Modeling Dynamics of Water Balance for Lakes in the Northwest Tibetan Plateau with Satellite-Based Observations

Abstract

The hydrological cycle in the Tibetan Plateau is experiencing notable changes in recent decades under a changing climate. The hydrological changes, however, are not well investigated due to the limitations in the availability of ground-based observations. In this study, by incorporating satellite-based observations into a hydrological modeling framework, seasonal and inter-annual dynamics of water balance for lakes in the northwest Tibetan Plateau are examined systematically for the period of 1990 to 2022. Satellite-based observations, including lake water area and water level, have been used to calibrate the hydrological model and to estimate lake water storage. The hydrological model performs satisfactorily, with the Nash–Sutcliffe efficiency coefficient (NSE) exceeding 0.5 for all 15 studied lakes. It is found that inflow contributes over 70% of annual water gain for most lakes, while percolation accounts for a larger portion (>60%) of total water loss than evaporation. The studied lakes have expanded substantially, with regional average increasing rates in lake level and water storage of 0.38 m/a and 3.12 × 10⁸ m³/a, respectively. Some lakes transitioned from shrinking to expanding around 1999, and expansion in most lakes has further accelerated since around 2012, primarily because of increased precipitation over the lake catchments, leading to greater inflow to the lakes. These findings provide important insights into understanding and predicting responses of lake water balance to climate change as well as for developing adaptative strategies.

1. Introduction

Lakes play a crucial role in biogeochemical processes and are irreplaceable in ensuring water resource security, maintaining ecological service functions, and protecting biodiversity [1,2]. Lakes, however, are highly sensitive to climate and hydrological changes, and are considered as sentinels, integrators, and regulators of environmental change [3,4,5]. Monitoring and modeling hydrological dynamics of lakes under changing climate and intensifying human activities are essential in sustaining human society and freshwater ecosystems worldwide.

The Tibetan Plateau is the highest and most lake-rich region in the world with a total lake area of about 50,000 km² and 1424 lakes larger than 1 km² [6]. The region is known as the Water Tower of Asia, serving as the source water of most of the largest rivers in Asia [7,8,9]. With the ongoing process of global warming, the Tibetan Plateau has become one of the most visibly affected regions in the world, with significant increases in temperature and precipitation [10,11,12]. This has profoundly impacted the regional hydrological cycle, leading to significant alterations in lake water balance in recent decades [13,14,15,16], which in turn affects the regional climate system, influencing plateau biomes, ecosystem functions, and human activities [17,18].

Despite increasing research efforts to understand changes in the hydrological cycle on the Tibetan Plateau, these changes remain insufficiently explored primarily due to limitations in ground-based observations. Consequently, satellite-based observations are increasingly vital for investigating hydrological dynamics in the region, particularly with recent advances in algorithms for retrieving hydrological variables (e.g., lake surface water extent and water level) and publicly available datasets [19,20,21,22,23]. For instance, satellite-based observations of lake area and level have been widely used in monitoring long-term changes in the terrestrial freshwater landscape on the Tibetan Plateau [24,25,26,27,28].

Additionally, remotely sensed datasets are increasingly utilized as model inputs, parameters, or observational references for calibrating and validating hydrological models [29,30]. Considerable research efforts have been dedicated to developing novel modeling frameworks that integrate satellite-based observations with hydrological models [31,32,33,34,35]. These integrated frameworks have proven to be powerful and valuable for regional hydrological research, particularly in data-scarce regions, as they enable the estimation of key hydrological variables that are not directly observable from remote sensing and facilitate the evaluation of their responses to external drivers [36,37,38,39,40].

The northwest Tibetan Plateau is characterized by harsh natural conditions and sparse population distribution. Due to limited data availability and the region’s poor accessibility, hydrological changes in lakes within this area are largely less known compared to those in the eastern Tibetan Plateau. Existing studies primarily relied on direct use of remote sensing data to examine changes in lake water levels or surface areas, often focusing on a limited number of lakes [41,42,43,44,45,46]. More systematic studies are expected to explore the dynamics of lake water balance in this region by integrating remote sensing observations with hydrological modeling.

This study aims to explore seasonal and inter-annual dynamics of water balance for lakes in the northwest Tibetan Plateau under a changing climate. A monthly hydrological model is formulated and calibrated for each lake against satellite-based observations to reconstruct the long-term time series of key water balance components for the period of 1990 to 2022. Seasonal and inter-annual variations of the water balance components are then investigated. The findings of this research are conducive to understanding the hydrological impacts of climate change in the Tibetan Plateau, informing the development of regional adaptative strategies.

