Climate Elasticity of Annual Runoff: Observation in Fifteen Forested Catchments on a Latitudinal Gradient in East Asia

: In order to overview the impact of climate change on runoff from forested catchments over Asian countries, we collected water balance data from ﬁfteen long-term catchment monitoring stations (total monitoring period 1975–2018, not continuous), spanning from Sabah, Malaysia (our southernmost site), to Hokkaido, Japan (our northernmost site). We then employed an elasticity analysis to the dataset to examine how the annual runoff from each catchment responded to inter-annual ﬂuctuations in annual rainfall and annual mean air temperature. As a result, we found that (1) the annual runoff was sensitive to annual rainfall for all the catchments examined. In addition, (2) the annual runoff from seven of the ﬁfteen catchments was sensitive to inter-annual changes in the mean air temperature, which was likely due to changes in forest evapotranspiration. Three catchments, however, exhibited an increased runoff in a hot year. Finally, (3) the annual rainfall from the previous year (carry-over soil moisture) was important in explaining the variation in annual runoff in two tropical montane forest catchments. This study may serve as one of the pilot studies toward a comprehensive understanding of the climate elasticity of runoff in countries over Asia, because the examined catchments are unevenly and sparsely distributed over the area.


Introduction
The water balance in forested catchments and its interaction with climatic variables have long been a core research subject in ecohydrology e.g., [1][2][3][4].This is because evapotranspiration (ET), which is strongly influenced by climate [5,6] is potentially higher in forests compared to in other vegetated landscapes [1].As a result, the water balance in forested catchments is expected to be more sensitive toward variations in climate compared to catchments with other land-uses.Even though some past studies are available, continuous investigations that span across geographical regions and climatic zones remain important because (i) there may be differences in the observed data due to differences in the local geology and vegetation and (ii) the ever-changing climate at local, regional, and global scales [7].In view of water resource management and downstream flood control, runoff (R) is a variable of higher interest in catchment water balance compared to ET.However, because R is P minus ET, and ET is affected by climate, R is ultimately affected by variation in climate.
The analysis of climate elasticity of runoff, which was originally proposed by Schaake [8] and thereafter developed by a number of researchers e.g., [8], is a statistical approach that investigates the sensitivity of runoff to various climate variabilities such as rainfall, potential evaporation, air temperature, solar radiation, and wind speed.Several studies have employed the approach to examine the current status of climate elasticity of runoff using long-term catchment water balance data and to predict possible changes in runoff using global change scenarios [9][10][11][12][13][14][15][16][17].Among Asian countries, China is one of the most studied in terms of modeling the climate elasticity of runoff [12][13][14][18][19][20].However, far fewer studies have been conducted in other Asian countries despite increasing public concerns over the impact of climate changes on the hydrologic cycle.
In order to fill the geographical gaps in the study of climate elasticity of runoff, the authors assembled as many available data as possible in their respective areas and, subsequently, annual water balance data for fifteen forested catchments spanning from Sabah, Malaysia (southernmost, equatorial), to Hokkaido, Japan (northernmost, temperate), were produced.The elasticity analysis was then applied to the collected dataset for the purpose of understanding the spatial distribution of the climate elasticity of runoff across the study region.
Specifically, this study sought to (1) understand the response of annual runoff to inter-annual fluctuations in rainfall, mean air temperature, and past-year rainfall in each forested catchment, and (2) to propose future research directions toward a comprehensive understanding of the climate elasticity of runoff in the Asian region.

Data
Fifteen catchments across a gradient of climatic zones in East Asia were selected for this study (Tables 1 and 2).According to Trewartha climate classification [21][22][23], the fifteen catchments were distributed over three major classes (Table 1): Class A (tropical climate), Class C (subtropical climate), and Class D (temperate climate).Both Gunung Alab in Malaysia (ALA) and Kog Ma D Watershed in Thailand (KOG) in Table 1 are upland catchments in a tropical climate, but they are classified under Class C due to their high altitudes (>1000 m above sea level, masl.)[23,24].Nan Watershed Research Station Experimental Watershed in Thailand (NAN) is the only catchment belonging to Class A (Table 1).Lienhuachih Watersheds 3, 4, and 5 in Taiwan (LH3, LH4, and LH5) are located almost on the Tropics of Cancer and they belong to Class C (Table 1).Three lowland catchments in Japan, Jyugei No. 1 (JY1), No. 3 (JY3), and Fukuroyamasawa Watershed A (FUA), also belong to Class C. The remaining four catchments in Japan, Shirasaka Experimental Watershed (SEW), Ananomiya Experimental Watershed (AEW), Bakemonosawa (BKE), and Maruyamazawa (MAR), and two catchments in Korea, Bakmoongol (BMG) and Baramgol (BRG), are classified as having a temperate climate.Although not the most extensive network, the fifteen catchments provided a good geographical coverage, with latitudinal ranges between 5 • 49 N and 43 • 15 N, and altitudinal ranges between 120 and 1970 masl.(Table 2).Due to differences in both climate and forest management practices, each catchment is distinct in terms of forest type, which includes evergreen broad-leaved forest, deciduous broad-leaved forests, pine forests, mixed forests, and conifer and broad-leaved plantations (Table 2).Other catchment information is summarized in Table 2.
Table 3 summarizes the mean annual rainfall (P), mean annual runoff (R), and mean annual air temperature (Ta) over the period of data collection for each catchment.Unless noted below, both P and Ta were measured at a weather station nearby each catchment and R was monitored by a weir.Additional information on runoff measurement can be found in existing publications for ALA [24], KOG [25], LH3, LH4, LH5 [26], FUA, SEW, AEW, BKE, MAR [27], BMG, and BRG [28,29].

