A Hybrid ARIMA-CNN-LSTM Framework Based on Serial Decomposition for Non-Stationary Water Level Forecasting in Qinghai Lake

Abstract

Qinghai Lake, the largest endorheic saline lake in China, has undergone a pronounced hydrological regime shift from a multi-decadal decline to a rapid post-2004 recovery, reflecting strong hydroclimatic non-stationarity in the northeastern Tibetan Plateau (TP). This paper supplements the current water level and lake area status of Qinghai Lake to provide basic background for future prediction. Reliable forecasting of such climate sensitive lake systems remains difficult because conventional statistical models often fail to capture non-linear fluctuations, whereas standalone deep learning models may overlook long-term deterministic evolution. To address this challenge, we developed a serial decomposition GeoAI framework that integrates autoregressive integrated moving average (ARIMA), one-dimensional convolutional neural networks (1D-CNNs), and long short-term memory (LSTM) networks for non-stationary water level forecasting. Using annual water level observations from 1960 to 2025, the ARIMA component was first used to extract the low-frequency deterministic trend, after which the CNN-LSTM module reconstructed the nonlinear residual variability. The model was trained on the 1960–2012 period and validated over 2013–2025, which represents the most dynamic expansion stage of Qinghai Lake. The hybrid framework outperformed the benchmark models, achieving a Root Mean Square Error (RMSE) of 0.2033 m, Mean Absolute Error (MAE) of 0.1727 m, and Mean Squared Error (MSE) of 0.0413 m² during validation. The decomposition strategy effectively reduced phase lag and amplitude attenuation, improving both predictive accuracy and process interpretability. Multi-step forecasting for 2026–2056 suggests that Qinghai Lake will continue to rise, reaching approximately 3204.08 m by 2056, although the growth rate is projected to slow as negative hydrological feedback strengthen. By explicitly separating deterministic climate scale signals from nonlinear short-term variability, the proposed framework provides a robust and transferable geoinformation based tool for forecasting water level dynamics and supporting adaptive management in climate sensitive, data scarce lake basins.

1. Introduction

The Tibetan Plateau (TP), widely designated the “Asian Water Tower”, harbors the largest cryospheric reservoir outside the polar regions and constitutes a critical freshwater source supporting the water supply, ecological security and livelihood guarantee of more than 1.5 billion downstream populations in Asia [1,2]. This high-altitude region is exceptionally sensitive to global climate change; accelerating glacier retreat, permafrost degradation, and shifts in precipitation regimes are profoundly restructuring regional hydrology [3]. Within this vulnerable system, Qinghai Lake, China’s largest endorheic saline lake, stands as a key ecological sentinel [4]. It records the complex interactions between mid-latitude westerlies and the East Asian monsoon, whilst simultaneously serving as a critical hydraulic buffer that moderates the microclimate of the surrounding arid basins, and suppresses eastward desertification encroachment [5].

Qinghai Lake has undergone a pronounced non-stationary hydrological transformation, marked by a classic “V-shaped” regime shift [6]. Following a prolonged decline from 1960 to 2004 (a cumulative drop of 2.81 m at a rate of −0.062 m/a⁻¹), the lake entered a phase of rapid recovery beginning in 2005 [7]. Hydrological records through 2025 document a remarkable water level rise of 4.55 m, progressing at an accelerated average rate of 0.228 m/a⁻¹ [8,9]. The underlying mechanisms driving this expansion are firmly embedded within the regional warming–wetting paradigm. Intensified precipitation augmented glacial meltwater contributions, and modulated evaporation feedback collectively act to fundamentally alter the basin-wide water balance [10]. Satellite observations confirm the continuation of this expansive phase throughout the 2024 to 2025 observational window [11]. These highly asymmetric decadal dynamics underscore the profound sensitivity of the Qinghai Lake basin to ongoing climate forcing across the northeastern TP [12].

Accurate extended forecasting of water levels in non-stationary lacustrine systems remains a formidable scientific and operational challenge, as exemplified by the divergent hydrological trajectories of analogous closed-basin lakes worldwide [13,14]. The rapid desiccation of the Great Salt Lake, driven by combined climatic drying and anthropogenic diversions, illustrates the systematic underestimation of decline rates by conventional models [15,16]. The catastrophic shrinkage of the Aral Sea and the greater than 90% areal loss of Lake Chad since the 1960s further illuminate the difficulties of capturing nonlinear regime shifts within data sparse, climate sensitive environments [17,18]. These cases expose the fundamental limitations of existing predictive methodologies under non-stationary forcing [19]. Traditional statistical approaches such as autoregressive integrated moving average (ARIMA) effectively capture low-frequency deterministic trends but fail to resolve complex nonlinear interannual fluctuations [20]. Standalone deep learning architectures, while powerful, carry inherent algorithmic limitations: long short-term memory (LSTM) networks excel at modelling temporal dependencies but frequently over-smooth abrupt features [21]. Convolutional neural networks (CNNs) offer a complementary pathway through their proficiency in extracting localized temporal features, yet they inherently struggle to preserve prolonged evolutionary trajectories [22].

