Consecutive one-week model predictions of land surface temperature stay on track for a decade with chaotic behavior tracking

The study addresses whether weekly land surface temperatures can be predicted accurately over decadal horizons despite inherent chaotic dynamics. Decadal-scale temperature forecasts support planning in agriculture, health, and biodiversity conservation, where week-level variability strongly influences decisions. Traditional simulation-based approaches (NWP, GCM, and CMIP ensembles) face uncertainty amplification due to sensitivity to initial conditions and require frequent calibration and substantial computational resources. Pure machine learning methods, while strong for short-term prediction, typically suffer from exponential error accumulation when rolled out without frequent access to ground truth. The authors propose a data-driven approach that augments a dependency learning component with an information tracking component that provides probabilistic feedback on next-step error based on first-order differences, aiming to mitigate error growth and enable stable decadal predictions at weekly resolution.

Simulation-based models (NWP and GCM) have evolved since the 1970s, integrating ocean, land surface, hydrology, and vegetation components. Ensemble methods quantify forecast uncertainty but are computationally intensive and rely on frequent calibration, which is challenging for decade-long forecasts. CMIP provides state-of-the-art ensemble simulations but shares these limitations. ML-based approaches have shown competitive short-term skill but typically degrade over long horizons due to error accumulation. Hybrid workflows combine ML with dynamical models for pre/post-processing or component replacement, improving resolution or blending predictions, but remain sensitive to initial conditions and computational costs. These gaps motivate a new ML-based design that explicitly tracks uncertainty and dynamics to control long-horizon error growth.

Data: Global Daily Land (Experimental; 1880–Recent) dataset from Berkeley Earth at 1°×1° resolution; daily data aggregated to weekly averages. Training period: 1880–2010; prediction target: 2011–2020 (ten-year-ahead). A complementary five-year-ahead setting uses training through 2015 and testing 2016–2020. All locations are modeled jointly: at time i, x_i ∈ R^N contains temperatures at all N land grid cells. First-order difference is Δx_{i+1} = x_{i+1} − x_i. Inputs are sliding windows X_i comprised of d previous steps; d∈{30,40,50} with exhaustive search selects d=50. Model: Two components, both based on MLPs. The dependency learning component (DLC) is a five-layer MLP (input, three hidden, output) with ReLU activations that predicts ŷ_i. The information tracking component (ITC) uses an encoder (same structure as DLC) to produce a hidden representation r_i, from which two one-layer MLPs output μ = NN_μ(r_i) and σ = NN_σ(r_i) parameterizing a normal distribution N(μ,σ). A latent vector z ~ N(μ,σ) is fed to a one-layer decoder MLP to generate the feedback Δx̂_i that estimates the next-step prediction error (supervised by the true first-order difference). The final prediction is O_{i+1} = ŷ_{i+1} + Δx̂_{i+1}. During training, the sum of DLC and ITC outputs is supervised by the ground truth temperature; ITC is additionally supervised by the true first-order difference. The overall loss sums squared errors for temperature and first-order differences plus a KL divergence regularizer: ∑_i (||x_{i+1} − x̂_{i+1}||_2^2 + ||Δx_{i+1} − Δx̂_{i+1}||_2^2) + D_KL(N(μ,σ)||N(0,1)). Prediction: No ground truth is used at inference. A warm-up window uses part of training data to seed the first d steps. Thereafter, predictions are generated autoregressively, with both DLC and ITC taking the previous prediction O_{i−1} as input. The ITC continues to provide next-step probabilistic feedback Δx̂_i by sampling from N(μ,σ) parameterized by the current encoded state r_i, which is then added to DLC’s output to form O_i. Evaluation: Metrics include mean absolute error (MAE), root mean squared error (RMSE), and dynamic time warping (DTW) to assess both pointwise error and temporal shape similarity. Baselines include VMD-ARIMA, MLP, GRU, LSTM, Informer, and CMIP models (CanCM4 for ten-year-ahead and CanESM5 DCPP for five-year-ahead, reporting member r1i1p1l).

