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Article

Patterns of Groundwater Flow Systems and Travel Times Controlled by Leaking Streams, Evapotranspiration, and Pumping Wells in the Kongqi River Basin, China

by
Qian Xu
1 and
Xu-Sheng Wang
2,*
1
Key Laboratory of Groundwater Conservation of Ministry of Water Resources, China University of Geosciences (Beijing), Beijing 100083, China
2
Frontiers Science Center for Deep-Time Digital Earth, China University of Geosciences (Beijing), Beijing 100083, China
*
Author to whom correspondence should be addressed.
Water 2025, 17(17), 2542; https://doi.org/10.3390/w17172542
Submission received: 29 June 2025 / Revised: 7 August 2025 / Accepted: 25 August 2025 / Published: 27 August 2025
(This article belongs to the Special Issue Research on Hydrogeology and Hydrochemistry: Challenges and Prospects)
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Abstract

Groundwater flow systems (GFSs) and associated distribution of travel times provide critical insight into the regional subsurface hydrology, especially in arid regions experiencing intensive groundwater use. This study examines the impact of large-scale irrigation pumping on GFS patterns in the arid Kongqi River Basin, China. A three-dimensional (3D) steady-state groundwater flow model was constructed using MODFLOW, and flow paths were delineated through particle tracking to quantify travel time and residence time distributions. Two scenarios with and without pumping were compared. Results show that groundwater abstraction significantly alters GFS patterns, lowering water tables in pumping zones while raising them in irrigation areas fed by surface water. This hydrologic redistribution fragments recharge and discharge zones, particularly under the influence of evapotranspiration (ET) from shallow groundwater. Simulated travel times range up to ~506 ka, with median values decreasing from 9.7 ka (no-pumping) to 8.3 ka (pumping). Both travel time distribution (TTD) and residence time distribution (RTD) exhibit power-law characteristics, reflecting the dominance of slow flow paths in deep GFSs. While the modeling results provide valuable insight into current regional groundwater flow, it does not account for transient flow effects and hydrodynamic dispersion of solutions. Future research should incorporate groundwater isotope data to validate the model and assess time-dependent changes in GFSs.

Key Points

1.
Heavy groundwater abstraction significantly changes the GFS patterns.
2.
Pumping wells accelerate the groundwater flow and reduce the travel time.
3.
The power-law distribution fits the TTD and RTD better than the exponential distribution.

1. Introduction

Groundwater is a critical source of drinking and irrigation water in semi-arid to arid regions. The sustainable utilization of groundwater in a region is highly dependent upon the subsurface processes of the water cycle at the regional scale, involving groundwater recharge, flow, and discharge. In an arid region undergoing scarce precipitation, leaking streams may be a major or sole source of groundwater recharge, while ET may be a major natural way of groundwater discharge. The groundwater flow in aquifers driven by such recharge and discharge forces creates a redistribution of water resources over the region. The spatial patterns of this groundwater flow process have been well known as GFSs [1,2,3]. A major challenge in semi-arid to arid regions is to understand the changes in GFSs under the influence of various human activities, especially when large volumes of groundwater are extracted for cropland irrigation.
Patterns of GFSs have been primarily investigated using the two-dimensional (2D) cross-section models, based on Tóth’s hypothesis that the undulating shapes of the topography and the phreatic surface are similar. Analytical solutions [1,4,5], numerical simulations [6,7,8,9,10], and laboratory experiments [11] have revealed nested patterns of topography-driven groundwater flow. In 2D models, GFSs can be clearly delineated by identifying dividing streamlines that terminate at stagnation points. However, delineating GFSs in topography-driven 3D groundwater flow is considerably more challenging. Several studies have introduced novel conceptual definitions of 3D GFSs to identify them based on the relationship between recharge and discharge zones [2,3]. This process, which requires high-resolution 3D groundwater flow modeling and particle tracking along streamlines, significantly increases the computational costs. Nevertheless, by adopting these conceptual frameworks, regional-scale 3D GFSs can still be approximately identified using the coarse-resolution numerical model, provided that recharge and discharge zones are properly defined.
In recent decades, a new method for partitioning GFSs based on residence time distributions (RTD) [12,13] has attracted increasing research attention. Residence time refers to the total duration that a groundwater particle spends within the flow domain, from entry at the recharge zone to exit at the discharge zone. In fact, travel time is more commonly used than residence time in hydrological and biogeochemical studies of the subsurface environment [14,15,16,17,18,19]. Travel time is zero at the recharge point and increases progressively along the flow path. Studies have shown that both RTD and travel time distribution (TTD) are significantly influenced by the spatial patterns of GFSs [8,20,21,22]. In particular, features of RTD have been proposed to delineate local (shallow) versus regional (deep) GFSs [12,13]. Preferential pathways of groundwater flow may also influence RTD [23,24]. However, the changes in the RTD and TTD with changing GFSs under the impact of groundwater abstraction are not well known.
Water shortages are a critical challenge in northwest China for economic development and eco-environmental protection [25,26]. In recent years, groundwater overdraft in the Kongqi River Basin, Xinjiang, China, has raised serious concerns regarding its impact on groundwater resources and dependent ecosystems [27,28,29,30,31]. Due to the extremely arid climate, natural ecosystems are mostly groundwater-dependent and sensitive to groundwater level changes. The local government is trying to save surface water in the Kongqi River for the plant ecosystems in the downstream area. This effort has promoted groundwater and vegetation recovery in several areas [29,30,31,32], but groundwater levels in irrigation districts have not yet shown signs of recovery. Han et al. [28] conducted a preliminary numerical study on GFS changes induced by pumping wells in irrigation districts. The model was limited to irrigation districts and did not include groundwater response in the downstream region. They did not analyze the change in the travel time or residence time of the GFS.
The objective of this study is to perform a more comprehensive investigation on GFSs in the Kongqi River Basin, considering the spatial patterns and travel time distributions. We develop a modified model for the regional-scale groundwater flow in the basin and obtain groundwater travel time along streamlines using particle tracking. Results are used to analyze the roles of leaking streams, ET, and pumping wells in controlling GFSs. RTD and TTD characteristics are compared with previous studies to reveal new relationships between flow system patterns and travel time distributions.

