The research team, led by Huasu Fang of the Heilongjiang Province Hydraulic Research Institute together with colleagues from the Institute of Engineering Mechanics of the China Earthquake Administration and Harbin University of Science and Technology, focused on canal slopes in a cold region of northeastern China. Their goal was deceptively simple to state but difficult to achieve: estimate temperatures at depths of 100 to 250 centimeters at the same moments when shallower measurements were taken, using only information available at or before those moments. Deep temperature monitoring of this kind is expensive, and sensors buried in frozen, wet soil are notoriously prone to failure, leaving dangerous gaps in the record precisely where frost damage begins.

To build their dataset, the researchers assembled 204 irregularly spaced multi-depth observations collected between 2018 and 2022, pairing each with a rich set of predictors drawn from meteorological conditions, hydrological variables, surface and shallow-ground temperatures, soil moisture, and seasonal indicators such as the phase of the annual cycle. This multi-source framing matters because the temperature at two meters below a canal slope is not simply a delayed copy of the air temperature above it; it is shaped by snow cover, solar radiation, water movement in the soil, and the slow conduction of heat through layered earth materials. By feeding all of these influences into the models, the team gave the algorithms a physically meaningful picture of the system rather than a single temperature trace.

Seven machine-learning models were put through their paces, spanning classical approaches such as support vector regression, random forests, and XGBoost alongside deep learning architectures including long short-term memory networks, better known as LSTM, and the Transformer, the attention-based architecture that has revolutionized fields from language translation to weather forecasting. Model selection was carried out with two-fold forward-chaining validation, a scheme that respects the ordered nature of time-series data by training on earlier periods and testing on later ones. The models were then refitted on data from 2018 to 2021 and evaluated on an independent test set from 2022, a design that guards against the optimism that arises when a model is judged on data it has already seen.

The verdict was that the two deep learning approaches stood out. Transformer and LSTM delivered the most competitive overall performance across the depth range, with the Transformer achieving depth-averaged error metrics of 0.968 degrees Celsius in mean absolute error and 1.188 degrees Celsius in root mean square error, a normalized root mean square error of 30.89 percent, and a coefficient of determination of 0.886. In practical terms, the model could reconstruct temperatures several feet underground with an accuracy close to one degree, a level of precision that could make the difference between detecting an incipient frost problem and missing it entirely. Yet the team was careful about overclaiming: when pairwise comparisons of root mean square error were subjected to paired moving-block bootstrap tests and corrected for multiple comparisons using the Holm procedure, none of the Transformer’s advantages over rival models remained statistically significant. The edge was real in magnitude but not decisive in a statistical sense, a nuance that reflects the genuine difficulty of the prediction task.

Before turning to prediction, the researchers first characterized how temperature behaves as it travels downward through the slope. The records showed the two classic signatures of heat conduction in soil: progressive attenuation, meaning the seasonal swing in temperature shrinks with depth, and phase delay, meaning the annual warm and cold peaks arrive later the deeper one looks. Summer heat that scorchers the surface in July may not reach its maximum influence at 250 centimeters until well into autumn, and winter cold penetrates in similarly lagged fashion. These evolutionary patterns are not academic curiosities; they dictate how deeply frost penetrates, how long frozen layers persist, and how much heave and settlement a slope endures over a season.

The team also tested how well the models could identify whether the ground was frozen or thawed, a binary distinction that matters enormously for frost heave prediction. Frozen-state identification proved reliable at depths of 100 and 120 centimeters, where freeze-thaw transitions are frequent and strongly expressed, but weakened at 150 and 180 centimeters. At 200 and 250 centimeters, the test set contained no frozen observations at all, meaning the deepest soil at the site never crossed the freezing threshold during the evaluation year. This depth-dependent reliability is a candid reminder that data-driven models inherit the structure of their training data: where the physics is active and the labels abundant, they excel; where transitions are rare or absent, their skill remains unverified.

One of the study’s most valuable contributions is its use of SHAP, or SHapley Additive exPlanations, a technique borrowed from cooperative game theory that assigns each input variable a quantified share of the model’s output. Rather than treating the neural networks as black boxes, the researchers could ask which predictors actually drove the deep temperature estimates. The answer aligned neatly with the physics. Temperatures measured at 50 and 80 centimeters, the shallow layers closest to the atmosphere, dominated the model’s contributions, acting as a thermal memory from which deeper conditions could be inferred. Meanwhile, the importance of seasonal-phase variables grew steadily with depth, mirroring the increasing phase lag of the seasonal signal. The explainability analysis thus served as an independent check that the models had learned genuine thermal dynamics rather than spurious correlations.

The implications extend well beyond a single canal. Canals in seasonally frozen regions are lifelines for agriculture and water delivery across vast stretches of North America, northern Europe, Central Asia, and China, and climate warming is altering freeze-thaw regimes in ways that make historical design assumptions increasingly unreliable. Related efforts have applied artificial intelligence to permafrost and active-layer temperatures on the Alaskan North Slope and to soil temperature forecasting in subtropical grazing lands, suggesting a broader movement toward data-driven cryosphere monitoring. The framework presented here adds an important engineering dimension to that movement, showing that a site-specific model can serve as a complement to direct deep-ground monitoring, particularly when deep sensors are sparse, degraded, or temporarily offline.

The authors are careful to position the approach as a supplement rather than a replacement for physical instrumentation. Machine-learning reconstructions are only as good as the shallow observations and auxiliary data they are trained on, and the site-specific nature of the models means they cannot simply be transplanted to new locations without retraining. Still, the combination of rigorous time-series validation, bootstrap-based significance testing, phase-specific error analysis, and SHAP interpretability sets a high methodological standard for a field where black-box predictions are too often accepted at face value. For engineers charged with keeping frozen slopes stable, the study offers something genuinely useful: a way to estimate what is happening at depths they cannot easily measure, grounded in data they already have, with an honest accounting of where the estimates can be trusted and where uncertainty still reigns. As sensors fail and climates shift, that ability to intelligently fill the gaps in the thermal record may prove one of the quiet but essential technologies of cold-region water infrastructure.

Subject of Research: Machine-learning-based prediction of deep ground temperature fields in cold-region canal slopes

Article Title: Evolutionary patterns and intelligent prediction of temperature fields in cold-region canal slopes

Article References: Evolutionary patterns and intelligent prediction of temperature fields in cold-region canal slopes. (n.d.). https://doi.org/10.1007/s12145-026-02245-0

Image Credits: AI Generated

DOI: 10.1007/s12145-026-02245-0

Keywords: cold-region canals, soil temperature prediction, machine learning, Transformer model, LSTM, freeze-thaw cycles, frost heave, SHAP interpretability, soil freezing, geotechnical engineering, time-series forecasting, canal slope stability