1 Introduction
Anthropogenic activities and climate change have significant impact on hydrological processes, including evaporation, infiltration, and runoff (Duan
et al.,
2016; Wang
et al.,
2021; Zhang
et al.,
2021; Jiang
et al.,
2022; Jin
et al.,
2023). As a result, hydrological systems have become increasingly complex, deviating from a state of equilibrium and leading to severe water crisis issues such as drought, floods, and water shortages (Padrón
et al.,
2017; Arheimer and Lindström,
2019). The interactions between hydrological responses and climate change, as well as landscape processes, have been a subject of significant concern (Ning
et al.,
2019; Zhou
et al.,
2023a;
2023b). Runoff, which is the most sensitive component in the hydrological cycle, has been significantly influenced by both climate factors, such as precipitation, potential evaporation, and temperature, and human activities, including water extraction, urbanization, dam construction, and reservoir development (Arheimer and Lindström,
2019; Luo
et al.,
2020; Shao
et al.,
2020). Accurately quantifying the respective impacts of climate change and human activities on the original changes in hydrological processes is essential to effectively addressing water crisis issues (Ma
et al.,
2008; Jiang
et al.,
2022).
Numerous studies have been conducted to quantify hydrological responses (Wang and Hejazi,
2011; Knoben
et al.,
2018; Li
et al.,
2020; Duan
et al.,
2022; Zhang
et al.,
2022; Wang
et al.,
2023). Attribution methods have been commonly used to achieve this through sensitivity analysis based on conceptual or physically based hydrologic models (Dey and Mishra,
2017; Duan
et al.,
2019). Among these methods, the Budyko framework coupled with climate elasticity has proven to be robust and has been widely used to separate the contributions of climate change and human activities on runoff due to its simple calculation procedure and fewer parameters compared to hydrological models (Cui
et al.,
2020). For instance, Wang
et al. (
2016) decomposed the potential evaporation elasticity into five climate-related elasticities (i.e., sunshine duration, maximum and minimum temperature, wind speed, and relative humidity) through the first-order differentiation of the FAO 56 Penman-Monteith equation. Additionally, Patterson
et al. (
2013) used Budyko curves to describe changes in streamflow due to climate and human factors between natural and human-modified time periods in the South Atlantic, USA. Previous studies have primarily attributed runoff responses to climate change and human activities, and subsequently analyzed their spatial patterns (Wang
et al.,
2016; Dey and Mishra,
2017; Zhao
et al.,
2023).
However, it is currently not well understood why these substantial or similar patterns have occurred and what factors control them, or whether the spatial patterns (distribution and predictability) of runoff response can be accurately predicted. Resolving these scientific problems requires the development of multi-source attribution methods to separate the impacts of climate change and landscape processes on runoff from the original changes.
The term “runoff response changes” (RRC) refers to alterations in runoff resulting from climate and catchment attributes, and the sensitivity of runoff to each influencing factor. Runoff changes exhibit considerable variations between adjacent catchments with differing climate, vegetation, soil, land use/cover, and urbanization (Zhang
et al.,
2021; Yu
et al.,
2022). It is reasonable to attribute these substantial spatial variations to the unique climate and land surface conditions in each catchment. Zou
et al. (
2022) associated hydrological processes with sediment, finding that watersheds with high connectivity are typically located in areas with dense vegetation and flat terrain. The sensitivity of runoff to climate, often perceived as constant within a catchment, is generally high in arid/semi-arid regions (Sankarasubramanian
et al.,
2001). This implies that runoff is more influenced by climate change in these regions than in others.
While previous studies have attempted to explore the spatial distribution mechanism of runoff response, pure correlation analysis cannot identify the controlling or secondary factors of RRC and the nonlinear effect. Therefore, there is still limited understanding of how dominant factors govern the spatial patterns of RRC, particularly with regard to nonlinear and secondary effects.
The accurate prediction of patterns is a crucial measure of the depth of understanding in any field. Previous research regarding predictions in ungauged basins has primarily focused on water balance components, such as runoff signatures (Hrachowitz
et al.,
2013; Ni
et al.,
2022). However, there is limited research on runoff changes and their sensitivity (Kalugin,
2019; Somorowska and Laszewski,
2019).
Typically, three approaches are employed to predict runoff response changes (RRC) based on predictors of climatic and physiographic attributes: (i) statistical models using catchment attribute predictors (Beck
et al.,
2013; Kuentz
et al.,
2017), (ii) interpolation using similar catchments between adjacent gauged basins (Westerberg and McMillan,
2015), and (iii) hydrological models with regionalized parameters based on catchment attributes (Wagener and Wheater,
2006; Ragettli
et al.,
2017).
Machine learning models, as data-driven methods, have become increasingly popular for predicting or reconstructing historical runoff due to their strong mathematical foundation in model development and their ability to effectively process large-sample data (Addor
et al.,
2018; Cheng
et al.,
2022; Zhuang
et al.,
2023). In addition to their high predictive performance, machine learning models can also rank the importance of influencing factors for RRC and demonstrate the influence process of individual factors and combined effects from multiple factors.
Until now, studies towards answering the three interrelated research questions are lacking or inadequate. (1) What are the spatial patterns of runoff response changes (RRC) and which factor contributes the most to runoff changes? (2) How effectively can a statistical model predict runoff response changes (RRC) by accounting for nonlinear relationships? (3) How do the primary factors influence runoff response changes (RRC), and what are the patterns of the second-order effects of these factors?
To answer abovementioned questions, we first decompose the contributions of climate change and catchment properties to runoff into precipitation, potential evaporation, average temperature, and changes induced by catchment characteristics (along with the sensitivity of runoff to these factors) across 1003 catchments within the contiguous United States (CONUS). To investigate the spatial patterns of RRC, we assessed the presence of a clustering phenomenon and analyzed their spatial consistency over CONUS using global and local Moran’s Index (Moran’s I). Additionally, we examined the relationship between the spatial pattern of RRC, their spatial consistency, the distribution of ecoregions, and climatic trends. Then, we utilized the random forest approach, which accounts for nonlinear relationships, to assess the predictability of RRC in a spatial context based on catchment attributes across six categories (topography, geology, climate, hydrology, land use/cover, and soil characteristics) represented by 56 indicators for 1003 catchments in the contiguous United States (CONUS). We investigated the predictability in relation to spatial consistency and quantified the influence of catchment attributes on RRC by measuring the increase in the mean square error (IncMSE) of prediction when each predictor’s value was shuffled in the random forest model, thus allowing us to rank the importance of predictors for RRC. Finally, once the key factors were identified through the second step, we assessed the nonlinear relationship between RRC and the key factors using the accumulated local effect. Furthermore, we delved into the second-order effects of these factors to comprehend the combined impact of multiple factors on RRC.
