Many natural and social phenomena depend on river flow regimes
that are being altered by global change. Understanding the mechanisms behind
such alterations is crucial for predicting river flow regimes in a changing
environment. Here we introduce a novel physical interpretation of the scaling
properties of river flows and show that it leads to a parsimonious
characterization of the flow regime of any river basin. This allows river basins to be classified as regulated or unregulated, and to identify a critical
threshold between these states. We applied this framework to the Amazon river
basin and found both states among its main tributaries. Then we introduce the
“forest reservoir” hypothesis to describe the natural capacity of river
basins to regulate river flows through land–atmosphere interactions (mainly
precipitation recycling) that depend strongly on the presence of forests. A
critical implication is that forest loss can force the Amazonian river basins
from regulated to unregulated states. Our results provide theoretical and
applied foundations for predicting hydrological impacts of global change,
including the detection of early-warning signals for critical transitions in
river basins.
Introduction
Mean and extreme river flows are global-change-sensitive components of river
flow regimes that are determinant for many ecological and societal processes
. Landscape and climate
alterations foreshadow shifts in precipitation and river flow regimes
.
The conversion of precipitation into river flow through the accumulation of runoff depends on a suite of complex
and heterogeneous biophysical processes and attributes of river basins, on
different scales . This
conversion results in spatial scaling properties – properties that do not
vary within a wide range of scales – observable through river flow records
. The existence of scaling
properties in river basins implies a power law correlation between the system
response (river flows) and a scale parameter (typically the drainage
area) . Power laws go beyond statistical fitting;
they indicate scale invariance as a fundamental emergent property arising
from the self-organization of many complex systems in nature
. Scaling
properties are common to river basins with very different environmental
conditions . This suggests
that the spatial scaling properties of river flows have a common, mechanistic
origin, which has been related to conservation principles and the fractal
nature of river networks .
The values of the scaling parameters – the scaling exponent and coefficient
of a given power law – are neither universal nor static features of river
basins, because they depend on runoff production processes that are spatially
heterogeneous and sensitive to
both climate and land cover change . Understanding the
mechanisms behind the scaling parameters in river basins, as well as their
sensitivity to global change, is a crucial step for enabling the use of the
scaling theory in hydrological prediction in ungauged basinsthe “PUB problem”; and, more generally, in
a changing environment where the processes governing the hydrological cycle
are not static the “Panta Rhei–Everything Flows”
debate;. We address this problem by linking the
scaling properties of river flows to the capacity of river basins for
regulating their hydrological response.
Scaling properties reveal river flow regulation
The scaling properties of river flows are evidenced through power laws of the
form EQik=αiSβi,
where E[Qik] is the kth-order statistical moment of the probability
distribution function of river flows, S is a scale parameter, and
αi and βi are the scaling coefficient and exponent,
respectively. Qi can be floods (i=F), mean flows (i=M) or low flows
(i=L). The scaling parameters (αi and βi) vary among river
basins and flow types and are always positive because river flows cannot be
negative and increase downstream as a consequence of mass continuity.
The state of a river basin can be classified as regulated or
unregulated depending on its river flow regime, which determines how
the scaling exponents for floods (βF), mean flows (βM) and low
flows (βL) are organized. Regulation is defined here as the capacity
of river basins to attenuate the amplitude of the river flow regime, that is,
to reduce the difference between floods and low flows. A river basin is
regulated if βL>βM>βF or unregulated if
βL<βM<βF. A metric of the amplitude of the extremes is the difference
(ΔQ) between long-term average floods (E[QF]) and low
flows (E[QL]), relative to mean flows (E[QM]):
ΔQ=EQF-EQLEQM=αFSβF-αLSβLαMSβM.
Our distinction between regulated and unregulated states is consistent with
the definition of regulation in artificial reservoirs, whereby a reservoir
regulates river flows by either mitigating floods through water retention or
enhancing low flows through water release . The
amplitude of the extremes is dampened in the regulated state (ΔQ is reduced
as S increases) or amplified in the unregulated state (ΔQ is
increased as S increases), as a consequence of how river flows grow
downstream in a river basin. These contrasting behaviours are reflected by
the scaling exponents through the spatial rate of change
∂ΔQ∂S=αFSβFβF-βM+αLSβLβM-βLαMSβM+13<0,ifβL>βM>βF(regulatedstate)=0,ifβL=βM=βF(criticalthreshold)>0,ifβL<βM<βF(unregulatedstate).
The difference between the regulated and unregulated states is evidenced by
the theoretical limit
limS→∞ΔQ=40,ifβL>βM>βF(regulatedstate)αF-αL/αM(apositiveconstant),ifβL=βM=βF(criticalthreshold)∞,ifβL<βM<βF(unregulatedstate).
