# Changing the retention properties of catchments and their influence on runoff under climate change

Hui Yang, Shilong Piao, Chris Huntingford, Philippe Ciais, Yue Li, Tao Wang, Shushi Peng, Yuting Yang, Dawen Yang, Jinfeng Chang

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Hui Yang, Shilong Piao, Chris Huntingford, Philippe Ciais, Yue Li, et al. Changing the retention properties of catchments and their influence on runoff under climate change. Environmental Research Letters, 2018, 13, 10.1088/1748-9326/aadd32. insu-03721861

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LETTER • OPEN ACCESS

# Changing the retention properties of catchments and their influence on runoff under climate change

To cite this article: Hui Yang *et al* 2018 *Environ. Res. Lett.* **13** 094019

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

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LETTER

# Changing the retention properties of catchments and their influence on runoff under climate change

Hui Yang<fnref n="1" />, Shilong Piao<fnref n="1" />,<fnref n="2" />,<fnref n="6" />, Chris Huntingford<fnref n="3" />, Philippe Ciais<fnref n="4" />, Yue Li<fnref n="1" />, Tao Wang<fnref n="2" />, Shushi Peng<fnref n="1" />, Yuting Yang<fnref n="5" />, Dawen Yang<fnref n="3" /> and Jinfeng Chang<fnref n="4" />

E-mail: slpiao@pku.edu.cn

**Keywords:** runoff, water retention, climate change, atmospheric CO₂, hydrological cycle, drought risk

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

## Abstract

Many studies on drought consider precipitation and potential evapotranspiration (PET) impacts. However, catchment water retention is a factor affecting the interception of precipitation and slowing down runoff which also plays a critical role in determining the risks of hydrological drought. The Budyko framework links retention to the partitioning of precipitation into runoff or evapotranspiration. Applied worldwide, we demonstrate that retention changes are the dominant contribution to measured runoff changes in 21 of 33 major catchments. Similarly, assessing climate simulations for the historical period suggests that models substantially underestimate observed runoff changes due to unrepresented water management processes. Climate models show that water retention (without direct water management) generally decreases by the end of the 21st century, except in dry central Asia and northwestern China. Such decreases raise runoff, mainly driven by precipitation intensity increases (RCP4.5 scenario) and additionally by CO₂-induced stomata closure (RCP8.5). This mitigates runoff deficits (generally from raised PET under warming) by increasing global mean runoff from -2.77 mm yr⁻<fnref n="1" /> to +3.81 mm yr⁻<fnref n="1" /> (RCP4.5), and -6.98 mm yr⁻<fnref n="1" /> to +5.11 mm yr⁻<fnref n="1" /> (RCP8.5).

## 1. Introduction

There is compelling evidence that climate change has profound impacts on regional and global hydrological cycles (Huntington 2006, Piao et al 2007). Reconstructions of global river runoff show that one-third of the 200 largest rivers have significantly changed flows since the 1950s. More of these rivers experienced a runoff decrease rather than an increase, in an approximate ratio of 3:1 (Dai et al 2009). Due to the uncertainty of regional climate changes, however, no consistent conclusion is reached on the trend of the global mean runoff (Labat et al 2004, Milliman et al 2008,

Dai et al 2009). In contrast, a majority of Earth System Model (ESM) projections from the Coupled Model Intercomparison Project Phase 5 (CMIP5) show an increase in global runoff for the future. This is particularly true for the high latitudes and humid tropics, while models predict that rivers in most dry tropical regions may experience reduced runoff (Cisneros et al 2014, Prudhomme et al 2014). Understanding the mechanisms that control changes in contemporary runoff is essential for constraining climate model projections, alongside the identification of any missing or poorly represented processes in climate models. The strong predictive capability of

<footnote n="1">¹ Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, Peking University, Beijing 100871, People's Republic of China</footnote>

<footnote n="2">² Key Laboratory of Alpine Ecology and Biodiversity, Institute of Tibetan Plateau Research, Center for Excellence in Tibetan Earth Science, Chinese Academy of Sciences, Beijing 100085, People's Republic of China</footnote>

<footnote n="3">³ Centre for Ecology and Hydrology, Benson Lane, Wallingford OX10 8BB, United Kingdom</footnote>

<footnote n="4">⁴ Laboratoire des Sciences du Climat et de l'Environnement, CEA CNRS UVSQ, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="5">⁵ State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, People's Republic of China</footnote>

<footnote n="6">⁶ Author to whom any correspondence should be addressed.</footnote>
<figure><img src="image_4.png" /></figure>

models is needed to help with decision-making to ensure sustainable future water resource management (Oki and Kanae 2006, Hall et al 2014).

ESMs capture processes to high accuracy through fine resolution discretization of responses in both time and space. However, their complexity can make them difficult to fully understand. It can also prevent characterization of their broad hydrological behaviours. Here we tackle the complexity challenge of ESMs by applying a well-established, conceptualized, and ‘lumped parameter’ Budyko framework to describe river flow measurements, along with ESM flow estimates for now and projecting the future. We do this to generate a far better overall understanding of the factors that contribute to historical and future runoff changes.

