Introduction
Vegetation, as a core component of the water cycle, shapes the partitioning of
water fluxes on the catchment scale into runoff components and evaporation,
thereby controlling fundamental processes in ecosystem functioning
(Rodriguez-Iturbe, 2000; Laio et al., 2001; Kleidon, 2004), such as flood
generation (Donohue et al., 2012), drought dynamics
(Seneviratne et al., 2010; Teuling et al., 2013), groundwater recharge
(Allison et al., 1990; Jobbágy and Jackson, 2004) and land–atmosphere
feedback (Milly and Dunne, 1994; Seneviratne et al., 2013; Cassiani et
al., 2015). Besides increasing interception storage available for evaporation
(Gerrits et al., 2010), vegetation critically
interacts with the hydrological system in a co-evolutionary way by root water
uptake for transpiration, towards a dynamic equilibrium with the available
soil moisture to avoid water shortage (Donohue et al., 2007; Eagleson,
1978, 1982; Gentine et al., 2012; Liancourt et al., 2012) and related adverse
effects on carbon exchange and assimilation rates (Porporato et al., 2004;
Seneviratne et al., 2010). Roots create moisture storage volumes within their
range of influence, from which they extract water that is stored between
field capacity and wilting point. This root-zone storage capacity
SR, sometimes also referred to as plant available water holding capacity, in the
unsaturated soil is therefore the key component of many hydrological systems
(Milly and Dunne, 1994; Rodriguez-Iturbe et al., 2007).
There is increasing theoretical and experimental evidence that vegetation
dynamically adapts its root system, and thus SR, to environmental
conditions, to secure, on the one hand, access to sufficient moisture to
meet the canopy water demand and, on the other hand, to minimize the carbon
investment for sub-surface growth and maintenance of the root system
(Brunner et al., 2015; Schymanski et al., 2008; Tron et al., 2015). In
other words, the hydrologically active root zone is optimized to guarantee
productivity and transpiration of vegetation, given the climatic
circumstances (Kleidon, 2004). Several studies
previously showed the strong influence of climate on this hydrologically
active root zone (e.g. Reynolds et al., 2000; Laio et al., 2001; Schenk
and Jackson, 2002). Moreover, droughts are often identified as critical
situations that can affect ecosystem functioning evolution (e.g. Allen et
al., 2010; McDowell et al., 2008; Vose et al., 2016).
In addition to their general adaption to environmental conditions, vegetation
has some potential to adapt roots to such periods of water shortage
(Sperry et al., 2002; Mencuccini, 2003; Bréda et al., 2006). In the
short term, stomatal closure and reduction of leaf area will lead to reduced
transpiration. In several case studies for specific plants, it was also
shown that plants may even shrink their roots and reduce soil–root
conductivity during droughts, while recovering after re-wetting (Nobel
and Cui, 1992; North and Nobel, 1992). In the longer term, and more
importantly, trees can improve their internal hydraulic system, for example
by recovering damaged xylem or by allocating more biomass for roots
(Sperry et al., 2002; Rood et al., 2003; Bréda et al., 2006).
Similarly, Tron et al. (2015) argued that roots follow
groundwater fluctuations, which may lead to increased rooting depths when
water tables drop. Such changing environmental conditions may also provide
other plant species with different water demand than the ones present under
given conditions, with an advantage in the competition for resources, as for
example shown by Li et al. (2007).
The hydrological functioning of catchments (Black, 1997; Wagener et al.,
2007) and thus the partitioning of water into evaporative fluxes and runoff
components is not only affected by the continuous adaption of vegetation to
changing climatic conditions. Rather, it is well understood that
anthropogenic changes to land cover, such as deforestation, can considerably
alter hydrological regimes. This has been shown historically through many
paired watershed studies (e.g. Bosch and Hewlett, 1982; Andréassian,
2004; Brown et al., 2005; Alila et al., 2009). These studies found that
deforestation often leads to generally higher seasonal flows and/or an
increased frequency of high flows in streams, while decreasing evaporative
fluxes. The timescales of hydrological recovery after such land-cover
disturbances were shown to be highly sensitive to climatic conditions and
the growth dynamics of the regenerating species (e.g. Jones and Post,
2004; Brown et al., 2005).
Although land-use change effects on hydrological functioning are widely
acknowledged, it is less well understood which parts of the hydrological
system are affected in which way and over which timescales. As a
consequence, most catchment-scale models were originally not developed to
deal with such changes in the system, but rather for “stationary” conditions
(Ehret et al., 2014).
This is true for both top-down hydrological models, such as HBV
(Bergström, 1992) or GR4J (Perrin et al., 2003), and
bottom-up models, such as MIKE-SHE (Refsgaard and Storm, 1995) or
HydroGeoSphere (Brunner and Simmons, 2012).
Several modelling studies have in the past incorporated temporal effects of
land-use change to some degree (Andersson and Arheimer, 2001; Bathurst et
al., 2004; Brath et al., 2006), but they mostly rely on ad hoc assumptions
about how hydrological parameters are affected (Legesse et al., 2003;
Mahe et al., 2005; Onstad and Jamieson, 1970; Fenicia et al., 2009).
Approaches which incorporate the change in the model formulation itself are
rare and have only recently gained momentum (e.g. Du et al., 2016;
Fatichi et al., 2016; Zhang et al., 2016). This is of critical importance as
ongoing changes in land cover and climate dictate the need for a better
understanding of their effects on hydrological functioning
(Troch et al., 2015) and their explicit consideration in
hydrological models for more reliable predictions under change
(Hrachowitz et al., 2013; Montanari et al., 2013).
Overview of the catchments and their sub-catchments (WS).
Catchment
Deforestation
Treatment
Area
Affected
Aridity
Precipitation
Discharge
Potential
Time series
period
[km2]
Area [%]
index [–]
[mm yr-1]
[mm yr-1]
evaporation
[mm yr-1]
HJ Andrews WS1
1962–1966
Burned 1966
0.956
100
0.39
2305
1361
902
1962–1990
HJ Andrews WS2
–
–
0.603
–
0.39
2305
1251
902
1962–1990
Hubbard Brook WS2
1965–1968
Herbicides
0.156
100
0.57
1471
1059
784
1961–2009
Hubbard Brook WS3
–
–
0.424
–
0.54
1464
951
787
1961–2009
Hubbard Brook WS5
1983–1984
No treatment
0.219
87
0.51
1518
993
746
1962–2009
As a step towards such an improved understanding and the development of
time-dynamic models, we argue that the root-zone storage capacity, SR,
is a core component determining the hydrological response, and needs to be
treated as a dynamically evolving parameter in hydrological modelling as a
function of climate and vegetation. Gao et al. (2014)
recently demonstrated that catchment-scale SR can be robustly estimated
exclusively based on long-term water balance considerations.
Wang-Erlandsson et al. (2016)
derived global estimates of SR using remote-sensing based precipitation
and evaporation products, which demonstrated considerable spatial
variability of SR in response to climatic drivers. In traditional
approaches, SR is typically determined either by the calibration of a
hydrological model (e.g. Seibert and McDonnell, 2010; Seibert et al.,
2010) or based on soil characteristics and sparse, averaged estimates of
root depths, often obtained from literature (e.g. Breuer et al., 2003;
Ivanov et al., 2008). This does neither reflect the dynamic nature of the
root system nor does it consider to a sufficient extent the actual function
of the root zone: providing plants with continuous and efficient access to
water. This leads to the situation where soil porosity often effectively
controls the values of SR used in a model. Consider, as a thought
experiment, two plants of the same species growing on different soils. They
will, with the same average root depth, then have access to different
volumes of water, which will merely reflect the differences in soil
porosity. This is in strong contradiction to the expectation that these
plants would design root systems that provide access to similar water
volumes, given the evidence for efficient carbon investment in root growth
(Milly, 1994; Schymanski et al., 2008; Troch et al., 2009) and posing
that plants of the same species have common limits of operation. This
argument is supported by a recent study, in which was shown that water-balance-derived estimates of SR are at least as plausible as soil-derived estimates (de Boer-Euser et al., 2016) in many
environments and that the maximum root depth controls evaporative fluxes and
drainage (Camporese et al., 2015).
