Impact of Climate Change and Human Activities on Streamﬂow Variations Based on the Budyko Framework

: In recent years, the inﬂuence of climate change and human activity on the global environment have become a concern. It is essential to better understand the hydrologic environment to evaluate water availability and related issues. In this study, we perform a trend and breakpoint analysis on streamﬂow time series in the Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping River Basins in northern Taiwan. Furthermore, we apply the Budyko–Fu equation and the Budyko–Mezentsev–Choudhury–Yang equation to evaluate the elasticity of streamﬂow with respect to climate factors and the catchment characteristics parameter. We discuss the sensitivity of streamﬂow to climate factors (precipitation and potential evapotranspiration), as well as sensitivity to human activities such as land use changes. We detected breakpoints in the streamﬂow time series for the Lanyang and Keelung rivers in in 1993 and 1990, respectively. The streamﬂow of Lanyang River increased by 32.50% during the variation period (1993–2017), with 109.00% of the variation caused by non-climate factors. The Keelung River’s streamﬂow was reduced by 18.11% during the variation period (1990–2017), and the dominant factor was climate change, accounting for 71.53% of the reduction. Sensitivity analysis showed that precipitation changes were the most sensitive factor of streamﬂow variation. For every 1% increase in precipitation, the streamﬂow would increase by 1.05% to 1.37%. These results could serve as a reference for the sustainable development of water resources and territorial policies in northern Taiwan. mm, in which the Keelung River Basin has the highest precipitation and the lowest precipitation is in the Fengshan River Basin. The long-term precipitation of Dahan and Youluo river basins showed an upward trend, with the highest slope of 5.578 mm / year appearing in the Youluo River Basin. Meanwhile, the precipitation in Lanyang, Keelung, Fengshan, and Shangping river basins shows a downward trend; the basin showing the largest slope value is the Keelung River Basin, which decreases at − 13.72 mm / year. The Mann–Kendall trend test is applied to analyze the signiﬁcance of the annual precipitation variation. The results indicate that the Z value of the annual precipitation in the Lanyang, Keelung, Dahan, Fengshan, Youluo, and Shangping river basins is sequentially shown as − 0.05, − 0.86, 0.11, − 0.14, 0.38, and 0.23, as shown in Table 3. According to the trend test, there is no signiﬁcant trend in the annual precipitation in any of the analyzed basins. Keelung, Dahan, Fengshan, Youluo and Shangping river basins are 0.55, 1.51, 1.11, 1.58, 1.38 and 1.38, respectively, and this indicates that the trends of potential evapotranspiration in all of the study basins are not statistically signiﬁcant. study divides the streamﬂow and climate data into a baseline period and variation period to discuss the hydrological variation occurring between these two periods.