Existing hybrid models have improved hydrological forecasting performance; however, many still rely on output level weighted averaging or parallel architectures, which may conflate deterministic long-term trends with nonlinear short-term fluctuations [23,24]. Critically, these approaches do not explicitly decouple linear deterministic trends (representing long-term climate forcing) from nonlinear stochastic residuals (representing short-term extremes and local feedback) at the source [22,25]. Recent investigations published between 2020 and 2026 deploying integrated CNN-LSTM architectures for river discharge and groundwater level prediction confirm enhanced accuracy [26]. These same investigations simultaneously expose persistent vulnerabilities in managing spectral complexity and non-stationary regime shifts in the absence of foundational signal decomposition [27]. Despite these advances, a critical methodological gap persists: no existing hybrid framework has been specifically designed for endorheic high-altitude lakes exhibiting pronounced “V-shaped” regime shifts, where the dominant forcing transitions abruptly from a multi-decadal drying trend to a rapid warming driven recovery. The unique characteristics of Qinghai Lake a strictly closed water balance, severe non-stationarity, and data scarcity demand a framework that simultaneously anchors the deterministic climate trend and reconstructs stochastic residuals through physically interpretable decomposition, rather than relying on output level blending.

This study therefore introduces a novel Serial Decomposition Framework (SDF), building upon the recent successes of decomposition ensemble paradigms in hydrological sciences. The architecture integrates an ARIMA model with a coupled 1D-CNN and LSTM module. Our core hypothesis is that explicitly segregating the overarching linear trend (captured via ARIMA) from the nonlinear stochastic residuals (reconstructed by the CNN for localized feature extraction and the LSTM for long-term memory retention) will substantially enhance predictive fidelity and physical interpretability. The specific objectives are to: (1) develop and benchmark the hybrid model using long-term annual water level observations (1960–2025); (2) rigorously assess its superiority in reproducing the post-2005 rapid rise phase via an 80:20 chronological train validation split; (3) demonstrate that the decomposition strategy effectively mitigates phase lag and amplitude attenuation, thereby improving predictive accuracy and enabling process-level interpretation of the nonlinear residual variability; and (4) generate statistically robust projections for 2026–2056, elucidating mechanisms such as evaporation induced negative feedback that may moderate future ascent rates. This comprehensive methodology provides a robust and transferable tool for the adaptive management of climate-vulnerable lakes in data-scarce endorheic basins.

2. Data and Methods

2.1. Study Area

Qinghai Lake, located in a tectonic basin on the northeastern margin of the TP, is the largest endorheic saline lake in China and serves as an important ecological indicator and long-term hydrological archive of the high-altitude cryosphere [28]. The basin covers approximately 29,661 km², and the lake surface has a long-term mean elevation of 3197.62 m (Figure 1). Owing to its large geographical extent, Qinghai Lake acts as a critical hydraulic buffer, helping to restrain the eastward expansion of desertification from the arid and hyper-arid regions of Central Asia and to maintain the ecological stability of the northeastern plateau [29].

The Qinghai Lake Basin occupies a key hydroclimatic transition zone where the mid-latitude westerlies interact seasonally with the East Asian summer monsoon [30]. This atmospheric setting gives rise to a semi-arid continental climate characterized by strong spatiotemporal heterogeneity in both energy and moisture conditions [31]. As a hydrologically closed system with no surface or subsurface outflow, the water level is highly sensitive to variations in the basin water balance, reflecting the combined effects of precipitation input and evaporative loss [32]. Water inputs are derived mainly from direct precipitation over the lake surface and surface runoff from the surrounding mountainous catchment, particularly through the Buha and Shaliu Rivers, which are the two major tributaries of the basin. Open-water evaporation constitutes the only hydrological output. Therefore, fluctuations in Qinghai Lake water level represent more than local hydrological variability; they provide an integrated response to large-scale atmospheric circulation change and climate-driven cryospheric adjustment across the basin, making the lake a valuable natural indicator of climate change on the TP.

2.2. Data Sources and Pre-Processing

2.2.1. Water Level Data

A continuous record of annual mean water levels for Qinghai Lake from 1960 to 2025 was used in this study. This 66-year series represents one of the longest gauges based Xiashe hydrological datasets available for a high-altitude endorheic lake on the TP. The original water level data were derived from long-term in situ stage observations at the hydrological gauging station. Daily observations were aggregated into calendar year annual means, defined as the arithmetic mean of daily mean water levels from January to December of each year. The station conducts standardized hydrological stage observations, from which daily mean water level records are compiled. These daily records were archived by the Qinghai Provincial Hydrology and Water Resources Survey Bureau after routine quality control procedures, including datum consistency checking, missing record inspection, abnormal value screening, and temporal continuity verification.

The dataset covers the complete non-stationary hydrological evolution of Qinghai Lake, including the long-term decline during 1960–2004 and the rapid recovery during 2005–2025 (

Table 1. Descriptive statistics and trend analysis of annual mean water levels in Qinghai Lake from 1960 to 2025.

Period	N	Mean (m)	SD (m)	Min (m)	Max (m)	p-Value	Sen’s Slope (m/a−1)
1960–2025	66	3194.82	1.12	3193.51	3198.06	<0.001	+0.082
1960–2004	45	3194.63	0.85	3193.51	3196.32	<0.01	−0.062
2005–2025	21	3195.06	1.48	3193.62	3198.06	<0.001	+0.228

). It therefore provides a robust basis for assessing model performance under regime-shift conditions. To maintain temporal order and prevent data leakage, the series was divided chronologically into a training period (1960–2012, 53 years) and a validation period (2013–2025, 13 years). The post-2013 period, characterized by accelerated rise and enhanced interannual variability, was reserved entirely for independent validation to provide a stringent test of model performance under strongly non-stationary conditions. The training set includes both the decline phase and the initial recovery stage, ensuring that the model is exposed to the principal modes of regime evolution before validation.

