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the Creative Commons Attribution 4.0 License.
| 01 Sep 2026
Effects of atmospheric turbulence on vertical dispersion of carbon dioxide and methane over subtropical paddy fields
Abstract. Paddy fields serve as a critical methane (CH4) source and carbon dioxide (CO2) sink, playing an essential role in terrestrial carbon cycling and greenhouse gas budgets. The effects of atmospheric turbulence on the vertical dispersion of CO2 and CH4 were investigated in this study, using high-frequency observations over subtropical paddy fields. The pronounced diurnal variations in surface concentrations and turbulent fluxes of both gases suggest the dominant control of boundary-layer turbulent diffusion. Focusing on nocturnal stable conditions, mutual information was introduced to characterize relevant nonlinear processes. Turbulence over the paddy fields becomes intermittent when the nighttime wind speed falls below 1.5 m s−1. This weak and intermittent turbulence generally leads to the accumulation of CO2 and CH4 near the surface, whereas short turbulent bursts promote rapid dispersion, showing strong non-stationarity. Under intermittent turbulence, interference from submeso motions renders similarity relationships inapplicable for describing the transport of momentum, heat, as well as passive scalars (CO2 and CH4). This limitation can be effectively mitigated by removing submeso components from original observations. The distinct spectral gap between submeso and turbulent scales indicates the breakdown of energy cascade. As submeso energy is confined to its original scale, the energy supply for small-scale turbulence is limited and turbulence becomes more stochastic. This study reveals the effects of intermittent turbulence on the vertical diffusion of CO2 and CH4 under nocturnal stable conditions, but also highlights the challenges in parameterizing such stable-boundary-layer processes. This provides new insights for understanding carbon cycling over terrestrial ecosystems.
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Status: open (until 13 Oct 2026)
- RC1: 'Comment on egusphere-2026-3201', Anonymous Referee #2, 16 Sep 2026 reply
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RC2: 'Comment on egusphere-2026-3201', Anonymous Referee #3, 23 Sep 2026
reply
The manuscript addresses an interesting and relevant topic using valuable high-frequency observations; however, the methodology is not always described with sufficient clarity, and several of the conclusions are not adequately supported by the analyses presented.
Major Comments
- The study needs to address better the relationship between stability, low-wind conditions, submeso, scalar dispersion. It is recognized that MOST works for weakly-stable stratification while it fails (broadly speaking) in very stable stratification. Submeso motions generally become increasingly important under very stable, weak-turbulence conditions. Low-wind conditions favour the occurrence of horizontal meandering, that deeply influence dispersion, but horizontally more than vertically. Horizontal submeso variability may strongly affect concentration records and contaminate flux estimates without representing vertical turbulent dispersion. Throughout the paper the authors do not address the difference between weakly stable and very stable stratification.
- Data processing. The authors do not justify the choice of 30 minutes intervals.
Under weak turbulence, a fixed 30-minute interval may also include submeso variability, waves, meandering, regime transitions, and non-stationarity. Conversely, a 30-minute record cannot adequately characterize submeso motions whose periods are comparable to or longer than 30 minutes. - Data processing. The criteria to identify stable conditions not discussed in the paper as it should (I suggest following Dupont and Patton, 2012). Not considering the difference between very stable and weak stable stratification a major flaw of the analysis. A statement like the one on lines 281-282 (In contrast, the small nighttime flux, which possibly contains large uncertainties associated with intermittent turbulence, cannot resolve the underlying physical mechanisms) is not precise. The night-time part of Figure 4 is influenced by the 30 min average time. The authors should examine the sensitivity of the results to shorter averaging intervals, including one-minute or few-minute averages, and justify the selected interval based on the relevant turbulent and submeso timescales. .
- The Hilbert-Huang Transform is not introduced in the introduction and its use is not discussed against other methodologies like wavelets (see for example Baars et al. 2015), auto-correlation functions or multiresolution decomposition (Vickers and Mahrt, 2003) among others.