Therefore, using water-balance-based estimates of SR in several
deforested sites as well as in untreated reference sites in two experimental
forests, we test the hypotheses that (1) the root-zone storage capacity
SR significantly changes after deforestation, (2) the evolution in
SR can explain post-treatment changes to the hydrological regimes and
that (3) a time-dynamic formulation of SR can improve the performance
of a hydrological model.
Study sites
The catchments under consideration are part of the HJ Andrews Experimental
Forest and the Hubbard Brook Experimental Forest. A summary of the main
catchment characteristics can be found in Table 1. Daily discharge
(Campbell, 2014a; Johnson and Rothacher, 2016), precipitation
(Campbell, 2014b; Daly and McKee, 2016) and temperature time series
(Campbell, 2014c, d; Daly and McKee, 2016) were obtained from the
databases of the Hubbard Brook Experimental Forest and the HJ Andrews
Experimental Forest. Potential evaporation was estimated by the Hargreaves
equation (Hargreaves and Samani, 1985).
HJ Andrews Experimental Forest
The HJ Andrews Experimental Forest is located in Oregon, USA
(44.2∘ N, 122.2∘ W) and was established in 1948. The
catchments at HJ Andrews are described in many studies (e.g. Rothacher,
1965; Dyrness, 1969; Harr et al., 1975; Jones and Grant, 1996; Waichler et
al., 2005).
Before vegetation removal and at lower elevations the forest generally
consisted of 100- to 500-year old coniferous species, such as Douglas fir
(Pseudotsuga menziesii), western hemlock (Tsuga heterophylla) and western red cedar (Thuja plicata), whereas upper elevations
were characterized by noble fir (Abies procera), Pacific silver fir (Abies amabilis), Douglas fir, and
western hemlock. Most of the precipitation falls from November to April
(about 80 % of the annual precipitation), whereas the summers are
generally drier, leading to signals of precipitation and potential
evaporation that are out of phase.
Deforestation of HJ Andrews Watershed 1 (WS1) started in August 1962
(Rothacher, 1970). Most of the timber was removed with skyline
yarding. After finishing the logging in October 1966, the remaining debris
was burned and the site was left for natural regrowth. Watershed 2 (WS2) is the reference
catchment, which was not harvested.
Hubbard Brook Experimental Forest
The Hubbard Brook Experimental Forest is a research site established in 1955
and located in New Hampshire, USA (43.9∘ N, 71.8∘ W).
The Hubbard Brook experimental catchments are described in a many
publications (e.g. Hornbeck et al., 1970, 1997; Hornbeck, 1973; Dahlgren and
Driscoll, 1994; Likens, 2013).
Prior to vegetation removal, the forest was dominated by northern hardwood
forest composed of sugar maple (Acer saccharum), American beech (Fagus grandifolia) and yellow birch
(Betula alleghaniensis) with conifer species such as red spruce (Picea rubens) and balsam fir (Abies balsamea) occurring at
higher elevations and on steeper slopes with shallow soils. The forest was
selectively harvested from 1870 to 1920, damaged by a hurricane in 1938, and
is currently not accumulating biomass (Campbell et al., 2013; Likens,
2013). The annual precipitation and runoff is less than in HJ Andrews
(Table 1). Precipitation is rather uniformly spread throughout the year
without distinct dry and wet periods, but with snowmelt-dominated peak flows
occurring around April and distinct low flows during the summer months due
to increased evaporation rates (Federer et al., 1990). Vegetation
removal occurred in the catchment of Hubbard Brook WS2 between 1965 and 1968 and in Hubbard Brook Watershed 5
(WS5)
between 1983 and 1984. Hubbard Brook Watershed 3 (WS3) is the undisturbed reference catchment.
Hubbard Brook WS2 was completely deforested in November and December 1965
(Likens et al., 1970). To minimize disturbance, no roads were
constructed and all timber was left in the catchment. On 23 June 1966,
herbicides were sprayed from a helicopter to prevent regrowth. Additional
herbicides were sprayed in the summers of 1967 and 1968 from the ground.
In Hubbard Brook WS5, all trees were removed between 18 October 1983 and
21 May 1984, except for a 2 ha buffer near an adjacent reference catchment
(Hornbeck et al., 1997). WS5 was harvested as a whole-tree
mechanical clearcut with removal of 93 % of the above-ground biomass
(Hornbeck et al., 1997; Martin et al., 2000), thus including smaller
branches and debris. Approximately 12 % of the catchment area was
developed as the skid trail network. Afterwards, no treatment was applied
and the site was left for regrowth.
Methodology
To assure reproducibility and repeatability, the executional steps in the
experiment were defined in a detailed protocol, following
Ceola et al. (2015), which is provided
as Supplement Sect. S1.
Applied parameter ranges for root-zone storage derivation.
Catchment
Imax,eq
Imax,change
Tr
(mm)
(mm)
(days)
HJ Andrews WS1
1–5
0–5
0–3650
HJ Andrews WS2
1–5
–
–
Hubbard Brook WS2
1–5
5–10
0–3650
Hubbard Brook WS3
1–5
–
–
Hubbard Brook WS5
1–5
0–5
0–3650
Water-balance-derived root-zone moisture capacities SR
The root-zone moisture storage capacities SR and their change over time
were determined according to the methods suggested by
Gao et al. (2014) and subsequently successfully tested
by de Boer-Euser et al. (2016) and
Wang-Erlandsson et al. (2016).
Briefly, the long-term water balance provides information on actual mean
transpiration. In a first step, the interception capacity has to be assumed,
in order to determine the effective precipitation Pe (LT-1),
following the water balance equation for interception storage:
dSidt=P-Ei-Pe
with Si (L) interception storage, P the precipitation (LT-1),
Ei the interception evaporation (LT-1). This is solved with the
constitutive relations:
Ei=EpifEpdt<SiSidtifEpdt≥SiPe=0ifSi≤ImaxSi-ImaxdtifSi>Imax
with, additionally, Ep the potential evaporation (LT-1) and
Imax (L) the interception capacity. As Imax will also
be affected by land cover change, this was addressed by introducing the
three parameters Imax,eq (long-term equilibrium interception capacity)
(L), Imax,change (post-treatment interception capacity) (L) and Tr
(recovery time) (T), leading to a time-dynamic formulation of Imax:
Imax=fort<tchange,t>tchange,end+Tr:Imax,eqfortchange, start<t<tchange,end:Imax,eq-Imax,eq-Imax,changetchange,end-tchange,startt-tchange,startfortchange,end<t<tchange,end+Tr:Imax,change+Imax,eq-Imax,changeTrt-tchange,end
with tchange,start the time that deforestation started and
tstart,end the time deforestation finished.
Following a Monte Carlo sampling approach, upper and lower bounds of Ei
were then estimated based on 1000 random samples of these parameters,
eventually leading to upper and lower bounds for Pe. The interception
capacity was assumed to increase after deforestation for Hubbard Brook WS2,
as the debris was left at the site. For Hubbard Brook WS5 and HJ Andrews WS1
the interception capacity was assumed to decrease after deforestation, as
here the debris was respectively burned and removed. Furthermore, in the
absence of more detailed information, it was assumed that the interception
capacities changed linearly during deforestation towards Imax,change
and linearly recovered to Imax over the period Tr as well. See
Table 2 for the applied parameter ranges.