In the regulated state, the flow regime tends to the limit of complete
regulation (constant flow: E[QF]=E[QM]=E[QL]), owing to the capacity of
the river basin to dampen extremes (ΔQ→ 0). The opposite
occurs in the unregulated state: the extremes are amplified
(ΔQ→∞) and, hence, E[QF]≫E[QM]≫E[QL]. Therefore, in a
given river basin, reversing the direction of the inequality from
βL>βM>βF to
βL<βM<βF indicates a shift between
the regulated and unregulated states, with βL=βM=βF
being a critical threshold. This agrees with the definition of a tipping
point as “the corresponding critical point – in forcing and a
feature of the system – at which the future state of the system is
qualitatively altered” . The difference
(βL-βF) denotes a metric of the regulation level that indicates
the proximity to the critical threshold in a river basin. Everything else
being equal, a reduction in βL indicates an increased severity of low
flows, whereas an increase in βF indicates an increase in flood severity.
The Amazon basin and its major sub-basins. The map shows the long-term
leaf area index averaged over the period 1981–2012, boundaries and drainage
network of the sub-basins, and river flow gauges provided by the SO-HYBAM project
(http://www.ore-hybam.org). Detailed information about the gauges is in
Table S1. Tables show the parameters of power laws for mean and extreme river
flows in each basin.
The occurrence of regulated or unregulated states depends on the combined
effect of dampening and amplification processes operating
within a river basin. Both processes can coexist in a regulated river basin
because higher regulation implies both reducing floods through a dampening
effect produced by water retention within the basin, and increasing low flows
through an amplification effect resulting from the release of water stored
within the basin. The occurrence of either of these effects is described by
how the rate of change
∂EQik∂S=αiβiSβi-1
grows with increasing scale. If ∂E[Qik]/dS decreases with S –
i.e. the power law (Eq. ) is convex in S, – then the flows are
dampened within the river basin, meaning that the production of runoff per
unit area decreases downstream along the river network. The opposite occurs
if ∂E[Qik]/dS increases with S – i.e. the power law
(Eq. ) is concave in S. Whether ∂E[Qik]/dS
increases or decreases with increasing S is determined by the value of the
scaling exponent βi relative to 1, as given by
∂2EQik∂S2=αiβiβi-1Sβi-26<0,if0<βi<1(dampeningprocess)=0,ifβi=1(criticalpoint)>0,ifβi>1(amplificationprocess),
whereby 0 <βi< 1 and βi> 1 represent, respectively, the dampening
and amplification processes, and βi= 1 is a critical value around
which the curvature of the power law (Eq. ) – and therefore the
sign of its second derivative – changes. Higher regulation leads to dampened
floods (0 <βF< 1) and enhanced low flows (βL> 1).
Power laws of the form E[Qi]=αiLAβi
(Eq. 7 with k= 1) for low flows (i=L), mean flows (i=M)
and floods (i=F). Points are observed river flows and lines are the
scaling relations (in all cases r> 0.88 and p< 0.05).
(a) Amazon: E[QL]=exp(-7.53)LA1.08;
E[QM]=exp(-4.18) LA0.94; E[QF]=exp(-1.70)LA0.82.
(b) Negro: E[QL]=exp(-5.72)LA0.99;
E[QM]=exp(-3.09) LA0.90; E[QF]=exp(-0.71)LA0.77.
(c) Solimões: E[QL]=exp(-14.75)LA1.62;
E[QM]=exp(-7.40)LA1.18; E[QF]=exp(-2.99)LA0.91.
(d) Madeira: E[QL]=exp(-6.05)LA0.93;
E[QM]=exp(-4.08)LA0.91; E[QF]=exp(-2.00)LA0.82.
(e) Xingu: E[QL]=exp(-11.22)LA1.28;
E[QM]=exp(-4.05) LA0.90; E[QF]=exp(-2.03)LA0.83.
(f) Tapajós: E[QL]=exp(-2.49)LA0.75;
E[QM]=exp(-3.25)LA0.88; E[QF]=exp(-2.80)LA0.90.
For convenience, αi is expressed as exp(ln(αi)).
Observed patterns of the values of the scaling exponents (βi)
for low flows (L), mean flows (M) and floods (F) in the Amazon basin and its
six major sub-basins. Dots over the bars indicate whether the scaling exponent
is significantly different to 1 (p< 0.05, the dot is not over 1) or not
(the dot is over 1). Details about the t tests are in Tables S3 to S8. In
regulated states (green, a–d), the exponents decrease from
low flows to floods, whereas in unregulated states (brown, f), the
exponents increase from low flows to floods. In the Xingu river basin (e),
the hypothesis that all exponents are equal to 1 cannot be rejected (p> 0.05)
because of the small number of degrees of freedom (gauges).