2. Materials and Methods

2.1. Study Area

The Kongqi River Basin is located in the northeast of the Tarim Basin, in Xinjiang, China. The Kongqi River does not directly receive runoff from the Tianshan Mountains. Instead, it originates from the Bosten Lake, which is fed by the Kaidu River carrying meltwater from the Tianshan Mountains (Figure 1). Surface water from the Kongqi River and local groundwater resources support the cities of Korla and Yuli, as well as the surrounding artificial oases.
Historically, approximately 60 years ago, the Kongqi River functioned as a tributary of the Tarim River and could bring water to the ancient Lop Nor Lake, with a long mainstream length extending more than 700 km [31]. Since the 1990s, due to rapid expansion of oases [33] and increasing utilization of water resources for agricultural development, the middle and lower reaches of the Kongqi River became seasonally wet or perennially dry. Groundwater levels have declined significantly at the regional scale in the basin. Before the end of the last century, both downstream areas of the Kongqi River and Tarim River were on the verge of ecological collapse. In 2000, the Chinese government launched a water conveyance project in the Tarim River to restore and protect the ecological environment [34]. Surface water in the Tarim River was regulated well through the project, ensuring annual wetting of the lower river channels during the flood season [35]. A similar water conveyance project was also carried out for the Kongqi River since 2016 [29]. However, balancing ecological water needs and artificial water consumption remains a major challenge because of limited water resources in the regions.
The Kongqi River Basin is characterized by a warm temperate continental desert climate, where the mean annual temperature and precipitation are 12 °C and 57 mm at Korla City. Human settlements, agriculture, and local ecosystems heavily rely on both surface and groundwater resources. Groundwater exists in multiple aquifers and is highly connected with streams. As shown in Figure 2, the aquifer–aquitard system is mainly composed of Quaternary sediments, where the alluvial–pluvial sandy sediments serve as aquifers, while clayey or silty sediments act as aquitards. The underlying Pliocene and Miocene formations are composed of weakly consolidated mudstones and sandstones, generally acting as aquicludes. Groundwater gains recharge from the leaking streams because the water table is generally lower than the water level in streams. A large amount of river water is introduced into croplands for irrigation, partially contributing to groundwater recharge through canal leakage and infiltration from irrigated soils. Subsurface recharge from mountain blocks also occurs in the north edge of the Kongqi River Basin. In natural conditions, the water table exceeds 900 m a. s. l. in Korla City and declines towards the southern part of the basin. Before flowing into the area of the Tarim River, where the water table is generally lower than 900 m a. s. l., groundwater undergoes significant discharge via ET. Currently, the groundwater flow has been significantly disturbed by human activities. A groundwater depression cone appears in a zone between Korla City and Yuli City, caused by intensive groundwater extraction for irrigation via numerous pumping wells. Reservoirs were constructed to regulate surface water, for example, the Tarim Reservoir located between boreholes H10 and H1 (Figure 2), also contributing to local groundwater recharge through seepage.
Natural vegetation in the region includes Populus euphratica and Tamarix chinensis woodlands, shrubs such as Tamarix ramosissima Ldb and Nitraria tangutorum Bobrov, and grasses like Achnatherum splendens and Artemisia arenaria. These species are mainly distributed along riversides, roadsides between croplands, and low-lying areas in the Taklimakan Desert. Most native vegetation species are adapted to an environment with a certain water table depth (WTD) that is, in general, smaller than 4 m. Some plants, for example trees of Populus euphratica, can live in places with deep groundwater, even when the WTD exceeds 6 m. Nevertheless, widespread groundwater table decline poses a threat to the natural vegetation system.

2.2. Data

Meteorological data were available at the Korla meteorological station. We collected the meteorological data in the period from 1970 to 2020 to characterize the climate features in the study area over the past half century. Time series of annual precipitation and annual mean temperature were derived from monthly records. Evaporation from open water surface was observed at the meteorological station using a 20 cm diameter pan. The actual potential evaporation was then estimated from the monthly pan evaporation by multiplying an empirical coefficient. The annual potential evaporation was then obtained from the monthly evaporation data. As shown in Figure 3, the annual precipitation in the 1970–2020 period fluctuated significantly between 17 mm and 144 mm, with a mean of 64 mm. The annual mean air temperature varied between 10.6 °C and 13.5 °C (Figure S1), with a mean value of 11.9 °C. Both the annual precipitation and annual mean air temperature exhibited slightly increasing trends. The annual potential evaporation varied between 1326 mm and 1632 mm, with a mean value of 1465 mm (Figure S1). It exhibited a decreasing trend, in contrast to the trends of the precipitation and air temperature.
Annual streamflow records from 1970 to 2020 were collected at the Tashidian hydrological station (Figure 1) and are presented in Figure 3. As indicated, prior to 2000, the annual streamflow in the Kongqi River was generally lower than 15 × 108 m3 and exhibited a relatively small variation. After 2000, the streamflow fluctuated significantly between 9.5 × 108 m3 and 26.5 × 108 m3, with an average of approximately 16 × 108 m3. According to the water resources bulletin of the Bayingolin Mongolian Autonomous Region, the water usage for the industrial and agricultural demand in the Kongqi River Basin varied between 8 × 108 m3 and 20 × 108 m3 during the 2000–2020 period, showing an increasing trend. Most of the irrigation water was provided by introducing the river water through canals. Groundwater abstraction became necessary in years when streamflow was insufficient to meet water demand and in areas without access to irrigation canals. As a result, pumping rate in this area varied significantly, typically ranging from 2 × 108 m3/a to 10 × 108 m3/a. In 2016, the use of the river water was restricted as part of the ecological water conveyance project, which aimed to save 3 × 108 m3 of water annually for downstream ecological restoration. This policy increased the reliance on groundwater abstraction for irrigation in cropland areas.
Groundwater-level data from observation wells were collected in 1971 and 2019. The 1971 data, obtained from 90 wells, represent near-natural conditions when the pumping rate was minimal. In contrast, a hydrogeological survey conducted in 2019 provided groundwater levels from 307 wells, reflecting conditions of intensive groundwater extraction in recent years. Both data represent the annual mean groundwater levels.