Derivation of root-zone storage capacity (SR) for one
specific time period in Hubbard Brook WS2 as difference
between the cumulative transpiration (Et) and the cumulative effective
precipitation (PE).
Hereafter, the long-term mean transpiration can be estimated with the
remaining components of the long term water balance, assuming no additional
gains or losses, storage changes and/or data errors:
E‾t=P‾e-Q‾,
where Et‾ (LT-1) is the long-term mean actual transpiration,
Pe‾ (LT-1) is the long-term mean effective precipitation and
Q‾ (LT-1) is the long-term mean catchment runoff. Taking into
account seasonality, the actual mean transpiration is scaled with the ratio
of long-term mean daily potential evaporation Ep over the mean annual
potential evaporation Ep:
Et(t)=Ep(t)Ep‾×Et‾.
Based on this, the cumulative deficit between actual transpiration and
precipitation over time can be estimated by means of an
“infinite-reservoir”. In other words, the cumulative sum of daily water
deficits, i.e. evaporation minus precipitation, is calculated between
T0, which is the time the deficit equals zero, and T1, which is the
time the total deficit returned to zero. The maximum deficit of this period
then represents the volume of water that needs to be stored to provide
vegetation continuous access to water throughout that time:
SR=max∫T0T1(Et-Pe)dt,
where SR (L) is the maximum root-zone storage capacity over the time
period between T0 and T1. See also Fig. 1 for a graphical
example of the calculation for the Hubbard Brook catchment for one specific
realization of the parameter sampling. The SR,20yr for drought return
periods of 20 years was estimated using the Gumbel extreme value
distribution (Gumbel, 1941) as previous work suggested that
vegetation designs SR to satisfy deficits caused by dry periods with
return periods of approximately 10–20 years (Gao et al., 2014; de
Boer-Euser et al., 2016). Thus, the maximum values of SR for each year,
as obtained by Eq. (7), were fitted to the extreme value distribution of
Gumbel, and subsequently, the SR,20yr was determined.
For the study catchments that experienced logging and subsequent
reforestation, it was assumed that the root system converges towards a
dynamic equilibrium approximately 10 years after reforestation. Thus, the
equilibrium SR,20yr was estimated using only data over a period that
started at least 10 years after the treatment. For the growing root systems
during the years after reforesting, the storage capacity does not yet reach
its dynamic equilibrium SR,20yr. Instead of determining an equilibrium
value, the maximum occurring deficit for each year was in that case
considered as the maximum demand and thus as the maximum required storage
SR,1yr for that year. To make these yearly estimates, the mean
transpiration was determined in a similar way as stated by Eq. (5).
However, the assumption of no storage change may not be valid for 1-year
periods. In a trade-off to limit the potential bias introduced by
inter-annual storage changes in the catchments, the mean transpiration was
determined based on the 2-year water balance, thus assuming negligible
storage change over these years.
The deficits in the months October–April are highly affected by snowfall, as
estimates of the effective precipitation are estimated without accounting
for snow, leading to soil moisture changes that spread out over an unknown
longer period due to the melt process. Therefore, to avoid this influence of
snow, only deficits as defined by Eq. (7), in the period of May–September are taken into consideration, which is also the period where
deficits are significantly increasing due to relatively low rainfall and
high transpiration rates, thus causing soil moisture depletion and drought
stress for the vegetation, which in turn, shapes the root zone.
Model-derived root-zone storage capacity Su,max
The water-balance-derived equilibrium SR,20yr as well as the
dynamically changing SR,1yr that reflects regrowth patterns in the
years after treatment were compared with estimates of the calibrated
parameter Su,max, which represents the mean catchment root-zone storage
capacity in lumped conceptual hydrological models. Due to the lack of direct
observations of the changes in the root-zone storage capacity, this
comparison was used to investigate whether the estimates of the root-zone
storage capacity SR,1yr, their sensitivity to land-cover change and
their effect on hydrological functioning, can provide plausible results.
Model-based estimates of root-zone storage capacity may be highly influenced
by model formulations and parameterizations. Therefore, four different
hydrological models were used to derive the parameter Su,max in order
to obtain a set of different estimates of the catchment-scale root-zone
storage capacity. The major features of the model routines for root-zone
moisture tested here are briefly summarized below and detailed descriptions
including the relevant equations are provided in the Supplement
(Sect. S2).
FLEX
The FLEX-based model (Fenicia et al., 2008) was applied in a
lumped way to the catchments. The model has nine parameters, eight of which are
free calibration parameters, sampled from relatively wide, uniform prior
distributions. In contrast, based on the estimation of a Master Recession
Curve (e.g. Fenicia et al., 2006), an informed
prior distribution between narrow bounds could be used for determining the
slow reservoir coefficient Ks.
The model consists of five storage components. First, a snow routine has to
be run, which is a simple degree-day module, similar to that used in, for
example, HBV (Bergström, 1976). After the snow routine, the
precipitation enters the interception reservoir. Here, water evaporates at
potential rates or, when exceeding a threshold, directly reaches the soil
moisture reservoir. The soil moisture routine is modelled in a similar way
to the Xinanjiang model (Zhao, 1992). Briefly, it contains
a distribution function that determines the fraction of the catchment where
the storage deficit in the root zone is satisfied and that is therefore
hydrologically connected to the stream and generating storm runoff. From the
soil moisture reservoir, water can further vertically percolate down to
recharge the groundwater or leave the reservoir through transpiration.
Transpiration is a function of maximum root-zone storage Su,max and the
actual root-zone storage, similar to the functions described by Feddes
et al. (1978). Water that cannot be stored in the soil moisture storage
is then split into preferential percolation to the groundwater and runoff
generating fluxes that enter a fast reservoir, which represents fast-responding system components such as shallow subsurface and overland flow.
HYPE
The HYPE model (Lindström et al., 2010) estimates soil
moisture for hydrological response units (HRU), which is the finest
calculation unit in this catchment model. In the current set-up, 15
parameters were left free for calibration. Each HRU consists of a unique
combination of soil and land-use classes with assigned soil depths. Water
input is estimated from precipitation after interception and a snow module
at the catchment scale, after which the water enters the three defined soil
layers in each HRU. Evaporation and transpiration occurs in the first two
layers and fast surface runoff is produced when these layers are fully
saturated or when rainfall rates exceeds the maximum infiltration
capacities. Water can move between the layers through percolation or
laterally via fast flow pathways. The groundwater table is fluctuating
between the soil layers with the lowest soil layer normally reflecting the
base flow component in the hydrograph. The water balance of each HRU is
calculated independently and the runoff is then aggregated in a local stream
with routing before entering the main stream.
TUW
The TUW model (Parajka et al., 2007) is a conceptual
model with a structure similar to that of HBV (Bergström, 1976)
and has 15 free calibration parameters. After a snow module, based on a
degree-day approach, water enters a soil moisture routine. From this soil
moisture routine, water is partitioned into runoff-generating fluxes and
evaporation. Here, transpiration is determined as a function of maximum root-zone storage Su,max and actual root-zone storage as well. The runoff-generating fluxes percolate into two series of reservoirs. A fast-responding
reservoir with overflow outlet represents shallow subsurface and overland
flow, while the slower responding reservoir represents the groundwater.
HYMOD
HYMOD (Boyle, 2001) is similar to the applied model structure for FLEX,
but only has eight parameters. Besides that, the interception module and
percolation from soil moisture to the groundwater are missing. Nevertheless,
the model accounts similarly for the partitioning of transpiration and
runoff generation in a soil moisture routine. Also for this model,
transpiration is a function of maximum storage and actual storage in the
root zone. The runoff-generating fluxes are eventually divided over a slow
reservoir, representing groundwater, and a fast reservoir, representing the
fast processes.