We leveraged the extensive GAGES-II catchment dataset, which encompasses various attributes, including human activities, to investigate the behaviour of RRC. The overarching goal is accomplished by pursuing the following specific objectives: (1) disaggregating the runoff response into different components and examining their spatial distributions; (2) assessing the spatial predictability of RRC and investigating the reasons behind variations in predictability; (3) identifying the primary drivers of RRC and comprehending how these dominant factors individually and collectively influence RRC; and (4) exploring the links between RRC and climatic trends, as well as ecoregion patterns across the CONUS. In contrast to previous studies focused on the impact of environmental changes on runoff response, our novelty lies in our attempt to elucidate the physical significance underlying runoff behaviour from three perspectives, which include: 1) component-based partitioning of RRC; 2) spatial predictability of RRC and associated factors; and 3) the controlling factors of RRC and their corresponding influence processes.
2 Data and methods
2.1 GAGES-Ⅱ data set
The catchment attributes and daily discharge data utilized in this study were sourced from the GAGES-II dataset, which was developed by the United States Geological Survey (USGS) and can be accessed at
http://esapubs.org/Archive/ecol/E091/045/default.htm (Falcone
et al.,
2010; Dudley
et al.,
2019). GAGES-II comprises 9322 hydrological stations across the United States, encompassing Alaska, Hawaii, and Puerto Rico. These stations are categorized as either “reference” or “interference” sites. The “reference” sites (2057 in GAGES-II) are considered to be minimally impacted or unaffected by human interference and are evenly distributed across the 12 ecoregions of the CONUS, while the “interference” sites are subject to the influences of both climate change and human activities, and there are 7265 such sites in GAGES-II, distributed outside ecoregions. The geospatial data for catchments encompass a wide array of catchments attributes, including climate, hydrology, landform, land use/cover, geology, and human activities. In our study, six types of catchment attributes—topography, geology, climate, hydrology, land use/cover, and soil characteristics—were considered. A detailed description of these catchment attributes is provided in Table S1 in the Supporting Information.
The daily discharge data from the hydrological sites in GAGES-II were acquired from the USGS Water Information System, accessible at
https://waterdata.usgs.gov/nwis/. When obtaining this data, the completeness and duration of discharge records were taken into consideration, with a minimum requirement of at least 20 years of data and at least 80% data completeness. Ultimately, we obtained data from 2482 sites spanning the years 1966-2015, with 203 sites having data from 1916-2015, and 1408 sites from 1941-2015. The study period was determined as 1941-2015, and after considering sites with a runoff coefficient exceeding 1, a final selection of 1003 sites was included in our study (refer to
Figure 1).
Figure 1 A total of 1003 hydrological sites across catchments distributed in nine ecoregions over the contiguous United States. Red line is 100-degree meridian which splits United States into west and east. |
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Maps delineating watershed boundaries were procured from the U.S. Department of Agriculture-Natural Resources Conservation Service (USDA-NRCS) (
https://www.nrcs.usda.gov/wps/portal/nrcs/main/national/water/watersheds/). Due to factors such as variations in the precision of digital elevation models (DEMs) and diverse extraction methods, watershed boundaries tend to evolve over time and may be nested within one another. However, in our study, only a small number of watersheds were affected by these issues. Notably, no watersheds in our study were impacted. Notably, approximately 8% of the hydrological sites in the dataset had been previously utilized in a study conducted by the USGS National Water-Quality Assessment Program (NAWQA). For the remaining sites, initial basin boundaries were obtained from Michael Wieczorek, a colleague from NAWQA, who based the delineations on NHDPlus 30-m flow direction and flow accumulation grids (refer to
Figure 1). These basin boundaries underwent meticulous algorithmic processing and manual review, and any catchments that did not meet the review criteria were excluded from the dataset. Roughly 83% of the delineations were derived from the NHDPlus data processed by Wieczorek, 8% were from the NAWQA archives, 6% were sourced from EDNA data/tools, 2% were obtained from the AK-HI-PR Water Science Centers, and the remaining 1% were acquired through ArcToolBox/NHDPlus or manual digitization (Falcone
et al.,
2010).
2.2 Meteorological data
Meteorological time series encompassing daily precipitation, maximum, and minimum daily temperatures were sourced from the Parameter-Elevation Regressions on Independent Slopes Model (PRISM) dataset. PRISM is an elevation-regression model independent of slope, as proposed by Daly
et al. (
2008), and is a theory-based systematic model used to spatially interpolate climatic factors across complex landscapes. PRISM has the capability to estimate climatic factors at various temporal scales, including annual, monthly, daily, and event-based, utilizing point data, digital elevation models (DEMs), other spatial datasets, and a coded spatial climate theory library. The climatic data within the PRISM dataset underwent validation through peer-reviewed precipitation and temperature maps published by the U.S. Department of Agriculture for 50 states, the Caribbean, the Pacific Islands, and the official climate atlas of the United States, as well as a 112-year series of monthly temperature, precipitation, and dew point maps. Furthermore, detailed precipitation and temperature maps for Canada, Mongolia, and China have also been incorporated (Daly
et al.,
2008; Strachan and Daly,
2017; Daly
et al.,
2021). The PRISM Climate Group employs an extensive monitoring network to collect observations, implements rigorous quality control measures, and develops spatial climate datasets to unveil short- and long-term climatic patterns. The resultant dataset integrates multiple modeling techniques and is available at diverse spatial and temporal resolutions, encompassing data from 1895 to the present, and is accessible free of charge (Strachan and Daly,
2017). While the original grid resolution of the PRISM dataset was 800 meters, it was downsampled to a 4-km resolution to facilitate ease of download and manipulation.
2.3 Budyko framework coupled with climate elasticity to estimate runoff response
Budyko (1974) assumed the ratio of mean annual actual evapotranspiration to mean annual precipitation [
E/P] as a function of the ratio of mean annual potential evapotranspiration to mean annual precipitation [
PE/P] and other watershed properties. The Budyko theory has different mathematical functions (Zhang
et al.,
2001; Porporato
et al.,
2004; Donohue
et al.,
2012; Wang and Tang,
2014). In our study, the function proposed by Yang
et al. (
2008) was adopted as follows
where
E is the long-term average annual evaporation (mm),
P is the long-term average annual precipitation (mm),
PE is the long-term average potential evaporation (mm), and
n is the catchment characteristic. For a catchment, given a value of
P and runoff
Q,
E can be calculated by water balance equation,
n then can be calculated by equation (1). The lower the value of
n, the lower the underground water level, which means that the catchment area is generally rocky and mountainous, and rainfall completely forms runoff. For a high
n, the catchment area is mostly plain with deep quaternary soil and rich groundwater content, and the actual evaporation energy in this catchment area reaches its maximum (Yang
et al.,
2008).