Introduction
Water resources are essential assets for the development of human society. However, in recent years, changes in the hydrologic environment due to the combination of climate change and other human activities have triggered water resource difficulties in many regions. Events associated with extreme weather and environmental disasters such as heavy rainfall, floods and droughts are being reported more frequently [1][2][3][4]. Therefore, assessing hydrological responses under the influences of human activities and climate change has become an important issue for policy makers.
Human activities, including land use change, water diversion, dam construction, and soil and water conservation policies [5][6][7], cause variation of the environment. The change of streamflow is one of the key factors in understanding the pattern of the hydrological cycle in a watershed [8].
Depending on the source of the environmental disturbance, the cause of the change in streamflow can be divided into climate change and non-climate factors. Climate factors that may affect streamflow include precipitation and potential evapotranspiration variation caused by global warming, and non-climate factors include human activities such as land use and land cover changes in the basin; e.g., dam construction and clear cutting [9,10].
where Q denotes the streamflow and x is the factor affecting the runoff, such as precipitation (P) or potential evapotranspiration (E 0 ). Budyko [21,22] assumed that the annual average evapotranspiration and runoff in a region are mainly controlled by the available energy in the atmosphere (demand, often in the form of net radiation Water 2019, 11,2001 3 of 22 (R n ) or potential evapotranspiration (E 0 )) and available water (supply, represented by precipitation). This relationship can be expressed in an equation over a long-term time scale: where F(∅) is the equation of the Budyko curve, E is the evapotranspiration, and ∅ is the drought index of the Budyko framework (defined as ∅ = E 0 /P, if ∅ < 1 represents an arid climate; ∅ > 1 means a humid climate). According to the development and derivations of different scholars, different Budyko curve equations are listed in Table 1. The first four equations in the table belong to the non-parameter method. These models mainly focus on evaluating the impact of climate change. The Fu, Mezentsev-Choudhury-Yang, Milly-Porporato, Zhang, and Wang-Tang models contain parameters related to the watershed characteristics, such as land cover, vegetation, soil properties, and geomorphology. Under Budyko's hypothesis, if a basin is extremely arid (i.e., the precipitation is much smaller than E 0 ), the available energy is much greater than the energy required for the evapotranspiration. Under this condition, the annual evaporation will be limited by the available water and approach the precipitation. Conversely, if the basin is extremely humid (i.e., the precipitation is much larger than the potential evapotranspiration), the available energy is much smaller than the evapotranspiration requirement, and thus the annual evapotranspiration is limited by the available energy and approaches the potential evapotranspiration [7,30,31]. The mathematical expressions for extremely arid and humid situations are shown in Equations (3) and (4), respectively: These two assumptions form a boundary condition on the Budyko curve: the upper boundary represents the water limit, and left boundary represents the energy limit.
Models developed from the Budyko framework have been extended and applied very widely. Many people still propose new models based on the Budyko framework to evaluate the hydrological response of the watershed [7,[32][33][34]. In assessing the impact of the hydrological environment, this type of method continues to be applied and developed, because the Budyko analytical method is supported by the physical background and does not require substantial historical data. For example, Sankarasubramanian et al. [28], Arora [30], Roderick and Farquhar [14], Yang and Yang [15], and others propose further analysis and discussion within the Budyko framework. Xu et al. [6] used the Budyko-Mezentsev-Choudhury-Yang equation to estimate the impact of climate change and human activities on runoff reduction in the Haihe River Basin. The data used in this study include precipitation, discharge and other data used to calculate potential evapotranspiration (e.g., temperatures, sunshine duration, wind speed, and relative humidity); thus, the watershed characteristics parameter and Budyko curve can be obtained. Xu et al. [6] show that 73.1% of the runoff reduction in the Haihe River Basin was caused by changes in land use and land cover. Gao et al. [20] used the Budyko-Fu equation to evaluate the effect of climate change and human activities on the hydrology of the Weihe River Basin from 1961 to 2009. They found that climate change accounted for 63.9% of the decrease in runoff in the basin. Xue et al. [35] used the double mass curve method and the elasticity method to quantify the runoff variation in the Tarim River Basin from 1960 to 2015. Their study used the Budyko, Mezentsev-Choudhury-Yang, and Budyko-Fu equations to show that human activities were the main cause of the reduction in runoff in the basin. The results of these studies show that the Budyko framework is a practical and dependable method that can provide assessments consistent with the actual situation.