Model calibration
Each model was calibrated using a Monte-Carlo strategy within consecutive
2-year windows in order to obtain a time series of root-zone moisture
capacities Su,max. FLEX, TUW and HYMOD were all run 100 000 times,
whereas HYPE was run 10 000 times and 20 000 times for HJ Andrews WS1 and
the Hubbard Brook catchments respectively, due to the required runtimes. The
Kling–Gupta efficiency for flows (Gupta et al., 2009) and
the Kling–Gupta efficiency for the logarithm of the flows were
simultaneously used as objective functions in a multi-objective calibration
approach to evaluate the model performance for each window. These were
selected in order to obtain rather balanced solutions that enable a
sufficient representation of peak flows, low flows and the water balance.
The unweighted Euclidian distance of the three objective functions
served as an informal measure to obtain these balanced solutions (e.g.
Hrachowitz et al., 2014; Schoups et al., 2005):
Lθ=1-1-EKG2+1-ElogKG2,
where L(θ) is the conditional probability for parameter set θ [–], EKG the Kling–Gupta efficiency [–], ElogKG the Kling–Gupta
efficiency for the log of the flows [–].
Eventually, a weighing method based on the GLUE-approach of
Freer et al. (1996) was applied. To estimate posterior parameter
distributions all solutions with Euclidian distances smaller than 1 were
maintained as feasible. The posterior distributions were then determined
with the Bayes rule (cf. Freer et al., 1996):
L2θ=Lθn×L0θ/C,
where L0(θ) is the prior parameter distribution [–],
L2(θ) is the posterior conditional probability [–] , n is a
weighing factor (set to 5) [–], and C is a normalizing constant [–].
5/95th model uncertainty intervals were then constructed based on the
posterior conditional probabilities.
Trend analysis
To test if SR,1yr significantly changes following de- and subsequent
reforestation, which would also indicate shifts in distinct hydrological
regimes, a trend analysis, as suggested by Allen et al. (1998), was
applied to the SR,1yr values obtained from the water-balance-based
method. As the sampling of interception capacities (Eq. 4) leads to
SR,1yr values for each point in time, which are all equally likely in
absence of any further knowledge, the mean of this range was assumed as an
approximation of the time-dynamic character of SR,1yr.
Briefly, a linear regression between the full series of the cumulative sums
of SR,1yr in the deforested catchment and the unaffected control
catchment is established and the residuals and the cumulative residuals are
plotted in time. A 95 %-confidence ellipse is then constructed from the
residuals:
X=n2cos(α),Y=nn-1Zp95σrsin(α),
where X presents the x coordinates of the ellipse (T), Y represents the
y coordinates of the ellipse (L), n is the length of the time series (T),
α is the angle defining the ellipse (0–2π) between the
diagonal of the ellipse and the x axis (–), Zp95 is the value belonging
to a probability of 95 % of the standard student t-distribution (–) and
σr is the standard deviation of the residuals (assuming a
normal distribution) (L).
When the cumulative sums of the residuals plot outside the 95 %-confidence
interval defined by the ellipse, the null-hypothesis that the time series
are homogeneous is rejected. In that case, the residuals from this linear
regression where residual values change from either solely increasing to
decreasing or vice versa, can then be used to identify different sub-periods
in time.
Thus, in a second step, for each identified sub-period a new regression,
with new (cumulative) residuals, can be used to check homogeneity for these
sub-periods. In a similar way to before, when the cumulative residuals of
these sub-periods now plot within the accompanying newly created
95 %-confidence ellipse, the two series are homogeneous for these
sub-periods. In other words, the two time series show consistent behaviour
over this particular period.
Model with time-dynamic formulation of Su,max
In a last step, the FLEX model was reformulated to allow for a time-dynamic
representation of the parameter Su,max, reflecting the root-zone
storage capacity.
As a reference, the long-term water-balance-derived root-zone storage
capacity SR,20yr was used as a static formulation of Su,max in
the model, and thus kept constant in time. The remaining parameters were
calibrated using the calibration strategy outlined above over a period
starting with the treatment in the individual catchments until at least 15
years after the end of the treatment. This was done to focus on the period
under change (i.e. vegetation removal and recovery), during which the
differences between static and dynamic formulations of Su,max are
assumed to be most pronounced.
To test the effect of a dynamic formulation of Su,max as a function of
forest regrowth, the calibration was run with a temporally evolving series
of root-zone storage capacity. The time-dynamic series of Su,max were
obtained from a relatively simple growth function, the Weibull function
(Weibull, 1951):
Su,max(t)=SR,20yr1-e-atb,
where Su,max (t) is the root-zone storage capacity t time steps after
reforestation (L), SR,20yr is the equilibrium value (L), and a
(T-1) and b (–) are shape parameters. In the absence of more
information, this equation was selected as the first, simple way of
incorporating the time-dynamic character of the root-zone storage capacity
in a conceptual hydrological model. In this way, root growth is exclusively
determined dependent on time, whereas the shape parameters a and b merely
implicitly reflect the influence of other factors, such as climatic forcing,
in a lumped way. These parameters were estimated based on qualitative
judgement so that Su,max(t) coincides well with the suite of SR1yr
values after logging. In other words, the values were chosen by trial and
error in such a way that the time-dynamic formulation of Su,max(t)
shows a visually good correspondence with the SR1yr values. This
approach was followed to filter out the short-term fluctuations in the
SR1yr values, which is not warranted by this equation. Note that this
rather simple approach is merely meant as a proof of concept for a dynamic
formulation of Su,max.
Overview of the hydrological signatures.
Signature
Description
Reference
SQMA
Mean annual runoff
SAC
One day autocorrelation coefficient
Montanari and Toth (2007)
SAC,summer
One day autocorrelation the summer period
Euser et al. (2013)
SAC,winter
One day autocorrelation the winter period
Euser et al. (2013)
SRLD
Rising limb density
Shamir et al. (2005)
SDLD
Declining limb density
Shamir et al. (2005)
SQ5
Flow exceeded in 5 % of the time
Jothityangkoon et al. (2001)
SQ50
Flow exceeded in 50 % of the time
Jothityangkoon et al. (2001)
SQ95
Flow exceeded in 95 % of the time
Jothityangkoon et al. (2001)
SQ5,summer
Flow exceeded in 5 % of the summer time
Yilmaz et al. (2008)
SQ50,summer
Flow exceeded in 50 % of the summer time
Yilmaz et al. (2008)
SQ95,summer
Flow exceeded in 95 % of the summer time
Yilmaz et al. (2008)
SQ5,winter
Flow exceeded in 5 % of the winter time
Yilmaz et al. (2008)
SQ50,winter
Flow exceeded in 50 % of the winter time
Yilmaz et al. (2008)
SQ95,winter
Flow exceeded in 95 % of the winter time
Yilmaz et al. (2008)
SPeaks
Peak distribution
Euser et al. (2013)
SPeaks,summer
Peak distribution summer period
Euser et al. (2013)
SPeaks,winter
Peak distribution winter period
Euser et al. (2013)
SQpeak,10
Flow exceeded in 10 % of the peaks
SQpeak,50
Flow exceeded in 50 % of the peaks
SQsummer,peak,10
Flow exceeded in 10 % of the summer peaks
SQsummer,peak,50
Flow exceeded in 10 % of the summer peaks
SQwinter,peak,10
Flow exceeded in 10 % of the winter peaks
SQwinter,peak,50
Flow exceeded in 50 % of the winter peaks
SSFDC
Slope flow duration curve
Yadav et al. (2007)
SLFR
Low flow ratio (Q90 / Q50)
SFDC
Flow duration curve
Westerberg et al. (2011)
SAC,serie
Autocorrelation series (200 days lag time)
Montanari and Toth (2007)
In addition, the remaining parameter directly related to vegetation, the
interception capacity (Imax), was also assigned a time-dynamic formulation. Here,
the same growth function was applied (Eq. 12), but the shape of the growth
function was assumed fixed (i.e. growth parameters a and b were fixed to
values of 0.001 (day-1) and 1 (–)) loosely based on the posterior
ranges of the window calibrations, with qualitative judgement as well. This
growth function was used to ensure the degrees of freedom for both the
time-variant and the time-invariant models, leaving the equilibrium value of
the interception capacity as the only free calibration parameter for this
process. Note that the empirically parameterized growth functions can be
readily extended and/or replaced by more mechanistic, process-based
descriptions of vegetation growth if warranted by the available data, and
they were
here merely used to test the effect of considering changes in vegetation on
the skill of models to reproduce hydrological response dynamics.
