Derivation and validation of estimation model of rainfall kinetic energy under canopy

Li, Zixi; Tian, Fuqiang

doi:https://doi.org/10.5194/egusphere-2025-3294

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https://doi.org/10.5194/egusphere-2025-3294

Preprints

19 Sep 2025

| 19 Sep 2025

Status: this preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).

Derivation and validation of estimation model of rainfall kinetic energy under canopy

Zixi Li and Fuqiang Tian

Abstract. The interception effect of the canopy on rainfall alters the kinetic energy of the rainfall as it reaches the ground, which is crucial for soil and water conservation, ecosystem stability, and energy transfer within environmental systems. A novel estimation model for the kinetic energy of rainfall under canopy is developed by stratifying the canopy using parameters such as leaf area index and leaf inclination angle, explicitly distinguishing between canopy-dripped and splashed raindrops. The efficacy of the model is subsequently assessed and analyzed through a comprehensive examination of 9 field datasets encompassing LiDAR and raindrop spectrum observations. The simulated under-canopy total kinetic energy, splashing drop kinetic energy, and dripping drop kinetic energy showed average R² values of 0.788, 0.613, and 0.768, and average RMSE values of 19.9, 2.2, and 21.1 J/m²h, respectively. Simulations reveal that the canopy exerts a complex influence on the kinetic energy of rainfall beneath it, which may either increase or decrease depending on the physical characteristics of the canopy. The canopy may stabilize the raindrop spectrum and kinetic energy beneath it. Regardless of external variations, these parameters remain constant under an unchanged canopy.

Received: 09 Jul 2025 – Discussion started: 19 Sep 2025

Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.

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.

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Zixi Li and Fuqiang Tian

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RC1:
'Comment on egusphere-2025-3294', Anonymous Referee #1, 14 Oct 2025 reply

Manuscript number: egusphere-2025-3294
Authors: Zixi Li, Fuqiang Tian

Comments to authors

Overall comments
This study derived and validated raindrop kinetic energy estimation model for tree canopy based on microphysical processes. The model was developed based on Li and Tian 2025 and Li et al. 2025. The series of papers that take physical properties of leaf, microstructure of the canopy and microphysical processes into consideration are novel and have potential for development. Overall, this present manuscript is well organized and well written.
The weak point is that variables and constants are difficult to follow because there are numerous of them. That makes the manuscript hard to read. Relevant to that, for some variables and constants, there are no explanations and descriptions. I advise making the list of variables and constants at the end of the text like Li and Tian 2025 did, in addition to describing and defining them in the text firmly. However, it is not feasible to explain all variables and constants perfectly in the manuscript due to large number of them. Instead of omitting exact and detailed explanations on variables and constants, authors should refer readers to Li and Tian 2025 and Li et al. 2025 by explicit description, although I think most readers will likely do so without such description.
There are many points to be modified regarding format and lack of references. Please refer to https://www.hydrology-and-earth-system-sciences.net/submission.html

Specific comments

L18
“external variations”
I think the following description is better.
“variations in rainfall characteristics”

L19
“an unchanged”
I think the following description is better.
“a certain”

L35 to 36
“the number of raindrops …in kinetic energy”
I suggest modification as follows.
-> large raindrops are formed and the number of raindrops beneath the canopy is reduced, which results in a broader distribution range and an increase in kinetic energy

L38
measurement, mainly -> measurement,

L47
DSD -> raindrop size distribution

L50 to 53
This paragraph looks like the index of the paper. Readers would like to know the objectives of this study at the end of Sect 1 reflecting the background of the study stated earlier in the section. Authors need to add one or more specific objective(s) of this study here.

Between L90 and 91
It is advisable to explicitly encourage readers to refer Li and Tian 2025 and Li et al. 2025. Additionally, compiling a list of variables and constants and presenting it at the end of the main text would be useful for readers.

L96
Please delete “is the total kinetic energy calculation”.

