Multiyear drought has been demonstrated to cause non-stationary rainfall–runoff relationship. But whether this change can occur in catchments that have also experienced vegetation change and whether it invalidates the most widely used methods for estimating impacts of vegetation change – i.e., the paired-catchment method (PCM), the time–trend method (TTM), and the sensitivity-based method (SBM) – on runoff is still unknown and rarely discussed. Estimated inconsistent afforestation impacts were 32.8 %, 93.5 %, and 76.1 % of total runoff changes in the Red Hill paired experimental catchments in Australia during the period of 1990–2015 by the PCM, TTM, and SBM, respectively. In addition to afforestation, the Red Hill paired experimental catchments have experienced a 10-year drought (2000–2009) and have been demonstrated to lead to non-stationary rainfall–runoff relationships of paired catchments. Estimated impacts of vegetation change by the PCM (32.8 %) is still reliable and is not invalided by multiyear drought-induced non-stationarity, because the PCM can eliminate all impacts by different factors on paired catchments (multiyear drought and climate variability), except the purposed treatment (afforestation). For the TTM and SBM, traditional application did not further differentiate different drivers of non-stationary rainfall–runoff relationship (i.e., multiyear drought and vegetation change), which led to significant overestimation of afforestation effects. A new framework was further proposed to separate the effects of three factors on runoff changes, including vegetation change, climate variability, and hydroclimatic non-stationarity (i.e., multiyear drought). Based on the new framework, impacts of multiyear drought and climate variability on runoff of the control catchment (Kileys Run) were 87.2 % and 12.8 %, respectively. Impacts of afforestation, multiyear drought, and climate variability on runoff of the treated catchment (Red Hill) were 32.8 %, 54.7 %, and 23.9 %, respectively. Impacts of afforestation on runoff were 38.8 % by the TTM and 21.4 % by the SBM, agreeing well with that by the PCM (32.8 %). This study not only demonstrated that multiyear drought can induce non-stationary rainfall–runoff relationship using field observations, but also proposed a new framework to better separate the impact of vegetation change on runoff under climate-induced non-stationary condition. More importantly, it is shown that non-stationarity induced by multiyear drought does not invalidate the PCM, and PCM is still the most reliable method even though the control catchment experienced climate-induced shift in the rainfall–runoff relationship.
Vegetation change can exert significant impacts on catchment runoff (Farley et al., 2005; Filoso et al., 2017; Hallema et al., 2018). In addition to vegetation change, climate variability can also cause changes in catchment flow regimes and water yield (Kim et al., 2011; Ryberg et al., 2012). Understanding of the response of runoff to vegetation change was mainly gained through the use of paired-catchment experiments over the past century (Wei et al., 2018). The paired-catchment method (PCM), which is the standard approach for quantifying the effects of forest management on runoff, is based on paired-catchment experiments, and is still used today (Van Loon et al., 2019). However, separating the effects of vegetation change and climate variability on runoff remains a great challenge due to the complex interactions between climate variability and vegetation change (Cavalcante et al., 2019; Jones et al., 2006; Zhang et al., 2021). Moreover, persistent hydroclimatic non-stationary changes observed during the past few decades have increased both temperatures and occurrences of extreme weather events (such as multiyear drought). These changes have led to non-stationary rainfall–runoff relationships in many catchments around the world (Li et al., 2018; Wang et al., 2013; Zhang et al., 2016). Therefore, the combined effect of these influencing factors will lead to greater uncertainty in estimating the impact of vegetation change on runoff using different methods. In particular, is the paired-catchment method still valid under non-stationary rainfall–runoff relationships?
Hydroclimatic non-stationary changes such as multiyear drought-induced non-stationarity in rainfall–runoff relationships have been reported in some catchments around the world, such as prolonged drought in the United States (Griffin and Anchukaitis, 2014), Amazonia (Lewis et al., 2011), and China (Tian et al., 2018). It is widely known that Australia experienced multiyear drought (known as the Millennium Drought) between 1997 and 2009 (King et al., 2020; Peterson et al., 2021). Some studies have also reported that stationary rainfall–runoff relationships in southeast regions of Australia were broken by multiyear drought (Chiew et al., 2014; Petrone et al., 2010; Saft et al., 2016). Multiyear drought can also lead to a shift in catchment rainfall–runoff relationship (or non-stationarity) as vegetation changes, and thus poses great challenges to the basic idea of methods for quantifying runoff changes caused by vegetation change as well as how to separate the effects of vegetation change under multiyear drought conditions.
