Introduction

Water is the essence of life, the cornerstone of production and ecology, and a vital natural resource1. Currently, China’s water resources confront significant problems, including limited total water availability and severe water pollution. As the social economy rapidly develops, the demand for water resources is steadily rising2. Surface water and groundwater are interconnected and vital elements of water supplies. They can closely trade water quality and quantity, which significantly influences the creation and structural attributes of regional water resources. The interplay between surface water and groundwater significantly influences the development, regional distribution, and evolution of water resource quantity and chemical composition3,4. Effective management, planning, and optimal allocation of water resources necessitate a comprehensive understanding of the conversion between surface water and groundwater, a critical aspect of terrestrial hydrological cycle research5. The advancements in agriculture and the grain industry in this region are attributable to the water transport provided by numerous inland rivers, particularly the main channel of the Songhua River. The river starts in the top mountainous region, where numerous tributaries disperse in the middle and lower piedmont plain, and the conversion between surface water and groundwater is common6. Consequently, examining the relationship between surface water and groundwater conversion in the middle and lower portions of the Songhua River basin is crucial for ecological preservation, judicious water resource allocation, and the sustainable development of the basin.

The techniques employed to examine the interplay between surface water and groundwater transformation encompass hydrological data analysis7, isotope tracer methodology8, and hydrological modeling approaches9. The distributed hydrological model technique effectively captures the temporal and spatial heterogeneity of the basin and demonstrates strong performance in simulating the water cycle10,11. Nonetheless, the distributed hydrological model primarily emphasizes the characterization of surface water circulation, while the characterization of groundwater is significantly oversimplified12. Researchers have increasingly acknowledged the significance of modeling surface water and groundwater collectively in regions where the interaction between the two is intricate, leading to the development of the coupled surface water-groundwater model13,14,15.

Currently, pertinent researchers both domestically and internationally have achieved significant advancements in the study of method selection and related issues within the same region.

Recent years have seen a more profound exploration of the coupling model method. In accordance with the many forms of model coupling16. Currently, coupling models are mostly classified into three categories: Loosely connected models, shown by the four-water conversion model17,18, which is predicated on the principles of water circulation and balance within a basin, streamline the interaction and conversion of surface-groundwater models, thereby exhibiting certain limitations. The SWAT model employs a semi-loosely coupled approach, wherein its groundwater calculation module is inadequate for precise simulation of groundwater processes. Consequently, the established MODFLOW model is utilized to supplant the original groundwater calculation module, enhancing the accuracy of groundwater simulation12,19. Tightly coupled models (MIKE-SHE)20, possess comprehensive surface water and groundwater modules with great computational accuracy; nevertheless, the extensive fine data necessary for modeling restricts their practical application. The semi-loosely coupled model is extensively utilized due to its considerable flexibility in modeling and superior simulation accuracy21. Kim22 and Sophodeous23 validated the SWATMOD coupling model in a natural watershed, yielding excellent simulation results. To enhance the spatial scale and resolve the calculation unit discrepancy in the coupling process of SWAT and MODFLOW, Liu Luguang et al.24 modified the SWAT source code and developed the SWATMOD coupling model for irrigation districts to address the issue of calculation unit mismatch in the coupling process. Simultaneously, it advocates for the implementation of the SWATMOD coupling model in regions characterized by frequent human activity, transitioning from natural river basins. Aliyari et al.25 confirmed the feasibility of the SWAT-MODFLOW coupling model in a substantial agricultural and urban mixed watershed. The results indicate that the coupled model enhances the accuracy of the groundwater model in comparison to the conventional groundwater model. Bailey26 developed a simplified package (SWATMOD-PREP) using the Python programming language to simplify the coupling process. Utilizing the QGIS platform, Park27 built the QSWATMOD2 plug-in in Python, enhancing the development of coupling models, operations, result visualization, and other facets.

Scholar Zhou Yubo28 employed numerical simulation techniques to quantify the exchange of river and groundwater in the Yilan to Fujin segment of the Songhua River, assessing the conversion of groundwater and surface water during three representative years characterized by abundance, stability, and aridity. Scholar Tian Haoran29 employed various methodologies, including the surface water balance method, groundwater balance method, and GMS numerical simulation, to thoroughly assess the surface-groundwater exchange quantity of the Songhua River. Scholar Zhang Bing30 employed the isotope tracer method to investigate the regional variation in the connection between surface water and groundwater in the Second Songhua River. Despite the excellent theoretical outcomes achieved by the aforementioned three experts through various methodologies, and their constructive recommendations for the management of Songjiang River water resources, many deficiencies remain: (1) The influence of natural variables, such precipitation and evaporation, on groundwater levels is hardly acknowledged. (2) Historically, the majority of studies focused on the interaction between surface water and groundwater conversion within the mainstream or a tributary of the basin, but research on the entire basin channel network has been comparatively limited.