2.3. Numerical Modeling of Regional Groundwater Flow Scenarios

2.3.1. Model Setup and Boundary Conditions

In this study, numerical modeling of groundwater flow at the regional scale in the Kongqi River Basin was conducted using MODFLOW-2000 [36]. The model contains three layers of grids (Figure 4a), schematically representing the upper sandy aquifer, the middle aquitard of clay and silts, and the lower sandy aquifer, as shown in Figure 2. The thickness of grid blocks varies by positions, depending on the topography and hydrogeological conditions. Each grid block is square-shaped in the plan view, with a width of 1 km. The grids cover a rectangular region in the plan view (Figure 4b), with an area of 21,384 km2. However, the active area in the model is restricted by the Tarim River in the south and the mountain foot in the north, covering about 14,161 km2. Thus, the number of active cells used in the three-layer model is close to 42,483.
It is assumed that the Tarim River serves as a known head boundary in the top model layer (Figure 4b). Mean annual river stages are used. Due to leakage recharge, a groundwater divide forms beneath the Tarim River, which acts as a no-flux boundary in other model layers. The northern boundary serves as an inflow boundary for all model layers, receiving subsurface lateral recharge from mountains. Known flow rates for this boundary were derived from hydrogeological survey data. The western boundary also receives lateral recharge from higher zones in the west. In the MODFLOW model, inflow along boundaries is equivalently treated with the WELL package, represented as injection wells uniformly distributed along a segment. The eastern boundary acts as the outflow boundary, releasing groundwater to downstream areas. The discharge rate along this boundary significantly depends on results of the hydraulic head, which is equivalently calculated via the GHB package, representing a general head boundary that allows groundwater discharge to a distant hydrogeological unit with a specified hydraulic head. The RIV package is used to simulate interactions between the Kongqi River and groundwater, automatically estimating leakage or gain, depending on whether the annual mean river stage is above or below the water table in the shallow, unconfined aquifer.

2.3.2. Modeling Scenarios, Driving Forces, and Parameters

Steady-state groundwater flow is simulated with the MODFLOW model for two specific scenarios, named M1 and M2. Scenario M1 represents a no-pumping situation that is similar to the conditions around 1971. In contrast, scenario M2 represents a situation with intensive pumping that is similar to conditions around 2019. These two scenarios use the same hydraulic conductivity data, but they apply different groundwater recharge and discharge fluxes based on varying river and groundwater water levels, as well as pumping rates. The major hydrogeological conditions of the two scenarios are listed in Table 1. Spatial distributions of croplands are presented in Figure S2. The MODFLOW package, RCH, is used for the input of groundwater recharge flux, including the precipitation infiltration recharge in natural lands and return flow recharge in croplands. In this region, 20% to 25% of the annual precipitation serves as groundwater recharge through vertical infiltration. Recharge in croplands is calculated as the product of the irrigation flux and the return flow ratio. As indicated in Table 1, the ratio of return flow in M2 (5%) is significantly smaller than that in M1 (27%) because of the widespread use of drip irrigation systems. Groundwater abstraction in M2 is simulated using the WELL package. Both the unconfined aquifer (Lay-1 in the model) and the confined aquifer (Lay-3 in the model) include WELL blocks because approximately half of the pumping rate is extracted from the confined aquifer. Leakage from main irrigation canals is also represented with the WELL package by using injection rates determined from diversion volumes and the canal system efficiency.
The hydraulic conductivity exhibits spatial patterns, following the spatial distributions of aquifer–aquitard media. It is large in mountain-front areas where sediments are coarse, while it is small in the low-plain areas where sediments are fine. In the model, these patterns are represented by zones divided for different model layers, as shown in Figure S3. The hydraulic conductivity values in the horizontal and vertical directions are specified within the ranges listed in Table 1.

2.3.3. Modules Selection for Groundwater ET

ET in natural lands, as an essential component of groundwater discharge in the study region, is highly dependent upon WTD [37,38]. When a linear relationship exists, the groundwater ET can be simulated in MODFLOW-96 [39] using the EVT package. However, this may not be valid in the Kongqi River Basin, as experimental studies in similar arid regions [40,41] have revealed nonlinear dependencies. The empirical formula suggested by Averianov [42] is widely adopted for nonlinear conditions:
Eg = Emax [(Dmax − D)/Dmax]n, 0 ≤ D ≤ Dmax
Eg = 0, D > Dmax
where Eg is the groundwater ET rate [LT−1]; D is the WTD [L]; Emax refers to a specific groundwater ET rate when the groundwater table is significantly close to the ground surface [LT−1]; Dmax is an extinction WTD for the positive groundwater ET rate [L]; and n is a constant between 1 and 3 [-]. When n = 1, the Averianov formula reduces to the linear relationship adopted in the EVT package. A parabolic function is commonly adopted by using n = 2. In practice, the Emax value can be approximately estimated as follows:
Emax = k E0
where E0 is the potential evaporation obtained from the meteorological station [LT−1], and k is the coefficient [-]. We apply k = 0.52, n = 2, and Dmax = 6.0 m based on existing studies in similar regions [43,44], while the values of E0 for scenarios M1 and M2 are determined from the mean annual potential evaporation data listed in Table 1. The ETS1 package [45] incorporated in MODFLOW-2000 is used to deal with the nonlinear function of Eg(D), in which a segmented function is implemented. In this study, we use a parabolic function approximately represented by three segments, with the two breakpoints at D/Dmax being 0.50 and 0.75, respectively. The finite-difference equations in MODFLOW are solved with the geometric multi-grid solver implemented in the GMG package [46], which performs best to achieve a convergent result when groundwater ET exists.