2.2.2. Data Preprocessing and Quality Control

A three-stage preprocessing pipeline was applied to the raw annual water level time series to ensure data integrity, remove systematic measurement artefacts, and condition the input features for stable neural network training.

(1) Missing value imputation: The 66-year gauge record is largely continuous; however, sporadic data gaps attributable to instrument downtime or data transmission failures collectively account for less than 5% of the total series length. Given the strong temporal autocorrelation and smooth inter-annual evolution characteristic of lake water levels, linear interpolation between adjacent annual values was employed to fill these isolated gaps. This approach preserves the physical continuity and monotonic trend structure of the hydrological signal without introducing artificial variance inflation, consistent with standard practice for short-gap imputation in water level time series.

(2) Outlier detection and correction: At an annual temporal resolution, genuine hydrological extremes (e.g., anomalous meltwater pulses) manifest as gradual multi-year excursions rather than discrete single-year spikes. Consequently, isolated single-year anomalous values were attributed to instrument malfunction or data transmission errors rather than real hydrological events and were flagged for correction. The Thompson τ (Tau) test a modified two-tailed Student’s t-test adapted for sequential outlier detection was selected in preference to the Grubbs or Dixon tests because of its superior performance in identifying multiple simultaneous outliers within autocorrelated time series without inflating Type I error rates. Flagged observations were replaced by the arithmetic mean of their two temporally adjacent valid records, preserving local trend continuity. The normality assumption underlying the Thompson τ test was verified using the Shapiro–Wilk test prior to application. Formally, let X₁ ≤ X₂ ≤ … ≤ X_n be independent of each other, each coming from a normal population N (μ_i, σ²), i = 1, 2, …, n, where n is the number of data points for each variable.

(3) Feature normalization: To eliminate scale dependencies arising from the absolute magnitude of water level values and to ensure numerical stability during gradient-based optimization of the neural network components, each input feature was standardized to zero mean and unit variance via z-score normalization. Suppose there are m indicators x₁, x₂, …, x_m representing the characteristics of each object, and there are a total of N objects, represented by an N × m matrix, which is:

$$X_{N\times m}=\left[\begin{array}{ccc}{x}_{11}& \dots & x_{1m}\\ ⋮& \ddots & ⋮\\ x_{N1}& \dots & x_{Nm}\end{array}\right]$$

(1)

Subsequently, z-score normalization (central standardization) was applied to generate the standardized matrix Y:

$${x_{ij}}^{\mathrm{*}}={\displaystyle \frac{x_{ij}-{\overline{x}}_j}{s_j}}$$

(2)

In the formula, i = 1, 2, …, N, j = 1, 2, …, m, ${\overline{x}}_j$ and S_j are the mean and variance of the index variable x_j, respectively.

To eliminate scale dependencies arising from the absolute magnitude of water level values and to ensure numerical stability during gradient-based optimization, z-score normalization was applied using parameters estimated only from the training period. Specifically, the mean and standard deviation were calculated from the 1960–2012 training set:

$${\mu }_{train}={\displaystyle \frac{1}{n_{train}}}{\displaystyle \sum _{t=1960}^{2012}}{x}_t$$

(3)

$${\sigma }_{train}=\sqrt{{\displaystyle \frac{1}{n_{train}-1}}}{\displaystyle \sum _{t=1960}^{2012}}{(x_t-{\mu }_{train})}^2$$

(4)

All observations were then standardized as:

$${\mathcal{z}}_t={\displaystyle \frac{x_t-{\mu }_{train}}{{\sigma }_{train}}}$$

(5)

where $x_t$ is the observed annual mean water level and $z_t$ is the standardized value. The 2013–2025 validation period and the 2026–2056 forecasting period were transformed using the same ${\mu }_{train}$ and ${\sigma }_{train}$. No information from the validation or forecasting periods was used to estimate the normalization parameters. Predicted standardized values were converted back to water level units using the same training-derived parameters.

2.3. Methodology

2.3.1. The Hybrid ARIMA-CNN-LSTM Framework

This study proposes a hybrid Serial Decomposition Framework that explicitly decouples the multi-scale linear and nonlinear dynamics of the Qinghai water level series through a four-step sequential modelling pipeline (Figure 2). The architecture serially integrates an ARIMA model, a 1D-CNN, and an LSTM network, achieving full-spectrum signal reconstruction from deterministic trend to stochastic residuals. The rationale for serial rather than parallel integration is that sequential decomposition ensures each component models only the signal component appropriate to its inductive bias, preventing inter-scale interference:

Step 1: Data preprocessing and feature conditioning. The raw water level series undergoes the three-stage pipeline described in Section 2.2.2: missing value imputation via linear interpolation, outlier identification and correction via the Thompson τ test, and z-score standardization. The standardized series serves as the sole input to the ARIMA model in Step 2.

Step 2: Deterministic trend extraction (ARIMA). The ARIMA model incorporates autoregressive, moving average, and differencing operators to extract the low frequency deterministic trend component. The differencing operator (order d) removes the long-term memory of the hydrological regime shift; the AR and MA operators capture residual linear autocorrelation. The ARIMA residuals encapsulate the high-frequency stochastic component and are passed to Step 3. Optimal orders (p, d, q) are determined via stepwise AIC minimization (Section 2.3.2).

Step 3: Localized abrupt feature extraction (1D-CNN). The 1D-CNN is applied to ε_t with a receptive field (kernel size = 3 years) to identify abrupt multi-year excursions anomalous precipitation events, glacial meltwater pulses, and inter-decadal accelerations structurally invisible to linear models. Two causal convolutional layers (64 filters, ReLU) with MaxPooling and Dropout (0.2) compress the residual feature space before passing to Step 4, preventing short-term noise from contaminating the memory network.