This work examines the impact of precipitation and evaporation on groundwater levels using wavelet analysis, in light of the aforementioned research context. To investigate the interplay between surface water and groundwater dynamics in the middle and lower reaches of the Songhua River basin, the SWAT model was developed utilizing a database comprising soil, land use, and meteorological data from the study area. Subsequently, parameter sensitivity analysis, calibration, and validation of the model were conducted using the observed runoff data from the Tongjiang hydrology station within the study area. The MODFLOW model was developed using GMS software based on the gathered hydrogeological data, groundwater extraction, and mechanical well information from several irrigation regions within the study area. The SWAT-MODFLOW coupling model is ultimately developed using the QSWATMOD2 plug-in within the QGIS platform. Based on the model’s effectiveness, the regional river network is categorized according to prior research findings and the actual geographical context of the study area, and the relationship between surface water and groundwater conversion is examined.

Study area profile

The middle and lower reaches of the Songhua River basin are located in the eastern part of Heilongjiang Province, China. It is a plain formed by the joint impact of the Jiamusi - Tongjiang section of the Songhua River and its tributaries. It is located between 46°45 ‘5 “N ~ 47°38’ 17” N,130°18 ‘47 “E ~ 132°32’ 07” E, with a total area of about 6,720km231. The terrain in the basin is low and flat, mainly within the range of 50 ~ 80 m. The terrain is high in the northwest and southwest, low in the northeast, and the total land gradient is 0.10‰. The south of the middle and lower reaches of the Songhua River basin is the alluvial plain of the Qixing River and Naoli River, which is raised on both sides, the east is the flat terrain of the Qihulin flood area, the west is the hills and mountains, and the north is the Amur River basin.

The main river in the study area is the Jiamusi-Tongjiang section of the Songhua River main stream. The Songhua River originates from the Tianchi and Greater Khingan Mountains of Changbai Mountains, with a total length of 939 km in the main stream and a total basin area of 565,900 km2. The river length in the study area reaches 209 km32. The main tributaries in the study area are Wutong River, Anbang River, Dulu River, Meandering River, etc., whose tributaries mainly originate from mountainous areas. The tributaries of Songhua River system have the characteristics of steep slope and rapid flow in the upper reaches, large mountain floods, and narrow and narrow river channels in the middle and lower reaches, poor flood discharge and river spreading.

The study area is located in the eastern edge of the middle latitude Asian continent, which belongs to the middle temperate continental monsoon climate area, with a low average annual temperature of 1 ~ 4℃ and four distinct seasons. The spring is short and windy, the summer is wet and rainy, the average temperature in July can reach 25℃, the autumn is short and sharply cooling, the winter is long and cold and dry, the average temperature in the coldest month (January) is lower than − 18℃. The annual sunshine duration is 2400–2500 h, the freezing period is from November to March each year, and the maximum freezing depth is 1.6–2.2 m33. According to the precipitation data collected from Jiamusi meteorological station in the study area, the annual average precipitation was 425.5 mm ~ 688 mm, and the precipitation showed a slow increase trend from 2008 to 2016, and mainly concentrated in July and August, accounting for about 65% of the annual precipitation. Evaporation data in the study area generally ranged from 600 mm to 843 mm, which decreased from 2008 to 2010, and remained relatively stable from October to 201634.

There are many soil types in the middle and lower reaches of Songhua River basin, meadow soil and white pulpy soil are the most widely distributed, and black soil has the highest fertility. Black soil in the basin is mainly distributed in the mountain front area, with a thickness of more than 30 cm and an average organic matter content of 5–6%. Meadow soil is mainly distributed in the flood plain of small and large rivers in the basin35. According to the remote sensing monitoring data of land use in 2022 released by the National Academy of Space and Space Sciences, the watershed mainly includes paddy fields, dry fields, marshlands, woodlands, grasslands, and land for human habitation and construction36. Paddy fields and dry fields occupy the main part, and the land use is mainly agricultural.

The overall stratigraphic structure of the study area is complex. The basin, formed by the neotectonic movement, is a depression zone at the northern end of the second uplift zone of the Neocaysian tectonic system. Tectonically, it belongs to the Tongjiang inland fault depression and is a large subsidence area of the Middle and Cenozoic era. The basin formed by the Tertiary depression (fault depression) has the characteristics of continuous large-scale intermittent subsidence. The formation lithology in the study area is mainly Quaternary strata, mainly composed of sand and gravel, and the thickness of most areas is 100 ~ 200 m. The riverbed and floodplain of the Songhua River main stream and its tributaries in the basin are mainly composed of the Holocene (Q4), that is, thin layer of yellow clay and sub-clay, and the sand, gravel and gravel in the lower part of the basin. The terrace of the interriver zone in the basin is mainly composed of the Upper Pleistocene (Q3), that is, yellow brown sand and gravel, and overlying discontinuous sub-clay. The plain area is in the Middle Pleistocene (Q2), that is, gray-brown and gray-black silty sand, sand and gravel, and the bottom is partially intermingled with sub-clay and silty sub-clay, while the overall bottom of the basin is in the Lower Pleistocene (Q1), that is, yellow-green and gray-green medium sand, fine sand, silty sand and gravel37. According to the hydrogeological data of Sanjiang Plain collected above, the hydrogeological parameters of the study area are processed, and the initial values are determined. In addition, there is a strong hydraulic relationship between the northwestern and southern boundaries of the study area and the basin in the study area, and the northwestern and southern mountains of the study area receive piedmont lateral recharge, so they are all generalized as lateral inflow boundaries. The northern part of the study area is the intersection of Heilongjiang basin and Songhua River basin, which is approximately parallel to the isowater line, so it is generalized as the lateral inflow boundary, and the eastern boundary is generalized as the zero flow boundary because the approximate vertical flow is small. The western boundary of the study area has many tributaries flowing out, such as Wutong River and Anbang River, so it is generalized as the constant head boundary.