Evolution of signatures in time of (a–c) the runoff coefficient,
(d–f) the 1-day autocorrelation, (g–i) the declining limb density, (j–l) the
rising limb density with the reference watersheds in grey and periods of
deforestation in red shading. The flow duration curves for HJ Andrews WS1,
Hubbard Brook WS2 and Hubbard Brook WS5 are shown in (m)–(o), where years
between the first and last year are coloured from light gray to dark grey
as they progress in time.
To assess the performance of the dynamic model compared to the
time-invariant formulation, beyond the calibration objective functions,
model skill in reproducing 28 hydrological signatures was evaluated
(Sivapalan et al., 2003). Even though the signatures are not
always fully independent of each other, this larger set of measures allows a
more complete evaluation of the model skill as, ideally, the model should be
able to simultaneously reproduce all signatures. An overview of the
signatures is given in Table 3. The results of the comparison were
quantified on the basis of the probability of improvement for each signature
(Nijzink et al., 2016):
PI,S=PSdyn>Sstat=∑i=1nPSdyn>Sstat|Sdyn=riPSdyn=ri,
where Sdyn and Sstat are the distributions of the signature
performance metrics of the dynamic and static model, respectively, for the
set of all feasible solutions retained from calibration, ri is a single
realization from the distribution of Sdyn and n is the total number of
realizations of the Sdyn distribution. For PI,S > 0.5
it is then more likely that the dynamic model outperforms the static model
with respect to the signature under consideration, and vice versa for
PI,S < 0.5. The signature performance metrics that were used
are the relative error (for single-valued signatures) and the Nash–Sutcliffe
efficiency (Nash and Sutcliffe, 1970), for signatures that
represent a time series.
In addition, as a more quantitative measure, the ranked probability score,
giving information on the magnitude of model improvement or deterioration,
was calculated (Wilks, 2005):
SRP=1M-1∑m=1M∑k=1mpk-∑k=1mok2,
where M is the number of feasible solutions, pk the probability of a
certain signature performance to occur and ok the probability of the
observation to occur (either 1 or 0, as there is only a single observation).
Briefly, the SRP represents the area enclosed between the cumulative
probability distribution obtained by model results and the cumulative
probability distribution of the observations. Thus, when modelled and
observed cumulative probabilities are identical, the enclosed area goes to
zero. Therefore, the difference between the SRP for the feasible set of
solutions for the time-variant and time-invariant model formulation was used
in the comparison, identifying which model is quantitatively closer to the
observation.
Results
Deforestation and changes in hydrological response dynamics
We found that the three deforested catchments in the two research forests
show on balance similar response dynamics after the logging of the
catchments (Fig. 2). This supports the findings from previous studies of
these catchments (Andréassian, 2004; Bosch and Hewlett, 1982;
Hornbeck et al., 1997; Rothacher et al., 1967). More specifically, it was
found that the observed annual runoff coefficients for HJ Andrews WS1 and
Hubbard Brook WS2 (Fig. 2a, b) change after logging of the catchments, also
in comparison with the adjacent, undisturbed reference watersheds. Right
after deforestation, runoff coefficients increase, followed by a
gradual decrease.
The annual autocorrelation coefficients with a 1-day lag time are generally
lower after logging than in the years before the change, which can be seen
in particular from Fig. 2e and f as here a long pre-treatment time
series record is available. Nevertheless, the climatic influence cannot be
ignored here, as the reference watershed shows a similar pattern. Only for
Hubbard Brook WS5 (Fig. 2f) does the autocorrelation show reduced values in the
first years after logging. Thus, the flows at any time t+1 are less
dependent on the flows at t, which points towards less memory and thus less
storage in the system (i.e. reduced SR), leading to increased peak
flows, similar to the reports of, for example, Patric and
Reinhart (1971) for one of the Fernow experiments.
The declining limb density for HJ Andrews WS1 (Fig. 2g) shows increased
values right after deforestation, whereas a longer time after deforestation, the
values seem to plot closer to the values obtained from the reference
watershed. This indicates that for the same number of peaks, less time was
needed for the recession in the hydrograph in the early years after logging.
In contrast, the rising limb density shows increased values during and right
after deforestation for Hubbard Brook WS2 and WS5 (Fig. 2k–l), compared to
the reference watershed. Here, less time was needed for the rising part of
the hydrograph in the more early years after logging. Thus, the recession
seems to be affected in HJ Andrews WS1, whereas the Hubbard Brook watersheds
exhibit a quicker rise of the hydrograph.
Eventually, the flow duration curves, as shown in Fig. 2m–o, indicate a
higher variability of flows, as the years following deforestation plot with
an increased steepness of the flow duration curve, i.e. a higher flashiness.
This increased flashiness of the catchments after deforestation can also be
noted from the hydrographs shown in Fig. 3. The peaks in the hydrographs
are generally higher, and the flows return faster to the baseflow values in
the years right after deforestation than some years later after some
forest regrowth, all with similar values for the yearly sums of
precipitation and potential evaporation.
Hydrographs for HJ Andrews WS1 in (a) 1962 (annual precipitation
PA= 2018, Ep,A= 951 mm yr-1) and (b) 1989
(PA= 1752, Ep,A= 846 mm yr-1), Hubbard
Brook WS2 in (c) 1966 (PA= 1222, Ep,A= 788 mm yr-1 and (d) 2004 (PA= 1296, annual
Ep,A= 761 mm yr-1 and Hubbard Brook WS5 in (e) 1984 (PA= 1480, annual Ep,A= 721 mm yr-1) and
(f) 2004
(PA= 1311, Ep,A= 731 mm yr-1).
Evolution of root-zone storage capacity SR,1yr from
water balance-based estimation (green shaded area, a range of solutions due
to the sampling of the unknown interception capacity) compared with
Su,max,2yr estimates obtained from the calibration of four models
(FLEX, HYPE, TUW, HYMOD; blue box plots) for HJ Andrews WS1, Hubbard
Brook WS2 and Hubbard Brook WS5. Red shaded areas are periods of
deforestation.
Temporal evolution of SR and Su,max
The observed changes in the hydrological response of the study catchments
(as discussed above) were also clearly reflected in the temporal evolution
of the root-zone storage capacities as described by the catchment models
(Fig. 4). The models all exhibited Kling–Gupta efficiencies ranging between
0.5 and 0.8 and Kling–Gupta efficiencies of the log of the flows between 0.2
and 0.8 (see the Supplement Figs. S5–S7, with all posterior
parameter distributions in Figs. S10–S27, and the number of feasible
solutions in Tables S5–S7 in the Supplement). Comparing the water-balance- and model-derived
estimates of root-zone storage capacity SR and Su,max,
respectively, then showed that they exhibit very similar patterns in the
study catchments. Especially for HJ Andrews WS1 and Hubbard Brook WS2, root-zone storage capacities sharply decreased after deforestation and gradually
recovered during regrowth towards a dynamic equilibrium of climate and
vegetation, whereas the undisturbed reference catchments of HJ Andrews WS2
and Hubbard Brook WS3 showed a rather constant signal over the full period
(see Fig. S8).