2.3.4. Model Calibration

The model is calibrated through a trial-and-error process to match observation data of groundwater levels. The calibration objective in scenario M1, based on observations from 1971, is to identify the distributed hydraulic conductivity of aquifer–aquitard media and the hydraulic conductance of the streambed represented in the RIV package. In scenario M2, these parameters are fixed, whereas the relative distributions of groundwater recharge and pumping rates are identified to match observations in 2019. The regional-scale source and sink terms in Table 1 are required to be satisfied in the calibration. As a result, hydraulic conductivity values identified from the model calibration are listed in Table S1 for different model layers and zones.

2.4. Streamlines Tracking and Flow Systems Delineation

The hydraulic head and Darcy velocities of active cells in the model are obtained from MODFLOW. Then, these results are used to identify streamlines via the particle-tracking program MODPATH version 3.0 [47,48], which incorporates a semi-analytical particle-tracking method with MODFLOW [49,50]. Pathlines estimated from MODPATH represent streamlines for the steady-state groundwater flow. A streamline links the inflow and outflow points for a particle moving in the groundwater flow field. The forward particle tracking terminates when the particle arrives at the model boundary or an internal sink (e.g., a block including pumping wells). In this study, we obtain streamlines of particles released on the water table, i.e., in the top model grid, by using the forward particle-tracking process. One particle is placed in a grid cell. The particle does not move when the grid cell serves as a groundwater discharge site.
GFSs are delineated by grouping streamlines with unique connections between recharge and discharge zones. Various approaches have been proposed in literature for delineating GFSs. The classic method is to identify dividing streamlines from the distribution of stagnation points [1,4,7]. This method is effective for 2D models, whereas it becomes a challenge for 3D models because the dividing surface (not lines) in the 3D space is difficult to identify. An alternative way is grouping streamlines according to the distribution of recharge and discharge zones [2,3]. In this study, we adopt the latter approach. Each flow system is manually delineated as a group of streamlines, linking a unique recharge zone to a unique discharge zone. Recharge zones include boundaries with the mountain-block recharge or horizontal inflow; linear-shaped zones along leaking stream segments; and areal districts with positive vertical groundwater recharge from precipitation infiltration and irrigation return flow. Discharge zones include outflow boundaries, linear-shaped zones along gaining stream segments, irrigation districts with pumping wells, and areas with strong groundwater ET that lead to a net upward outflow. Small individual recharge or discharge zones are combined into larger zones to show the regional-scale patterns of GFS.

2.5. Statistics of Travel and Residence Times

Particle tracking can also be used to check the distribution of travel times [51,52]. MODPATH estimates the travel time, step by step, for a particle moving along a pathline. The moving speed is estimated based on the effective porosity of the media and the Darcy velocity. In this study, we use 0.3 and 0.2 as the effective porosities for the aquifer and aquitard media, respectively. The residence time is determined as the maximum travel time for a streamline with respect to the terminal position.
We analyze the distribution of travel time and residence time using the probability density function (PDF) curve and normal statistics, such as the minimum, maximum, mean, median, standard deviation (Std Dev), and coefficient of variation (CV). The PDF result of the travel time in a modeling scenario may satisfy an empirical distribution, such as the exponential distribution or the power-law distribution. Haitjema [53] derived an analytical solution for the RTD for an idealized system with only horizontal groundwater flow, which can be expressed as follows:
f(t/T1) = exp(−t/T1)
where t is the residence time or travel time [T]; T1 refers to the flux-weighted mean value of t [T]; and f(t/T) is the PDF of t/T [-]. Equation (4) suggests an exponential distribution. Haitjema [53] provided a formula for a simple aquifer that is not applicable in this study. Alternatively, we obtain the best-fit value of T1 by comparing simulation results with the exponential distribution. For 3D groundwater flow, a power-law distribution may be more realistic [8,20,21], as shown as follows:
f(t/T2) = (t/T2)−α
where T2 is a reference time [T], and α is a constant [-]. The power-law distributions will be evaluated against the modeling results to obtain the best-fit values of α and T2.

3. Results

3.1. Groundwater-Level Distributions

Distribution of the hydraulic head dominates the flow direction of groundwater in the aquifer–aquitard system. At the regional scale, the 3D hydraulic head distribution can be approximately represented by the shape of the water table. We extract simulated groundwater levels of the top model layer (Lay-1) to show the water table shape. Results of scenario M1 are shown in Figure 5 with contours (a) and in comparison to observations in 1971 (b). As indicated by the high value of R2 (0.93) and the relatively small absolute errors (0.8 m in median), the estimated groundwater levels agree well with the observed results in 1971. Thus, the calibrated model in M1 is reliable for the investigation of the nature of groundwater flow in the study region.
Groundwater-level contours of scenario M2 are shown in Figure 5c, where the depression cone of the water table on the eastern side of the Kongqi River can be clearly identified. In the depression cone center, the groundwater level is lower than 860 m, and the drawdown is larger than 30 m, in comparison to the groundwater level in scenario M1. Such a significant drop in the water table is caused by heavy groundwater abstraction in the southern area of Korla City, where a large irrigation district exists. The modeled groundwater level of scenario M2 generally agrees with the observation in 2019, as indicated in Figure 5d, where the value of R2 is 0.84, and the median absolute error is 2.6 m. Points of large errors generally fall in irrigation districts where observation wells are near pumping wells and there are uncertainties in the distribution of pumping rates. This does not indicate a flaw in the model for scenario M2, as the objective of this study is not to predict groundwater levels in observation wells but rather to identify regional-scale patterns of groundwater flow and travel times.