A plot of the study area can be seen in Fig. 1 below.

Fig. 1
figure 1

Study area map (Maps are made using Arcgis10.8 (version: 10.8; URL link: https://www.esri.com/en-us/arcgis/about-arcgis/overview) and MODFLOW10.6 (Version: 10.6; URL link: https://www.gms-worldwide.com)).

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Methods

Construction of SWAT model

Introduction to the SWAT model

The ArcSWAT model38 is a long-term distributed hydrological model for river basins, created by the Agricultural Research Institute of the United States Department of Agriculture during the mid to late 1990s. This model has been enhanced at a fundamental level regarding its physical process compared to earlier versions. It can not only characterize hydrological situations by linear regression but also comprehensively account for various processes of surface water bodies in its characterisation. The model may replicate several physical processes, including water migration, sediment transport, and crop growth, by incorporating pertinent data regarding production and surface confluence. Nonetheless, it is important to note that the simulation accuracy of the groundwater process is significantly inadequate; therefore, if this model is to be utilized in groundwater applications, further enhancements and optimizations are necessary.

SWAT model data Preparation and database construction

The fundamental data necessary for SWAT model development can be categorized into two types: geographical data and attribute data. Spatial data primarily encompass digital elevation models, soil distribution maps, and land use distribution maps. Attribute data consist of meteorological and hydrological data.The data formats required for this survey are shown in Table 1.

Table 1 Basic geographic data required for constructing SWAT model in the study area.
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The delineation of watersheds constitutes the preliminary phase in the creation of the SWAT model. This research presents the geographic elevation data of the study area (shown in Fig. 2a), which was incorporated into the model’s initial module to simulate depression filling, resulting in the formation of 32 sub-basins within the study area, as depicted in Fig. 2b. The Soil data used in the construction of the SWAT model soil Database in this paper comes from the Harmonized World Soil Database downloaded by the National Qinghai-Tibet Plateau Scientific Data Center, which is the main input parameters required for the construction of the SWAT model, including: Soil type distribution map, soil index table and soil physical property file39. After projection and clipping, the soil type distribution map was compared with the soil physical property file, and sub-soil types with the same physical properties were reclassified to obtain the soil type distribution map shown in Fig. 2c below. Soil data parameters of SWAT model were calculated by SPAW40(Soil Profile Water Transfer) software, wherein the amount of carbon deposited in soil layer should be converted into organic mass and then input into SPAW software for calculation. In addition, in order to facilitate the calculation of USLE-K parameters in the model, the amount of clay loam and clay contained in the database was calculated using the replacement formula proposed by Williams41. Finally, the calculated values of soil layer 1 and soil layer 2 are imported into the SWAT model to complete the construction of soil database. The land use data comes from the global 30-meter resolution land cover in 2022 released by the Academy of Aerospace Information Innovation of the Chinese Academy of Sciences. The land use types in the study area were reclassified into 6 categories, namely cultivated land, forest land, grassland, water area, urban and rural areas, industrial and mining land, residential land, and unused land (see Fig. 2d below).

The meteorological data used in this paper mainly include precipitation, temperature, relative humidity, solar radiation and wind speed daily data. The meteorological data used were CMADSV1.1 data downloaded from the National Tibetan Plateau Scientific Data Center42. The time length is from 2008 to 2016, which basically meets the requirements of the time scale of the model operation. This database is one of the most widely used meteorological data of the SWAT model. After repeated application by many scholars, this database meets the accuracy requirements of the final output results of the model43. Finally, all the construction operations of the above model were completed and the hydrologic response unit (HRU) was calculated. Hydrological response unit is the core step of SWAT modeling. Each hydrological response unit contains soil type, land use type and slope information, and each sub-basin contains multiple hydrological response units. The calculation method is as follows: firstly, the hydrological process of each HRU is independently calculated, and finally, the runoff production of all HRU is summarized at the outlet of the basin. In addition, due to the subsequent construction of the SWAT-MODFLOW coupling model, in order to ensure the accuracy of the calculation, this paper set the slope, land use and soil reclassification thresholds to 10%, and finally superimposed to generate the corresponding hydrological units. Finally, a total of 112 hydrological response units (HRUs) were divided in the study area. Figure 2e shows the HRU data display diagram constructed.

Fig. 2
figure 2

SWAT model input and output data (Maps are made using Arcgis10.8 (version: 10.8; URL link: https://www.esri.com/en-us/arcgis/about-arcgis/overview)).