If Budyko’s theory is defined as f=(PE, P, n), the differential form is as follows:
In long-term period, the change in catchment storage is negligible for catchment areas with >1000 km2 and long-time series (>11 years). Therefore, Eq. (2) can be rewritten as follows:
where
Q is the long-term average runoff depth (mm), here,
Q is average value from 1941-2015, which is like the work of Wang
et al. (
2016).
By dividing the left and right sides of Eq. (3) using Q, the relative runoff changes can be obtained as follows:
where εp is the precipitation elasticity, εPE is the potential evaporation elasticity, and εn is the catchment characteristic elasticity, i.e., runoff sensitivities. Climate elasticity can be defined as the ratio of proportional changes in streamflow and climatic variables such as precipitation and potential evapotranspiration.
The non-parametric method was used to estimate temperature elasticity considering the large number of the study catchments and the lack of meteorological series such as relative humidity, wind speed, and radiation. The method has low bias and is non-parametric (Yang
et al.,
2008). Its form is as follows:
where Xi and Qi is climatic variable values and runoff depth in the ith year, respectively, and ε is climate elasticity.
Potential evaporation was estimated using the Penman-Monteith temperature (PMT) method (Moratiel
et al.,
2020). Although there is a deviation from the results calculated by the Penman-Monteith FAO-56 equation, some scholars have proven that the deviation is negligible, especially for potential evaporation on an annual scale (Moratiel
et al.,
2020; Senatore
et al.,
2020).
In the following part of paper, we used runoff response changes (RRC) represent runoff changes and runoff sensitivities.
2.4 Random forests to predict runoff changes and their sensitivities to factors based on catchment attributes
The random forest is a machine-learning model that incorporates an ensemble of regression trees (Breiman,
2001). Random forests offer numerous advantages for regression and classification, including high flexibility, the ability to capture nonlinear relationships, and the combination of multiple predictors without the risk of overfitting. This method is widely employed in diverse areas of geoscience (Booker and Woods,
2014; Chaney
et al.,
2016). For further details, please consult Breiman (
2001).
We employed 500 trees to predict each of the five factor-induced changes and four runoff sensitivities, allowing each tree to grow unrestrictedly, thereby establishing the robustness of random forests. The predictors were randomly selected at each node, while the remainder were allocated to other nodes, ensuring that the significant predictors for users would not be excluded. Generally, the utilization of 500 trees yielded favorable prediction performance, and the removal of predictors at each node was less than one-third of the total number, exerting minimal impact on the prediction outcomes (Addor
et al.,
2018). The predictions were assessed using 10-fold cross-validation, where 70% of the catchments comprised the training set and the remaining 30% constituted the testing set. This process was iterated nine additional times. All procedures were implemented in R.
2.5 Global and local Moran’s Index approach to measuring spatial smoothness
A comprehensive dataset of catchments facilitated the straightforward capture of spatial patterns in hydrological variables. In our investigation, we utilized global Moran’s Index (Moran’s I) to gauge the presence of clusters and/or outliers across CONUS, as postulated by Patrick Alfred Pierce Moran in 1950 (Moran,
1950). Local Moran’s I enabled us to pinpoint precisely where the clusters and/or outliers were situated (Anselin,
1995). Addor
et al. (
2017) assessed the spatial correlation between climate indices and hydrological signatures across CONUS and determined that climate indices exhibit smoother patterns compared to signatures, demonstrating significant disparities between adjoining catchments. Sawicz
et al. (
2011) observed that the runoff ratio across the eastern United States exhibits a more gradual spatial variation than the slope of the flow duration curve.
The global Moran’s I was used to investigate the spatial association of runoff changes and their sensitivity to factors in space:
where N is the number of catchments, y is the variable of interest, is the mean of y, w is the weight associated with each pair of catchments, I is the global Moran’s Index, S0:
The global Moran’s I is a rational number, and after normalization of the variance, its value will be constrained to a range between -1.0 and 1.0. A value greater than 0 for Moran’s I indicates a positive spatial correlation among attribute values in all regions, implying that larger (or smaller) attribute values are more likely to cluster together. Conversely, a value less than 0 signifies a negative spatial correlation among the attribute values in all regions, indicating that larger (or smaller) attribute values are less (or more) likely to cluster together. When Moran’s I equals 0, it indicates random spatial distribution of the regions, with no discernible spatial correlation.
Compared to the global Moran’s I, local Moran’s I can specifically investigate the spatial associations in each local region, Moran’s I values that pass the significance test can be presented by LISA cluster maps (Anselin,
1995).
The higher the Moran’s I, the smoother the spatial pattern in each region. Note that |I| can exceed 1 (Jong
et al.,
1984). Local Moran’s I have rarely been used in previous studies. Strictly speaking, the global Moran’s I being equal to 0 does not mean there is no cluster phenomenon; it only represents spatial randomness. Therefore, it is necessary to use local Moran’s I to explore spatial patterns specifically.
3 Results
3.1 Spatial patterns of runoff changes
Figure 2 illustrates the spatial variations in runoff changes for the 1003 catchments across the CONUS. Overall, total changes predominantly demonstrate positive fluctuations across the CONUS, observed in 55% of the total catchments (
Figure 2a), with a mean of 4.28% per decade (
Figure 2b). Conversely, negative changes are primarily concentrated in the western mountains and southeast regions. As anticipated, precipitation, being the dominant factor influencing runoff, predominantly induces positive changes (1.8%-17% per decade) in the eastern region of the 100th meridian (as indicated by the red line in
Figure 1). The spatial pattern of precipitation-induced changes displays relatively smooth (with a mean of 2% per decade,
Figure 2a) among all components of runoff changes, a subject to be further discussed in the subsequent section. Runoff changes attributed to anthropogenic factors exhibit an average of 1.79% per decade, as suggested in previous studies (Ma
et al.,
2008; Jiang
et al.,
2015; Dey and Mishra,
2017).
