Projections of changes in the hydrological cycle from global hydrological models (GHMs) driven by global climate models (GCMs) are critical for understanding future occurrence of hydrological extremes. However, uncertainties remain large and need to be better assessed. In particular, recent studies have pointed to a considerable contribution of GHMs that can equal or outweigh the contribution of GCMs to uncertainty in hydrological projections. Using six GHMs and five GCMs from the ISI-MIP multi-model ensemble, this study aims: (i) to assess future changes in the frequency of both high and low flows at the global scale using control and future (RCP8.5) simulations by the 2080s, and (ii) to quantify, for both ends of the runoff spectrum, GCMs and GHMs contributions to uncertainty using a two-way ANOVA. Increases are found in high flows for northern latitudes and in low flows for several hotspots. Globally, the largest source of uncertainty is associated with GCMs, but GHMs are the greatest source in snow-dominated regions. More specifically, results vary depending on the runoff metric, the temporal (annual and seasonal) and regional scale of analysis. For instance, uncertainty contribution from GHMs is higher for low flows than it is for high flows, partly owing to the different processes driving the onset of the two phenomena (e.g. the more direct effect of the GCMs' precipitation variability on high flows). This study provides a comprehensive synthesis of where future hydrological extremes are projected to increase and where the ensemble spread is owed to either GCMs or GHMs. Finally, our results underline the need for improvements in modelling snowmelt and runoff processes to project future hydrological extremes and the importance of using multiple GCMs and GHMs to encompass the uncertainty range provided by these two sources.

The ongoing intensification of the water cycle at the global scale is
expected to continue in the coming decades

Recently, model inter-comparison projects like
WaterMIP

The ISI-MIP data set has been used to assess future changes in runoff at
global and regional scales.

In this context, modelling-induced uncertainty (i.e. inter-model spread of GCMs and GHMs)
has been expressed by looking at the variance across both types of models.
For example,

The studies cited above have provided useful knowledge on climate change
impacts on the water cycle using the ISI-MIP data set, however, a synthesis of
future projections for high and low flows along with a consistent estimation
of uncertainties is still missing. The present study builds on the work on
low flows of

By comparing an ensemble of GCMs (5) and GHMs (6) for future projections (2066–2099) against the historical period (1972–2005), this study aims (i) to assess future high and low flows changes at global and annual and seasonal scales, and (ii) to quantify the uncertainty attributable to GHMs and GCMs using ANOVA. In the next section, the data set and the different steps of the methodology are detailed. The results of projected hydrological extremes and respective uncertainty are presented in Sect. 3 before discussing the important and wider implications of this research in the fourth and final section.

The data set used herein comes from the Inter-Sectorial Impact Model
Intercomparison Project (ISI-MIP)

Our analytical framework was composed of four steps: (i) time series of days classified as high and low flows were extracted from daily total runoff record; (ii) high and low flow indices (i.e. change in frequency of high/flow flows) were calculated (future minus historical period) and mapped; (iii) ANOVA was carried out on the high and low flow indices considering GCMs and GHMs as factors; and (iv) the dominant uncertainty factors were explored for high and low flows across different climate regions based on the Köppen–Geiger classification.

Change in the frequency (in %) of days under high (left)
and low (right) flow conditions for the period 2066–2099 relative
to 1972–2005, based on a multi-model ensemble (MME) experiment under
RCP8.5 from five GCMs and six GHMs:

To quantify high and low flow inter-annual variability, daily binary series
(zero or one) were extracted for every land grid cell: high flow days, HFD;
and low flows days, LFD. The series extraction uses daily varying threshold
curves obtained from the daily runoff series for the historical period
(1972–2005), which are then applied to the historical period and future
projections to identify days above (for HFD) or below thresholds (for LFD),
as in e.g. (for low flows)

We use indices to express the change in the frequency (in %) of:
future high (HFI) and low (LFI) flows. These indices are calculated as
follows: for each ensemble member HFI (LFI) is equal to the difference
between the frequency (in %) of high (low) flows days (100

PDFs of mean changes in high (HFI) and low (LFI) flows, annually and per season (DJF and JJA) for North, Tropics, and South latitude bands.

