Quantifying the streamflow change and influencing factors with a spatio-temporal coupling analysis framework

In the context of global change (both climate change and human activities), hydrological elements such as streamflow (Dariane & Pouryafar 2021) and evapotranspiration (Wang et al. 2021) have exhibited significant variability, causing a variation in the spatio-temporal distributions of water resources, which threatens national or regional water security, energy security, and food security. Therefore, investigating the spatio-temporal characteristics of streamflow change and its influencing factors is the key to successful water resources management, as it helps managers to plan and utilize water resources rationally and improve flood and drought prevention and mitigation capabilities.

Hydrological elements are subject to complex variations, including non-repeatability in temporal terms and non-uniformity in spatial terms (Pan et al. 2018). On the one hand, with the development of hydrological observation and the improvement of hydrometeorological data collection, people can obtain long-term time series data about various hydrological elements to study their spatio-temporal patterns following proven time series analysis methods. A variety of analytical methods, including the Mann–Kendall test, Sen's slope estimator, and the Pettitt test, are often utilized jointly to analyze the temporal heterogeneity of hydrometeorological elements. For instance, Bae et al. (2008) investigated the spatio-temporal changes of runoff in South Korea from 1968 to 2001 with the Precipitation-Runoff Modelling System, Mann–Kendall's test, regression analysis, and Moran's I. They noted that the long-term trend of annual runoff is increasing in the north and decreasing in the southwest. Zhong et al. (2021) detected the streamflow trends and their change-points from 1956 to 2017 in the Yellow River Basin (China) using five statistical methods, showing a clear downward trend in streamflow. On the other hand, hydrological elements also have a certain heterogeneity of spatial distribution. At present, the popular analytical methods for studying spatial patterns of hydrological elements are empirical orthogonal function (EOF) and cluster analysis. For example, McCabe & Wolock (2014) classified the stream gauges into 14 clusters based on cluster analysis to increase understanding of the variability of annual mean streamflow from 1951 to 2009 in the conterminous United States. Similarly, Gornik (2020) examined the spatio-temporal variations of streamflow in the Upper Vistula Basin (East-Central Europe) from 1951 to 2015 with Ward's hierarchical cluster analysis. Undeniably, assessing streamflow change is challenging because they interact on temporal and spatial scales and are difficult to disentangle. Unfortunately, in the aforementioned studies, the researchers did not sufficiently consider the synchronization and correlation of spatio-temporal variations for streamflow.

Many attribution methodologies have been developed to detect changes in streamflow, including statistical methods and hydrological models (Zhang et al. 2021a). For example, Zhai et al. (2016) investigated the spatial and temporal patterns of streamflow and its drivers from 1964 to 2010 in the Lancang River by the Mann–Kendall statistics and dual mass curve analysis. The results showed that the hydropower plants, land-use/land-cover change (LUCC), and precipitation patterns are the main influencing factors. Li et al. (2020) developed a framework to quantify the impacts of climate change and human activities on streamflow based on the SWAT model and Weather Research and Forecasting model in the Yihe River basin (China) from 1951 to 2013. Yang et al. (2022) noted that the land surface changes were the dominant factor in river streamflow change in the major river basins of China in recent years based on the Budyko theory. Recently, Li & Quiring (2021) found that the main influencing factors of streamflow change are time-varying rather than constant. This suggests that we need to consider the spatial and temporal characteristics of the influencing factors when conducting attribution analysis of streamflow changes, which is not covered by many current studies.

The paper aims to quantify the streamflow change and its influencing factors from a two-dimensional perspective in space and time with a spatio-temporal coupling analysis framework. Under the framework, the Mann–Kendall test, Sen's slope estimator, Pettitt test, cluster analysis, and Ripley's L-function were linked and used to examine spatio-temporal heterogeneity of streamflow, including the trends of streamflow, spatial patterns of streamflow in different sub-periods, and spatial patterns of streamflow change between sub-periods. The SWAT model was employed to quantify the impacts of climate and human activities on streamflow change. Also, the Dawen River Basin (DRB) was taken as a case study to verify the reasonableness and effectiveness of the proposed framework. This work can provide a theoretical basis for water resources management in the context of global change.

Step 1: The Mann–Kendall test is used to reveal the long-term trend in the yearly streamflow (Q); Pettitt's test is employed to detect change-points in the yearly streamflow (Q) and to divide the study period into multiple sub-periods (T₁, T₂, … , T_m).

Step 2: The basin is divided into sub-basins based on a digital elevation map (DEM) (B₁, B₂, … , B_n).

Step 3: Identification of the study objects of spatio-temporal heterogeneity of streamflow.