Three commonly used methods for separating the impacts of vegetation change on catchment water yield are the paired-catchment method (PCM), the time–trend method (TTM), and the sensitivity-based method (SBM). The PCM requires a control and treated catchment located in close proximity, and the primary role of the control catchment is to eliminate the impact of climate change on runoff. Essentially, observations from the control catchment can remove the effect of all factors that lead to change in the rainfall–runoff relationship, except vegetation change between two paired catchments (Lee, 1980). This method has been applied in many paired catchments around the world to provide fundamental understanding and knowledge for water resource management under vegetation change (Brown et al., 2005; Stoof et al., 2012; Van Loon et al., 2019). The time–trend method (TTM) assumes that the rainfall–runoff relationship driven by climate variability during pre- and post-change periods is stationary. Thus the impact of vegetation change on runoff is obtained as the difference between observed runoff during post-change period and estimated runoff based on the rainfall–runoff relationship obtained during the pre-change period (Lee, 1980; Zhang et al., 2019; Zhao et al., 2010). The sensitivity-based method (SBM) is a combination of the Budyko framework (Budyko, 1974) and the elastic response of runoff to rainfall and potential evapotranspiration developed by Zhang et al. (2001). The direct result from the SBM is runoff change caused by climate variability, and the effect of vegetation change on runoff is derived by subtracting the effects of climate variability on runoff from total runoff changes. Generally, the PCM, TTM, and SBM should provide consistent results for a specific catchment where non-stationary change in the rainfall–runoff relationship is only affected by vegetation change. Zhang et al. (2011) applied the TTM and SBM to 15 catchments in Australia and demonstrated that these two methods yielded similar estimates with differences smaller than 25 %.
However, the Red Hill catchment (treated catchment for afforestation), which
is located in southeast Australia, has experienced multiyear drought. Based on the data from 1990–2009, including the Millennium Drought period,
Zhao et al. (2010) showed that estimated contributions of afforestation to
the decrease in runoff between pre- and post-change periods using the PCM is
only 27 %, which was even smaller than
Location and satellite remote sensing image map of the Red Hill/Kileys Run catchments in New South Wales, Australia (© Google Earth).
The Red Hill catchment (1.95 km
Daily rainfall and runoff from these two catchments were collected during
the period of 1990–2015. The daily rainfall was measured by tipping bucket
rain gauges that had been located at the catchment outlet, and the daily runoff was measured by a flat
Rainfall anomaly (%) as a percentage of the mean annual rainfall of the Kileys Run and Red Hill catchments, New South Wales, Australia. Red bars represent dry years and blue bars represent wet years. The black line represents the 3-year moving average of the rainfall anomaly.
The Mann–Kendall test (Kendall, 1975; Mann, 1945) was used to detect the
long-term trend of annual rainfall, runoff, and potential evapotranspiration,
and the Sen's slope estimator (Sen, 1968) was used to obtain the degrees
of the above changes. If the
Double mass curves (DMCs), flow duration curves (FDCs), and rainfall–runoff linear regression curves were employed to detect changes in the rainfall–runoff relationship caused by vegetation change and multiyear drought. The DMCs plot the accumulated values of one variable against the accumulated values of another related variable for a concurrent period (Searcy and Hardison, 1960; Wang et al., 2013). It can still appear as a straight line when both hydrometeorological variables (rainfall and runoff) equilibrate quickly or at the same rate under the condition of stationary changes. A break in the slope of the DMCs detected by the Pettitt method means that a change in the constant of proportionality between rainfall and runoff has occurred. The difference in the slope of the lines indicates the shift in the rainfall–runoff relationship and the degree of change in the relation. The FDCs represent the relationship between magnitude and frequency of runoff, thus providing an important synthesis of the relevant hydrological processes occurring at the catchment scale (Pumo et al., 2013), and apparent change in the shape of the FDCs indicates the change in the rainfall–runoff relationship. Moreover, the upward or downward changes in rainfall–runoff linear regression curves also can detect non-stationary rainfall–runoff relationship (Liu et al., 2021).