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Construction of MODFLOW model

Introduction to MODFLOW model

At present, the main groundwater numerical simulation methods include finite difference method and finite element method, among which the finite difference method is widely used by researchers. Scholars at home and abroad have also used various forms of MODFLOW software44 to conduct a lot of research on groundwater science. In this paper, the MODFLOW module in GMS software with simple interface operation and good 3D visual effect was used to build a groundwater flow model in the middle and lower reaches of Songhua River basin45. The flow model program adopted this time is MODFLOW-2005 version. The program was developed by the U.S. Geological Survey to better address unconfined aquifers. This module is an independent program designed to solve nonlinear non-confined aquifers involving dry and humid aquifers.

Space-time dispersion and initial condition calibration of the model

Grid division: The area extracted by SWAT was taken as the research area of MODFLOW, the effective calculation area was 10788.1km2, and the research area was discrete into 1000 m×1000 m square grids (grid division results were given), which were divided into 168 rows, 198 columns and 3 layers, of which 99,792 effective grids were included. In this simulation, the iso-water level line of the middle and lower reaches of Songhua River basin on January 31, 2008 was taken as the initial water level of the model (see Fig. 3a). The stress period was selected from January 2008 to December 2016 as the simulation period, and the month as the stress period.

Water conduction coefficient and water supply degree are important parameters for the construction of MODFLOW model. The relevant parameters in this paper are selected based on the geological distribution of the study area (the geological situation has been described in detail in the section “Study Area Overview”), and then the groundwater level obtained after the operation of the model is compared with the measured value of the observation well. Then, repeated experiments of manual parameter adjustment were carried out, and the final value was determined based on the standard that the difference between the simulated value and the actual value was less than 0.6 m. The initial value range was shown in Table 2.

Fig. 3
figure 3

Hydrogeological generalization map of the study area (Map using MODFLOW10.6 (version: 10.6; The URL link: https://www.gms-worldwide.com) is drawn).

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Table 2 Initial value range of model geological parameters.
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Introduction to SWAT-MODFLOW coupling model

The SWATMOD coupling model integrates the strengths of the SWAT model for surface water analysis and the MODFLOW model for groundwater analysis. It can analyze the alterations in water resource utilization and agricultural production resulting from irrigation, fertilization, tillage, and other interventions, as well as assess the variations in surface water resources and the comprehensive dynamic changes in groundwater levels across each study area. The precision of assessing the correlation between surface water and groundwater in a region is enhanced.

This study utilizes the mapping relationship between the hydrological response unit of the SWAT basic computing unit and the basic computing unit of MODFLOW, established via the QGIS platform, to transfer the soil seepage flow calculated by SWAT software to the MODFLOW grid, assigning values to each grid as RCH recharge packets. The subsurface water quantity computed by MODFLOW is conveyed to the SWAT sub-watershed via a mapping connection. The specific operation method can be referred to the relevant references46,47.

Specific research ideas can be referred to Fig. 4.

Fig. 4
figure 4

Technology roadmap (Maps are made using Arcgis10.8 (version: 10.8; URL link: https://www.esri.com/en-us/arcgis/about-arcgis/overview) and MODFLOW10.6 (version: 10.6; The URL link: https://www.gms-worldwide.com)).

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Results

The calibration of the model

Calibration and verification of SWAT model

The runoff simulation of the SWAT model involves numerous factors. To diminish the intricacy of parameter calibration, SWAT-CUP software is employed to assess the sensitivity of model parameters and identify those that significantly influence the model’s simulation outcomes. This research employs P-value and t-statistic to assess parameter sensitivity. The t-statistic indicates the sensitivity of the parameter, whereas the p-value denotes the significance degree of that sensitivity. A greater absolute value of the T-value correlates with a p-value approaching 0, signifying an elevated significance level of the parameter’s sensitivity.

This study utilizes the SUFI2 algorithm, characterized by low computational accuracy yet high efficiency, in conjunction with SWAT-CUP software—a calibration uncertainty program appropriate for basins exhibiting relatively uncomplicated runoff variations—based on runoff data from Jiamusi City’s Tong Jiang Hydrological Station collected between 2008 and 201648,49. Twenty-two parameters closely related to runoff were selected for sensitivity analysis. In order to eliminate the error of model operation or the uncertainty of system operation as much as possible, the number of iterations was set to 500 times, and global sensitivity analysis was adopted for sensitivity analysis. The sensitivity analysis results can be referred to Fig. 5, and the optimal parameter values are shown in Table 3.

Table 3 Specifies the final value of SWAT model parameters.
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Fig. 5
figure 5

Results of global sensitivity analysis.

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Reinsert the revised parameters into the model, revise the worksheet, and execute the validation once more. The findings of the runoff rate calibration and verification are presented in Fig. 6. The experimental results indicate that the runoff simulation of the Tongjiang hydrological station is optimal, with a rate period of R2 > 0.87 and NSE > 0.76, and a validation period of R2 > 0.81 and NSE > 0.76.

Fig. 6
figure 6

Calibration and verification of the runoff rate of the model (the longitudinal coordinate indicates the runoff unit: m3/s). In this paper, the warm-up period of SWAT model was selected from 2008 to 2010, and the period from 2010 to 2014 was selected as the rate period. After parameter modification, the model was brought back into the model, and the accuracy of the model was verified again with the validation period from 2014 to 2016.