2. Materials

2.1. Study Area

The study area (78°E–84°E, 32°N–36°N) is located in the northwest Tibetan Plateau and the southern slope of the western Kunlun Mountains, bordering Kashmir (Figure 1). The region has an average elevation of about 4840 m and receives less than 300 mm of annual precipitation, resulting in harsh living conditions. The lack of meteorological stations makes it a typical data-scarce region. The area includes 15 lakes with an area above 5 km², the physical properties of which are given in Table 1. The surface area of these lakes ranges from 9 to 467 km², with corresponding catchment areas varying from 543 to 25,306 km².

Figure 1. Location of the study area and the studied lakes. The lake numbers correspond to the IDs in Table 1.

Table 1. Characteristics of the lakes considered in this study. Altitude and lake areas are long-term means for the period of January 1990 to December 2022 based on satellite observations. Long-term mean annual precipitation, temperature, and potential evapotranspiration (PET) are estimated based on ERA5-Land for the period 1990–2022.

ID	Name	Abbr.	Latitude	Longitude	Altitude (m)	Lake Area (km2)	Catchment Area (km2)	Precipitation (mm)	Temperature (°C)	PET (mm)
1	Aksai Chin	AKC	35.20	79.87	4854.6	201.0	8187.4	192.0	−7.6	778.7
2	Pangong Co	PGC	33.62	79.47	4245.2	466.6	25,305.6	250.6	−4.6	756.4
3	Longmu Co	LMC	34.61	80.46	5009.1	107.8	1120.2	346.4	−8.2	669.5
4	Mang Co	MAC	34.50	80.44	5023.8	12.3	725.6	368.5	−8.6	847.6
5	Bangdag Co	BDC	34.94	81.56	4912.9	99.8	4683.4	311.4	−7.5	734.9
6	Dulishi Lake	DLS	34.73	81.89	5046.3	93.2	1864.3	371.3	−8.5	783.1
7	Qingce Lake	QCL	34.48	81.79	5103.6	64.1	957.2	387.4	−7.9	751.8
8	Luotuo Lake	LTL	34.44	81.94	5104.0	64.1	1007.0	380.8	−7.9	697.7
9	Lumajiangdong Co	LMJD	34.02	81.61	4816.3	365.3	6806.0	296.2	−5.5	802.0
10	Qagong Co	QGC	34.44	82.33	5096.4	25.5	542.9	372.5	−7.9	892.7
11	Memar Co	MMC	34.22	82.31	4927.3	146.2	2013.0	348.3	−6.6	829.7
12	Heishi North Lake	HSN	35.56	82.74	5053.0	104.6	1591.8	413.1	−9.8	587.5
13	Salt Water Lake	SWL	35.28	83.07	4899.8	139.7	6472.0	308.4	−7.5	826.5
14	Xiajian Lake	XJL	34.16	82.77	4979.2	9.0	783.2	337.7	−6.1	1045.9
15	Katiao Co	KTC	33.96	82.97	4950.3	40.1	2096.9	339.1	−6.2	1073.8

The cold and dry climate conditions in the region have led to a dense distribution of glaciers in the region. Using glacier boundaries from the Second Glacier Inventory Dataset of China (https://www.tpdc.ac.cn/home (accessed on 17 January 2024)), the lakes are classified based on the presence of glaciers within their corresponding catchments. It is found that except for Qagong Co, Xiajian Lake, and Katiao Co, the remaining lakes are all glacier-fed. All the 15 studied lakes are endorheic (closed basin) lakes with no surface outflow to the downstream.

2.2. Satellite-Observed Lake Area and Lake Level

Lake surface extent is a critical variable for estimating water storage. In this study, the lake surface extent is obtained from the Global Surface Water Explorer (GSWE) dataset developed by the European Commission’s Joint Research Centre [47]. This dataset, generated from over 3 million 30 m resolution Landsat satellite images, maps the location and temporal distribution of water surfaces at the global scale for the period of 1984 to 2020 on a monthly and annual basis. The monthly water history dataset used in this study (https://developers.google.cn/earth-engine/datasets/catalog/JRC_GSW1_4_MonthlyHistory (accessed on 6 November 2023)) is available on Google Earth Engine (GEE). This dataset classifies each pixel as either water or non-water. Since efficiency in identifying the water pixel can be affected when lakes are frozen, in this study, only lake areas of the largely ice-free months (May to October) are estimated. In addition, with the consideration of the influence of snow cover and cloud contamination, the Median Absolute Deviation (MAD) method is applied to exclude outliers, which are data points deviating more than three times the MAD value from the median [48].

