Spatiotemporal variations in the elasticity of runoff to climate change and catchment characteristics with multi-timescales across the contiguous United States

Runoff, the most important component of the hydrological cycle, undergoes an alteration over space and time due to climate change and human activities (Dey & Mishra 2017). Understanding quantitively climate change- and human activities-induced runoff changes in long-term periods at a regional and/or basin scale is of importance for regional water planning and management. Runoff elasticity, which was defined by Schaake (1990) as the ratio of proportional change in streamflow to proportional change in climatic variables, can well reflect the sensitivity of runoff to multiple influential factors including climate change and anthropogenic activities, and which can further obtain runoff changes. Therefore, investigating spatiotemporal variations in runoff elasticity is vital for understanding spatiotemporal variation characteristics of runoff influenced by climate change and human activities.

Under a changing environment, total changes in runoff can be obtained by the difference between natural and changed periods in the measured long-term runoff (Sun et al. 2014; Wang et al. 2019). However, individual factor-induced changes (climatic factors and human activities-induced changes) may not be directly calculated by comparing the natural runoff with the changed runoff. An essential step for obtaining an individual factor-induced change in runoff is identifying clearly the impact of climate change and human activities on runoff; in other words, we need to distinguish the climatic or anthropogenic component from total runoff changes. Presently, there are a large number of methods for separating the individual impacts of climate variability and human activities on streamflow (Dey & Mishra 2017). These methods can be categorized as hydrological modeling (Wang et al. 2010; Chang et al. 2015), conceptual approaches (Tomer & Schilling 2009; Jiang et al. 2015), analytical approaches (Sun et al. 2014; Yang et al. 2014), and experimental approaches (Brown et al. 2005; Zhao et al. 2010). The conceptual approaches include applications of the Budyko hypothesis (Budyko 1974) and the Tomer–Schilling framework (Tomer & Schilling 2009). Budyko (1974) assumed the ratio of the mean annual actual evapotranspiration to the mean annual precipitation as a function of the ratio of the mean annual potential evapotranspiration to the mean annual precipitation and other watershed properties. The analytical approach includes climate elasticity and hydrological sensitivity methods. Schaake (1990) defined elasticity as the ratio of proportional change in streamflow to proportional change in climatic variables. However, these two approaches have their own shortcomings in applications, for example, a constant value of parameter represented catchment properties throughout the analysis was used based on the Budyko hypothesis for the former method (Jiang et al. 2015), and the major shortcoming of the latter is that the change in streamflow due to human activities cannot be expressed explicitly in terms of elasticity coefficients (Wang et al. 2016; Dey & Mishra 2017). Therefore, considering the temporal variation of catchment characteristic parameters in the Budyko hypothesis is vital for analyzing accurately the runoff alteration.

The Budyko hypothesis-coupled climate elasticity method was commonly used to detect influential factors-induced changes (Zheng et al. 2009; Wang & Hejazi 2011; Patterson et al. 2013). For example, Yang et al. (2014) estimated the climate elasticity and evaluated the contribution of climate change to runoff for 210 catchments to understand the spatial variation of hydrologic response to climate change, and further calculated the parameter n in the Budyko hypothesis. They have shown that the value of n is different between catchments, and the contribution of climate change to runoff has a distinct spatial pattern. Wang et al. (2019) used climate elasticity and hydrological sensitivity analysis to estimate the contributions of climate change and human activities in the Beichuan River Basin in the northeastern Tibetan Plateau, China, and they found the dominant factor is human activities. However, the elasticity of runoff is usually calculated by long-term average hydrometeorological data, and the minimum data length is not less than 11 years because soil water storage can be neglected (Shao et al. 2012). So far, the impact of data length or timescales on climate elasticity is not clear. Although some scholars have shown that climate elasticity is catchment-based, for example, Sankarasubramanian et al. (2001) found that precipitation elasticity is independent of precipitation but sensitive to model structure and calibration error. Climate elasticity acts as a function of climate and catchment conditions, and it may also be explained by other factors such as the aridity index and catchment characteristics. Therefore, apart from analyzing the impact of data length on climate elasticity, relationships of climate elasticity to other factors are also necessary.

