Physics-Informed Graph Neural Networks for Evapotranspiration Projection under Climate Variability = 물리 정보 기반 그래프 신경망 접근을 통한 기후 변동성 하에서의 증발산량 예측

다국어 초록 (Multilingual Abstract)

Title: Physics-Informed Graph Neural Networks for Evapotranspiration Projection under Climate Variability. This dissertation develops and validates a physics-informed, teleconnection aware spatio-temporal graph neural network (ST-GNN) for the prediction of evapotranspiration (ET) across the Korean Peninsula, quantifying uncertainty, and the projection of future ET under CMIP6 scenarios. The framework integrates physical constraints from the surface energy balance, dynamic graph learning across a dense meteorological station network, and an El-Nino Southern Oscillation (ENSO) aware attention mechanism that is seasonally synchronized and modulated by coastal distance. Comprehensive experiments show that the proposed model consistently improves accuracy, physical consistency, and interpretability relative to both traditional and deep learning baselines. The study targets station level ET prediction using historical meteorological drivers including maximum and minimum air temperature (tasmax, tasmin), relative humidity (RH), shortwave and longwave radiation (rsds, rlds), and near surface wind speed (sfcwind), with soil moisture (sm) incorporated to better represent water- limited regimes. The dataset covers multiple years with 372 stations distributed across coastal and inland regions of the Korean Peninsula. Multiple graph encoders (Graph Convolution Network [GCN], Graph Sample and Aggregate [GraphSAGE], Graph Attention [GAT], Graph Isomorphism Network [GIN], and Message Passing Neural Network [MPNN]) and temporal architectures (Gated Recurrent Unit [GRU], Long Short Term Memory [LSTM]) are evaluated, alongside non-graph baselines such as the Penman–Monteith (PM) equation, Convolution Neural Network (CNN) +LSTM, a Temporal Transformer, and MODIS16 ET products. The core model architecture combines a spatial graph encoder (best performing: GraphSAGE) with a GRU-based temporal unit. Graph edges are constructed using both geographic proximity and statistical correlation, and in certain experiments, physically motivated decay functions such as the thermal advection based kernel and coastal attenuation were used to account for spatial teleconnection patterns. A physics-informed loss function constrains the model using the surface energy balance by linking ET to available net radiation (latent heat flux), thus improving physical realism, drought response, and extrapolation capacity. To capture remote climatic influences, an ENSO aware attention mechanism is introduced. This mechanism injects the Niño 3.4 anomaly into the attention computation with a seasonally synchronized cosine gating function, allowing the model to dynamically adjust inter station dependencies based on the ENSO phase and time of year. Lagged teleconnection effects are modeled through an exponential kernel that distributes influence across lead–lag windows. Analytical results show a coastal intensification of ENSO sensitivity and an asymmetric lag structure, with ET responding strongest when ENSO leads by one to six months, particularly for stations within 100 km of the coastline. The full modeling structure includes data standardization, sequence preparation, and graph construction. Hyperparameters such as hidden dimensions, number of layers, dropout rates, learning rate, and teleconnection kernel parameters were optimized using Optuna. Predictive uncertainty is quantified through the Monte Carlo (MC) dropout, and calibration is achieved through an isotonic regression. Model evaluation uses both deterministic (Mean Absolute Error [MAE], Root Mean Squared Error [RMSE], R2) and probabilistic metrics (Continuous Ranked Probability Score [CRPS], Prediction Interval Coverage Probability [PICP], Mean Prediction Interval Width [MPIW]). Training and validation loss curves show stable convergence and negligible overfitting, while residual distributions are nearly Gaussian, centered around zero. Model interpretability is examined at several levels. Two-dimensional T-Stochastic Neighbourhood Embeddings (t-SNE) of final step node representations form distinct spatial clusters, confirming that the GNN learns meaningful hydroclimatic organization. Feature importance analyses via Permutation Feature Importance (PFI) and SHAP consistently identify tasmax, RH, and rsds as dominant variables, emphasizing the dual control of energy and moisture availability on ET. When soil moisture is included, residuals stratified by quartile show reduced bias and variance, validating its role in capturing water limited processes. Edge structure