For a given catchment, the change in mean annual runoff between two periods
can be estimated as
The total runoff change can be considered to result from vegetation change (
The PCM assumes that the correlation between runoff in two paired catchments will remain the same if the vegetation cover remains the same or changes in a similar fashion. This correlation is established by regression analysis during the calibration period, and then is used to predict the runoff for the treated catchment during the prediction period. The difference between the measured and predicted runoff of the treated catchment during the prediction period represents the impact of the vegetation treatment (e.g., afforestation, deforestation) on runoff (Bosch and Hewlett, 1982; Lee, 1980; Stoneman, 1993; Williamson et al., 1987):
During the calibration period,
The TTM can be applied to a single catchment that experienced vegetation change during two different periods. Runoff without vegetation change can be simulated by using the rainfall–runoff relationship that was developed over the calibration period (Lee, 1980).
During the calibration period,
When the rainfall–runoff relationship of the treated catchment is not subject to hydroclimatic non-stationarity, the third term of Eq. (2) (i.e.,
The SBM is widely used to directly estimate runoff change caused by climate
variability. Runoff change caused by vegetation change can be estimated by
subtracting the runoff change caused by climate variability from the total
runoff changes. Runoff change caused by climate variability can be determined by changes in precipitation and potential evapotranspiration (Koster and Suarez, 1999; Milly and Dunne, 2002), expressed as
When the rainfall–runoff relationship of the treated catchment is not subject to hydroclimatic non-stationarity, the third term of Eq. (2) can be
ignored. Runoff change caused by vegetation change can be estimated by
subtracting the runoff change caused by climate variability from the total
runoff changes.
The calibration and prediction periods for paired-catchment studies are usually defined by the vegetation change history. However, calibration period data were absent for the Red Hill and Kileys Run catchments because runoff observations started only about 1 year before the treatment. Therefore, the calibration period and the prediction period were taken as the pre-change period and post-change periods of runoff, respectively, as determined by the step change-point in the runoff of the treated catchment by previous studies on this site. This approximation will have little effect on the results, as previous studies have shown that the establishment of the young pine tree plantation at the Red Hill catchment had very limited impacts on runoff in the first several years of establishment (Zhao et al., 2010).
The three methods have been successfully applied to paired-catchment studies
to estimate the effect of vegetation change on runoff, and there is little
difference amongst
Schematic diagram showing principles of the traditional application and the new framework. PCM means paired-catchment method, TTM means time–trend method, SBM means sensitivity-based method and subscripts “c” and “t” represent the control catchment and the treated catchment.
In previous studies on the Red Hill paired-catchment site, the third term (
The control catchment is only affected by climate variability and
hydroclimatic non-stationarity, and the impact of hydroclimatic non-stationarity on runoff can be estimated by the TTM and the runoff and
rainfall data. In view of the similarity of the attributes of the control and treated catchments, the impact of hydroclimatic non-stationarity on runoff of the treated catchment can be indirectly obtained by the control catchment and the runoff data.
The simulated runoff not affected by hydroclimatic non-stationarity during the prediction period can be obtained by Eq. (14), while the runoff change
caused by hydroclimatic non-stationarity (
The percentage runoff reduction (
For the PCM, the actual effects of vegetation change on runoff (
For the PCM, the actual effects of climate variability on runoff (
The percentage contribution of vegetation change, climate variability, and
hydroclimatic non-stationarity to total runoff reduction can be estimated
as
The double mass curves (DMCs) of monthly rainfall and runoff of the two paired catchments are shown in Fig. 4a and b. The cumulative rainfall–runoff relationship of the two catchments changed significantly twice as seen in the slope changes of the regressions applied to the DMCs data. Two change points estimated by the Pettitt method occurred in December 1996 and January 2010 in the Red Hill catchment and in October 2001 and May 2010 in the Kileys Run catchment. Thus, the entire study period can be divided into three periods in the two catchments, i.e., the first period (January 1990 to December 1996 in the Red Hill catchment and January 1990 to October 2001 in the Kileys Run catchment), the second period (January 1997 to December 2009 in the Red Hill catchment and November 2001 to May 2010 in the Kileys Run catchment), and the third period (January 2010 to December 2015 in the Red Hill catchment and June 2010 to December 2015 in the Kileys Run catchment).