The selection of influential factors is a primary question for attribution analysis of runoff alteration. Whether the selection of influential factors is reasonable is directly related to whether the cause of runoff variation can be accurately found. Recently, the factors causing runoff alteration have mainly been climatic factors and anthropogenic activity and have been gradually developed from single to comprehensive. The study area expanded from a small basin to a large basin or a small region to a large region when evaluating the impact of these two types of factors on runoff (Cheng et al. 2019; Li et al. 2020). For instance, while analyzing the impact of climatic factors on runoff in the 1990s, only the effect of precipitation was considered. With the research development, climatic factors such as potential evaporation, air temperatures (mean or extreme temperatures), ocean–atmosphere interactions that lead to interannual and decadal quasiperiodic behavior (e.g., Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO)) were found to have a non-negligible effect on runoff (Prokoph et al. 2012; Nalley et al. 2019). Yang & Yang (2011) further combined the first-order differential of the Penman equation and the elasticity of runoff to precipitation, net radiation, air temperature, wind speed, and relative humidity to derive and separate the contributions of different climatic variables. Wang et al. (2016) further explored the impact of maximum and minimum temperatures on runoff based on Yang & Yang's (2011) research and found that extreme temperatures may have a greater influence on runoff than precipitation and potential evaporation. Therefore, maximum and minimum temperatures and catchment characteristic elasticity should be considered.

Over the contiguous United States, there are many interesting studies in quantifying streamflow variations using different methods. For example, paired catchment approaches and the Distributed Hydrology Soil 38 Vegetation Model, embedded with a multi-purpose reservoir module (DHSVM-Res), were used to simulate streamflow and reservoir storage in south-central Texas, and they found that urbanization and climate change are the major drivers of variations in the monthly maximum streamflow. Ravindranath & Devineni (2020) applied an extended sequent peak algorithm to streamflow reconstructions in the Upper Missouri River Basin. A monthly water balance model was validated and applied by Li et al. (2020) to quantify the hydrologic responses of 81,900 12-digit Hydrologic Unit Code (HUC) watersheds to historical and projected land use/land change (LULC) in 2000, 2010, 2050, and 2100 in the contiguous United States (CONUS). Stepwise and geographically weighted regression models were used to identify key factors controlling the spatially varied hydrologic impacts across the CONUS. Davenport et al. (2020) quantified the size of streamflow peaks in response to both seasonal and event-specific rain-fraction using stream gage observations from watersheds across the western United States. Also, some scholars quantified runoff changes caused by precipitation, potential evaporation, and human activities over the contiguous United States (Wang & Hejazi 2011; Patterson et al. 2013; Rice et al. 2015; Sang et al. 2020). In our study, we investigated the spatiotemporal pattern of elasticity of runoff to multiple factors, as an index reflecting the sensitivity of runoff to factors, especially for extreme temperature elasticity, because the temperature has a profound effect on the hydrological process (little analysis for previous studies). Our special analytical perspective can illustrate spatiotemporal pattern characteristics of runoff changes in some way, and provide a reference to quantify runoff changes using the climate elasticity method.

The primary objectives of this study are (1) to analyze the temporal trend and spatial pattern of elasticity of runoff to multiple factors (precipitation, potential evaporation, maximum and minimum temperatures, and catchment characteristics) at different timescales, and (2) to explore the relationships of elasticity of runoff with other factors (mean rainfall, mean runoff, aridity index, runoff coefficient, and catchment characteristic). We select four slipping windows (11, 20, 40, and 60 a) according to our length of data, and then the elasticity of runoff series in each timescale can be obtained by calculating the elasticity of runoff in each timescale in 188 catchments of the CONUS. The original Mann–Kendall method is used to test the trend significance of the series. This work is helpful to determine in detail the variation process of sensitivity of runoff to influential factors under climate change and human interference.

Daily streamflow data were obtained from the United States Geological Survey (USGS). The USGS has collected water resource data at approximately 1.5 million sites in all 50 states. Those sites were selected from the Geospatial Attributes of Gages for Evaluating Streamflow, version II (GAGES-II) database. The GAGES-II database contains many basin-specific characteristics for 9,322 basins throughout the United States, including climatic, hydrologic, topographic, land cover and land use, and geologic attributes.

