>Melton et al (2020)</td></tr><tr><td>CWatM</td><td>Change in calculation of evapotranspiration with Penman-Monteith using CO2 response of vegetation</td><td>Using time varying land use instead of static</td><td></td><td>Burek et al (2020)</td></tr><tr><td>H08</td><td>Land surface model parameters have been optimized at each climatic zone</td><td></td><td></td><td>Boulange et al (2023), Yoshida et al (2022)</td></tr><tr><td>HyroPy</td><td></td><td></td><td>Did not participate in ISIMIP2, model was rewritten based on MPI-HM which did participate in ISIMIP2, changes in model infrastructure, numerics and documentation</td><td>Stacke and Hagemann (2021)</td></tr><tr><td>JULES-W2</td><td>(1) snow process module upgraded to 10-layer scheme; (2) soil hydrology scheme was changed to TOPMODEL scheme</td><td>(1) plant functional type (PFT) representation was changed from 5 PFTs to 13 PFTs, (2) used time varying land use instead of static</td><td></td><td>Tsilimigkras et al under review, Best et al (2011)</td></tr><tr><td>MIROC-INTEG-LAND</td><td></td><td>Same as ISIMIP2a</td><td></td><td>Yokohata et al (2020)</td></tr><tr><td>ORCHIDEE-MICT</td><td>Improvements for high-latitude processes including snow and permafrost, specifically (1) soil freezing and snow processes; (2) soil hydrology and river routing; (3) soil carbon discretization and SOM-dependent soil thermal and hydraulic parameters for permafrost representation; (4) reformulation of soil hydric stress above the permafrost table; (5) fires</td><td></td><td></td><td>Guimberteau et al (2018)</td></tr><tr><td>WaterGAP2-2e</td><td>Updated input for sectoral water use models, updated and extended data base for calibration, modified calibration routine to consider observation uncertainty; storage-based river velocity algorithm; updated input for surface water bodies (e.g. GRanD 1.3), implemented river water temperature, diverse corrections in water abstraction procedure</td><td></td><td></td><td>Müller Schmied et al (2021, 2023)</td></tr><tr><td>WEB-DHM-SG</td><td></td><td>Used time varying land use instead of static</td><td></td><td>Qi et al (2022)</td></tr></tbody></table>
<table><caption>Table 1. Model improvements implemented since ISIMIP2a for models evaluated in this study. More details on models in table S1.</caption><thead><tr><th>Model</th><th>Hydrological processes</th><th>Land-cover representation</th><th>Comment</th><th>Reference</th></tr></thead><tbody><tr><td>CLASSIC</td><td></td><td></td><td>Did not participate in ISIMIP2a</td><td>Melton et al (2020)</td></tr><tr><td>CWatM</td><td>Change in calculation of evapotranspiration with Penman-Monteith using CO2 response of vegetation</td><td>Using time varying land use instead of static</td><td></td><td>Burek et al (2020)</td></tr><tr><td>H08</td><td>Land surface model parameters have been optimized at each climatic zone</td><td></td><td></td><td>Boulange et al (2023), Yoshida et al (2022)</td></tr><tr><td>HyroPy</td><td></td><td></td><td>Did not participate in ISIMIP2, model was rewritten based on MPI-HM which did participate in ISIMIP2, changes in model infrastructure, numerics and documentation</td><td>Stacke and Hagemann (2021)</td></tr><tr><td>JULES-W2</td><td>(1) snow process module upgraded to 10-layer scheme; (2) soil hydrology scheme was changed to TOPMODEL scheme</td><td>(1) plant functional type (PFT) representation was changed from 5 PFTs to 13 PFTs, (2) used time varying land use instead of static</td><td></td><td>Tsilimigkras et al under review, Best et al (2011)</td></tr><tr><td>MIROC-INTEG-LAND</td><td></td><td></td><td>Same as ISIMIP2a</td><td>Yokohata et al (2020)</td></tr><tr><td>ORCHIDEE-MICT</td><td>Improvements for high-latitude processes including snow and permafrost, specifically (1) soil freezing and snow processes; (2) soil hydrology and river routing; (3) soil carbon discretization and SOM-dependent soil thermal and hydraulic parameters for permafrost representation; (4) reformulation of soil hydric stress above the permafrost table; (5) fires</td><td></td><td></td><td>Guimberteau et al (2018)</td></tr><tr><td>WaterGAP2-2e</td><td>Updated input for sectoral water use models, updated and extended data base for calibration, modified calibration routine to consider observation uncertainty; storage-based river velocity algorithm; updated input for surface water bodies (e.g. GRanD 1.3), implemented river water temperature, diverse corrections in water abstraction procedure</td><td></td><td></td><td>Müller Schmied et al (2021, 2023)</td></tr><tr><td>WEB-DHM-SG</td><td></td><td>Used time varying land use instead of static</td><td></td><td>Qi et al (2022)</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Figure 1.** The location of the 644 GRDC stations used for model evaluation.</figcaption></figure>

(Yamazaki *et al* 2011) can perform better than the model's internal routing scheme (Zhao *et al* 2017). CaMa-Flood differs from other routing schemes in that it explicitly also parameterizes flood inundation dynamics and provides water depth and inundation extent as output variables (Yamazaki *et al* 2011). It is therefore often used in combination with GHMs for flood modelling. CaMa-Flood provides its own routing scheme on a 15' grid. However, CaMa-Flood does not include the lakes and reservoirs routines simulated by GHMs, which can result in some models performing better without CaMa-Flood. Thus, in addition to discharge routed with each model's internal routing scheme (specified in table S1), we use each model's simulated runoff to drive CaMa-Flood and then derive river discharge. Daily runoff is provided by all nine models listed above, and discharge modelled with the model's internal routing scheme is provided by seven models. JULES-W2 provides discharge routed with the 'native JULES' river topography (Total Runoff Integrating Pathways scheme) that includes spatially distributed meandering and velocity data (Tsilimigkras *et al* 2023), and has been shown to improve the accuracy of river flow simulations (Tsilimigkras *et al* under review). In addition, JULES-W2 provides discharge routed with the DDM30 river topology.