Figure 4a and b shows that the slopes and intercepts of the DMCs regressions of the two catchments in the different periods were quite different. The slopes of the linear regression lines in the first, second, and third periods were 0.27, 0.11, and 0.19 in the Kileys Run catchment, respectively. The slopes were 0.21, 0.02, and 0.06 in the Red Hill catchment, respectively. Runoff of the two catchments both experienced a large reduction during the second period (i.e., the period of multiyear drought), and then slightly increased during the third period (i.e., the post-drought period), but still well below the runoff of the first period. The decrease of runoff or the change of the rainfall–runoff relationship in the second period of the Red Hill catchment was much higher than that of the Kileys Run catchment, suggesting that the Red Hill catchment was affected by both vegetation change and multiyear drought, while the Kileys Run catchment was only affected by multiyear drought. It showed that the rainfall–runoff relationships of the two catchments became non-stationary during and after multiyear drought.
The linear regression lines defining the relationship between annual rainfall and runoff for the periods of 1990–1996, 1997–2009, and 2010–2015 in the Red Hill catchment and the periods of 1990–2001, 2002–2010, and 2011–2015 in the Kileys Run catchment are shown in Fig. 4c and d. The differences in the slope and intercept of the Red Hill catchment were
Estimated trends and abrupt change points in annual runoff (
Note:
The daily flow duration curves (FDCs) of the two catchments in three different periods (same as periods for DMCs analysis) are shown in Fig. 5. Zero flows were not observed during the first period (before the drought period), but they were observed in 14 % and 8 % of the times during the second and third periods (i.e., the multiyear drought period and the post-drought period), respectively, in the Kileys Run catchment. But in the Red Hill catchment, zero flows were observed in 3 %, 70 %, and 59 % of the times during the three periods, respectively. The FDCs during the first period (purple line) were flatter and smoother than the lines for the other two periods, indicating that runoff changes before the multiyear drought period or runoff reached a new equilibrium state were relatively stable and had a stationary relationship with rainfall. However, for most percentages of the FDCs during the second period (red line), runoff decreased by more than 50 %. Especially low flow decreased most rapidly, and there were 14 % and 70 % no-flow days. Runoff during the third period (blue line) increased compared with the second period. Especially in the high flow region, daily flow recovered to more than 50 % of the runoff that occurred before the multiyear drought, but the low flow increased relatively less, and there were also 8 % and 59 % no-flow days. In summary, the shape and percentage of the zero flows of FDCs in Fig. 5 further demonstrated that the relationship between rainfall and runoff of the two catchments changed significantly over the three periods, especially for the Red Hill catchment suffering from both multiyear drought and afforestation.
Daily flow duration curves of
The statistical information of the trends and change points in annual
runoff, rainfall, and PET of both catchments based on observed data from 1990 to 2015 are shown in Table 1. The change point in annual runoff in the
Red Hill catchment occurred in 1996 and annual runoff decreased significantly after 1996 (
The
Estimated runoff change caused by vegetation change in the Red Hill catchment using the traditional three methods with 26 years of data are shown in Table 2. The total runoff change was
Total runoff reduction (
The results presented in Sect. 4.2 demonstrated that the rainfall–runoff
relationship of the control catchment (Kileys Run) was altered by multiyear
drought, and the rainfall–runoff relationship of the treated catchment (Red
Hill) was altered by both multiyear drought and afforestation. Based on the
new framework, impacts of vegetation change on runoff of the Red Hill catchment were re-estimated using the three methods again, and the results
are listed in Table 2. The percentage runoff reduction induced by multiyear
drought (
The contribution of vegetation change to the total runoff changes of the Red Hill catchment, New South Wales, Australia, estimated using this three methods under the traditional application and the new framework.
Based on the above analysis, we found that multiyear drought changed the rainfall–runoff relationships of the control catchment (Kileys Run) and the treated catchment (Red Hill). And differences among the three methods at the Red Hill experimental site still existed, although a much longer observation period was used. The reason for the big difference is that the non-stationary rainfall–runoff relationship of the treated catchment caused by multiyear drought was neglected in the TTM and the SBM.