Our first objective is to quantify the contributions of change in runoff from precipitation amount (*P*), potential evapotranspiration (PET), and land surface characteristics. Here PET is derived from the Penman-Monteith equation (Shuttleworth 1993). Changes in land surface characteristics in particular alter terrestrial water retention capability, which in turn strongly influences the partitioning of precipitation into evapotranspiration and runoff. We place an initial emphasis on determining the water retention capability for historical measurement-based runoff changes. To achieve this, we use the Budyko framework (Budyko 1958, 1974). Although established six decades ago, the Budyko framework is still successfully used to explain and predict the variability of the terrestrial hydrological cycle and the associated runoff (Roderick et al 2014, Zhou et al 2015, Zhang et al 2016). We then also map this framework on to CMIP5 model outputs, to better understand the factors that control ESM projections of future runoff changes. Some recent studies (Sheffield and Wood 2008, Greve et al 2014, Zhao and Dai 2015) project that future potential evapotranspiration increases will dominate over raised precipitation amounts, leading to enhanced soil water deficits known as agricultural drought for many regions. Those studies were based on drivers of changing moisture supply (*P*) and demand (PET) only. Here we explore the potential for hydrological drought, which is associated with runoff deficits. Hydrological drought differs from agricultural drought, being additionally strongly dependent on the specific properties of catchments to retain precipitation and partition it to evapotranspiration and runoff. High retention implies less water lost by runoff in rivers and more water recycled to the atmosphere by evapotranspiration.

Water retention capability in a catchment can be diagnosed by a parameter *n* in the Budyko framework. The value of *n* is a simple parameterization, yet it is known to be effective at capturing many complex features of catchment properties in a combined way. Such features include vegetation properties (cover, structure, rooting depth, and water use efficiency),

physical characteristics (soil water holding capacity, topography and stream density), and climate patterns (temporal and spatial distribution of rainfall) (Donohue et al 2007, Roderick and Farquhar 2011, Li et al 2013). For a given catchment, natural physical properties usually remain static over hundreds of years or more. However, vegetation transpiration is responsive to climate and CO₂ change through impacts on leaf area and leaf physiology (Ito and Inatomi 2012, Zhu et al 2016). In particular, CO₂-induced physiological changes (via stomatal closure) and structural changes (via vegetation cover) in vegetation are two key factors influencing *n*. Additionally, not only the amount but also the intensity and seasonality of rainfall are expected to change in a warmer climate (Chou et al 2013, Westra et al 2013). More intense rainfall events will raise runoff if infiltration capacity is exceeded (Xue and Gavin 2008). And changes in seasonal precipitation magnitude, timing and duration altering the timing of plant activities will also impact evaporative losses (Feng et al 2013). Lastly, changes in retention also occur through the direct management of catchments, for example by wetlands drainage, river channeling, damming and water withdrawals for irrigation and other purposes. The sum of these processes can be diagnosed by varying water retention, in historical data.

Our second objective is to make a direct comparison between observed and multi-models' simulated changes in runoff for the recent historical period. We propose here a new application of the Budyko framework to diagnose how changing environmental factors affect runoff in both measurements and ESMs estimates over recent decades, and thus facilitating comparison. This approach also illustrates whether there are any additional potential drivers of land surface water retention changes that are not presently included or properly parameterized in climate models.

Our third objective is to quantify the separate driving factors of future changes in water retention, as determined in the future scenario projections of CMIP5 ESMs. Recent modeling analyses demonstrate that future plant physiology responses to rising CO₂ will significantly increase runoff (Gedney et al 2006, Betts et al 2007, Swann et al 2016), overtaking and offsetting the influence of increased vegetation cover due to CO₂-induced plant fertilisation. The most recent study was based on a conceptual scenario of 1% per year cumulative increase in atmospheric CO₂ concentrations, reaching 1140 ppm after 140 years (Swann et al 2016). Here we extend that analysis, using CMIP5-based projections under different future scenarios of raised atmospheric greenhouse gas concentrations (known as Representative Concentration pathways, or RCPs).
<figure><img src="image_5.png" /></figure>

## 2. Methods

The Budyko framework (Budyko 1958, 1974) is based on verified empirical relationships between the evaporative index (ET/P) and the aridity index (PET/P). We use the measured runoff (Q, mm yr⁻¹), observation-based precipitation (P, mm yr⁻¹) and Penman-Monteith potential evapotranspiration (PET, mm yr⁻¹) to estimate parameter *n* of the Choudhury-Yang formulation of Budyko framework (Choudhury 1999, Yang et al 2008):

$$ \frac{ET}{P} = \frac{PET/P}{[1 + (PET/P)^n]^{1/n}} \quad (1) $$

Annual mean evapotranspiration (ET, mm yr⁻¹) is calculated as the measured precipitation *P* minus runoff *Q*. Together six *P* and two PET data result in 12 combinations of data for the 1981–2005 period. Datasets are described in the supplementary material. With the quantities of *P*, ET, and PET available, we estimate parameter *n* for each 5-year period of a 25-year period (i.e. 1981–2005). Next, we estimate trends in the *n*-parameter, *P*, *Q*, ET, and PET using a least-squares 2-parameter linear regression (Y = At + B, where *t* is time in years). We then multiply these fitted linear trends (i.e. A) with 25 years to estimate the full change during the period of 1981–2005. Furthermore, we separate the contributions of *P*, PET and *n*-parameter changes to the measured runoff changes for the same period 1981–2005 (see below).