In this study, the uncertainty is reflected by the spread of the flow indices
due to the choice of GCM or GHM. To quantify the individual contribution of
GCMs and GHMs to total uncertainty, a 2-factor ANOVA was carried out on the
flow indices HFI and LFI for each grid cell. For this data set, model runs had
no replicates, therefore the ANOVA model considers one case per treatment

Summary of mean changes, signal-to-noise S2N, and sources of variance for high and low flows at the annual and seasonal (DJF, JJA) scale, and at the global and climate region scale. The first source of variance is shown in bold, the second one in italic font.

Annual mean changes and associated S2N across all GHMs and GCMs are shown
for HFI and LFI in Fig.

As Fig.

As Figs.

The results of the ANOVA across the 30 members of HFI and LFI are shown in
Fig.

To capture better the spatial distribution of the major sources of
uncertainty, ANOVA results are aggregated by climatic homogeneous regions
based on the climatological Köppen–Geiger classification. Scatterplots
in Fig.

Using six global hydrological models (GHMs) fed by five global climate models
(GCMs) under the RCP8.5 scenario, this study aimed to assess future high and
low flow changes globally by the 2080s, and to quantify the uncertainty
attributable to GHMs and GCMs. We decided to focus solely on the uncertainty
coming from GHMs and GCMs using as many ensemble members (from the ISI-MIP
project data set) as possible under the RCP8.5, in which change signals are
expected to be larger (i.e. emissions continue to rise leading to global
radiative forcing levels of 8.5

High and low flow changes in the future (2066–2099) relative to the
control period (1972–2005) exhibit a number of robust large-scale features.
Increases in high flow days were found at northern latitudes, with a strong
signal over eastern Canada, Scandinavia, northwestern Russia, and around the
Bering Sea (eastern Russia and Alaska). Increases in low flow days were found
in southern Europe, southwestern and central Latin America, southeastern USA,
more southerly parts of Central Africa, and southwestern Australia. These
patterns are largely consistent with the few other studies carried out on
runoff at the global scale with several GHM–GCM combinations: e.g. for high
flows

In this study we provide for the first time a comprehensive
assessment of both ends of the runoff spectrum at the same time using the
same data set globally. Moreover, we undertake a consistent partition of
uncertainty via ANOVA for both high and low flows, showing that GCMs provide
the largest uncertainty, although the GHM contribution can be substantial
in particular regions. The results from our ANOVA framework are consistent
with other global studies based on the ratios between the variances (or
standard deviations) of ensemble members averaged per type of model

At the regional level, the uncertainty partition enables us to delineate in
which climate region each factor (GCMs or GHMs) provides the largest
uncertainty at the annual and seasonal scales. Notably, for snow- and ice-dominated polar regions, and for arid zones, GHMs bring about the largest
portion of uncertainty, especially for low flows. This is likely to reflect
uncertainty in the way the hydrological storage–release processes can modify
the climate signal, particularly where these storage components are
relatively large or water residence times high – hence the importance of
considering several GHMs in studying changes in high and low flows. GCM
and GHM uncertainty shares are similar for HFI and LFI globally, although
the spatial patterns differ slightly (e.g. northeastern Russia,
southwestern Australia and Alaska are GCM driven in HFI, and GHM driven in
LFI). This could reflect different dominant processes for high and low flow
generation, with high flow events mainly driven by precipitation inputs or
snow/ice-melt (i.e. atmospheric-driven processes); whereas low flows event
develop over longer durations and are influenced more by land-surface
processes like evaporation, infiltration and storage, which are simulated by
the GHMs, each one with its own scheme and parametrization: e.g. for
evapotranspiration, Penman–Monteith, Hamon (

To put the current study in context and to provide suggestions for further studies, it is worth making a few considerations on the hydrological index extraction and clarify a few aspects of the uncertainty partition concerning the method and the data set we used.

ANOVA sum of squares (SS) of the two factors (GHM

The identification of high and low flows over long time series, and
particularly over climate projections, is nontrivial. As an illustration,

The model runs used in this study have no replicates; therefore, our ANOVA
partition set-up poses some limitations as it assumes that the factors do not
interact (no degrees of freedom are available for the estimation of the
experimental error). However, interactions between the factors may indeed be
present and, as pointed out by

As Fig.