ablations demonstrate that hybrid geographic/statistical graphs outperform purely distance-based or correlation-based structures, and that physically motivated decay kernels enhance teleconnection sensitivity, particularly under ENSO-active conditions. Lag correlation analyses between attention scores and Niño 3.4 anomalies re- veal maximum correlation when ENSO leads ET, peaking at about one month lag for coastal nodes. Seasonal attention curves show distinct regimes for El Niño, La Niña, and Neutral phases, confirming that the seasonal gating mechanism successfully modulates teleconnection influence. Distance-binned analyses further demonstrate the gradual inland decay of ENSO sensitivity, consistent with physical coastal advection processes. The complete Physics-Informed GraphSAGE+GRU model with ENSO gating and seasonal synchronization achieves the highest accuracy among all configura- tions. Across test stations, it reduces RMSE by more than 30% compared to the base ST-GNN and achieves an R2 exceeding 0.99, outperforming the PM, CNN+LSTM, Temporal Transformer, and MODIS16 approaches. Incremental ablations show consistent performance gains from adding the physics-informed loss, ENSO attention, and seasonal synchronization, confirming the complementary value of each enhancement. Future projections under CMIP6 scenarios (SSP2–4.5 and SSP5–8.5) reveal an increase in mean ET, with markedly higher interannual variability under the high emission SSP5–8.5 scenario. The largest increases occur in northern and interior regions, consistent with amplified warming and evaporative demand. The coefficient of variation of annual ET, computed across stations and GCMs, is higher under SSP5–8.5, indicating intensified hydroclimatic variability. Latitudinal analyses show poleward intensification of ET trends under warming, and model specific patterns (presented in Appendix A) confirm the robustness of these tendencies across GCMs. This work makes several contributions. First, it presents a unified, physics- informed, teleconnection-aware ST-GNN framework that captures both local spatio- temporal dynamics and remote ENSO influences. Second, it enhances interpretability through multi level diagnostics: embedding visualization, feature attribution, teleconnection lag analysis, and calibrated uncertainty quantification. Third, it establishes methodological rigor by combining physically consistent loss constraints with data driven deep learning in a unified structure. Finally, it provides credible future ET projections that align with established hydrometeorological understanding, offering new insight into how warming and teleconnections jointly modulate evaporative processes in East Asia. The findings have practical implications for hydrological forecasting, agricultural water management, and climate risk planning. Increasing ET and variability imply higher irrigation demands and more frequent evaporative stress events, especially during strong ENSO phases. The teleconnection-aware design demonstrates that incorporating exogenous indices such as Niño 3.4 enhances predictive skill, suggesting that operational ET forecasting systems should adopt regime-aware and lag-sensitive drivers. The hybrid physical graph design also offers a generalizable template for other climate variables that exhibit spatially coherent but teleconnected patterns. Despite its success, the framework has limitations. Model performance depends on station data coverage and quality, as well as on the fidelity of downscaled GCM predictors. The physics-informed constraint simplifies certain processes such as ground heat flux and aerodynamic resistance, and only ENSO was explicitly rep- resented among teleconnections. Future work could extend this to include the Pacific Decadal Oscillation (PDO), Indian Ocean Dipole (IOD), and Arctic Oscillation (AO), as well as develop multi-teleconnection gating mechanisms and causal graph rewiring strategies. More sophisticated formulations, such as multi-modal components or coupled land–ocean GNN architectures, would further strengthen process fidelity. In summary, this dissertation advances the state of evapotranspiration model- ing by combining the strengths of physics based reasoning, graph neural architectures, and teleconnection aware learning. The proposed framework achieves high accuracy, strong physical coherence, and rich interpretability, making it a robust tool for present and future hydroclimate analysis. By uniting machine learning, physical constraints, and large-scale climate connectivity, the study contributes both methodological innovation and practical insight into the evolving dynamics of land/atmosphere interactions in a warming world.