For the model-based analysis, we instead use simulated *P*, ET, along with derived PET from ten individual CMIP5 models. We use these to create their ensemble mean, CMIP5-EM, to estimate the *n*-parameter. We again consider the contributions of the ESM-based precipitation amount, PET, and *n*-parameter on runoff changes for the recent historical past. This allows direct comparison against our analysis of measurements. Similarly, we separate the contributions of future changes in precipitation amount, PET and *n*-parameter to the projected changes in runoff, from 1981–2005 to 2076–2100.

We use the first-order Taylor expansion of Choudhury-Yang equation to quantify the direct contributions of precipitation amount, PET, and *n*-parameter changes to runoff changes. The change in ET is:

$$ \Delta ET = \frac{\partial ET}{\partial P} \Delta P + \frac{\partial ET}{\partial PET} \Delta PET + \frac{\partial ET}{\partial n} \Delta n \quad (2) $$

These partial differentials are then found by differentiation of equation (1), giving:

$$ \frac{\partial ET}{\partial P} = \frac{ET}{P} \left( \frac{PET^n}{P^n + PET^n} \right) \quad (3a) $$

$$ \frac{\partial ET}{\partial PET} = \frac{ET}{PET} \left( \frac{P^n}{P^n + PET^n} \right) \quad (3b) $$

$$ \frac{\partial ET}{\partial n} = \frac{ET}{n} \left( \frac{\ln(P^n + PET^n)}{n} - \frac{P^n \ln(P) + PET^n \ln(PET)}{P^n + PET^n} \right) \quad (3c) $$

Over the multi-year timescale, changes in water storage are small relative to the magnitude of fluxes (i.e. *P*, *Q*, *ET*) (Roderick and Farquhar 2011). Assuming steady state conditions of the water balance, changes in runoff can be separated into three components: precipitation amount (Δ*Q*<sub>P</sub>), potential evapotranspiration (Δ*Q*<sub>PET</sub>), and catchment properties (Δ*Q*<sub>n</sub>), which is written as:

$$ \Delta Q = \left(1 - \frac{\partial ET}{\partial P}\right) \Delta P - \frac{\partial ET}{\partial PET} \Delta PET - \frac{\partial ET}{\partial n} \Delta n \\ \equiv \Delta Q_P + \Delta Q_{PET} + \Delta Q_n \quad (4) $$

A note on terminology is made at this point as the name ‘retention’ has the potential to be confused with storage. The changes of ‘retention’ are reflected by variations in the *n* parameter in the Budyko framework. The raised retention over short timescales (i.e. annual) might slow down the transition of rainfall, making it more amenable to evaporation either naturally or via irrigation. Any remaining water is passed to river systems and hence in general the assumption of negligible storage change is reasonable, especially when averaging at the long-term timescales (i.e. multi-year period). For retention changes, however, although short-term, their effects are present throughout the year. Hence at the longer timescales, retention does impact on the overall partitioning of rainfall.

In addition, we investigate the dominant factors driving future changes in *n*-parameter itself. Three ESM outputs are analyzed in relation to Δ*n*: vegetation structure measured by changes in leaf area index (ΔLAI); plant water use measured by changes in transpiration per leaf area (Δ[Tr/LAI]); and the daily precipitation intensity (ΔSDII; Hartmann et al 2013). Because changes in *n*-parameter are spatially correlated (according to the Moran's I index), that is, *n*-parameter changes over one grid cell not only depend on the local explanatory variable but also *n*-parameter changes over the adjacent grid cells. Thus, we apply a conditional autoregressive (CAR) model (a form of spatial lag model) to identify the dominant driving factors for Δ*n*. This CAR model is used to remove any confounding effects of spatial autocorrelations between grid cells. The dependent variable is Δ*n* and independent variables are ΔLAI, Δ[Tr/LAI], ΔSDII:

$$ \Delta n = a\Delta LAI + b\Delta[Tr/LAI] + c\Delta SDII + \varepsilon \\ \equiv \Delta n_{LAI} + \Delta n_{[Tr/LAI]} + \Delta n_{SDII} + \varepsilon \quad (5) $$

We achieve this by spatial regression for twenty-five 1° × 1° grid cells within each spatial window of 5° × 5°. This gives the local regression coefficients *a*,
<figure><img src="image_6.png" /><figcaption>a. Changes in water retention capability (Δn, 1981-2005)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>b. Budyko-estimated runoff change (mm yr⁻¹)

Y = 0.98X + 4.38
R² = 0.95
RMSE = 10.16

Observed runoff change (mm yr⁻¹)</figcaption></figure>

**Figure 1.** Historical retention changes and historical runoff changes due to the three contributions of ΔP, ΔPET, and Δn. (a) A map of 33 major basins (coloured, non-grey) and their water retention capability changes, from 1981 to 2005, as characterised by changes in parameter *n* of the Budyko framework. Grey land areas are omitted from the analysis because insufficient runoff observations are available. (b) Comparison of runoff change (ΔQ) measured at gauging stations versus ΔQ estimated by the Budyko framework, with change in precipitation amount and PET (orange) only, or with all three factors of change (i.e. precipitation amount, PET, and additionally water retention capability; blue).

b, and c for each 5° × 5° spatial window. Then, the factor (Δn<sub>LAI</sub>, Δn<sub>[Tr/LAI]</sub> or Δn<sub>SDII</sub>) whose absolute value makes the largest contribution to changes in water retention capability, Δn, is regarded as the dominant driving factor.