The HJ Andrews WS1 shows the clearest signal when looking at the water-balance-derived SR, as can be seen by the green shaded area in Fig. 4a. Before deforestation, the root-zone storage capacity SR,1yr was
found to be around 400 mm. During deforestation, the SR,1yr required
to provide the remaining vegetation with sufficient and continuous access to
water decreased from around 400 to 200 mm. For the first 4–6 years after
deforestation the SR,1yr increased again, reflecting the increased
water demand of vegetation with the regrowth of the forest. In addition, it
was observed that in the period 1971–1978 SR,1yr slowly decreased
again in HJ Andrews.
The four models show a similar pronounced decrease of the calibrated,
feasible set of Su,max during deforestation and a subsequent gradual
increase over the first years after deforestation. The model concepts, and thus
our assumptions about nature, can therefore only account for the changes in
hydrological response dynamics of a catchment, when calibrated in a window
calibration approach with different parameterizations for each time frame.
The absolute values of Su,max obtained from the most parsimonious HYMOD
and FLEX models (both with 8 free calibration parameters) show a somewhat higher
similarity to SR,1yr and its temporal evolution than the values from
the other two models. In spite of similar general patterns in Su,max,
the higher number of parameters in TUW (i.e. 15) result, due to compensation
effects between individual parameters, in wider uncertainty bounds which are
less sensitive to change. It was also observed that in particular TUW
overestimates Su,max compared to SR,1yr, which can be attributed
to the absence of an interception reservoir, leading to a root zone that has
to satisfy not only transpiration but all evaporative fluxes.
Observed and modelled hydrograph for HJ Andrews WS1 for the years of
1978 and 1979, with the red coloured area indicating the 5/95 % uncertainty
intervals of the modelled discharge. Blue bars show daily precipitation.
Hubbard Brook WS2 exhibits a similarly clear decrease in root-zone storage
capacity as a response to deforestation, as shown in Fig. 4b. The water-balance-based SR,1yr estimates approach values of zero during and
right after deforestation. In these years the catchment was treated with
herbicides, removing effectively any vegetation, thereby minimizing
transpiration. In this catchment a more gradual regrowth pattern occurred,
which continued after logging started in 1966 until around 1983.
Generally, the models applied in Hubbard Brook WS2 show similar behaviour to
those
in the HJ Andrews catchment. The calibrated Su,max clearly follows
the temporal pattern of SR,1yr, reflecting the pronounced effects of
de- and reforestation. It can, however, also be observed that the absolute
values of Su,max exceed the SR,1yr estimates. While FLEX on
balance exhibits the closest resemblance between the two values, the TUW model in
particular exhibits wide uncertainty bounds with elevated
Su,max values. Besides the role of interception evaporation, which is
only explicitly accounted for in FLEX, the results are also linked to the
fact that the humid climatic conditions with little seasonality reduces the
importance of the model parameter Su,max, and makes it thereby more
difficult to identify by calibration. The parameter is most important for
lengthy dry periods when vegetation needs enough storage to ensure
continuous access to water.
The temporal variation in SR in Hubbard Brook WS5 does not show such a
distinct signal as in the other two study catchments (Fig. 4c). Moreover,
it can be noted that in the summers of 1984 and 1985 the values of
SR,1yr are relatively high. Nevertheless, the model-based values of
Su,max show again similar dynamics to the water-balance-based
SR,1yr values. TUW and HYMOD show again higher model-based values, but FLEX is
also now overestimating the root-zone storage capacity.
Observed and modelled hydrograph for Hubbard Brook WS2 for (a) the
years of 1984 and 1985 and (b) the years of 1986 and 1987, with the red
coloured area indicating the 5/95 % uncertainty intervals of the modelled
discharge. Blue bars show daily precipitation.
Trend analysis for SR,1yr in HJ Andrews WS1, Hubbard Brook
WS2 and WS5 based on comparison with the control watersheds with (a–c)
cumulative root-zone storages (SR,1yr) with regression, (d–f) residuals
of the regression of cumulative root-zone storages, (g–i) significance test;
the cumulative residuals do not plot within the 95 %-confidence ellipse,
rejecting the null-hypothesis that the two time series are homogeneous, (j–l)
piecewise linear regression based on break points in residuals plot, (m–o)
residuals of piecewise linear regression, (p–r) significance test based on
piecewise linear regression with homogeneous time series of SR,1yr. The
different colours (green, blue, red, violet) indicate individual homogeneous
time periods.
Process understanding – trend analysis and change in hydrological
regimes
The trend analysis for water-balance-derived values of SR,1yr suggests
that for all three study catchments significantly different hydrological
regimes in time can be identified before and after deforestation,
linked to changes in SR,1yr (Fig. 7). For all three catchments, the
cumulative residuals plot outside the 95 %-confidence ellipse, indicating
that the time series obtained in the control catchments and the deforested
catchments are not homogeneous (Fig. 7g–i).
Rather obvious break points can be identified in the residuals plots for the
catchments HJ Andrews WS1 and Hubbard Brook WS2 (Fig. 7d–e). Splitting up
the SR,1yr time series according to these break points into the
periods before deforestation, deforestation and recovery resulted in three
individually homogenous time series that are significantly different from
each other, indicating switches in the hydrological regimes. The results
shown in Fig. 4 indicate that these catchments developed a rather stable
root-zone storage capacity sometime after the start of deforestation (for HJ
Andrews WS1 after 1964, for Hubbard Brook WS2 after 1967). Hence, recovery
and deforestation balanced each other, leading to a temporary equilibrium.
The recovery signal then becomes more dominant in the years after
deforestation. The third homogenous period suggests that the root-zone
storage capacity reached a dynamic equilibrium without any further
systematic changes. This can be interpreted in the way that in the HJ
Andrews WS1, hydrological recovery after deforestation due to the recovery of
the root-zone storage capacity took about 6–9 years (Fig. 7p), while Hubbard
Brook WS2 required 10–13 years for hydrological recovery (Fig. 7q). This
strongly supports the results of Hornbeck et al. (2014), who reported
changes in water yield for WS2 for up to 12 years after deforestation.
The time invariant Su,max formulation represented by
SR,20yr (yellow) and time dynamic Su,max fitted Weibull
growth function (blue) with a linear reduction during deforestation (red
shaded area) and mean 20-year return period root-zone storage capacity
SR, 20yr as equilibrium value for (a) HJ Andrews WS1 with
a= 0.0001 days-1, b= 1.3 and SR,20yr= 494 mm with (b) the objective function
values, (c) Hubbard Brook WS2 with a= 0.001 days-1, b= 0.9 and SR,20yr= 22 mm
with (d) the objective function values, and (e) Hubbard Brook WS5 with
a= 0.001 days-1, b= 0.9 and SR,20yr= 49 mm and with (f) the objective function
values. The green shaded area represents the maximum and minimum boundaries
of SR,1yr from the water balance-based estimation, caused by the
sampling of interception capacities.
The identification of different periods is less obvious for Hubbard Brook
WS5, but the two time series of control catchment and treated catchment are
significantly different (see the cumulative residuals in Fig. 7i).
Nevertheless, the most obvious break point in residuals can be found in 1989
(Fig. 7f). In addition, it can be noted that turning points also exist in
1983 and 1985. These years can be used to split the time series into four
groups (leading to the periods of 1964–1982, 1983–1985, 1986–1989 and
1990–2009 for further analysis). The cumulative residuals from the new
regressions, based on the grouping, plot within the confidence bounds again,
and show a period with deforestation (1983–1985) and recovery (1986–1989).