3.2. Patterns of Streamlines and Statistics of Travel Times

The distribution of streamlines in scenario M1 is shown in Figure 6a. Each streamline is colored according to segments representing different travel time ranges. Thus, the travel time increases as a particle moves along the streamline from the recharge point to the discharge location. Most particles experience a long travel time of at least 2 ka. The statistical distribution of travel times is shown in Figure 6b, where the PDF decreases as the travel time increases. The probability density is estimated based on the number of particle positions (over 100) within equal travel time intervals of 2 ka. The distribution shows a nearly smooth decreasing trend in Figure 6b, and the corresponding cumulative curve shows a median value at t = 9.7 ka.
In contrast to scenario M1, scenario M2 exhibits different streamline patterns, as shown in Figure 6c. On the eastern side of the Kongqi River, streamlines are attracted to the depression cone of the water table where pumping wells are intensively distributed. The travel time of groundwater particles in this zone is generally less than 2 ka. A special zone emerges between the Tarim River and the Kongqi River, where streamlines link recharge areas in an irrigation district to the surrounding discharge zone. This irrigation district receives surface water input and generates groundwater recharge through irrigation return flow. Due to weak recharge, groundwater flows slowly, and the residence time of those streamlines is generally higher than 10 ka. The travel time distribution of particles in the model is shown in Figure 6d. As indicated, the PDF curve in scenario M2 shows a similar shape to that in scenario M1. However, a lower median travel time of 8.3 ka is observed, mainly due to changes in streamline patterns within irrigation districts.
We also provide Figure S4 to show streamlines with different ranges of residence times, using the threshold of 20 ka. In scenario M1, most of the streamlines starting from the northwestern boundary have residence times that are lower than 20 ka, which represent quick groundwater flow. In contrast, streamlines between the Kongqi and Tarim Rivers generally exhibit residence times exceeding 20 ka. In scenario M2, quick-flow streamlines dominate the pumping zone in the eastern side of the Kongqi River.
Statistics of the travel time and residence time distributions are listed in Table 2 for scenarios M1 and M2. The median values of the travel time and residence time in scenario M2 are smaller than those in scenario M1, whereas their coefficients of variation (CV) in M2 are higher than those in M1. This may indicate that the pumping wells accelerated groundwater flow but also induced more spatially heterogeneous streamline patterns. In both scenarios, the power-law distribution fits the travel time and residence time better (R2 > 0.8) than the exponential distribution (R2 < 0.8).

3.3. Patterns of GFS

Streamlines in Figure 6 are used to identify GFSs linking major recharge sources and discharge ways. Each flow system is marked with a number, such as Sj, where S refers to the index of recharge sources, and j denotes the index of discharge zones. The major recharge sources include: (K) leaking stream recharge from the Kongqi River; (N) mountain-block recharge along the northern boundary; (S) return flow recharge in irrigation districts fed by surface water; (T) leaking stream recharge from the Tarim River; and (W) lateral inflow from the western boundary. The major discharge zones include: (1) stream segments gaining groundwater; (2) ET zone in the northern bank area of the Kongqi River; (3) ET zone between the Kongqi River and the Tarim River; (4) ET zone in the western bank area of the Kongqi River; and (P) irrigation districts with strong groundwater abstraction.
Delineation results of GFSs for scenario M1 are shown in Figure 7a, where nine flow systems exist. Note that the eastern boundary with the lateral outflow is not considered a separate discharge zone but is instead integrated into ET zones N2, K2, K3, and T3. This classification is reasonable, as ET is also the dominant form of groundwater discharge beyond the eastern boundary. Among the flow systems, K1 is the only one that gains recharge from and discharges to the same stream (the Kongqi River). Along the stream segment between K1 and K3, groundwater seems to flow through the surface water body, leading to multiple transitions between groundwater and surface water. Nevertheless, outflow through the southern side of the Kongqi River is considered as a new recharge for K3 with zero travel time because it primarily consists of fresh river water moving downstream through the channel.
Patterns of GFSs in scenario M2 are shown in Figure 7b, where 11 flow systems exist. Among them, KP and NP are two flow systems that experience significant impacts of pumping. Compared to scenario M1, KP appears to be a modified version of K1, while NP corresponds to a modified portion of N2. The flow system S3 alters a portion of T3, though the affected area is limited. The size of K2 is significantly reduced because a long segment of the Kongqi River becomes dry in scenario M2.
Han et al. [28] reported preliminary delineation results of GFSs in the area of irrigation districts without analysis of the travel time. Their delineated GFS patterns are generally consistent with ours, though their model featured smaller spatial scales and a greater number of subdivided recharge and discharge zones. The model area in Han et al. [28] is ~8900 km2, significantly smaller than our study area (14,161 km2). S3 in scenario M2 is a new flow system identified in this study but was missed in the previous one.

4. Discussion

4.1. Formation Mechanism of GFS Patterns

The development of GFSs has been explained in Tóth’s theory using 2D models, where flow links distributed recharge and discharge zones with differing groundwater levels. This is also the major formation mechanism of GFSs in the 3D space. The GFS patterns identified with a groundwater flow model are subject to the simulated flow field, represented by hydraulic heads and velocities. These results are primarily controlled by the model’s structural settings, including recharge inputs, boundary conditions, and parameter heterogeneity. In our model, major recharge zones are spatially constrained to linear inflow boundaries and leaking streams, while major discharge zones are distributed across areas with sufficient groundwater ET across the entire plain, controlled by WTD. Irrigation pumping in croplands also creates areal discharge zones in scenario M2. These factors, along with assigned hydraulic conductivity values and boundary conditions, shape the overall flow field. The simulated streamlines and travel time distributions are thus not isolated outcomes but are directly governed by the spatial heterogeneity in recharge, discharge, and aquifer properties. For example, both of the GFSs K1 and K4 gain recharge from the Kongqi River, whereas they have different discharge forms: K1 discharges to the lower part of the Kongqi River, and K4 flows to the ET zone. GFSs in the northern and southern areas of the Kongqi River are different in hydraulic conductivity and gradient (both are larger in the north), leading to quicker flow velocity and shorter residence times in the northern areas. The impact of ET on GFS patterns is a fresh topic and will be analyzed in particular in the next section.