Daily streamflow data from the climatic year 1916 through the climatic year 2015 were selected, and we also considered daily streamflow from the climatic year 1941 through the climatic year 2015. We selected the water year (1 April to 31 March of the next year), not the calendar year, as the yearly scale. These daily streamflow data were downloaded from the USGS National Water Information System (NWIS). We downloaded data according to the standard in Dudley et al. (2019). The selection criteria resulted in 2,482 total study gauges: 1,408 for the 1941–2015 period and 203 for the 1916–2015 period. We extracted a large number of catchments according to the stream network and digital elevation of the United States and then filtered some excess sites that were not distributed in the selected catchments. The above process resulted in 128 runoff gauges, and those sites were generally located at the outlet of the catchment from 1941 to 2015 and 60 from 1916 to 2015.

The Global Historical Climatology Network-Daily (GHCN-D) was produced and archived by the National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center. It comprises over 96,000 sites worldwide that capture all or a subset of daily maximum and minimum temperatures, precipitation, snowfall, and snow depth. The record period varies by the station from less than 1 year to 177 years, with the average precipitation record spanning 33.1 years. We also required that each year's data records be at least 80% complete in two periods (1916–2015 and 1941–2015). In this study, we need daily precipitation and maximum and minimum temperature records. Based on these selection criteria, we finally obtained 993 meteorological stations for 1916–2015 and 1,116 meteorological stations for 1941–2015. Maximum and minimum temperatures were averaged to yield mean daily temperature, and daily meteorological element values (mean daily precipitation and daily temperature) were multiplied by the total days of each year to obtain annual total amounts. The process that filters extra rainfall gauges is similar to the method of selecting runoff gauges, and there are a number of precipitation sites in selected catchments. The above process resulted in 186 rainfall sites from 1941 to 2015 and 103 from 1916 to 2015.

The continental United States was divided and subdivided into successively smaller hydrologic units classified into four levels: regions, subregions, accounting units, and cataloging units. The hydrologic units are arranged or nested within each other, from the largest geographic area (regions) to the smallest geographic area (cataloging units). The watershed boundary dataset (WBD) consists of the newest and the most recent HUC delineation and further divides the HUC levels into fifth and sixth levels. Hydrologic unit boundaries in the WBD are determined based on topographic, hydrologic, and other relevant landscape characteristics without regard for administrative, political, or jurisdictional boundaries. We obtained hydrologic units, which are shapefile or geodatabase data types, across the contiguous United States from the National Hydrography Dataset (NHD) in the USGS and downloaded national 30 m digital elevation data from the Soil and Water Hub (SWH, https://soilandwaterhub.brc.tamus.edu/Home/GISData). We extracted the streamflow network and then selected the catchment according to the streamflow gauges and meteorological stations mentioned in the ‘Streamflow and meteorological data’ section based on having obtained hydrological units with varied levels. A catchment defines the areal extent of drainage to an outlet point (streamflow gauges) on a dendritic stream network or multiple outlet points where the stream network is not dendritic and one or more meteorological stations are distributed throughout the catchment of interest by using the hydrological analysis tool in ArcGIS 10.5. The above procedure resulted in 60 study catchments for 1916–2015 and 128 for 1941–2015 (Figure 1).

The Food and Agricultural Organization (FAO) of the United Nations improved and upgraded the methodologies for reference evapotranspiration (ET₀) estimation by introducing the reference crop (grass) concept, described by the FAO Penman–Monteith (PM − ET₀) equation (Allen et al. 1998), and this approach was tested well under different climates and time step calculations and is currently adopted worldwide (Almorox et al. 2015). However, the high cost and maintenance of agrometeorological stations and the high number of sensors required to estimate ET₀ make it non-plausible, especially in rural areas (Moratiel et al. 2020). For this reason, the estimation of ET₀ using air temperature in places where wind speed, solar radiation, and air humidity data are not readily available is particularly attractive (Moratiel et al. 2020). Methods of estimating ET₀ based on only the air temperature have been recommended by many researchers. Allen et al. (1998), in the guidelines for PM − ET₀, recommended two approaches: (a) using the equation of Hargreaves–Samani (Hargreaves et al. 1985) and (b) using the Penman–Monteith temperature (PMT) method that requires temperature data to estimate net radiation and vapor pressure deficit to obtain ET₀. Our study only obtained temperature data (daily maximum and minimum temperatures). Therefore, the PMT method is applied in this study to estimate ET₀, and its calculation process for more details can be seen in the Supplementary material.