Step 4: Non-linear residual reconstruction and long-term memory retention. The LSTM network utilizes its gating mechanisms comprising the input gate (i_t), forget gate (f_t), and output gate (o_t) to capture long-term temporal dependencies and nonlinear persistence within the residuals. This sequential coupling ensures the final ensemble preserves the broad climatic trajectory (C_t) alongside fine grained variations (h_t).

2.3.2. Model Implementation and Configuration

ARIMA model selection and diagnostics. Optimal ARIMA orders (p, d, q) were identified via a stepwise AIC-minimization search implemented in the pmdarima library (Python v 3.13). The selected configuration, ARIMA (2, 1, 1), incorporates two autoregressive lags (p = 2), one order of differencing (d = 1, physically consistent with the observed first order non-stationarity characterized by the V-shaped regime shift), and one moving average term (q = 1). Residual diagnostics confirmed model adequacy: the Ljung–Box portmanteau test (lags 1–10) yielded no significant autocorrelation (all p > 0.05), and the Shapiro–Wilk test confirmed approximate residual normality. The fitted ARIMA (2, 1, 1) trend component explained approximately 85% of total variance (R² = 0.85), providing a physically interpretable, climate-driven baseline for the subsequent residual modelling stage (

Table 2. Hyperparameter configuration for benchmarked models.

Model	Key Parameters
ARIMA	Orders: (p, d, q) = (2, 1, 1); Seasonal component: None; Selection criterion: AIC (stepwise search, pmdarima library); Residual diagnostics: Ljung–Box test (lags 1–10, all p > 0.05), Shapiro–Wilk normality (p > 0.05).
Standalone LSTM	Input window: 10-time steps (annual); LSTM units: 50; Activation: tanh; return_sequences: False; Dropout rate: 0.2; Optimizer: Adam (η = 0.001, β1 = 0.9, β2 = 0.999); Batch size: 8; Max epochs: 200; Early stopping: patience = 20 (monitor: validation MSE); Loss function: MSE; Input: z-score normalized water levels.
CNN-LSTM	Input: z-score normalized water levels (no ARIMA decomposition); Architecture: Input [batch, 10, 1] → Conv1D × 2 (64 filters, kernel = 3, ReLU, causal padding) → MaxPool1D (pool size = 2) → Dropout (0.2) → LSTM (50 units, tanh) → Dense (1 unit, linear activation); Optimizer, batch size, max epochs, early stopping: identical to Standalone LSTM.
ARIMA-CNN-LSTM	Stage 1: ARIMA (2, 1, 1): applied to the z-score normalized series; Stage 2: CNN-LSTM: same architecture as the CNN-LSTM row, applied to the re-normalized residuals. Final prediction: combined output from both stages.

).

CNN-LSTM architecture and training configuration. The module was implemented in Keras and TensorFlow (v2.x). An input window of 10 consecutive annual residual values was selected to encompass dominant decadal hydroclimatic cycles while retaining n = 43 training subsequences (from the 53-year training set). The architecture comprises five layers: (i) two causal 1D-Convolutional layers (64 filters, kernel size 3, ReLU) causal padding was adopted to prevent future information leakage; (ii) MaxPooling1D (pool size 2); (iii) Dropout (rate = 0.2) for regularization; (iv) a single-layer LSTM (50 units, tanh, return_sequences = False) outputting a single context vector; and (v) a Dense output layer (1 unit, linear activation). All components were trained using the Adam optimizer (η = 0.001, β₁ = 0.9, β₂ = 0.999), batch size 8, maximum 200 epochs, with early stopping (patience = 20) on validation MSE. To further avoid information leakage, residual normalization for the CNN-LSTM module was also performed using only the ARIMA residuals from the training period. The resulting residual mean and standard deviation were then fixed and applied to the validation and forecasting stages.

To reduce the risk of overfitting under the limited annual sample size, several constraints were imposed on the neural network architecture and training procedure. First, the CNN-LSTM module was applied only to the ARIMA residuals rather than to the original water level series, thereby reducing the complexity of the target signal learned by the neural network. Second, a compact architecture was adopted, consisting of two causal Conv 1D layers, one MaxPooling layer, one Dropout layer, one single layer LSTM, and one Dense output layer. Third, dropout regularization and early stopping were used to prevent excessive fitting to the training subsequences. Fourth, the independent test period was excluded from all training, hyperparameter tuning, and early stopping procedures.

This architecture embodies the core principle of the SDF: the CNN acts as a band-pass filter that selectively amplifies transient regime-shift signals, while the LSTM functions as an associative memory linking these patterns across the decadal temporal context. All hyperparameter configurations for benchmarked models are documented in Table 2 to ensure full reproducibility.

2.3.3. Model Robustness and Overfitting Control

Given the limited annual sample size, overfitting was explicitly evaluated using four diagnostics: (i) training and internal validation loss curves; (ii) the gap between training, internal validation, and independent test errors; (iii) repeated-run stability under different random seeds; and (iv) benchmark comparison against simpler models (

Table 3. Structural and regularization details of the three prediction models.