Figure 2e demonstrates that anthropogenic factors are the predominant influence on runoff in certain catchments, leading to changes of up to approximately 60% per decade. Precipitation impacts runoff primarily through the process of runoff generation, while landscapes influence it during the routing process. Changes induced by potential evaporation are largely positive across the entire domain, with exceptions in a few catchments. These changes are relatively low, with a mean of 0.5% per decade, compared to changes caused by precipitation and anthropogenic factors. The lower changes tend to occur in the eastern and western mountainous regions (
Figure 2c). On the other hand, temperature-induced changes, with a mean of 0.26% per decade, are considerably lower than other components of runoff changes in most catchments (
Figures 2d and
2c). However, temperature-induced changes in individual catchments are surprisingly higher (e.g., 10% per decade to 24% per decade in the central plains and western mountainous areas), possibly due to low evapotranspiration and extensive snow cover.
Figure 2 Spatial patterns and box-plot statistics of runoff changes for total changes (a), changes induced by precipitation (b), potential evaporation (c), average temperature (d), and catchment properties (e) over the contiguous United States (R_total, R_P, R_ET, R_T, R_n represents total runoff changes, precipitation-, potential evaporation-, catchment characteristics n-induced changes, respectively). The right column is box plots of runoff changes. A, B, and C are grouped due to order of magnitude. Symbol “×” is the mean value, and the horizontal solid line is the median value. Outliers of changes in box plot are removed. Red line is 100-degree meridian which splits United States into west and east. |
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3.2 Spatial patterns of runoff sensitivities
Precipitation plays the most crucial role in influencing runoff changes across the majority of catchments (
Figure 3), with values ranging from 1.0 to 2.0 and peaking at 11 in the south-central regions (
Figure 3a). In comparison to runoff changes caused by precipitation (
Figure 2b), there exists a collaborative relationship throughout the CONUS. For instance, the precipitation elasticity ranges approximately from 2.0 to 11.0 around the 100th meridian and in the south-central regions (precipitation of 1.6 mm/year, Figure S1(a) in the Supporting Information), resulting in total changes ranging from 2.0% to 17% per decade, indicating that precipitation has a significant impact on alterations in runoff. However, an incongruous relationship between runoff changes and potential evaporation elasticity is evident for catchments in the western and eastern regions of the 100th meridian, with potential evaporation elasticity ranging from 0 to -1 and -1 to -10 respectively (
Figure 3b). For instance, changes in potential evaporation range from 6% to 19% per decade over the south-central and south-eastern regions (where the elasticity is approximately -1.0 to -4.0), while potential evaporation decreases at a rate of -0.92 to -0.27 mm per year (Figure S1(b) in the Supporting Information). The temperature elasticity exhibits both positive and negative values in catchments, with the highest positive value ranging from 3.0 to 20.6 observed in the west of the 100th meridian (
Figure 3c). This heterogeneous pattern of temperature elasticity may be attributed to the different types of runoff generation mechanisms in various parts of the basin, such as in catchments where snow-melting is the dominant runoff mechanism, temperature emerges as a crucial factor for runoff generation (Arrigoni
et al.,
2010). Furthermore, temperature-induced changes are considerably lower than other components, even when the elasticity is relatively high, owing to a relatively minor variation in temperature. The average temperature increases or decreases within a range of -0.48 to 0.11°C per decade in those catchments (Figure S1(c) in the Supporting Information). The elasticity of catchment properties exhibits a relatively homogenous distribution, with a range of -1 to -5, predominantly observed around the 100th meridian (
Figure 3d). However, the corresponding runoff changes present a heterogeneous pattern similar to the total changes across the CONUS (
Figure 2e), possibly attributed to variations in surface conditions (refer to Figure S1(d) in the Supporting Information).
Figure 3 Spatial patterns and box plot of runoff sensitivity to precipitation (a. Elasticity P), potential evaporation (b. Elasticity ET), average temperature (c. Elasticity T), and watershed properties (d. Elasticity n) over 1003 watersheds of the contiguous United States. In the box plot, the symbol “×” is the mean value, and the horizontal solid line is the median value. Red line is 100-degree meridian which splits United States into west and east. |
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3.3 Spatial smoothness of runoff changes
As presented in
Table 1, global Moran’s I serves as a predictor to a certain extent for the spatial distribution of runoff changes. Precipitation-induced changes have the highest global Moran’s I value of 0.55, signifying the most homogeneous distribution among all components. The global Moran’s I for total changes (0.38) and catchment characteristics-induced changes (0.35) are similar and display a comparable pattern. This similarity in spatial pattern is also observed in the case of temperature- and potential evaporation-induced changes.
Table 1 Global Moran’s Index (Global Moran’s I) for total changes (R_total), precipitation (R_P), potential evaporation (R_ET), average temperature (R_T), and catchment characteristics-induced changes (R_n)), and for precipitation-, potential evaporation-, temperature-, catchment characteristics elasticity). |
Runoff changes | Moran’s I | p | Runoff sensitivities | Moran’s I | p |
R_total | 0.380 | <0.01 | - | - | - |
R_P | 0.550 | <0.01 | Elasticity P | 0.383 | <0.01 |
R_ET | 0.212 | <0.01 | Elasticity PET | 0.383 | <0.01 |
R_T | 0.27 | <0.01 | Elasticity T | 0.202 | 0<0.01 |
R_n | 0.350 | <0.01 | Elasticity n | 0.626 | <0.01 |
The local Moran’s I would provide a more straightforward illustration of the spatial patterns of runoff response compared to the global Moran’s I. As depicted in
Figure 4, total changes and catchment characteristics-induced changes display heterogeneous smoothness across the CONUS, with both positive and negative connections, indicating diverse spatial patterns. Precipitation- and potential evaporation-induced changes exhibit relatively smooth patterns, whereas temperature-induced changes show minimal significant spatial correlation. Hence, it can be inferred that local Moran’s I may serve as a reliable predictor of the spatial patterns of runoff changes.
Figure 4 Local Moran’s I pattern for runoff changes in the contiguous United States (a. R_total: total changes; b. R_P: precipitation-induced changes; c. R_ET: potential evaporation-induced changes; d. R_T: temperature-induced changes; e. R_n: catchment characteristics-induced changes). Not Significant means Moran’s I failed the test at a significance of 0.05, High-High (Low-Low) means the spatial unit of high (low) observation value is the positive form of spatial connection surrounded by areas with high (low) value; High-Low (Low-High) means this spatial correlation is negative. |
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3.4 Spatial smoothness of runoff sensitivities
Table 1 reveals that catchment characteristic elasticity has the highest global Moran’s I (0.626) among all components, followed by precipitation (0.550), potential evaporation (0.383), and temperature elasticity (0.202). Temperature elasticity exhibits the most erratic pattern over distance compared to the other factors. Therefore, global Moran’s I can offer better predictability for spatial patterns of runoff sensitivities.