## 2.2. Station selection and observed discharge data

To evaluate model performance, we use daily discharge data from the Global Runoff Data Centre (GRDC). GHMs use different river routing schemes (detailed in table S1) and the spatial coordinates of stations with observational data often do not match the coarser gridded river networks (Müller Schmied and Schiebener 2022). To ensure comparability, we base the selection of stations on a previously published report that analysed how well ISIMIP GHMs'

routing schemes align with the location of a selection of GRDC stations and are thus suitable for evaluating river discharge (Müller Schmied and Schiebener 2022). 1096 out of 1509 stations were found to be compatible (Müller Schmied and Schiebener 2022). Of those, we select stations for which daily data was available for at least five years, and we only retain years with less than 10 d of missing data, which are the same criteria as used by Zhao *et al* (2017). In the end, we use 644 stations for model evaluation (figure 1), corresponding to 106 basins according to HydroBASINS level 3 from the HydroSHEDS database (figure S1, Lehner and Grill 2013).

## 2.3. Model evaluation

We analyse the extent to which model simulations can reproduce variability in daily discharge and maximum annual discharge. For both these metrics, and for each station and each GHM, we compare observed discharge to discharge routed with the model's internal routing scheme, and discharge routed with CaMa-Flood, respectively. To evaluate model performance, we calculate the Kling–Gupta efficiency (KGE) and its three components: correlation ($r$), bias ratio ($\beta$), and variability ratio ($\gamma$) (Kling et al 2012). The KGE is used to evaluate hydrological models (e.g. Krysanova et al 2017, Veldkamp et al 2018) and measures the ability of a model to reproduce observed values. It is calculated by equally weighing the three components, where $r$ is the linear correlation between observed and simulated values, $\beta$ is the ratio of the mean simulated value to the mean observed value, and $\gamma$ is the ratio of the standard deviation of simulated values to the standard deviation of observed values (Knoben et al 2019). The KGE metric is dimensionless. We calculate the KGE for daily and maximum annual discharge for each model and each station.
<figure><img src="image_5.png" /><figcaption>**Figure 1.** The location of the 644 GRDC stations used for model evaluation.</figcaption></figure>

(Yamazaki *et al* 2011) can perform better than the model's internal routing scheme (Zhao *et al* 2017). CaMa-Flood differs from other routing schemes in that it explicitly also parameterizes flood inundation dynamics and provides water depth and inundation extent as output variables (Yamazaki *et al* 2011). It is therefore often used in combination with GHMs for flood modelling. CaMa-Flood provides its own routing scheme on a 15' grid. However, CaMa-Flood does not include the lakes and reservoirs routines simulated by GHMs, which can result in some models performing better without CaMa-Flood. Thus, in addition to discharge routed with each model's internal routing scheme (specified in table S1), we use each model's simulated runoff to drive CaMa-Flood and then derive river discharge. Daily runoff is provided by all nine models listed above, and discharge modelled with the model's internal routing scheme is provided by seven models. JULES-W2 provides discharge routed with the 'native JULES' river topography (Total Runoff Integrating Pathways scheme) that includes spatially distributed meandering and velocity data (Tsilimigkras *et al* 2023), and has been shown to improve the accuracy of river flow simulations (Tsilimigkras *et al* under review). In addition, JULES-W2 provides discharge routed with the DDM30 river topology.

## 2.2. Station selection and observed discharge data

To evaluate model performance, we use daily discharge data from the Global Runoff Data Centre (GRDC). GHMs use different river routing schemes (detailed in table S1) and the spatial coordinates of stations with observational data often do not match the coarser gridded river networks (Müller Schmied and Schiebener 2022). To ensure comparability, we base the selection of stations on a previously published report that analysed how well ISIMIP GHMs'

routing schemes align with the location of a selection of GRDC stations and are thus suitable for evaluating river discharge (Müller Schmied and Schiebener 2022). 1096 out of 1509 stations were found to be compatible (Müller Schmied and Schiebener 2022). Of those, we select stations for which daily data was available for at least five years, and we only retain years with less than 10 d of missing data, which are the same criteria as used by Zhao *et al* (2017). In the end, we use 644 stations for model evaluation (figure 1), corresponding to 106 basins according to HydroBASINS level 3 from the HydroSHEDS database (figure S1, Lehner and Grill 2013).

## 2.3. Model evaluation

We analyse the extent to which model simulations can reproduce variability in daily discharge and maximum annual discharge. For both these metrics, and for each station and each GHM, we compare observed discharge to discharge routed with the model's internal routing scheme, and discharge routed with CaMa-Flood, respectively. To evaluate model performance, we calculate the Kling–Gupta efficiency (KGE) and its three components: correlation ($r$), bias ratio ($\beta$), and variability ratio ($\gamma$) (Kling et al 2012). The KGE is used to evaluate hydrological models (e.g. Krysanova et al 2017, Veldkamp et al 2018) and measures the ability of a model to reproduce observed values. It is calculated by equally weighing the three components, where $r$ is the linear correlation between observed and simulated values, $\beta$ is the ratio of the mean simulated value to the mean observed value, and $\gamma$ is the ratio of the standard deviation of simulated values to the standard deviation of observed values (Knoben et al 2019). The KGE metric is dimensionless. We calculate the KGE for daily and maximum annual discharge for each model and each station.
For daily discharge, we also evaluate timing differ-
ences by testing whether shifting the simulated time
series by up to 31 d (back- and forward) improves cor-
relation, as has been suggested by Zhao *et al* (2017).