Amplitude of the extremes, ΔQ=(E[QF]-E[QL])/E[QM],
as observed (crosses) and simulated (lines) by (αFLAβF-αLLAβL)/αMLAβM
(from Eq. with S= LA), using the scaling parameters
of each basin. ΔQ either decreases or increases with spatial scale (LA)
depending on whether the river basin is regulated (βL>βM>βF,
e.g. Solimões) or unregulated (βL<βM<βF,
e.g. Tapajós).
Regulated and unregulated basins in the Amazon
We tested our physical interpretation of the scaling properties in the Amazon
river basin as a whole, and in its major sub-basins treated as independent
systems (Fig. 1). Large-scale forest degradation or loss is a major driver of
environmental change in these river basins .
The capacity to maintain high evapotranspiration rates is a key attribute of Amazonian
forests associated with their large cumulative area of leaves
. We
take this into account by setting the scaling parameter as S= LA =A×LAI‾,
where LAI‾ is the leaf area index averaged over
the drainage area A of each basin, so the power law (Eq. ) becomes
EQik=αiLAβi.
We tested the consistency of our results when using E[Qik]=γiAδi
instead of Eq. (), i.e. by setting A as
the scale parameter (results are included in the Supplement).
Using basin topographic data and daily river flow records from 85 gauges from
the SO-HYBAM project Fig. S1 and Table S1 in the Supplement, and LAI data
averaged for 1981–2012 (Fig. 1), we found that annual mean and extreme river
flows (E[Qik] with k= 1) in the Amazonian basins exhibit significant
(p<0.05, t-test results are in Table S2) scaling properties
through power laws of the form of Eq. () (Fig. 2). Likewise,
the scaling properties are evident when using A as the scale parameter
(Figs. S1–S7 and Table S9).
Estimated values of the scaling exponents reveal the existence of both
regulated and unregulated basins within the Amazon (Figs. 3 and S8).
The Amazon, Negro, Solimões and Madeira river basins are regulated
as indicated by their scaling exponents: βL>βM>βF. The statistical
significance of the comparisons between the scaling exponents
in the Xingu river is limited because of the few degrees of freedom
determined by the number of gauges, so we excluded this basin from this
analysis. In these regulated basins, ΔQ decreases with the spatial
scale, as given by Eqs. () and () with
βL>βM>βF (Figs. 4 and S9). In contrast, the
scaling exponents (βL<βM<βF) indicate that the Tapajós
river basin has already transitioned into the unregulated state, whereby
ΔQ is not reduced with the spatial scale (Fig. 4f).
River basins can be classified by their regulation level: βL-βF
(Table 1). The Solimões is the more regulated basin (βL-βF= 0.70 > 0),
while the Madeira is still regulated but close to the critical
threshold (βL-βF= 0.11 > 0) and the Tapajós basin has already
transitioned into the unregulated state (βL-βF=-0.16 < 0). The
Amazon as a whole is in the regulated state, but it is less regulated than
the Solimões (βL-βF= 0.26), consistent with the presence of the
less regulated basins within the whole Amazon. In the following section, we
explore the physical mechanisms behind the occurrence of different regulation states.
DiscussionThe use of LA as scale parameter
Our general idea about the classification of river basins is independent of
using LA as the scale parameter. The interpretation of the scaling
properties presented in Section 2 is based only on the assumption that river
flows in a given river basin exhibit scaling properties through power laws of
the form of Eq. (). This does not require the use of
LA as the scale parameter. Instead, it allows the investigation of the use of
different scale parameters e.g.: all of the
equations in Sect. 2 use S as a general scale parameter that could be
replaced by different factors depending on the case study. LA was
introduced as the scale parameter for the application of our general
framework (Sect. 2) to the particular case of the Amazon (Sect. 3). The
idea is not that LA must be used as the scale parameter in any river basin,
but to show that it can be successfully used as a scale parameter in the Amazon.
Although using LA as the scale parameter does not always improve R2 in
the scaling power laws (Figs. S1–S6), the main results of our
study are statistically significant and consistent among the two scaling
models: E[Qik]=αiLAβi (using LA) and
E[Qi]=γiAδi (using A). Both models agree in the ordering of basins by
their regulation level, and that the Tapajós basin is unregulated (Table 1).