Eq. (2)
E(D) -> E(D_i)
Please note that subscripts and superscripts are in the standard font, not italics.

L99
the unit area unit rainfall depth kinetic energy -> kinetic energy per unit area and unit rainfall depth

L99
What does “(KE)” mean? Does it mean E_Kp is a function of kinetic energy? If so, I think the expression is redundant and “(KE)” should be deleted.

L100
Please replace "t is the drop spectrometer observation time (60s)” with “P is the amount of rainfall”, because t does not appear in Eq. (3).

L102
Please delete “, A is the drop spectrometer observation area (54cm²),” as A has already been defined on line 100.

L104
the canopy density -> fractional vegetation cover (FVC)

Eq. (6)
There is no explanation for σ.
In the upper equation for s_max:
The denominator in the root symbol includes sinα, but Eq. (1) in Li et al. 2025, which I think original equation, does not.
In the lower equation:
Inside the root symbol in Eq. (2) in Li et al. 2025, (sinα)/2 is multiplied, but not in this present manuscript.
What is the cause of these differences?

L114
Please insert “that reflects wind load effect and” after “a coefficient”.

Eq. (7)
Please add explanation for "s”.

L119
Pleas insert “Li and Tian, 2025” after “function”.

Eq. (10)
There is no description on G. It appears on L184 to 185 but should be presented here.

L139
the proportion of splash drops -> the proportion of canopy and stem splash drops
Please consider that in Table 1 the terms “Leaf splashing” and “Stem splashing” are used.

L140
canopy drip -> canopy and stem drip

L164
the splash intensity (mm/h) -> the portion of canopy and stem splash drops

L164 to 165
the canopy dripping intensity (mm/h) -> the portion of canopy and stem dripping

L169 to 175
Please add the stand characteristics like average tree height, average diameter at breast height and stem density.

L187 to 188
“The model was… in Table 3.”
This sentence describes on validation not the method and should be moved after “these nine rainfall events” on line 198 as in, “these nine rainfall events along with accumulated rainfall, mean wind speed and mean rainfall intensity.”

Table 2
Symbol “R” should be replaced with “I” as already shown on line 158.
Symbol “LAD” should be replaced with “f(α)” or “α” because Li and Tian 2025 used them as leaf inclination distribution function and leaf inclination angle, respectively.

L209
Please insert “through the coefficient k” after “wind load effects”.

L215
Please insert “in total and dripping energy” after “performance”.

Figure 4
The vertical axis in Figure 4, f(ds), means raindrop size distribution but the maximum values in the figure range from 0.8 in Fig. 4a to 2.5 in Fig. 4b. Does it mean the number of raindrops in the measurement volume in OTT Parsivel2 laser spectrometer?

Figure 5: vertical axis labels
For Fig. 5a and 5d, please replace E_k with E_K.
For Fig. 5b and 5e, please replace E_k with E_s.
For Fig. 5c and 5f, please replace E_k with E_d.

Figure 6a, b
Please replace E_kt with ΣE_K considering Eq. (4).

Figure 6b
In Table 3, accumulated rainfall on 26 August was 6.71 mm but in Fig. 6b it is some 30 mm or more. Please explain or clarify the cause of the difference.

Technical comments

L13
9 field datasets -> nine field datasets
That holds true throughout the text.

L15
J/m² h -> J m^-2 h^-1
That holds true throughout the text.

L50
This section 2 delves into -> In Sect 2., we delve into
The abbreviation holds true throughout the text.

Figure 1
The combination of red, brown and green are not good for readers with color vision deficiencies. Please modify.

L105
E_d and -> and E_d

L106
Please put a space between “1.3” and “mm”.

L107
Please put a space between “0.8” and “mm”.

References

In the running text, please replace “&” with “and”, e.g. L49 Frasson & Krajewski, 2013.

L303 de Moraes Frasson et al. 2013 is in the reference list but not in the text.

L312 Fernández-Raga et al. 2010 is not in alphabetical order.