The treated catchment (afforestation) experienced four different periods: (I) 1990–1996, pre-drought and untreated; (II) 1997–2001, pre-drought and treated; (III) 2002–2009, in-drought and treated; and (IV) 2010–2015, post-drought and treated. During period (I), runoff of the treated catchment has not been significantly affected, and it can be considered as the calibration period for evaluating the impact of vegetation change on runoff. During period (II), the treated catchment was affected by both vegetation change and climate variability. During periods (III) and (IV), the treated catchment was affected by multiyear drought, vegetation change, and climate variability, because the rainfall–runoff relationship after multiyear drought may not recover to that before multiyear drought (Fig. 4) yet and may persist in such a state for a long time (Peterson et al., 2021). When separating impacts of vegetation change and multiyear drought on runoff, the data of the control and treated catchments need to be used in the same period, that is, the same period needed to be applied to these two catchments. The (II), (III), and (IV) periods of the treated catchment were combined into one period as the prediction period. Thus, Table 2 and Fig. 6 essentially compared runoff between the untreated (1990–1996) and treated (1997–2015) periods. Runoff difference between the untreated and treated periods in the treated catchment was caused by vegetation change, climate variability, and multiyear drought, and runoff difference in the control catchment was caused by climate variability and multiyear drought. Comparing the results of the traditional application with the result of the new framework, the time–trend method (TTM) and the sensitivity-based method (SBM) significantly overestimate runoff reduction caused by vegetation change. The main reason for this difference is that runoff changes estimated by the TTM and the SBM are caused by the total non-stationary changes, and the non-stationary changes are caused by both vegetation change and multiyear drought in the Red Hill catchment. That is, both TTM and SBM significantly overestimate the impact of vegetation change on mean annual runoff, as both afforestation and multiyear drought induce runoff decrease.
Estimated changes between period (I) (i.e., 1990–1996, pre-drought and untreated) and period (II) (i.e., 1997–2001, pre-drought and treated) and between period (I) (i.e., 1990–1996, pre-drought and untreated) and period (III) and (IV) (i.e., 2002–2015, in- and post-drought and treated) can be seen in Fig. S1 in the Supplement. Impacts of afforestation on runoff were 34.3 %, 65.9 %, and 41.5 % of the total runoff changes during the period of 1997–2001 by the PCM, TTM, and SBM, respectively. Impacts of afforestation on runoff were 32.4 %, 100.8 %, and 68.4 % of the total runoff changes during the period of 2002–2015. It can be seen that results of the TTM and SBM during the period of 2002–2015 were significantly higher than those during the period of 1997–2001, while the results of PCM were close. Because multiyear drought happened in 2002–2009 and caused persistent effects in 2010–2015, it had a great impact on the rainfall–runoff relationship of the Red Hill catchment, which made the TTM and SBM overestimate the impact of vegetation change on runoff markedly. That is, errors of the impact of vegetation change on runoff estimated by the TTM and SBM will be larger as effects caused by multiyear drought are imposed on the paired catchments.
The response of runoff to vegetation change is estimated as
The TTM eliminates the influence of the stationary components by making use of the rainfall–runoff relationship of the treated catchment during the calibration period. The result of the TTM, which is about 2.8 times greater than that of the PCM (see Table 2), is essentially runoff changes caused by the non-stationary changes in the rainfall–runoff relationship induced by both vegetation change and multiyear drought. Significant overestimation by the TTM is actually the effect of multiyear drought on runoff.
The SBM is sourced from the Budyko framework (Budyko, 1974). It assumes that the steady state of catchment water balance is fundamentally determined by water input (represented by precipitation) and energy demand (represented by potential evapotranspiration), and the transition from one steady state to another without any change in catchment properties should be moving on the Budyko curve (Roderick and Farquhar, 2011; Sun et al., 2014; Wang et al., 2021). Therefore, stationary changes driven by climate variability during post-treatment period can be separated by sensitivity of runoff to
Changes in
There are missing values in both rainfall and runoff data. Both runoff and rainfall observations are missing from November 1999 to November 2000 and from October 2006 to October 2007. In order to minimize the influences of missing values on the annual total values, annual total is regarded as missing value if more than 1 month is missing. Thus, there are four missing data points in the annual time series of rainfall (Fig. 7). Two periods with missing data are just at the beginning and end of multiyear drought. Missing rainfall values should not differ significantly from the annual rainfall values during the multiyear drought period. The overall trend or segmented trend during drought will not change much due to the lack of rainfall data. This is also true for annual runoff. In addition, the change point of annual runoff calculated with data including missing values was consistent with that by Zhao et al. (2010); both appeared in 1996. Based on data including missing data, estimated afforestation impacts were 31.4 %, 84.7 %, and 64.9 % of the total runoff changes during the period of 1990–2005 by the PCM, TTM, and SBM, respectively. Results of Zhao et al. (2010) were 27.0 %, 71.0 %, and 57 % by the PCM, TTM, and SBM, respectively. They were very close. Furthermore, the same analysis was conducted based on the gridded rainfall data from SILO. Estimated afforestation impacts were 32.8 %, 93.5 %, and 73.0 % of the total runoff changes during the period of 1990–2015 by the PCM, TTM, and SBM, respectively. The results were very close to results using in situ observed rainfall as presented in this study. Therefore, we believe processing of missing data has little influence on the estimated changes.