As shown in
Figure 5, runoff sensitivities have a smoother pattern over distance than runoff changes, which is expected as runoff sensitivities are more stable than runoff changes across spatiotemporal scale. Catchment characteristics elasticity is the smoothest, followed by precipitation and potential evaporation elasticity, temperature elasticity has the poorest pattern over distance.
Figure 5 Local Moran’s I for runoff sensitivities in the contiguous United States (a. Precipitation elasticity; b. potential evaporation elasticity; c. average temperature elasticity; d. catchment characteristics elasticity). Not significant means Moran’s I failed the test at a significance of 0.05, High-High (Low-Low) means the spatial unit of high (low) observation value is the positive form of spatial connection surrounded by areas with high (low) value; High-Low (Low-High) means this spatial correlation is negative. |
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Our results showed that runoff sensitivities are more easily related with each other across catchments over CONUS, which are indicated by local/global Moran’s I. Global Moran’s I sometimes cannot predict patterns of RRC, especially for runoff changes. However, local Moran’s I appear to better predict patterns of RRC, and runoff sensitivities are better than runoff changes, we assume that runoff sensitivities are more predictable in space.
3.5 Predictions in space based on random forests model
We utilized a comprehensive dataset of GAGES-II catchment attributes, encompassing 56 indicators (refer to Table S1 in the Supporting Information), to employ random forests in predicting RRC. As depicted in
Figure 6, we assessed the performance of the random forest model by comparing the observed and predicted RRC using the coefficient of determination, R
2. Our results indicate that total changes and catchment characteristic-induced changes can be reliably predicted (R
2 = 0.6) based on catchment attributes, followed by precipitation-induced changes (R
2 = 0.5) and potential evaporation-induced changes (R
2 = 0.3). In contrast, temperature-induced changes present a lower predictability (R
2 = 0.1). Notably, the model performs better for runoff sensitivities compared to runoff changes, with R
2 ranging from 0.94 (catchment characteristic elasticity) to 0.2 (temperature elasticity), while the predictions for precipitation- and potential evaporation elasticity exceed 0.6 (
Figure 6b). It is worth mentioning that De Roo
et al. (
2015) successfully employed the random forest approach to predict certain hydrological signatures, such as mean annual flow and half-flow date, with high accuracy.
Figure 6 The random forest prediction for runoff changes (a) and runoff sensitivities (b) determined by R2 between observed and predicted changes. Both runoff changes and runoff sensitivities are ordered from left to right based on how well they can be predicted using random forest based on 56 catchment attributes, which is represented by R2. R_total, R_n, R_P, R_ET, and R_T represents total changes, catchment characteristics-, precipitation, potential evaporation-, and average temperature-induced changes; catchment characteristics-, potential evaporation-, precipitation-, and temperature elasticity is represented by Elasticity n, Elasticity ET, Elasticity P, and Elasticity T. |
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Addor
et al. (
2018) have shown that hydrological signatures with a high global Moran’s I yield more accurate predictions compared to those with a low global Moran’s I. However, in our study, this alone may not be sufficient. For instance, the predictability of precipitation elasticity (>0.6) is greater than that of precipitation-induced changes (0.5), despite the former having a lower global Moran’s I (0.38). This difference might be illustrated by local patterns as indicated by the local Moran’s I. Runoff elasticities exhibit a more uniform local pattern compared to runoff changes, a distinction that cannot be discerned by the global Moran’s I, which only helps in determining the presence of connections between catchments without identifying their specific locations. The response of runoff to catchment characteristics displays the smoothest pattern and the highest spatial predictability (refer to
Figures 4-
5 and
Figure 6). Consequently, local Moran’s I appears to be a more effective approach for predicting spatial patterns and the predictability of RRC compared to global Moran’s I.
3.6 The controlling factors of runoff response changes
We established the top five attributes based on their importance by analyzing the mean square error (IncMSE) of prediction in the random forest model (refer to
Figures 7-
8). The determination of the most significant features among the 56 indicators was achieved through a 10-fold cross-validation curve, which illustrates the relationship between the model error and the number of predictors used for the fit. The error initially decreases as the number of predictors increases, showing a prominent drop at the beginning. Beyond a certain value, the error ceases to decline and eventually starts to increase (refer to the black curve line in
Figures 7-
8). The optimal number of predictors selected results in the best model performance. It is evident that three primary categories (climate, hydrology, topography), excluding NO10 soil types, exert control over runoff changes for total changes and catchment characteristic-induced changes. Annual runoff is particularly influential for total changes, catchment characteristic-induced changes, and potential evaporation-induced changes. Notably, the most critical factor for precipitation-induced changes is longitude, supporting the presence of an evident east-west pattern from the 100th meridian. Catchment area also emerges as a significant factor for total changes and catchment characteristic-induced changes, a factor that has been infrequently considered in prior studies (Yang
et al.,
2008,
2011). Furthermore, the top three factors (hydrology, topography, and soil characteristics) remain consistent for total changes and catchment characteristic-induced changes, with both components displaying similar spatial patterns across CONUS (refer to
Figure 2). For temperature-induced changes, the precipitation pattern is a controlling factor, particularly the low precipitation pattern. Generally, monitoring low precipitation (< 1 mm/day) presents substantial challenges due to the limited sensitivity of precipitation stations, potentially leading to considerable uncertainty in estimating runoff changes. This could be a contributing factor to the poor prediction of temperature-induced changes.