Mou et al. (1993) reported similar findings with the highest
biomass accumulation in 1986 and 1988, and slower vegetation growth in the
early years. Therefore, full recovery took 5–6 years in Hubbard Brook WS5.
Time-variant model formulation
The adjusted model routine for FLEX, which uses a dynamic time series of
Su,max, generated with the Weibull growth function (Eq. 12), resulted in
a rather small impact on the overall model performance in terms of the
calibration objective function values (Fig. 8b, d, f) compared to the
time-invariant formulation of the model. The strongest improvements for
calibration were observed for the dynamic formulation of FLEX for HJ Andrews
WS1 and Hubbard Brook WS2 (Fig. 8b and d), which reflects the rather
clear signal from deforestation in these catchments.
Signature comparison between a time-dynamic and time-invariant
formulation of root-zone storage capacity in the FLEX model with (a) probabilities of improvement and (b) Ranked Probability Score for 28
hydrological signatures for HJ Andrews WS1 (HJA1), Hubbard Brook WS2 (HB2)
and Hubbard Brook WS5 (HB5). High values are shown in blue, whereas a low
values are shown in red.
Evaluating a set of hydrological signatures suggests that the dynamic
formulation of Su,max allows the model to have a higher probability
of
better reproducing most of the signatures tested here (51 % of all
signatures in the three catchments) as shown in Fig. 9a. A similar pattern
is obtained for the more quantitative SRP (Fig. 9b), where in
52 % of the cases improvements are observed. Most signatures for HJ
Andrews WS1 show a high probability of improvement, with a maximum PI,S= 0.69 (for SQ95,winter) and an average PI,S= 0.55.
Considering the large difference between the deforested situation and the
new equilibrium situation of about 200 mm, this supports the hypothesis that
here a time-variant formulation of Su,max does provide means for an
improved process representation and, thus, hydrological signatures. Here,
improvements are observed especially in the high flows in summer
(SQ5,summer, SQ50,summer) and peak flows (e.g. SPeaks,
SPeaks,summer, SPeaks,winter), which illustrates that the root-zone
storage affects mostly the fast-responding components of the system.
At Hubbard Brook WS2 a more variable pattern is shown in the ability of the
model to reproduce the hydrological signatures. It is interesting to note
that the low flows (SQ95, SQ95,summer, SQ50,summer) improve,
opposed to the expectation raised by the argumentation for HJ Andrews WS1
that peak flows and high flows should improve. In this case, the peaks are
too high for the time-dynamic model.
The probabilities of improvement for the signatures in Hubbard Brook WS5
show an even less clear signal: the model cannot clearly identify a
preference for either a dynamic or static formulation of Su,max (relatively white colours in Fig. 9). This absence of a clear preference
can be related to the observed patterns in water-balance-derived SR
(Fig. 4c), which also does not show a very clear signal after deforestation, indicating that the root-zone storage capacity is of less importance
in this humid region characterized by limited seasonality.
Discussion
Deforestation and changes in hydrological response dynamics
The changes found in the runoff behaviour of the deforested catchments point
towards shifts in the yearly sums of transpiration, which can, except for
climatic variation, be linked to the regrowth of vegetation that takes place
at a similar pace to the changes in hydrological dynamics. This coincidence
of regrowth dynamics and evolution of runoff coefficients was not only
noticed by Hornbeck et al. (2014) for the Hubbard Brook, but was also
previously acknowledged for example by Swift and Swank (1981) in
the Coweeta experiment or Kuczera (1987) for eucalypt regrowth
after forest fires.
Therefore, the key role of vegetation in this partitioning between runoff
and transpiration (Donohue et al., 2012), or more
specifically root zones (Gentine et al., 2012), necessarily
leads to a change in runoff coefficients when vegetation is removed.
Similarly, Gao et al. (2014) found a strong correlation
between root-zone storage capacities and runoff coefficients in more than
300 US catchments, which lends further support to the hypothesis that root-zone storage capacities may have decreased in deforested catchments right
after removal of the vegetation.
Temporal evolution of SR and Su,max
The differences between the Hubbard Brook catchments and HJ Andrews
catchments can be related to climatic conditions. In spite of the high
annual precipitation volumes, high SR,1yr values are plausible for HJ
Andrews WS1 given the marked seasonality of the precipitation in the
Mediterranean climate (Köppen–Geiger class Csb) and the approximately 6-month phase shift between precipitation and potential evaporation peaks in
the study catchment, which dictates that the storage capacities need to be
large enough to store precipitation, which falls mostly during winter, throughout
the extended dry periods with higher energy supply throughout the rest of
the year (Gao et al., 2014). At the same time, low
SR,1yr values in Hubbard Brook WS2 can be related to the relatively
humid climate, and the absence of pronounced rainfall seasonality strongly
reduces storage requirements.
It can also be argued that there is a strong influence of the inter-annual
climatic variability on the estimated root-zone storage capacities. For
example, the marked increase in SR,1yr in Hubbard Brook WS2 in
1985 rather points towards an exceptional year, in terms of climatological
factors, than a sudden expansion of the root zone. It can also be observed
from Fig. 3a that the runoff coefficient was relatively low for 1985,
suggesting either increased evaporation or a storage change. A combination
of a relatively long period of low rainfall amounts and high potential
evaporation, as can be noted by the relatively high mean annual potential
evaporation on top of Fig. 4b, may have led to a high demand in 1985.
Parts of the vegetation may not have survived these high-demand conditions
due to insufficient access to water, explaining the dip in SR,1yr for
the following year, which is also in agreement with reduced growth rates of
trees after droughts as observed by for example Bréda et al. (2006). The hydrographs of 1984–1985 (Fig. 6a) and 1986–1987
(Fig. 6b) also show that July–August 1985 was exceptionally dry, whereas the next
year in August 1986 the catchment seems to have increased peak flows. This
either points towards an actual low storage capacity due to contraction of
the roots during the dry summer or a low need of the system to use the
existing capacity, for instance to recover other vital aspects of the
system.
Nevertheless, Hubbard Brook WS2 does not show a clear signal of reduced root-zone storage, followed by a gradual regrowth. Here, the forest was removed
in a whole-tree harvest in winter 1983–1984, followed by natural regrowth. The
summers of 1984 and 1985 were very dry summers, as also reflected by the
high values of SR,1yr. The young system had already developed enough
roots before these dry periods to have access to a sufficiently large water
volume to survive this summer. This is plausible, as the period of the
highest deficit occurred in mid-July and lasted until approximately the end
of September, thus long after the beginning of the growing season, allowing
enough time for an initial growth and development of young roots from April
until mid-July. In addition, the composition of the new forest differed from
the old forest, with more pin cherry (Prunus pensylvanica) and paper birch (Betula papyrifera). This supports the
statements of a quick regeneration as these species have a high growth rate
and reach canopy closure in a few years. Furthermore, the forest was not either
treated with herbicides (Hubbard Brook WS2) or burned (HJ Andrews
WS1), leaving enough low shrubs and herbs to maintain some level of
transpiration (Hughes and Fahey, 1991; Martin, 1988). It can thus
be argued, similar to Li et al. (2007), that the
remaining vegetation experienced less competition and could increase root
water uptake efficiency and transpiration per unit leaf area. This is in
agreement with Hughes and Fahey (1991), who also stated that
several species benefited from the removal of canopies and newly available
resources in this catchment. Lastly, several other authors related the
absence of a clear change in hydrological dynamics to the severe soil
disturbance in this catchment (Hornbeck et al., 1997; Johnson et al.,
1991). These disturbances lead to extra compaction, whereas at the same time
species were changing, effectively masking any changes in runoff dynamics.