For maximum annual discharge, we quantify
which part of the distribution is over- or underestim-
ated. For each station, we first identify the lower 50%
of observational values and count the years where the
simulated values are lower or higher, and then we do
the same for the upper 50% of observed values.

To assess the capability of models to simulate low
flow, we first determine the tenth quantile of daily dis-
charge, i.e. the amount of discharge that is exceeded
90% of the time (Q90, Gosling *et al* 2017, Krysanova
*et al* 2017). We then divide the difference between
simulated tenth percentile and observed tenth per-
centile by observed tenth percentile. Thus, a value of
zero implies a perfect match between observation and
simulation, negative values imply that the simulated
low flow is too low, while positive values indicate that
the simulated low flow is simulated as too high. This
is implemented for discharge routed with the model’s
internal routing scheme, and discharge routed with
CaMa-Flood.

To depict spatial heterogeneity in model perform-
ance, we calculated for each model the mean low flow
index and mean KGE for maximum annual discharge
for each of the 106 basins (figure S1, Lehner and Grill
2013).

**2.4. Station characteristics**

We use station characteristics data from the Global
Streamflow Indices and Metadata Archive (GSIM)
that provides metadata for more than 30 000 stations
(Do *et al* 2018, Gudmundsson *et al* 2018). GSIM data
is only available for a subset of stations in this study.
We use the following catchment properties from the
database (number of stations with data available
in parentheses): clay content (432), drainage dens-
ity (379), elevation (436), irrigated area [%] (436),
nightlight development index (176), number of dams
upstream (436), population count (435), population
density (435), sand content (432), silt content (433),
slope (436), storage volume (total upstream stor-
age volume, 436), and topographic index (436). The
upstream catchment area from the gauge is taken
from the GRDC database. To characterize how dry
or wet the area is where a station is located, we used
data from the Global Aridity Index and Potential
Evapotranspiration Database (Zomer *et al* 2022).
This aridity index is defined as the ratio of precipit-
ation to potential evapotranspiration and is unitless
(Zomer *et al* 2022). Both, catchment area and aridity
index are available for all stations.

To further investigate model performance at
(sub-)arid stations, we first identified all stations with
an aridity index less than or equal to 0.5 (Zomer *et al*

2022). For these 236 stations, we calculated the KGE
and its three components for daily discharge, max-
imum and mean annual discharge, mean monthly
and long-term mean monthly discharge.

3. Results

**3.1. Daily discharge**

In general, models can reproduce the variability of
daily river discharge at most stations (e.g. time-series
plot with corresponding KGE values in figures S2
and S3). The median KGE across all stations ranges
from −0.43 for model WEB-DHM-SG to 0.46 for
WaterGAP2-2e (figure 2(a), table S2). The median
correlation ranges from 0.17 for the model CLASSIC
to 0.68 for WaterGAP2-2e (figure 2(b), table S2).
Most models (seven out of nine) tend to overes-
timate daily discharge at a majority of stations (bias
ratio *β* larger than one), but there is a large vari-
ation in the magnitude of overestimation between
models, as well as between stations (figure 2(c), table
S2). Results for the variability ratio (γ) are mixed,
with two (out of nine) models overestimating variab-
ility (e.g. HydroPy), while the remaining models tend
to underestimate variability (e.g. MIROC-INTEG-
LAND, figure 2(d), table S2).

Models tend to perform well at stations in wet-
ter areas (i.e. higher aridity index, table S3, figure 3),
and less well at stations at higher elevations (table
S3, figure 4), while in drier areas and at lower elev-
ations there is a large spread across stations includ-
ing good and poor model performance. The bias ratio
tends to be larger at stations in drier areas (figure S4,
table S5). For several models (six out of nine), the
variability ratio is larger at higher catchment eleva-
tions (table S6, figure S5) and steeper slopes (table
S6, figure S6). Stations for which models perform
best (i.e. highest KGE and correlation across all mod-
els) are, for example, located at the Mekong River
in Southeast Asia, and the Amazon River in South
America.

Shifting the time series can lead to improved cor-
relation (figure S7), but the more shifting is required
the worse model performance of shifted time-series is
(figure S8).

Regarding the use of river routing schemes, dis-
charge routed with CaMa-Flood performs better for
three out of seven models, especially for ORCHIDEE-
MICT and WEB-DHM-SG (figure 2(a)). For these
cases, KGE and especially its first component (cor-
relation) is higher (figures 2(a) and (b)), but at the
same time bias and variability are more strongly
overestimated (figures 2(c) and (d)). In contrast, for
HydroPy and to a lesser extent also for CWatM, dis-
charge routed with CaMa-Flood tends to be worse
compared to the model’s internal routing scheme
For daily discharge, we also evaluate timing differ-
ences by testing whether shifting the simulated time
series by up to 31 d (back- and forward) improves cor-
relation, as has been suggested by Zhao *et al* (2017).

For maximum annual discharge, we quantify
which part of the distribution is over- or underestim-
ated. For each station, we first identify the lower 50%
of observational values and count the years where the
simulated values are lower or higher, and then we do
the same for the upper 50% of observed values.

To assess the capability of models to simulate low flow, we first determine the tenth quantile of daily discharge, i.e. the amount of discharge that is exceeded 90% of the time (Q90, Gosling *et al* 2017, Krysanova *et al* 2017). We then divide the difference between simulated tenth percentile and observed tenth percentile by observed tenth percentile. Thus, a value of zero implies a perfect match between observation and simulation, negative values imply that the simulated low flow is too low, while positive values indicate that the simulated low flow is simulated as too high. This is implemented for discharge routed with the model's internal routing scheme, and discharge routed with CaMa-Flood.

To depict spatial heterogeneity in model perform-
ance, we calculated for each model the mean low flow
index and mean KGE for maximum annual discharge
for each of the 106 basins (figure S1, Lehner and Grill
2013).