Figure 7 The importance of catchment attributes to runoff changes (a. Precipitation-induced changes (R_P); b. total changes (R_total); c. potential evaporation- (R_ET); d. temperature- (R_T); e. catchment characteristics-induced changes (R_n)), which is represented by the increase in the mean square error (IncMSE, %). The black line is the variation for the error of the random forest model as the number of catchment features after 10-fold cross-validation. The red dashed line is the minimum error corresponding to the optimal number of features. The red number is the total features that impact runoff changes. Here, we present only 5 features according to the rank of importance—the descriptions of catchment attributes are in Appendix A. |
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Figure 8 The importance of catchment attributes to runoff sensitivities (a. Elasticity of precipitation; b. potential evaporation; c. temperature; d. catchment characteristics), which is represented by the increase in the mean square error (IncMSE, %). The black line is the variation for the error of the random forest model as the number of catchment features after 10-fold cross-validation. The red dashed line is the minimum error corresponding to the optimal number of features. The red number is the total features that impact runoff. Here, we present only 5 features according to the rank of importance—the descriptions of catchment attributes are in Appendix A. |
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The number of significant factors for catchment characteristics, potential evaporation, precipitation, and temperature elasticity are 5, 7, 17, and 25, respectively. By analyzing the top five important factors for runoff sensitivity (refer to
Figure 8), we can demonstrate that climate, hydrology, and topography are the three primary controlling factors. Specifically, annual runoff emerges as the most critical factor, with the exception of temperature elasticity. The response of runoff to temperature is predominantly influenced by the precipitation pattern (refer to
Figure 7d). Notably, the drainage area also plays a crucial role in runoff sensitivity, particularly in precipitation and potential evaporation elasticity.
3.7 An understanding of the relationship between the controlling factors and runoff response changes
We compared the spatial smoothness between RRC and the controlling catchment attributes (those top two most important attributes to RRC in
Figures 7-
8). We further used accumulated local effect (ALE) to evaluate the degree of non-linearity in relationships (ALE, details see reference Stein
et al.,
2021).
The longitudinal positioning of rain gauges, which is the most crucial factor influencing precipitation-induced changes, exhibits a consistently smooth pattern across CONUS (followed by aridity, precipitation falling as snow, annual runoff, and low precipitation patterns, with drainage area being the most erratic, as shown in
Figure 9). This smooth pattern demonstrates a positive correlation (High-High and Low-Low) within certain regions, while the relationship is negative in others, aligning with the pattern of precipitation-induced changes across CONUS (refer to
Figure 2). Annual runoff also emerges as a significant factor for precipitation-induced changes (refer to
Figures 7-
8), displaying a moderately smooth pattern across CONUS (global Moran’s I is 0.566, as depicted in
Figure 9a). These smooth patterns of key factors appear to serve as predictors of spatial patterns of runoff changes to some extent, with the exception of temperature-induced changes. Low precipitation patterns are identified as the top two important factors influencing the response of runoff to temperature, and they also demonstrate a relatively smooth pattern over distance. The smooth patterns exhibited by controlling factors further corroborate the spatial patterns of runoff sensitivities.
Figure 9 Global and local Moran’s I for the controlling catchment attributes in the contiguous United States (a. Annual runoff (Annual_Run); b. gage longitude (Gage_Long); c. aridity; d. low precipitation frequency (low_prcp_freq); e. low precipitation duration (low_prcp_dur); f. fraction of precipitation falling as snow (frac_prcp_snow); g. drainage area (drain_area)). Not Significant means Moran’s I failed the statistical test at a significance of 0.05, High-High (Low-Low) means the spatial unit of high (low) observation value is the positive form of spatial connection surrounded by areas with high (low) value; High-Low (Low-High) means this spatial correlation is negative. |
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Figures 10-
12 show relationship between the top two important factors and RRC. Annual runoff increases the total changes, but the drainage area decreases it. The dual factors of annual runoff and precipitation falling as snow have an increasing influence on the temperature elasticity. The nonlinear impacts on RRC may enable to understand why there is a unique spatial pattern for each RRC component, and which would not be illustrated only by single factors.
Figure 10 Accumulated local effect for the top two important catchment attributes showing how they impact runoff changes (a-b. Annual runoff (Annual_Run) and drainage area (drain_area) to total changes (R_total); c-d. annual runoff (Annual_Run) and gage longitude (Gage_Long) to precipitation-induced changes (R_P); e-f. annual runoff (Annual_Run), low precipitation duration (low_prcp_Long) to potential evaporation-induced changes (R_ET); g-h. low precipitation frequency (low_prcp_freq), low precipitation duration (low_prcp_dur) to temperature-induced changes (R_T); i-j. annual runoff (Annual_Run), drainage area (drain_area) to catchment characteristics-induced changes (R_n). The rank of importance of catchment attributes to runoff changes in Figure 7. The full names of the catchment attributes are provided in Table S1 in Supporting Information. |
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Figure 11 Accumulated local effect for the second-order effect of the top two important catchment attributes on the runoff changes (a. Drainage area (drain_area) and annual runoff (Annual_Run) to total changes (R_total); b. gage longitude and annual runoff (Annual_Run) to precipitation-induced changes (R_P); c. low precipitation duration (low_prcp_dur) and annual runoff (AnnualRun.) to potential evaporation-induced changes (R_ET); d. low precipitation frequency (low_prcp_fre) and low precipitation duration (low_prcp_dur) to temperature-induced changes; e. drainage area (drain_area) and annual runoff (Annual_Run) to catchment characteristics-induced changes). The rank of the importance of catchment attributes to runoff changes in Figure 7. The full names of the catchment attributes are provided in Table S1 in Supporting Information. |
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Figure 12 Accumulated local effect for the effect of the top two important catchment attributes on runoff sensitivities (a-b. Annual runoff (Annual_Run) and drainage area (drain_area) to precipitation elasticity (Elasticity P); c-d. annual runoff (Annual_Run) and drainage area (drain_area) to potential evaporation elasticity (Elasticity ET); e-f. annual runoff (Annual_Run), fraction of precipitation falling as snow (low_prcp_snow) to temperature elasticity (Elasticity T); g-h annual runoff (Annual_Run) and aridity to catchment characteristics (Elasticity n). The rank of the importance of catchment attributes to runoff sensitivities is in Figure 8. The full names of the catchment attributes are provided in Table S1 in Supporting Information. |
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Now, we proceed to analyze the combined impact of the dual factors on RRC. As illustrated in
Figure 11, within the range of 0-500 mm for annual runoff or < 5000 km
2 for drainage area, the total changes can reach up to -100%/10a. As the catchment’s drainage area increases, the total changes conversely decrease when considering a given annual runoff or drainage area. The areas with the maximum precipitation-induced changes are those where annual runoff is below 1000 mm, while the minimum changes occur in the longitudinal region of 100-90 degrees west and in areas where the annual runoff exceeds 1500 mm. Furthermore, when the low precipitation duration ranges from 10-40 days and the annual runoff is above 1500 mm, the potential evaporation-induced changes are approximately 4%-8%/10a and 0-2%/10a, respectively. It is notable that catchment characteristics-induced changes display a more heterogeneous pattern across different levels of drainage area and annual runoff when compared to other components, being maximal in catchments with a drainage area of 5000-1000 km
2 and an annual runoff above 1500 mm, and minimal in areas where the annual runoff is 500 mm and the drainage area exceeds 1.0. It is important to acknowledge the potential uncertainty in predictions, for instance, the temperature-induced changes reaching up to 1200%-1400%/10a in regions with a low precipitation frequency of 300-340 days/year and a low precipitation duration below 5 days, possibly due to the limited predictive performance of the random forest model.
