Study on Hydrological–Meteorological Response in the Upper Yellow River Based on 100-Year Series Reconstruction

Abstract

Precipitation, as a key input in the water cycle, directly influences the formation and change process of runoff. Meanwhile, the return runoff intuitively reflects the available quantity of water resources in a river basin. An in-depth analysis of the evolution laws and response relationships between precipitation and return runoff over a long time scale serves as an important support for exploring the evolution of hydrometeorological conditions and provides an accurate basis for the scientific planning and management of water resources. Taking Lanzhou Station on the upper Yellow River as a typical case, this study proposes the VSSL (LSTM Fusion Method Optimized by SSA with VMD Decomposition) deep learning precipitation element series extension method and the SSVR (SVR Fusion Method Optimized by SSA) machine learning runoff element series extension method. These methods achieve a reasonable extension of the missing data and construct 100-year precipitation and return runoff series from 1921 to 2020. The research results showed that the performance of machine learning and deep learning methods in the precipitation and return runoff test sets is better than that of traditional statistical methods, and the fitting effect of return runoff is better than that of precipitation. The 100-year precipitation and return runoff series of Lanzhou Station from 1921 to 2020 show a non-significant upward trend at a rate of 0.26 mm/a and 0.42 × 10⁸ m³/a, respectively. There is no significant mutation point in precipitation, while the mutation point of return runoff occurred in 1991. The 100-year precipitation series of Lanzhou Station has four time-scale alternations of dry and wet periods, with main periods of 60 years, 20 years, 12 years, and 6 years, respectively. The 100-year return runoff series has three time-scale alternations of dry and wet periods, with main periods of 60 years, 34 years, and 26 years, respectively. During the period from 1940 to 2000, an approximately 50-year cycle, precipitation and runoff not only have strong common-change energy and significant interaction, but also have a fixed phase difference. Precipitation changes precede runoff, and runoff responds after a fixed time interval.

1. Introduction

As the key entry point for analyzing the evolution of the law of hydrometeorological situations, precipitation and runoff accurately record the dynamic change process of hydrometeorological elements in the basin. In-depth exploration of the response relationship between precipitation and runoff is helpful to accurately grasp the dynamic change of water resources and provide the core basis for the rational planning and scheduling of water resources. The Yellow River, the second-longest river in China and one of the world’s major rivers, has a basin located in northern China—roughly between 32° N–42° N latitude and 96° E–119° E longitude—with a total drainage area of approximately 752,400 square kilometers. As an important ecological barrier and economic zone, the hydrometeorological situation of the Yellow River Basin plays a decisive role in the regulation and allocation of regional water resources. An in-depth exploration of its historical change law is key to understanding the evolution of the hydrometeorological situation in the basin [1,2,3]. However, there are varying degrees of data missing in many hydrometeorological stations within the Yellow River Basin, which seriously restricts the in-depth understanding of hydrometeorological processes and the accurate management and control of water resources, affects the accurate analysis of historical hydrometeorological change trends, and increases the uncertainty of predicting future changes in water resources, making the rational allocation and scientific scheduling of water resources challenging.

Many scholars have carried out in-depth research on solving the problem of missing historical data of hydrological and meteorological stations. In the early stage, most studies used traditional statistical methods [4,5,6], which established linear regression models based on existing observation data to infer the missing data. However, when the data had complex nonlinear characteristics, the accuracy of the extension was often not high. With the rapid development of computer technology and data science, new theoretical methods, such as fractal geometry, machine learning, and deep learning, have been gradually applied to the field of hydrological and meteorological series extension [7,8,9,10]. Zhang et al. proposed a new data assimilation (DA) method named DA_(DL), which uses the ability of deep learning (DL) to model nonlinear relationships and recognize complex patterns to generate training data through a prior set and train the model to update the system knowledge [11]. In hydrological data assimilation with Gaussian and non-Gaussian distributions, DA_(DL) performs better than traditional ensemble smoothing methods and provides a new path for data extension under complex hydrological systems. Youssef Saliba et al. proposed an analysis method based on the minimum description length (MDL) framework to deeply analyze the monthly precipitation series of 46 weather stations in the Dobrogea region (a geographical region in southeastern Europe) from 1965 to 2005, and successfully identified significant changes in precipitation patterns [12]. At least two change points were detected in the monthly precipitation series of 10 main hydrometeorological stations, which provided a new perspective and effective way to study precipitation rules in this region, providing strong support for understanding precipitation changes under complex climate conditions. Zhang Liang proposed a physics-based Long Short-Term Memory (PiLSTM) model for runoff prediction, which combined the physical precipitation and runoff model with the LSTM model, and applied it to eight intensively monitored water basins in the United States [13]. In non-stationary and data-scarce scenarios, PiLSTM performs equivalent or better than LSTM, and physical constraints make the prediction more in line with the physical process, which provides a reference for balancing data-driven and physical mechanisms and improving the accuracy of hydrological data extension. Compared with traditional statistical methods, these new methods show unique advantages in dealing with complex data and identifying potential rules of data, providing a more accurate and efficient solution for hydrological and meteorological data extension.