**2.4. Station characteristics**

We use station characteristics data from the Global Streamflow Indices and Metadata Archive (GSIM) that provides metadata for more than 30 000 stations (Do *et al* 2018, Gudmundsson *et al* 2018). GSIM data is only available for a subset of stations in this study. We use the following catchment properties from the database (number of stations with data available in parentheses): clay content (432), drainage density (379), elevation (436), irrigated area [%] (436), nightlight development index (176), number of dams upstream (436), population count (435), population density (435), sand content (432), silt content (433), slope (436), storage volume (total upstream storage volume, 436), and topographic index (436). The upstream catchment area from the gauge is taken from the GRDC database. To characterize how dry or wet the area is where a station is located, we used data from the Global Aridity Index and Potential Evapotranspiration Database (Zomer *et al* 2022). This aridity index is defined as the ratio of precipitation to potential evapotranspiration and is unitless (Zomer *et al* 2022). Both, catchment area and aridity index are available for all stations.

To further investigate model performance at
(sub-)arid stations, we first identified all stations with
an aridity index less than or equal to 0.5 (Zomer *et al*

2022). For these 236 stations, we calculated the KGE
and its three components for daily discharge, max-
imum and mean annual discharge, mean monthly
and long-term mean monthly discharge.

3. Results

**3.1. Daily discharge**

In general, models can reproduce the variability of daily river discharge at most stations (e.g. time-series plot with corresponding KGE values in figures S2 and S3). The median KGE across all stations ranges from −0.43 for model WEB-DHM-SG to 0.46 for WaterGAP2-2e (figure 2(a), table S2). The median correlation ranges from 0.17 for the model CLASSIC to 0.68 for WaterGAP2-2e (figure 2(b), table S2). Most models (seven out of nine) tend to overestimate daily discharge at a majority of stations (bias ratio *β* larger than one), but there is a large variation in the magnitude of overestimation between models, as well as between stations (figure 2(c), table S2). Results for the variability ratio (γ) are mixed, with two (out of nine) models overestimating variability (e.g. HydroPy), while the remaining models tend to underestimate variability (e.g. MIROC-INTEG-LAND, figure 2(d), table S2).

Models tend to perform well at stations in wet-
ter areas (i.e. higher aridity index, table S3, figure 3),
and less well at stations at higher elevations (table
S3, figure 4), while in drier areas and at lower elev-
ations there is a large spread across stations includ-
ing good and poor model performance. The bias ratio
tends to be larger at stations in drier areas (figure S4,
table S5). For several models (six out of nine), the
variability ratio is larger at higher catchment eleva-
tions (table S6, figure S5) and steeper slopes (table
S6, figure S6). Stations for which models perform
best (i.e. highest KGE and correlation across all mod-
els) are, for example, located at the Mekong River
in Southeast Asia, and the Amazon River in South
America.

Shifting the time series can lead to improved cor-
relation (figure S7), but the more shifting is required
the worse model performance of shifted time-series is
(figure S8).

Regarding the use of river routing schemes, dis-
charge routed with CaMa-Flood performs better for
three out of seven models, especially for ORCHIDEE-
MICT and WEB-DHM-SG (figure 2(a)). For these
cases, KGE and especially its first component (cor-
relation) is higher (figures 2(a) and (b)), but at the
same time bias and variability are more strongly
overestimated (figures 2(c) and (d)). In contrast, for
HydroPy and to a lesser extent also for CWatM, dis-
charge routed with CaMa-Flood tends to be worse
compared to the model’s internal routing scheme
<figure><img src="image_6.png" /><figcaption>**Figure 2.** Evaluation of daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 644 stations for Kling-Gupta efficiency (KGE) and its three components. JULES-W2 provides discharge routed with two routing schemes (Mir, Mir2, details in table S1). Thick lines: median, box: first and third quartile, whiskers: 10th and 90th percentile. Details table S2.</figcaption></figure>

(figure 2(a)), likely because variability is overestimated (figure 2(d)). For CWatM, HydroPy, and JULES-W2, CaMa seems to particularly overestimate variability at higher elevations and steeper slopes (table S7).

## 3.2. Low flow

Most models (six out of nine) do not capture the strength of low flow events, i.e. their magnitude of low flow is simulated too high (figures 5, S9 and S10). However, HydroPy and JULES-W2 are often close to observed low flow, while WEB-DHM-SG tends to underestimate low flow (figure S9). Consistent with the above results, low flow is overestimated in arid regions, especially in the Australian and African

basins (figures 5 and S10). The exception is WEB-DHM-SG, which tends to underestimate low flow in these regions as well.

## 3.3. Maximum annual discharge

Model performance is often worse for maximum annual discharge compared to daily discharge (seven of nine models, figures 6, S11 and S12). The median KGE of annual maximum discharge across all stations ranges from -0.94 for WEB-DHM-SG to 0.24 for WaterGAP2-2e (figure 6(a), table S8), and median correlation ranges from 0.31 for CLASSIC to 0.58 for WaterGAP2-2e (figure 6(b), table S8). There is a tendency to overestimation (six of nine models), and for
<figure><img src="image_6.png" /><figcaption>**Figure 2.** Evaluation of daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 644 stations for Kling-Gupta efficiency (KGE) and its three components. JULES-W2 provides discharge routed with two routing schemes (Mir, Mir2, details in table S1). Thick lines: median, box: first and third quartile, whiskers: 10th and 90th percentile. Details table S2.</figcaption></figure>

(figure 2(a)), likely because variability is overestimated (figure 2(d)). For CWatM, HydroPy, and JULES-W2, CaMa seems to particularly overestimate variability at higher elevations and steeper slopes (table S7).

## 3.2. Low flow

Most models (six out of nine) do not capture the strength of low flow events, i.e. their magnitude of low flow is simulated too high (figures 5, S9 and S10). However, HydroPy and JULES-W2 are often close to observed low flow, while WEB-DHM-SG tends to underestimate low flow (figure S9). Consistent with the above results, low flow is overestimated in arid regions, especially in the Australian and African

basins (figures 5 and S10). The exception is WEB-DHM-SG, which tends to underestimate low flow in these regions as well.