The lake level data product used in this study is the High-space-coverage Lake Level Change Datasets on the Tibetan Plateau for the period of 2002 to 2021 (TPLL) [49]. This product provides water level above sea level change sequences for 364 lakes larger than 10 km² on the Tibetan Plateau from 2002 to 2021 by processing and merging data from eight different altimetry missions. The dataset is found to be highly consistent (R² > 0.97) with the lake level dataset (Hydroweb, https://hydroweb.theia-land.fr/ (accessed on 21 October 2023)) provided by the Laboratory for Spatial Geophysical and Oceanographic Studies (LEGOS), as evaluated with 37 common lakes over the entire Tibetan Plateau. The average lake level of a lake for each specific month is calculated as the mean of water level of all data points within the lake for that month.

2.3. Climate Forcings from ERA5-Land

The lake water balance model used in this study requires temperature, precipitation, and potential evaporation as inputs, which are obtained from the ERA5-Land dataset in this study. The ERA5-Land dataset is a high-resolution reanalysis product released by the European Centre for Medium-Range Weather Forecasts (ECMWF) [50]. This product was developed based on the land surface component of the ERA5 reanalysis, spanning from 1950 to the present. The spatial resolution of the ERA5-Land dataset is 0.1° × 0.1°, and the temporal resolution is 1 h. The gridded hourly data are aggregated to provide daily catchment or lake-wide mean temperature, precipitation, and potential evaporation for the full years from 1990 to 2020.

Considering possible uncertainties induced by climate forcings, the CMFD dataset [51,52] is also used in this study. The CMFD dataset is a gridded reanalysis dataset with a spatial resolution of 0.1° and a temporal resolution of 3 h. The CMFD dataset was produced by fusing station data, remote sensing products, and reanalysis datasets. It includes meteorological variables such as precipitation, temperature, air pressure, specific humidity, wind speed, shortwave radiation, and longwave radiation. Similarly, the dataset is aggregated for providing daily-catchment mean meteorological inputs for hydrological modeling for comparison.

3. Methods

In this study, a monthly hydrological model is developed together with a water storage model to estimate key water balance components of the studied lakes for the period 1990–2022. The components include two state variables (i.e., relative lake water storage and water level), two water gain items (i.e., lake-top precipitation and inflow), and two water loss items (lake evaporation and percolation). Lake level and surface area retrieved from multiple remote sensing data sources are used to determine the hypsometric curve of the lakes, which is then used to estimate relative water storage. Satellite-observed lake level was employed to calibrate and validate the hydrological model. For each lake, complete monthly time series of water balance components for the period 1990–2022 are reconstructed using the calibrated hydrological model and climate inputs from ERA5-Land. Seasonal and inter-annual dynamics of lake water balance are then investigated based on the reconstructed time series. Figure 2 illustrates the overall framework developed in this study, with specific details explained in the following sections.

Figure 2. The overall framework for modeling dynamics of lake water balance.

3.1. Modeling the Monthly Lake Water Balance

The monthly hydrological model introduced in Wu et al. [53] is used in this study to simulate hydrological processes of the lakes in the northwest Tibetan Plateau for the period of 1990 to 2022. The model extends the monthly watershed water balance model proposed by Zhang et al. [54] by incorporating modules for glacial, snow, and lake water balance processes tailored to the hydrological characteristics of lakes in the Tibetan Plateau. The model has been successfully applied to Nam Co [53], which is the largest lake in the Tibetan Plateau.