Seasonal changes in
According to the results in Sect. 4.2, multiyear drought has led to a shift in the rainfall–runoff relationship of paired catchments, which is similar to the significant downward shift of rainfall–runoff regression lines in basins in southeast Australia, the United States, and China (Avanzi et al., 2020; Saft et al., 2015; Tian et al., 2018), and the increases in zero-flow days with low flows being more affected than high flows of daily flow duration curves (FDCs) in 10 catchments from southeastern Australia, New Zealand, and South Africa (Lane et al., 2005). In this study, the runoff coefficient decreased by 87.8 % and 63.3 % during the drought period in the Red Hill and Kileys Run catchments, respectively. The latter was close to the decrease of runoff coefficient of 65.8 % in Texas caused by extreme drought (Allen et al., 2011). Runoff coefficient decrease of the Red Hill catchment was higher than that of the Kileys Run catchment because runoff of the Red Hill catchment was also affected by afforestation, which can increase annual evaporation and decrease streamflow (Bruijnzeel, 1989; Cheng et al., 2017; Hoek Van Dijke et al., 2022). Multiyear drought can lead to more runoff reduction than predicted based on the rainfall–runoff relationship established during pre-drought period, as ignoring the impact of non-stationary changes may cause large errors in the results (Zhao et al., 2010). Compared with the line during the drought period, the rainfall–runoff regression line moved up after multiyear drought due to heavy rainfall of 2010, but it did not return to the state before the multiyear drought. Peterson et al. (2021) suggested that these changes may be due to severe water loss from transpiration during the drought period.
Inter-annual rainfall variability decreased and high rainfall years were missing during the drought period (see Fig. 2). Similar changes were also reported in 124 watersheds in Australia during the drought period (Saft et al., 2015). The reduction of rainfall reduced runoff. In the Kileys Run and Red Hill catchments, rainfall primarily occurred in autumn and winter; less rainfall in autumn may have resulted in lower antecedent soil moisture, which means more precipitation was used to replenish the soil water deficit in winter (Fig. 8). As a result, runoff in winter during the drought period was less than that during the pre-drought period, and the decrease of rainfall in the next spring further aggravated runoff reduction. It was consistent with less runoff during the second period under the same rainfall in Fig. 4. The decrease of GRACE satellite-observed average monthly terrestrial water storage and estimated groundwater storage in the Murray–Darling Basin may support the above speculation about runoff reduction (van Dijk et al., 2013). The decline in groundwater levels may also be the reason for runoff reduction. Decline in precipitation usually resulted in a decline in groundwater levels (Peters et al., 2003), and may cause disconnection between groundwater and surface water (Kinal and Stoneman, 2012). Brutsaert (2008) demonstrated that annual lowest 7 d flow can be used indirectly to indicate the change of ground water storage. The annual lowest 7 d flow in the Kileys Run catchment generally declined from 1990 to 1999, and was reduced further to zero from 2001 to 2010, suggesting ground water storage had dried up for a long time during multiyear drought.