The Mann–Kendall test (Mann 1945) (p ≤ 0.05) is applied to calculate the statistical significance of trends for time-series data because this method is distribution-free, robust against outliers, and has higher power for non-normally distributed data. The significance of trends over time is easily affected by assumptions of whether the time-series data are independent, have short-term persistence (STP), or have long-term persistence (LTP) (Sagarika et al. 2014). The Mann–Kendall test assumes the input data to be serially independent, but the presence of positive serial correlation in the time-series data can overestimate the significance of trends (Yue et al. 2002). To overcome the effect of serial correlation, the Mann–Kendall test after trend-free pre-whitening, as suggested by Yue et al. (2002), and the modified Mann–Kendall test, as suggested by Hamed (2008), can be adopted. Apart from STP, the presence of LTP behavior in the time-series data led to an underestimation of serial correlation in the data structure and an overestimation of the significance of the Mann–Kendall test. Hamed (2008) proposed a technique to incorporate the LTP behavior in the Mann–Kendall test, but the method is suitable for serial data with lengths of at least 100 years. In this study, our data series, data record lengths less than 100, are elasticities of climate and catchment characteristics of streamflow during each sliding window; therefore, we adopted the original Mann–Kendall method with assumption-independent time-series data.

Therefore, by substituting climatic factors, runoff series, and their mean values in each slipping window into Equations (6), (9), and (10), we can obtain the climate, watershed characteristic elasticity of runoff in each slipping window.

First, we analyzed the volatility of climate and catchment characteristic elasticity of runoff over time in each timescale. The standard deviation (STD) was used to reflect the degree to which these elasticity time-series deviated from the mean value, which was calculated within each timescale, and a box plot was depicted to show the STD distribution of multiple elasticities of runoff in all catchments (Figure 2). The results show that precipitation, potential evapotranspiration, and watershed characteristic elasticity have a similar and tiny STD in each slipping window and far less than the STD of maximum and minimum temperature elasticities during both 1941–2015 and 1916–2015. The STD value of watershed characteristic elasticity is the lowest among them. These conclusions illustrate that precipitation, potential evapotranspiration, and watershed characteristic elasticity are relatively steady over time compared to maximum and minimum temperature elasticities; the large STD value for extreme temperature may be caused by disturbance from climate change and human activities. Watershed characteristic elasticity is the steadiest among all elasticities of runoff. In addition, there are higher outliers of the STD value and elasticity value in 1941–2015 compared with 1916–2015 in Figures 2 and 3, and the reason why this difference may be runoff is (1) more vulnerable to interference from human activity and (2) shorter lengths of data during 1941–2015. Wang & Hejazi (2011) showed that human activities caused the mean annual streamflow to experience upward changes and those anthropogenic activities have played a vital role in runoff change since the 1970s in the contiguous United States. Timescale means the time period used for calculating elasticity, also known as data length. We must recognize that the STD values of elasticity within different timescales, i.e., we suggest the 20-year data length, are used to quantify runoff changes, because the short data length causes large STD, whereas the long data length is not easily obtained. We can also now demonstrate that the longer time period, the steadier elasticity, and further steadier runoff changes. Therefore, long-term average changes in runoff are reasonable in previous studies.

Due to its low STD for the elasticity of runoff, we compared the mean value of impact factor elasticity of runoff under each slipping window in all catchments with that of the long-term average value (100 and 75 years) during the two study periods, and a box plot was depicted (Figure 3). The results show that the average values for the same factor elasticity of runoff in the four slipping windows are approximately close to each other and that the long-term average value, in other words, the selection of the calculation period, has no impact on the influential factor elasticity of runoff value in the catchment. However, some small differences in the distribution of the long-term (75 and 100 a) average value are more dispersed than the average value in the four slipping windows for the maximum and minimum temperature elasticities of runoff during 1916–2015, which may be caused by the large fluctuation in temperature, especially extreme temperature. Sankarasubramanian et al. (2001) demonstrated that precipitation elasticity is fixed in basins. In our study, we found that not only precipitation elasticity but also other climate elasticities (potential evapotranspiration and maximum and minimum daily temperature elasticities) and watershed elasticity are stable over time. Comparing Figures 2 and 3, we should recognize that there is a relatively large STD compared to a long time period even though there is a close average value of elasticity within different time periods, which indicate that the long-term average elasticity of runoff in previous studies may hide volatility, further affecting the spatial pattern, which can be further studied in the future.