For the water balance of the lake, it can be expressed as follows:

$$∆L={\displaystyle \frac{A_c}{A_l}}{Q}_{in}+P_l-E_l-Q_{out}={\displaystyle \frac{R_t}{r_a}}+P_l-E_l-Perc$$

(1)

where $∆L$ represents the change in lake water level (mm), $P_l$ is lake-top precipitation (mm), $E_l$ is lake surface evaporation (mm), $A_c$ and $A_l$ are the catchment area and lake area (km²), and $Q_{in}$ and $Q_{out}$ refer to the lake inflow (mm) and outflow (mm). Here, $Q_{in}$ is equal to the catchment runoff $R_t$. $r_a$ is the ratio of lake area to total catchment area, which is used to convert catchment runoff depth to lake water inflow depth. Since all the studied lakes are endorheic, percolation to the groundwater ($Perc$) is considered as the only outflow loss of the lake system. According to Darcy’s law, percolation is estimated as follows [55,56]:

$$Perc=kL$$

(2)

where $k$ is the hydraulic conductivity depending on the permeability of the soil or rock beneath the lake. The water level ($L$) is assumed to be equivalent to the water head in Darcy’s law. Lake evaporation is considered equal to potential evapotranspiration during the ice-free season and is assumed to be zero during the frozen season [57,58]. Equation (1) mechanistically links lake water level dynamics to catchment hydrology and in-lake processes. This critical linkage ensures that the model captures both catchment-scale water generation (via snow/glacier melt and runoff) and lake-specific water balance drivers. Further details about the model can be found in [53].

The required inputs of the model include monthly temperature ($T$), precipitation ($P$), and potential evaporation ($E_0$) for the simulation periods, all sourced from the ERA5-Land dataset. The model outputs include lake water level and water balance components such as inflow runoff, evaporation, and percolation. The model has 8 parameters to be calibrated. Due to the lack of ground-based observations of streamflow or lake level for calibration, satellite-observed monthly lake level together with a reliable lake level estimated based on the hypsometric curve (described in Section 3.2) are used to calibrate the hydrological model. The objective function used in model calibration is the Nash–Sutcliffe efficiency coefficient (NSE) [59], expressed as follows:

$$NSE=1-{\displaystyle \frac{{\sum }_{t=1}^T{\left(L_r^t-L_m^t\right)}^2}{{\sum }_{t=1}^T{\left(L_r^t-\overline{L_r}\right)}^2}}$$

(3)

where $L_r$ is the satellite-observed lake water level, $L_m$ is the simulated lake water level, $L^t$ refers to the simulated or reconstructed value at time $t$, and $\overline{L_r}$ is the mean of the reconstructed values over the entire period. The NSE ranges from −∞ to 1, with a value greater than 0.5 indicating satisfactory model performance [60]. The model is validated using the monthly lake level series derived from satellite-based observation, and the evaluation metrics include R², RMSE, and relative error percentage (REP) which is expressed as follows:

$$\mathrm{R}\mathrm{E}\mathrm{P}={\displaystyle \frac{\overline{\left|L_o^t-L_m^t\right|}}{L_{o,max}-L_{o,min}}}\times 100\%$$

(4)

where $L_{o,max}$ and $L_{o,min}$ are the maximum and minimum lake water level observed by satellites during the studied period. The REP indicates the simulation error in relation to the fluctuation range of the water level. The REP defined here is with the consideration that water levels of the lakes in the Tibetan Plateau are all above 4000 m, which can lead to a very low percentage bias if it is not normalized.

3.2. Estimating Relative Lake Water Volume

The hydrological model produces lake water level as an output but does not directly simulate lake water volume. The simulated lake water level, however, can be used to estimate relative lake water volume, which is lake water storage relative to water storage at the first month of the simulation period, expressed as follows [61,62]:

$$V_r={\int }_{L_1}^{L_t}A\left(L\right)dL$$

(5)

where $V_r$ is lake water storage between the reference lake water level (i.e., water level at the first month) and the lake water level (L_t) at time $t$. $A\left(L\right)$ denotes the corresponding lake area as a function of lake water level. The function describes the hypsometric curve of a lake and is determined based on the remotely sensed lake area from GSWE and lake level from TPLL dataset for the period of 1990 to 2020.

The shape of a hypsometric curve generally can be approximated by linear, polynomial, exponential, logarithmic, or power functions [63,64]. With known hypsometric curves, relative lake water volume can be estimated by integrating Equation (5), resulting in volume–water level relationships (i.e., V-L function). Table 2 shows polynomial functions of hypsometric curves and their corresponding V-L functions. For the studied lakes, polynomial regression is conducted to find the best fitted hypsometric curves, with results shown in Table 3. It can be seen that the hypsometric curves are reliable, with R² mostly above 0.5, and are statistically significant at the 0.05 level. It should be noted that, in developing the hypsometric curves, outliers have been removed by using the Cook’s distance method [65].

Table 2. Function of hypsometric curve and the corresponding formula in estimating relative lake water storage.