## 3. Results

### 3.1. Historical changes in water retention capability

The analytical form of Choudhury-Yang formulation of Budyko framework (equation (1)) used here contains a parameter *n* reflecting catchment water retention capability. Figure 1(a) shows the change in water retention capability (Δ*n*) for 33 river basins during the period of 1981–2005. During this period, wet large catchments (i.e. Congo, Amazon, Mississippi, Yukon, Mackenzie, Volga and Yenisey basins) generally show decreases in *n*, indicating water retention capability in these basins has declined. That is the fraction of *P* lost by evapotranspiration decreased and instead runoff increased. In contrast, the values of *n* are found to increase dramatically in dry basins such as the Murray, Colorado, Yellow River and three river catchments in the southern Africa (figures 1(a) and S1 is available online at stacks.iop.org/ERL/13/094019/mmedia).

Despite the simplicity of the Budyko framework, the observed magnitude and spatial variability of runoff changes can be well reproduced by this theoretical framework. Using measurement-based values of *P*, PET along with our fitted time dependent *n* values to estimate runoff, we obtain a small RMSE of 10.2 mm yr⁻¹ (figure 1(b), blue dots) against annual runoff measurements. This good fit of the sum of Budyko-estimated components (i.e. Δ*Q*<sub>P</sub> + Δ*Q*<sub>PET</sub> + Δ*Q*<sub>n</sub>; equations (3a)–(3c)) against measured runoff is in part expected, as the components use the fitted *n* values. However, such linearization into the separate

components does allow an assessment of the individual contributions to total changes in runoff. If we consider ΔQ<sub>P</sub> + ΔQ<sub>PET</sub> only, we just capture 38% of spatial variability in observational changes in runoff (RMSE = 30.6 mm yr<sup>-1</sup>; figure 1(b), orange dots). This illustrates the impact on runoff projections of neglecting changes in parameter-*n*, which some earlier studies have done. That is, we verify that this new part, ΔQ<sub>n</sub>, is an important contributor to recent runoff changes. We analyze this further by a first-order linear Taylor series expansion of equation (1) to separate the direct impacts of *P*, PET and *n* changes on runoff changes in the recent past (ΔQ<sub>P</sub>, ΔQ<sub>PET</sub> and ΔQ<sub>n</sub> respectively). Figure 2 illustrates that 11 out of 33 catchments (e.g. Fitzroy, Congo, Mississippi, St Lawrence, Rhine) experienced decreases in precipitation amount or increases in PET over the period 1981–2005, both acting to reduce runoff. However, the component data shown in figure 2 also illustrate that for these catchments, changes in water retention had the opposite effect to increase runoff markedly, making overall runoff changes positive (see also table S1). Figure 2 thus shows that the effect of decreased *n* is in general to mitigate the *P*- or PET-induced reduction in river runoff. Our result confirms the dominant contribution of water retention capability changes on runoff changes in 21 out of 33 major catchments (table S1). This also explains the large difference that can occur when this effect is prevented from changing in flow estimates (figure 1(b)).

The inferred decreases in water retention capability may be partly related to plant physiological stomatal response to rising atmospheric CO₂ concentration and vapour pressure deficit, both leading to a higher fraction of *P* converted to runoff. In one study, there is strong detectable evidence that rising CO₂ concentration leads to reduced opening of stomata, which in turn is associated with lower leaf-level transpiration and higher runoff (Gedney et al 2006). In addition, land use change
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 2.** The contributions of the individual changes in precipitation amount (ΔQ<sub>P</sub>; blue), PET (ΔQ<sub>PET</sub>; red), and water retention capability (ΔQ<sub>n</sub>; yellow) to overall changes in runoff. The observed runoff changes measured at gauging stations are marked as white dots. The basins are sorted (as named on horizontal axis) according to the latitudes of the gauge stations closest to the estuary, from 40 °S to 90 °N. The location of each basin is indicated in figure S1. Error bars in (b) and (c) represent the ±1 standard deviation of estimates from 12 data combinations.</figcaption></figure>

with the replacement of forest by short vegetation, which
has less transpiration ability, may also explain some run-
off increases diagnosed by the decrease of *n*. This may be
expected to apply in the Congo Basin, where extensive
deforestation has occurred (Duveiller *et al* 2008). In con-
trast to the tropical regions, decreased runoff in the tem-
perate catchments such as the Yellow River may be partly
attributed to recent afforestation, reflected by an increase
of *n*. This will induce an increase in evapotranspiration,
and in rainfall interception loss (Yang *et al* 2009, Feng
*et al* 2016). Additionally, direct physical engineering of
the terrestrial hydrological system (e.g. dam construc-
tion, reservoir building and river channeling) and agri-
cultural management (e.g. irrigation and terraces) also
lead to a significant change in *n*, and thus alter runoff
(Jaramillo and Destouni 2015). Such water management
can act to either decrease *n* and facilitate runoff (wetland
suppression, river channeling), or to increase *n* and
reduce runoff (evaporation from dams, and re-use of
stream water for irrigation).