Model Budyko Curve Equation Parameter Reference
Budyko-Schreiber Turc [38]; Pike [39] Budyko-Fu Milly [44]; Porporato et al. [45] Budyko-Zhang Wang and Tang [47] The precipitation in Taiwan mainly comes from the spring frontal system, tropical cyclones and the heavy rain caused by the southwesterly flow in summer, and the northeast monsoon which brings moisture and rainfall to northern Taiwan in the winter. These climate events have brought abundant rainfall to Taiwan in different seasons, with the average annual precipitation reaching 2510 mm from 1949 to 2018 [48]. However, Taiwan still faces insufficient water resources due to its geography. Because most of Taiwan's rivers are short and have steep slopes and a high flow velocity, the basin cannot fully conserve water resources, causing most of the precipitation to be lost to runoff. Limited by the innate geographical conditions and the influence of human activities, Taiwan faces multiple water resource problems, such as development difficulties, water quality, availability and flooding. Under climate change, rainfall patterns change over time and space, making it more challenging to manage water usage. At present, the annual precipitation over Taiwan as a whole remains approximately steady, but the precipitation in northern Taiwan is increasing and the precipitation in southern Taiwan is decreasing, indicating that the rain belt has moved northward. In addition, the average number of rainy days across Taiwan has decreased, and the rainfall intensity (the ratio of rainfall to rainy days) has also increased in various regions [49]. This result indicates that we are facing increasingly extreme weather. Northern Taiwan is a densely populated area; thus, the land and water resources are very valuable. In the past, the impact of human activities and land policies on the hydrological environment have not been well quantified, and so the extent of their impact is difficult to determine. Gaining a better understanding of how the hydrological cycle will change in river basins in northern Taiwan due to climate change and human activities and providing quantitative results will be helpful in developing water resource management and soil conservation policies in the future.

Study Area
The administrative districts in northern Taiwan include Yilan County, Keelung City, New Taipei City, Taipei City, Taoyuan City, and Hsinchu County. The main basins in the area are Lanyang, Danshui, Fengshan and Touqian river basins, with drainage areas of 978, 2726, 250.1 and 565.9 km 2 , respectively, among which the Danshui River Basin covers the largest area. From 1949 to 2017, the average annual streamflow of the entire area was 15.15 billion m 3 . The average annual streamflow during the wet season (May-October) was 9.52 billion m 3 , and that in the arid season (January-April) was 5.62 billion m 3 ; the difference of streamflow between wet and arid seasons is relatively low compared to other regions of Taiwan. The winter rainfall in the region mainly comes from the northeast monsoon, and typhoons are the dominant source of water in the summer. The average annual precipitation from 1949 to 2017 was 2933.90 mm. Northern Taiwan is a relatively wet area compared to the central, southern and eastern parts of Taiwan [48].
For this study, we selected the Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping river basins in northern Taiwan as the study area. The Dahan and Keelung Rivers are tributaries of the Danshui River Basin, and Youluo and Shangping Rivers belong to the sub-basin of the Touqian River Basin. This study uses the streamflow gauging station established by the Water Resources Agency of the Ministry of Economic Affairs to define watershed areas of 820.69, 622. 8 Figure 1.

Methodology
To evaluate the variation of precipitation and streamflow in northern Taiwan, we selected the rainfall stations and streamflow gauging stations set up by the Water Resources Agency for analysis. The details are shown in Table 2, the coordinate in two-degree zone Transverse Mercator projection is represented in TM2_X and TM2_Y. The average precipitation in each basin is calculated using the Thiessen polygon method [50]. If there are less than three rainfall stations available in the basin, the average precipitation is calculated by the arithmetic average method. This study uses potential evapotranspiration data provided by Global Land Evaporation Amsterdam Model (GLEAM) [51,52].