## 3.3. Maximum annual discharge

Model performance is often worse for maximum annual discharge compared to daily discharge (seven of nine models, figures 6, S11 and S12). The median KGE of annual maximum discharge across all stations ranges from -0.94 for WEB-DHM-SG to 0.24 for WaterGAP2-2e (figure 6(a), table S8), and median correlation ranges from 0.31 for CLASSIC to 0.58 for WaterGAP2-2e (figure 6(b), table S8). There is a tendency to overestimation (six of nine models), and for
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Relationship between aridity and model performance for daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 644 stations. The aridity index is the ratio of precipitation to potential evapotranspiration (unitless, lower values correspond to more arid conditions, details in Zomer *et al* 2022).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Relationship between mean catchment elevation and model performance for daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 436 stations.</figcaption></figure>

five models, river routing with CaMa-Flood leads to a stronger overestimation compared to the model's internal routing scheme (figure 6(c), table S8). The maximum annual discharge is more strongly overestimated at stations in dry areas (figure S13, table S11). Spatial analysis shows that eight out of nine models have a low KGE for most African basins, but a high

KGE for most basins in Asia (figures 7 and S14). At the same time, performance for the other regions is more heterogeneous.

The analysis of which part of the distribution of annual maxima is over- or underestimated shows that five models (of nine) overestimate low and high maximum discharge (figure 8). Except
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Relationship between aridity and model performance for daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 644 stations. The aridity index is the ratio of precipitation to potential evapotranspiration (unitless, lower values correspond to more arid conditions, details in Zomer *et al* 2022).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Relationship between mean catchment elevation and model performance for daily discharge routed by the model's internal routing scheme (Mir) and CaMa-Flood (CaMa) across 436 stations.</figcaption></figure>

five models, river routing with CaMa-Flood leads to a stronger overestimation compared to the model's internal routing scheme (figure 6(c), table S8). The maximum annual discharge is more strongly overestimated at stations in dry areas (figure S13, table S11). Spatial analysis shows that eight out of nine models have a low KGE for most African basins, but a high

KGE for most basins in Asia (figures 7 and S14). At the same time, performance for the other regions is more heterogeneous.

The analysis of which part of the distribution of annual maxima is over- or underestimated shows that five models (of nine) overestimate low and high maximum discharge (figure 8). Except
<figure><img src="image_9.png" /></figure>

for MIROC-INTEG-LAND, discharge routed with CaMa-Flood tends towards a stronger overestimation when compared to the model's internal routing scheme. There are some cases where models overestimate low values of annual maximum discharge and underestimate high values. In those cases, the average correlation between observed and simulated discharge is around 0.5. There are only individual stations where models consistently overestimate low values of annual maxima and underestimate high values (example in figures S15 and S16).

### 3.4. Arid stations

Analysis of model performance across arid stations shows that all models perform better for mean monthly and mean annual discharge than for daily discharge due to a higher correlation coefficient (tables S13–S17, figures S17–S21). The correlation is highest for all models for long-term monthly discharge (table S15, figure S19), suggesting that models can reproduce the seasonal flows.

## 4. Discussion

We demonstrate that in general, the evaluated models are able to reproduce observed time series of daily and maximum annual discharge. The performance of ISIMIP3a models is similar to evaluation studies of earlier simulation rounds. For example, Veldkamp et al (2018) estimated for monthly discharge simulated by ISIMIP2a models a median correlation of more than 0.6, and Hou et al (2023) derived very similar results for monthly runoff simulated by ISIMIP2a GHMs.

In line with previous studies (Veldkamp et al 2018), the bias ratio is the evaluation parameter that contributed most to a reduced performance in KGE. We find that most models overestimate discharge

and that the overestimation tends to be stronger for maximum annual discharge. For ISIMIP2a models, Hattermann et al (2017) also identified that models tend to overestimate monthly discharge, and similarly Zaherpour et al (2018) found that models overestimate extreme runoff. This suggests that applications further down the modelling chain, for example, for flooded areas or flood damages could be affected as well as other sectors such as agriculture or energy production. This is in line with a study showing that simulations with some GHMs led to an overestimation of flooded areas (Mester et al 2021).

Our further investigation of model performance for maximum annual discharge reveals that both low and high values are either over- or underestimated (figure 8) as has been found by Zaherpour et al (2018) for ISIMIP2a models. Thus, contrary to the suggestion by Mester et al (2021), we identify only a few cases where a model overestimates low values and underestimates high values, i.e. a ‘too flat’ simulation. This implies that we find no evidence for the proposal by Mester et al (2021) that the flood return period by GHMs is simulated too short.

Our evaluation setup of including seven GHMs with discharge routed by both, the model's internal routing scheme and CaMa-Flood, allows for investigating the role of the routing scheme. While Zhao et al (2017) detected that routing with CaMa-Flood led to a lower multi-year mean maximum discharge (ISIMIP2a models), we here find that CaMa-Flood routing results in a higher proportion of years being overestimated for maximum annual discharge (figure 8). Also, except for WEB-DHM-SG, routing with CaMa-Flood has a higher bias ratio than the model's internal routing (figure 6(c)). Other studies found mixed performances for CaMa-Flood. Yang et al (2019) demonstrated that CaMa-Flood performs well for the amplitude of peak discharge but not the
<figure><img src="image_9.png" /></figure>

for MIROC-INTEG-LAND, discharge routed with CaMa-Flood tends towards a stronger overestimation when compared to the model's internal routing scheme. There are some cases where models overestimate low values of annual maximum discharge and underestimate high values. In those cases, the average correlation between observed and simulated discharge is around 0.5. There are only individual stations where models consistently overestimate low values of annual maxima and underestimate high values (example in figures S15 and S16).