L352, 355 There are two Nanko et al. 2008 that are not distinguishable.

The following papers that appear in the text are not found in References.
L27 Angulo-Martínez et al., 2016
L29 Jeong et al., 2024
L39 Mosley et al., 1983
L40 Yan et al., 2021
L49, 74 Frasson and Krajewski, 2013

L36 Katayama et al., 2024 -> Katayama et al., 2023

L49, 79 Murakami et al., 2021 -> Murakami, 2021

L67 Gash and Morton, Valente and Gash -> Gash and Morton (1978), Valente and Gash (1997)

L75 Rutter et al. (1997) -> Rutter et al. (1971)

L120 Mou J (1983) -> Mou (1983)

Reply

Citation: https://doi.org/10.5194/egusphere-2025-3294-RC1
- AC1: 'Reply on RC1', Zixi Li, 14 Oct 2025 reply
  
  We sincerely thank the referee for the constructive and encouraging comments on our manuscript. We agree that the large number of variables and constants makes the manuscript somewhat difficult to follow. In the revised version, we will:
  1、Add a comprehensive list of variables and constants at the end of the manuscript (similar to Li and Tian, 2025), including their definitions and units.
  2、Provide clearer explanations in the main text, especially when new variables or constants are first introduced.
  In addition, we will carefully revise the errors, format and references according to the specific comments and submission guidelines (https://www.hydrology-and-earth-system-sciences.net/submission.html).
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2025-3294-AC1
RC2:
'Comment on egusphere-2025-3294', Kazuki Nanko, 20 Oct 2025 reply
Review of egusphere-2025-3294
Overview:
The manuscript develops a process-based model of under-canopy throughfall kinetic energy (KE) by partitioning throughfall into splash, drip, and penetration components, assigning each a size and velocity distribution, and integrating to obtain KE. The attempt to link canopy microphysics to under-canopy KE is novel and worth pursuing. However, several core elements—parameter definitions and provenance, observational partitioning of the components, explicit assumptions about drop-size distributions (DSDs), and the consistency of terminology—are currently underspecified. These issues reduce clarity, limit reproducibility, and make it difficult to evaluate the results. A thorough revision focused on reproducible methods, consistent definitions, and transparent validation would substantially improve the manuscript.
Major comments
Framing and objectives

The Introduction reviews field work on under-canopy KE, but soon after states that the method for studying KE under canopy mainly uses experimental measurement. Please streamline the framing to avoid internal inconsistencies and clearly articulate the specific research objectives at the end of the Introduction.

Positioning relative to the throughfall partitioning literature

Because component partitioning is central to your approach, the literature review should explicitly situate the work with respect to key studies on throughfall partitioning, such as Levia et al. (2019, Hydrological Processes, doi:10.1002/hyp.13432), Nanko et al. (2022, Journal of Hydrology, doi:10.1016/j.jhydrol.2022.128144), and Nanko et al. (2025, JGR-Biogeosciences, doi:10.1029/2024JG008340). Clarifying how your definitions and assumptions align (or intentionally differ) from these studies will help readers evaluate the contribution.

Consistent terminology for throughfall types

Standard forest hydrology usage distinguishes free/direct throughfall, splash throughfall, and canopy drip (e.g., Levia et al., 2017, WIREs Water, doi:10.1002/wat2.1225). You use “penetration,” which risks confusion unless mapped clearly to prior terms. Please define precisely whether “penetration” is synonymous with free/direct throughfall or whether it includes drops secondarily generated by in-canopy splash (as your schematic may imply). If your category differs physically from free/direct throughfall, explain the rationale and adopt consistent wording throughout figures, equations, and text.

Equation (5): definition and coefficient consistency

The symbol γ is described as canopy density/FVC in different places, and Eq. (5) scales a KE term by γ. If γ denotes fractional vegetation cover, the direct/free-throughfall fraction is commonly represented by (1−γ). Rather than asserting an error, I recommend clarifying the physical meaning of γ and revisiting the coefficient so that the term associated with direct/free-throughfall is consistently represented (which may imply using (1−γ)). Please ensure that the terminology (FVC vs canopy density) is consistent across the paper.