Affected by the complex and diverse topography in the upper Yellow River—including high-altitude plateaus (e.g., the Qinghai–Tibet Plateau margin), deep valleys (such as the Liujia Gorge), and undulating mountainous areas—and significant differences in climatic conditions, the hydrometeorological process in this region is extremely complex [14,15]. These topographic variations directly influence precipitation distribution (e.g., orographic rainfall in mountainous areas) and runoff generation pathways (e.g., rapid surface runoff in valleys vs. slow infiltration in plateau areas), contributing to the spatial and temporal heterogeneity of hydrological elements. Lanzhou Station is located in Lanzhou City, Gansu Province, China, with a geographical coordinate of approximately 103°49′ E and 36°03′ N. Lanzhou Station, a key control station of the upper Yellow River, was established on 18 July 1934. It is the national basic hydrological station, the national key flood report station, and the main control station of the upper Yellow River. The accumulated long series of hydrometeorological data is of great significance for the study of water resources change law, flood control and drought relief, and ecological protection of the basin in the upper Yellow River. The catchment area of Lanzhou Station is 222,500 km², accounting for only 28.0% of the basin area, but the annual natural river runoff of Lanzhou Station accounts for 66.1% of the natural river runoff of Lijin Station (a key hydrological control station near the Yellow River estuary, located in Dongying City, Shandong Province, China, and responsible for monitoring the river’s runoff into the sea), which plays an important role in the water resource monitoring and management of the Yellow River basin. However, due to the time and history of Lanzhou Station, some historical data of Lanzhou Station are missing, which creates difficulties in conducting an in-depth analysis of the hydrometeorological situation in the upper Yellow River. In view of this, it is urgent to conduct an extended analysis of hydrometeorological elements, such as precipitation and runoff, at Lanzhou Station, which will help to understand the hydrometeorological characteristics of the region more comprehensively and accurately and provide solid data support and a scientific basis for the sustainable development of the upper Yellow River.

Taking Lanzhou Station in the upper Yellow River as a typical case, this study proposes two extension methods for precipitation and runoff element series, respectively: the VSSL method for the precipitation element series and the SSVR method for the runoff element series. The complete data series of Lanzhou Station in the existing years was used to infer the missing part of the historical time series, and the 100-year precipitation and runoff series from 1921 to 2020 were constructed. Compared with previous studies, this study has a longer time span and can analyze the long-term evolution trend and change characteristics of hydrological and meteorological elements more comprehensively and deeply. It analyzes the trend, variability, periodicity, and correlation of the 100-year series, thereby providing important technical support for understanding the evolution of hydrometeorological conditions in the upper Yellow River and offering a more targeted, practical scientific basis for water resource regulation and allocation in the region.

2. Materials and Methods

2.1. Research Data

As shown in

Table 1. Research data.

Data Time	Data Type	Source of Data
1956–2020	Annual precipitation, return runoff and restored runoff	Hydrological Bureau of the Yellow River Water Resources Commission
1921–1955	Restored runoff	Yellow River Water Conservancy Commission

, the annual precipitation, return runoff and restored runoff data of Lanzhou Station in the upper Yellow River from 1956 to 2020 were obtained from the results of the third water resources survey and evaluation by the Hydrological Bureau of the Yellow River Water Resources Commission and the results of the Yellow River Water Resources Bulletin. The data on restored runoff from 1921 to 1955 were obtained from the results of the annual survey of the Yellow River Water Resources Commission.

Restored runoff refers to the measured runoff, surface water loss (including agricultural irrigation water consumption, industrial water consumption, domestic water consumption, ecological water consumption and inter-basin diversion) in the Lanzhou Station control section, plus the reduced series of river runoff calculated by flood diversion and storage. Return runoff refers to the runoff series under the current underlying surface in the historical period. These data cover different source channels, which provide a rich information basis for constructing the complete hydrometeorological element series of Lanzhou Station, and ensure that the study can comprehensively and accurately reflect the historical changes of hydrometeorology in the upper Yellow River.

2.2. Research Methods

2.2.1. Precipitation Element Series Extension Method

VSSL Method Based on Deep Learning Framework

In this study, the VSSL method is proposed for the extension of precipitation element series. That is, a long short-term memory (LSTM) fusion method based on variational mode decomposition (VMD) preprocessing and Sparrow Search algorithm (SSA) optimization. The VSSL method integrates the unique advantages of multiple algorithms, which are used to solve the problem of poor extension accuracy of traditional statistical methods when dealing with complex nonlinear data. For precipitation series, the VSSL method excels by decomposing multi-scale periodic signals via VMD and capturing long-term nonlinear dependencies through LSTM, adapting to the data’s non-stationarity and sparse extreme events.