목차 (Table of Contents)

• 1 Introduction 1
• 1.1 Motivation 1
• 1.2 Research Questions 4
• 1.3 Problem Statement and Objectives 5
• 1.4 Contributions 8
• 1.5 Thesis Structure 10
• 2 Theoretical Foundations 13
• 2.1 Fundamentals of Graph Theory 13
• 2.1.1 Graph Definition and Basic Terminology 13
• 2.1.2 Adjacency and Degree Matrices 14
• 2.1.3 Graph Laplacian and Its Properties 14
• 2.1.4 Spectral Decomposition and Graph Fourier Transform 15
• 2.1.5 Normalized Adjacency and Propagation Operators 15
• 2.1.6 Graph Connectivity and Spectral Properties 16
• 2.1.7 Weighted and Spatio-Temporal Graphs in Environmental Ap-
• plications 16
• 2.2 Neural Network Fundamentals 17
• 2.2.1 Feedforward Neural Networks 17
• 2.2.2 Activation Functions 18
• 2.2.3 Loss Functions and Optimization 18
• 2.2.4 Gradient-Based Learning and Backpropagation 18
• 2.2.5 Regularization and Generalization 19
• 2.2.6 Convolutional and Recurrent Extensions 20
• 2.2.7 Universal Approximation and Expressivity 20
• 2.2.8 Relevance to Graph Neural Networks 21
• 2.3 Graph Neural Network Formulation 21
• 2.3.1 General Message Passing Framework 21
• 2.3.2 Graph Convolutional Network 22
• 2.3.3 GraphSAGE 22
• 2.3.4 Graph Attention Network 23
• 2.3.5 Graph Isomorphism Network 23
• 2.3.6 Message Passing Neural Network 24
• 2.3.7 Unified Matrix Formulation 24
• 2.3.8 Integration in Spatio-Temporal Framework 24
• 2.3.9 Summary 25
• 2.4 Teleconnection Representation and ENSO Dynamics 25
• 2.4.1 Attention-Based Teleconnection Framework 25
• 2.4.2 Seasonal Synchronicity Modulation 26
• 2.4.3 Distance-Weighted Attention with Physical Decay 26
• 2.4.4 Thermal-Advection Decay Kernel 27
• 2.4.5 Teleconnection-Aware Attention Update 28
• 2.4.6 Physical Interpretation 28
• 2.4.7 Summary 29
• 2.5 Physics-Informed Constraints 29
• 2.5.1 Physical Background: Surface Energy Balance 29
• 2.5.2 Physics-Based Regularization Losses 30
• 2.5.3 Graph-Level Physical Consistency 30
• 2.5.4 Summary 30
• 2.6 Uncertainty Quantification and Calibration 30
• 2.6.1 Sources of Uncertainty 31
• 2.6.2 Monte Carlo Dropout 31
• 2.6.3 Prediction Intervals and Coverage Metrics 31
• 2.6.4 Isotonic Regression Calibration 32
• 2.6.5 Evaluation Metrics 32
• 2.6.6 Interpretation 33
• 2.6.7 Summary 33
• 3 Data and Preprocessing 34
• 3.1 Study Area and Station Network 34
• 3.2 Data Sources and Description 35
• 3.2.1 Historical Reference Data 35
• 3.2.2 CMIP6 Climate Projections 37
• 3.2.3 Teleconnection Data 37
• 3.3 Data Cleaning and Quality Control 38
• 3.4 Feature Engineering and Normalization 38
• 3.4.1 Spatial and Temporal Features 38
• 3.4.2 Standardization 39
• 3.4.3 Dimensional Consistency 40
• 3.5 Temporal Sequence Preparation 40
• 3.5.1 Sequence Windowing and Sliding Strategy 41
• 3.5.2 Incorporation of Seasonal and Lagged Information 41
• 3.5.3 Sequence Normalization and Tensorization 42
• 3.5.4 Train–Validation–Test Partitioning 42
• 3.5.5 Summary 43
• 4 Physics-Informed ST-GNN Framework for ET Prediction 44
• 4.1 Introduction 44
• 4.2 Evapotranspiration Modeling Approaches 44
• 4.2.1 Empirical and Analytical Methods 44
• 4.2.2 Satellite- and Remote-Sensing-Based ET 45
• 4.2.3 Data-Driven and Hybrid Models 46
• 4.3 Deep Learning in Climate and Hydrology 47
• 4.3.1 Convolutional and Recurrent Architectures 47
• 4.3.2 Limitations for Irregular Climate Networks 48
• 4.4 Graph Neural Networks in Environmental Sciences 50
• 4.4.1 Early Developments 50
• 4.4.2 Applications in Environmental Modeling 50
• 4.4.3 Challenges and Gaps 51
• 4.5 Core Methodological Components 52
• 4.5.1 Graph Construction 52
• 4.5.2 Spatial Graph Encoder 54
• 4.5.3 Unified Spatial Representation 55
• 4.5.4 Summary 56
• 4.6 Temporal Modeling 56
• 4.6.1 Temporal Input Representation 56
• 4.6.2 GRU 57
• 4.6.3 LSTM 57
• 4.6.4 Fusion and Output of Temporal Encoder 58
• 4.7 Physics-Informed Loss Formulation 58
• 4.7.1 Data Fidelity Loss 58
• 4.7.2 Energy Balance Principle 59
• 4.7.3 Physics-Informed Energy Balance Loss 59