4.2. The Role of Groundwater ET

The role of ET in GFSs has not been well documented in literature. In the Kongqi River Basin, however, groundwater ET should be seriously considered because it is a key discharge pathway of groundwater and may control the natural patterns of GFSs. As declared in Section 2.3, the groundwater ET rate decreases with WTD and is positive only when D < Dmax. In this study, we use Dmax = 6.0 m. Thus, groundwater discharge zones of ET can be identified from places with a D that is smaller than 6 m. In scenario M1, the simulated distribution of D is shown in Figure 8a, where the area proportion with D < 6 m is approximately 63%, according to Figure 8b. Thus, groundwater ET zones occupy the majority of the study area. However, the net discharge zones are limited to areas where D < 4 m in order to counterbalance infiltration recharge from precipitation. As a result, the area proportion of net discharge zones is reduced to about 31% (Figure 8b), exhibiting a fragmented pattern. Only in the flow systems N4 and K4 (Figure 7a) do they form a continuous discharge area. In scenario M2, WTD changes significantly (Figure 8c), with D increasing substantially due to a lowered water table. The area proportion of net discharge zones reduces to 15% (Figure 8d), with finer granularity and more scattered distribution in comparison to that in scenario M1. The flow systems KP and NP do not contain discharge zones of groundwater ET, as D exceeds 6 m throughout these areas. Note that a large number of grid cells near the northern side of the Tarim River show a high groundwater ET rate (red cells) in scenario M1 (Figure 8a), whereas most of them do not serve as net discharge positions in scenario M2 (Figure 8c) due to drops in river water and groundwater levels.
A noticeable feature of the DTW distribution in the plain area of the basin is that the water table is not strongly governed by the topography. As indicated in Figure S5, pixels of a small WTD (0–1 m) are predominantly located in zones of a moderate land surface altitude (890–910 m) and tend to form ET discharge fragments in the flow system N4 (Figure 7). The second concentrated altitude is ~870 m, in places that are close to the Kongqi River and Tarim River. The data point cloud does not exhibit a significant linear relationship between WTD and terrain elevation. This is different from findings in many previously investigated basins [54,55], where the water table can be sufficiently regarded as a replica of the topography along preferential pathways. Such a feature is mainly attributed to the nonlinear change in the terrain slope from the mountain foot to the lowlands, in comparison to the smooth pattern of groundwater levels. It is also influenced by the significant decrease in the hydraulic conductivity of geological formations from the mountain foot (zones 2 and 4 in Figure S3) to the plain area (zones 8 and 9 in Figure S3), which act as a dam and create an overflow condition for groundwater. Nevertheless, the envelope line in Figure S5 still reflects the linear relationship between the maximum DTW and the terrain elevation.
The fragmentation pattern of ET discharge zones is a challenge for down-scaling GFSs because small local individual discharge zones are hard to distinguish, and the number may be huge. It may also result in an uncertainty in particle tracking for streamline delineation. When a groundwater particle moves across a block where D < 4 m, it may not stop but instead continue to move due to the hydraulic gradient. In reality, a part of groundwater must leave through ET. It implies that a partitioning process of groundwater flow would need to be performed when high-resolution patterns of GFSs are required. This can be implemented by using many modeling layers (e.g., 30–50 layers). However, it often leads to a significant divergence problem in solving the model because several grid cells may frequently switch between dry and wet states. In this study, the model comprises only three layers, so GFSs are identified in a relatively low-resolution pattern, i.e., at the regional scale. In fact, many GFSs not only have fragments of ET discharge zones but also have fragments of infiltration recharge zones (D > 6 m). Accordingly, the patterns shown in Figure 7 do not precisely represent groundwater circulation cells defined in [3] but reveal regional-scale connections between different recharge sources and discharge zones.

4.3. Compare to Existing Studies on Residence Time Distributions

As indicated in Table 2, the statistical distribution of the travel time in this study is similar to that of the residence time under the same scenario model, as evidenced by comparable statistical parameters. Therefore, the residence time results from this study can be used for comparison with analytical or numerical findings in literature.
For scenario M1, the overall shape of the residence time PDF is broadly consistent with an exponential decay, which has been widely adopted to represent idealized flow-through systems [53]. However, noticeable deviations are observed for a short residence time (<30 ka), where the PDF exhibits a steeper initial drop compared to the exponential fit (Figure 9a). This early faster regime is not necessarily attributable to a shallow flow domain as in previous studies using 3D Tóthian models [12] but rather arises from the distinct fast-flow paths represented by flow systems K1, K4, N2, and N4 (Figure 6a and Figure 7a). These systems exhibit similar flow depths, suggesting that flow velocity differences, rather than depth stratification, dominate the early-time dynamics. The same result was also compared with a fitted power-law distribution, as shown in Figure 9b. In the log–log plot, the PDF exhibits a gradually changing slope with increasing residence time, a behavior consistent with numerical simulations of the topography-driven groundwater flow [8,20]. Although neither the exponential nor the power-law distribution perfectly captures the full shape of the PDF, their combination may provide a better approximation for the full spectrum of residence times. Similar hybrid behaviors have been reported in an agricultural catchment [22], indicating a mixture of advection-dominated and diffusive flow regimes.
Under pumping conditions (scenario M2), the PDF exhibits similar structural features but with certain notable distinctions. Compared to M1, the exponential fit better captures the tail behavior in Figure 9c, while a local peak near 30 ka becomes more evident in both the linear and log–log plots (Figure 9c,d). Unlike traditional shallow local GFSs that yield an early peak, this late-time peak may reflect the distinct transition behavior induced by fast-flow systems such as KP, K4, NP, and N4. The emergence of this peak can be interpreted as a manifestation of multimodal residence time distributions, as previously described in [8,13]. However, the absence of an early peak in our model and the strong correspondence between the observed turning point and the travel-time gap among flow paths suggest that the multimodality arises primarily from spatial heterogeneity in flow velocities rather than from hierarchical flow domains.
Overall, our findings support the notion that groundwater residence time distributions in large-scale arid basins are shaped by both system geometry and hydrodynamic contrasts among flow systems. While the exponential distribution may suffice for regional-scale flow, the power-law characteristics and late-time anomalies highlight the importance of incorporating heterogeneous patterns of fast and slow GFSs. The exponential laws of the terrain elevation [54] and preferential permeable pathways [55] may also control the residence time distributions at the regional scale. Decrease in the residence time with large-scale pumping is also a notable finding.