(1)

Variational mode decomposition

VMD has the ability to make automatic adjustments. It is an adaptive and completely non-recursive method for signal processing and mode decomposition [16]. By using the non-recursive method, the complexity of the non-stationary and nonlinear time series can be reduced, and the number of decompositions can be determined according to the actual situation. While overcoming the end effects and mode mixing problems in the traditional empirical mode decomposition, the intrinsic mode components can be effectively separated, and the relatively stable subsequence containing multiple frequency scales can be obtained by decomposition [17].

The core of VMD is to construct and solve a variational problem. Suppose that the original signal f is decomposed into K modal components of finite width with central frequencies, and the sum of the estimated broadband of each mode is minimized, and the constraint condition is that the sum of all modes is equal to the original signal, then the corresponding constraint variational expression is as follows [18]:

$$\underset{\left\{{\mathrm{u}}_{\mathrm{k}}\right\},\left\{{\mathsf{\omega }}_{\mathrm{k}}\right\}}{\min }\left\{\sum _{\mathrm{k}=1}^{\mathrm{K}}\Vert {\partial }_{\mathrm{t}}\left[\left(\mathsf{\delta }\left(\mathrm{t}\right)+\mathrm{j}/\mathsf{\pi }\mathrm{t}\right)\ast {\mathrm{u}}_{\mathrm{k}}\left(\mathrm{t}\right)\right]{\mathrm{e}}^{-\mathrm{j}{\omega }_{\mathrm{k}}\mathrm{t}}{\Vert }_2^2\right\}$$

(1)

$$\mathrm{s}.\mathrm{t}\sum _{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{u}}_{\mathrm{k}}=\mathrm{f}$$

(2)

where K is the number of decomposed modes, {ωk} corresponds to the k-th mode component and the center frequency after decomposition, δ(t) is the Dirac delta function, * is the convolution operator, and f is the original time series.

(2)

Sparrow search algorithm

SSA is a new swarm intelligence optimization algorithm, which skillfully simulates the behavior pattern of a sparrow foraging and avoiding predators in the natural environment. It continuously explores the huge parameter space to find the optimal parameter combination. It has the remarkable characteristics of strong optimization ability and fast convergence speed [19,20,21].

In the algorithm model, each sparrow represents a location attribute, that is, the location of the found food. In the d-dimensional solution space, the location of each sparrow is represented by X = (x1, x2, …, xd), whose fitness value is fi = (x1, x2, …, xd), the mean square error (MSE) index is selected as the fitness evaluation function, and its calculation formula is as follows:

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{ı}}}\right)}^2$$

(3)

where ${\mathrm{y}}_{\mathrm{i}}$ represents the true value, $\widehat{{\mathrm{y}}_{\mathrm{ı}}}$ represents the predicted value, and n represents the number of samples.

(3)

Long Short-Term Memory

As a special recurrent neural network (RNN), LSTM can transfer the current time information to the next time. As an improved version of RNN, LSTM mainly solves the problem of gradient disappearance or gradient explosion in RNN network, so as to have a good effect on the modeling of long time series data [22,23,24].

Traditional Linear Fitting Method

For comparative analysis, this study also used the traditional statistical method to extend the precipitation series, which was compared with the VSSL method. Linear fitting is a classic and commonly used method in precipitation series extension. By establishing a statistical relationship between precipitation and runoff, it can effectively use relatively complete runoff records to infer historical precipitation information.

Based on the annual data of precipitation and restored runoff from 1956 to 2020, a linear fitting model between them was constructed and the linear fitting equation was determined. Then, the annual values of restored runoff from 1921 to 1955 were substituted into the equation to obtain the extended annual values of precipitation from 1921 to 1955. Furthermore, according to the proportion of the monthly precipitation values in the annual average of 1956–2020, the annual precipitation extended values were allocated, and finally, the monthly precipitation extended values were obtained.

2.2.2. Runoff Element Series Extension Method

SSVR Method Based on Machine Learning Framework

In the process of runoff element series extension, this study proposes SSVR method, which is a support vector regression (SVR) fusion method based on SSA optimization. The SSVR method fully integrates the optimization ability of SSA and the advantages of SVR in small sample prediction, aiming to solve the limitations of traditional methods in dealing with runoff data extension. For the runoff series, the SSAR method outperforms by optimizing SVR with SSA to model complex human-influenced dynamics, better handling abrupt changes and multi-factor nonlinear relationships compared to rigid traditional methods.

