A hybrid deep learning framework for estimating urban tree transpiration

Urban trees regulate urban water-energy exchange via transpiration, yet accurate estimates in urban settings remain challenging. Traditional Jarvis-type models often require frequent recalibration and can produce biased estimates when parameters vary or structural assumptions are violated. Alternatively, hybrid deep learning (DL) models that integrate data-driven approaches with process knowledge represent a promising alternative, merging the flexibility of DL with prior information from process models. Nonetheless, the effectiveness of these hybrids for estimating urban tree transpiration has rarely been evaluated. This study investigates three physics-guided DL strategies that incorporate the Jarvis model: residual learning (M2), weighted fusion (M3), and feature learning (M4), against three baselines: Jarvis, pure DL, and Random Forest (RF). We also analyze SHAP-based explainability to assess feature contributions and interactions. Utilizing observed hourly sap flow and environmental data from Munich and Würzburg (2015-2021), we estimate hourly latent heat flux (LE) for two physiologically contrasting species, Tilia cordata and Robinia pseudoacacia, from shortwave radiation (R_s), air temperature (T_a), vapor pressure deficit (VPD), soil moisture content (θ), and day of year (DOY). All DL models outperform the Jarvis baseline, with M4 showing the best overall performance: test NSE 0.86 (0.90) and RMSE 11.43 (1.93) W/m² for two species, while maintaining strong performance with limited training data. SHAP identifies model-derived species-specific response patterns consistent with known differences in hydraulic architecture, and diagnoses regimes where Jarvis assumptions underperform. This framework offers a practical pathway for embedding process knowledge into broader urban evapotranspiration and microclimate models.