4.4. Future Research Directions

This study presents an initial investigation into GFS patterns and travel time distributions in the Kongqi River Basin. However, several limitations in the current steady-state model point towards key directions for further investigations.
First, the assumption of steady-state flow oversimplifies dynamic processes, such as the seasonal variation in groundwater recharge, long-term climatic transitions, and transient response of flow to intensive pumping. Future research should develop models for the unsteady-state groundwater flow with time-dependent driving forces to simulate the evolution of GFSs from scenario M1 to scenario M2, allowing for more accurate prediction of system response to anthropogenic impacts.
Second, while the model captures regional-scale patterns, it lacks the resolution to characterize local flow systems driven by heterogeneously distributed recharge and ET rates. Developing high-resolution, multi-layered models is essential for investigating finer-scale groundwater flow patterns, especially in areas characterized by highly meandering river channels and fragmented ET zones. Efficient modeling strategies in handling highly heterogeneous recharge and discharge zones, especially in such an arid region, are a critical next step.
Third, the current model does not explicitly simulate transport processes of isotopic or geochemical age tracers. A transport model of groundwater age–mass involves advective–dispersive transport of solutes and radioactive decay. This would account for dispersion, mixing, and evapotranspiration effects that can bias groundwater dating results in arid environments. Incorporating multiple tracers (e.g., 14C, 18O, and noble gases) will improve model calibration and interpretation of GFS patterns.
To support these improvements, future studies are expected to deal with additional questions, such as: How do GFSs evolve under changing recharge and discharge conditions? What are the dominant controls on groundwater age distribution in shallow vs. deep GFSs? Can incorporating isotope and hydraulic data reduce uncertainty in the modeling of regional groundwater flow? Addressing these challenges will enhance both scientific understanding and management practices for groundwater resources in arid inland basins.

5. Conclusions

This study investigates the evolution of GFS patterns and travel time distributions in the arid Kongqi River Basin, where the climatic aridity, leaking streams, and overdraft of groundwater in croplands lead to complex connections between recharge and discharge zones. Using the regional-scale, steady-state 3D numerical model and the particle-tracking method, we characterize changes in hydraulic gradients and flow paths under scenarios with and without agricultural pumping.
Modeling results reveal that GFS patterns are strongly modified by human-induced changes in water table and influenced by fragmented ET discharge zones. The global travel time distribution shifts towards younger ages under pumping stress and follows a power-law form rather than the classical exponential assumption. These findings contribute a refined conceptual and quantitative understanding of how human activities reshape regional groundwater flow in arid basins.
Nonetheless, several limitations should be acknowledged. The current model assumes a steady-state flow, excluding seasonal and interannual variations. Chemical transport and the mixing of age–mass are not simulated. The impact of uncertainty on parameters such as the infiltration recharge rates and hydraulic conductivity remains unquantified. Future work should incorporate the simulation of unsteady-state groundwater flow and isotope-based model validation to make better evaluations of groundwater resource sustainability in such arid regions.
Despite these limitations, our study offers useful insights for arid-zone hydrogeology. It emphasizes the importance of capturing fragmented ET-driven discharge zones, challenges the classical interpretation of residence time distributions, and provides a modeling framework applicable to other arid basins. The results have potential implications for regional groundwater policy, including the agricultural program and long-term aquifer protection strategies.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/w17172542/s1, Table S1: Identified hydraulic conductivity in each zone (m/d); Figure S1: Time series of annual mean air temperature (a) and annual potential evaporation (b) at the Korla meteorological station; Figure S2: Zone numbers of hydraulic conductivity in the model; Figure S3: Distribution of croplands in 1971 and 2019 (after Han et al. [28]); Figure S4: Streamlines with double ranges of residence times in scenarios M1 and M2; Figure S5: The relationship between water table depth and land surface altitude in scenarios M1 and M2.

Author Contributions

Conceptualization, X.-S.W.; methodology, X.-S.W. and Q.X.; software, Q.X.; data curation, Q.X.; writing—original draft preparation, Q.X.; writing—review and editing, X.-S.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the “Deep-time Digital Earth” Science and Technology Leading Talents Team Funds for the Central Universities for the Frontiers Science Center for Deep-time Digital Earth, China University of Geosciences (Beijing), grant number 2652023001.

Data Availability Statement

The original contributions presented in this study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

Acknowledgments

We thank Song Yang, Pengfei Han, and Duo Hui for their help in building the model.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
GFSGroundwater flow systems
ETEvapotranspiration
TTDTravel time distribution
RTDResidence time distribution
WTDWater table depth
PDFProbability density function
Std DevStandard deviation
CVCoefficient of variation