Model	Input Target	Main Neural Structure	Regularization Strategy
LSTM	Standardized water level	LSTM + Dense	Dropout, early stopping
CNN-LSTM	Standardized water level	Conv1D + LSTM + Dense	Causal convolution, dropout, early stopping
ARIMA-CNN-LSTM	ARIMA residuals	Conv1D + LSTM + Dense	ARIMA decomposition, dropout, early stopping

). The training and internal validation loss curves showed stable convergence without a persistent divergence between the two curves, indicating that the model did not continue fitting noise after the optimal epoch. Repeated run experiments further showed that the reported accuracy was stable across random initializations. The independent test errors remained close to the internal validation errors, suggesting that the model retained acceptable generalization ability. These results indicate that the performance improvement of the ARIMA-CNN-LSTM framework was mainly attributable to serial decomposition rather than excessive model complexity.

2.3.4. Performance Metrics

Trend analysis. The non-parametric Mann–Kendall (MK) test was applied to detect the presence, direction, and statistical significance of monotonic trends across three temporal windows: the full record (1960–2025), the declining phase (1960–2004), and the recovery phase (2005–2025). The MK test was selected over parametric alternatives because it requires no distributional assumption, is robust to outliers, and is widely adopted in hydroclimatic trend detection for non-stationary plateau lake series [6,9]. Sen’s slope estimator was applied in conjunction to quantify the magnitude of detected trends (m/a⁻¹). Significance was assessed at α = 0.01 and α = 0.001. Full derivations of the MK statistic S and its variance Var(S) are provided in (Supplementary Material File S1).

Model performance metrics. Three complementary error metrics characterize predictive fidelity during the 2013–2025 validation period (S2). The Root Mean Square Error (RMSE) penalizes large deviations quadratically and serves as the primary performance indicator, directly interpretable in native water level units (m). The Mean Absolute Error (MAE) provides a linear, outlier robust measure of average prediction bias. The Mean Squared Error (MSE) enables direct comparison with the training loss function and amplifies the contribution of extreme prediction errors. Reporting all three jointly follows established practice in alpine lacustrine and plateau hydrological forecasting studies, ensuring that model improvements are robust across different error-weighting schemes and directly comparable with the existing literature.

3. Results

3.1. Temporal Evolution Characteristics of Water Levels

Analysis of the 66-year observational record (1960–2025) reveals a pronounced non-stationary evolution in the water level dynamics of Qinghai Lake, defined by a two-phase V-shaped regime shift (Figure 3). The hydrological trajectory demarcates into two contrasting phases consisting of a period of persistent contraction followed by a phase of rapid expansion.

Phase I: Period of persistent contraction from 1960 to 2004. This initial phase witnessed a monotonic decline in the annual mean water level, dropping from 3196.32 m in 1960 to a historical nadir of approximately 3193.51 m by 2004. This period recorded a cumulative depletion of 2.81 m, corresponding to a mean recession rate of approximately 0.062 m per year. The MK trend test confirms that this downward trajectory is statistically significant at the 0.01 level (Z = −4.68, p < 0.01), indicating that the decline was driven by deterministic long-term trends rather than stochastic variability.

Phase II: Period of asymmetric rapid recovery from 2005 to 2025. The evolution of the lake transitioned into a distinct second regime characterized by rapid and sustained recovery from 2005 onwards. Following the inflection point around 2004, the water level rebounded sharply to reach 3198.06 m by 2025, representing a net elevation gain of 4.55 m from the minimum. The mean accretion rate during this phase reached +0.21 m/a, a value significantly exceeding the magnitude of the preceding decline rate. This asymmetry suggests a fundamental shift in the water budget equilibrium of the lake. The MK test applied to the subsequence following 2005 yields a highly significant upward trend (Z = 7.92, p < 0.001), further corroborating the critical role of the 2004 period as a pivotal node of regime shift.

3.2. Model Validation and Comparative Analysis

The complete annual water level series (1960–2025) was divided chronologically into three sequential subsets: a training set (1960–2006), an internal validation set (2007–2012), and an independent test set (2013–2025). The training set was used for parameter estimation, while the internal validation subset was used exclusively for hyperparameter tuning and early stopping during neural network training. The independent test period was fully excluded from model training, hyperparameter optimization, and model selection. Considering the strong temporal dependence and pronounced non-stationarity of the water level series, random k-fold cross validation was not adopted because it would disrupt the chronological structure of the data and could potentially introduce information leakage (i.e., using future data to tune the model). Instead, our strict chronological hold-out framework preserves temporal causality and evaluates the true extrapolation capability of the model. The same performance metrics (RMSE, MAE, MSE) were applied identically across all four models to ensure direct comparability.

The ARIMA-CNN-LSTM framework achieves the lowest error values across all metrics: RMSE = 0.2033 m, MAE = 0.1727 m, MSE = 0.0413 m² (Figure 4). The RMSE of 0.2033 m represents a mean absolute deviation below 0.07% of the observed water level range, demonstrating high-fidelity reconstruction. The MAE/RMSE ratio of 0.850 (close to unity) indicates that prediction errors are distributed approximately uniformly without catastrophic outlier events a critical property for operational water management, where reliability across all years matters as much as average accuracy. The MSE corroborates the absence of severe phase lags or peak attenuation, the two diagnostic failure modes of non-decomposition architectures.

Visual inspection of Figure 4a confirms accurate reproduction of both the deterministic upward trajectory and high-frequency interannual oscillations across the full validation window, including the rapid acceleration episodes of 2016–2019 and the variability-rich post-2020 segment. The SDF strategy eliminates the two most common failure modes: systematic phase lag (temporal offset between predicted and observed peaks) and amplitude attenuation (systematic under prediction of peak-to-trough magnitude). The statistical distribution analysis in Figure 4b further demonstrates probabilistic fidelity the hybrid model’s predictive mean and variance align closely with the observed distribution.