- The statement that “the normalized mutual information between LIST and wind speed is the highest among all variables” requires a more cautious interpretation. Although LIST is not a component of the mean wind speed, its components are obtained from the same wind record, and their relationship is physically expected within the HOST framework. Therefore, the relatively large mutual information between them does not by itself demonstrate that wind speed controls turbulence intermittency. Mutual information quantifies statistical dependence but does not establish either causality or its direction. Further, mean wind speed is not a direct measure of mechanical turbulence production. The authors should replace the statement that “mechanical forcing is a key driver” with a more limited statement describing the observed statistical association between wind speed and LIST. The methodology used to estimate mutual information also requires further explanation. It is not straightforward to understand how Eqs. 18-23 were applied to the data.
- Figure 8. How would the stable part look like if only weak stable stratification and 1- minute (or few minutes) averages were considered? Figure 8 may simply show that the average time is not appropriate, submeso motion might not need to be removed if they were not considered in the first place in the averaging procedure.
- Line 324 and Figure 6. The fact that scalars are rapidly dispersed upward was not sufficiently proven. The authors should also plot the vertical scalar fluxes.
- Figure 10. What is depicted in Figure 10? Single case spectra? Average spectra? If average spectra were evaluated what is the criteria used to define the subset on which averaging? What is the +- sigma interval? Further, Figure 10 then shows that the low-LIST records have greater relative low-frequency energy and interprets this as independent evidence of dominant submeso motions. However, that spectral characteristic is already embedded in the procedure used to define LIST.
- The introduction lacks some fundamental bibliography. For example, Acevedo et al. 2019 and Maroneze et al. (2019,2021) discuss the transition between weakly and very stable stratification and its link to HOST and intermittent turbulence. Mortarini et al. (2019) discuss the influence of submeso motions on the Rotta scheme in turbulence closure models. Mortarini and Anfossi (2015), Mortarini et al. (2016), Cava et al. (2019) and Urbancic et al. (2021) discuss the characterization of submeso motions and presents spectra very similar to the one presented in Fig. 10. The application of information theory to turbulence is very interesting, I would consider looking at Martínez-Sánchez et al. (2024) and references within to add some references in the introduction.
Minor Comments
Lines 34-38 the sentence seems to imply that low wind conditions and stable stratification are synonyms of intermittent turbulence. This is not necessarily true. Please, rephrase.
Line 149 and Equation 16. The use of LIST depends on the filter used to define V_{smeso}. In the literature other parameters that do not require an explicit HHT-based separation between turbulent and submeso components were used like the velocity aspect ratio (Vickers and Mahrt, 2006) or the ratio between the vertical and horizontal velocity variances (Mortarini et al., 2019). Can the authors comment on this?
Line 153. The choice of the LIST threshold is crucial to this study. Zhang et al. (2024) discuss it using two LIST parameters, one for dynamics and one for thermodynamics, they also provide a figure similar to Figure 4 in which stability was considered. It would also be nice to colour the HOST (Figure 4a) points with their respective LIST values.
Line 157. Please, check Eq. 17.
Lines 163-164. As commented above, 30 min may not be enough to identify submeso activity.
Figure 2. Interpreting a single Fourier spectrum as representative of the entire period implicitly assumes that the statistical properties do not change substantially, whereas the authors identify three distinct stages. Since three stages were identified, why not considering single spectrum for each stage? How the single stage spectra compare to the full period one? A wavelet of the whole period would also be more informing.
Line 298. The wind-speed threshold also depends on the height above the ground (see for example Acevedo et al. 2021), hence the comparison among site should be done carefully.
Line 414. I do not understand what the author means with “suppressed magnitude”. The spectra are normalized, hence they describe the relative variance distribution, not its absolute value.
Bibliography
Acevedo OC, Maroneze R, Costa FD, et al. The nocturnal boundary layer transition from weakly to very stable. Part I: Observations. Q J R Meteorol Soc. 2019; 145: 3577–3592. https://doi.org/10.1002/qj.3642
Acevedo OC, Costa FD, Maroneze R, Carvalho A, Puhales FS, Oliveira PES. External controls on the transition between stable boundary-layer turbulence regimes. QJR Meteorol Soc. 2021; 147: 2335–2351. https://doi.org/10.1002/qj.4027
Baars, W.J., Talluru, K.M., Hutchins, N. et al. Wavelet analysis of wall turbulence to study large-scale modulation of small scales. Exp Fluids 56, 188 (2015). https://doi.org/10.1007/s00348-015-2058-8
Cava, D., Mortarini, L., Anfossi, D. et al. Interaction of Submeso Motions in the Antarctic Stable Boundary Layer. Boundary-Layer Meteorol 171, 151–173 (2019). https://doi.org/10.1007/s10546-019-00426-7
Sylvain Dupont, Edward G. Patton, Influence of stability and seasonal canopy changes on micrometeorology within and above an orchard canopy: The CHATS experiment, Agricultural and Forest Meteorology, Volume 157, 2012 10.1016/j.agrformet.2012.01.011.