Curve Type	Hypsometric Curve	Relative Lake Water Storage
Linear	$A=aL+b$	$V_r={\displaystyle \frac{L}{2}}\left(A+b\right)-{\displaystyle \frac{L_1}{2}}\left(A_1+b\right)$
Quadratic	$A=a{(L-b)}^2+c$	$V_r={\displaystyle \frac{L}{3}}(A+{\displaystyle \frac{b·L}{2}}+2c)-{\displaystyle \frac{L_1}{3}}(A_1+{\displaystyle \frac{b·L_1}{2}}+2c)$
Cubic	$A=a({L-b)}^3+cL+d$	$V_r={\displaystyle \frac{L}{4}}(A+{\displaystyle \frac{b·L^2}{3}}+c·L+3d)-{\displaystyle \frac{L_1}{4}}(A_1+{\displaystyle \frac{b·{L_1}^2}{3}}+c·L_1+3d)$

Table 3. The area–level relationship of the studied lakes.

Lake	Number of Data Pairs	Relationships	R2
AKC	64	$A=8.74({L-4854.28)}^3$	0.71
PGC	43	$A=8.37L-35056.58$	0.81
LMC	20	$A=2.80({L-5014.05)}^3-9.41\times {10}^{4}L+4.85\times {10}^8$	0.50
MAC	7	$A=0.14L-700.91$	0.47
BDC	34	$A=0.13({L-5049.41)}^3-2.62\times {10}^{5}L-1.13\times {10}^9$	0.69
DLS	33	$A=1.54L-7679.42$	0.66
QCL	20	$A=0.39({L-5061.28)}^3+2.59\times {10}^{5}L-7.51\times {10}^8$	0.89
LTL	22	$A=1.19L-6021.42$	0.86
LMJD	41	$A=0.11({L-4796.45)}^3+3.77\times {10}^{4}L-1.19\times {10}^8$	0.94
QGC	8	$A=1.04L-5290.13$	0.52
MMC	25	$A=0.08{(L-5049.83)}^3-1.42\times {10}^{5}L-7.27\times {10}^8$	0.92
HSN	39	$A=1.53L-7617.21$	0.85
SWL	33	$A=9.59L-46867.74$	0.56
XJL	12	$A=2.49L-12393.56$	0.69
KTC	10	$A=1.83L-9030.49$	0.90

4. Results

4.1. Model Performance

Figure 3 shows the performance of the hydrological model during the calibration phase by comparing the simulated monthly lake water level against that reconstructed lake level (including both satellite-observed lake water level and that reconstructed based on the hypsometric curves). The model performs well in most lakes with NSE above 0.5, while 12 out of the 15 lakes have an NSE above 0.7. Overall, the model performs better in lakes with larger catchment or lake area (e.g., HSN and LMJD) than in smaller lakes or catchments (e.g., LMC and XJL). One of the possible reasons for this can be because the lake level reconstructed based on hypsometric curves may have a relative lower quality for smaller lakes due to the limitations in spatial resolution and revisiting frequency of the sensors.

Figure 3. Comparison of reconstructed and simulated lake levels during the model calibration phase.

The monthly time series of simulated and satellite-observed lake water levels for the studied lakes are shown in Figure 4. Overall, the satellite-based observations align well with the simulated lake water levels, with all lakes showing a coefficient of determination (R²) greater than 0.7, and as many as 12 lakes exhibiting R² values exceeding 0.8. However, for some lakes, a few satellite observations exhibit significant deviations in specific values despite matching the general trends of the simulations such as AKC (RMSE = 2.96, REP = 45.08%) and KTC (RMSE = 5.01, REP = 36.12%), which show anomalously significant water level changes. The results indicate that the model may have limitations in capturing dramatic shifts in lake water levels caused by extreme hydroclimatic events or some satellite observations may have systematic bias needing to be corrected. Therefore, to better integrate remotely sensed data into hydrological modeling, it is essential to implement a strict quality check of the data to identify and filter out outliers that could significantly impact model calibration and validation. The filtering of the outliers, however, should be based on deep understanding of hydrological processes in the region and limitations in the remotely sensed data.

Figure 4. Comparison of satellite-observed and simulated monthly lake levels for studied lakes for the period 1990–2022.

