Multi-Horizon, Multi-Depth Forecasting of Pavement Temperature in a Continental Climate: Machine Learning Methods Benchmarked Against a Persistence Baseline

Technical Summary: Multi-Horizon, Multi-Depth Forecasting of Pavement Temperature in a Continental Climate

Problem Statement
Accurate forecasting of pavement temperature at multiple depths is critical for mechanistic-empirical pavement design, including thermal-stress analysis, rutting prediction, low-temperature cracking assessment, and freeze-thaw cycle management. While machine learning (ML) has been increasingly applied to this problem, recent literature frequently reports high coefficients of determination ($R^2 > 0.95$) without benchmarking against trivial baselines. This study addresses three methodological gaps in existing research: (1) the failure to account for the extreme autocorrelation inherent in pavement temperature time series, which can inflate apparent predictive skill; (2) the reliance on single chronological train-test splits that fail to capture seasonal variance; and (3) the omission of naive persistence baselines, which are the standard benchmark in operational forecasting. The study aims to determine the specific conditions (depth, forecast horizon, and data volume) under which ML methods genuinely add value over a simple persistence forecast.

Methodology
The research utilizes one year of hourly temperature data ($n = 7,067$ observations) from an automated monitoring station near Astana, Kazakhstan, in a sharply continental climate. The dataset includes measurements at eight subsurface depths (3 cm to 300 cm) and ambient air temperature.

• Forecasting Task: The study evaluates predictions at three horizons: 24 hours (daily), 168 hours (weekly), and 720 hours (30 days).
• Models: Six ML algorithms were evaluated: Linear Regression, Ridge Regression, Lasso Regression, Random Forest, Gradient Boosting, and Extreme Gradient Boosting (XGBoost).
• Baseline: A naive persistence baseline ($\hat{y}_{t+h} = y_t$) was used as the primary benchmark.
• Feature Engineering: A "leak-free" protocol was implemented. Features included lagged values (1, 3, 6, 12, 24, 72, 168 hours), rolling window statistics (24h and 168h means/SDs), and cyclical encodings of time. Crucially, no same-timestep cross-depth information was used as a predictor to prevent the task from devolving into spatial interpolation.
• Validation: A five-fold expanding-window blocked time-series cross-validation was employed. This approach exposes models to seasonal distribution shifts (e.g., training on summer/autumn data and testing on winter) rather than relying on a single static split.
• Metrics: Performance was assessed using Root-Mean-Squared Error (RMSE), Mean Absolute Error (MAE), and $R^2$.

Key Results

1. Dominance of Persistence at Short Horizons: At the 24-hour horizon, the persistence baseline outperformed all six ML algorithms at every depth. Persistence achieved $R^2$ values between 0.94 and 0.999 with RMSEs ranging from 0.23°C (at 180 cm) to 4.37°C (at 3 cm). No ML model exceeded the persistence baseline in mean RMSE.
2. Limited ML Value at Intermediate/Long Horizons: ML methods began to show competitive or superior performance only under specific conditions:
   • 168-hour horizon: Lasso regression achieved the lowest RMSE in 22% of depth-fold combinations, primarily at intermediate depths (120 cm and 180 cm), but persistence remained superior in the overall mean across folds.
   • 720-hour horizon: At the 30-day horizon, ML methods became competitive at deeper layers. Random Forest achieved a 20% RMSE reduction compared to persistence at the 300 cm depth. Lasso showed modest improvements at intermediate depths (40–180 cm). However, at near-surface depths (3–20 cm), no ML method approached the performance of persistence.
3. Impact of Training Data Size: ML performance was highly sensitive to training set size. With small datasets (~1,245 hours), ML models performed significantly worse than persistence. Stable, competitive performance required approximately 4,000–5,000 hours (six months) of training data.
4. Depth-Dependent Predictability: A monotonic increase in predictability with depth was observed across all methods, including persistence. This reflects the physical thermal inertia of the pavement system, where deeper layers exhibit slower, smoother temperature evolution, rather than an improvement in algorithmic capability.

Key Contributions and Significance
The paper provides a corrective to the prevailing narrative in pavement temperature literature that ML "solves" prediction problems. Its primary contributions include:

• Methodological Benchmarking: This is the first study to explicitly benchmark a comprehensive suite of ML algorithms against a naive persistence baseline across multiple horizons and depths for pavement temperature. It demonstrates that many previously reported high $R^2$ values likely reflect the exploitation of autocorrelation (persistence) rather than genuine predictive skill.
• Regime Identification: The study establishes clear boundaries for ML utility. ML adds value only at longer horizons (≥168 hours) and greater depths (≥60 cm) where thermal diffusion dampens high-frequency variability and the persistence assumption begins to fail. For short-term operational decisions (e.g., daily maintenance), persistence is sufficient and more robust.
• Leak-Free Protocols: By enforcing a strict "no same-timestep cross-depth" feature engineering rule, the study highlights how standard practices in the field may inadvertently turn forecasting tasks into spatial interpolation, artificially inflating performance metrics.
• Practical Guidance: The findings offer evidence-based guidance for engineers: use persistence for short-term forecasts; consider Lasso regression for medium-term, intermediate-depth planning; and consider tree-based ensembles only for long-term, deep-layer seasonal planning, provided sufficient historical data (≥6 months) is available.

Limitations
The authors acknowledge that the results are based on a single station and a single annual cycle. While the site is representative of the continental climate, cross-station validation across the wider KazDorNII network (spanning different latitudes and soil types) is required to confirm generalizability. Additionally, the feature set excluded meteorological covariates such as solar radiation and wind speed, which may limit the performance of surface temperature forecasting. Finally, the study used the simplest persistence baseline; future work should compare ML against more sophisticated baselines like seasonal-naive or ARMA models.