Section 2.2 parameter definitions and provenance

Several parameters critical to reproducibility lack values, units, or sourcing: leaf surface contact angle θ (and how measured or sourced), the pinning proportion p, the retention coefficient β, surface tension σ, the wind-load parameter k, and the contact-angle hysteresis term X. Please provide a single comprehensive parameter table listing, for every symbol in Eqs. (5)–(14): name, definition, units, typical value or range, whether measured/assumed/fitted, the measurement/estimation method, and literature sources.

Observational partitioning of splash, drip, and direct/free components

Tabled statistics are reported separately for splash and drip KE, yet the Methods do not explain how the disdrometer observations were partitioned into these components. Please describe a transparent and reproducible diagnostic (e.g., thresholds in size–velocity space, spectral shape, timing relative to wind gusts or canopy shaking), provide sensitivity to threshold choices, and clarify how any ambiguity was handled. Without this, component-specific R² and RMSE are difficult to interpret.

Explicit DSD assumptions for each component

For splash, you indicate a range (e.g., 0.3–1.3 mm) and a central tendency, while for canopy drip you derive a representative size but do not state a distribution form. Because Eq. (14)-type integrals over size strongly depend on f(D), please specify explicit DSD functional forms for each component (e.g., gamma, lognormal, triangular, uniform), justify them with observations or literature, and ensure they are consistent with Fig. 4. State whether Fig. 4’s vertical axis is number-based or volume-based frequency.

Wind effects and leaf inclination

You state that Eq. (6) accounts for wind load via parameter k, and leaf inclination α appears elsewhere. Please clarify the physical role and calibration of k, whether α varies with wind, and how these influences were implemented (event-wise or time-varying). If wind effects were ultimately small in your validation, it would help to show a brief sensitivity analysis.

Raindrop velocity relation

Equation (8) uses a piecewise V–D relation with a breakpoint near 1.9 mm. Consider replacing or benchmarking against a widely used continuous relation (e.g., Atlas et al., 1973) to avoid artifacts at the breakpoint, and report the sensitivity of KE to the velocity model.

Fall height for drip and splash

The fall height h appears to be fixed as the mid-height of the last canopy layer for both drip and splash. Because origins differ (leaf tips vs branch edges) and canopy structure is heterogeneous, please justify this assumption or, preferably, derive h from your LiDAR geometry (e.g., distributions of likely origin heights) and examine sensitivity.

Definition and wording for pt

pt is defined as SAI/(LAI+SAI) but is referred to as “stem flow ratio” in places. In forest hydrology, “stemflow ratio” usually denotes the fraction of rainfall routed as stemflow, not an area fraction. Please adopt “stem area proportion” (or similar) consistently to avoid confusion.

Figure 4 — axis definition only

Please clarify the axis definitions: specify whether the vertical axis represents number-based or volume-based drop-size frequency (and provide units), indicate any normalization (e.g., per mm, per bin, probability density), and state the bin widths used on both axes.

Treatment of branch/twig drips

The model and figures emphasize leaf drip, but branch/twig drips can be important—especially in broadleaf canopies—and can alter DSDs. Please clarify whether branch-origin drips are included in your “canopy drip” category, whether they are distinguishable in the data, and how (or if) they are represented in the model. If neglected, state this explicitly and discuss implications.

Validation design, reporting granularity, and interpretability

It is unclear whether R² and RMSE are computed from 5-min bins within each event, then averaged, or from another aggregation. Please report the exact time aggregation, the number of samples per event, and the comparison targets (modeled vs measured component KE). For each event, provide measured KE (with uncertainty), rainfall duration, and a bias metric (e.g., modeled/observed mean ratio). Without this context, the reported RMSE values (≈20 J m⁻² h⁻¹) are hard to judge.