**3.2. Comparison of model versus measurement for**
**historical period**

Here we apply the same Budyko-based attribution of
runoff changes to P, PET and n changes. These are
simulated by ten state-of-the-art ESMs from the
CMIP5 database (Methods, section S3). The estimate
of changes to historical runoff amounts, and using the
Ensemble Mean of these CMIP5 models (CMIP5-
EM), are shown in figure 3(a). Such estimates based on
CMIP5-EM in general project lower values of runoff
change (i.e ΔQ). We compare differences in the Taylor
series-based individual components ΔQp, ΔQPET and
ΔQn value, and between CMIP5-EM and measure-
ments in figures 3(b)–(d). Values also in table 1
(standard deviations across catchments). Magnitudes
of ΔQp for CMIP5-EM are in general smaller than
those from measurements (figure 3(b)). This arises
in part due to ESMs differing markedly from

observations for precipitation estimates. This even
includes the signs of these changes in some regions
(Knutti and Sedláček 2012, Flato et al 2013), which will
balance to suppress mean CMIP5-EM estimates.
Other suppression of changes in CMIP5-EM is also
due to decadal timescale precipitation fluctuations,
which reflects natural variability caused by the chaotic
nature of large-scale atmospheric circulations and
unforced variance in the coupled land-ocean-atmos-
phere system (Deser et al 2012). Random internal
variations in PET are smaller, and there is better
agreement for ΔQPET between model and measure-
ment-based values (figure 3(c)).

For runoff changes attributable to retention,
figure 3(d) shows a severe underestimation of ΔQn
change magnitudes (both positive and negative) by
ESMs, compared to measurements during the histor-
ical period. We conjecture that in the instances where
ESMs fail to capture the observed decreases in ΔQn, it
is a consequence of missing components of physical
engineering and water management in the models.
This is despite most ESMs having some representation
of land use change. Besides physical changes, these
alterations to the land surface may increase ET (for
instance re-use of stream water in irrigation water and
dam evaporation) which will also decrease ΔQn i.e.
raise retention. In instances where ΔQn increases in
data, but not in models (figure 2(d)), then this may be
due to the omissions of channeling of small streams,
wetland and riparian area suppression, and of some
land management practices (e.g. no crop cover in win-
ter). All these actions may increase runoff, i.e. raise
ΔQn increase by lowering retention.

We formalize the impact of these missing ΔQn
components in a simple statistic. We calculate an
overall standard deviation across catchments (SD;
mm yr⁻¹) with data values from table 1 as σD =
√σ²ΔQₚ + σ²ΔQₚET + σ²ΔQn (this statistic assumes
independence between components in the Budyko
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 3.** Comparisons between measurements and model outputs of runoff features for the historical period. (a) Similar to figure 1(c), except that the water flux components (i.e. runoff, precipitation and ET) are estimated by the model ensemble mean (CMIP5-EM). The observed runoff changes measured at gauging stations are marked as white dots, hence identical values to figure 1(c). Catchment names as labelled. (b)–(d) Model and measurement-based separated contributions of (b) precipitation amount ($\Delta Q_p$), (c) PET ($\Delta Q_{PET}$), and (d) water retention capability ($\Delta Q_n$) to historical changes in runoff, from 1981 to 2005. Horizontal error bars represent one standard deviation of the ten CMIP5 individual ESM estimates. Vertical error bars represent the ±1 standard deviation of estimates from 12 data combinations.</figcaption></figure>

<table><caption>**Table 1.** Standard deviations (SDs) of $\Delta Q_p$, $\Delta Q_{PET}$, $\Delta Q_n$ across catchments. The individual catchment values are based on the changes in $P$, PET and $n$ from both measurements and model ensemble mean (CMIP5-EM). The ‘Data’ values below are the standard deviations of the histogram columns in figure 2, for the three quantities. The ‘CMIP5-EM’ values are the standard deviations of the histogram columns in figure 4(a), again for the three quantities.</caption><thead><tr><th>SD (mm yr<sup>-1</sup>)</th><th>ΔQ<sub>p</sub></th><th>ΔQ<sub>PET</sub></th><th>ΔQ<sub>n</sub></th></tr></thead><tbody><tr><td>Data</td><td>25.2</td><td>13.6</td><td>33.9</td></tr><tr><td>CMIP5-EM</td><td>21.0</td><td>11.7</td><td>9.3</td></tr></tbody></table>

framework). In order to estimate the effect of model underestimation of inter-catchment variability in ‘n-induced’ runoff changes, we then recalculate an overall SD statistic, but instead replace $\Delta Q_n$ with the CMIP5-EM based value (replacing 33.9 with 9.3; table 1). This then gives a new overall SD (i.e. $\sigma_{D,n}$). The two values allow us to represent, as a percentage, the effect on runoff of missing water managements processes on modelled water retention changes, returning a value of underestimation as: $S = 100 \times (1 - \sigma_{D,n}/\sigma_D) = 32\%$. This value quantifies the extent to which CMIP5 models lack the representation of physical engineering processes and water

management impacts on observed spread of runoff changes observed across catchments. This is a severe limitation to the proper evaluation of models with observed runoff changes, except in catchments with minimum human intervention.