Second, to further identify the trend significance of multiple influential factor elasticity of runoff over time in four slipping windows, the original Mann–Kendall method was used to test the trend significance (p ≤ 0.05) of multiple influential factor elasticity of runoff over time in each slipping window during two periods (1916–2015 and 1941–2015) (Figure 4). We find that the elasticity of runoff with different factors has different trends in the United States. Precipitation elasticity of runoff mainly presents a significant declining trend in all slipping windows in the middle north regions of the United States, especially in the Upper Mississippi Region. The significant increasing trends are heterogeneously distributed in other regions of the United States. However, we can see roughly that the number of catchments with a significant increasing trend in the eastern region is more than that in the western region, southern parts are more than northern parts (Figure 4 and Table 1), and a negative trend but similar spatial distribution pattern for evapotranspiration elasticity. The distribution of catchments with trend significance for the maximum temperature elasticity is similar to the minimum temperature elasticity. The number of catchments with a significant increasing trend is a little higher than that with a significant declining trend (Table 1), catchments with a significant decreasing trend are mainly located in eastern regions of the United States for maximum and minimum temperature elasticities, especially the Mid-Atlantic Region and the South Atlantic-Gulf Region, and a significant increasing trend is mainly distributed in northern regions of the United States, especially the Upper Mississippi Region. This conclusion is opposite to the trend of precipitation elasticity (Figure 4). Watershed characteristic elasticity mainly presents a significant increasing trend, those catchments are mainly distributed in the middle and eastern regions (Figure 4), and few catchments present a significant declining trend in the western parts (Table 1).

All in all, we can demonstrate that the elasticity of runoff is not only stable over time but also its trend is almost not affected by calculation timescales.

To investigate the spatial distribution of the impact factor elasticity of runoff, bar charts of influential factor elasticity (precipitation, potential evapotranspiration, maximum and minimum daily temperatures, and watershed characteristics) of runoff in 188 catchments of the CONUS were drawn (Figure 5) during 1916–2015 and 1941–2015. The ‘Spatiotemporal change of catchment characteristic n’ section has shown that influential factor elasticity of runoff has no difference in various time windows; thus, we analyzed the long-term average impact factor elasticity of runoff in the whole study period (75 and 100 a). The results show that most of the factor elasticities of runoff are negative apart from precipitation in the CONUS. The sensitivity of runoff to precipitation is the greatest in the northeastern CONUS. However, the most sensitive factor converts to the maximum temperature in the central and western regions. The impact of potential evapotranspiration, maximum temperature, and catchment characteristics on runoff gradually becomes important from east to west. In some western regions, catchment characteristics may be the second-most sensitive runoff factor, following the most sensitive maximum temperature factor. The sensitivity of runoff to the minimum temperature is the smallest among all influential factors. This indicates that temperature is also an important factor that affects runoff.

We concluded that the elasticity of runoff presents a distinct spatial distribution. To further investigate whether the elasticity of runoff can be explained by other factors, the relationships between the elasticity of runoff and P (precipitation), R (runoff), aridity index (φ), runoff coefficient (α), and catchment characteristics (n) were studied, and a graph in the form of a correlation for their relationships was depicted in our study (Figure 6). Figure 6 shows that arid regions have higher precipitation, potential evaporation, maximum and minimum temperatures, and catchment characteristic elasticity. Maximum temperature and catchment characteristic elasticity scatter against the aridity index compared to the elasticity of the other three factors. Wang & Hejazi (2011) plotted direct human-induced changes against the climate dryness index and the evaporation ratio to further investigate whether the estimated climate- and direct human-induced changes can be explained by other factors, and they found that arid regions (i.e., water-limited) are more vulnerable to climate change and direct human interferences than wet regions (i.e., energy limited). The relationship between the elasticity of runoff and the runoff coefficient for multiple factors presents an exponential trend and a high elasticity value in regions with a low runoff index. Meanwhile, we can also find that the relationship between the multiple factor elasticity and the mean runoff is consistent with the relationship between the elasticity of runoff and the runoff index. However, this relationship tends to be a horizontal line trend for mean rainfall. This result indicates that multiple climate factors (precipitation, potential evaporation, and maximum and minimum temperatures) and catchment characteristic elasticity are independent of precipitation and that wet regions tend to have lower elasticity of runoff values. This conclusion can illustrate the spatial distribution of the multiple factor elasticity of runoff in the United States in Figure 5 and is the same as the result of Sankarasubramanian et al. (2001), who used Kendall's τ test to document that estimates of precipitation elasticity are independent of P at each site and showed that humid basins tend to have significantly lower values of precipitation elasticity and tend to be much more homogeneous in terms of precipitation elasticity than arid regions. The relationship between catchment characteristics and the catchment characteristic elasticity of runoff tends to be a line trend and the values of multiple factor elasticity of runoff increase with the ascent of n. Catchment characteristic n reveals inter-related dynamics between vegetation type, soil properties, and topography (Dey & Mishra 2017). Its value impacts the evaporation of the catchment. Higher values of n indicate that the watershed characteristics favor evapotranspiration (for densely vegetated basins). In this study, we can demonstrate that the evaporation ratio and the multiple factor elasticity are affected by catchment characteristic n.