Maroneze R, Acevedo OC, Costa FD, et al. The nocturnal boundary layer transition from weakly to very stable. Part II: Numerical simulation with a second-order model. Q J R Meteorol Soc. 2019; 145: 3593–3608. https://doi.org/10.1002/qj.3643
Maroneze, R., Acevedo, O.C., Costa, F.D. et al. How is the Two-Regime Stable Boundary Layer Reproduced by the Different Turbulence Parametrizations in the Weather Research and Forecasting Model?. Boundary-Layer Meteorol 178, 383–413 (2021). https://doi.org/10.1007/s10546-020-00581-2
Martínez-Sánchez, Á., Arranz, G. & Lozano-Durán, A. Decomposing causality into its synergistic, unique, and redundant components. Nat Commun 15, 9296 (2024). https://doi.org/10.1038/s41467-024-53373-4
Mortarini, L. and Anfossi, D. (2015), Proposal of an empirical velocity spectrum formula in low-wind speed conditions. Q.J.R. Meteorol. Soc., 141: 85-97. https://doi.org/10.1002/qj.2336
Mortarini, L., D. Cava, U. Giostra, F. D. Costa, G. Degrazia, D. Anfossi, and O. Acevedo, 2019: Horizontal Meandering as a Distinctive Feature of the Stable Boundary Layer. J. Atmos. Sci., 76, 3029–3046, https://doi.org/10.1175/JAS-D-18-0280.1.
Mortarini, L., Maldaner, S., Moor, L.P., Stefanello, M.B., Acevedo, O., Degrazia, G. and Anfossi, D. (2016), Temperature auto-correlation and spectra functions in low-wind meandering conditions. Q.J.R. Meteorol. Soc., 142: 1881-1889. https://doi.org/10.1002/qj.2796
Urbancic GH, Suomi I, Vihma T. A general theory for the characterization of submeso-scale motions and turbulence in the atmospheric surface layer. Q J R Meteorol Soc. 2021; 147: 660–678. https://doi.org/10.1002/qj.3939
Vickers, D., and L. Mahrt, 2003: The Cospectral Gap and Turbulent Flux Calculations. J. Atmos. Oceanic Technol., 20, 660–672, https://doi.org/10.1175/1520-0426(2003)20<660:TCGATF>2.0.CO;2.
Vickers, D., Mahrt, L., 2006. A solution for flux contamination by mesoscale motions with very weak turbulence. Bound.-Layer Meteorol. 118, 431–447
Citation: https://doi.org/10.5194/egusphere-2026-3201-RC2
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- 1
Based on a high-frequency observation system, this paper analyzes the effects of nocturnal intermittent turbulence on the vertical transport of CO₂ and CH₄ in rice paddies. The research questions are clearly defined, the analytical framework is relatively comprehensive, and the main observational conclusions are reasonably persuasive. The research focus of the paper aligns with the requirements of the ACP journal. However, there are still issues that require further clarification regarding data screening, the validation of passive scalar similarity relations, and the explanation of energy cascade mechanisms.
Major comments
The focus of this study is on nighttime conditions with light winds and intermittent turbulence; however, the description of data quality control and the final sample selection process in Section 2.2 is currently insufficient. The authors primarily describe routine preprocessing steps such as spike removal, coordinate rotation, linear detrending, and density correction, while the screening criteria actually used for subsequent analysis mainly include stability and CO₂ and CH₄ flux thresholds. The authors need to further explain the rationale for selecting these thresholds and report the number of raw 30-minute samples, the rejection rates at each screening step, and the final number of samples retained under continuous and intermittent turbulence conditions. In particular, they need to clarify whether the u* and flux thresholds might preferentially exclude data under conditions of weak turbulence and weak transport, as these conditions are precisely the focus of this study. We recommend that the authors conduct necessary sensitivity analyses to demonstrate that results such as those in Figs. 8–9 are not significantly affected by the sample screening criteria.