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Calibration and verification of SWAT-MODFLOW coupling model

The calibration of the SWAT-MODFLOW coupling model comprises two primary components: the calibration of the SWAT model and the calibration of the MODFLOW model. For the calibration of the SWAT model, the five parameters exhibiting high sensitivity, as depicted in Fig. 5, were initially chosen. The calibration utilized the measured runoff data from the Jimusi Hydrological Station spanning 2008 to 2016, The two periods 2010–2014 and 2014–2016 are designated as the rate periodic period and the validation period, respectively.The linear regression coefficient R² and the Nash-Sutcliffe efficiency (NSE) were employed to assess the model’s simulation performance. The calibration and verification outcomes are presented in Fig. 7a, exhibiting a periodic R2 of 0.86 and an NSE of 0.87. The validation period R2 is 0.77 and the NSE is 0.75, indicating a favorable simulation impact.

For the calibration of the MODFLOW model, the hydraulic conductivity (k) and the degree of specific yield (µ) were chosen as parameters for calibration. The groundwater level recorded from January 2008 to December 2012 served as the foundation for parameter calibration, while the water level monitored from January 2012 to December 2016 was utilized for parameter verification. The ideal parameters were ultimately acquired, as illustrated in Table 4. Furthermore, Fig. 7b illustrates that the R² of the periodic rate is 0.98 and the R² of the validation period is 0.97, demonstrating that the simulation outcomes of the groundwater level model align closely with the measured results, thereby indicating that the model satisfactorily fulfills the criteria for scientific research.

Fig. 7
figure 7

SWAT-MODFLOW calibration verification results (Arcgis10.8 (version: 10.8; The URL link: https://www.esri.com/en-us/arcgis/about-arcgis/overview) is used for the map is drawn.)

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Table 4 Final values of geological parameters.
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Analysis of influencing factors of groundwater level

Surface water and groundwater constitute an interconnected hydrologic continuum in nature. The intricate and variable interplay among them influences the hydrologic cycle and water balance assessment in the basin. Precipitation and evaporation are the primary sources of groundwater replenishment. The lag effect of precipitation recharge and the impact of evaporation on groundwater levels govern the fluctuations of the water table. This chapter employs cross wavelet transform50,51,52,53,54,55,56,57,58,59,60,61,62 to elucidate the interrelationship between groundwater levels and precipitation and evaporation.

The cross wavelet transform of groundwater levels (refer to Fig. 8C) and precipitation data (refer to Fig. 8B) for Jimusi, Fujin, and Tongjiang was conducted using MATLAB software. Figure 8 (A) illustrates the results, with red and blue denoting the peak and valley values of energy density, respectively, thereby demonstrating the location and dynamic properties of the time-frequency transition of the predominant wave group. The enclosed region delineated by the thick black solid line is depicted by a red noise test at a 95% confidence level, while the envelope formed by the thin black solid line signifies the cone of wavelet effect (COI). Figure 8A(a) illustrates that the elevated energy regions of groundwater levels and precipitation in Jiamusi City predominantly occur between 10 and 15 months. These findings passed the red noise test at a 95% confidence level from 2008 to 2016, indicating a significant correlation between the two variables, with the primary resonance period approximately 1 year. Figure 8A(b) illustrates that the groundwater level and precipitation in Fujin City successfully passed the red noise test at the 95% confidence level from 2008 to 2016, indicating that the majority of time periods met the significance criterion, with a predominant resonance period of approximately 1 year over this interval. Figure 8A(c) illustrates that the groundwater level and precipitation in Tongjiang City successfully passed the red noise test at a 95% confidence level from 2009 to 2014 and throughout 2016, with significant results for the majority of time periods, indicating a primary resonance period of approximately one month during this interval. Furthermore, the phase relationship is quantified using the mean phase angle of a significance test beyond the coherence of interest, followed by an analysis of the delay characteristics between the two-time series. The cross-phase of time series between precipitation and groundwater levels for considerable periods outside the cone of influence can be derived by integrating Fig. 8A. The lag period of groundwater levels in Jiamusi City, Fujin City, and Tongjiang City in relation to precipitation is approximately 10.56 days, 10.58 days, and 3.15 days, respectively. The wavelet analysis of evaporation (refer to Fig. 8B) and groundwater levels throughout the three regions indicates that evaporation exhibits a coherent period of 10 to 13 months concerning groundwater levels, with analogous results observed at other sites. Evaporation exhibits a robust correlation with groundwater at each station, and this correlation is generally consistent; the impact of evaporation on groundwater levels across the stations is analogous.

The variation in groundwater level across the entire study area is quite consistent. Aside from the weak correlation between groundwater levels in the northwestern region of the study area and other regions, the water level disparity peaks at approximately 30 m. The temporal variation trend of groundwater levels is markedly distinct, while the correlation among the central, northern, eastern, and northeastern plains of the study area is strong, with minimal fluctuations in spatial scale at any given time. The highest variation of the water table is within 15 m. The correlation between rainfall and evaporation concerning the groundwater table of each sub-basin indicates that precipitation exerts a greater influence on the fluctuations of the groundwater table than evaporation. Furthermore, the changes in the groundwater table in sub-basins 1, 2, 3, and 11, as well as sub-basins 16 to 20, are significantly influenced by both precipitation and evaporation, with a P value approaching 0.05. The fluctuation pattern of groundwater levels between 4 and 10 and 22 to 32 in sub-basins is minimally influenced, with a P value approaching 0.3, as illustrated in Fig. 8d for further details.

