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Performance comparison of the Penman-Monteith-based evapotranspiration models in a citrus orchard of Southwest China

This study evaluates five Penman-Monteith-based models using four years of eddy covariance data in a Southwest China citrus orchard, revealing that the Hybrid-Dual Source (H-D) model generally outperforms others across temporal scales and growth stages while highlighting the critical sensitivity of evapotranspiration estimates to canopy resistance and soil water content.

Original authors: Bin Zhu, Qingyan He, Ningbo Cui, Manxue Zhang, Ziling He, Yu Feng, Yuelei Liu, Zhihui Wang, Guoyu Zhu, Liwen Xing, Shouzheng Jiang

Published 2026-06-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bin Zhu, Qingyan He, Ningbo Cui, Manxue Zhang, Ziling He, Yu Feng, Yuelei Liu, Zhihui Wang, Guoyu Zhu, Liwen Xing, Shouzheng Jiang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out exactly how much water a citrus orchard is "drinking" and "sweating" (a process called evapotranspiration) every day. This is crucial for farmers who want to water their trees perfectly—giving them just enough to thrive without wasting precious water.

This paper is like a taste test where researchers tried five different "recipes" (mathematical models) to predict how much water these orange trees use. They compared these recipes against a "gold standard" measurement taken by a high-tech weather tower in a real orchard in Southwest China.

Here is the breakdown of what they found, using simple analogies:

The Contestants: Five Different "Recipes"

The researchers tested five different ways to calculate water use. Think of them as different chefs trying to guess how much water a tree needs:

The "One-Size-Fits-All" Chef (Penman-Monteith / P-M): This chef treats the whole orchard as one giant, uniform leaf. It's simple and famous, but it assumes the ground is completely covered by leaves. In a young orchard where you can still see the dirt between trees, this chef gets confused and guesses too high.
The "Layered" Chef (Shuttleworth-Wallace / S-W): This chef tries to be very detailed, separating the water used by the leaves from the water evaporating from the soil. It's a complex recipe with many ingredients. While smart, it tends to overcook the meal (overestimate water use), especially around noon.
The "Patchwork" Chef (Two-Patch / T-P): This chef looks at the orchard as a quilt. Some patches are green leaves, and some are bare soil. They calculate the water use for the green patches and the dirt patches separately and then add them up. This is much more accurate for orchards where the ground isn't fully covered.
The "Hybrid" Chefs (TVET and H-D): These are the advanced chefs who combine the best parts of the "Layered" and "Patchwork" approaches. The H-D (Hybrid-Dual Source) model is the star of the show. It's like a chef who not only separates the soil and leaves but also checks the wind and air stability to adjust the recipe in real-time.

The Results: Who Won?

The researchers tested these chefs over four years, looking at the data every 30 minutes and every day.

The Winner: The H-D model was the clear champion. It was the most accurate at predicting exactly how much water the trees used, whether looking at a 30-minute snapshot or a full day. It was the only model that didn't consistently guess too high or too low.
The Runner-Up: The T-P (Patchwork) model was also very good, especially when the fruit was growing big and the tree canopy was thick.
The Losers: The simple "One-Size-Fits-All" (P-M) and the overly complex "Layered" (S-W) models struggled. They often thought the trees were drinking way more water than they actually were, particularly when the trees were young or when the sun was hottest at noon.

The "Secret Ingredients" (Sensitivity Analysis)

The researchers also asked: "If we change one ingredient in the recipe, how much does the final guess change?" This is like asking, "If I add a pinch more salt, does the soup taste totally different?"

The Most Sensitive Ingredient (Canopy Resistance): This is like the "stomach" of the tree. It represents how tightly the tree closes its tiny pores (stomata) to hold onto water. If the tree opens its pores a little wider (resistance goes down), the model predicts a huge jump in water use. All models were very sensitive to this.
The Second Most Sensitive Ingredient (Soil Moisture): This is the water in the dirt. If the soil gets wetter, the trees drink more. The models were very reactive to this; a small change in soil wetness caused a big change in the prediction.
The Surprising Twist (Temperature): You might think hotter weather means trees drink more. However, the models showed that when it gets too hot, the trees actually close their pores to protect themselves, which lowers the predicted water use. The models caught this clever biological reaction.
The Leaf Count (LAI): The "Layered" chef (S-W) was very sensitive to the number of leaves. If you guessed the leaf count wrong, the whole prediction went off the rails. The "Patchwork" chefs were more forgiving; they could handle a few more or fewer leaves without panicking.

The Bottom Line

If you are a farmer in a hilly, subtropical area trying to water your citrus trees:

Don't use the simple "One-Size-Fits-All" recipe; it will waste water by guessing too high.
The Hybrid-Dual Source (H-D) model is the most reliable tool for your job because it understands that an orchard is a mix of leaves and soil, and it adjusts for the wind and air conditions.
However, if the trees are fully grown and the ground is completely shaded, the simpler "Patchwork" (T-P) model is also a great, easy-to-use option.

This study helps farmers and scientists choose the right "calculator" to ensure trees get the right amount of water without wasting a drop.