4.2. Seasonal Dynamics of Lake Water Balance

Based on the hydrological model and the model estimating relative water storage, monthly time series of water balance components are obtained for the period 1990–2022. These components include two state variables (water level L and relative water storage Vr), two water gain variables (lake-top precipitation P and inflow Q), and two water loss variables (lake evaporation ET and percolation PER). Long-term means of each component are calculated for each calendar month to demonstrate the seasonal dynamics of water balance of the studied lakes, presented in Figure 5 and Figure 6.

Figure 5. Intra-annual variations in water level and relative water storage of the studied lakes. The red axis represents lake water level, corresponding to the red line; the blue axis represents relative water storage, corresponding to the blue bars.

Figure 6. Intra-annual variation in water balance components of the studied lakes. Water gain components include lake-top precipitation and inflow (or catchment runoff). Water loss components considered include lake evaporation and percolation.

Figure 5 shows seasonal dynamics of the long-term mean monthly water level and relative water storage. Except for PGC, most studied lakes exhibit the highest water level and water storage in September or October while having the lowest level and storage around April or May. Among the studied lakes, the one with the largest intra-annual fluctuation in water level is KTC, with the highest water level at 4956.0 m in September and the lowest at 4950.8 m in May. Correspondingly, the relative water storage is 8.5 × 10⁸ m³ and 6.0 × 10⁸ m³, respectively. The strong fluctuation in water level and storage indicates intense water exchange and high renewability of the water in the lake. The PGC located at the lowest elevation but with the largest lake and catchment area has substantial different seasonal variation in lake level and water storage as compared with the other lakes. The water level of PGC reaches its highest in May and August (4244.9 m) but is at the lowest in January (4244.8 m), with fluctuation ranges within 0.1 m. The results are consistent with the findings of Zhaxi et al. [66]. This suggests that PGC maintains a much closer balance between water gain and loss throughout the year. The peak water level or storage observed in May can be because of contributions from glaciers and snowmelt.

Intra-annual variation of the water gain and loss components is illustrated in Figure 6, where the long-term monthly mean of each component is calculated based on the output of the hydrological model. For the two water gain components (lake-top precipitation and inflow, i.e., catchment runoff), the results show that they both peak between July and August in most catchments. The lake with the largest intra-annual fluctuation in inflow is KTC, partially explaining its water level fluctuations. For most lakes, inflow accounts for a large portion (>70%) of water gain throughout the year, particularly for AKC, LMC, BDC, and SWL. Inflow contributions typically peak during the wet months (May to October). However, for PGC, inflow is more evenly distributed throughout the year compared to most other lakes, which helps explain the relatively weaker fluctuations in its water level and storage.

The two main water loss components, lake evaporation and percolation, both peak in August, largely coinciding with the peak in water gain for most studied lakes. Among them, KTC has the highest evaporation (169 mm) and percolation (5069 mm) losses, while BDC has the lowest evaporation (17 mm) loss, and DLS has the lowest percolation (184 mm) loss. Percolation accounts for a larger portion (>60%) of total water loss than evaporation in most lakes. It is worth noting that percolation losses exhibit much slighter intra-annual variation than lake evaporation. In warmer summer months, in lakes such as PGC and DSL, evaporation contributes more than half of the monthly water losses.

4.3. Long-Term Changes in Lake Water Balance

Changes in estimated annual mean relative water storage and water level of the studied lakes for the period 1990–2022 are detected by the Mann–Kendall test [67] with a change rate calculated by the Theil–Sen approaches [68]. As shown in Figure 7, all the 15 lakes have experienced significant increase both in relative water storage and water level. Mean annual water storage of the 15 lakes has increased at a rate of 3.12 × 10⁸ m³/a, with a mean increase rate in water level of 0.38 m/a. Spatially, lakes located in the northeastern part of the study area generally experienced higher increase rates in water storage as compared to those in the southwestern part. On an annual scale, lakes with the largest increase rate in water storage are SWL (1.00 × 10⁸ m³/a), KTC (0.66 × 10⁸ m³/a), and BDC (0.43 × 10⁸ m³/a), while MAC has the lowest increase rate (0.005 × 10⁸ m³/a).

Figure 7. Long-term trends of lake water storage and water level of the studied lakes for the period 1990–2022. The plot on the (left) shows the annual water storage change rate; the plot on the (right) shows the monthly time series of lake-wide mean water storage and water level, where the red axis represents lake water level corresponding to the red line, and the blue axis represents relative water storage corresponding to the blue line.