Bias correction and

As mentioned in the Introduction, biome models have shown a larger spread
than GHMs without varying

Were biome models' shortcomings not present, their inclusion in our
ensemble would have required a modification of our uncertainty partition
strategy because the presence of outliers (likely introduced by biome models)
would limit our ANOVA model (whose assumptions include no or minimal presence
of outliers). For their distinct behaviour from the other GHMs, biome models
could be considered as a factor level in a two-way ANOVA framework with unequal
sample sizes

Finally, the focus of our uncertainty analysis was on GCMs and GHMs,
therefore the effect of emission scenarios (RCPs) was neglected. The few
studies that have considered this aspect hint at a relatively small role of
emission scenarios

To conclude, knowledge of the dominant source of uncertainty in
climate-to-hydrology signal is critical to modellers for improving modelling of
the terrestrial water cycle and to scientists for putting together targeted
multi-model ensembles for climate impact studies. In addition to GHMs and
GCMs, further work is needed to assess the degree to which internal
variability, bias correction, biome models (i.e. GHMs that simulate
vegetation dynamics and varying

The global hydrological models (GHMs) vary in the types of processes
represented and the parametrizations used. Table

Inter-annual dynamics in mean daily runoff (smoothed with a 7-day moving average)
relative to the period 1972–2005 for selected Köppen–Geiger region grid cells:
A, Tropical (

Global hydrological models' main characteristics (after

The schematic of extraction of binary series of days under high (HFD) and low
(LFD) flows is shown in Fig.

The percentiles are

Percentage of available land grid cells after masking per GHM–GCM model combination.

Schematic of HFD and LFD extraction (days under high and low
flows):

The choice of a fixed 5-day time window with interpolation was preferred
over the 30-day moving average used in e.g.

The index extraction described above is not applicable when the runoff is very low, i.e. when
long periods of the year have the same value. Therefore, with reference to
the control period (1972–2005), grid cells showing little or no seasonal
change in daily runoff were screened out (represented in grey on the
maps) using the 5-day percentiles series that form the threshold curves (i.e. one mask for HF and one for
LF) following these rules: (i) percentiles are equal to zero for more than one-third of the year (ii) standard
deviation of percentiles of first and/or second half-year equals zero (iii) annual percentiles

Mean changes for each ensemble member (GHM–GCM combination) are shown in
Figs.

As Fig.

As Fig.

To verify whether the ANOVA model assumptions hold, statistical tests were performed on the ANOVA residuals. For every unmasked grid cell, for both HFI and LFI, residuals were assessed as follows: we tested (i) normality with the Lilliefors test; and then, for grid cells for which the null hypothesis (that the residuals' vector comes from a distribution in the normal family) was not rejected, we tested (ii) constancy of variance with the Hartley test. Results for the annual and seasonal ANOVAs show that HFI has higher rates of residuals for which the hypotheses of normality and constancy of variance were rejected compared to the LFI. For the year, the percentages of unmasked grid cells not meeting the residuals requirements were: HFI 22 % not normal, 15 % no constant variance, for a total of 37 % globally; LFI 12 % not normal, 15 % no constant variance, for a total of 27 % globally. JJA and DJF have the lowest proportions of residuals' requirements not met for HFI and LFI respectively. We also applied the ANOVA on HFI and LFI transformed via the normal-score method (seeking normality of the data); this showed lower percentages of cells not satisfying the ANOVA assumptions of normality and constant variance (HFI: 7.5 and 11 %; and LFI: 7 and 12 % respectively) for a total of 19 % globally. It should be noted that the residuals' contribution to uncertainty tends to be lower for the transformed data (e.g. grid cells with residuals' dominated uncertainty decreased by 6 % for HFI and 1 % for LFI). Because the partition of uncertainty between GCMs and GHMs are similar from both ANOVA applied to raw and transformed data sets, and because the areas of nonsatisfaction of normality are not located where the residuals dominate the uncertainty, we discussed results obtained from the raw, nontransformed data.

We acknowledge the World Climate Research Programme's Working Group on
Coupled Modelling responsible for the Coupled Model Intercomparison Project
(CMIP); and we thank the CMIP climate and hydrology modelling groups for their
model outputs. For CMIP the US Department of Energy's Program for Climate
Model Diagnosis and Intercomparison provided coordinating support and led
development of software infrastructure in partnership with the Global
Organization for Earth System Science Portals. This work has been conducted
under the framework of the Inter-Sectoral Impact Model Intercomparison
Project (ISI-MIP). The ISI-MIP Fast Track project was funded by the German
Ministry of Education and Research, with project funding reference number
01LS1201A. To obtain access to data, please refer to the “data archive”
section of the project portal