The evolutionary characteristics of streamflow at the basin scale are not only reflected in temporal variability, but also in spatial differences. The study objects that need to consider spatio-temporal heterogeneity for the analysis of streamflow variability include two categories: the spatial distribution of streamflow characteristics in each sub-period and the spatial distribution of streamflow variability characteristics between sub-periods. As shown in Figure 1, the streamflow characteristics of the jth sub-basin in the ith sub-period are denoted as ⁠, and the streamflow variation characteristics of the jth sub-basin between the ith and (i + 1)th sub-periods are denoted as ⁠. Thus, the spatial distribution characteristics of streamflow in the ith sub-period can be denoted by ⁠, and the spatial distribution characteristics of the streamflow variation from the ith sub-period to the (i + 1)th sub-period can be denoted by ⁠. and are the study objects to be considered when studying the spatio-temporal heterogeneity of streamflow at a basin scale.

Step 4: Hierarchical cluster analysis and Ripley's L-function are employed to evaluate the spatial heterogeneity of the temporal evolution of streamflow.

We first use the hierarchical cluster method to cluster n sub-basins and obtain several clusters with different streamflow characteristics, where each cluster contains several sub-basins with similar streamflow characteristics. Each sub-basin is then generalized to a point so that the problem of the spatial distribution of streamflow in the basin can be abstracted as a point pattern problem. Finally, Ripley's L-function is employed to analyze the spatial distribution pattern of each cluster, specifically: the corresponding L-value is calculated by selecting the distance scales according to the basin area, and the simulated L(d) Monte Carlo curve is plotted with the actual L(d) curve so that the spatial distribution of each cluster can be identified.

Step 5: The SWAT model is employed to quantify the impacts of climate and human activities on streamflow change at spatial and temporal scales.

The SWAT model, a physically based, continuous-time, and semi-distributed hydrological model developed by the United States Department of Agriculture (USDA) Agricultural Research Service, can predict the water movement in complex basins with varying soils, land use, and management conditions over long-term periods (Li et al. 2019). In this study, we used the SWAT model to reconstruct natural streamflow in the study area. First, the meteorological data such as precipitation and temperature for the same period are used as model inputs. Then, sub-basins in the basin that are less affected by human activities are selected for model calibration, and the rationality is verified by the observed data. Finally, the natural streamflow of each sub-basin is calculated by the model.

The Mann–Kendall test, Sen's slope estimator, and Pettitt test are usually linked and used when detecting trends and change-points of hydrometeorological variables, including streamflow, precipitation, and potential evapotranspiration (Meng et al. 2019). The Mann–Kendal test, which was proposed by Mann and Kendall, was employed to ascertain the trends of streamflow at key stations over the study area (at a significance level of P ≤ 0.05), with the magnitudes of the trends characterized using Sen's slope. The Pettitt test, which was proposed by Pettitt, was used to detect the change-point with a significance test (at a significance level of P ≤ 0.05). The results provide a reasonable division of the period, which is crucial for the spatio-temporal coupling analysis.

Cluster analysis is an unsupervised multivariate technique for characterizing the grouping structure of specific datasets (Yang et al. 2019). The hierarchical clustering method is one of the most commonly used cluster analysis methods, which is simple, intuitive, and easy to interpret, and is widely used in hydrology and ecology (Gornik 2020). Therefore, we choose the method to cluster the sub-basins to describe the spatial variability of streamflow in terms of clusters and determine the spatial distribution pattern of each cluster with different streamflow characteristics separately.

The principle of this method is to consider the sub-basin as the smallest cluster and calculate the distance between clusters, then merge the two clusters with the shortest distance into a new cluster; then calculate the distance between the new, and remaining, clusters, and merge the two clusters with the shortest distance into a new cluster again, and so on, until they are merged into one large cluster (Supplementary Figure S1).

In practical applications, the simulated L(d) curve obtained from the random distribution was plotted in the same coordinate system as the actual L(d) curve, and the type of spatial distribution was judged by the relationship between the positions of the curves. In the present study, the Monte Carlo method was used to solve the upper and lower envelope (99% confidence interval) of the random distribution and the judgment criteria are as follows (Lancaster & Downes 2004): if the actual L-value of the point events lies above the upper envelope, the point events are aggregated in space; if the actual L-value of the point events lies between the upper and lower envelopes, the point events are randomly distributed in space; and if the actual L-value of the point events lies below the lower envelope, the point events are regularly dispersed in space.

Daily streamflow data from five hydrological stations (Figure 2, see Supplementary Table S1 for more details) and daily precipitation data of 57 meteorological stations from 1968 to 2013 were collected from the China Annual Hydrological Reports. The local DEM was derived from the Shuttle Radar Topography Mission (SRTM) dataset with a resolution of 30 m. Land-cover maps from 1990 to 2000 were obtained from https://www.resdc.cn. The soil types in the DRB were derived from the Harmonized World Soil Database (HWSD) with a resolution of 1 km (https://www.fao.org).