It is noted that changes in lake water storage and water level are not necessarily linear or with a constant change rate throughout the period (Figure 8). Turning points of the annual lake water storage and water level are identified by the piecewise linear regression approach [69]. Results have shown that lakes such as AKC, PGC, LMC, MAC, BDC, QCL, LMJD, and XJL exhibit a transition from a shrinking to an expanding trend around 1999—earliest in 1996 (e.g., PGC) and latest in 2000 (e.g., AKC). It indicates that these lakes may have experienced a negative water surplus (i.e., water gains smaller than water loss) before the turning point but positive water surplus thereafter. Since around 2012, the increase in water storage and water level has accelerated in most of the studied lakes, including AKC, LMC, MAC, BDC, QCL, LTL, QGC, MMC, HSN, SWL, and KTC, approximately following a power law. Meanwhile, the increasing trend is slowing down in MAC, LMJD, and XJL in recent years, particularly since 2018.

Figure 8. Long-term changes in lake water storage and water level of the studied lakes for the period 1990–2022. The blue axis represents relative water storage, the red axis represents lake water level, and the color of the text labels for the rate of change corresponds to the respective axes. The green lines indicate the detected turning years.

The increasing trends in lake water storage and water level are primarily determined by increases in annual inflow to the lakes (Figure 9). Lakes with pronounced increases in inflow include BDC, SWL, and KTC, all with an increment rate above 30 mm/a. Though lakes such as XJL, MMC, and LTL have a significant increasing trend in lake-top precipitation, the increasing rate is around 2 mm/a. However, it is worth noting that a large portion of the inflow increase can be attributed to increased precipitation across the entire lake catchment, indicating considerable impacts of climatic change. For water loss components, except for KTC, SWL, and BDC, the increase in evaporation is much higher than that in percolation. Lakes with significant increase in evaporation such as XJL, LMJD, and LTL have an increasing rate above 1.25 mm/a. The increasing rate, however, is much lower than that of inflow and lake-top precipitation.

Figure 9. Inter-annual variation of water budget components of lakes in the northwest Tibetan Plateau. Light blue represents precipitation, dark blue represents inflow, light green represents evaporation, and dark green represents percolation.

5. Discussion

5.1. Comparison with Existing Studies

Several existing studies have investigated long-term changes in lake area or water level within the study region based on remote sensing data though they have not systematically examined changes in lake water balance [42,44,45]. To further validate our findings, in this study, we have generated a complete monthly time series of water areas for the studied lakes based on simulated water levels and the hypsometric curves derived. Long-term trends of water area for each lake are then identified and compared against those reported in the existing studies. The results of this study are found to be consistent with existing studies, demonstrating the reliability of the methods used in this study. For example, the expansion rate of LMJD for the period 2001–2012 is 3.1 km²/a, which is 0.6 km²/a lower than that reported in [44]. Meanwhile, the expansion rate of AKC during 1996–2005 is around 6.2 km²/a, which is 1.0 km²/a higher than that reported in [42]. In addition, the water level change rate for MMC during 2016–2019 is estimated to be 0.65 m/a in this study, close to the 0.80 m/a reported in [45]. The difference between our simulation results and those of existing studies, however, suggests inherent uncertainties due to the methods and data used.

Existing studies [70,71] have examined changes in water storage for four lakes within our study region, including AKC, DLS, LMJD, and SWL. The results from [70] were based on estimated water storage for the years 2005, 2010, and 2015, while the results from [71] provided annual relative water storage for the period of 2002 to 2015. For comparison, we considered water storage changes over three periods: 2010 vs. 2005, 2015 vs. 2010, and 2015 vs. 2005. As shown in Figure 10, our results align more closely with those from Yao [71]. While there is a strong correlation between our findings and those of Zhang [70], Zhang’s estimates tend to show a higher rate of change, even when compared to Yao’s results. This suggests that the results derived from more complete and continuous time series are likely more reliable than those based on time-slice data, which may be more susceptible to biases introduced by outliers.

Figure 10. Comparison of changes in relative lake water storage with existing studies. The results represented on the horizontal axis are from Yao [71], and those on the left (vertical) axis are from Zhang [70].