The most conspicuous difference between the models is that they do not fully
agree in the description of amplifying and dampening processes in the Tapajós
basin (Table 1). However, both models agree that, in this basin (i) low
flows are not amplified and can even be dampened (βL= 0.75 < 1.00;
δL= 0.89 ≤ 1.00), and (ii) floods are less dampened than low flows
(1.00 ≥βF= 0.90 >βL= 0.75) or even amplified
(δF= 1.09 > 1.00 ≥δL= 0.89). Both models show significant
differences between the scaling exponents for low flows and floods
(βL<βF and δL<δF),
consistent with unregulation in the Tapajós basin.
The use of A as the scale parameter relies on the idea that it represents
the horizontal area over which precipitation falls. Using LA is
conceptually consistent with this same idea, because LA describes the area
through which evapotranspiration is transferred to the atmosphere. LA is an
important descriptor of differences between forest and non-forest cover. Our
focus on forests is due to these ecosystems being highly threatened worldwide
, while
there are important uncertainties about the potential consequences of forest
loss on continental water balances e.g., including the
possibility of forest loss tipping points .
Using LA instead of A as the scale parameter has practical implications
for future studies. Using LA allows the influence of a changing
scale parameter to be explored. LA is much more sensitive to global change
than A, on
timescales that are relevant for decision-making processes. Although
studying this sensitivity is out of the scope of our present study, present
results provide a basis for future studies.
Forest cover fraction (2003 data from )
and (a) the regulation level (βL-βF,
this study); (b) the long-term (2002–2014) average variability of the
land water storages as indicated by the amplitude of the liquid water equivalent
thickness, LWET (data from GRACE, CSR-v 5.0), and (c) the long-term (2002–2014)
average amount of atmospheric water as indicated by the column-integrated
precipitable water (data from ERA-Interim reanalysis). The Xingu was excluded
because the scaling exponents are not significantly different from 1 (Fig. 3e).
The “forest reservoir” hypothesis
The less regulated river basins, Tapajós and Madeira, are also the ones with
the less forest cover (Fig. 5a). Forest cover is not a static characteristic
of river basins, so different values of the forest cover fraction can be
assigned to each basin depending on the selected data source and time: we use
2003 data from – 2003 is within the range of all
of the studied river flow records. However, what is important to our
argument is not the precise value of the forest cover fraction in each basin,
but the observation that, among the Amazon tributaries, the Tapajós and
Madeira river basins have experienced large forest cover reductions mainly as
a result of forest loss and/or degradation along the so-called
arc of deforestation in south-southeastern Amazonia
.
Using 2002–2014 land water data (GRACE, CSR-v 5.0;
), and 2002–2014 atmospheric water data (ERA-Interim
reanalysis; ), we also observed that Tapajós and Madeira
are the river basins with the higher long-term average variability of the
terrestrial water storages (amplitude of the liquid water equivalent
thickness, LWET, Fig. 5b), and the lower long-term average amount of water
stored in the atmosphere (column-integrated precipitable water, Fig. 5c).
Taken together, these characteristics are consistent with a river basin with
lower capacity to store water within the coupled land–atmosphere system.
These observations led us to propose the “forest reservoir” hypothesis that
relates the regulation level of the Amazonian river basins with their forest cover.
The physical causes for a river basin to be regulated or unregulated are
summarized by its capacity for storing water and controlling its release.
Analogously, the capacity of artificial reservoirs to regulate river flows
depends on its capacity for storing water and operation rules about how to
release it . River basins have natural
mechanisms to implement these processes of water handling. These mechanisms
depend not only on relatively invariant physical attributes
(e.g. geomorphological and geological properties), but also on biophysical
processes and characteristics of river basins that can be highly sensitive to
global change on policy-relevant timescales, such as forest cover in the
Amazon .
Identifying those factors that are both highly sensitive to global change and
strongly influential on runoff production is crucial for predicting the
potential effects of global change on river flow regimes. Vegetation cover
and vegetation-related processes meet these two conditions in many river
basins of the world ,
and particularly in the Amazon where the role of forests is
so relevant that forest loss could force the system beyond a tipping point
.
Forests can exert strong effects on the store and release of water through a
variety of mechanisms. These mechanisms include large evapotranspiration
fluxes linked to large precipitation recycling
ratios , accumulation and
redistribution of soil moisture by root systems ,
strong capacity for stomatal regulation due to
the large cumulative surface area of leaves ,
production of biogenic cloud condensation nuclei
, below-canopy shading and temperature inversions
that restrict direct soil evaporation , and the
surface drag that is caused by the large height of trees and affects the flow
of air over the forests .
River flow regulation state and level in each basin as revealed by
the scaling exponents of power laws E[Qi]=αiLAβi (or
E[Qi]=γiAδi). Difference βL-βF (or
δL-δF) indicates both the regulation state (regulated if
positive, unregulated if negative) and the proximity to the critical
threshold or regulation level (magnitude of the difference). Basins are
ordered from top to bottom by their regulation level.