SVR has the characteristics of fewer model parameters and high training efficiency. Its basic idea is to map nonlinear data to a high-dimensional space by a kernel function to make the data linearly separable, and then use the principle of structural risk minimization to process the data, which has unique advantages in small sample prediction [25]. The SVR method uses a support vector on behalf of the entire sample space, which makes the final decision function calculation easier. For the purposes of this study, runoff elements of small sample series extension problems, SVR can give full play to its unique advantages, in the effective analysis and forecast of runoff data.

Traditional Fixed Ratio Method

For the runoff element series extension, the traditional statistical method is also used for comparison. The fixed ratio method is a common traditional method in runoff series extension. It realizes series extension by maintaining the proportional relationship between runoff components, which is more in line with the correlation characteristics of various components in the runoff formation process and has been maturely applied in basin water resources assessment practices.

Based on the results of the third Water Resources Assessment of the Hydrological Bureau of the Yellow River Water Resources Commission, assuming that the proportion of the return runoff series and the restored runoff series remain unchanged, the proportion of the return runoff series and the restored runoff series from 1956 to 2020 was calculated. The annual value of the restored runoff from 1921 to 1955 and the ratio value were used to calculate the current value of the runoff from 1921 to 1955. Then, based on the annual average proportional distribution of each month from 1956 to 2020, the return runoff value of each month in each year was calculated.

2.2.3. Precipitation and Runoff Element Characteristics Analysis Method

In this study, trend analysis, variability analysis and periodicity analysis were used to analyze the characteristics of precipitation and runoff elements. In trend analysis, the Mann–Kendall (M-K) test and Theil–Sen median trend analysis were used to determine the trend changes of hydrological and meteorological elements over a 100-year scale. Variability analysis with the aid of the M-K mutation testing method, to explore the variation of hydrological–meteorological elements. In the periodic analysis, Morlet wavelet analysis was used to reveal the periodic variation law of precipitation and runoff series under different time scales. Based on the results obtained from the above characteristic analysis, the response relationship between precipitation and runoff is further discussed. By comparing and analyzing the consistency or difference between precipitation and runoff in terms of trend, variability and periodicity, the response relationship between them was explored.

Trend Analysis Method

To explore the changing trend of hydrometeorological elements, this study employs the M-K test and Theil–Sen trend analysis—two nonparametric statistical methods widely used in hydrology and meteorology. The M-K test, with the advantages of not needing to meet a specific type of data distribution and using meteorological and hydrological data in dealing with all kinds, shows good adaptability and has become a trend analysis method commonly used in this field [26,27]. Theil–Sen median trend analysis is known for its robustness, which can effectively reduce the interference of outliers on trend calculation and ensure the reliability of analysis results. The time series in this study spans 100 years, from 1921 to 2020, using test statistics Un trend inspection and test of significance showed a level of alpha = 0.05, Un = 1-a/2, and Un = 0.975 1.96. When β > 0 and |Un| > 1.96, the series showed a significant upward trend, and when β > 0 and |Un| ≤ 1.96, the series showed no significant upward trend. When the beta < 0 and | Un | > 1.96, the series shows a significant decline; when the beta < 0 and |Un| is 1.96 or less, the series does not show a significant decline. Through this test system, the trend changes of hydrological and meteorological elements on a 100-year scale can be accurately determined.

Variability Analysis Method

The analysis of the variability of hydrometeorological elements is very important for an in-depth understanding of their change characteristics. In this study, the M-K mutation test method was used to analyze the variability of hydrometeorological elements. The M-K mutation testing method, when there is a separation of values in the data, has the advantage that outliers will not interfere with the result of analysis, and as a nonparametric test method, the M-K mutation testing method has a broad scope. UFk and UBk are statistical metrics derived from the Mann–Kendall test, where UFk represents the forward trend statistic and UBk the backward trend statistic. Their intersection points beyond the significance threshold are interpreted as potential mutation points. In the analysis, a significance level is first specified. The UFk and UBk curves are then derived through computational procedures. When these curves lie above the significant horizontal line, it indicates that the time series has a changing trend. This means that at a certain time point, hydrometeorological elements exhibit relatively significant changes, and such mutations may be related to factors such as climate change and human activities.

Periodic Analysis Method

Morlet wavelet analysis is widely used in the study of periodic variation of hydrological and meteorological series [28,29,30]. Hydrometeorological elements, such as precipitation and runoff, often show complex periodic variation characteristics, which are closely related to the natural oscillation of the climate system, the difference in geographical environment, and the impact of human activities. The core principle of Morlet wavelet analysis is to analyze one-dimensional signals in two dimensions of time and frequency. Through wavelet transform, it can be associated with the time and frequency of the wavelet coefficients, which contain a wealth of information. Using these coefficients, not only can the change trend of time series be clearly observed, but they can also accurately determine the time of the change and the variation characteristics under different frequencies. The transformation results are presented in two-dimensional form, such as the time-frequency distribution map of the real part of wavelet coefficients and the wavelet variance map, which can intuitively show the periodic changes under different time scales.