Fig. 8
figure 8

Cross wavelets transform of precipitation, evaporation and groundwater level and their correlation heat map. The direction of the arrows in the figure reflects the phase relationship between groundwater level and precipitation. The arrows from left to right indicate that the two are in phase, and the arrows from right to left indicate that the two are in reverse phase. The vertical downward means that the wavelet transform of precipitation advances the groundwater level 1/4 cycle, and the vertical upward means that the precipitation advances the groundwater level 3/4 cycle. Other meanings of colors and symbols are described in the text.

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Analysis of the transformation relationship between surface water and groundwater

To enable the analysis of the spatial variation of surface water-groundwater conversion in the main stream of the Songhua River, this study segmented the river, as extracted by the SWAT-MODFLOW model, into 11 sections and illustrated the surface water-groundwater conversion relationships in the study area using distinct colors, as depicted in Fig. 9. The link between surface water and groundwater conversion exhibits significant regional heterogeneity, with the blue part of the river indicating that the prevailing tendency throughout the years in river reaches is surface water recharging groundwater. The yellow part of the river signifies that the interaction between surface water and groundwater has been often altered throughout the years, with a modest trend towards groundwater recharging surface water. The dark blue area signifies that the prevailing tendency of surface water to groundwater conversion in the river segment throughout the years is surface water recharge, and this pattern is markedly evident. In the entire basin, the river channel responsible for surface water recharging groundwater constitutes 41.75% of the total length, predominantly occurring in river segments 1, 5, 6, 8, and 9, with an annual average recharge of 3.60 × 107 m³/d. It constitutes 50.84% of the average yearly total water exchange. Groundwater recharge to surface water occurs mostly in river Sects. 2, 3, 4, 7, 10, and 11, with an average annual groundwater discharge of 5.02 × 107 m³/d, or 58.25% of the average annual total water exchange.

Fig. 9
figure 9

Spatial distribution characteristics of surface water-groundwater conversion relationship in the study area (Maps are made using Arcgis10.8 (version: 10.8; URL link: https://www.esri.com/en-us/arcgis/about-arcgis/overview)).

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To investigate the seasonal fluctuation of the surface water-groundwater conversion relationship in the basin’s rivers and channels, January, March, July, and October are designated to represent winter, spring, summer, and fall, respectively, as illustrated in Fig. 10. Seasonally, the conversion relationship and water volume of each river reach exhibit significant variations due to the presence of numerous river reaches in the studied area. Consequently, three river segments—1, 7, and 5—exhibiting significant alterations, extended lengths, and distinctive geographical positions are chosen for research. The annual average monthly recharge of surface water to groundwater in reach 1 during winter, spring, summer, and autumn is 2.8 × 107 m³/d, 2.6 × 107 m³/d, 7.8 × 107 m³/d, and 3.0 × 107 m³/d, respectively. The annual average monthly discharge of groundwater to surface water in reach 7 for winter, spring, summer, and autumn was 6.5 × 104 m³/d, 6.0 × 104 m³/d, 1.5 × 105 m³/d, and 8.1 × 104 m³/d, respectively. In Sect. 5, where surface water predominantly contributes to groundwater recharge across several seasons, the average monthly recharge rates are as follows: 2.5 × 104 m³ in autumn, 2.7 × 104 m³/d in spring, 2.8 × 104 m³/d in winter, and 6.5 × 104 m³/d in summer. The investigation of the aforementioned 11 river segments reveals characteristics that align with the seasonal fluctuations of precipitation in the Songhua River basin. Furthermore, the monthly average surface-groundwater recharge in the Songhua River Basin from 2008 to 2016 indicates significant seasonal variability, with groundwater recharge to surface water not falling below 4.0 × 104 m³/d, and the average fluctuation range for each river reach is approximately − 52–55%. The recharge of surface water to groundwater exhibits significant seasonal variability, peaking in summer, particularly in July, and reaching its nadir during the winter and spring exchange period, typically between December and April. This mostly pertains to the significant seasonal fluctuations in water quality within the basin and the frigid winter environment in northeastern China. Figure 11 illustrates that the interannual variability of the surface water-groundwater conversion relationship in the research area indicates a significant fluctuation in the recharge volume of surface water to groundwater, with a range of -37–63%. From 2008 to 2009, there was a rising trend; from 2009 to 2014, a general declining trend prevailed; and from 2014 to 2016, there was a modest increase. This pertains to the augmentation of precipitation in the Songhua River basin. The range of fluctuation in groundwater recharge to surface water is between − 35% and 52%, and this variance is directly influenced by precipitation. The pattern mirrors that of river recharge to groundwater, exhibiting frequent variations in each river segment; yet, overall, the entire basin reflects a tendency of surface water transitioning to groundwater.

Fig. 10
figure 10

Average monthly conversion volume of surface water to groundwater from 2008 to 2016 (unit: ×106m3/d).

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Fig. 11
figure 11

Annual seasonal conversion of surface water to groundwater from 2008 to 2016.