Figure 13 illustrates the second-order influence of the top two significant catchment attributes on runoff sensitivities. Annual runoff emerges as the most influential factor for all components, albeit with varying effects on each. For instance, in regions where the drainage area is below 5000 km
2 and the annual runoff exceeds 1000 mm, and when the drainage area surpasses 20,000 km
2, the precipitation elasticity reaches its maximum values of -5 and 6, respectively. The combined impact of catchment attributes on potential evaporation and temperature elasticity exhibits a relatively intricate pattern. Conversely, catchment characteristics elasticity demonstrates a more consistent trend. In general, catchment characteristics elasticity increases as aridity decreases, given a certain drainage area.
Figure 13 Accumulated local effect for the second-order effect of the top two important catchment attributes on the runoff sensitivities (a. Drainage area (drain_area) and annual runoff (Annual_Run) to precipitation elasticity (Elasticity P); b. drainage area (drain_area) and annual runoff (Annual_Run) to potential evaporation elasticity (Elasticity ET); c. fraction of precipitation falling as snow (frac_prcp_snow) and annual runoff (Annual_Run) to temperature elasticity (Elasticity T); d. annual runoff (Annual_Run) and aridity to catchment characteristics elasticity (Elasticity n)). The rank of the importance of catchment attributes to runoff sensitivities is in Figure 8. The full names of the catchment attributes are provided in Table S1 in Supporting Information. |
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4 Discussion
4.1 The relationship between the spatial distribution of runoff response and climatic factors
This study demonstrated that local Moran’s I can serve as a predictor of the spatial patterns of RRC. Climate has a direct and/or indirect impact on runoff response, influencing processes such as the generation and convergence of runoff, infiltration, and evaporation. Consequently, it prompts us to consider the relationship between the spatial patterns of RRC and the climate gradient.
In the western mountain ecoregion, the decrease in runoff at a rate of 2.54 mm per year may be attributed to a declining trend in climatic factors, where both precipitation and potential evaporation decrease at rates of 1.94 mm and 1.5 mm per year, respectively (Figure S1 in the Supporting Information). Total changes in the western mountain regions (
Figure 2) exhibit a negative variation, with annual precipitation and runoff showing decreasing trends, and potential evaporation showing an increasing trend. Furthermore, runoff with an increasing trend of 30%-55% per 10 years is mainly observed in the western plain, where there is low precipitation, low leaf area index, high evaporation, and increasing rainfall at a rate of 4.4 mm per year. The factors influencing runoff alternately involve climatic factors and anthropogenic activities, suggesting that climate alone is not the sole cause of the total changes; human activities may be more significant in certain regions (Ravindranath and Devineni,
2020; Duan
et al.,
2022).
Precipitation-induced changes have a relatively homogeneous pattern; catchments with a decreasing trend are mainly in the western mountains and southeast plain, where precipitation and runoff decrease with ratio of 0.9 and 2.54 mm per year, respectively. And positive changes occurred in most regions over CONUS; these ecoregions are characterised by high annual precipitation (>1000 mm per year) and even annual distribution.
Investigating the positive impacts of potential evaporation-induced changes across the CONUS region may present challenges. Yang
et al. (
2011) calculated the elasticities of runoff in response to precipitation, net radiation, air temperature, wind speed, and relative humidity by employing the first-order differential of the Penman equation. Their findings indicated that wind speed had a significant effect on runoff. In our study, potential evaporation-induced changes are influenced by various climatic factors, contributing to the heterogeneous patterns observed in potential evaporation-induced changes.
Identifying patterns of temperature-induced changes is challenging through the analysis of climatic factors and ecoregion distributions. We hypothesized that the uncertainty surrounding temperature-induced changes may stem from low precipitation patterns. Additionally, non-parametric methods may lead to an overestimation of temperature elasticity, consequently resulting in an overestimation of runoff changes. Yang
et al. (
2011) demonstrated that the runoff change estimated by non-parametric methods was five times larger than the observed runoff change.
The response of catchment characteristics is a comprehensive outcome of the interplay between soil, vegetation, and climate (Ning
et al.,
2019; Meng
et al.,
2023; Zhou
et al.,
2023a). In previous studies, changes attributed to catchment properties have often been categorized as landscape-induced changes, in line with the Budyko hypothesis. Upon comparison with the distribution of catchment properties denoted by “n” (see Figure S1e in the Supporting Information), regions exhibiting relatively high values of “n” (0.06-6.71) tend to display the most significant “n”-induced changes. Intriguingly, the pattern of the annual runoff trend mirrors that of catchment characteristics. The non-linear relationship between “n”-induced changes and annual runoff seems irregular (see
Figure 10i), yet there appears to be an exponential growth trend between “n” elasticity and annual runoff (see
Figure 12g).
4.2 Regional patterns of runoff sensitivities
Climate elasticities are conventionally assumed to be constant within specific regions (Sankarasubramanian
et al.,
2001). Gong
et al. (
2022) elucidated the intricate interplay between various elasticities and factors such as annual rainfall, annual runoff, aridity index, runoff ratio, and catchment characteristics. Sankarasubramanian
et al. (
2001) established that precipitation elasticity tends to be low in basins with significant snow accumulation, and in regions where moisture and energy inputs synchronize seasonally. This value tends to be high in arid regions and low in humid regions. We generated a contour plot of runoff elasticities (see Figure S2 in the Supporting Information), which reaffirmed the findings of prior studies (Sankarasubramanian
et al.,
2001; Gong
et al.,
2022). Furthermore, the spatial distribution of runoff elasticities tends to align with ecoregions across the CONUS (refer to
Figures 2-
3). For instance, in the western plains, most runoff elasticities tend to be high, while temperature elasticity appears to be high in the western mountains. Ecoregion delineations, based on hydrology, climate, vegetation, and topography (Rice
et al.,
2016; Zhou
et al.,
2023b), were found to correlate with the crucial factors influencing runoff elasticities. This study underscores the significance of these attributes in influencing runoff elasticities, thereby elucidating why the patterns of runoff ratio changes can be effectively illustrated by ecoregions.
