Background and Motivation
The temperature of the soil surrounding buried pipes is an important quantity for the thermal analysis of water distribution networks, but it is not generally available at pipe depth. Soil probes measure at fixed standardized depths rather than at the depth of any particular pipe [1], their readings cannot simply be transferred to another depth because subsurface heat transport depends on soil properties, groundwater and surface cover [2], and in older networks the burial depth of individual pipes is often undocumented.
A preceding project at the Pattern Recognition Lab [3] proposed that smart water meters can help close this gap: when the water in a pipe stands still for long enough, it takes on the temperature of the surrounding soil, so meter temperature readings taken during such stagnation periods serve as soil-temperature measurements at pipe depth. These measurements, however, exist only where and when water happens to stagnate, and never for a future moment. Building on this work, the present thesis develops machine-learning models, an approach already established for soil-temperature prediction at standard probe depths [4], that predict soil temperature at pipe depth from weather data alone, for the current time and for future times.
Objectives
- Data quality: assess the reliability of the meter-derived soil temperatures and establish physically motivated criteria for selecting usable meters and time periods
- Estimation: develop models that estimate soil temperature at pipe depth from weather variables, without relying on the meters’ own readings as model input
- Forecasting: extend the models to predict soil temperature at operationally relevant lead times, and characterize how accuracy changes with lead time
- Comparison: compare classical, tree-based and neural sequence models against physically motivated and naive baselines under a single, leakage-free evaluation protocol
- Uncertainty: attach calibrated uncertainty estimates to the predictions so that results are usable for operational decisions
Research Questions
- How accurately can soil temperature at pipe depth be estimated from weather data alone, and how does accuracy change with forecast lead time?
- Do the meter-derived equilibrium measurements agree with independent soil measurements, and which physical criteria identify sensors that are not measuring soil temperature?
- Which model families and target formulations remain valid when predicted temperatures fall outside the range observed during training, and can a physically motivated target transformation improve extrapolation?
- Can calibrated prediction intervals be provided so that forecasts express quantified uncertainty rather than point estimates alone?
Planned Approach
Ground truth will be taken from the thermal-equilibrium periods of the smart meters and validated against independent soil measurements. Model inputs will be restricted to weather variables and calendar information, using strictly causal features so that one formulation serves both estimation and forecasting. Naive and physically motivated baselines, persistence, climatology and an analytical heat-conduction model, will provide reference points. Model families of increasing complexity, from regularized linear regression through gradient-boosted trees to recurrent and attention-based sequence models, will be compared under an identical evaluation protocol. Since non-linear regression is known to perform poorly outside the range of values covered by the training data [5], target formulations intended to improve prediction beyond that range will be examined as part of the comparison. Evaluation will use chronological splits with multiple test periods, per-horizon error analysis and conformal prediction intervals. Implementation in Python using PyTorch, scikit-learn, XGBoost and pandas.
The available data covers a single season. Claims of year-round generalization are therefore outside the scope of this thesis, and the analysis will instead quantify how far predictions remain reliable beyond the conditions observed during training.
References
[1] World Meteorological Organization, Guide to Instruments and Methods of Observation (WMO-No. 8), Volume I, Chapter 2: Measurement of Temperature, Geneva, 2018.
[2] E. Nissler, S. Scherrer, H. Class, T. Müller, M. Hermannspan, E. Osmancevic, C. Haslauer, “Heat transport from atmosphere through the subsurface to drinking-water supply pipes”, Vadose Zone Journal 22(5), 2023, e20286. doi:10.1002/vzj2.20286.
[3] A. Farhat, “AI-driven Subsurface Temperature Modeling for Water Networks”, Projektarbeit in Computer Science, Lehrstuhl für Mustererkennung (Informatik 5), Friedrich-Alexander-Universität Erlangen-Nürnberg, 2026.
[4] L. Mampitiya et al., “Artificial intelligence to predict soil temperatures by development of novel model”, Scientific Reports 14, 2024, art. 9889. doi:10.1038/s41598-024-60549-x.
[5] X. Shen, N. Meinshausen, “Engression: Extrapolation through the Lens of Distributional Regression”, Journal of the Royal Statistical Society Series B 87(3), 2025, pp. 653–677. doi:10.1093/jrsssb/qkae108.