- The proposed method achieved the lowest errors among all baselines for global weekly land surface temperature prediction over a decade and five years. Ten-year-ahead (2011–2020) global results (MAE/RMSE/DTW): • Proposed: 1.829 / 2.375 / 2.141 • Informer: 7.823 / 9.260 / 14.433 • MLP: 9.446 / 11.301 / 33.656 • LSTM: 10.293 / 12.530 / 52.527 • GRU: 12.000 / 15.346 / 48.679 • CMIP (CanCM4): 9.798 / 13.505 / 22.819 • VMD-ARIMA: 12.044 / 15.123 / 53.671 Five-year-ahead (2016–2020) global results (MAE/RMSE/DTW): • Proposed: 2.177 / 2.806 / 1.437 • Informer: 8.311 / 9.851 / 4.902 • MLP: 9.382 / 11.171 / 15.946 • LSTM: 10.329 / 12.707 / 25.663 • GRU: 12.367 / 15.889 / 24.681 • CMIP (CanESM5 DCPP): 10.281 / 13.901 / 12.213 • VMD-ARIMA: 11.348 / 14.230 / 24.832 - Visual comparisons for weeks in 2020 show close agreement between predicted and observed global temperature patterns, with differences mapped for January and July. - Country-level series (12 showcased, 26 risk-vulnerable plus 10 high-variability regions in total) display diverse and irregular weekly patterns; the model tracks seasonal and intra-annual variability, including complex sawtooth and multi-peak behaviors in tropical and Southeast Asian countries. - The ITC’s estimated next-step error (based on first-order differences) closely follows the actual first-order differences over half-year windows, illustrating effective feedback that mitigates error accumulation. - Correlation analyses of predicted sequences across continents reveal relationships consistent with known climate teleconnections (details in Supplementary Figs. 15–19). - Theoretical analysis (Supplementary) shows the method avoids exponential error accumulation and maintains errors at a bounded, approximately constant level during rollout.

The findings demonstrate that explicitly tracking the first-order difference—closely related to Lyapunov exponents and entropy changes in dynamical systems—provides informative probabilistic feedback that stabilizes long-horizon, weekly temperature predictions. By integrating this feedback into the objective and prediction process, the model counteracts error growth when ground truth is unavailable, directly addressing the core challenge of chaotic error amplification. The superior MAE, RMSE, and DTW metrics over both simulation-based and ML baselines indicate that the approach captures both pointwise values and temporal shape. Country-level case studies confirm robustness across diverse climatic regimes and seasonal structures. These results support the feasibility of data-driven, feedback-regularized ML methods for decadal-scale climate-related temperature forecasting, with implications for planning in agriculture, health, and biodiversity under climate change.

The study introduces a two-component ML framework—DLC for spatiotemporal dependency learning and ITC for probabilistic information tracking—that enables weekly global land surface temperature prediction over a decade while mitigating chaotic error amplification. Empirical results across global and country scales and theoretical analysis collectively show that the approach maintains stable errors and outperforms classical ML, statistical baselines, and CMIP models in this task. Future work includes expanding the framework to incorporate additional Earth system factors (e.g., atmospheric, topographic, vegetation) and extending information tracking to coupled, multivariate settings by modeling entropy changes across interacting subsystems, thereby enhancing sustainability-focused forecasting applications.

- The model is evaluated on a single consolidated dataset (Berkeley Earth land temperatures aggregated to weekly scale) and a specific global task; generalization to other datasets, variables, or resolutions is not directly assessed in the main text. - The approach focuses on univariate temperature prediction without explicit exogenous forcings or additional physical variables; incorporating broader Earth system factors is proposed as future work. - The architecture is based on MLPs; comparisons to alternative deep architectures integrated with similar feedback mechanisms are limited. - Code is available upon reasonable request rather than fully open-sourced at publication, which may affect reproducibility until shared.