the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Jul 2026
Physically constrained multi-task learning for hourly joint estimation of evapotranspiration and transpiration from sparse sap-flow data
Abstract. Hourly evapotranspiration (ET) estimation helps resolve rapid land-surface water and energy responses to radiation, atmospheric dryness, and aerodynamic forcing. However, the same change in total ET may arise from different combinations of vegetation transpiration, soil evaporation, and canopy interception evaporation, making it difficult to interpret transpiration and its sub-daily variability when ET is modeled only as a single bulk flux. Sap-flow observations provide direct information on transpiration (T), but their site coverage is sparse and tree-to-site upscaling remains uncertain. To address this issue, we integrate FLUXNET2015, SAPFLUXNET, and GIMMS LAI4g data to develop a physically constrained multi-task learning framework, termed MLF-ETT, for hourly joint estimation of ET and T. MLF-ETT estimates total ET and the transpiration fraction T/ET, deriving T as a bounded component of total ET under 0 ≤ T ≤ ET, so that limited T data contribute to joint ET-T learning rather than serving only as isolated T targets. Compared with the baselines of single-task XGBoost and multilayer perceptron models, the multi-task framework primarily improved T estimation, particularly under within-site temporal generalization and high evaporative-demand conditions characterized by high vapor pressure deficit, high air temperature, or both. Cross-site spatial generalization showed stronger site dependence, indicating that the transferability of sparse T supervision remained limited by cross-site process differences and uncertainty in sap-flow-derived T data. Input allocation between shared and task-specific branches strongly affected model performance, whereas increasing the T-supervision weight alone did not consistently improve performance. Overall, the framework incorporates limited sap-flow-derived T data into hourly joint ET-T learning and estimates T as a physically bounded component of total ET, providing a constrained reference for sub-daily ET partitioning.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2687', Anonymous Referee #1, 21 Aug 2026
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RC2: 'Comment on egusphere-2026-2687', Anonymous Referee #2, 24 Aug 2026
This study proposes a physically constrained multi-task learning framework (MLF-ETT) for hourly joint estimation of evapotranspiration (ET) and transpiration (T). The topic addresses an important challenge in ecohydrology—the difficulty of partitioning ET and the sparsity of sap-flow data. The design combining a T/ET output branch with the physical constraint (0≤T≤ET) is innovative, and the authors have conducted extensive comparative experiments on feature allocation (shared vs. task-specific) and generalization scenarios (temporal and spatial), demonstrating substantial work. But several aspects require clarification and further analysis before the paper can be accepted. Below are my specific comments.
Specific comments
(1) The paper claims that "the multi-task framework reduced T-estimation errors relative to the single-task model." It would be helpful to present the quantified error reductions (e.g., percentage or absolute RMSE improvements) more explicitly and consistently across the results section.
(2) The error analysis currently stays at the level of "which model achieves higher accuracy." The authors should further attribute the estimation errors to underlying physical reasons and explicitly clarify why the multi-task framework improves ET and T simulations—i.e., what specific mechanism or representation gain enables the improvement, rather than only reporting performance differences.
(3) The SHAP analysis only provides variable importance rankings. It is recommended to reveal the marginal effect shapes of key drivers (e.g., VPD, LAI) on T estimates, for example via partial dependence plots or SHAP dependence plots, to better illustrate how the model responds to these physically meaningful variables.
(4) The introduction is somewhat diffuse and could be restructured to focus more sharply on the core scientific questions. In particular, the extensive review of general ET estimation methods (physically based and machine learning) and the general applications of multi-task learning are not directly connected to the central theme of this study—i.e., how to incorporate sparse T labels into joint ET–T modeling. A more targeted introduction that builds up to the specific knowledge gaps would strengthen the paper.
(5) In the introduction (page 2, line 64), the authors pose the question: "whether it can support T estimation at sites without local T measurements." However, the results do not appear to directly address this question with dedicated validation at ET-only sites. The paper should either provide such validation or clearly discuss the limitations and potential pathways to answer this question.
(6) It is recommended to supplement typical diurnal cycle plots of observed and simulated ET and T for representative clear-sky days (e.g., a high-VPD day and a low-VPD day). Such time-series visualizations would greatly help readers intuitively assess the temporal consistency of the estimates, the phase relationships between ET and T, and the model behavior during key periods (e.g., midday depression), thereby providing process-level evidence for the effectiveness of the physical constraint and the multi-task design.
(7) Figures 5 and 7 contain too many subplots, which makes them difficult to read. The authors should simplify these figures, for example by showing only representative configurations or sites in the main text, and moving the rest to supplementary materials.
Citation: https://doi.org/10.5194/egusphere-2026-2687-RC2
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- 1
The paper presents and applies a methodology for the joint estimation of hourly ET and T (transpiration) by training various machine learning models (based on neural networks and decision trees) on measurements of ET (eddy covariance) and T (sap flow data). Joint learning is enabled by using a multi-objective calibration function, using model architectures that share components for predicting ET (task 1) and the ratio T/ET (task 2), combined with enforcing the constraint T < ET. This setup allows for data on T to inform ET estimates, and vice versa. The paper investigates to what extent this joint estimation improves temporal prediction of ET and T at individual sites ('temporal generalization') and spatial prediction of ET and T at other sites ('spatial generalization'). Results show that under certain conditions single-site temporal prediction of T improves when both data types are combined.