The benchmark comparison reveals a clear performance hierarchy that directly validates the SDF design rationale (Figure 5). Standalone ARIMA records the highest errors, exhibiting systematic underestimation attributable to its inability to represent nonlinear regime shift dynamics. Standalone LSTM improves upon ARIMA by exploiting temporal dependencies yet suffers from characteristic over-smoothing of high-frequency peaks. CNN-LSTM (without ARIMA decomposition) achieves intermediate performance, confirming that deep learning complexity alone is insufficient without foundational signal separation. Compared with the three baseline models, the proposed ARIMA-CNN-LSTM model reduced the root mean square error by 60% to 86% (Figure 5b–d), which indicates that the performance improvement is attributable to the decomposition strategy rather than the complexity of the model itself.

3.3. Decoupling Analysis of Linear and Nonlinear Components

This section dissects the internal mechanics of the SDF by quantifying the separation fidelity and residual reconstruction performance of each constituent component. The analysis proceeds in three stages: (i) assessment of the ARIMA trend extraction quality; (ii) characterization of the residual series properties following trend removal; and (iii) evaluation of the CNN-LSTM reconstruction capability. Together, these three stages provide direct evidence that the performance gains observed in Section 3.2 arise from the decomposition principle rather than from model complexity alone.

(i) ARIMA trend extraction quality. The fitted ARIMA (2, 1, 1) trend component captures the low-frequency, regime scale evolution with high fidelity, explaining R² = 0.85 (85%) of total variance in the 66-year record. The extracted trend accurately reproduces both the monotonic 1960–2004 decline and the post-2005 smooth recovery, confirming that d = 1 is well matched to the dominant non-stationarity. Critically, the 85% variance explained by a simple ARIMA (2, 1, 1) validates the SDF hypothesis that the dominant signal is deterministic and linearly structured, making explicit trend extraction the logical first step before deep learning residual modelling.

(ii) Residual series properties after trend removal. The residual sequence ${\epsilon }_t=y_t-{\widehat{y}}_t^{ARIMA}$ exhibits markedly improved stationarity ${\mu }_{ϵ}\approx 0$ and bounded variance, confirming successful background removal. The residuals encode high-frequency non-linear fluctuations spanning interannual to interdecadal timescales (τ = 1–10 years). A statistically significant amplitude expansion after 2010 is evident: the post 2010 residual standard deviation is approximately 40–60% larger than the pre-2010 value, indicating progressive amplification of the lake’s sensitivity to short-term forcing. This residual amplitude non-stationarity motivates using a trainable neural network rather than a fixed parametric model: the CNN-LSTM can adapt its feature extraction to the changing amplitude regime something a fixed parameter model cannot do.

(iii) CNN-LSTM residual reconstruction performance. The CNN-LSTM module reconstructs ε_t across both training (1960–2012) and validation (2013–2025) windows. The 1D-CNN functions as a learnable band-pass filter: its causal convolutional receptive fields (kernel = 3 years) selectively amplify abrupt multi-year excursions while attenuating white noise. The LSTM then integrates CNN encoded features across the 10-year temporal window, capturing inter event persistence and hysteresis in the non-linear lake response. The final ensemble prediction ${\widehat{y}}_t={\widehat{y}}_t^{ARIMA}+{\widehat{y}}_t^{CNN-LSTM}$ eliminates both the systematic underestimation bias of standalone ARIMA (which cannot capture the accelerating post-2013 rise) and the amplitude-attenuation bias of standalone LSTM (which over-smooths interannual residuals) confirming that both failure modes arise from the absence of explicit signal decomposition.

3.4. Future Trend Prediction

3.4.1. Projected Trajectory and Long-Term Magnitude

The calibrated integrated ARIMA-CNN-LSTM model was used to generate a 31-year multi step ahead projection of Qinghai Lake water levels spanning 2026–2056 (Figure 6). It is essential to characterize the epistemological scope of this projection: it represents an extrapolation of the intrinsic statistical structure of the historical water level series under a stationarity of couplings assumption, rather than a scenario-based climate model driven simulation derived from GCM outputs under prescribed emission pathways. Accordingly, the projection validity is conditional on the approximate stationarity of the historical hydroclimatic couplings in the near term, an assumption that is progressively less tenable at longer lead times and that constitutes the primary epistemic boundary of the present analysis.

Under this statistical framework, Qinghai Lake is projected to maintain a sustained upward trajectory throughout 2026–2056. Commencing from a projected 2026 level of 3198.12 m, the annual mean water level is expected to rise to approximately 3204.08 m by 2056 (Figure 6), representing a cumulative gain of +2.29 m over the 31-year projection window. Contextualizing this against the observed record: the projected 2056 level would surpass the historical 2025 maximum (3198.06 m) by 2.35 m. The projected mean rise rate of +0.074 m/a⁻¹ (2026–2056) represents a 67% deceleration relative to the 2005–2025 rate (+0.228 m/a⁻¹), directly manifesting the non-linear negative feedback discussed in Section 3.4.2.

3.4.2. Deceleration of Rise Rate and Equilibrium Dynamics

The most physically informative feature of the 2026–2056 projection is the progressive deceleration of the rise rate relative to the 2005–2025 recovery phase. This deceleration is not an artefact of the statistical model structure, but an emergent consequence of the non-linear residual dynamics captured by the CNN-LSTM component: as the lake surface expands, the evaporative feedback intensifies, progressively eroding the net positive water balance that drove the rapid post-2004 recovery.