Analysis
In order to evaluate the sensitivity of runoff to a climate variable such as rainfall, Schaake (1990) [8] introduced the concept of "elasticity of runoff", in which the percentage change in runoff was defined as the percentage change in the climate variable multiplied by the elasticity (ε).More specifically, in case of an investigation on the effects of annual rainfall in a year i (P i ) on annual runoff in the same year (R i ), the elasticity can be expressed as follows [9]: where P, R, and ε P R are mean annual rainfall, mean annual runoff, and the elasticity of annual runoff to annual rainfall, respectively.In addition, ∆P i and ∆R i in Equation ( 1) are deviations of rainfall and runoff in a particular year from their respective means As evapotranspiration (ET) can affect catchment water balance particularly in forested catchments, many previous studies have incorporated potential evaporation into Equation (1).However, due to poor availability of ET data throughout the studied catchments, air temperature (Ta) was used as a surrogate in place of ET [11,14].The elasticity model in Equation ( 1) was then expanded into a two-parameter model, where ∆Ta i and ε Ta R is the departure of annual mean air temperature in a year i from its long-term mean (Ta) and the elasticity of runoff to air temperature, respectively.Because there was considerable variation in Ta in the examined catchments (Table 2), we have opted to use the non-normalized ∆Ta i instead of the normalized ∆Ta i /Ta, which may dampen the influence of air temperature in warmer regions due to larger denominators (Ta).
Carry-over soil moisture and/or groundwater, which was stored in the catchments from a preceding year, can also influence the annual runoff of the current year [11].Therefore, we tested another two-parameter elasticity model, which is expressed as follows: where ∆P i−1 and ε R are a departure of annual rainfall in a year i − 1 from P and the elasticity of annual runoff in the current year to annual rainfall in the previous year.
We finally developed a three-parameter elasticity model, incorporating all the variables above to produce the following: Hereafter, the elasticity models based on Equations ( 1)-( 4) are denoted by M1, M2, M3, and M4, respectively.A multiple regression analysis without a constant term (i.e., by setting an intercept at zero) was performed for determining coefficients in all the models.In addition to the various elasticity coefficients, the runoff coefficient (C) was computed and assessed.Both analyses were executed by R software version 3.6.1.For each catchment, the best elasticity model was selected based on the adjusted coefficient of determination (R 2 ), because (1) number of independent variables (i.e., degrees of freedom) varies by models and (2) several catchments have shorter-term data set (as short as five years for BKE, see Table 3).

Overall Water Balances and Selected Elasticity Models
Figure 1 shows the time series of annual rainfall and runoff for each catchment.Although there are inter-annual fluctuations in rainfall and runoff for all the catchments, it can be found from Figure 1 that the annual runoff fluctuated in accordance with the annual rainfall.
Figure 2 compares the mean annual rainfall and runoff across all catchments.The mean annual rainfall ranged from 1051 mm at the northernmost MAR to 3873 mm at the southernmost ALA.The mean annual runoff ranged from 169 mm at NAN to 2841 mm at ALA.Although there were differences in climate, forest type, and geological characteristics between catchments (Tables 1 and 2), there was a significant positive correlation between the annual rainfall and annual runoff, indicating a strong influence of annual rainfall on annual runoff, as found in most similar studies [10,[30][31][32].
The best elasticity model, model coefficients, and their respective adjusted R 2 value for each catchment is summarized in Table 4.We have also plotted the various elasticity indices against the runoff coefficient, C (Figure 3).Results for all elasticity models in all catchments is in Appendix A.   1 and 2), there was a significant positive correlation between the annual rainfall and annual runoff, indicating a strong influence of annual rainfall on annual runoff, as found in most similar studies [10,[30][31][32].Figure 2 compares the mean annual rainfall and runoff across all cat mean annual rainfall ranged from 1051 mm at the northernmost MAR to 38 southernmost ALA.The mean annual runoff ranged from 169 mm at NAN ALA.Although there were differences in climate, forest type, and geologica tics between catchments (Tables 1 and 2), there was a significant positive c tween the annual rainfall and annual runoff, indicating a strong influence o fall on annual runoff, as found in most similar studies [10,[30][31][32].The best elasticity model, model coefficients, and their respective adjusted R 2 value for each catchment is summarized in Table 4.We have also plotted the various elasticity indices against the runoff coefficient, C (Figure 3).Results for all elasticity models in all catchments is in Appendix A.