Technical Summary: Performance Comparison of Penman-Monteith-Based Evapotranspiration Models in a Southwest China Citrus Orchard

Problem Statement
Accurate estimation of crop evapotranspiration (ET) is fundamental for optimizing irrigation strategies and ensuring sustainable water use in agriculture. While the Penman-Monteith (P-M) model is the industry standard for well-vegetated ecosystems, its classical single-source "big-leaf" framework struggles in heterogeneous landscapes like citrus orchards. The model's inability to separate soil evaporation (E) from plant transpiration (T) and its simplification of complex stomatal responses into a bulk resistance term often lead to inaccuracies, particularly in sparsely vegetated or patchy canopies. Although dual-source and hybrid models have been proposed to address these limitations, there is a lack of rigorous, multi-scale comparative studies in subtropical orchard ecosystems that evaluate model performance across different temporal resolutions (half-hourly to daily) and phenological stages, alongside a quantitative sensitivity analysis of their structural drivers.

Methodology
This study utilized four years of eddy covariance (EC) data (2020–2023) from a sugar orange (Citrus Tachibana) orchard in Qionglai City, Sichuan Province, Southwest China. The research evaluated five P-M-based ET models with varying conceptual structures:

Penman-Monteith (P-M): A single-source model.
Shuttleworth-Wallace (S-W): A dual-source layered model.
Two-Patch (T-P): A dual-source patch model assuming independent soil and vegetation patches.
Topography and Vegetation-based surface energy partitioning algorithm (TVET): A hybrid combining S-W resistance networks with T-P aggregation.
Hybrid-Dual Source (H-D): A model employing a layered scheme for energy distribution and a patch method for flux aggregation, incorporating atmospheric stability corrections.

Model performance was assessed at half-hourly, daily, and growth-stage-specific scales (flowering/fruiting, young fruit, fruit swelling, and fruit ripening) using statistical metrics including $R^2$ , RMSE, MAE, and the consistency index ( $d_1$ ). Furthermore, a global sensitivity analysis was conducted to quantify the influence of key resistance parameters (canopy/leaf stomatal resistance, aerodynamic resistances, soil resistance) and environmental inputs (radiation, temperature, VPD, wind speed, soil water content, and leaf area index) on simulated ET.

Key Results

Temporal Scale Performance: Model performance varied significantly by temporal resolution. At the half-hourly scale, the H-D model achieved the highest accuracy ( $R^2 = 0.84$ , RMSE = 0.038 mm·0.5h⁻¹), effectively reproducing diurnal cycles. The S-W model exhibited systematic overestimation during noon hours. On a daily scale, patch-based models (T-P, TVET, H-D) consistently outperformed single-source (P-M) and layered (S-W) models. The H-D model again demonstrated superior accuracy ( $R^2 = 0.91$ , RMSE = 0.47 mm·d⁻¹) with minimal average underestimation (1.63%).
Phenological Sensitivity: Model efficacy was growth-stage dependent. The H-D model excelled during the flowering/fruiting and fruit ripening periods. Conversely, the simpler T-P model performed best during the fruit expansion period ( $R^2 = 0.88$ ), suggesting that under dense canopy conditions where soil evaporation is suppressed, complex resistance networks may introduce diminishing returns or additional errors.
Sensitivity Analysis: Simulated ET was most sensitive to canopy resistance ( $r_c$ ) in the P-M model and leaf stomatal resistance ( $r_{sc}$ ) in the other models; a 20% decrease in these parameters increased ET by 3.71%–7.41%. Among environmental inputs, soil water content (SWC) was the most responsive factor, with a 20% increase in SWC causing ET variations between 10.43% and 32.27% across models. The S-W model showed the highest sensitivity to Leaf Area Index (LAI), with a 20% LAI decrease reducing ET by 11.38%, whereas patch-based models showed lower sensitivity due to the compensatory trade-off between transpiration and evaporation.

Key Contributions
This study provides a systematic, multi-scale evaluation of the P-M model family in a subtropical orchard, moving beyond simple performance ranking to uncover the structural reasons behind model behavior. It identifies the H-D model as the most robust option for heterogeneous orchard environments due to its integration of atmospheric stability corrections and dual-source energy partitioning. Additionally, the research clarifies that model selection should be context-dependent; while H-D is generally superior, simpler patch-based models like T-P may be sufficient and more efficient during periods of dense canopy cover. The sensitivity analysis further deconstructs the reliance of these models on specific resistance parameters and environmental forcings, highlighting SWC and stomatal resistance as primary drivers of uncertainty.

Significance
The findings offer a mechanistic basis for model selection and improvement in subtropical orchard ecosystems. By identifying optimal models for specific temporal and phenological contexts, this research supports more precise water management and irrigation strategies for citrus production. The study underscores the necessity of accurately parameterizing plant physiological responses and soil hydraulic processes to reduce ET estimation errors, ultimately contributing to improved water use efficiency and regional water resource management in water-sensitive agricultural systems.

The Contestants: Five Different "Recipes"

The Results: Who Won?

The "Secret Ingredients" (Sensitivity Analysis)

The Bottom Line

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