the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 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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Status: open (until 13 Jul 2026)
- RC1: 'Comment on egusphere-2026-1898', Anonymous Referee #1, 02 Jun 2026 reply
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RC2: 'Comment on egusphere-2026-1898', Anonymous Referee #2, 11 Jun 2026
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This manuscript develops polynomial emulators of a stability-corrected energy-balance model for crop canopy temperature and embeds them in LPJmL without adding too much runtime. I thinkk the problem is well motivated, the method is openly archived, and the honest reporting that canopy temperature does not beat air temperature for daily means is a strength. The core idea is sound and within GMD's scope. But the current version has several methodological and evaluation weaknesses that I think are addressable within a revision and that, if addressed, would substantially raise the paper's value to the modeling community. My three main concerns are listed below:
1. The fitted air-temperature coefficient of the upper-limit emulator is essentially one (Table A4: 0.959 for the mean setup, 0.997 for the maximum). This shows the polynomial is spending its leading term reconstructing the identity T_c,U ≈ T_a + small correction, which Eq. (4) already gives in closed form. Maybe you can emulate only the expensive unknown, the stability-corrected aerodynamic resistance, and compute the limits from the physical equations. Because the stability correction depends on the surface temperature, this requires two resistances (r_a for the cool lower-limit case and for the hot upper-limit case), or one neutral r_a plus stability factors, not a single object. The benefit is that the additive dependence on T_a and the multiplicative dependence on R_n are then exact rather than approximated, so the two artifact guards in Table 1 (the T_c,L > T_c,U check and the +/-10 K clamp) become unnecessary. I want to be precise that this would not remove the physically motivated thresholds (LAI < 1.5, low radiation, and especially low wind, where the EBSC itself is unreliable and r_a is intrinsically hard to emulate).
2. Also I strongly recommand to validate the water-stress scaling factor K_WS. Currently the K_WS = min(1, g_c,LPJmL / g_c,opt) divides an LPJmL photosynthesis-based canopy conductance (computed with air temperature, by your own statement in Sect. 2.5) by an optimum conductance defined as 1/r_c,L, where r_c,L derives from a grass reference stomatal resistance (r_1 ≈ 100 s/m, Allen and Wright, 1997). These two conductances are not guaranteed to share a definition or scale, so their ratio can be biased even when each is individually reasonable. Since the emulator reproduces the EBSC to about 1 K while the site RMSE is 3.6 K, the scaling step is one of the candidate sources of the residual error and is currently the least validated link in the chain.
3. The Discussion right now lists four qualitative causes of the site mismatch but quantifies none, so the reader cannot separate emulation error (about 1 K) from the two-limit linear-scaling approximation (Eq. 5 interpolates a quantity that is nonlinear in r_c) from the K_WS proxy. A clean decomposition is feasible with objects you already have, evaluated on the validation cell-days: (i) full EBSC with actual r_c, (ii) the two-limit linear scaling with the true transpiration ratio, (iii) the same with emulated limits, (iv) the LPJmL chain with K_WS. The successive differences attribute the error to each step and would tell future users which part to improve.
4. The current cross-validation draws the validation set from the same distribution as the training set, so it demonstrates interpolation skill, whereas the paper's motivation is future, hotter, higher-VPD conditions, which is extrapolation. Please add an explicit out-of-domain test: hold out the upper decile of temperature or VPD, or hold out the entire future SSP5-8.5 subset, refit on the remainder, and report emulator-versus-EBSC error in the held-out tail. Relatedly, the training LAI comes from a standard air-temperature-driven LPJmL run, but the emulator is applied inside a canopy-temperature-driven run where phenology and LAI will differ. This is harmless only if runtime inputs stay inside the training envelope, and it is precisely the heat-stressed, water-limited cells that are most likely to drift outside it.
5. For the maximum setup you substitute T_max, VPD_max, and a 3 pm radiation value (Eqs. 8 to 10), but wind speed appears to be left at its daily mean even though afternoon wind and atmospheric stability differ substantially and r_a is sensitive to both. Please state explicitly how wind is handled in the maximum setup. Separately, the soil heat flux G appears in Eqs. (1), (2), (4) but is not one of the six regressors and its computation is never described (set to zero for daily means, a fixed fraction of R_n, and how it is treated at 3 pm where it is not negligible).