2.2.4. Precipitation and Runoff Element Correlation Analysis Method

This research adopts the cross-wavelet transform elements of precipitation and runoff correlation analysis, and based on the results obtained by the correlation analysis, further explores the response of the relationship between precipitation and runoff [31,32]. Cross-wavelet transform combines wavelet transform and cross-spectrum analysis to signal multi-resolution analysis, fine capture signals under different time scales. Cross-spectral analysis is focused on the frequency of the correlation between two signals. A combination of cross-wavelet transform, applied to precipitation and runoff element analysis, can accurately analyze the precipitation and runoff series in the correlation of different frequencies and time scales, revealing the precipitation and runoff in the long-term trend and short-term fluctuations in the different frequency components, such as correlation.

3. Results

3.1. Extension Results of Precipitation and Runoff Element Series

3.1.1. Extension Results of Machine Learning and Deep Learning Methods

As shown in Figure 1 and Figure 2, the machine learning SSAR method stretches into the 1921–1955 monthly runoff, and the deep learning VSSL method stretches into the monthly precipitation from 1921 to 1955. The change tendency and historical data on the whole are relatively fit. The results show that the machine learning SSAR method and the deep learning VSSL method can better capture the characteristics of the data and extend the missing data reasonably. For the extension of the runoff results, the variation trend of the curve reflects the runoff with the change of time, and the actual hydrological process has a certain logical consistency, such that the SSAR method can effectively deal with the complex relation between runoff data. In the precipitation extension results, the VSSL method shows good ability to capture the long-term and short-term dependence of precipitation time series, so that the predicted precipitation value is more reasonable in terms of trend and fluctuation range. The machine learning SSAR method and deep learning VSSL method have carried out scientific and reasonable historical data extensions. The relationship between precipitation and runoff response work laid a solid foundation for follow-up studies.

3.1.2. Extension Results of Traditional Statistical Method

The linear regression model of precipitation and runoff at Lanzhou Station was constructed based on the annual precipitation, return runoff and restored runoff data of the control section of Lanzhou Station in the upper Yellow River from 1956 to 2020. The precipitation extended series was obtained based on the restored runoff series from 1921 to 1955, and then the annual distribution was carried out according to the average proportion of monthly precipitation in multiple years from 1956 to 2010. Lanzhou Station’s monthly precipitation extension values are shown in Figure 3. It can be seen from Figure 3 that the proposed method can also reflect the general trend of precipitation to a certain extent, but its ability to capture data details is weak compared with machine learning and deep learning methods.

Based on the traditional statistical method, the ratio of restored runoff value and return runoff value was calculated by proportion, and the ratio of the mean value of restored runoff value and return runoff value of Lanzhou Station from 1956 to 2010 was 1.03. Then, the monthly restored runoff value of each year was deduced according to the restored runoff value of each month in 1956–2010. Lanzhou Station monthly runoff extension values are shown in Figure 4. As can be seen from Figure 4, because the traditional statistical method relies extensively on linear relationships and is difficult to adapt to complex hydrological data changes, the runoff extension results obtained are relatively smooth and do not reflect the complex characteristics of runoff changes.

3.1.3. Comparison and Analysis Results of Extension Results of Precipitation and Runoff Series

As shown in

Table 2. Results of monthly and monthly scale test sets for precipitation and runoff elements at Lanzhou Station from 2000 to 2010.

Elements	Methods	RMSE	MAE	R2
Precipitation	Traditional linear fitting method	25.24	19.85	0.59
	VSSL	16.87	12.60	0.82
Runoff	Traditional fixed ratio method	6.18	4.29	0.87
	SSAR	0.60	0.02	0.96

, the monthly precipitation and return runoff data of Lanzhou Station from 2000 to 2010 were used as the test set, and the evaluation indexes, such as root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²), were used to compare and analyze the extended results of precipitation and runoff element series obtained by the machine learning method SSAR, the deep learning method VSSL, and the traditional statistical method.

RMSE and MAE quantify the deviation between the extended results and the actual test data. Smaller values indicate closer alignment with real-world observations. R² reflects the degree of fit between the extended results and the test data, with values closer to 1 indicating a better fit.

Results show that the precipitation and runoff test set, machine learning and deep learning methods were better than traditional methods. In terms of hydrological elements of runoff, the traditional statistical method and machine learning method SSAR, from 1921 to 1955, can achieve a good extension of the hydrological series. For precipitation, compared with the traditional statistical method, the deep learning method VSSL can better use the changes of meteorological elements in each month of the year to clearly show the changes of the historical meteorological series from 1921 to 1955, highlighting the characteristics of the annual changes.