### 3.4. Arid stations

Analysis of model performance across arid stations shows that all models perform better for mean monthly and mean annual discharge than for daily discharge due to a higher correlation coefficient (tables S13–S17, figures S17–S21). The correlation is highest for all models for long-term monthly discharge (table S15, figure S19), suggesting that models can reproduce the seasonal flows.

## 4. Discussion

We demonstrate that in general, the evaluated models are able to reproduce observed time series of daily and maximum annual discharge. The performance of ISIMIP3a models is similar to evaluation studies of earlier simulation rounds. For example, Veldkamp et al (2018) estimated for monthly discharge simulated by ISIMIP2a models a median correlation of more than 0.6, and Hou et al (2023) derived very similar results for monthly runoff simulated by ISIMIP2a GHMs.

In line with previous studies (Veldkamp et al 2018), the bias ratio is the evaluation parameter that contributed most to a reduced performance in KGE. We find that most models overestimate discharge

and that the overestimation tends to be stronger for maximum annual discharge. For ISIMIP2a models, Hattermann et al (2017) also identified that models tend to overestimate monthly discharge, and similarly Zaherpour et al (2018) found that models overestimate extreme runoff. This suggests that applications further down the modelling chain, for example, for flooded areas or flood damages could be affected as well as other sectors such as agriculture or energy production. This is in line with a study showing that simulations with some GHMs led to an overestimation of flooded areas (Mester et al 2021).

Our further investigation of model performance for maximum annual discharge reveals that both low and high values are either over- or underestimated (figure 8) as has been found by Zaherpour et al (2018) for ISIMIP2a models. Thus, contrary to the suggestion by Mester et al (2021), we identify only a few cases where a model overestimates low values and underestimates high values, i.e. a ‘too flat’ simulation. This implies that we find no evidence for the proposal by Mester et al (2021) that the flood return period by GHMs is simulated too short.

Our evaluation setup of including seven GHMs with discharge routed by both, the model's internal routing scheme and CaMa-Flood, allows for investigating the role of the routing scheme. While Zhao et al (2017) detected that routing with CaMa-Flood led to a lower multi-year mean maximum discharge (ISIMIP2a models), we here find that CaMa-Flood routing results in a higher proportion of years being overestimated for maximum annual discharge (figure 8). Also, except for WEB-DHM-SG, routing with CaMa-Flood has a higher bias ratio than the model's internal routing (figure 6(c)). Other studies found mixed performances for CaMa-Flood. Yang et al (2019) demonstrated that CaMa-Flood performs well for the amplitude of peak discharge but not the
<figure><img src="image_10.png" /></figure>

timing. In another study, the magnitude of 100 years floods was overestimated in Western and Central USA but underestimated in Eastern USA (Devitt et al 2021). However, in these studies, either CaMa-Flood was used as the only routing model (Yang et al 2019) or combinations of different GHMs, routing schemes, and climate forcing data were compared (Devitt et al 2021). Therefore, it is not clear which components of the modelling chain contribute errors. Our finding that CaMa-Flood tends to overestimate peak discharge, especially at higher elevations with steep slopes, suggests that too much water is transported in the river and floodplain during peak discharges. This may be explained by the fact that evapotranspiration

over floodplains and transmission losses are not included in CaMa-Flood (Zhao et al 2017). In addition, routing by CaMa-Flood could be too efficient (i.e. water reaches a station too quickly), suggesting that flow velocity in the river channel or floodplain is overestimated. Unlike kinematic wave approaches, CaMa-Flood includes a diffusion term that allows the wave to spread spatially. While capturing the spatial variability of flow velocity within the channel, the diffusive wave equation tends to concentrate the flow more rapidly in the case of rapid changes in flow, e.g. due to sudden changes in channel slope or rapid increases in discharge. As a result, peak discharges may be overestimated, particularly in higher elevation
<figure><img src="image_10.png" /></figure>

timing. In another study, the magnitude of 100 years floods was overestimated in Western and Central USA but underestimated in Eastern USA (Devitt et al 2021). However, in these studies, either CaMa-Flood was used as the only routing model (Yang et al 2019) or combinations of different GHMs, routing schemes, and climate forcing data were compared (Devitt et al 2021). Therefore, it is not clear which components of the modelling chain contribute errors. Our finding that CaMa-Flood tends to overestimate peak discharge, especially at higher elevations with steep slopes, suggests that too much water is transported in the river and floodplain during peak discharges. This may be explained by the fact that evapotranspiration

over floodplains and transmission losses are not included in CaMa-Flood (Zhao et al 2017). In addition, routing by CaMa-Flood could be too efficient (i.e. water reaches a station too quickly), suggesting that flow velocity in the river channel or floodplain is overestimated. Unlike kinematic wave approaches, CaMa-Flood includes a diffusion term that allows the wave to spread spatially. While capturing the spatial variability of flow velocity within the channel, the diffusive wave equation tends to concentrate the flow more rapidly in the case of rapid changes in flow, e.g. due to sudden changes in channel slope or rapid increases in discharge. As a result, peak discharges may be overestimated, particularly in higher elevation
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

areas. In addition, flow velocity is influenced by river channel and floodplain characteristics, some of which are derived empirically in CaMa-Flood. This leads to uncertainties and potential biases in the estimation of peak discharges (Yamazaki *et al* 2011).