6. Also, ERA5 daily-maximum skin temperature is not a direct measure of crop canopy temperature (or how you assess the gaps between skin temperature of the models vs the canopy temperature?) and carries two opposing biases of unknown net size: a warm representativeness bias, because the 0.5° value mixes in hot midday bare soil and sparse cover, and a cold model bias, because ERA5 daytime land-surface temperature is documented to be underestimated where vegetation cover is overestimated (Johannsen et al., 2019, Iberian Peninsula, correlation about -0.45). Since the sign of the net mismatch is unknown, the quantitative agreement for daily-maximum Tc (bias, slope, MSD partition in Figs. 5 and 6) should not be read as a clean measure of skill; only the qualitative ranking is robust, because air temperature underestimates the surface maximum under either bias. We recommend stating the result at the ranking level and, for a cleaner test, comparing against satellite land-surface temperature at a known overpass time (e.g. MODIS Aqua near 13:30, aggregated from native 1 km and restricted to high crop-fraction cells), which removes the reanalysis bias and the constructed daily maximum. But at the same time, the remote sensing derived skin temperature will also have bias with the real canopy temperature, but it shall be good to see the differences between models and remote sensing products.
Citation: https://doi.org/10.5194/egusphere-2026-1898-RC2 -
CEC1: 'Comment on egusphere-2026-1898 - No compliance with the policy of the journal', Juan Antonio Añel, 21 Jun 2026
reply
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
For part of the data used in your study, you cite external sites and papers that do not comply with the requirements for data archival of the journal, namely the maximum crop height data and the climate data from the ISIMIP3b:
- They do not appear to have a published policy for data preservation over many years or decades (some flexibility exists over the precise length of preservation, but the policy must exist).
- Also, they do not appear to have a published mechanism for preventing authors from unilaterally removing material. Archives must have a policy which makes removal of materials only possible in exceptional circumstances and subject to an independent curatorial decision,If we have missed a published policy which does in fact address this matter satisfactorily, please post a response linking to it. If you have any questions about this issue, please post them in a reply.
The GMD review and publication process depends on reviewers and community commentators being able to access, during the discussion phase, the code and data on which a manuscript depends, and on ensuring the provenance of replicability of the published papers for years after their publication. Please, therefore, publish your code and data in one of the appropriate repositories and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible. We cannot have manuscripts under discussion that do not comply with our policy.
Later, if the Topical Editor decides to continue with the review or publication process of your manuscript and you are requested to upload a new version of it, then The 'Code and Data Availability’ section of your manuscript must also be modified to cite the new repository locations, and corresponding references added to the bibliography.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in GMD.
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2026-1898-CEC1 -
RC3: 'Comment on egusphere-2026-1898', Anonymous Referee #3, 21 Jun 2026
reply
The manuscript presents a valuable contribution toward improving the representation of canopy temperature in large-scale crop models while maintaining computational efficiency. The study is well structured and the proposed framework is clearly evaluated. However, there are several concerns need to be addressed before publishing:
- The manuscript demonstrates that the proposed emulator can reproduce canopy temperature reasonably well. However, it remains unclear whether the improved representation of canopy temperature translates into meaningful improvements in crop simulations. Since canopy temperature is introduced primarily to better represent crop physiological responses to heat stress. Stronger evidence may be needed about the improvement of crop simulations under current canopy temperatures setup.
- The proposed framework introduces several additional components, including the emulator, boundary-condition estimation, water-stress scaling, and interpolation procedures. While the overall methodology is clearly described, it remains unclear whether the added complexity is justified by substantial improvements in model performance or crop-relevant outcomes. The manuscript would benefit from a more explicit assessment of the trade-off between model complexity and predictive gain. For example, comparisons against simpler empirical approaches or reduced-form implementations could help demonstrate the practical value of the proposed framework. Without such analysis, it is difficult to evaluate whether the additional methodological burden in your LPJML is warranted.
- The proposed workflow consists of multiple sequential steps, each of which may introduce uncertainty. However, the manuscript currently provides limited insight into how errors accumulate throughout the workflow or which components contribute most strongly to the final prediction uncertainty. A quantitative error attribution or sensitivity analysis would substantially improve the methodological evaluation. Such an analysis could help identify the dominant sources of uncertainty and provide guidance for future model development efforts.
