| 18 May 2026
Canopy temperatures in computationally expensive crop models: A resource-efficient emulator approach applied in LPJmL (version 5.9.18)
Abstract. Crop yields are determined by multiple process chains that respond to environmental conditions. The very complex interactions between the different processes as well as the effects of isolated and combined process-level signals on final yields can be examined with process-based models. One of the key signals for crop development and growth dynamics is temperature, which is subject to change under global warming. While some crop models compute temperatures at the canopy level, others take 2 m air temperatures as input. However, the two temperatures can deviate significantly, potentially leading to different process responses when the less accurate 2 m air temperatures are used. This particularly applies to high-temperature processes that exhibit nonlinear dynamics and are very sensitive to small temperature variations. For global models, a major limitation is the computational resources required by suitable canopy temperature approaches. In this study we present computationally efficient emulators based on a complex energy balance approach (EBSC) to simulate daily mean and maximum canopy temperatures of twelve different crops. The emulators are statistical models that include six variables describing weather conditions and crop status. Furthermore, the emulators contain interaction terms to consider the response of canopy temperature on interactions between the variables. We apply and evaluate the emulators in the global, process-based Lund-Potsdam-Jena managed Land (LPJmL) model and show that the emulator approach reproduces observed canopy heating and cooling effects depending on the water and nitrogen status of wheat. Furthermore, we compare the simulated daily mean and daily maximum canopy temperatures of all twelve crops to a global dataset of ERA5 skin temperatures. We find that, for daily mean temperatures, 2 m air temperatures are the better approximation of skin temperatures than the simulated canopy temperatures, whereas for daily maximum temperatures simulated canopy temperatures consistently outperform 2 m air temperatures in terms of bias and nonunity slope. Our results indicate that heat effects are substantially underestimated with 2 m air temperatures, while they are significantly better captured with simulated canopy temperatures. This suggests that replacing the 2 m air temperature input by simulated canopy temperatures considerably improves the ability to model high temperature impacts on crop growth.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Geoscientific Model Development.
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This manuscript presents a computationally efficient canopy-temperature emulator derived from a complex energy-balance model and implemented in LPJmL. The topic is highly relevant because canopy temperature is increasingly recognized as a key variable for representing heat stress processes in crop models, while computational constraints have limited its adoption in large-scale simulations. The manuscript is generally well written, the model description is clear, and the code and parameterization are made openly available. The proposed emulator reproduces the parent EBSC model with high accuracy and is integrated into a widely used global crop model. Overall, the study represents a useful methodological contribution that fits well within the scope of GMD. However, several aspects require clarification and further justification before publication.
Major comments
1. A central conclusion of the manuscript is that simulated maximum canopy temperatures outperform 2 m air temperatures because they agree better with ERA5 skin temperatures. However, ERA5 skin temperature represents the uppermost land surface temperature of the grid cell, which integrates crops, natural vegetation, bare soil, and other land-cover components. It is not a direct observation of crop canopy temperature. The authors themselves acknowledge potential mismatches in vegetation structure, LAI, land cover, and water status between ERA5 and LPJmL. Consequently, the comparison may not provide strong evidence that the emulator improves crop canopy temperature realism. The manuscript would benefit from a more cautious interpretation of these results and a clearer discussion of the limitations of using ERA5 skin temperature as a surrogate for crop canopy temperature. The current conclusions appear stronger than the validation evidence supports.
2. The main motivation is that canopy temperatures should improve representation of heat-sensitive processes and ultimately crop growth and yield responses. However, the manuscript stops at evaluating canopy temperature itself and does not assess whether the new temperature estimates alter phenology, heat stress, biomass accumulation, or yield outcomes in LPJmL. As a result, the practical significance of the emulator remains uncertain. Even a limited sensitivity analysis comparing crop responses under air-temperature versus canopy-temperature forcing would greatly strengthen the study and demonstrate the value of the new module beyond reproducing temperatures.
3. The final emulator contains 84 terms for the lower limit and 56 terms for the upper limit, including numerous higher-order interactions. While cross-validation statistics are excellent, the manuscript provides little discussion of model complexity, parameter stability, extrapolation behavior, or risks of overfitting. The authors note that the emulator may produce artifacts outside the training domain and therefore introduce threshold constraints. This suggests that the statistical model may have limited robustness under novel climate conditions, particularly under future warming scenarios where extrapolation is likely. More justification is needed regarding why this highly parameterized formulation was preferred over simpler machine-learning or reduced-form approaches and how robust it remains under climates beyond the training range.
4. The maximum-temperature emulator assumes that canopy temperature peaks simultaneously with maximum air temperature and that radiation follows a sinusoidal diurnal pattern with a fixed maximum at noon. These assumptions may be reasonable for large-scale applications but could introduce systematic biases, especially under cloudy conditions, advection events, or water-limited environments. The manuscript would benefit from quantitative evidence demonstrating that these assumptions do not substantially affect emulator performance.
5. The emulator is presented as a general solution for twelve crops, yet most detailed evaluations (field experiments, canopy-air temperature differences, and discussion) are conducted only for wheat. The global ERA5 comparison includes other crops, but this remains an indirect evaluation. The authors should clarify the extent to which performance can be generalized across crops with substantially different canopy architecture, aerodynamic properties, and transpiration characteristics. Additional crop-specific validation or a stronger discussion of this limitation is warranted.
Minor comments
1. Please provide additional information on computational performance. Reporting absolute runtimes and hardware specifications would help readers assess the practical value of the claimed 3% runtime increase.
2. The rationale for selecting 90,000 training samples and 45,000 validation samples should be explained. Was emulator performance insensitive to sample size?
3. More information should be provided regarding the spatial distribution of training samples and whether certain climatic regions are over- or under-represented. Figure B1 is useful but deserves more discussion.
4.Please clarify whether the emulator coefficients are expected to remain stable across future LPJmL versions or whether retraining may be required when crop parameterizations change.