### 3.3. Future projections

Although there are noted deficiencies of ESMs depiction of retention, compared to measurements, due to their non-representation of water management processes, we can still explore future water retention changes within the CMIP5 model ensemble. These changes in $n$ reflect rising atmospheric $CO_2$ concentrations, changing imposed climate, varying vegetation distribution and its water use, along with land use change. We again do this via analysis of the ensemble mean of the CMIP5 models (CMIP5-EM), but here to analyze future runoff changes (we additionally provide individual model estimates in the SI). Figure 4(a) shows the estimated annual runoff change from CMIP5-EM by the end of this century under the RCP4.5 scenario, relative to the recent historical past (1981–2005). The increase in runoff mainly occurs in the Arctic region, northeastern China, South Asia, and North Africa, while the Amazon region, western and southern Africa, the United States, southern Europe,
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 4.** The contributions of precipitation amount, PET, and *n* to future runoff changes. Spatial patterns of (a) future runoff changes (ΔQ) projected by the model ensemble mean (CMIP5-EM) for the period 2076–2100 relative to 1981–2005 and under RCP4.5 scenario; (b) future runoff change estimated by the Budyko framework with the change in precipitation amount, PET, and water retention capability (ΔQ<sub>P</sub> + ΔQ<sub>PET</sub> + ΔQ<sub>n</sub>), fitted to CMIP5-EM, same period and scenario. Separated contributions of these components to runoff changes, based on Budyko framework, and shown as (c) precipitation amount (ΔQ<sub>P</sub>), (d) PET (ΔQ<sub>PET</sub>), (e) both precipitation amount and PET (ΔQ<sub>P</sub> + ΔQ<sub>PET</sub>), and (f) water retention capability (ΔQ<sub>n</sub>). Dots indicate where more than 80% of individual climate models show agreement on the direction of runoff changes (also shown in the supplementary information, figure S3). The grey areas have insufficient data.</figcaption></figure>

and central Asia experience decreased runoff (by
-20 mm yr⁻¹ or more; figure 4(a)). Similar patterns
for runoff changes occur under the more intensive
RCP8.5 scenario across most regions (figure S2(a)). As
for the analysis of historical measurements, the
heterogeneity in future runoff change is successfully
captured by the Budyko framework. The Taylor series
expansion of the Choudhury-Yang equation allows
the separation of runoff changes into precipitation
amount, PET, and water retention capability driven
components. These sum up to the total future runoff
changes (similarities of figures 4(a) versus 4(b), and
also S2(a) versus S2(b)).

In figure 4(c), the future precipitation amount
generally increases, leading to an increase in runoff.
This is for most regions (more than 65.4% of land sur-
face). Decreases in P-induced runoff only can be found
in Central America, southeastern Amazon, southern

Europe, Australia and southern Africa. Driven by ris-
ing temperatures, PET consistently increases across all
the land surface (Scheff and Frierson 2014), resulting
in a negative runoff change component (figure 4(d)).
This cancels out the upward effect on runoff of increa-
ses in the precipitation amount in temperate North
America, southern China, western Africa, and the
northwestern Amazon region (figure 4(e)). For reten-
tion changes, represented in the 'n-parameter', we find
in general reduced values of that parameter, contribut-
ing to increased runoff (i.e. ΔQn) values. This n-
induced increase is projected over much of the globe,
particularly in most parts of South America, large parts
of central and southern Africa, the eastern part of
North America, southeast China, and eastern Siberia
(figure 4(f)). In these regions, the increase in runoff
associated with decreased n is generally larger than
+20 mm yr-1 (figure 4(f)). However, there are regions
<figure><img src="image_14.png" /></figure>

a Change in water retention capability, RCP4.5

<figure><img src="image_15.png" /></figure>

b Change in water retention capability, RCP8.5

<figure><img src="image_16.png" /></figure>

c Spatial distribution of dominant factors, RCP4.5

<figure><img src="image_17.png" /></figure>

d Spatial distribution of dominant factors, RCP8.5

<figure><img src="image_18.png" /></figure>

**Figure 5.** Future changes in water retention $\Delta n$ and its dominant factors. (a) Spatial pattern of the changes in water retention capability ($\Delta n$) for the period 2076–2100 relative to 1981–2005, based on projections by the model ensemble mean (CMIP5-EM) and under RCP4.5 scenario. Dots indicate where more than 80% of individual climate models show agreement on the direction of change in water retention capability (also shown in the supplementary information, figure S5). (b) Same as (a) but under RCP8.5 scenario. (c) Spatial pattern of dominant driving factors of the change in water retention capability from the CMIP5-EM under RCP4.5 scenario. The driving factors considered are leaf area index ($\Delta$LAI), the transpiration per unit leaf area ($\Delta$[Tr/LAI]) and precipitation intensity ($\Delta$SDII). (d) Same as (c) but under RCP8.5 scenario. In (c) and (d), different colours differentiate whether the dominant driver is contributing to either a positive or negative change in quantity $n$.

where *n*-driven future runoff change is negative, including dry central Asia and northwest China. Critically, over much of the globe, future projections show that the changes in $\Delta Q_n$ are of similar order of magnitude to $\Delta Q_p$ and $\Delta Q_{PET}$ (figure 4). When assessing individual models, rather than the ensemble mean, we find that the inter-model contributions from changes in PET and water retention capability on runoff show relatively high consistency. However, models disagree on the contributions of precipitation amount (figures S3 and S4).