When analysing which catchment properties are linked to model performance we find that two natural features, and not anthropogenic ones, are especially relevant. First, it is well established that hydrological models perform less well in arid and semi-arid regions (Zaherpour *et al* 2018, Hou *et al* 2023). We find that this is also the case for ISIMIP3a GHMs

(figure 3). Dry areas have a low runoff coefficient meaning that a large proportion of the precipitation evaporates, and thus a small underestimation of evapotranspiration by a model can lead to a strong overestimation of discharge (Hattermann *et al* 2017). As we find that discharge is more strongly overestimated in arid areas compared to humid areas (figure S4), this could mean that evapotranspiration may be underestimated particularly in arid areas. Given the relevance of hydrological modelling for projecting climate change impacts on drought prevalence in (semi-) arid areas (Wang *et al* 2022), reducing
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

areas. In addition, flow velocity is influenced by river channel and floodplain characteristics, some of which are derived empirically in CaMa-Flood. This leads to uncertainties and potential biases in the estimation of peak discharges (Yamazaki et al 2011).

When analysing which catchment properties are linked to model performance we find that two natural features, and not anthropogenic ones, are especially relevant. First, it is well established that hydrological models perform less well in arid and semi-arid regions (Zaherpour et al 2018, Hou et al 2023). We find that this is also the case for ISIMIP3a GHMs

(figure 3). Dry areas have a low runoff coefficient meaning that a large proportion of the precipitation evaporates, and thus a small underestimation of evapotranspiration by a model can lead to a strong overestimation of discharge (Hattermann et al 2017). As we find that discharge is more strongly overestimated in arid areas compared to humid areas (figure S4), this could mean that evapotranspiration may be underestimated particularly in arid areas. Given the relevance of hydrological modelling for projecting climate change impacts on drought prevalence in (semi-) arid areas (Wang et al 2022), reducing
bias in simulating discharge under dry conditions is an important area of future model improvement. However, as we find that the models show a high correlation for long-term mean monthly discharge, GHMs could be used to analyse changes in seasonal flows in (semi-) arid areas.

Second, we find that models perform less well at higher elevations, as has been shown for ISIMIP2a (Yang et al 2019). This suggests that cold dynamics, i.e. glaciers, permafrost, and snowmelt, are important hydrological processes that are not yet adequately included in many models and are thus a further relevant area of model development (Gädeke et al 2020).

As the output of GHMs is used to answer a range of different research questions including the impact of climate change on various aspects of the water cycle (Krysanova et al 2020), it is important to assess additional hydrological variables. For example, there is ongoing work evaluating terrestrial water storage and soil moisture simulated by GHMs from ISIMIP3a (Tiwari et al under review). A next step would be to validate other GHM output variables, such as evapotranspiration and groundwater recharge, as has been done in ISIMIP2 assessment studies (Wartenburger et al 2018, Pokhrel et al 2021, Gnann et al 2023).

We conclude that our results help to identify areas where we have greater confidence in the ability of GHMs to simulate hydrological processes, particularly in humid areas, at low elevations and in areas with strong and regular seasonality. Stations in these areas are therefore likely to be best suited to studies aimed at attributing historical climate change based on the output of the investigated GHMs. We also identify areas where improved process simulation is needed, i.e. evapotranspiration, transmission losses and cold dynamics.

## Data availability statement

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

## Acknowledgments

This research has received funding from the German Federal Ministry of Education and Research (BMBF) under the research projects QUIDIC (01LP1907A) and ISIAccess (16QK05). Support for this publication was provided by COST Action CA19139 PROCLIAS (PROcess-based models for CLimate Impact Attribution across Sectors), supported by COST (European Cooperation in Science and Technology; www.cost.eu).

## ORCID iDs

Stefanie Heinicke https://orcid.org/0000-0003-0222-5281

Jacob Schewe https://orcid.org/0000-0001-9455-4159

Simon N Gosling https://orcid.org/0000-0001-5973-6862

Hannes Müller Schmied https://orcid.org/0000-0001-5330-9923

Sandra Zimmermann https://orcid.org/0009-0005-0130-0528

Matthias Mengel https://orcid.org/0000-0001-6724-9685

Inga J Sauer https://orcid.org/0000-0002-9302-2131

Peter Burek https://orcid.org/0000-0001-6390-8487

Jinfeng Chang https://orcid.org/0000-0003-4463-7778

Sian Kou-Giesbrecht https://orcid.org/0000-0002-4086-0561

Manoli Grillakis https://orcid.org/0000-0002-4228-1803

Naota Hanasaki https://orcid.org/0000-0002-5092-7563

Aristeidis Koutroulis https://orcid.org/0000-0002-2999-7575

Kedar Otta https://orcid.org/0000-0002-2540-9879

Yusuke Satoh https://orcid.org/0000-0001-6419-7330

Tobias Stacke https://orcid.org/0000-0003-4637-5337

Katja Frieler https://orcid.org/0000-0003-4869-3013

## References

Best M J et al 2011 The joint UK land environment simulator (JULES), model description—Part 1: energy and water fluxes Geosci. Model Dev. 4 677–99

Boulange J, Yoshida T, Nishina K, Okada M and Hanasaki N 2023 Delivering the latest global water resource simulation results to the public Clim. Serv. 30 100386

Burek P, Satoh Y, Kahil T, Tang T, Greve P, Smilovic M, Guillaumot L, Zhao F and Wada Y 2020 Development of the community water model (CWatM v1.04)—a high-resolution hydrological model for global and regional assessment of integrated water resources management Geosci. Model Dev. 13 3267–98

Dankers R et al 2014 First look at changes in flood hazard in the inter-sectoral impact model intercomparison project ensemble Proc. Natl Acad. Sci. 111 3257–61

Devitt L, Neal J, Wagener T and Coxon G 2021 Uncertainty in the extreme flood magnitude estimates of large-scale flood hazard models Environ. Res. Lett. 16 064013

Do H X, Gudmundsson L, Leonard M and Westra S 2018 The global streamflow indices and metadata archive (GSIM)—Part 1: the production of a daily streamflow archive and metadata Earth Syst. Sci. Data 10 765–85
bias in simulating discharge under dry conditions is an important area of future model improvement. However, as we find that the models show a high correlation for long-term mean monthly discharge, GHMs could be used to analyse changes in seasonal flows in (semi-) arid areas.