Annual Rainfall in the Current Year
The elasticity of the annual runoff to the annual rainfall in the current year (   ) was positive, but it showed varying statistical significance in the studied catchments (Table 4).This indicated that changes in  are directly proportionate to changes in   .The overall mean    and its standard deviation for all the catchments was 1.467 ± 0.720 (not shown in tables), with minimum and maximum values of 0.720 (p < 0.05) and 3.550 (p < 0.001) in the BMG (temperate lowland) and NAN (tropical lowland) catchments, respectively (Table 4).
The overall mean    of 1.467 indicates that a 1% increase in annual rainfall would cause a 1.467% increase in annual runoff, on average.Such amplified changes in  caused by   were most pronounced in NAN.In contrast, BRG was the most stable catchment, whereby changes in  caused by changes in   were well attenuated.

Annual Rainfall in the Current Year
The elasticity of the annual runoff to the annual rainfall in the current year (ε P R ) was positive, but it showed varying statistical significance in the studied catchments (Table 4).This indicated that changes in R are directly proportionate to changes in P i .The overall mean ε P R and its standard deviation for all the catchments was 1.467 ± 0.720 (not shown in tables), with minimum and maximum values of 0.720 (p < 0.05) and 3.550 (p < 0.001) in the BMG (temperate lowland) and NAN (tropical lowland) catchments, respectively (Table 4).
The overall mean ε P R of 1.467 indicates that a 1% increase in annual rainfall would cause a 1.467% increase in annual runoff, on average.Such amplified changes in R caused by P i were most pronounced in NAN.In contrast, BRG was the most stable catchment, whereby changes in R caused by changes in P i were well attenuated.
The geographical distribution of ε P R over the studied regions in terms of magnitude is illustrated in Figure 4a.Compared to other elasticity indices (ε R and ε Ta R ), the intercatchment variation in ε P R was smaller (Table 4).Nevertheless, Figure 4a implies that midand high-altitude catchments in temperate climates have a relatively smaller ε P R (MAR and BKE, see also Table 4).However, a more homogenously distributed observation with increased catchment diversity is necessary to draw a solid conclusion with regards to the altitudinal and latitudinal variation.In addition, there is a geographical gap of low-altitude catchments in tropical climates (Figure 4a), which should be addressed in future studies.As indicated by the largest ε P R in NAN, R in lowland tropical catchments may show large responses to P i fluctuation.Plots of    against C (Figure 3a) showed an inverse relationship, as has been reported in past studies [9,10,31,33].This is natural following the law of conservation of mass-a high runoff coefficient (i.e., more rainfall immediately ending up as runoff) would result in low elasticity (i.e., less remaining rainfall entering storage to be released as delayed runoff, either soon after or in the following year).

Annual Mean Air Temperature
For seven out of the fifteen catchments, the elasticity of  to the annual mean air temperature (   ) was incorporated into the best elasticity model, with varying levels of significance (Table 4).In four out of the seven catchments,  had a negative influence on R, while three other catchments had positive -R relationships (Table 4). decreased significantly with increasing  at a subtropical (JY3, p < 0.05) and a temperate (AEW, p < 0.01) catchment, but increased with increasing  at another subtropical catchment (LH3, p < 0.001, Table 4).This indicates that an increase in Ta by 1 °C resulted in a 31.1% and 22.9% reduction in  in JY3 and AEW, respectively.In the LH3 however, a 1°C increase in  was accompanied by a 15% increase in .Such changes in R show that year-to-year fluctuations in Ta may be capable of altering the catchment water balance regardless of positive or negative changes-at least in the three forested catchments above.
Predictably, increases in  will result in increases in the potential evaporation (ETp) [5].Therefore, for catchments that showed negative    in this study, decreases in  that accompanied increases in Ta are likely a result of enhanced ET.However, it is known that actual forest ET may not be directly proportional to ETp because Ta influences forest ET by affecting both the evaporative demand of the atmosphere and the stomatal behavior of Plots of ε P R against C (Figure 3a) showed an inverse relationship, as has been reported in past studies [9,10,31,33].This is natural following the law of conservation of mass-a high runoff coefficient (i.e., more rainfall immediately ending up as runoff) would result in low elasticity (i.e., less remaining rainfall entering storage to be released as delayed runoff, either soon after or in the following year).

