Characteristics of potential evapotranspiration and its estimation from hydrological observation in the Budyko framework

Cheng, Changwu; Liu, Wenzhao; Chen, Rui; Mu, Zhaotao; Zhou, Haixiang; Han, Xiaoyang; Li, Zhi; Feng, Hao

doi:10.5194/egusphere-2025-5898

Preprints

https://doi.org/10.5194/egusphere-2025-5898

Preprints

04 Dec 2025

| 04 Dec 2025

Characteristics of potential evapotranspiration and its estimation from hydrological observation in the Budyko framework

Changwu Cheng, Wenzhao Liu, Rui Chen, Zhaotao Mu, Haixiang Zhou, Xiaoyang Han, Zhi Li, and Hao Feng

Abstract. Potential evapotranspiration (E_P) is one of input variables in the Budyko framework, yet the diverse estimation methods cause discrepancies in its values. This raises a question about whether there exists a kind of E_P specially satisfying the Budyko framework. Based on the relationships among variables in the Budyko models and the deterministic value of E_P with known mean annual precipitation and runoff, we uncover the characteristics of E_P and its estimation method from hydrological observation in the Budyko framework. Accordingly, we introduce the concept of Budyko E_P. The non-parametric and parametric Budyko equations correspond to the reference and the adjustable Budyko E_P, respectively. For the Model Parameter Estimation Experiment catchments, the reference Budyko E_P is higher in the central and southern contiguous United States and lower in the northeastern and northwestern regions. The linear conversion functions are established from the meteorological E_P to the reference and optimized adjustable Budyko E_P separately. When estimating actual evapotranspiration (E) by Budyko models with the same data resources, employing two conversion functions with the meteorological E_P reduces the mean absolute error of E estimation by 33 % and 35 %, respectively, compared to using the optimized Budyko model parameter with the meteorological E_P. Further investigation suggests that the complementary relationship for evapotranspiration is one factor affecting the expression of the region-specific conversion function. Future in-depth exploration of the spatiotemporal differences in conversion functions will advance E estimation and the applications of Budyko E_P.

Received: 27 Nov 2025 – Discussion started: 04 Dec 2025

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 1254 KB)

Supplement (292 KB)

Download & links

Changwu Cheng, Wenzhao Liu, Rui Chen, Zhaotao Mu, Haixiang Zhou, Xiaoyang Han, Zhi Li, and Hao Feng

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-5898', Anonymous Referee #1, 17 Dec 2025
The manuscript titled “Characteristics of potential evapotranspiration and its estimation from hydrological observation in the Budyko framework”, addresses the discrepancies between meteorologically derived potential evapotranspiration (E_P), specifically the Penman method, and the theoretical Budyko-derived E_P. The authors introduce a concept termed “Budyko E_P, which is inversely derived from observed precipitation (P) and runoff (Q) using both parametric and non-parametric Budyko equations. The manuscript presents a novel perspective and uses the extensive MOPEX dataset which provides a robust statistical basis for the analysis. However, according to the following comments, I recommend a major revision for this manuscript.
There are significant conceptual concerns regarding the physical interpretation of the Budyko E_P and whether the improved performance is simply a result of mathematical fitting rather than physical insight.

Calculated E_Pusing the classic equations such as Penman is a climatic variable representing the atmospheric demand which is independent of moisture supply, but the Budyko E_Pseems to be a fitted parameter. Thus, the authors may need to discuss if the Budyko E_Pis yet a physical measure of atmospheric demand, or only a structural error-correction term. In this context, a discussion of how Budyko EP relates to the surface energy balance, and whether it can be interpreted consistently across different climatic regimes, is necessary.

It would be informative to explore how the results might change if the Budyko parameter (n) is estimated based on the watershed characteristics such as vegetation, soil, topography, etc., rather than treated as a purely fitting parameter.

Since the proposed method requires the runoff observed data (Equation 5), its applicability to ungauged basins is unclear. In addition, the authors should discuss how the method performs under non‑stationary conditions.

In Equation 7, do the parameters “a” and “b” depend on the climate characteristics (for example, aridity index) across the US? In Figure 5, if the points represent different aridity indices it would be helpful to assess whether the outliers from the linear regression correspond to particular climate types.

Page 2, Line 41: the word “Potential” has been repeated twice and should be corrected.
Citation: https://doi.org/10.5194/egusphere-2025-5898-RC1
- AC1: 'Reply on RC1', Wenzhao Liu, 25 Jan 2026
  
  A detailed response to all comments from Reviewer 1 is provided in the attached PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-5898-AC1
- AC3: 'Additional Reply on RC1', Wenzhao Liu, 14 Feb 2026
  
  We previously responded to the comments of Reviewer #1. After further consideration, we have prepared an additional response. Please find the details in the attached PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-5898-AC3
CC1:
'Comment on egusphere-2025-5898', Nima Zafarmomen, 25 Dec 2025

The study is highly commendable for its conceptual paradigm shift. Rather than treating EP solely as a meteorological input derived from independent equations (like Penman or Priestley-Taylor), the authors introduce the concept of "Budyko EP." By inverting the Budyko framework to derive EP from observed precipitation (P) and runoff (Q), the authors effectively treat EP as a variable constrained by the catchment's water-energy balance. The development of a conversion function to bridge the gap between meteorological EP and Budyko EP is a practical and elegant solution. It significantly improves actual evapotranspiration (E) estimation accuracy (by ~35%) without requiring the complex auxiliary data (soil, vegetation, etc.) typically needed to calibrate the Budyko parameter (n). This makes the method particularly valuable for data-scarce regions.
Minor comments:

1. You utilize an 11-year window to assume ΔS≈0. While this is standard in Budyko literature, the MOPEX dataset includes catchments where human interventions (e.g., groundwater extraction or reservoir regulation) might impact this assumption. A brief sentence in the Discussion regarding the sensitivity of "Budyko EP" to non-zero storage changes would add robustness.
2. The contrast between the MOPEX catchments and the Chinese Loess Plateau (CLP) regarding the "negative conversion relationship" (Fig. 7) is one of the most interesting parts of the paper. I suggest expanding slightly on the physical mechanism here—specifically, how the high aridity and limited water availability in the CLP drive the strong negative correlation between E and meteorological EP.
3. In Eq. (3) and (5), n is the landscape parameter. It would be beneficial to explicitly state that in the "reference Budyko EP" approach, the framework essentially reverts to a non-parametric state, thereby shifting the "catchment-specific information" from the parameter n into the adjusted EP value itself.
4. The study successfully demonstrates that EP is not just a climate driver but is intrinsically linked to the catchment's hydrological state. To further strengthen the discussion on how surface characteristics and vegetation dynamics influence these water-energy interactions—which indirectly affect the Budyko EP you've defined—I strongly recommend considering and citing studies that explore the integration of surface-level observations into hydrological frameworks, such as: Assimilation of sentinel‐based leaf area index for modeling surface‐ground water interactions in irrigation districts.
5. In Section 3.3, you employ a linear form for the conversion function (EPBudyko=aEPmeteor+b). While the scatter plots (Fig. 5) support this, did you test any non-linear (e.g., power or exponential) forms? Briefly mentioning why the linear form was preferred (likely for simplicity and parsimony) would be helpful.

Citation: https://doi.org/10.5194/egusphere-2025-5898-CC1
- AC2: 'Reply on CC1', Wenzhao Liu, 05 Feb 2026
  
  A detailed response to all comments from Dr. Nima Zafarmomen is provided in the attached PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2025-5898-AC2
RC2: 'Comment on egusphere-2025-5898', Anonymous Referee #2, 09 Feb 2026

General Comments: In Budyko-related research, the choice of E_P estimation method has long been an overlooked issue. The novelty of this manuscript lies in the in-depth investigation into the characteristics of E_P and its estimation methods under the Budyko framework. Furthermore, the authors apply this E_P to hydrological simulation and demonstrate its effectiveness by constructing the conversion function. The proposed approach is concise, has low data requirements, and demonstrates good practical value. Overall, the manuscript is well structured and methodologically sound, and is suitable for publication in HESS journal after moderate revision. My specific comments are as follows:
Q1: In a parametric Budyko model, the model parameter is commonly interpreted as representing catchment characteristics. In the conversion function approach with the adjustable Budyko E_P, the parameter is also involved. How should the role of this parameter be interpreted?
Q2: There are many meteorological methods for estimating E_P now. Please further compare the differences and similarities between these E_P estimates and the Budyko E_P, as well as its applicability.
Q3: In Figure 3, E_P-Bref exceeds 3000 for many catchments. However, E_P values are typically below 2000 in related studies (e.g., Zomer et al., 2022). How to explain this discrepancy?
Zomer, R. J., Xu, J., and Trabucco, A.: Version 3 of the Global Aridity Index and Potential Evapotranspiration Database, Sci. Data, 9, https://doi.org/10.1038/s41597-022-01493-1, 2022.
Q4: The intercept of the conversion function for E_P-Bref is above 900 for the MOPEX catchments, whereas it reaches as high as 8000 for the CLP catchments. When fitting this conversion function, should the intercept be appropriately constrained?

Other minor comments and suggestions:
Line 112. Section 2.2 introduces three different evapotranspiration estimation methods and compares them. I suggest adding a schematic diagram of the methodological framework in this section to improve readability and logical clarity.
Line 175. I suggest also plotting the data points of water balance for the MOPEX catchments in Figure 2.
Line 305. Two conversion functions were established, rather than one.

Citation: https://doi.org/10.5194/egusphere-2025-5898-RC2

Changwu Cheng, Wenzhao Liu, Rui Chen, Zhaotao Mu, Haixiang Zhou, Xiaoyang Han, Zhi Li, and Hao Feng

Supplement

https://doi.org/10.5194/egusphere-2025-5898-supplement

Changwu Cheng, Wenzhao Liu, Rui Chen, Zhaotao Mu, Haixiang Zhou, Xiaoyang Han, Zhi Li, and Hao Feng

Viewed

Total article views: 551 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
361	148	42	551	50	134	72

HTML: 361
PDF: 148
XML: 42
Total: 551
Supplement: 50
BibTeX: 134
EndNote: 72

Views and downloads (calculated since 04 Dec 2025)

Month	HTML	PDF	XML	Total
Dec 2025	156	73	24	253
Jan 2026	105	43	9	157
Feb 2026	98	32	9	139
Mar 2026	2	0	2

Cumulative views and downloads (calculated since 04 Dec 2025)

Month	HTML	PDF	XML	Total
Dec 2025	156	73	24	253
Jan 2026	105	43	9	157
Feb 2026	98	32	9	139
Mar 2026	2	0	2

Viewed (geographical distribution)

Total article views: 529 (including HTML, PDF, and XML) Thereof 529 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 02 Mar 2026

Short summary

Our study defines the potential evapotranspiration specifically suited the Budyko framework and explores its use in hydrological modeling. This potential evapotranspiration is deterministic when long-term catchment rainfall and runoff are known, and its two forms are derived from the non-parametric and parametric Budyko models. Converting commonly used potential evapotranspiration into these forms greatly enhances evapotranspiration estimates and supports better assessment of water availability.


Total:	0
HTML:	0
PDF:	0
XML:	0