RiverβL-βFStateBehaviour of the extremes with increasing spatial scale (LA or A)basin(δL-δF)Solimões0.70RegulatedThe amplitude of the extremes (ΔQ) is greatly reduced (Figs. 4c and S9c) because of a strong(0.67)capacity of the basin for amplifying low flows (βL= 1.62 ≫ 1.00 and δL= 1.55 ≫ 1.00) whilenot amplifying floods (βF= 0.91 ≤ 1.00 and δF= 0.88 ≤ 1.00).Amazon0.26RegulatedΔQ is reduced (Figs. 4a and S9a) due to the combined effect of low-flow amplification(0.31)(βL= 1.08 ≥ 1.00 and δL= 1.17 > 1.00) and flood dampening (βF= 0.82 < 1.00 andδF= 0.86 < 1.00).Negro0.22RegulatedΔQ is reduced (Figs. 4b and S9b) because of the basin's capacity for dampening floods(0.17)(βF= 0.77 < 1.00 and δF= 0.90 < 1.00) while not dampening low flows. Low flows growapproximately linearly with scale (βL= 0.99 ≈ 1.00 and δL= 1.07 ≥ 1.00).Madeira0.11RegulatedΔQ is reduced (Figs. 4d and S9d) mainly because of the basin's capacity for dampening floods(0.14)(βF= 0.82 < 1.00 and δF= 0.86 < 1.00). Low flows are not amplified (βL= 0.93 ≤ 1.00 andδL≈ 1.00).Tapajós-0.16UnregulatedΔQ is increased (Figs. 4f and S9f) because low flows are not amplified (βL= 0.75 < 1.00,(-0.20)δL= 0.89 ≤ 1.00) and floods are less dampened than low flows (1.00 ≥βF= 0.90 >βL= 0.75)or even amplified (δF= 1.09 > 1.00 ≥δL= 0.89).
Collectively, these mechanisms imply that forests have a strong potential to
enhance the capacity of river basins for storing water and controlling its
release, as well as for producing contrasting and time-variable
(e.g. seasonally different) effects on the water balance components. These dual and
dynamic effects are key for regulation because it requires opposite effects
on low flows (amplification) and floods (dampening). The forest reservoir
describes the natural capacity of river basins (in the Amazon or similar basins) to store water and control its release through land–atmosphere interactions (mainly precipitation recycling) that depend strongly on the presence of forests. This hypothesis considers a river basin
as the coupled land–atmosphere system comprising not only the terrestrial
fluxes and storages of water but also the atmospheric ones (Fig. 6). Although
the capacity of the atmosphere to store water is relatively small, its
capacity to transport water within or outside a system is huge
. Indeed, in the long term, all continental
water comes from the ocean through the atmosphere because the atmospheric
fluxes of water are the only ones that flow upstream in river networks, while
terrestrial fluxes are directed into the ocean by gravitational forces.
The water balance equation for the forest reservoir control volume (Fig. 6),
dSl+Sadt=∇Q-R,
establishes that changes in water storage – including both land (Sl) and
atmospheric (Sa) components – are governed by differences between the net
atmospheric moisture convergence (∇Q, the only input flux) and runoff
(R, including both surface and sub-surface fluxes, the only output flux).
P (precipitation), ET (evapotranspiration) and I (infiltration) are not
external fluxes but components of complex land–atmosphere interactions
(e.g. precipitation recycling) that occur within the system and, therefore, are
fundamental to the mechanisms that can explain the capacity of a basin system
for regulating river flows. Although external forcings (e.g. climate change
or variability effects) do affect the response of the system (R is not
independent of ∇Q), the capacity for regulating river flows can only
be a consequence of the system's internal dynamics. Otherwise, if the
response of a system simply follows external forcings (if R were entirely
governed by ∇Q), then there would be no capacity for regulation.
Variations in the internal dynamics of water storage allow for the occurrence
of different river flow regimes under the same external forcings.
Forest reservoir control volume including the coupled land–atmosphere
basin system. The system exchanges water with its exterior through the net
atmospheric moisture convergence (∇Q) and runoff (R which includes
surface and sub-surface fluxes). P (precipitation), ET (evapotranspiration)
and I (infiltration) are internal fluxes that determine the distribution of
water storage between land (Sl) and atmospheric components (Sa).
Precipitation recycling (PR) can occur within the system.