As an important component of water resource management, detailed characterization to reveal the spatio-temporal evolution of natural streamflow is the key to a success for adaptive water resources management and a prerequisite for sustainable water resources utilization. Thus, this study took the natural streamflow as the research object and conducted the spatio-temporal evolution analysis of streamflow, aiming to provide a theoretical basis for water resources management in the basin. The SWAT model was employed to reconstruct the natural streamflow of the DRB, and the calibration and validation were described in the Supplementary Information. Evidently, the SWAT model has high precision of the streamflow simulation in the DRB, with all R² greater than 0.9. Meanwhile, the DRB was divided into 54 sub-basins with coding by the SWAT model, as shown in Supplementary Figure S2. Here, we used the proposed framework to study the spatio-temporal heterogeneity of natural streamflow change and its influencing factors in the DRB, specifically including long-term trend and change in natural streamflow and spatial heterogeneity in the temporal evolution of natural streamflow.

The Pettit test was adopted to detect the change-point of natural streamflow at Daicunba station from 1956 to 2013 which is the key station of DRB with a controlling area of 91.12% of the basin. According to the results, 1990 was the change-point with P = 0.8870 (at a significant level of P > 0.05), which indicated that the test was statistically insignificant. According to Zhong et al. (2021), the turning point of the streamflow in the lower Yellow River Basin from 1956 to 2017 occurred in 1990 following five statistical methods, including Mann–Whitney U-test, Moving t-test, Mann–Kendall test, Ordered cluster analysis, and Pettitt test. Therefore, the study period (1956–2013) was derived into two sub-periods by 1990: the early period (1956–1990) and the recent period (1991–2013).

Table 1 lists the results of the analysis of natural streamflow trends at the five hydrological stations, and it can be seen that all stations show an increasing trend throughout the entire study period (1956–2013), and a decreasing trend in the early period (1956–1990), and an increasing trend in the recent period (1991–2013). In addition, the magnitude of streamflow change during the recent period at the four stations (except for the Daicunba) is greater than that in the early period, which may be related to the extent of climate change during the recent period compared with that in the early period (Johnson et al. 2020). However, the changes in the trend in the three periods at all stations are not statistically significant (at P > 0.05), which is mainly because this study restores the observed streamflow to natural streamflow and weakens the effects of human activities.

In this study, we took the average streamflow of three periods in the DRB as an example to study its spatial pattern and verify the feasibility of the proposed framework. Here, the average values of natural streamflow from 1956 to 1990 under the underlying surface in 1990 were calculated as the result of natural streamflow during the early period and the average values of streamflow from 1991 to 2013 under the underlying surface in 2010 were derived as the result of natural streamflow during the recent period for the 54 sub-basins in the DRB. The spatial heterogeneity of the temporal evolution of natural streamflow was studied in terms of the spatial pattern of natural streamflow in early and recent periods, and the spatial patterns of streamflow change from the early to the recent period.

The L-functions for clusters I–V in the early period are shown in Figure 3(c), and the distance scales studied are from 0 to 50 km. Based on the positional relationship between the simulated L(d) curve with a 99% confidence interval by the Monte Carlo method and the actual L(d) curve, we find that sub-basins included in Cluster I with very small streamflow have an aggregated distribution at distances 6 ≤ d ≤ 21 km and a random distribution at the rest of the distances; sub-basins included in Cluster II with small streamflow have an aggregated distribution at 3 ≤ d ≤ 18 km and a random distribution at the rest of the distances; sub-basins included in Cluster III with moderate streamflow have a uniform distribution at 16 ≤ d ≤ 17.5 km and a random distribution at the rest of the distances; sub-basins included in Cluster IV with large streamflow are uniformly distributed at 10.5 ≤ d ≤ 13 km and randomly distributed at the rest of the distances; Cluster V with very large streamflow are aggregated at 25 ≤ d ≤ 27.5 km and randomly distributed at the rest of the distances. Overall, Clusters I and II show aggregation at intermediate distances, and Clusters III, IV, and V show aggregation at small distances.

The L-functions for clusters i–iv in the recent period are illustrated in Figure 4(c): sub-basins included in Cluster i with very small streamflow have an aggregated distribution at 3.5 ≤ d ≤ 31 km and a random distribution at the rest of the distances; the sub-basins included in Cluster ii with small streamflow have a uniform distribution at 10.5 ≤ d ≤ 13 km and a random distribution at the rest of the distances; the sub-basins included in Clusters iii (large streamflow) and iv (very large streamflow) are randomly distributed across all distances. In summary, Cluster i shows aggregation on large distances, Cluster ii shows aggregation on small distances, and Clusters iii and iv do not show aggregation.