- The evaluation relies primarily on ERA5 skin temperature as a reference dataset. However, ERA5 skin temperature is a reanalysis product rather than a direct observation of crop canopy temperature. The authors should acknowledge this limitation more explicitly and discuss its implications for the interpretation of model performance. Additional evaluation against independent canopy temperature observations or remotely sensed datasets, where available, would strengthen the validation.
- The introduction can benefit from an additional paragraph between the discussion of EBSC computational constraints and the study objectives (around line56). This paragraph can introduce the class of methods used in this study, briefly review their current development status, and explain why they offer a promising solution to the computational challenges outlined above. This would improve the overall flow and motivation of the Introduction.
Citation: https://doi.org/10.5194/egusphere-2026-1898-RC3 -
RC4: 'Comment on egusphere-2026-1898', Anonymous Referee #4, 23 Jun 2026
reply
The manuscript presents a computationally efficient approach for representing crop canopy temperature in LPJmL using polynomial emulators derived from a stability-corrected energy-balance model. The topic is relevant to large-scale crop modeling, and the study is generally well organized and clearly presented. The emulator shows good agreement with the parent model while adding only limited computational cost. However, I have several concerns that should be addressed before publication.
1. The coupling between the emulator and LPJmL requires further clarification and validation. The final canopy temperature is obtained by interpolating between the upper and lower temperature limits using a water-stress factor derived from LPJmL canopy conductance. However, the canopy conductance calculated by LPJmL and the optimum conductance used to define the lower temperature limit may not be fully consistent in their definitions or scales. Since this scaling directly controls the final canopy temperature, the authors should provide a clearer justification for this formulation and evaluate its sensitivity. It would also be helpful to clarify which physiological processes are driven by canopy temperature and which remain driven by air temperature.
2. The conclusions regarding the improved representation of high-temperature conditions appear stronger than the current validation evidence supports. ERA5 skin temperature is not a direct observation of crop canopy temperature because it integrates the thermal characteristics of multiple land-cover components within each grid cell. Therefore, better agreement with ERA5 skin temperature does not necessarily demonstrate improved realism in simulated crop canopy temperature. The authors should interpret this comparison more cautiously and clearly distinguish between an improved representation of land-surface temperature extremes and a direct validation of crop canopy temperature. In addition, the practical relevance of the new module would be clearer if the authors demonstrated whether canopy-temperature forcing affects simulated heat stress, phenology, biomass accumulation, or yield.
3. The workflow contains several sequential sources of uncertainty, including the parent EBSC model, polynomial emulation of the temperature limits, interpolation between these limits, and the LPJmL-based water-stress scaling. At present, these uncertainties are evaluated mainly through their combined effect, making it difficult to identify which step contributes most strongly to the final prediction error. A quantitative error-attribution or sensitivity analysis would substantially strengthen the methodological evaluation. Such an analysis would help readers assess the robustness of the full workflow and identify priorities for future model development.
Citation: https://doi.org/10.5194/egusphere-2026-1898-RC4 -
RC5: 'Comment on egusphere-2026-1898', Anonymous Referee #5, 24 Jun 2026
reply
This work developed a statistical emulator based on training data from a complex energy balance approach (EBSC) and applied the emulator at LPJmL model and hence enable canopy temperature simulation. The authors showed such approach could reproduce observed canopy heating and cooling effects as site observations. This work demonstrated a very interested way to develop empirical functions within land surface models. The overall manuscript is well written. There are only minor revisions are required before considering for publications.
Minor comments:
Please be specific how many grids for which crops and which years are used for the 90000 entries. Are they evenly distributed geographically?
Lin 113-115. Please define the logics behind the selection of LAI of 33 days and 11 years, as well as 40 days of 9 future years. Based on several tests or what else? Is that based on the threshold of LAI >1.5, temperature > 273.15K and solar radiation <50W.m-2? If so, please restructure the flow of the paragraph.
Please show R2 in figure 1.
The validation focused on the temperature differences rather than canopy temperature simulation. I think it is also very important to show the canopy temperature validations. Please add another plot to show the comparison of observed and simulated canopy temperature in Figure 3. Furthermore, how well the method capture the monthly or interannual variation of canopy temperature at the sites?
The main results of the global simulation is still a scatter plot, how about show a global spatial distribution of simulated canopy temperature versus ERA5 skin temperature?
Citation: https://doi.org/10.5194/egusphere-2026-1898-RC5
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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.