The occurrence of floods or low flows is related, respectively, to the
abundance or scarcity of water, which depend on external forcings that
determine whether ∇Q is large or small during any given time period
(e.g. wet and dry seasons). Flood dampening depends on the capacity of the
basin to retain water when ∇Q is large (wet season), which implies
increasing water storage, consistent with
dSl+Sadt9>0,if∇Q>R(floodsdampeningviawaterstorage)≤0,if∇Q≤R(nodampeningorevenamplificationoffloods).
Analogously, low-flow amplification depends on the basin's capacity for
releasing previously stored water when ∇Q is small (dry season),
therefore reducing water storage as described by
dSl+Sadt10≥0,if∇Q≥R(noamplificationorevendampeningoflowflows),<0,if∇Q<R(lowflowsamplificationviawaterrelease).
The importance of forests for the system's internal dynamics of water storage
is highlighted by their relation with precipitation. Precipitation is not
entirely determined by external forcings nor independent of the presence of
forests. If precipitation regimes were independent of forest-related
processes, then those regimes should not significantly change in response to
forest cover change. This is contradicted by an increasing body of scientific
evidence indicating that forest cover change can significantly alter
precipitation regimes in the Amazon
.
Through its impact on precipitation, forest cover
change can affect all other water balance fluxes e.g. river
flows;, as
well as terrestrial and atmospheric storages. Notably, the simulated impacts
of deforestation on river flows can be opposite depending on whether the
precipitation response to deforestation is included or not .
Recycled precipitation (PR) is a key factor for regulation because it
represents a potentially large amount of water that can be retained within
the system through land–atmosphere circulation (Fig. 6). Therefore, in
largely forested basins, the precipitation recycling ratio is indicative of
the importance for regulation of the forest-mediated land–atmosphere
interactions. Global estimates indicate that land evaporation accounts for
about half of continental precipitation , of which forests are major
contributors . In the
Amazon river basin, recycled precipitation also accounts for about half of
the total precipitation . With this amount of
forest-related precipitation, a disruption of the recycling mechanism has a
strong potential to modify the internal dynamics of water transport and
storage, which control river flow regulation e.g..
Precipitation recycling is not a dominant process on all spatial and temporal
scales in every basin of the world. It is difficult to quantify the degree to
which terrestrial evapotranspiration supports the occurrence of precipitation
within a certain region, partly because this mechanism has characteristic
time and length scales and depends on the size, shape and location of
basins, as well as on the atmospheric pathways of moisture transport
. However, it is widely recognized that precipitation
recycling is a crucial process in the hydrological cycle of the Amazon and
neighbouring basins .
All of the studied large basins are sinks (receive
recycled precipitation) and sources (feed recycled precipitation through
evapotranspiration) of significant amounts of continental moisture, with
impacts that can be spread throughout the continent by complex cascading
effects that are sensitive to forest cover change
. Global estimates indicate the length
scale of precipitation recycling can be as low as 500 km in tropical regions
, which is not excessively large compared with the size
of the basins. The observed seasonal variability of atmospheric moisture
pathways over South America allows for the occurrence of significant
precipitation recycling all over the Amazon basin .
Our conclusion that the Madeira and Tapajós are the less regulated basins,
with Tapajós being unregulated (Table 1), relies only on the observed values
of the scaling exponents, following the theoretical framework developed in
Sect. 2. Therefore, this conclusion does not ignore the important role of
geological and geomorphological processes . Depending on the case
study, different levels of regulation or transitions between states could be
attributed to different causes. The forest reservoir hypothesis provides a
potential explanation linking forest cover and river flow regulation. The
idea is not that the effect of land cover (particularly forest cover in the
Amazon) on river flow regulation is stronger than any other effect
(e.g. geological and geomorphological effects), but that the role of land cover is
not negligible and critically important because of its sensitivity to global
change, especially in a region such as the Amazon where forest ecosystems are
highly threatened and forest-related precipitation recycling plays a major
role . We foresee a potential danger in the
assumption that the regulation capacity of river basins depends on
geomorphological and geological processes with land cover playing a
negligible role. Under this assumption, land cover change (e.g. forest loss)
would not change the capacity of river basins to regulate river flows.
The forest reservoir mechanisms may have been previously overlooked because
the size of the atmospheric storage is much smaller than that of the
terrestrial storage (Sa<≪Sl; ), and also
because the size of the terrestrial storage (e.g. aquifer systems) is mainly
determined by geological and geomorphological properties. However, the key
factor for regulation is not the size of the atmospheric storage but the
possibility of retaining large amounts of water within the system through
land–atmosphere interactions.
Forest loss effects on regulation: a potential critical threshold
Forest loss does not reduce or increase river flows in every basin on every
temporal and spatial scale .
