Scale knowledge guided deep learning for simulating ecosystem carbon fluxes

<sec><p indent="0mm">Deep learning methods have increasingly been applied to simulate carbon fluxes in terrestrial ecosystems, owing to their superior fitting capabilities for complex systems. However, widely used “end-to-end” modeling frameworks, while effective at capturing seasonal variations in net ecosystem carbon exchange (NEE), tend to underestimate the magnitudes of interannual variability. This limitation may stem from spectral bias during the training process, as these models primarily rely on raw observational signals and tend to prioritize smoother temporal components of the time series data. To improve the accuracy of deep learning models for estimating ecosystem carbon fluxes, this study aims to clarify how the modeling frameworks contribute to uncertainties in carbon flux modeling. </sec><sec> This study introduces a novel “knowledge-guided” modeling framework that leverages prior knowledge about the memory effects of ecosystems and the distinct responses of NEE at seasonal and interannual scales. By integrating nonparametric Singular Spectrum Analysis (SSA), this framework facilitates the temporal decomposition of seasonal and interannual signals, thereby guiding the modeling of unique NEE responses across timescales. The recurrent neural network Long Short-Term Memory (LSTM) is employed to capture the cumulative impacts of climate change and accurately represent state changes within the ecosystem. Utilizing observational data from FLUXNET sites, the study conducts validations across various ecosystems. Performance assessments demonstrate that the implemented LSTM model effectively captures the nonlinear responses of NEE to meteorological factors, outperforming baseline models, including LASSO regression, Random Forest, Support Vector Machines, and Feedforward Neural Networks. Simulations based on historical climate conditions also reveal that the “end-to-end” LSTM model overlooks NEE responses at the interannual scale, while the “knowledge-guided” models better reproduce both seasonal and interannual variations. According to SHAP (SHapley Additive exPlanations) values derived from these models, radiation and temperature are identified as the driving factors for both the “end-to-end” LSTM and seasonal LSTM models. Therefore, the “end-to-end” deep learning framework is predominantly driven by seasonal processes, while the “knowledge-guided” models improve the representation of scale-specific patterns under the guidance of scale knowledge. </sec><sec> The distinct mechanisms of NEE response across scales can be further elucidated through the “knowledge-guided” models. Cross-scale experiments and wavelet analyses reveal significant differences in the NEE response patterns captured by seasonal versus interannual LSTM models. Using a seasonal model to simulate interannual variations or an interannual model for seasonal changes leads to inaccuracies in signal properties such as amplitude, resonance periods, and phase, ultimately resulting in degraded performance. According to SHAP values derived from “knowledge-guided” models, radiation and temperature are identified as primary drivers of seasonal NEE changes, accounting for 46.9% and 24.5% of seasonal variation, respectively. At the interannual scale, temperature emerges as the most influential factor, contributing 24.5% to changes, while the contribution of radiation decreases to 21.1%. Additionally, the contributions of precipitation, vapor pressure deficit (VPD), and wind speed all exceed 15%. Factorial simulations conducted with the trained “knowledge-guided” models reveal the synergistic effects of rising temperature and radiation on seasonal NEE, while the interactions at the interannual scale prove to be more complex. These findings underscore the importance of integrating prior knowledge into deep learning models to mitigate uncertainties and enhance interpretability. Overall, this study optimizes the modeling framework of deep learning models to enhance their fitting capabilities for NEE responses at different timescales, providing effective numerical simulation methods and analytical tools for assessing the impact of climate change on the terrestrial carbon cycle. </sec>