Major 2. Insufficient direct evidence for the “breakdown–recovery” of the CO₂ and CH₄ similarity relationship
Fig. 8 clearly shows that, under steady-state conditions, continuous turbulence generally conforms to the MOST similarity relationship, whereas intermittent turbulence deviates significantly; after removing the submesoscale components, the reconstructed wind speed and potential temperature values once again approach the similarity relationship. However, Fig. 9 presents results for water vapor, CO₂, and CH₄ only under continuous turbulence conditions; the reconstructed results for intermittent turbulence and after removing the submesoscale components are not provided. Potential temperature exhibits scaling behavior similar to that of passive scalar variables, which provides a physical basis for this inference; however, it does not directly prove that CO₂ and CH₄ also experience the same degree of similarity breakdown under intermittent turbulence conditions and recover after the removal of mesoscale motion. Given that CO₂ and CH₄ are the core subjects of this study and that this conclusion occupies a prominent position in the abstract and conclusions, it is recommended that the authors at least directly present the scaling relationships for CO₂ and CH₄ under the three conditions—continuous, intermittent, and reconstructed—to provide direct empirical support for this core conclusion.
Major 3. Figs. 10–11 are insufficient to support the mechanistic conclusion of “energy cascade breakdown”
Fig. 10 clearly shows that under intermittent turbulence conditions, the low-frequency mesoscale components are enhanced, the high-frequency turbulent components are weakened, and a distinct spectral gap appears between the submesoscale and turbulent scales. These results support the existence of distinct scale separation and the suppression of small-scale turbulent activity under intermittent turbulence conditions; however, the spectral gap itself does not directly prove a “breakdown” in energy cascade from large to small scales, as the energy spectrum primarily reflects the distribution of energy across different scales rather than directly measuring energy transfer between scales. We recommend that the authors refine their description.
The authors further attempt to support this mechanistic explanation using the incremental self-mutual information in Fig. 11, but there is a key issue here that requires clarification. The authors calculated the information required between the current state X(t) and the increment:
ΔX(t) = X(t+τ) − X(t)
rather than the mutual information between the current state X(t) and the future state X(t+τ). If the research objective is to quantify the information retention or “memory” of turbulence over time, the latter has a more direct physical significance. The authors are asked to clarify this point.
Minor comments
Minor 1. It is recommended to supplement information on the station’s surrounding environment and source areas
It is recommended to add a schematic diagram of the land surface or land use around the observation station in Section 2.1, labeling major potential local sources and prevailing wind directions. If conditions permit, a simple EC footprint analysis could be provided to illustrate the range of the land surface represented by the flux observations under major meteorological conditions. This is particularly meaningful for this paper because the authors discuss both local rice paddy CO₂/CH₄ sources and sinks and use wind direction to explain regional CO₂ and PM₂.₅ transport; therefore, a clearer distinction between the local/sub-local footprint and regional advection effects is needed.
Minor 2. Suggest adding simple quantitative statistics on meteorological differences across the three stages
The authors note that nighttime wind speeds in Stage 2 were generally higher than in Stage 1, particularly on multiple occasions between August 13 and 18 when they exceeded 1.5 m/s; however, this difference is not readily apparent from the dense time series in Fig. 1. We recommend reporting the mean or median of nighttime wind speeds across different stages, the degree of dispersion, and the proportion of samples with wind speeds > 1.5 m/s to more directly support the inter-stage differences. Additionally, given that wind direction is used later in the text to discuss regional transport, we suggest including a wind rose diagram or other more intuitive wind direction statistics.
Minor 3. Explanation of the method used to determine the 1.5 m/s transition wind speed in Fig. 4
The HOST relationship in Fig. 4 indicates a wind speed threshold of approximately 1.5 m/s for the transition between strong and weak winds, and this threshold is generally consistent with the intermittent/continuous turbulence classification at LIST = 0.75. This result is reasonable in itself, and the authors compare it in the text with the 2.5 m/s threshold obtained by Zhang et al. (2004) over a desert surface. It is recommended that the authors explicitly state how the 1.5 m/s velocity inflection point was derived—whether through statistical optimization or visual judgment—to enhance the method’s reproducibility.