• 4.7.4 Physical Interpretation and Advantages 60
• 4.8 Training Strategy and Optimization 60
• 4.8.1 Training Workflow 60
• 4.8.2 Optimization Procedure 61
• 4.8.3 Hyperparameter Optimization with Optuna 61
• 4.8.4 Regularization and Uncertainty Estimation 62
• 4.8.5 Early Stopping and Convergence Criteria 62
• 4.8.6 Summary 62
• 4.9 Experimental Setup and Results 63
• 4.9.1 Training Configuration and Computational Environment 63
• 4.9.2 Hyperparameter Optimization via Optuna 64
• 4.10 Model Architecture and Optimizer Comparison 65
• 4.10.1 Architectural Performance Evaluation 65
• 4.10.2 Optimizer Evaluation and Convergence Behavior 67
• 4.11 Uncertainty Quantification and Calibration 68
• 4.12 Embedding Interpretability 69
• 4.13 Temporal and Spatial Model Performance 71
• 4.14 Spatial Validation and Feature Importance Analysis 73
• 4.14.1 Variable Importance and Sensitivity Assessment 74
• 4.15 Role of Soil Moisture in ET Prediction 75
• 4.15.1 Feature Importance with SM Inclusion 77
• 4.15.2 Impact of Edge Structure on Model Performance 78
• 4.16 Summary 79
• 5 Enso Teleconnection Integration 80
• 5.1 Physics Information (hard constraints) 81
• 5.1.1 Uncertainty Quantification and Calibration in the ENSO-Aware
• Framework 82
• 5.2 Core Methodological Components 83
• 5.2.1 ENSO-Aware Dynamic Attention Mechanism 83
• 5.2.2 Base Graph Attention Formulation 84
• 5.2.3 ENSO-Aware Attention Modulation 85
• 5.2.4 Seasonal Synchronization Term 85
• 5.2.5 Decay Function Integration 85
• 5.2.6 Full Dynamic Attention Mechanism 86
• 5.2.7 Interpretation and Physical Relevance 87
• 5.2.8 Summary 88
• 5.3 Results 88
• 5.3.1 Effect of ENSO Integration and Seasonal Synchronization 88
• 5.3.2 Model Performance under Different ENSO Regimes 89
• 5.4 Temporal and Comparative Analysis of ENSO-Integrated Models 90
• 5.4.1 Spatial Attenuation of ENSO Influence and Coastal Decay
• Analysis 91
• 5.5 Temporal and Spatial Dynamics of ENSO Teleconnections 94
• 5.5.1 Lagged Relationship between ENSO Index and AttentionWeights 94
• 5.5.2 Seasonal Synchronization of ENSO-Regime Attention 95
• 5.5.3 Spatial Intensification and Distance Decay of ENSO Effects 96
• 5.6 Summary 97
• 6 Future Projections 99
• 6.1 Future Projections of ET under Climate Scenarios 99
• 6.1.1 Projected Temporal Trends and Interannual Variability 99
• 6.1.2 Spatial and Model-Specific Variability 100
• 6.1.3 Latitudinal Dependence and Zonal Gradients of Future ET 101
• 6.2 Comparative Analysis of Annual Evapotranspiration Dynamics Un-
• der ENSO and Non-ENSO Configurations 102
• 6.2.1 General Temporal Patterns Across Scenarios 102
• 6.2.2 Evaluation Against Physically Based PM ET 103
• 6.2.3 Impact of ENSO Integration 103
• 6.2.4 Scenario-Specific Differences 103
• 6.2.5 Implications for ET Modeling and Climate Impact Assessment 104
• 7 Discussion and Conclusion 106
• 7.1 Discussion 106
• 7.2 Conclusion 107
• 7.3 Future Work 107
• 7.4 Limitations 108
• 7.5 Overall Synthesis 109
• References 110
• A Additional figures and tables 120
• B GCM-Specific Future Projections 127
• C Detailed Derivations and Proofs 132
• C.1 Derivation of the Seasonal Synchronicity Modulation 132
• C.1.1 Notation and Objective 132
• C.1.2 Fourier/Least–Squares Derivation (First Harmonic) 132
• C.1.3 Probabilistic Derivation (von Mises Approximation) 133
• C.1.4 Mean-One Normalization and Positivity 133
• C.1.5 Differentiability and Gradients (for Learning) 134
• C.1.6 Insertion into Attention and Normalization 134
• C.1.7 Summary (Result Used in the Main Text) 135
• C.2 Energy-Balance Scaling: Relating ET [mm day−1] to Latent Heat [W
• m−2] 135
• C.2.1 Background and Definitions 135
• C.2.2 Derivation of the κ Factor 136
• C.2.3 Dimensional Consistency (Proof) 137
• C.2.4 Numerical Values and Sensitivity 137
• C.2.5 Practical Conversions 137
• C.2.6 Notes on Special Cases and Constants 138
• C.2.7 Summary 138
• C.2.8 Lookup Table for κ(T ) 138
• Korean Abstract 139
• Acknowledgements 143