Methodology
To evaluate the variation of precipitation and streamflow in northern Taiwan, we selected the rainfall stations and streamflow gauging stations set up by the Water Resources Agency for analysis. The details are shown in Table 2, the coordinate in two-degree zone Transverse Mercator projection is represented in TM2_X and TM2_Y. The average precipitation in each basin is calculated using the Thiessen polygon method [50]. If there are less than three rainfall stations available in the basin, the average precipitation is calculated by the arithmetic average method. This study uses potential evapotranspiration data provided by Global Land Evaporation Amsterdam Model (GLEAM) [51,52]. GLEAM is a database of evapotranspiration based on satellite telemetry data, providing a global raster with a 0.25 • × 0.25 • resolution between 1980 and 2017, including transpiration, bare-soil evaporation, interception loss, open-water evaporation, sublimation, and potential evapotranspiration calculated based on the Priestley-Taylor equation [53]. According to different datasets used to calculate the forcing variable, GLEAM can be divided into two versions: GLEAM v3.2a and GLEAM v3.2b. The GLEAM v3.2a version provides data from 1980 to 2017, while GLEAM v3.2b version only offers data from 2003 to 2017; accordingly, this study uses data from GLEAM v3.2a. Table 2. Information for the rainfall station and streamflow gauging station in northern Taiwan [48]. The data analysis methods used in this study to further evaluate the trends, breakpoints, and variation of hydrological data in northern Taiwan include the Mann-Kendall trend test, Mann-Whitney-Pettit test, and the elasticity method based on the Budyko framework.

Mann-Kendall Trend Test
The Mann-Kendall trend test [54,55] is a non-parametric analysis that has been widely deployed in various hydrological and meteorological studies, providing tests to determine the statistically significant trend of a data sequence. The Mann-Kendall trend test is remarkable for its high reliability; many studies have proved that it is valid for the trend verification of time series data [56,57]. The test is basically a double-tailed test with a null hypothesis that the data sequence does not have a significant trend. If the null hypothesis is rejected, then the data sequence has a significant trend. A statistic S is defined as . , x n are the data arranged in time, and n represents the amount of data. In the case of n ≥ 10, the statistic S will follow a normal distribution, meaning that the variation is as follows, and furthermore that the test statistic Z of the double-tailed test can be obtained: Under the 90% confidence level, according to the critical value method, if the Z value is larger (smaller) than positive (negative) 1.65, then the null hypothesis is rejected, indicating that the data have a significant trend.

Mann-Whitney-Pettit Test
The Mann-Whitney-Pettit test [58] has been generally applied in the detection of the existence of a break point in a data sequence. Assuming that there is a break point X t in the data sequence {X 1 , X 2 , X 3 , . . . , X n }, then this sequence can be divided into two unequal paragraphs F 1 (X) = {X 1 , X 2 , X 3 , . . . , X t } and F 2 (X) = {X t+1 , X t+2 , X t+3 , . . . , X n }; therefore, we define a statistic as If U t,n increases with time t, this signifies that the sequence does not have a break point; conversely, if U t,n presents a downward trend against time t, this indicates that a break point occurred in the series. Usually, if multiple adjacent break points exist in a series, the maximum value K n will be determined as the break point: The formula for calculating the probability of break points is defined as follows: Considering some data series may have multiple break points, Equation (13) can further determine the probability of a break point.

Elasticity Method
In an ideal watershed, the water balance equation can be expressed as where P is rainfall, E is the actual evapotranspiration, Q is the streamflow, and ∆S is the water storage change. When the study period is longer than a decade or uses a long-term scale, the water storage change within a basin can be assumed to be ignored [46]. In order to quantify the hydrological variation in the basin, this study uses streamflow as an indicator. If the break point is detected, the analysis period can be divided into the baseline period and the variation period. It is commonly assumed that the baseline period of the basin is a more undeveloped or less human disturbance; additionally, the variation period represents the basin being disturbed after the period of change in streamflow.
The quantity of streamflow variation can be expressed as where ∆Q total is the total streamflow change, Q variation represents the average annual observed streamflow during the variation period, and Q baseline is the average annual observed streamflow of the baseline period. The variation of streamflow is divided here by the summation of climatic factors and non-climate factors: where ∆Q climate denotes the amount of streamflow variation caused by climate change, and ∆Q non−climate is the amount of streamflow variation caused by non-climate factors. The percentage change caused by climate change and non-climate factors on streamflow can be further determined: where µ climate is the percentage change in streamflow caused by climate change, and µ non−climate is the percentage change caused by non-climate factors. According to Equation (2) Table 1.
Combining Equation (2) with Equation (14), the following relationship can be obtained: Based on the functional form of Equation (19), the change in streamflow caused by climate change and watershed characteristics can be expressed as According to the definition of elasticity (1), Equation (20) can be rewritten as where ε P , ε E 0 and ε N are the elasticity coefficients of streamflow to precipitation, potential evapotranspiration, and the watershed characteristic parameter, respectively. They can be obtained from the following formula: If the value of the elasticity coefficient is a, when the x factor is increased by 1%, the streamflow will increase by a%. Moreover, the quantity of streamflow change caused by climatic factors can be calculated as follows: where Q, E 0 and P are the long-term average annual streamflow, precipitation and potential evapotranspiration, respectively. After ∆Q climate is calculated, ∆Q non−climate can be solved by Equation (15); therefore, the change of streamflow contributed by climate change and non-climate factors can be identified.