Catchment characteristics were first mentioned by Budyko (1974) who assumed the ratio of the mean annual actual evapotranspiration to the mean annual precipitation evapotranspiration as a function of the ratio of the mean annual potential evapotranspiration to the mean annual precipitation and other watershed properties (represented by n or other parameters in functions), which reflected LULC, vegetation coverage changes, and topography in the watershed. No matter n or other parameters in different Budyko type curves, they all represent catchment characteristics and reveal inter-related dynamics between vegetation type, soil properties, and topography. The increase in the catchment characteristic parameter is thus regarded to result from increases in vegetation, which accordingly caused an increase in evaporation and a decline in runoff (Xu et al. 2014). Porporato et al. (2004) related the catchment characteristic to the relative soil water holding capacity, average rooting depth, and rain depth. Yang et al. (2007) related the relative infiltration capacity, the catchment average slope, and the relative soil storage capacity. In other words, catchment characteristics are synthesized parameters that represent catchment properties (soil, topography, vegetation, etc.), also indirect human activities which changed catchment physical properties, further causing runoff alteration in the runoff generation process. Vegetation coverage, LULC, and soil types change with time; therefore, the value of n changes with the seasonal scale or the annual scale. In general, the value of n is obtained by using the long-term average precipitation, runoff, and actual evaporation in a single watershed, which reflected a long-term average condition in the watershed. Thus, we assumed that the value of n is fixed, and studies on the impact of different values of n on hydrological variables are lacking. For instance, Donohue et al. (2011) assessed the influence of n on runoff and demonstrated that the uncertainty in the value of n for the study catchment produces only a small uncertainty in the modeled runoff. Jiang et al. (2015) built the relationship of the parameter w (also representing catchment characteristic) in each Budyko-type equation with climatic and human factors. They revealed the time-variation process of w by using an 11-year moving window and found that the parameter was a function of variables of both climate conditions and human activities improving the performance of simulating the mean annual runoff based on all the Budyko-type equations. Zhang et al. (2001) defined w as the plant-available water coefficient and it represents the relative difference in the way plants use soil water for transpiration. Li et al. (2013) found that catchment characteristic has regional pattern variability. Additionally, Wang et al. (2016) revealed that from low to high, and in turn to low, a broadly north-middle and middle-south gradient could be found in the spatial distribution of n. Thus, we can demonstrate that watershed characteristic possesses spatiotemporal variation and that its influence on mean runoff also has the same variation feature.

To investigate the spatiotemporal change characteristics of catchment characteristic n, we analyzed the temporal trend of catchment characteristic n during different slipping windows and the spatial distribution of its mean value across 188 catchments in the United States (Figures 7 and 8). Considering that the average value of n under the four slipping windows is similar, here, we analyzed the spatial distribution of the long-term average n during the two study periods (75 and 100 a) (Figure 8). Figures 7 and 8 show that a significant decreasing trend for n occurs mainly in the northeastern regions of the United States, catchments with the same trend are seldom concentrated in the south, and a significant increasing trend for n mainly occurs in the western regions. The value of n in the south is larger than that in the north, the n value in the east is larger than that in the west, and the largest value n occurs mainly in the eastern and southeastern regions.