5.2. Uncertainty from Climate Data and Satellite-Based Observations

There are certain uncertainties in this study, due to the reliability of climate data and the satellite-based observations used. To examine the uncertainty introduced by meteorological data, we have compared the modeling results of LMJD, driven by two widely used climate datasets (ERA5-Land and CMFD) for hydroclimate research in the Tibetan Plateau. Figure 11 shows the two products have higher consistency in temperature (R² = 0.95) and potential evaporation (R² = 0.81) than in precipitation (R² = 0.58). ERA5-Land generally reports higher precipitation than CMFD. The inconsistency in the two climate datasets has led to slight differences in model performance. With CMFD as input, the NSE of the modeled water level at LMJD is around 0.93, outperforming modeling results based on ERA5-Land (NSE = 0.902). It can be observed that modeling results based on the two climate datasets are highly consistent, with an R² value of 0.91. However, it is important to note that the simulated lake levels using ERA5-Land are generally higher than those from CMFD, owing to the higher precipitation in ERA5-Land.

Figure 11. Comparison of monthly precipitation (a), potential evaporation (b), temperature (c), and simulated lake water level (d) between ERA5-Land and CMFD for Lumajiangdong Co (LMJD) during 1990–2018. In panel (d), the right axis represents satellite-observed lake water level.

It is important to note that uncertainties may also arise from the satellite-derived lake water levels and hypsometric curves. Since lake level observations are used to calibrate and validate the hydrological model, their quality can significantly influence model performance and simulation outcomes. Together with lake area data, the quality of lake level observations also affects the robustness of the fitted hypsometric curves, thereby introducing uncertainty into the estimation of lake water storage. Although the satellite-based datasets used in this study have demonstrated high reliability, careful quality control remains essential before applying them to assess water balance dynamics in a specific lake. In the future, the establishment of ground observation stations in key lake regions, combined with remote sensing data, could improve the accuracy of lake level and water volume monitoring, further optimizing the model calibration. Additionally, the use of multi-source remote sensing data (such as SAR, InSAR, and high-precision satellite altimetry data) will help improve the accuracy of lake boundary and water level extraction, reducing the uncertainty introduced by a single data source.

5.3. Applicability and Limitations of the Modeling Framework

In the recent two decades, substantial expansion of lakes has been observed in the Tibetan Plateau [46,72] owing to changes in lake water balance, which, however, has not been well investigated, particularly for regions with limited ground-based hydrological observations. In this study, a monthly hydrological model was developed and calibrated against satellite-based observations. The modeling framework performs satisfactorily in generating complete and continuous monthly time series of key water balance components, including lake water storage, water level, inflow, evaporation, and percolation. It enables the exploration of lake water balance dynamics under a changing climate in the northwestern Tibetan Plateau and across the entire plateau.

However, the current hydrological model is designed specifically for endorheic lakes. To apply it to exorheic lakes, modifications would be necessary, particularly to account for lake outflows. Additionally, due to data limitations, certain hydrological processes, such as lake evaporation and lake–groundwater interactions, are simplified in the present model. In the future, integrating this model with a lake energy balance model and a groundwater model could enhance its ability to quantify lake water balance dynamics.

6. Conclusions

This study investigates the dynamics of water balance of lakes in data-scarce regions such as the northwest Tibetan Plateau by incorporating a hydrological model with observations from multiple satellites. Satellite-based observations, including lake water area and water level, have been used to calibrate the hydrological model and to formulate the water storage model. The hydrological model performs satisfactorily, with an NSE exceeding 0.5 for all 15 lakes. This provides a robust foundation for investigating seasonal and inter-annual variations in lake water balance.

It is found that most studied lakes reach their highest water level and water storage in September and October, while the lowest level and storage is reached in April and May. Inflow contributes over 70% of annual water gain for most lakes, peaking during the wet months (May to October). Percolation accounts for a larger portion (>60%) of total water loss than evaporation in most lakes, but with lower seasonal variation. For the period 1990–2022, lakes in the northwest Tibetan Plateau generally exhibit a significant expansion trend, with an average increasing rate of 0.38 m/a in lake level and 3.12 × 10⁸ m³/a in water volume. Spatially, lakes in the northeastern part of the study area show higher increase rates compared to those in the southwestern part. Some lakes transitioned from shrinking to expanding around 1999, and expansion in most lakes has further accelerated since around 2012. Analysis of water budget components reveals that the increasing trends in lake water storage and level are primarily driven by increases in annual inflow, largely attributed to increased precipitation across the lake catchments, highlighting the considerable impact of climate change.

The method developed in this study provides important support for future research on assessing lake responses to a changing climate, though with uncertainties inherited from the model and satellite-based observations. By combining climate projection data with the improved model, the future changes in lake water balance can be predicted, providing scientific guidance for the development of climate change adaptation and ecological protection strategies.