Trend Analysis
This study conducted trend analyses based on hydrological data of the major river basins in northern Taiwan, including the precipitation, streamflow, and potential evapotranspiration of Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping river basins. Figure 2 shows the trend of annual precipitation in each catchment. The average annual precipitation in the region during 1980~2017 is between 2043.57 to 4289.96 mm, in which the Keelung River Basin has the highest precipitation and the lowest precipitation is in the Fengshan River Basin. The long-term precipitation of Dahan and Youluo river basins showed an upward trend, with the highest slope of 5.578 mm/year appearing in the Youluo River Basin. Meanwhile, the precipitation in Lanyang, Keelung, Fengshan, and Shangping river basins shows a downward trend; the basin showing the largest slope value is the Keelung River Basin, which decreases at −13.72 mm/year. The Mann-Kendall trend test is applied to analyze the significance of the annual precipitation variation. The results indicate that the Z value of the annual precipitation in the Lanyang, Keelung, Dahan, Fengshan, Youluo, and Shangping river basins is sequentially shown as −0.05, −0.86, 0.11, −0.14, 0.38, and 0.23, as shown in Table 3. According to the trend test, there is no significant trend in the annual precipitation in any of the analyzed basins.
time with the highest probability of abrupt change in hydrological data, and P = 0.90 is defined as the threshold. The results are shown in Table 3. According to the test, the streamflow break points in the Lanyang and the Keelung river basins occurred in 1993 (P = 0.97) and 1990 (P = 0.94), respectively, while the other variables had no significant break point. Based on the abrupt change occurring at the time of the streamflow break point, this study divides the streamflow and climate data into a baseline period and variation period to discuss the hydrological variation occurring between these two periods.  The potential evapotranspiration of each basin is shown in Figure 3. The average annual potential evapotranspiration of the Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping river basins during 1980~2017 ranged from 1049.77 to 1138.40 mm, and the slope of the long-term data ranged from 0.27 to 0.78 mm/year, in which all the basins showed an upward trend. Among these, the Keelung River Basin has the highest slope, and the Lanyang River Basin has the lowest. The results of analyzing the trend of potential evapotranspiration through the Mann-Kendall trend test are shown in Table 3.
The Z values of potential evapotranspiration in Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping river basins are 0.55, 1.51, 1.11, 1.58, 1.38 and 1.38, respectively, and this indicates that the trends of potential evapotranspiration in all of the study basins are not statistically significant.      In this study, the Mann-Whitney-Pettit test is used to determine the break point, which is the time with the highest probability of abrupt change in hydrological data, and P = 0.90 is defined as the threshold. The results are shown in Table 3. According to the test, the streamflow break points in the Lanyang and the Keelung river basins occurred in 1993 (P = 0.97) and 1990 (P = 0.94), respectively, while the other variables had no significant break point. Based on the abrupt change occurring at the time of the streamflow break point, this study divides the streamflow and climate data into a baseline period and variation period to discuss the hydrological variation occurring between these two periods.

