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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.