In this study, precipitation and potential evaporation elasticity of runoff were obtained by conceptual approaches, i.e., Budyko hypothesis. Maximum and minimum temperature elasticities were calculated by a non-parametric estimation method due to insufficient meteorological data. The major advantage of the former method is that it can estimate the sensitivity of runoff to different climatic factors, and the latter method has low biasness and is non-parametric. There are many researchers who adopted these two methods in the contribution analysis of runoff. For example, Zheng et al. (2009) used a non-parametric method to assess the impacts of climate and land surface change on the streamflow. Results show that for the period 1960–2000, the elasticities of streamflow in relation to precipitation and potential evapotranspiration are 2.10 and −1.04, respectively. Li et al. (2012) adopted the sensitivity-based approach (including a non-parametric model and six Budyko framework-based models) and the hydrological modeling approach (using Xinanjiang and SIMHYD models) for three medium-sized catchments in Australia to investigate the impacts of increase or decrease in plantations and climate variability on streamflow. They found the sensitivity-based approaches are only applicable where long-term datasets are available and they only provide results at a mean annual timescale, and small variability in the reduction or increase in streamflow is estimated by these methods. Yang & Yang (2011) compared these two methods in the Futuo River catchment in the Hai River basin and found that the total changes in runoff were essentially different (−11% changes for the partial differential Budyko hypothesis-based method and −18% for the non-parametric estimator approach). The authors thought the reason for this difference was the short length of the data (1961–2000). We also found that precipitation and potential evaporation elasticity are similar to each other using the two methods, but largely biased for extreme temperature elasticity (for some catchments, values for the non-parametric method are higher than those for the conceptual method, here, results are not shown). At present, these two methods are commonly used to analyze runoff changes caused by climate change and human activities, and no one pointed out the inapplicability of the methods. A detailed reason for this difference has not been displayed, and efforts may be made by related scholars.

In this study, spatial and temporal variations in the elasticity of runoff to multiple climatic factors and catchment characteristics during 1916–2015 and 1941–2015 in the 188 catchments of the CONUS were first investigated. Then, we explored the relationships of the long-term average elasticity of runoff with other factors (aridity index, runoff coefficient, mean rainfall, mean runoff, and catchment characteristic). We found that (1) not only the elasticity of runoff to climatic factors and catchment characteristics but also its trend over time may not be affected by timescales. (2) Precipitation elasticity mainly presents a decreasing trend in the mid-north region and an increasing trend in the same location for the potential evaporation elasticity, an increasing trend for the minimum temperature and the catchment characteristic elasticity, and the heterogeneous trend over the United States for the maximum temperature elasticity. (3) The elasticity of runoff to multiple influential factors has a distinct spatial pattern over the CONUS. The most sensitive factor is precipitation for runoff in northeastern regions, and the roles of potential evaporation, maximum temperature, and catchment characteristics in runoff gradually become important from east to west. In some western regions, catchment characteristics may be the second-most sensitive runoff factor, following the maximum temperature factor. The sensitivity of runoff to the minimum temperature is the smallest among all influential factors in the United States. (4) Multiple climate factors (precipitation, potential evaporation, and maximum and minimum temperatures) and the catchment characteristic elasticity are independent of precipitation, and wet regions tend to have lower elasticity of runoff. The relationship of multiple factor elasticity of runoff with runoff coefficient presents an exponential trend, which is consistent with the relationship of multiple factor elasticity of runoff with mean runoff, but this relationship tends to be a horizontal line trend for mean rainfall. The relationship between the catchment characteristics and the elasticity of runoff presented a positive linear trend.

This study is supported by the Natural Science Foundation of Heilongjiang Province of China (No. E2017009).

X.G. conducted the supervision, writing, and review & editing of resources. S.D. conducted the conceptualization, methodology, validation, formal analysis, and writing – original draft. Y.Z. conducted the writing – review & editing. A.X. conducted the language and flow improvement.

All relevant data are available from streamflow data from http://esapubs.org/Archive/ecol/E091/045/default.htm and https://waterdata.usgs.gov/nwis/; watershed boundary data from https://www.nrcs.usda.gov/wps/portal/nrcs/main/national/water/watersheds/; climate data from https://www.ncei.noaa.gov/products/land-based-station/global-historical-climatology-network-daily/.