Impacts of Climate Change and Non-Climate Factors on Streamflow
This study uses the Budyko-Fu and Budyko-Mezentsev-Choundhury-Yang equations to evaluate streamflow trends in the Lanyang and Keelung river basins. The results are shown in Table 4. Compared with the baseline period, the streamflow of the Lanyang River Basin increased by 32.50% during the variation period. The influence of climate change on the streamflow change (η c1imate ) ranged from −9.01% to −8.99%, and the impact of the non-climate factors (η non-climate ) ranged from 109.01% to 108.99%, revealing that non-climate factors are a dominant factor in increasing streamflow. Conversely, the streamflow in the Keelung River Basin decreased by 18.11% during the variation period, and the impact of climate change was the critical factor of the streamflow variation, accounting for 71.75% to 71.30% of the total change, while non-climate factors accounted for 28.25% to 28.70% of the variation.
The effects of non-climatic factors include terrain changes, vegetation changes and human activities. In 1979, the Lanyang area implemented the "Integrated Conservation and Flood Control Program in Yilan Area and Eastern Taiwan". This work includes soil-water conservation on slope land, forest management, the treatment of landslides, engineering work on check dams and flood control. Due to the considerable work on soil and water conservation and regulation programs in the Lanyang River Basin during this period, we speculate that the fluvial pattern was changed, affecting the runoff response. We looked at the Normalized Difference Vegetation Index (NDVI) to evaluate the changes of vegetation cover in the Lanyang River Basin before and after the implementation of the program. Considering historical records, seasons, clouds and solar zenith angles, we selected images from Landsat2, Landsat5 and Landsat8 for analysis [61,62]. We analyzed the following cloudless satellite images from August to November  Table 5 lists the NDVI differences of the basin. The NDVI increased by 78.85% of the total area in the Lanyang River Basin between 1978 and 1993. It is notable that the NDVI reduction in the downstream Lanyang Plain originated from the seasonal changes in farming. Figure 6a shows that the vegetation in the basin increased during this period. However, between 1993 and 2004, the NDVI in the Lanyang River Basin shows a downward trend. The proportion of the area where NDVI values decreased in the basin was 71.32%, of which 47.74% was concentrated in the range of 0 to −0.1. From 2004 to 2018, NDVI presents a more strongly declining trend. The area of NDVI reduction reaches 91.76% of the total area, with most of the drop occurring between −0.2 to −0.3, accounting for 44.46% of the area. According to the environmental conservation policy implemented earlier in this region, the increase of NDVI in the baseline period could be evidence of afforestation. Nevertheless, from 1993 to 2018, the NDVI began to decline, revealing that the plant cover was also decreasing throughout the variation period.
Many studies have previously reported the case of large-scale afforestation-induced runoff reduction in this particular basin [8,14]. It is understood that the increase of forests regularly co-occurs with more vigorous evapotranspiration, which leads to the loss of streamflow; on the contrary, the reduction of vegetation coverage by clear cutting or similar behavior will increase runoff [14,63,64]. Due to implementation of the "Integrated Conservation and Flood Control Program in Yilan Area and Eastern Taiwan", the vegetation of the Lanyang River Basin increased during the baseline period, and, accordingly, the streamflow in the baseline period decreased. Nevertheless, the NDVI data indicate that the vegetation began to decrease in the post-1993 period, creating a breakpoint and causing the streamflow to increase. The results indicate that changes in vegetation are related to hydrological variation in the Lanyang River Basin, but the factors that triggered the decrease in vegetation in the Lanyang River Basin after 1993 may include human activities, natural disasters and climate change, which require further research.