3.2. Analysis Results of Characteristics and Response Relationship of Precipitation and Runoff Elements

3.2.1. Trend Analysis Results and Response Relationship Study

As shown in Figure 5 and Figure 6 and

Table 3. Significance test results of MK Sen for precipitation and return runoff at Lanzhou Station.

Elements	Un	β	Significance	Trend
Precipitation	1.31	0.26	Insignificant	Rising
Runoff	1.11	0.42	Insignificant	Rising

, the return runoff series and precipitation series of Lanzhou Station showed a non-significant increasing trend from 1921 to 2020. The growth rate of return runoff was 0.42 × 10⁸ m³/year, and the growth rate of precipitation was 0.26 mm/year. This trend indicates that the precipitation and the return runoff of Lanzhou Station in the upper Yellow River have increased as a whole in the past 100 years, but the growth trend is not significant. This insignificant upward trend may be affected by a variety of elements, such as the changes in atmospheric circulation caused by global climate change, the influence of regional topography on water vapor transport, and the changes in the underlying surface conditions caused to some extent by human activities. Although the rising trend of precipitation and return runoff is not significant, it can still provide a certain reference for long-term planning of water resources, suggesting that relevant departments should take this slow trend into account in water resource management.

Regarding the response relationship between precipitation and runoff, during the period from 1921 to 2020, Lanzhou Station’s precipitation and runoff have a close connection. In general, precipitation is the main source of runoff, and the increase in precipitation often leads to an increase in runoff. Through in-depth analysis of the series data, we found that when precipitation shows periodic growth, runoff witnesses a corresponding increase, and this trend is to a certain extent synchronous.

3.2.2. Variability Analysis Results and Response Relationship Study

According to Figure 7 and Figure 8, the precipitation series and the return runoff series of Lanzhou Station show different variation characteristics on the 100-year scale. On the whole, there was no significant mutation point in the precipitation series, which clearly indicated that the precipitation change was relatively stable, and there was no sudden and large fluctuation in the time span of 100 years. This stability ensures the relative balance of regional water resources replenishment to a certain extent. In addition, the abrupt change of the runoff series took place in 1991, and the abrupt change point was extremely significant. The annual runoff before and after the abrupt change point was 489.10 × 10⁸ m³ and 319.10 × 10⁸ m³, respectively.

The mutation of the runoff series may be caused by many complex elements. From the perspective of climate elements, it is highly likely that there were major climate anomalies around 1991, such as large-scale El Nino or La Nina phenomena. These global climate anomalies can significantly affect the regional atmospheric circulation model, and then profoundly change the precipitation and evaporation process, which will lead to the abrupt change of runoff. From the perspective of human activities, human exploitation and utilization of water resources may have changed greatly during this period. The construction of large water conservancy projects, such as reservoirs and DAMS, has changed the hydrodynamic conditions of rivers, and a large amount of water resources have been intercepted and stored, resulting in a significant reduction in runoff.

In summary, the precipitation and return runoff at Lanzhou Station show different trends in the 100-year scale, and the abrupt change of return runoff is affected by various elements such as climate anomalies and human activities, which is of great significance for an in-depth understanding of the law of evolution of regional water resources and scientific development of water resources management strategies.

3.2.3. Periodic Analysis Results and Response Relationship Study

Through the in-depth analysis of the 100-year precipitation series of Lanzhou Station, the time-frequency distribution diagram of the real part of wavelet coefficients and the wavelet variance results are obtained, as shown in Figure 9. The results show that the 100-year precipitation series of Lanzhou Station exhibits periodic variation characteristics at four time scales. On the longer time scale of 34–65 years, there were significant dry and abundant alternating oscillations of precipitation. In the 17–32, 10–16 and 2–9 time scales, the precipitation oscillation was also orderly. The oscillations at different time scales are intertwined to form a complex and orderly precipitation pattern. The first cycle is 60 years, and there are also periodic changes on 20-year, 12-year, and 6-year time scales. Such complex cyclical changes reflect that precipitation is affected by a variety of elements at different time scales. The long period of 60 years may be related to the large-scale oscillations of the global climate system, such as the Pacific Decadal Oscillation (PDO). The 20-year, 12-year, and 6-year cycles may be related to changes in the regional climate system, solar activity cycle, and monsoon activity.