The traditional application of the three methods in catchments that experienced multiyear drought may lead to a large error because only two factors including non-stationary changes (or vegetation change) and stationary changes (or climate variability) are considered to affect runoff, which is the essence of the limitations of traditional application (Dey and Mishra, 2017; Li et al., 2012; Zhang et al., 2019). In this study, a new framework was proposed by applying the TTM to the control catchment to quantify runoff changes caused by changes in the rainfall–runoff relationship induced by multiyear drought. Compared with the traditional application, the new framework further divided non-stationary changes into two parts, driven by vegetation change and multiyear drought separately. Thus runoff changes caused by vegetation change, multiyear drought, and climate variability can be partitioned and quantified (Fig. 3 and Table 2). This new framework also confirmed the fact that multiyear drought altered the rainfall–runoff relationship in the Red Hill catchment, and multiyear drought weakened the impact of vegetation change on runoff (see Table 2), which was important for us to design ecological engineering projects for sustainable water resources management (Brodribb et al., 2020; Newman et al., 2006; Xiao et al., 2020).
Climate variability and multiyear drought are supposed to have essentially different influences on the rainfall–runoff relationship in this study. Climate variability is not supposed to result in non-stationary changes in the rainfall–runoff relationship, that is, rainfall and runoff change at the same rate, while multiyear drought is assumed to result in non-stationary changes in the rainfall–runoff relationship, that is, it can be demonstrated by the significant abrupt change point on the double mass curves (DMCs) and the significant downward shift of rainfall–runoff linear regression line (Avanzi et al., 2020; Li et al., 2018). The multiyear drought in this study refers to drought with long duration and severe intensity, which can cause non-stationary changes in the rainfall–runoff relationship of catchments, as shown in Fig. 4 and discussed in Sect. 5.2. It is quite different from the wet/dry periods fluctuating near the average line (i.e., climate variability) (Han et al., 2019). For the two small studied catchments, the impact of climate fluctuations is very intense, and persistent fluctuations below the average are easy to cause non-stationary changes in the rainfall–runoff relationship because the long-term rainfall reduction may lead to changes of catchment characteristics, that is, lose connection between surface and groundwater. However, for large-scale watersheds, it is difficult to detect and to separate non-stationarity from variability because of the complexity and regional differences of positive and negative fluctuations or feedback of climate.(Clark et al., 2016; Murakami et al., 2020). Negligence of non-stationarity induced by multiyear drought can result in significant differences in estimated effects of vegetation change as shown in Fig. 6, which has also been reported by Zhao et al. (2010) using about 16 years data at the same site. In the new framework, the effect of multiyear drought is estimated between pre- and post-change periods as that of vegetation change, although 2 years of rainfall is above the average after 2000, because the slope of DMCs is still very close to that during the period after 2009 (post-drought) (see Fig. 4).
Interactions between the impact of prolonged drought and that of land use change may exist. Several studies have reported that not only land use types but also soil and catchment properties may lead to different effects of drought on runoff (Saft et al., 2015; van Dijk et al., 2013). Here, one of the assumptions of the new framework is that the effects of three factors (vegetation change, hydroclimatic non-stationarity, and climate variability) are independent of each other. We have to make this assumption to enable us to separate three effects with the help of paired catchments. The sum of the contribution of three factors to runoff changes is 111.4 % in the Red Hill catchment, which is close to 100 % and shows that the assumption is basically reasonable and valid. Considering these complex and secondary interactions amongst different factors, the new framework cannot separate them under the current experimental design and available data. How to estimate the interactions amongst different factors needs to be carefully observed and investigated in the future.
In the new framework, the control catchment plays an irreplaceable role in
estimating the impact of vegetation change and multiyear drought on runoff.