Overall the CMIP5-EM shows that the area projected to experience decreasing runoff under RCP4.5 scenario, when only considering the effects of precipitation amount and PET, is 47.6% of the land surface. However, when the additional effect of water retention change is included, i.e. with all factors changing, the area experiencing decreasing runoff reduces to 41.3% of land surface. At the global scale, mean runoff change associated only with changes in precipitation amount and PET is a decrease of -2.77 mm yr⁻¹. This is of opposite sign to the runoff change when all factors of change are included, which then gives an increase of +3.81 mm yr⁻¹. RCP8.5 scenario also shows a similar result. Under that scenario, the estimated global runoff associated with changes in precipitation amount and PET only is a decrease by -6.98 mm yr⁻¹. When all factors including water

retention changes are considered, the estimated global runoff is an increase of +5.11 mm yr⁻¹.

### 3.4. Drivers of future change in water retention

The importance of retention changes in projecting runoff has been established. We now identify and explore a range of complex processes in ESMs that contribute to driving estimated future retention changes. We plot changes in *n* (i.e. $\Delta n$) during the 21st century for the RCP4.5 scenario (figure 5(a)). The $\Delta n$ values exhibit substantial spatial heterogeneity of change, and as expected have similarities to $\Delta Q_n$ of figure 4(f). The increases in *n* associated with reduced $\Delta Q_n$ are found in some dry regions, while decreases in *n* appear in many other regions. The latter (i.e. lower retention *n*) dominates, covering more than 65.4% of land surface. These regions include wet tropical catchments, eastern North America, high-latitude Eurasia, and southeastern China. Similar spatial patterns of change in *n* are also found under RCP8.5 scenario (figure 5(b)). When forced with the more intensive warming scenario (i.e. RCP8.5), as expected the magnitude of $\Delta n$ is larger compared to RCP4.5 scenario (figure 5(a)). Although there is general agreement, $\Delta n$ diagnosed from individual ESMs shows a strong divergence in the high northern latitudes under RCP8.5 scenario (figure S6).
<figure><img src="image_19.png" /></figure>

Three ESM outputs are analyzed in relation to $\Delta n$: changes in leaf area index ($\Delta$LAI); changes in transpiration per leaf area ($\Delta$[Tr/LAI]); and changes in the daily intensity index $\Delta$SDII (Hartmann et al. 2013). SDII is designed to capture the situation where rainfall intensity is such that it exceeds infiltration capacity, increasing runoff. We find that in the dry mid-latitude regions, the water retention increases ($\Delta n > 0$) are mainly due to increased LAI for both RCP4.5 and RCP8.5 scenario (figures 5(c) and (d)). Higher atmospheric CO$_2$ levels lead to increased photosynthetic rate, thereby increased LAI, which raises transpiration and reduces runoff. A more complex situation emerges where $\Delta n$ is negative, causing raised runoff. In figure 5(c), negative $\Delta n$ change is mostly driven by precipitation intensity increases under RCP4.5 scenario (see also figure S8(d)). However, decreases in [Tr/LAI] instead dominate $n$ decreases under RCP8.5 scenario (figure 5(d)), particularly in tropical regions, northeast China, and part of the central North America (see also figure S8(g)). This finding of a switch in dominant driver between emission scenarios for year 2100 also exists in many individual climate models (figures S9 and S10).

We further consider the climate scenario dependence for the dominant driving factors of $\Delta n$ between RCP4.5 and RCP8.5 (figures 5(c) versus 5(d); figures S9 versus S10). It was previously reported (e.g. Gedney et al. 2006, Milly and Dunne 2016, Swann et al. 2016) that the reduction of stomata opening due to elevated atmospheric CO$_2$ concentration or changing climate (e.g. increased vapor pressure deficit) will impact transpiration and thereby alter runoff. However, our finding suggests that future precipitation intensity changes, rather than vegetation, play a major role in changing regional and global runoff over most land regions in the RCP4.5 (figure S4(c)). Based on both theoretical (O’Gorman and Schneider 2009) and modeling studies (Donat et al. 2016), the intensity of precipitation, coincident with global warming, is expected to rise (figure S8). More intense precipitation in arid and semiarid environments where the precipitation rate is higher than the infiltration rate of the soil would result in higher runoff (Dunne et al. 1991). Thus, for the same amount of annual precipitation, fewer but more heavy rainfall events will produce more runoff than many lighter ones, and result in parameter-$n$ decreases. Under the RCP8.5 scenario, and consistent with previous results, parameter-$n$ decreases are dominated by decreases in [Tr/LAI] (figure 5(d)), and this too will result in more water for runoff. Thus, high accuracy estimates of the expected increase in daily precipitation intensity and accurate parameterization of stomata closure in response to elevated CO$_2$ are important for ESM modeling community to achieve.