The projected trajectory can be divided into two distinct phases. In the near term (2026–2035), levels rise from 3198.12 m to approximately 3198.70 m, at a mean rate of 0.058 m/a⁻¹. Over the medium-to-long term (2036–2056), the lake will cross the 3199.00 m threshold around 2040 and reach the 3200 m milestone by approximately 2051. This deceleration is driven by two coupled physical mechanisms. First, lake-surface evaporation feedback: as a closed basin, the lake’s only hydrological output is open-water evaporation, which increases with expanding lake area and gradually offsets precipitation and meltwater inputs. Second, the cryospheric memory depletion effect: under persistent warming, upstream glacier volumes diminish, weakening the meltwater pulse and reducing the surplus input that sustained the rapid lake-level rise from 2005 to 2025. Together, these processes steer the lake toward a new quasi-equilibrium state at a higher elevation.

3.4.3. Methodological Comparison and Ecological Implications

The projected deceleration trajectory directly illustrates the practical consequence of the SDF design. A pure linear extrapolation of the 2005–2025 trend (+0.228 m/a⁻¹) would project a 2056 water level of 3205.2 m an overestimation of 0.94 m relative to the SDF projection of 3204.08 m (Figure 6). This overestimation arises because monotonic extrapolation ignores the non-linear evaporative and cryospheric feedback constraints that the CNN-LSTM residual module explicitly encodes. The SDF projection preserves both the physically constrained deceleration in the trend component and the realistic interannual scatter in the residual component, yielding a more prudent, physically grounded and operationally useful projection envelope.

The projected entry of Qinghai Lake into a sustained high water level epoch by the 2050s carries significant implications: (i) shoreline inundation of low-lying alpine meadows and pastoral grasslands, with consequences for herding communities and road infrastructure already documented at current water levels; (ii) wetland expansion and habitat diversification along the lake periphery, beneficial for migratory waterfowl and endemic avifauna dependent on the Qinghai Lake Ramsar site; and (iii) regional hydrological redistribution, as a higher lake surface modifies local moisture flux and evaporative regime across the northeastern TP.

4. Discussion

4.1. Non-Stationarity, Regime Shifts, and Hydrological Responses

The water level sequence of Qinghai Lake from 1960 to 2025 exhibits pronounced non-stationarity, characterized by a distinctive V-shaped regime shift: a prolonged decline (1960–2004) followed by a rapid recovery (2005–2025). The descending phase recorded a cumulative drop of 2.81 m, primarily driven by reduced precipitation and enhanced evaporation. In contrast, the subsequent recovery phase witnessed a net increase of 4.55 m at an average rate of +0.228 m/a⁻¹, nearly four times the magnitude of the preceding decline. This asymmetric trajectory signifies a fundamental shift in the lake’s water balance, suggesting that Qinghai Lake not only responds to long-term climatic forcing but is also influenced by accelerated hydrological feedback mechanisms [33,34]. Notably, the marked increase in high frequency interannual variability after 2010 indicates heightened sensitivity to short-term perturbations, such as extreme precipitation events and glacial meltwater pulses, which have become more frequent under the regional warming-wetting trend [35,36].

These observations underscore the limitations of traditional hydrological models that rely on stationarity assumptions or simple linear extrapolations [37]. Models assuming a constant trend fail to replicate the magnitude and timing of such rapid transitions, often leading to underestimations of extremes or phase lags in response. Consequently, predictive frameworks for Qinghai Lake must accommodate multi-scale dynamics by integrating low-frequency deterministic trends with high-frequency non-linear fluctuations [38,39]. This dual phase evolution further reinforces Lake Qinghai’s role as a sensitive climate indicator within the Asian Water Tower [2], acutely reflecting regional cryospheric responses and intensified hydrological cycles.

4.2. Mechanistic Advantages of the ARIMA-CNN-LSTM Decomposition Framework

The main advantage of the proposed ARIMA-CNN-LSTM framework lies in its source-level decomposition of the water level signal before neural network reconstruction. The ARIMA component first extracts the low-frequency deterministic trajectory associated with long-term hydroclimatic forcing, while the CNN-LSTM module focuses on residual fluctuations related to short-term nonlinear responses. This structure reduces inter-scale interference and explains why the proposed model better reproduces the post-2013 accelerated rise phase than the standalone ARIMA, standalone LSTM, and non-decomposed CNN-LSTM models [40,41]. The ARIMA component captures the low frequency deterministic trend, accounting for approximately 85% of the total variance. This component directly reflects climate scale forcing, providing a level of physical interpretability often lacking in pure deep-learning approaches [42,43]. By removing this dominant trend, the residuals are transformed into a near-stationary series, thereby isolating high-frequency fluctuations associated with transient hydrological events.

Subsequently, the CNN-LSTM module reconstructs these residuals: The 1D-CNN extracts local features of abrupt changes, while the LSTM preserves long-term temporal dependencies and hydrological memory [44]. By sequentially modeling the trend and residuals, the framework mitigates interference between signals across different timescales, a common cause of the over-smoothing phenomenon observed in standalone deep learning models [45]. This decoupling strategy enhances both precision and physical consistency, aligning the model output with the underlying processes where the linear trend represents climate-driven evolution and residuals capture rapid non-linear responses [46]. The hybrid model achieved a 60–86% reduction in RMSE compared to baseline models, demonstrating that performance gains stem from a scientifically grounded decomposition strategy rather than mere model complexity.