This is because the control catchment can eliminate the impact of climate variability and multiyear drought on runoff when the PCM is used to quantify runoff change caused by vegetation change, and the impact of multiyear drought on the treated catchment is transferred from the control catchment. The former must use the runoff data of the control catchment and the latter needs both the rainfall and runoff data of the control catchment. One of the hypotheses of the new framework is that the percentage of runoff reduction caused by multiyear drought of the control catchment (
According to the results of this study, the non-stationary change of
rainfall–runoff relationships in these two paired catchments caused by multiyear drought does not invalidate the paired-catchment method. The similar hydrological behaviour of the control and treated catchments in terms
of geomorphological, soil properties, and climatic conditions determines that
these two catchments have a relatively similar response process to multiyear
drought and climate variability, which can be seen from the close occurrence
time of the second abrupt change point in Fig. 4a and b. Therefore, the most significant difference between the control and treated catchments between pre- and post-change periods is the change of vegetation cover type (the control catchment was kept as grassland unchanged and the treated catchment was covered by
The length of data used in this study is extended from 16 years (used in
Zhao et al., 2010 study) to 26 years. The difference between the contribution of vegetation change to the changes in total runoff estimated by this study and Zhao et al. (2010) is only 5.8 %, which is also far less than the difference of the TTM and SBM. It shows that the increase of data length has little effect on the estimation of runoff change caused by vegetation change after the runoff of a catchment experiencing vegetation change has reached a new stable equilibrium state. The time required for runoff in different catchments to reach a new equilibrium state is different. For example, the Red Hill catchment takes 7 years (Zhao et al., 2010), Australia and New Zealand have suggested 3 to 10 years or even more (18 years for an afforested catchment in Biesievlei, South Africa; Brown et al., 2005), and a majority of time between 5 and 10 years (Lane et al., 2005) is required for the treated catchment to reach a reasonably stable rainfall–runoff relationship after vegetation change. Han et al. (2020) provided a global assessment of the steady-state assumption in catchment water balance calculations for 1,057 global unimpaired catchments, and showed that
For the Red Hill experiment site, the calibration period was from 1 year after
treatment to the abrupt change point of annual runoff (1990–1996, 7
years), because rainfall and runoff data before treatment were not measured. Zhao et al. (2010) compared the influences of two different methods for determining the calibration period on the estimated vegetation impacts at four paired-catchment sites. One is determined by the time of treatment. The other is determined by the abrupt change point of annual runoff. It was found that runoff changes caused by vegetation change were not sensitive to different calibration periods. Considering that runoff may not change significantly during the first few years after plantation of seedlings of
Through the study of the typical paired-catchment experimental site – Red Hill – we found that multiyear drought during 2000–2009 had altered the stationary rainfall–runoff relationship of both the treated and control catchments. The runoff coefficient decreased by 87.8 % and 63.3 % during the drought period in the Red Hill and Kileys Run catchments, respectively. The paired-catchment method (PCM) is not invalidated by the non-stationarity induced by multiyear drought because of the role of the control catchment. However, the essence of the time–trend method (TTM) and the sensitivity-based method (SBM) is to separate runoff changes caused by non-stationary (vegetation change or/and multiyear drought) and stationary (climate variability) changes in the rainfall–runoff relationship, which makes the TTM and SBM significantly overestimate the impact of vegetation change on runoff. Estimated afforestation impacts were 32.8 %, 93.5 %, and 76.1 % of total runoff changes by the PCM, TTM, and SBM, respectively. On this basis, we propose a new framework by applying the TTM to the control catchment to quantify runoff changes caused by changes in the rainfall–runoff relationship induced by multiyear drought. Impacts of afforestation, multiyear drought, and climate variability on runoff of the treated catchment (Red Hill) were 32.8 %, 54.7 %, and 23.9 %, respectively. The contribution of vegetation change to runoff reduction using the three methods under the new framework becomes consistent (32.8 %, 38.8 %, and 21.4 %). We demonstrated that the PCM was still a valid and fundamental method to estimate the impact of vegetation change on runoff, even if the control catchment experienced hydroclimatic non-stationarity in the rainfall–runoff relationship under changing environments. This study provides a new way to more accurately quantify the impacts of vegetation change, climate variability, and factors causing non-stationarity, except vegetation change on runoff. The findings in this study not only give insight to the change in hydrological processes caused by the combination of land use and climate changes, but can also help in developing strategies and management practices for ecological engineering under a changing climate with frequent extremes in the future.
The daily rainfall and runoff data are measured on site by government agency and are collected by Lu Zhang from CSIRO Land and Water, Black Mountain, Canberra, Australia. Therefore, the data are not publicly accessible. The monthly potential evapotranspiration data can be obtained from the SILO data (
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YZ conceived the study, performed the analyses, and prepared the paper. LC contributed to the study design and interpretation of the results. LZ provided data of rainfall and runoff. All the authors reviewed and edited the paper.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors would like to thank all people and institutions who provided the data used in this study and fruitful discussions and suggestions that helped improve the manuscript.
This research has been supported by the National Natural Science Foundation of China (grant nos. 51961145104, 51879193, and 41890822).
This paper was edited by Adriaan J. (Ryan) Teuling and reviewed by Warrick Dawes and two anonymous referees.