Sensitivity Analysis of Streamflow Variation
By analyzing the sensitivity of each basin, the response patterns of hydrological changes in the different basins of northern Taiwan can be understood, helping us to propose further analysis. Table  6 shows the sensitivity analysis of streamflow variation with respect to precipitation, potential evapotranspiration, and watershed characteristic parameters. The elasticities of streamflow to precipitation of the study basin are between 1.05 and 1.37, indicating that for every 1% increase in precipitation, the basins of northern Taiwan will increase their streamflow by 1.05% to 1.37%. Among the climate change factors, the sensitivity of the streamflow to the change of the potential evapotranspiration is not as significant as the precipitation, which has an elasticity between −0.04 and −0.37, suggesting that for each 1% increase in potential evapotranspiration, the streamflow will be reduced by 0.04% to 0.37%. The elasticity of the watershed characteristic parameter m of the Budyko-Fu equation, which represents the sensitivity of streamflow to human-induced changes to the basin, ranged from −0.27 to −0.79. The lowest and highest m elasticity values occurred in the Lanyang and the Dahan river basins during the baseline period, denoting that each 1% increase in the parameter m will reduce the streamflow in the basin by −0.28% to −0.79%. The elasticity of the Budyko-Mezentsev-Choudhury-Yang equation parameter n is between −0.13 and −0.33, and the lowest and highest elasticity values occurred during the baseline period of the Keelung and Fengshan river basins. For every 1% increase in n, the streamflow in the basin will be reduced by −0.13% to −0.33%. The sensitivity of the two equations varies among the basins, indicating that the watershed characteristic parameters perform differently for the variation of the watershed characteristics.
According to the results of the sensitivity analysis, the precipitation elasticity of streamflow in northern Taiwanese basins is higher than the elasticity to either potential evapotranspiration or watershed characteristics. The influence of the change of watershed characteristics is the second most important factor. These results indicate that under climate change, the spatial and temporal changes The Keelung River Basin has the most abundant precipitation of all the basins in the study area. Its decrease in streamflow was mainly caused by the decrease of precipitation. Therefore, the future management of the basin should consider the hydrological impact of precipitation changes due to climate change to establish an effective water use and deployment policy. The impacts of climate and non-climate factors on the streamflow changes in the basins of northern Taiwan are quite similar between the two Budyko models, indicating that either the Budyko-Fu model or the Budyko-Mezentsev-Choudhury-Yang model can be used for reliable watershed hydrological analysis.

Sensitivity Analysis of Streamflow Variation
By analyzing the sensitivity of each basin, the response patterns of hydrological changes in the different basins of northern Taiwan can be understood, helping us to propose further analysis. Table 6 shows the sensitivity analysis of streamflow variation with respect to precipitation, potential evapotranspiration, and watershed characteristic parameters. The elasticities of streamflow to precipitation of the study basin are between 1.05 and 1.37, indicating that for every 1% increase in precipitation, the basins of northern Taiwan will increase their streamflow by 1.05% to 1.37%. Among the climate change factors, the sensitivity of the streamflow to the change of the potential evapotranspiration is not as significant as the precipitation, which has an elasticity between −0.04 and −0.37, suggesting that for each 1% increase in potential evapotranspiration, the streamflow will be reduced by 0.04% to 0.37%. The elasticity of the watershed characteristic parameter m of the Budyko-Fu equation, which represents the sensitivity of streamflow to human-induced changes to the basin, ranged from −0.27 to −0.79. The lowest and highest m elasticity values occurred in the Lanyang and the Dahan river basins during the baseline period, denoting that each 1% increase in the parameter m will reduce the streamflow in the basin by −0.28% to −0.79%. The elasticity of the Budyko-Mezentsev-Choudhury-Yang equation parameter n is between −0.13 and −0.33, and the lowest and highest elasticity values occurred during the baseline period of the Keelung and Fengshan river basins. For every 1% increase in n, the streamflow in the basin will be reduced by −0.13% to −0.33%. The sensitivity of the two equations varies among the basins, indicating that the watershed characteristic parameters perform differently for the variation of the watershed characteristics. Table 6. Results of the sensitivity analysis of streamflow variation for precipitation, potential evapotranspiration, and watershed characteristics parameters.