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Discussion

Genetic analysis of surface-groundwater conversion relationship in Songhua river basin

The SWAT-MODFLOW coupling model indicates that the relationship between surface water and groundwater conversion occurs frequently throughout the year, with prolonged groundwater recharge predominantly occurring from October to April of the subsequent year. The overall trend of surface water to groundwater conversion in the study area indicates that surface water recharges groundwater. The primary reason is that the Songhua River basin is situated in northeastern China and influenced by the temperate monsoon climate. The temperature variation among the four seasons is significant, and the substantial increase in river runoff during seasonal transitions leads to a considerable fluctuation in groundwater supply from the river. The Songhua River basin exhibits the fourth highest porosity, with sand coverage encompassing 75%, and demonstrates significant water seepage capacity. Consequently, river recharge of groundwater markedly escalates with seasonal variations63. Groundwater recharge to surface water is influenced by seasonal variations; however, the inertia is substantial, resulting in the formation of groundwater recharge rivers in the Songhua River basin during winter and spring, while summer and autumn typically experience flood conditions. Locally, the surface water-groundwater conversion mode of the river (Sects. 10 and 11) in the northwest of the study area is characterized by groundwater recharge from surface water, primarily due to the river’s location in a mountainous region, where the geology influences recharge efficiency. Secondly, the region is situated between Hegang City and Luobei County. The Jiangluo, Fengxiang, Wutonghe, Puyang, and Suibin irrigation areas exhibit significant agricultural water extraction, which indirectly influences the relationship between surface water and groundwater conversion64. Furthermore, Sect. 1 experiences continuous surface water replenishment due to substantial groundwater availability throughout the year. Besides its geographical position at the basin’s ultimate outlet, the upstream region of this section is situated in Fujin City, Jiamusi City, which hosts numerous water storage projects; consequently, the river is influenced by factors such as the operation of reservoir gates and flood discharges throughout the year65. Over the past eight to nine years, the trend has shifted towards the recharge of groundwater by surface water. The primary reason is that the river is a lowland river adjacent to mountainous terrain, and its unique geographical position allows the river segment to remain unaffected by the recharge process impeded by the mountain geology, while also benefiting from lateral recharge from the foothill water. Moreover, Sect. 8 is part of the downstream confluence of mountainous rivers (Sect. 10, Sect. 11), which also exerts an indirect influence on the conversion between surface water and groundwater. In the central region of the basin, the conversion of surface water to groundwater occurs frequently, and the trend remains ambiguous due to geological conditions, water extraction in the irrigation zone, climate change, and minimal topographical variation in the area. In this study, despite the differing conversion trends of river segments 2 to 7, the disparity between recharge and excretion is minimal, with the conversion relationship primarily influenced by seasonal precipitation. By comparing the seasonal precipitation evaporation curve in Fig. 8b with the changes of seasonal recharge excretion in each river section in Fig. 10, it can be seen that recharge is mainly affected by precipitation. The peak recharge area occurs between April and August and is highly consistent with the peak precipitation line, and the peak excretion mainly occurs between October and January in autumn and winter. It is highly consistent with the peak period of the difference between evaporation and precipitation.The influence of other natural factors is comparatively minimal.

Analysis of differences with previous research results

Comparing with the prior research findings presented in the “Introduction” section of this publication reveals discrepancies in the results obtained through various methodologies.

Comparing the conversion of groundwater and surface water across three representative years—abundant, flat, and dry—of the Songhua River, as calculated by scholar Zhou Yubo through numerical simulation in 2011, reveals minimal discrepancies between the results of his study and those presented in this paper; however, his research contains numerous uncertain variables. The scholar’s simulation study utilizing a numerical model is constrained by the technology and data available at that time. The precision of river level data integrated by the model is inadequate. Consequently, our work integrated a more advanced model coupling strategy grounded in prior experience. The SWAT-MODFlow coupling model was employed, incorporating the SWAT module into the original GMS model, which thoroughly accounted for land use, soil type, and climate change in the study area, thereby addressing the issue of low numerical simulation accuracy attributed to the technological limitations of that period. Comparing Tian Haoran’s 2012 research results revealed that the extent of variation in the conversion volume of the upper reaches of the Songhua River was minimal, however a significant disparity was seen in the lower reaches. The primary reason is that since 2013, Fujin City has effectively adjusted the water intake for local agriculture and enhanced the restoration efforts for the water level of the Songhua River. The secondary reason is that, despite the scholar employing various methodologies, including the surface water balance method, groundwater balance method, and GMS numerical simulation, to thoroughly assess the conversion of surface water to groundwater in the Songhua River, the integration of multiple approaches enhanced the precision of the paper’s calculation results. Nevertheless, typical calculation methods exhibit relative flaws in summarizing the intricate surface water infiltration process through correlation coefficients, and the aggregation of these errors results in diminished calculation outcomes in the downstream catchment region. In comparison to the findings of Zhang Bing in 2015, this study reveals a low accuracy in the calculation results about the conversion quantity of an individual river reach. The disparity arises from the application of the isotope tracer method to examine the spatial interaction between surface water and groundwater in the Second Songhua River. In comparison to the model method, this approach provides a more precise depiction of the water flow seepage process. The experimental procedure for this method is complex, necessitating several steps including isotope labeling, sample preparation, and radioactive detection. Each link must be meticulously managed and regulated to guarantee the precision and dependability of trial outcomes. Moreover, the expense associated with this method is comparatively elevated for analyzing the trend of surface water-groundwater conversion in the Songhua River basin. This method examines the conversion relationship between surface water and groundwater in the Songhua River by analyzing a single river section, focusing solely on the primary segment of the river network. This approach fails to provide a comprehensive characterization of trends and neglects surface dynamics in favor of point-specific accuracy. This study, building on prior research, conducted a comprehensive analysis of the transformation dynamics of the Songhua River by segmenting it into 11 distinct sections within the middle and lower reaches of the basin. Each segment was analyzed independently to enhance the overall research outcomes; however, this approach resulted in a diminished accuracy of individual segment conversions.