Many studies have shown that streamflow change is mainly driven by climate change and human activities (Dey & Mishra 2017; Zhang et al. 2020). On the one hand, the key climatic influencing factors affecting streamflow are precipitation and temperature, with the former being the most important. On the other hand, the effects of human activities can be divided into two categories: (1) direct human influences, mainly water withdrawal from rivers and reservoir storage and discharge; and (2) indirect human influences, mainly LUCC (Ma et al. 2010). Accordingly, natural streamflow change is mainly driven by precipitation (climate change) and LUCC (human activities) (Yuan et al. 2018).

Cluster analysis was used to elucidate the spatial patterns of natural streamflow and its influencing factors (precipitation and LUCC), whereupon these three can be considered as categorical variables. Therefore, we employed the chi-squared test, a non-parametric test for categorical variables, with the number of sub-basins as the sampling frequency, to perform the correlation analysis of the three (i.e., natural streamflow, precipitation (climate change), and LUCC (human activities)) (Supplementary Table S2). The result shows that the significance levels of the test subjects with correlations are all below 10%, and the minimum can fall below 0.5%, which means that there is a significant correlation between the spatio-temporal distribution of natural streamflow and precipitation and LUCC in the DRB. This result further verifies that natural streamflow variability is mainly driven by precipitation and LUCC, which is also consistent with the findings of Yuan et al. (2018) and Ma et al. (2010).

Some studies demonstrated the temporal variations of streamflow by taking the basin as an entire (i.e., at the basin outlet cross-section) or dividing it into limited sub-basins according to upstream and downstream regions thereof, ignoring the streamflow characteristics within the basin (Yuan et al. 2018; Zhong et al. 2021), however, we found that streamflow change in the sub-basins of the DRB was inconsistent, with increases and decreases therein (Figure 5(b)). Meanwhile, some researchers focused on spatial patterns of streamflow in the same period, failing to reveal the evolution of streamflow spatial patterns over time (McCabe & Wolock 2014; Gornik 2020). Nevertheless, we found that the spatial patterns of streamflow vary with time (Figures 3(b) and 4(b)). Furthermore, the streamflow change may be superimposed or offset between sub-basins: streamflow change in the sub-basins are insignificant, but the superimposed effect is due to the inconsistent direction of streamflow in each sub-basin, resulting in the change of streamflow at the basin outlet section being significant; streamflow change in the sub-basins are significant, but the offsetting effect is due to the inconsistent direction of streamflow in each sub-basin, resulting in the change of streamflow at the basin outlet section being insignificant (a detail the likes of which the aforementioned studies could not capture).

At present, many scholars have researched adaptive regulation of streamflow change to mitigate the adverse effects of climate change and human activities on water resources systems (Zhang et al. 2021b), and the priority is to clarify the spatio-temporal distribution characteristics of streamflow and the driving factors; however, some existing studies have certain limitations, such as an inability to effectively reflect the streamflow characteristics of some sub-basins that are severely affected by direct human influences (i.e., water withdrawal from rivers and reservoir storage and discharge), and the differences in streamflow characteristics of different sub-basins within a basin, which may prevent water resource system managers from taking effective adaptive regulatory measures. Thus, the proposed spatio-temporal coupling analysis framework of streamflow change and its influencing factors is effective when trying to reflect the spatio-temporal characteristics of streamflow in sub-basins and fills the knowledge gap to a certain degree, which can consider the spatio-temporal synchronization and correlation of streamflow change.

This study aims to quantify the streamflow change and its influencing factors from a two-dimensional perspective in space and time with a spatio-temporal coupling analysis framework. The DRB (China) was taken as a case study and the key findings are as follows:

• (1)

  The temporal variations of streamflow in the sub-basins of the basin are inconsistent (either increasing, decreasing, or constant). Also, the spatial patterns are time-variant, but all are clustered. That is, streamflow changes are found to be spatially and temporally synchronous and correlated.

• (2)

  The natural streamflow change in the DRB during 1953–2013 is mainly affected by climate change–human activities, followed by climate change and human activities, accounting for a total area of 52.04, 24.90, and 23.06%, respectively.

• (3)

  The vast majority of sub-basins within the basin with relatively large natural streamflow change during 1953–2013 are mainly driven by climate change (i.e., precipitation), which is related to the fact that direct impacts of human activities were not considered in this study.

This study was supported by the National Key R&D Program of China (Grant No. 2021YFC3090105); the Projects of the National Natural Science Foundation of China (Grant No. 52209032); the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200160); the Science and Technology Cooperation Support Project of Guizhou Province, China (Grant No. [2019]2890); and the Special Research Fund of Nanjing Hydraulic Research Institute (Grant No. Y120011).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.