Annual Mean Air Temperature
For seven out of the fifteen catchments, the elasticity of R to the annual mean air temperature (ε Ta R ) was incorporated into the best elasticity model, with varying levels of significance (Table 4).In four out of the seven catchments, Ta had a negative influence on R, while three other catchments had positive Ta-R relationships (Table 4).R decreased significantly with increasing Ta at a subtropical (JY3, p < 0.05) and a temperate (AEW, p < 0.01) catchment, but increased with increasing Ta at another subtropical catchment (LH3, p < 0.001, Table 4).This indicates that an increase in Ta by 1 • C resulted in a 31.1% and 22.9% reduction in R in JY3 and AEW, respectively.In the LH3 however, a 1 • C increase in Ta was accompanied by a 15% increase in R. Such changes in R show that year-to-year fluctuations in Ta may be capable of altering the catchment water balance regardless of positive or negative changes-at least in the three forested catchments above.
Predictably, increases in Ta will result in increases in the potential evaporation (ET p ) [5].Therefore, for catchments that showed negative ε Ta R in this study, decreases in R that accompanied increases in Ta are likely a result of enhanced ET.However, it is known that actual forest ET may not be directly proportional to ET p because Ta influences forest ET by affecting both the evaporative demand of the atmosphere and the stomatal behavior of trees.Assuming the evergreen broad-leaved trees in LH3 exhibited isohydric behavior (stomatal shutdown) as a response to high temperatures, the actual forest ET could be reduced in a hot year instead (and vice versa), which may explain the negative ε Ta R values in catchments JY3, SEW, AEW, and MAR [34,35].
Plots of ε Ta R against C (Figure 3b) showed an inverse relationship, as did plots of ε P R against C.As data coverage is not contiguous over the studied regions (Figure 4c), it is premature to discuss the geographical distribution of ε Ta R at this point.However, if the hypothesis above was true, the response of R toward variation in Ta should depend more on a catchment tree's species composition rather than its geographical region (Figure 4c).This hypothesis is in-part supported by (i) the varying magnitudes of ε Ta R in the temperate region (Figure 4c) where there were relatively abundant conifer species known for conservative (isohydric or anisohydric).At this point, we suggest that the climate elasticity of runoff in a catchment depends on the tree's species composition and annual rainfall rather than the altitudinal and latitudinal position.
Even though the examined catchments were not contiguous, we were able to specify for each catchment the unique responses of annual runoff to inter-annual variabilities in rainfall and mean air temperature.However, due to insufficient geographical coverage at present, we were not able to draw a solid conclusion with regards to the spatial distribution of the climate elasticity of runoff over the East Asian region.For comprehensive understanding, further studies utilizing a spatially and temporally extended dataset would be needed.
In addition, as implied by the impacts of rainfall in the previous year, the elasticity models and variables used in the models could be refined considering the recent progress in climate elasticity modeling.Studies focusing on chemical signatures and isotopes in runoff are also recommended to understand the immediateness of direct runoff and the delay in groundwater runoff.As performed by several climate elasticity studies in the past, a prediction of the future changes in runoff in Asian forested catchments utilizing global change scenarios can be performed for adaptive water resource management under a changing climate.

Figure 1 .
Figure 1.Time series of annual rainfall (blue) and runoff (red) for each catchment.

Figure 2
Figure 2 compares the mean annual rainfall and runoff across all catchments.The mean annual rainfall ranged from 1051 mm at the northernmost MAR to 3873 mm at the southernmost ALA.The mean annual runoff ranged from 169 mm at NAN to 2841 mm at ALA.Although there were differences in climate, forest type, and geological characteristics between catchments (Tables1 and 2), there was a significant positive correlation between the annual rainfall and annual runoff, indicating a strong influence of annual rainfall on annual runoff, as found in most similar studies[10,[30][31][32].

Figure 1 .
Figure 1.Time series of annual rainfall (blue) and runoff (red) for each catchment.

Figure 1 .
Figure 1.Time series of annual rainfall (blue) and runoff (red) for each catchment.

Figure 2 .
Figure 2. Regression of mean annual runoff against mean annual rainfall.
studies.As indicated by the largest   in NAN,  in lowland tropical catchments may show large responses to   fluctuation.

Figure 4 .
Figure 4. Coefficient values in the elasticity models along altitudinal-and a latitudinal-gradients.Blue-colored and red-colored circles indicate positive and negative coefficients, respectively, and their magnitudes are represented by diameter size.

Figure 4 .
Figure 4. Coefficient values in the elasticity models along altitudinal-and a latitudinal-gradients.Blue-colored and red-colored circles indicate positive and negative coefficients, respectively, and their magnitudes are represented by diameter size.

Table 4 .
Selected elasticity model and its coefficients for each catchment.

Table 4 .
Selected elasticity model and its coefficients for each catchment.