River Basin
Period According to the results of the sensitivity analysis, the precipitation elasticity of streamflow in northern Taiwanese basins is higher than the elasticity to either potential evapotranspiration or watershed characteristics. The influence of the change of watershed characteristics is the second most important factor. These results indicate that under climate change, the spatial and temporal changes of precipitation have the most significant impact on water resources in the river basins of northern Taiwan, and anthropological activities will also have a certain degree of impact on the basins. Regardless of whether we examine the past or future, this result is a reminder of the importance of implementing governance policies that cope with environmental changes and keep pace with the times.

Conclusions
The river basins in northern Taiwan cover a large area of the original forest and play an important role in supplying water to nearby densely populated metropolitan areas. These river basins are valuable for soil and water conservation. Assessing changes in water resources due to environmental changes has become an important issue. In this study, we analyzed trends and breakpoints in precipitation, potential evapotranspiration and streamflow data in the Lanyang, Keelung, Dahan, Fengshan, Youluo and Shangping river basins from 1980 to 2017 and calculated the elasticity of streamflow to each change factor. We found no significant trend in the precipitation and potential evapotranspiration for any of the basins. The streamflow at the Lan Yang Bridge station, however, showed a significant upward trend. The results of the break point test further showed that the streamflow of the Lanyang River Basin and the Keelung River Basin change abruptly in the years 1993 and 1990. According to the Budyko-Fu equation and Budyko-Mezentsev-Choudhury-Yang equations, the factors affecting the increase of streamflow in the Lanyang River Basin are mainly non-climatic factors, accounting for 109.01% to 108.99% of the total streamflow variation after the baseline period, thus implying that all of the increase in streamflow is due to non-climate factors. The streamflow reduction in the Keelung River Basin is mainly attributed to climate change, accounting for 71.75% to 71.30% of the total change. Among the study basins, only the Lanyang River Basin is covered by the implementation area of the "Integrated Conservation and Flood Control Program in Yilan Area and Eastern Taiwan". According to the results of the streamflow variation analysis, the afforestation and water conservation engineering implemented within the program are highly correlated with the streamflow abrupt change in 1993; however, the factors affecting forest vegetation are quite complex. The induced factors of the vegetation decrease in the Lanyang River Basin during the variation period may include the impact of human activities, natural disasters or changes in climatic conditions, such as afforestation or land use change. In the case of complex mechanisms, further evidence and a discussion of this phenomenon are required. In any case, this result will be used as a reference for future economic development and environmental conservation policies in northern Taiwan, as a case study of the impact of large-scale watershed remediation on water resources.
We compared elasticity values in each basin and found that precipitation is the most sensitive factor for the change of streamflow in northern Taiwan, suggesting that the basins belong to a more stable hydrological environment which is less sensitive to human activities. The assumptions made in this study include the following: (1) the change of water storage in a basin is considered to be approximately equal to zero over a long-term period; (2) if a period of data is longer than 30 years, it is considered stable; and (3) the mean data value of the baseline period is assumed to represent the early conditions in the basin, which should be less affected by climate change and human activities. These assumptions are widely applied in many studies of Budyko curve and streamflow variation analysis, but how they affect the interpretation of Budyko curve analysis can still be discussed further. In addition, the uncertainty within the Budyko parameters is not discussed in this paper due to data limitation, but it does have an influence on the interpretation of results, which is recommended for discussion in future work.
For the planning and governance of river basins in the future, the impact of climate change on the hydrological environment will remain an important issue for water resources in northern Taiwan. At the same time, to achieve the purpose of the sustainable management and utilization of the environment, in the water sources of large-scale metropolitan and industrial areas, corresponding environmental policies (e.g., advanced investigation of environmental issues and restoration) should be further developed, and continuous attention to the impact of human activities on the watershed is still essential. This result could provide a basis for the quantification of the proposed basin governance policy in the future.