Discussion depth

The Discussion largely reiterates results. For example, please expand with (i) comparisons to prior under-canopy KE and partitioning studies (agreement/disagreement and causes), (ii) sensitivity to canopy traits (LAI, inclination, θ) and rainfall characteristics, and (iii) implications for erosion modeling and for transferring parameters to other sites/species.

Specific comments

• Lines ~95: For under-canopy drops, not all reach terminal velocity; “fall velocity” is more accurate than “terminal velocity.”

• Line ~104 and Table 1 note: Clarify whether γ denotes canopy density or FVC, and use one term consistently; revisit the coefficient in Eq. (5) accordingly.

• Eq. (6): Define σ (surface tension), k (wind-load parameter; units and calibration), and X (half the contact-angle hysteresis). Provide values and sources for θ and X for the study species.

• Line ~115: If wind effects are represented through k and/or through variations of α, please explain how α was measured or parameterized and whether it varies in time with wind.

• Line ~123: Clarify whether the fall height h is fixed at the mid-height of the last canopy layer for both drip and splash, and justify or test sensitivity.

• Line ~134: Avoid “stem flow ratio” for pt; use “stem area proportion (SAI/(LAI+SAI)).”

• Eq. (8): Consider adopting or benchmarking a continuous V–D relation (e.g., Atlas et al., 1973) to avoid artifacts near the current breakpoint.

• Fig. 2: State explicitly whether “penetration rain” includes splash-generated drops from upper layers. If yes, this differs from “free/direct throughfall” in prior literature; adjust terminology accordingly.

• Fig. 3 and Table 3: Report the number of time steps per event, the aggregation window used for statistics, event-level measured KE and duration, and a bias measure to contextualize RMSE.

• Section 3.1 and Fig. 4: Explicitly state that open-site and under-canopy KE were computed from Parsivel size–velocity spectra (referencing the equations), confirm that the open-site DSD shown is observation-based, and indicate whether the vertical axis is number-based or volume-based.

• Throughout: Define w, wl, and ws consistently, and supply units for every symbol on first use.

Reply
Citation: https://doi.org/10.5194/egusphere-2025-3294-RC2
- AC2: 'Reply on RC2', Zixi Li, 20 Oct 2025 reply
  
  We sincerely thank the referee for the careful reading and highly constructive comments. In the revised version, we will thoroughly revise the manuscript with a focus on improving clarity, reproducibility, and consistency in the following aspects:
  1. Framing and literature context: The Introduction will be streamlined to clarify the research objectives and to better position the study within the throughfall partitioning literature (e.g., Levia et al., 2019; Nanko et al., 2022, 2025).
  2.Terminology and parameter consistency: We will unify terminology for throughfall components (splash, drip, and direct/free throughfall), clarify the physical meaning of parameters (e.g., γ, pt), and ensure consistent definitions across text, figures, and equations.
  3. Model description and reproducibility: A comprehensive parameter table will be added with all symbols, units, sources, and typical values. We will also clarify the assumptions for drop-size distributions, fall height, wind effects, and velocity–diameter relations.
  4. Observation and validation details: The partitioning of observed throughfall components and the computation of validation metrics (R², RMSE) will be described transparently, including aggregation levels and uncertainty handling.
  5. Discussion enhancement: The Discussion will be expanded to include comparisons with previous under-canopy KE studies, sensitivity to canopy and rainfall characteristics, and implications for soil erosion and parameter transferability.
  We are grateful for these valuable suggestions, which will significantly improve the scientific rigor and clarity of the paper.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2025-3294-AC2

Zixi Li and Fuqiang Tian

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Short summary

Forests can change the kinetic energy of rain below them. We built a new model that breaks down the canopy into layers, and tracks two types of raindrop: direct splashes and water dripping from leaves. The model was validated through nine rainfall events. The canopy doesn't always reduce the rain's force, and sometimes it increases it, depending on the specific structure of the leaves and branches.


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