As shown in Figure 10, the time-frequency distribution of the real part of the wavelet coefficient and the wavelet variance results of the 100-year runoff series at Lanzhou Station show that the 100-year runoff series at Lanzhou Station exhibits the periodic variation law of three time scales. In the 48–65 year scale, the runoff showed significant dry and abundant alternating oscillations. At the 18–26 and 8–16 year scales, there was also an alternative phenomenon of runoff dryness and abundance. The first, second and third main cycles were 60 years, 22 years and 12 years, respectively. The periodic change of runoff is the result of multiple elements such as climate, topography and human activities. Different cycles reflect the dominant effects of different elements on runoff at different time scales. The long cycle may be more controlled by the macro regulation of the climate system, and the short cycle may be more affected by regional human activities and local climate fluctuations. The discovery of these periodic laws can help to predict the future change trend of precipitation and runoff, and provide a more scientific basis for the rational allocation of water resources.

There is a certain response relationship between the periodic changes of precipitation and runoff at Lanzhou Station. From the perspective of time scale, the 60-year main cycle is reflected in the precipitation and runoff series, indicating that on this long time scale, the common elements, such as large-scale oscillations of the global climate system, have a synergistic effect on precipitation and runoff, making their variation trends have a certain degree of synchronization. On the shorter time scale, such as 20 years and 6 years, although the cycle length of precipitation and runoff is not completely consistent, there is still a certain correlation between the change trends. The accurate revelation of these periodic laws provides an important basis for predicting the future variation trend of precipitation and runoff. Through the in-depth mining and analysis of the periodic change rules in the historical data, combined with the future development trend prediction of the global climate system, regional climate system and human activities, the change trend of precipitation and runoff on different time scales in the future can be more scientifically predicted, so as to provide a solid scientific support for the rational allocation of water resources. It can help the sustainable utilization and scientific management of regional water resources.

3.3. Correlation Analysis Results of Precipitation and Runoff Elements and Response Relationship Research

The cross-wavelet power diagram and phase diagram of the cross-wavelet are obtained through the cross-wavelet transform of the 100-year precipitation and runoff series of Lanzhou Station, as shown in Figure 11 and Figure 12. The results of the cross-wavelet power diagram show that the cross-wavelet power is high during the period from 1940 to 2000. and the period is about 50 years, which means that the energy of the co-variation of precipitation and runoff series is significantly enhanced in this time period, and the cycle scale of about 50 years and the interaction between them are extremely significant. Specifically, this high power value reflects that there is a close dynamic correlation between precipitation and runoff. As the main supply source of runoff, the fluctuations of precipitation in this period will be transmitted to the runoff system through complex hydrological processes, which will lead to a similar variation trend in runoff.

The phase relation plot further corroborates the conclusion of the cross-wavelet power plot. In the time axis near 1940 and 2000, and in the period axis near 50 years, there are areas of concentrated red. This indicates that there is a relatively fixed phase difference between the precipitation and runoff series at these time points and around the 50-year cycle, and there is a specific lead or lag relationship between the signals. Specifically, the study showed that precipitation changes first, and runoff responds after a fixed time interval.

4. Discussion

Focusing on Lanzhou Station in the upper Yellow River, this study reconstructed the 100-year series of precipitation and return runoff at Lanzhou Station from 1921 to 2020 by using the VSSL deep learning method and SSVR machine learning method, and analyzed the trend, variability, periodicity and correlation of precipitation and runoff elements based on the reconstructed series. Based on the reconstructed series, the trend, variability, periodicity and correlation of precipitation and runoff elements were analyzed, which revealed the variation law and response relationship of hydrological and meteorological elements in the upper Yellow River. The results have important scientific value and application significance, and also provide a direction for subsequent research.

Compared with previous similar studies, in data processing, the VSSL and SSVR methods adopted in this study effectively solved the problem of missing hydrological and meteorological data, broke through the limitations of traditional statistical methods, and improved the extension accuracy of precipitation and runoff elements from 0.59 and 0.87 to 0.82 and 0.96, respectively. This demonstrates the great advantage of this research method in solving the problem of missing hydrological and meteorological data and opens up a more accurate and efficient path for subsequent research. In terms of research scale, most previous studies focused on 5–50 years. By reconstructing the 100-year series of precipitation and return runoff from 1921 to 2020, this study provides a solid data foundation for in-depth exploration of the long-term evolution trend of hydrometeorological elements, which has significant advantages compared with most previous studies.

The variation characteristics and response relationship of precipitation and return runoff at Lanzhou Station are the results of multiple elements. From a trend point of view, the changes in atmospheric circulation caused by global climate change may bring more precipitation in this area, and then increase the return runoff. However, the obstruction or guidance of regional topography on water vapor transport and the change of underlying surface conditions caused by human activities weaken the increasing trend to a certain extent, resulting in the insignificance of both upward trends. Also, in 1991 runoff mutations, abnormal events may include climate change and the precipitation and evaporation model; at the same time, the human large-scale water conservancy project construction changed the development and utilization of water resources, directly affecting the river runoff. In terms of periodicity, the different periodic changes of precipitation and return runoff are closely related to the regulation of water flow by global and regional climate system oscillation, solar activity cycle, monsoon activity and topography. The long cycle may be related to global climate phenomena, such as the Pacific Decadal oscillation, while the short cycle may be more affected by local climate fluctuations and human activities in the region. The strong coupling and fixed phase difference between precipitation and runoff during 1940–2000 may be due to the fact that precipitation was the main supply source of runoff, and precipitation changes were transmitted to the runoff system through complex hydrological processes, such as surface interception, seepage, seepage, and surface runoff confluence, resulting in runoff response after a fixed time interval.