Fundamental reasons for this are that forests have an
inherent capacity to either increase or decrease the water balance
components, and that these effects have a complex and dynamic nature. For
instance, forests can increase or decrease ET via opening or
closing stomata, respectively, which is related to water availability: stomatal aperture
tends to be increased during drought stress and decreased during excessive
water stress . Further, forest
loss can significantly alter the hydraulic properties of soils, especially by
reducing infiltrability . Through these
impacts, forest loss can alter all the water balance components in complex
ways. If the effect of forest loss were always to reduce ET (due to
reduction in the cumulative leaf area) with no impact on P (as implicitly
assumed in hydrological models that use P as a fixed input) nor on the
hydraulic properties of soils and regulation capacity of the basin, then
forest loss should be always associated with increased R and, therefore,
increased floods and low flows. Likewise, if the effect of forest loss were
always to increase ET (related to weaker stomatal regulation,
disruption of below canopy shading and stability, and increased wind speed
over the surface, for example) with no other effects, then forest loss should always lead
to reduced R and, therefore, reduced floods and low flows. In both cases,
the effect of forest loss on extreme river flows would always be in the same
direction. In contrast, the forest reservoir hypothesis considers that forest
loss can have contrasting effects on low flows and floods, mainly because the
production of these extreme flows is governed by different processes
occurring during different seasons.
Potential weakening of the forest reservoir due to forest loss.
(a) The loss of forests can exacerbate floods through increases in the
direct runoff associated with reductions in the evapotranspiration and
infiltration fluxes. These effects are associated with a reduction in the
capacity of the coupled land–atmosphere system for retaining water during the
wet season. (b) Less water retention during the wet season can reduce
the base flow during the dry season. The loss of forests can reduce low flows
through reductions in base flow and precipitation, both of them associated with
a reduction in the capacity of the coupled land–atmosphere system for storing
and releasing water during different periods of time. Dashed arrows indicate
potential positive feedbacks to forest loss.
The forest reservoir hypothesis implies that the regulation capacity of a
river basin can be especially sensitive to forest cover change. The size of
artificial reservoirs determines their regulatory capacity. Likewise, the
regulatory capacity of the forest reservoir depends on its size, which is
related to the extent of forest cover. This implies that forest loss weakens
regulation. The lower levels of regulation in the Madeira and Tapajós river
basins (Table 1) are consistent with a weaker forest reservoir (these two
basins are the less forested ones, Fig. 5a), likely related to extensive
forest loss that has occurred along the arc of deforestation
.
Notably, these less regulated basins are also the ones
with more large artificial reservoirs in operation (http://dams-info.org/).
The introduction of artificial reservoirs can cause contrasting effects on
regulation. Assuming that an artificial reservoir is operated so as to reduce
floods and increase low flows, its introduction in a river basin should
enhance river flow regulation. However, the construction of reservoirs is
usually linked to other human activities – e.g. road construction, and
associated agricultural expansion and deforestation
– that can reduce the natural
capacity of river basins to regulate river flows. Our results suggest that
this is the case in the Madeira and Tapajós basins.
Forest loss does not weaken regulation because it changes the capacity of the
atmospheric and terrestrial water storages, but mainly because it reduces the
capacity of the basin system (Fig. 6) to retain water through its complex
internal dynamics of land–atmosphere interactions. Figure 7 shows a
conceptual example of how forest loss can disrupt river flow regulation
(increase the amplitudes of extremes) via weakening the forest reservoir. Forest
loss can exacerbate floods by increasing R through reduction in ET and I
during the wet season when P is large due to large ∇Q (Figs. 6
and 7a). ET and I reduction can be associated, respectively, with reduced
leaf area and infiltrability. ET reduction can weaken P recycling as a
mechanism for dampening floods by recirculating water within the system.
These effects are consistent with an enhanced conversion of P into R
during the wet season and, therefore, enhanced floods and reduced water
storage. This is described by Eq. () where floods
are not dampened if water storage (Sl+Sa) is not increased. Water storage
reduction during the wet season results in a decreased capacity of the system
to amplify low flows via base flow during the dry season (Fig. 7b).
Amplifying low flows when ∇Q is relatively small (the dry season)
requires the release of water that has been previously stored, consistent
with d(Sl+Sa)/dt< 0 in Eq. ().
Deforestation-induced reduction in P or
lengthening of the dry season ,
consistent with a disruption of the wet season onset ,
can further reduce low flows.