Second, we find that models perform less well at higher elevations, as has been shown for ISIMIP2a (Yang et al 2019). This suggests that cold dynamics, i.e. glaciers, permafrost, and snowmelt, are important hydrological processes that are not yet adequately included in many models and are thus a further relevant area of model development (Gädeke et al 2020).

As the output of GHMs is used to answer a range of different research questions including the impact of climate change on various aspects of the water cycle (Krysanova et al 2020), it is important to assess additional hydrological variables. For example, there is ongoing work evaluating terrestrial water storage and soil moisture simulated by GHMs from ISIMIP3a (Tiwari et al under review). A next step would be to validate other GHM output variables, such as evapotranspiration and groundwater recharge, as has been done in ISIMIP2 assessment studies (Wartenburger et al 2018, Pokhrel et al 2021, Gnann et al 2023).

We conclude that our results help to identify areas where we have greater confidence in the ability of GHMs to simulate hydrological processes, particularly in humid areas, at low elevations and in areas with strong and regular seasonality. Stations in these areas are therefore likely to be best suited to studies aimed at attributing historical climate change based on the output of the investigated GHMs. We also identify areas where improved process simulation is needed, i.e. evapotranspiration, transmission losses and cold dynamics.

## Data availability statement

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

## Acknowledgments

This research has received funding from the German Federal Ministry of Education and Research (BMBF) under the research projects QUIDIC (01LP1907A) and ISIAccess (16QK05). Support for this publication was provided by COST Action CA19139 PROCLIAS (PROcess-based models for CLimate Impact Attribution across Sectors), supported by COST (European Cooperation in Science and Technology; www.cost.eu).

## ORCID iDs

Stefanie Heinicke https://orcid.org/0000-0003-0222-5281

Jacob Schewe https://orcid.org/0000-0001-9455-4159

Simon N Gosling https://orcid.org/0000-0001-5973-6862

Hannes Müller Schmied https://orcid.org/0000-0001-5330-9923

Sandra Zimmermann https://orcid.org/0009-0005-0130-0528

Matthias Mengel https://orcid.org/0000-0001-6724-9685

Inga J Sauer https://orcid.org/0000-0002-9302-2131

Peter Burek https://orcid.org/0000-0001-6390-8487

Jinfeng Chang https://orcid.org/0000-0003-4463-7778

Sian Kou-Giesbrecht https://orcid.org/0000-0002-4086-0561

Manoli Grillakis https://orcid.org/0000-0002-4228-1803

Naota Hanasaki https://orcid.org/0000-0002-5092-7563

Aristeidis Koutroulis https://orcid.org/0000-0002-2999-7575

Kedar Otta https://orcid.org/0000-0002-2540-9879

Yusuke Satoh https://orcid.org/0000-0001-6419-7330

Tobias Stacke https://orcid.org/0000-0003-4637-5337

Katja Frieler https://orcid.org/0000-0003-4869-3013

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Gnann S et al 2023 Functional relationships reveal differences in the water cycle representation of global water models *Nat. Water* 1 1079–90

Gosling S N et al 2017 A comparison of changes in river runoff from multiple global and catchment-scale hydrological models under global warming scenarios of 1 °C, 2 °C and 3 °C *Clim. Change* 141 577–95

Gudmundsson L et al 2021 Globally observed trends in mean and extreme river flow attributed to climate change *Science* 371 1159–62

Gudmundsson L, Do H X, Leonard M and Westra S 2018 The global streamflow indices and metadata archive (GSIM)—Part 2: quality control, time-series indices and homogeneity assessment *Earth Syst. Sci. Data* 10 787–804

Guimberteau M et al 2018 ORCHIDEE-MICT (v8.4.1), a land surface model for the high latitudes: model description and validation *Geosci. Model Dev.* 11 121–63

Hallegatte S, Vogt-Schilb A, Bangalore M and Rozenberg J 2017 *Unbreakable: Building the Resilience of the Poor in the Face of Natural Disasters* (World Bank) (available at: http://hdl.handle.net/10986/25335)

Hattermann F F et al 2017 Cross-scale intercomparison of climate change impacts simulated by regional and global hydrological models in eleven large river basins *Clim. Change* 141 561–76

Hirabayashi Y, Tanoue M, Sasaki O, Zhou X and Yamazaki D 2021 Global exposure to flooding from the new CMIP6 climate model projections *Sci. Rep.* 11 3740

Hou Y, Guo H, Yang Y and Liu W 2023 Global evaluation of runoff simulation from climate, hydrological and land surface models *Water Resour. Res.* 59 e2021WR031817

Kling H, Fuchs M and Paulin M 2012 Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios *J. Hydrol.* 424–425 264–77

Knoben W J M, Freer J E and Woods R A 2019 Technical note: inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores *Hydrol. Earth Syst. Sci.* 23 4323–31

Krysanova V et al 2017 Intercomparison of regional-scale hydrological models and climate change impacts projected for 12 large river basins worldwide—a synthesis *Environ. Res. Lett.* 12 105002

Krysanova V, Hattermann F F and Kundzewicz Z W 2020 How evaluation of hydrological models influences results of climate impact assessment—an editorial *Clim. Change* 163 1121–41

Kumar A et al 2022 Multi-model evaluation of catchment- and global-scale hydrological model simulations of drought characteristics across eight large river catchments *Adv. Water Resour.* 165 104212

Lange S et al 2020 Projecting exposure to extreme climate impact events across six event categories and three spatial scales *Earth's Future* 8 e2020EF001616

Lange S et al 2021 WFDE5 over land merged with ERA5 over the ocean (W5E5 v2.0) *ISIMIP Repository* (https://doi.org/10.48364/data.isimip.org)

Lange S, Mengel M, Treu S and Büchner M 2023 ISIMIP3a atmospheric climate input data (v1.2). *ISIMIP repository* *ISIMIP Repository*

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

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