Although certain results have been achieved, this study still has several limitations that require further explanation:

(1)

Impact of historical data quality on reconstruction results

The precipitation and runoff data used in this study are all from the authoritative survey results of the Yellow River Water Resources Commission. Before being stored in the database, the data underwent quality control procedures such as outlier removal and missing value imputation. However, it should be acknowledged that potential instrument errors or differences in observation standards in historical observations may still be transmitted to the reconstruction results through the model.

(2)

Regional generalizability of research results

As a core control station in the upper Yellow River, Lanzhou Station’s hydrological processes are typical of the arid and semi-arid regions in the upper reaches. However, the Yellow River Basin spans a large area, and the middle and lower reaches are more significantly affected by agricultural irrigation and urbanization, with hydrological mechanisms quite different from those in the upper reaches. Therefore, the results of this study should not be directly extrapolated to the entire basin. In the future, it is planned to select typical stations in the middle and lower reaches for comparative studies to explore the applicability of the model under complex underlying surface conditions.

(3)

Impact of non-stationarity on the model

The non-stationarity of hydrological sequences, driven by climate change and human activities (e.g., the 1991 runoff mutation), has been explicitly identified via the M-K test in this study (see Section 3.2.2), indicating that our models partially capture the temporal dynamics of non-stationarity within the historical dataset. However, it is important to acknowledge that long-term climate change (such as intensified greenhouse effects) may further alter statistical relationships beyond the scope of historical variability. To address this, future work will incorporate climate indices as covariates to enhance the models’ capacity to track evolving trends under non-stationary conditions.

(4)

Model’s ability to capture extreme events

Due to the scarcity of extreme precipitation/runoff events in historical data, it is difficult for the model to fully learn their characteristics. In the future, “data augmentation techniques” (such as generating synthetic samples based on the characteristics of historical extreme events) can be used to expand the training set, and combined with hydrological extreme value theory (such as the Gumbel distribution) to calibrate the reconstruction results, so as to improve the reliability of extreme event assessment.

(5)

Omission of physical hydrological processes

The VSSL and SSVR models used in this study are data-driven methods, which do not directly incorporate physical hydrological processes, such as soil moisture dynamics, evapotranspiration, or groundwater interactions. In the future, we will attempt to integrate physical mechanisms, such as using the model output as boundary conditions for distributed hydrological models, or introducing the normalized difference vegetation index (NDVI) to indirectly reflect the impact of the underlying surface, so as to enhance the physical interpretability of the model.

5. Conclusions

In this study, Lanzhou Station in the Yellow River basin was selected as a typical case. On the basis of traditional statistical methods, machine learning and deep learning methods were used to extend the monthly values of precipitation and return runoff from 1921 to 1955, and then the 100-year precipitation and return runoff series in the upper Yellow River were constructed. On this basis, the trend, variability, periodicity and correlation analysis of the 100-year series were carried out, and the response relationship between precipitation and return runoff in the upper Yellow River was deeply explored.

The results show that (1) by comparing the extension results of the machine learning method SSAR and the deep learning method VSSL with traditional statistical methods, machine learning and deep learning methods show significant advantages, their performance is significantly better than that of traditional statistical methods, and the fitting effect of runoff is better than that of precipitation. (2) The 100-year precipitation series and the return runoff series of Lanzhou Station from 1921 to 2020 showed an insignificant increasing trend with the values of 0.26 mm/year and 0.42 × 10⁸ m³/year, respectively. (3) The changes in the precipitation series in the 100-year scale were relatively stable, and there were no significant mutation points. In addition, there was an abrupt change in the runoff series in 1991, and the difference in runoff before and after the abrupt change was significant. (4) The precipitation series of Lanzhou Station showed periodic changes on multiple time scales. The first cycle was 60 years, and the precipitation series also showed significant alternating oscillation phenomena of dryness and abundance on 20-, 12- and 6-year time scales. The runoff series also showed periodic characteristics, with the first, second and third main periods of 60, 22 and 12 years, respectively. (5) In the 50-year cycle from 1940 to 2000, precipitation and runoff not only changed together with strong energy and significant interaction, but also had a fixed phase difference. Precipitation changed before runoff, and runoff responded after a fixed time interval.