Process understanding – trend analysis and change in hydrological
regimes
The found recovery periods correspond to recovery timescales for forest
systems as reported in other studies (e.g. Brown et al., 2005; Hornbeck et al.,
2014; Elliott et al., 2016) which found that catchments reach a new
equilibrium with a similar timescale as reported here, but in this case with the direct link
to the parameter describing the catchment-scale root-zone storage capacity.
The timescales are also in agreement with regression models to predict water
yield after logging of Douglass (1983), who
assumed a duration of water yield increases of 12 years for coniferous
catchments.
The timescales found here are around 10 years (5–13 years for the
catchments under consideration), but will probably depend on climatic
factors and vegetation type. HJ Andrews WS1 has a recovery (6–9 years)
slightly shorter compared to Hubbard Brook WS2 (10–13 years), which could
depend on the different climatological conditions of the catchments.
Nevertheless, it could also be argued that the spraying of
herbicides had an especially strong impact on the recovery of vegetation in Hubbard
Brook WS2, as the Hubbard Brook WS5 does not show such a distinct recovery
signal.
Hydrograph of Hubbard Brook WS2 with the observed discharge
(blue) and the modelled discharge represented by the 5/95 % uncertainty
intervals (red), obtained with (a) a constant representation of the root-zone
storage capacity Su,max and (b) a time-varying representation of the
root-zone storage capacity Su,max. Blue bars indicate precipitation.
Time-variant model formulation
It was found that a time-dynamic formulation of Su,max merely improved
the high and peak flow signatures for HJ Andrews WS1. Other authors also
suggested previously (e.g. de Boer-Euser et al., 2016; Euser et al.,
2015; Oudin et al., 2004) that the root-zone storage affects mostly the
fast-responding components of the system, by providing a buffer to storm
response. Fulfilling its function as a storage reservoir for plant-available
water, modelled transpiration is significantly reduced post-deforestation,
which in turn results in increased runoff coefficients
(cf. Gao et al., 2014), which have been frequently
reported for post-deforestation periods by earlier studies (e.g. Hornbeck
et al., 2014; Rothacher, 1970; Swift and Swank, 1981)
Nevertheless, signatures considering the peak flows did not improve for the
Hubbard Brook catchments. Apparently, the model with a constant, and thus
higher, Su,max stored water in the root zone, reducing recharge to the
groundwater reservoir that maintains the lower flows and buffering more
water, reducing the peaks. This can also be clearly seen from the
hydrographs (Fig. 10), where the later part of the recession in the
late-summer months is much better captured by the time-dynamic model.
Nevertheless, the peaks are too high for the time-dynamic model, which here
is linked to an insufficient representation of snow-related processes, as
can be seen from the hydrograph (April–May) as well, and possibly by an
inadequate interception growth function, both leading to too high amounts of
effective precipitation entering the root zone. An adjustment of these
processes would have resulted in less infiltration and a smaller root-zone
storage capacity.
It was acknowledged previously by several authors that certain model
parameters may need time-dynamic formulations, like
Waichler et al. (2005) with time-dynamic formulations
of leaf area index and overstore height for the DHSVM model. In addition,
Westra et al. (2014) captured long-term dynamics in the storage
parameter of the GR4J model with a trend correction, in fact leading to a
similar model behaviour to the Weibull growth function in this study.
Nevertheless, they only hypothesized about the actual hydrological reasons
for this, which aimed at the changing number of farmer dams in the
catchment. The results presented here indicate that vegetation, and
especially root-zone dynamics, has a strong impact on the long term
non-stationarity of model parameters. The simple Weibull equation can be
used as an extra equation in conceptual hydrological models to more closely
reflect the dynamics of vegetation. The additional growth parameters may be
left for calibration, but can also be estimated from simple water-balance-based estimations of the root-zone storage. In this way, the extra
parameters should not add any uncertainty to the model outcomes.
General limitations
The results presented here depend on the quality of the data and several
assumptions made in the calculations. A limiting factor is that the
potential evaporation is determined from temperature only, leading to values
that may be relatively low and water balances that may not close completely.
Generally, this would lead to a discrepancy between the modelled
Su,max, where potential evaporation is directly used, and the water-balance estimates of SR. The models will probably generate higher root-zone storages in order to compensate for the rather low potential
evaporation. This can also be noted when looking at Fig. 4 for several
models.
In addition, the assumption that the water balance closes in the 2-year
periods under consideration may often be violated in reality. It can be
argued that the estimated transpiration for the calculation of SR
represents an upper boundary, when storage changes are ignored. This would
lead to estimates of SR that may be lower than presented here.
Nevertheless, attempts with 5-year water balances to reduce the influence of
storage changes (see Fig. S9), showed that
similar patterns were obtained. Values here were slightly lower due to more
averaging in the estimation of the transpiration by the longer time period
used for the water balance. Nevertheless, a strong decrease after
deforestation and gradual recovery can still be observed.
The issues raised here can be fully avoided when, instead of a water-balance-based estimation of the transpiration, remote sensing products are
used to estimate the transpiration, similar to
Wang-Erlandsson et al. (2016).
However, water-balance-based estimates may provide a rather quick solution.
The transpiration estimates were also only corrected for interception
evaporation, thus assuming a negligible amount of soil evaporation. Making
this additional separation is typically not warranted by the available data
and would result in additional uncertainty. The transpiration estimates
presented here merely represent an upper limit of transpiration and will be
lower in reality due to soil evaporation. Thus, the values for SR,1yr
may expected to be lower in reality as well.
Conclusions
In this study, three deforested catchments (HJ Andrews WS1, Hubbard Brook
WS2 and WS5) were investigated to assess the dynamic character of root-zone
storage capacities using water balance, trend analysis, four different
hydrological models and one modified model version. Root-zone storage
capacities were estimated based on a simple water balance approach. Results
demonstrate a good correspondence between water-balance-derived root-zone
storage capacities and values obtained by a 2-year moving window calibration
of four distinct hydrological models.
There are significant changes in root-zone storage capacity after
deforestation, which were detected by both a water-balance-based method and
the calibration of hydrological models in two of the three catchments. More
specifically, root-zone storage capacities showed, for HJ Andrews WS1 and
Hubbard Brook WS2, a sharp decrease in root-zone storage capacities
immediately after deforestation with a gradual recovery towards a new
equilibrium. This could to a large extent explain post-treatment changes to
the hydrological regime. These signals were however not clearly observed for
Hubbard Brook WS5, probably due to soil disturbance, a new vegetation
composition and a climatologically exceptional year. Nevertheless, trend
analysis showed significant differences for all three catchments with their
corresponding, undisturbed reference watersheds. Based on this, recovery
times were estimated to be between 5 and 13 years for the three catchments under
consideration.
These findings underline the fact that root-zone storage capacities in
hydrological models, which are more often than not treated as constant in
time, may need time-dynamic formulations with reductions after logging and
gradual regrowth afterwards. Therefore, one of the models was subsequently
formulated with a time-dynamic description of root-zone storage capacity.
Particularly under climatic conditions with pronounced seasonality and phase
shifts between precipitation and evaporation, this resulted in improvements
in model performance as evaluated by 28 hydrological signatures.
Even though this more complex system behaviour may lead to extra unknown
growth parameters, it has been shown here that a simple equation, reflecting
the long-term growth of the system, can already suffice for a time-dynamic
estimation of this crucial hydrological parameter. Therefore, this study
clearly shows that observed changes in runoff characteristics after land-cover changes can be linked to relatively simple time-dynamic formulations
of vegetation-related model parameters.