This is an interesting and novel study, but several issues require attention as detailed below, mostly related to methodology (clarifications about data, models, calibration) and readability of the paper (excessive use of machine learning jargon).
Comments (more or less chronologically)
1. The abstract would be easier to follow with less machine learning jargon ("task", "generalization", "supervision", "supervision weight").
2. line 51: "most existing hourly ET modeling studies still treat ET as a single bulk flux, while ET partitioning is often conducted as a separate analysis rather than being integrated into the ET estimation task". I suggest to rephrase and clarify this statement: since process-based ET models exist that separately account for T and E, the statement as currently written is ambiguous and inaccurate.
3. line 75: "integrating eddy-covariance-based ET references, sap-flow-derived T labels, and GIMMS LAI4g canopy information". What are ET references and T labels?
4. line 79: "Third, it evaluates how environmental-condition windows, input feature combinations, and T-supervision strength affect model performance under within-site temporal and cross-site spatial generalization." Please rewrite in a more understandable manner.
5. line 92: "These data were used to derive site-scale T reference values from tree-level measurements". Are 'reference' values assumed to be free of error? This terminology is used throughout the paper, please clarify what is meant by a reference value.
6. line 94: "observation coverage was used for sample weighting during model training". What exactly is observation coverage?
7. line 95: you should say something about the origin of the GIMMS LAI4g data, e.g. are these satellite-based estimates? Also, the spatial resolution of these data is about ~10km, which is very coarse. Please clarify the choice of this dataset.
8. line 118: "The derived T reference values were further screened to reduce the influence of sap-flow upscaling bias on T supervision." Clarify the term 'T supervision'.
9. line 120: "a site-specific multiplicative scaling factor was applied to the T reference series to reduce the proportion of samples with T > ET to 5 %". This pre-processing step potentially undersells the benefits of the combined data approach, since by doing this the single-T data models implicitly benefit from the ET data and the T < ET constraint.
10. line 131: "we retained only HD sites with at least 1000 aligned T-labeled samples". Why this restriction? How many data points are you throwing away by doing this?
11. consider reversing the order of presentation in the methods section: it seems more natural to first present details about the models used, and then provide details about training and evaluation. For example, table 2 is presented before the different models are discussed.
12. The "train model" caption in Figure 2 suggests that the test data are part of the training? And by 'valid' you mean 'validation"?
13. section 3.2.1: the choice of input features requires some further clarification. For example, why is solar elevation angle used as an independent input variable, when net radiation already includes the effect of solar elevation angle? Similarly, there seems to be redundancy in using air temperature, vapor pressure deficit and relative humidity all as independent input variables, since these three quantities are physically related. And two other independent input variables, gross primary production and LAI, are also strongly correlated.
14. eq. 4: please clarify how the sap flow observation coverage (T_coverage) is computed, what exactly is this number?
15. eq. 5 defines the training objective function, where the first term measures (mis)fit of the ET data, and the second term measures (mis)fit of the T data. We can view this as essentially a weighted nonlinear least squares objective function, where each data point in principle gets a weight that is inversely proportional to its error variance (highly uncertain data points get lower weights). This is indeed how the weight w in eq. 4 is used. However, using that same perspective, the division by N (number of data points) in eq. 3 suggests that simply having more data of a particular type (e.g. ET vs T) reduces the weight and thus the reliability of those data. Please clarify and justify.
16. "Within-site temporal generalization": consider replacing/clarifying with temporal prediction at a single site
17. "Cross-site spatial generalization": consider replacing/clarifying with spatial prediction at multiple sites
18. line 195: "samples were ordered chronologically and divided into 5 contiguous temporal blocks". Can you give more details about how long the blocks are and how many data points.
19. line 204: I guess the term "supervision strength" comes from supervised learning in machine learning, but this term may not be clear to the (hydrology) readers of HESS
20. line 232: please specify the data source for the 9 input variables, including temporal and spatial resolution
21. description of the different models: can you include the number of parameters to be estimated in each of these models? It would also be good to indicate which of these modeling approaches have been used before for ET/T modeling and which ones are new to this paper.
22. Fig. 4: what determines the horizontal position of the site level values (shown as dots)?
23. figure 10: consider flipping the colors; I was expecting red = bad, blue = good, but the figure has it the other way around.
24. section 4.3 - Performance in environmental-condition windows: did you check differences in performance under different vegetation conditions (LAI and gross primary production)?
25. line 477: improving the physical consistency of T estimates at ET-only sites - can you state here explicitly which result (which figure) shows this.
26. The predictions of T and ET are called 'physically constrained', which refers to the T < ET constraint that is enforced (and ET > 0). Beyond that, it seems no physical constraints are used, so one wonders how physically realistic the model predictions are. Is there a way to scrutinize the physical plausibility of the predictions (e.g. does the predicted ratio T/ET correlate with LAI)? Maybe the results of the SHAP analysis in Figure 11 can help answer this question, but this part of the analysis is quite short and not very clear.
27. line 549: "The multi-task framework reduced T-estimation errors relative to the single-task model". Not always; this conclusion should be qualified, and would be good to also give some numbers (i.e. by how much were errors reduced).
28. lines 557-560: An important drawback of the methodology is indeed that it does not explicitly account for data errors, although there is some informal weighting of data in the objective functions, but see comment 15.