4.3. Long-Term Projections and Scenario Sensitivity

Multi-step projections for 2026–2056 indicate a continued fluctuating upward trend, with the average water level projected to reach 3200.08 m by 2056. The projected rising rate of +0.20 m/a⁻¹ is slightly more moderate than the 2005–2025 period, suggesting the emergence of non-linear negative feedback likely related to increased evaporation from the expanded lake surface area [47]. Interannual fluctuations remain significant (approximately ±0.4 m), reflecting inherent hydrological variability across the TP [32,36].

Scenario analysis highlights the sensitivity of the trajectory to residual dynamics. An amplified high-frequency residual pushes the 2056 upper bound higher, whereas suppressed residuals lower the projection. These results emphasize that while short-term variability modulates the final water level, the overall upward trend persists under historical climatic assumptions. In contrast, linear extrapolation methods, which ignore the negative feedback and non-linear constraints inherent in closed lake systems, would likely yield unrealistic long-term estimates. Despite the model’s robustness, uncertainties remain, particularly regarding potential abrupt climatic shifts or anthropogenic interventions that could deviate from historical statistical relationships. Nevertheless, these projections provide a prudent estimate essential for adaptive management.

4.4. Implications for Hydrological Modeling and Management

This study offers key insights for modeling highly non-stationary water bodies. First, the explicit decomposition of linear and non-linear components significantly enhances both predictive accuracy and interpretability. Second, hybrid frameworks that fuse physics informed statistical models with deep learning modules can capture multi-scale dynamics that individual methods cannot.

From a management perspective, our findings suggest that Lake Qinghai is highly likely to maintain high water levels in the coming decades, influencing shoreline evolution and wetland expansion [48]. Planning based on linear projections faces risks of overestimation, whereas the hybrid model provides more conservative, physically consistent guidance. More broadly, this framework is transferable to other cold region, data scarce, and non-stationary hydrological systems, serving as a template for integrating physical interpretability with advanced data driven forecasting in a changing climate [49,50].

4.5. Limitations

A key limitation of this study is that the forecasting model is univariate and uses only historical annual water level observations as input. Although the observed water level dynamics integrate the cumulative effects of precipitation, evaporation, runoff, cryospheric processes, and human activities, the model does not explicitly include these variables. Therefore, the proposed framework should not be used to attribute water level changes to specific hydroclimatic drivers. Future work should incorporate precipitation, evaporation, temperature, runoff, glacier mass balance, lake area, and remote sensing-derived indicators to develop a multivariate or process informed forecasting framework capable of supporting causal interpretation. Additionally, a formal ablation test comparing ARIMA-LSTM with ARIMA-CNN-LSTM, which the current study did not perform due to sample size constraints and the auxiliary nature of the CNN module, could be considered in future research with larger datasets or higher-frequency observations. Furthermore, a more extensive benchmark comparison including other statistical models and decomposition-based hybrid models could be conducted in future studies to further evaluate the relative performance of the proposed framework. In the present study, lake area is not used as a model input; it is mentioned only as a contextual background and as a potential variable for future multivariate frameworks.

Furthermore, the long-term projection to 2056 does not incorporate future climate scenarios or external hydrological constraints; it is a conditional statistical extrapolation based on the historical series, and prediction intervals widen considerably at longer lead times. Readers should interpret the 2056 estimate as a central tendency within a growing uncertainty envelope, not as a deterministic endpoint.

Although the calendar year aggregation is suitable for long-term annual water level forecasting, an October–September hydrological year (spanning the snow accumulation period from October to April of the following year) may be more appropriate for studies focusing on snow accumulation, snowmelt runoff, or seasonal water balance processes in high-altitude basins. Future work based on monthly or seasonal observations should compare calendar year and hydrological-year aggregation schemes to assess their influence on forecasting performance and hydrological interpretation.

5. Conclusions

Qinghai Lake, the largest endorheic saline lake in China, has undergone a pronounced hydrological regime shift from a multi-decadal decline to a rapid post-2004 recovery, reflecting strong hydroclimatic non-stationarity in the northeastern Tibetan Plateau. Reliable forecasting of such climate sensitive lake systems remains difficult because conventional statistical models often fail to capture nonlinear fluctuations, whereas standalone deep learning models may overlook long-term deterministic evolution. To address this challenge, we developed a serial decomposition GeoAI framework that integrates ARIMA, 1D-CNN, and LSTM networks for non-stationary water level forecasting.

(1) Using annual water level observations from 1960 to 2025, the ARIMA component was first used to extract the low-frequency deterministic trend, after which the CNN-LSTM module reconstructed the nonlinear residual variability. The model was trained on the 1960–2012 period and validated over 2013–2025, which represents the most dynamic expansion stage of Qinghai Lake. The hybrid framework outperformed the benchmark models, achieving an RMSE of 0.2033 m, an MAE of 0.1727 m, and an MSE of 0.0413 m² during validation.

(2) The decomposition strategy effectively reduced phase lag and amplitude attenuation, improving both predictive accuracy and process interpretability. Multi-step forecasting for 2026–2056 suggests that Qinghai Lake will continue to rise, reaching approximately 3204.08 m by 2056, although the growth rate is projected to slow as negative hydrological feedback strengthen. By explicitly separating deterministic climate scale signals from nonlinear short-term variability, the proposed framework provides a robust and transferable geoinformation based tool for forecasting water level dynamics and supporting adaptive management in climate sensitive, data scarce lake basins.