Research uncertainty analysis

This study remains fraught with uncertainties, necessitating a substantial amount of high-quality data, including terrain, soil, meteorological, and hydrological information, to construct and operate the coupling model. The acquisition and processing of data can be challenging, particularly in regions with insufficient monitoring data. The groundwater level monitoring data in the study area is limited for various reasons, and this paper utilizes 11 groundwater level observation wells for calibration, resulting in unavoidable discrepancies between the model simulation outcomes and the actual conditions. Furthermore, the establishment of the MODFLOW model encountered inaccuracies in the simulation results due to the inability to acquire real-time water withdrawal data for each irrigation district in the study area, leading to the use of annual average water withdrawal figures for surface mining instead of real-time data. Furthermore, when configuring the SWAT module of the coupled model, it is permissible to input land use data from only one year, which is relatively straightforward. However, changes in land use significantly influence hydrology and non-point source pollution simulations. Particularly during the processes of flow, sediment, and non-point source pollution simulation, it is essential to dynamically update land use data to recalibrate the threshold value. To enhance the simulation accuracy of the model regarding land use change. Consequently, dynamic land use data must be incorporated into the model66. The Songnen Plain and Sanjiang Plain in northeastern China are the areas with the highest agricultural grain production in the country67. The topography in this area is intricate, featuring diverse land use and soil classifications. Nonetheless, the existing SWAT model is inadequate in handling high-precision and multi-transform terrain data, leading to inaccurate simulations of groundwater supply, waste, and pollution. A significant error exists in the shallow groundwater storage results68. It should be enhanced according to the planting configuration. The accurate planting structure data, derived from the integration of high-resolution drone imagery, remote sensing images, and ground-measured data, serves as the input land use data for the SWAT model. This approach aims to enhance the simulation of the migration and transformation processes of agricultural non-point source pollution, thereby improving the accuracy of watershed runoff simulations.

Conclusions

  1. 1.

    The SWAT-MODFLOW coupling model has good applicability in Songhua River Basin, and the simulated monthly runoff and groundwater level are in good agreement with the actual observed data.

  2. 2.

    For the whole study area, the correlation between the groundwater level in the northwest of the study area and other areas is weak, and the difference of the water level is about 30 m at the highest, and the variation trend of the groundwater level over time is quite different. The correlation between the central, northern, eastern and northeastern plains of the study area is high, and the difference of spatial-temporal scale is not significant, and the maximum difference of groundwater level is less than 15 m. Jiamusi City, Fujin City and Tongjiang City, which are geographically distributed in the study area, were selected to study the degree of influence of precipitation on the groundwater table. The lag time of precipitation on the groundwater table was about 10.56d, 10.58d and 3.15d.

  3. 3.

    Spatially, the recharge of surface water to groundwater in the Songhua River Basin from 2008 to 2016 mainly occurred in river segments 1, 5, 6, 8 and 9, while the recharge of groundwater to surface water was concentrated in river segments 2, 3, 4, 7, 10 and 11.

  4. 4.

    At the inter-annual scale, the recharge from surface water to groundwater varies significantly under the influence of precipitation, with a range of -37%~63%, while the recharge from groundwater to surface water is relatively stable, with a range of -35%~52%.

  5. 5.

    On the seasonal scale, combined with the analysis of 11 river segments, this feature is consistent with the seasonal variation of precipitation in the Songhua River Basin. The amount of groundwater recharge to surface water varies greatly with the seasons, not less than 4.0 × 104m3/d, and the average variation range of each river reach is about − 52% ~ 55%. The recharge of surface water to groundwater shows obvious seasonal variability, with the highest value in summer and the peak value in July, and the lowest value in winter and spring exchange season, and the lowest value usually appears between December and March to April.

  6. 6.

    In the Songnen Plain and Sanjiang Plain of northeast China, as well as other regions with significant agricultural and grain output, investments in UAV and remote sensing technology are being augmented to mitigate simulation errors arising from intricate geographical factors, including varied terrain, land use, and soil types. To enhance the model in the future, it should be refined according to the local planting structure. The accurate planting structure data, derived from the integration of high-resolution drone imagery, remote sensing images, and ground-measured data, serves as model-driven data to enhance the simulation of the migration and transformation processes of agricultural non-point source pollution, thereby improving the accuracy of watershed runoff simulations.