Furthermore, it is worth noting that the characteristics of rainfall seasonality including its magnitude, timing and duration components might affect plant

activities and runoff generations, altering the local water retention capability of watersheds (Roderick and Farquhar 2011). Yet its influences are not explicitly quantified in this study. For example, an asymmetry where a decrease in $P$ in the dry spell could lead to a small decrease in $Q$, while an increase in $P$ in the wet spell could lead to a larger increase in $Q$. This might be of particular interest given evidence that in a warming world, wet seasons are expected to get wetter (partly due to increased water holding capacity in the atmosphere), whilst for drier regions, are projected to dry seasons get drier (Chou et al. 2013).

## 4. Discussion and conclusion

The Budyko framework was proposed six decades ago, but new datasets have motivated a recent use of this integrated, elegant and intuitive framework to analyze changes in the land hydrological cycle (e.g. Berghuijs et al. 2014, Greve et al. 2014, Carmona et al. 2016). The Budyko framework distills complex systems to a key effective lumped parameter, which helps to understand and quantify measurements and model features. Large-scale effective parameters have prominent roles in other aspects of climate research, for instance overall equilibrium climate sensitivity that is routinely derived for different ESMs (Bindoff et al. 2013). Here we combine ESM diagnostics with data, and via the Budyko framework allow summary-level understanding of ESM predictions of runoff changes for historical and future periods, and their performance against river flow measurements. This is particularly difficult without utilizing a summary framework such as that of Budyko, because ESMs have different structures preventing comparison on a per-parameter, per-equation or per-grid basis. Our study contributes to four related and linked advances, which broadly follow our four main diagrams.

First, we demonstrate that the Budyko framework does perform well in modelling river flow across 33 spatially-diverse catchments. In particular, our catchment dependent and time dependent parameter $n$ allows rigorous isolation of the water retention influence on runoff. We find that the effect of water retention change on historical runoff changes is large and must be included in any assessment of river flow changes.

Second, we also compare the differences in three components of runoff changes in recent decades, between ESM estimates and observed data. Critically, we find that the water retention changes in the CMIP5 ensemble are too small for the historical period. This highlights the importance of direct human intervention impacts on water retention, which in turn strongly affects runoff. Thus, there is a need for inclusion within ESMs of direct physical engineering and water resource management, to enable comparison
<figure><img src="image_20.png" /></figure>

against any parallel changes caused by any imposed
climate change.

Third, when the Budyko framework is applied to
Earth system models future simulations, the retention
component is found to change in such a way to make
projected runoff higher than it would be if it was only
driven by *P* and PET. Earlier studies (e.g. Feng and
Fu 2013, Scheff and Frierson 2015, Huang *et al* 2016),
based on drought metrics characterized only by pre-
cipitation amount and PET. However, without includ-
ing retention changes, these assessments may not
therefore characterize in full the risks of hydrological
drought changes. In general, ignoring retention chan-
ges will lead to an over-estimation of future hydro-
logical drought severity.

Fourth, we investigate the separate drivers of
future change in water retention that are included,
implicitly, in ESMs. The physiological effect of
CO₂-induced stomatal closure (via Tr/LAI), rainfall
intensity changes (via SDII) and vegetation cover
changes (via LAI) all influence retention. Critically, we
find that by the end of the 21st century, the main cause
of retention decreases is different between the RCP8.5
and RCP4.5 scenarios. Under RCP8.5, the stomata
closure effect dominates, whereas for RCP4.5 it is the
increased rainfall intensity.

Correctly, full earth system models remain the
main and appropriate tool to perform high-resolution
estimates of climate change impacts. The Budyko fra-
mework and its proposed enhancement (Taylor series
development) is robust enough to better understand
such climate model projections of large-scale river
runoff. Our overarching finding is that when compar-
ing ESM outputs against historical measurements,
accurate representation of land surface water retention
effects is needed for reliable runoff estimates. These
effects require more accurate estimates of future rain-
fall features within ESMs. Currently, ESM estimates of
rainfall changes vary substantially between models
(Knutti and Sedláček 2012). Finally, although also a
somewhat intuitive finding, our analysis illustrates the
importance of accounting for direct human activity
impacts on runoff in ESMs. This includes changes to
irrigation, any new dam construction or small streams
channeling, and the suppression of wetland and ripar-
ian area. Our analysis has enabled us to compare much
more directly impacts on runoff through changes
imposed by local river management, with those due to
large-scale modelled climate change in ESMs as atmo-
spheric greenhouse gases rise.

Acknowledgements

This study was supported by the National Natural
Science Foundation of China (41530528), 111 project
(B14001), and National Youth Top-notch Talent
Support Program in China. CH acknowledges the
NERC Science Budget. PC acknowledges support

from the European Research Council Synergy
grant ERC-2013-SyG-610028 IMBALANCE-P. We
acknowledge the World Climate Research Pro-
gramme's Working Group on Coupled Modelling,
which is responsible for CMIP, and we thank the
climate modelling groups for producing and making
available their model output.

ORCID iDs

Hui Yang https://orcid.org/0000-0001-6454-8954

Shilong Piao https://orcid.org/0000-0001-8057-2292

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

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