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Figure 1. Location and background geographical elements of the study area.
Figure 1. Location and background geographical elements of the study area.
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Figure 2. Schematic profile of hydrogeological units, boreholes, and pumping wells along the cross-section A–B. Boreholes are named H10, H1, K2, and ZK3. The cross-section line, A–B, is shown in Figure 1.
Figure 2. Schematic profile of hydrogeological units, boreholes, and pumping wells along the cross-section A–B. Boreholes are named H10, H1, K2, and ZK3. The cross-section line, A–B, is shown in Figure 1.
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Figure 3. Time series of annual precipitation at the Korla meteorological station and annual streamflow of the Kongqi River at the Tashidian hydrological station.
Figure 3. Time series of annual precipitation at the Korla meteorological station and annual streamflow of the Kongqi River at the Tashidian hydrological station.
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Figure 4. Numerical model grids: (a) 3D shape; (b) plan view of active cells and boundary conditions for the top layer.
Figure 4. Numerical model grids: (a) 3D shape; (b) plan view of active cells and boundary conditions for the top layer.
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Figure 5. Modeling groundwater levels: (a) contours in scenario M1 and observation wells in 1971; (b) comparison with observation for scenario M1; (c) contours in scenario M2 and observation wells in 2019; (d) comparison with observation for scenario M2. Arrows indicate flow directions in the horizontal plane.
Figure 5. Modeling groundwater levels: (a) contours in scenario M1 and observation wells in 1971; (b) comparison with observation for scenario M1; (c) contours in scenario M2 and observation wells in 2019; (d) comparison with observation for scenario M2. Arrows indicate flow directions in the horizontal plane.
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Figure 6. Numerical modeling results of streamlines and travel times: (a) plan view of streamlines in scenario M1; (b) statistic curves of the travel time in scenario M1; (c) plan view of streamlines in scenario M2; (d) statistic curves of the travel time in scenario M2. In the plan views, only a part of the streamlines is shown for our convenience to identify the path and the groundwater flow directions, which are indicated by scattered arrows.
Figure 6. Numerical modeling results of streamlines and travel times: (a) plan view of streamlines in scenario M1; (b) statistic curves of the travel time in scenario M1; (c) plan view of streamlines in scenario M2; (d) statistic curves of the travel time in scenario M2. In the plan views, only a part of the streamlines is shown for our convenience to identify the path and the groundwater flow directions, which are indicated by scattered arrows.
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Figure 7. Plan views of identified groundwater flow systems: (a) scenario M1; (b) scenario M2. Arrows show the flow directions. Red dashed line encloses the depression cone of the water table near the Kongqi River. Green dashed line encloses an irrigation district only fed by introducing surface water.
Figure 7. Plan views of identified groundwater flow systems: (a) scenario M1; (b) scenario M2. Arrows show the flow directions. Red dashed line encloses the depression cone of the water table near the Kongqi River. Green dashed line encloses an irrigation district only fed by introducing surface water.
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Figure 8. Modeling results of WTD: (a) WTD distribution in scenario M1; (b) area proportions for different ranges of D in scenario M1; (c) WTD distribution in scenario M2; (d) area proportions for different ranges of D in scenario M2. The extinction depth of groundwater ET is 6 m.
Figure 8. Modeling results of WTD: (a) WTD distribution in scenario M1; (b) area proportions for different ranges of D in scenario M1; (c) WTD distribution in scenario M2; (d) area proportions for different ranges of D in scenario M2. The extinction depth of groundwater ET is 6 m.
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Figure 9. PDF curves of the residence time in comparison to empirical distributions: (a) compare with the fitted exponential distribution in scenario M1; (b) compare with the fitted power-law distribution in scenario M1; (c) compare with the fitted exponential distribution in scenario M2; (d) compare with the fitted power-law distribution in scenario M2. Fitting parameters are listed in Table 2.
Figure 9. PDF curves of the residence time in comparison to empirical distributions: (a) compare with the fitted exponential distribution in scenario M1; (b) compare with the fitted power-law distribution in scenario M1; (c) compare with the fitted exponential distribution in scenario M2; (d) compare with the fitted power-law distribution in scenario M2. Fitting parameters are listed in Table 2.
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Table 1. Modeling scenarios for the regional groundwater flow in the Kongqi River Basin.
Table 1. Modeling scenarios for the regional groundwater flow in the Kongqi River Basin.
ParametersUnitScenarios
M1M2
Hydraulic conductivity of aquifer mediahorizontalm/d2–80
verticalm/d0.2–20
Hydraulic conductivity of aquitard mediahorizontalm/d0.5–10
verticalm/d0.01–2
Mean annual precipitationmm4993
Mean annual potential evaporationmm15121400
Inflow from the northern mountain front×108 m3/a1.541.61
Inflow from the western boundary×108 m3/a0.630.67
Mean annual streamflow of the Kongqi River×108 m312.418.7
Effective length of the Kongqi Riverkm510350
Water levels in the Tarim Riverm. a.s.l.862–915861–913
Area of irrigated croplandskm217132381
Ratio of return flow in croplands [-]0.270.05
Water efficiency in canal system[-]49.5%85.6%
Mean annual usage of irrigation water×108 m3617
Mean annual pumping of groundwater×108 m307
Table 2. Statistics of the travel time and residence time in different scenarios.
Table 2. Statistics of the travel time and residence time in different scenarios.
Title 1StatisticsScenario M1Scenario M2
Travel time
(ka)		Minimum0.00.0
Maximum505.7414.7
Mean22.825.6
Median9.78.3
Std Dev34.743.6
CV [-]1.51.7
Fitting exponential distribution, Equation (4)T144.548.0
R20.670.64
Fitting power-law distribution, Equation (5)T29.48.9
α [-]1.091.06
R20.920.96
Residence time
(ka)		Minimum0.00.0
Maximum505.7414.7
Mean18.717.3
Median6.62.4
Std Dev30.636.3
CV [-]1.62.1
Fitting exponential distribution, Equation (4)T143.348.8
R20.750.65
Fitting power-law distribution, Equation (5)T214.016.1
α [-]1.181.26
R20.890.92
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Xu, Q.; Wang, X.-S. Patterns of Groundwater Flow Systems and Travel Times Controlled by Leaking Streams, Evapotranspiration, and Pumping Wells in the Kongqi River Basin, China. Water 2025, 17, 2542. https://doi.org/10.3390/w17172542

AMA Style

Xu Q, Wang X-S. Patterns of Groundwater Flow Systems and Travel Times Controlled by Leaking Streams, Evapotranspiration, and Pumping Wells in the Kongqi River Basin, China. Water. 2025; 17(17):2542. https://doi.org/10.3390/w17172542

Chicago/Turabian Style

Xu, Qian, and Xu-Sheng Wang. 2025. "Patterns of Groundwater Flow Systems and Travel Times Controlled by Leaking Streams, Evapotranspiration, and Pumping Wells in the Kongqi River Basin, China" Water 17, no. 17: 2542. https://doi.org/10.3390/w17172542

APA Style

Xu, Q., & Wang, X.-S. (2025). Patterns of Groundwater Flow Systems and Travel Times Controlled by Leaking Streams, Evapotranspiration, and Pumping Wells in the Kongqi River Basin, China. Water, 17(17), 2542. https://doi.org/10.3390/w17172542

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