4.3 Improved understanding of variables with poor predictability in space
Our study shows that there is a poor predictability for some RRC components over space, which does not mean that they should not be considered in hydrological response studies. Andréassian
et al. (
2016) also believed that it is difficult to identify physical reasons for the spatial variations in elasticity values. A better understanding of drivers of elasticity over space would be useful to assess if hydrological models can capture well the impacts of climate change and human activities on discharge (Vano
et al.,
2015; Addor
et al.,
2018).
One method of evaluating the unpredictability of hydrological components is to examine spatial smoothness (Addor
et al.,
2018). In our research, the changes induced by temperature and temperature elasticity exhibit the lowest level of predictability across space, and they also display the highest spatial variability. According to Addor
et al. (
2018), there is no conclusive evidence that the abrupt changes observed between these catchments truly reflect hydrological differences. Spatial distance is not a strong indicator of the poor predictability of hydrological disparities; instead, climate zones, human activities, and methodology could be more useful in illustrating this issue. We can infer that low precipitation patterns exert the most significant influence on temperature-induced changes and elasticity. Hydrological variables with low values often exhibit poor predictive performance in both spatial and temporal contexts, such as low flow, which may contribute to the lack of predictability in the response of runoff to temperature.
The high predictability of runoff response to catchment attribute “n” can be exemplified by its association with topography (Ning
et al.,
2019; Zhou
et al.,
2023a). The value of “n” is typically influenced by landscape conditions, with higher values often found in hilly areas characterized by high groundwater levels, deep quaternary soils, and increased energy flux. In contrast, for basins in areas with low groundwater levels, such as central plains, “n” tends to be relatively low. A comparison of the spatial pattern of the local Moran’s Index for catchment attribute elasticity reveals that the elasticity of “n” in the east exhibits a smoother variation compared to the west, where underground water levels are relatively high. This suggests that topography partially explains the predictability of “n” elasticity. However, when it comes to “n”-induced runoff changes, there is no clear relationship between topography and the predictability of these changes. This discrepancy may be due to the complex physical mechanisms underlying runoff changes, as the elasticity of runoff to climate factors tends to be consistent across different geographical locations (Zhou
et al.,
2023a). In other words, the physical drivers of runoff elasticity appear to offer a more stable explanation than the drivers of runoff changes themselves.
4.4 Limitations
The computation of potential evapotranspiration using the Penman-Monteith temperature method in our study has certain limitations, leading to uncertainty in the calculation of runoff response. The degree of uncertainty in RRC is determined by the sensitivity of runoff to hydroclimatic factors. Greater sensitivity of runoff to these factors results in increased uncertainty. Our extensive analysis indicates a substantial runoff response to temperature-related variables, specifically potential evapotranspiration and temperature. Notably, the potential evapotranspiration elasticity over the central South region is as high as -10, indicating that a 1% variation in potential evapotranspiration could lead to a 10% decrease in runoff, while a 1% variation in temperature could result in a decrease of up to 15%. In contrast, across the western and southern regions, the uncertainty of RRC due to potential evapotranspiration computation tends to be reduced, with potential evapotranspiration elasticity hovering around zero (refer to
Figure 3). Consequently, this propagation of uncertainty presents a spatial pattern consistent with the sensitivity of runoff to hydroclimate.
Currently, the FAO-56 Penman-Monteith equation is the standard method used to calculate potential evapotranspiration due to its comprehensive physical foundation. However, the high cost and maintenance requirements of agrometeorological stations, as well as the need for a large number of sensors, make this method impractical. As an alternative, several temperature-based models have been developed to estimate potential evapotranspiration by simplifying the original FAO-56 Penman-Monteith equation, thereby requiring only temperature data. These temperature-based models typically adjust solar radiation-related coefficient based on daily temperature to estimate potential evapotranspiration. Therefore, the uncertainty in potential evapotranspiration in our study mainly stems from the solar radiation-related coefficient.
Senatore
et al. (
2020) compared the Hargreaves-Samani (HS) model with the Penman-Monteith temperature model (utilized in our study) and demonstrated a high correlation between the solar radiation-related coefficient and the average daily temperature range, resulting in reliable estimation in homogeneous climatic regions. Furthermore, the performance of potential evapotranspiration is influenced by the time scales at which it is calculated. Moratiel
et al. (
2020) revealed that seven temperature-based models can provide acceptable results at an annual scale, while none of the models performed well in winter. In the remaining seasons, the Penman-Monteith temperature model, with the calibration of the Hargreaves empirical coefficient, yielded the best results.
In the future, remote sensing products could be valuable for calculating runoff response, as potential evapotranspiration is commonly estimated using the standard FAO-56 Penman-Monteith equation or its improved versions.
5 Conclusions
We conducted a systematic exploration of the spatial patterns and predictability of RRC for over 1000 catchments across the CONUS, utilizing the GAGE-II dataset, which includes various catchment attributes such as climatology, topography, land cover, soil, geology, hydrology, and human activities. Both global and local Moran’s I were employed to gain insights into the smoothness of hydrological response over distances. Additionally, the random forest machine learning algorithm was utilized for predicting hydrological responses based on catchment attribute predictors. Moreover, the Accumulated Local Effect (ALE) method was used to investigate the nonlinear relationship between dominant factors and hydrological response, as well as the secondary effects of these factors. Our study diverges from previous research by focusing on the physical significance behind runoff changes from three perspectives: 1) spatial correlations; 2) spatial predictability; and 3) controlling factors. This unique approach signifies the novelty of our study.
Our study highlights several key findings:
(1) We have demonstrated the feasibility of deriving spatial patterns and smoothness of runoff response to climatic factors (precipitation, potential evaporation, and average temperature) and catchment properties. The ecoregion patterns across CONUS are found to be somewhat correlated with the distribution of RRC.
(2) Predictive models utilizing machine learning algorithms based on catchment attributes have been successful in predicting RRC.
(3) RRC with significant positive or negative connections between catchments is generally well-predicted. While global Moran’s I may not fully capture the predictability and distribution of RRC, local Moran’s I can offer more accurate insights into these aspects.
(4) The combined influence of climate, hydrology, and topography strength, as well as the nonlinear relationships between RRC and controlling factors, collectively determine the heterogeneous spatial patterns of RRC. These findings have enabled us to predict RRC based on climate and catchment attributes. RRC with irregular patterns, such as runoff response to temperature, tend to exhibit poor predictability over space. Accordingly, we recommend that hydrological variables demonstrating poor spatial predictability should receive greater attention.
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