The forest reservoir hypothesis implies that forest loss can increase floods
while reducing low flows (Fig. 7). This is not inconsistent with increasing
scientific evidence that large-scale forest loss will reduce P over the
Amazon . Reduced P can explain a decrease in low
flows but does not necessarily imply a decrease in floods too. Floods strongly depend not only on the total amount of P but also on its temporal
distribution (rainfall intensity and duration) and the hydraulic properties
of the surface . Variations in the capacity of the
basin system for retaining and releasing water during wet and dry seasons
allow for the occurrence of larger floods with smaller P. A comparable
situation has been observed in the Nakambé River in Africa where reduced
precipitation has lead to the counter-intuitive effect of increased floods,
even despite an increase in the number of dams in the river basin .
The identification of alternative regulation states from scaling properties
in river basins (Sect. 2), together with the hypothesis that forest loss
weakens the regulatory capacity, implies that forest loss can cause a
transition from the regulated state to the unregulated state. This also
implies that there is a forest cover critical threshold where the transition
occurs. In our results, the forest cover fraction in the less regulated
basins is ∼ 0.60, while in the more regulated basins it is > 0.70
(Fig. 5a), which suggests a possible range for the critical threshold.
Although more-detailed studies are essential to understand regulation
dynamics in different regions, as well as to identify potential critical
thresholds, our analysis shows that scaling patterns may be used to
characterize regulation states and infer transitions in river basins. Such
empirical approaches are essential e.g. because
it is becoming clear that accurate mechanistic models to predict critical
thresholds (or tipping points) are currently beyond our reach
, and the detection of early-warning signals for
critical transitions in complex systems (e.g. river basins) remains a
fundamental challenge in environmental science today .
Conclusions
We have shown how the scaling properties of mean and extreme river flows are
a signature of the river flow regime in any river basin. Through the values
of the scaling exponents, a river basin can be classified as regulated or
unregulated, depending on whether it dampens or amplifies extreme river
flows, respectively. These scaling exponents are sensitive to global change,
so a river basin can shift from the regulated to the unregulated state. The
scaling exponents provide a metric for the proximity to the critical
threshold. Our results indicate that environmental perturbations that reduce
the natural capacity of river basins to regulate river flows tend to
increase the scaling exponent for floods and to decrease that for low flows.
This provides a prediction of the direction of change in the scaling
exponents of river basins as a result of global change, which can be used to
design and simulate scenarios of future river flow regimes. The theoretical
basis of our physical interpretation of the scaling properties of river flows
is generally applicable to any river basin.
We have applied the proposed interpretation of river flow scaling properties
to the Amazon river basin and found both the regulated (all except the
Tapajós) and unregulated (the Tapajós) states among its main tributaries.
Then we proposed the forest reservoir hypothesis to describe the natural
capacity of river basins to regulate river flows through land–atmosphere
interactions (mainly precipitation recycling) that depend strongly on the
presence of forests, especially in the Amazon. A critical implication of this
hypothesis is that forest loss can force the Amazonian river basins from
regulated to unregulated states. This provides further evidence about the
possible outcome of widespread forest loss in the Amazon, potentially
involving forest loss critical thresholds, a matter of great uncertainty and
concern .
These results provide foundations and a quantitative basis for using the
scaling theory in solving four fundamental challenges in river basin science:
the “PUB problem” that extends to every river basin in a changing
environment ; the detection of
early-warning signals of critical thresholds in river basins
; the production of parsimonious
river basin classifications based on dimensionless similarity indices (the
scaling exponents) or dominant processes (amplification or dampening of
extreme river flows) ; and the exploration of
the organizing principles that underlie the heterogeneity and complexity of
river flow production processes in river basins with different hydroclimatic
regimes and on different scales .
We addressed this by advancing from observed patterns
(Figs. 2–5) to processes: the forest reservoir hypothesis (Figs. 6 and 7), as
recommended by .
Data availability
All data for this paper are properly cited and referred to
in the reference list.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-22-1735-2018-supplement.
Author contributions
JFS, JCV, AMR and GP designed the research. JFS and AMR developed the
mathematical model. JFS, ER, IH and DM performed data analysis. JFS developed
the forest reservoir hypothesis and wrote the paper with input from
other authors. All authors discussed the results and conclusions.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We gratefully acknowledge constructive comments from editor Patricia Saco and
two anonymous referees. Funding was provided by “Programa de investigación
en la gestión de riesgo asociado con cambio climático y ambiental en
cuencas hidrográficas” (UT-GRA), Convocatoria 543-2011 Colciencias.
Juan Fernando Salazar was partially supported by the IAI-INPE Internship program
“Understanding Climate Change and Variability in the Americas”.
Angela María Rendón was partially supported by Colciencias grant 115-660-44588.
Juan Camilo Villegas was partially supported by NSF-EF-1340624 through the
University of Arizona.
Edited by: Patricia Saco
Reviewed by: four anonymous referees
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