the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Dec 2025
Aging of Droplet Size Distribution in Stratocumulus Clouds: Regimes of Droplet Size Distribution Evolution
Abstract. The climatic impact of maritime stratocumulus clouds depends on the evolution of their droplet size distribution (DSD), yet the mechanisms controlling its variability during evaporation remain poorly constrained. Using large-eddy simulations coupled with a Lagrangian cloud model, we demonstrate that the evolution of the DSD exhibits two primary regimes: an adiabatic growth regime and an entrainment–descent regime. Within the latter, DSD evolution follows divergent pathways determined by the droplet's history: direct mixing of entrained air near the cloud top causes rapid broadening, whereas large-scale boundary-layer descent leads to gradual evaporation. Our Lagrangian analysis of the Damköhler number reveals that the commonly observed vertical transition from inhomogeneous to homogeneous mixing signatures does not necessarily reflect a change in the mixing mechanism. Instead, it results from the divergent histories of droplets that are either mixed with dry air or remain undiluted. Droplets directly impacted by entrainment retain inhomogeneous signatures throughout their descent, while those unaffected by direct mixing exhibit homogeneous-like characteristics regardless of altitude. This distinction helps resolve ambiguities in interpreting in situ observations where mixing history is often unknown. Finally, we propose a combined analytical–empirical formulation that captures the relative dispersion during both growth and evaporation.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-6099', Anonymous Referee #1, 25 Jan 2026
- AC1: 'Reply on RC1', Jung-Sub Lim, 06 Mar 2026
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RC2: 'Comment on egusphere-2025-6099', Anonymous Referee #2, 26 Jan 2026
Review of “Aging of Droplet Size Distribution in Stratocumulus Clouds: Regimes of Droplet Size Distribution Evolution”
Authors: Jung-Sub Lim and Fabian Hoffmann
MS No.: egusphere-2025-6099
This is a clearly-written paper presenting results and interpretation of a novel simulation of cloud microphysical behavior in stratocumulus clouds. The investigation rests on the Lagrangian representation of microphysics, and it is exciting to see the insights that come from this powerful tool. The L^3 model is especially compelling because it includes sub-grid representation of turbulent fluctuations that are likely important for droplet growth and evaporation, especially in regions where supersaturation variability is large due to entrainment and mixing. I find the simulation results to be rigorous, and most of the presentation of results is clear and convincing. At the culminating stage of the paper, however, I have a fundamental disagreement with the interpretation that is provided, and either I have misunderstood the authors’ argument, or the authors have reached a conclusion that I believe is a misinterpretation of the results. I say this with full respect, wishing to engage the authors as a curious and truth-seeking colleague. My recommendation is that the paper should eventually be published, but I sincerely hope the authors will meaningfully engage and, as needed, reconsider the interpretation of their results in Section 3.3.3, revising the paper as needed. My central concern is described in the next paragraph, followed by several other significant questions or requests. Finally, the review ends with a list of detailed comments that I hope will improve the paper.
The simulation results convincingly show that inhomogeneous mixing is predominant near cloud top (e.g., lines 247-248), and although there is a confusing statement on lines 391-392 that sounds contradictory to this, my understanding is that the earlier data presentation agrees with this: i.e., droplet diameter changes only slightly, and primarily it is droplet number concentration that is reduced due to entrainment and evaporation near cloud top. The authors then lead us through the compelling investigation of the diversity of pathways for droplet evaporation upon descent in the cloud. The confusion, or at least the argument that I do not follow, comes on lines 309-323, where the authors suggest signatures of homogeneous-like mixing. It is stated that the mixing is homogeneous-like because the phase relaxation time is small compared to the evaporation time, and that “droplets undergo gradual changes in r_m and N_c during descent…”. First, how does N_c change if there is no complete droplet evaporation? That seems inconsistent with the rest of the argument. Unless there is gradual mixing between more- and less-diluted parcels that are descending together, leading to some parcels having increasing N_c and others having decreasing N_c. After studying these results over quite some time, I find them largely consistent with (not contradicting and not providing an alternative interpretation to) the picture that has emerged over the last decade or so to explain the commonly-noted change from inhomogeneous signatures near cloud top to more homogeneous mixing signatures deeper in the cloud. That is, parcels that are mixed and diluted with entrained air at cloud top, to varying extents, i.e., resulting in different levels of \chi in this paper’s notation, then have reduced liquid water content, and therefore increased z at which all droplets evaporate upon descent. Assuming liquid water content decreases approximately linearly with height, droplets have to evaporate at larger z, and this is perfectly consistent with the observation in the paper that the deactivation zone height z increases steadily with increasing \chi (e.g., see Figure 9 e and h, specifically the blue region, and Figure 12 f and i, specifically the cyan region). The implication of this diversity in entrainment mixing near cloud top leading to diversity of parcel properties when descending through the cloud, is that droplet radius will change at different rates with decreasing height, in order to reach zero at different heights corresponding to the adjusted liquid water contents. Thus, what was unambiguously characterized as inhomogeneous mixing at cloud top, looks increasingly homogeneous with descent due to the different r vs z profiles. This concept was first introduced by Telford and Chai (“A new aspect of condensation theory” Pure Appl Geophys 1980), and the picture has been filled in with greater detail by many others, including Wang et al. (“Observations of marine stratocumulus microphysics and implications for processes controlling droplet spectra: Results from the Marine Stratus/Stratocumulus Experiment”, JGR 2009), Yum et al. (2015), and Yeom et al. (2023). [The latter two are already cited in the paper, the former two are not, so I have provided the journal and title for each.]
Lines 90-91: The resolution of 10 m x 10 m x 5 m is specified as essential for resolving the small-scale turbulence inherent in the entrainment problem. But of course we all know that the cascade extends to ~1 mm scales, so is there a justification for this being small enough, or somehow adequate for the entrainment problem? It’s fine if the answer is that this is a limitation due to computational resources, but if that’s the case, then perhaps it’s better not to imply that this resolution is adequate for a physically-based reason. If there is a reason, then that’s great… I look forward to learning what it is.
Line 96: Is it reasonable to neglect droplet sedimentation when the vertical resolution is 5 meters? Droplet setting is thought to be particularly important near stratocumulus cloud top. I guess the answer is yes, since this is a non-drizzling case, but perhaps some brief justification of the neglect could be provided.
Nitty-gritty:
Line 21: I wouldn’t call the DSD a “parameter”… usually I think of a parameter as being a coefficient or constant that describes the state of a system.
Line 39: I think I know what you mean by “transient process,” but in a mixed-layer model, entrainment rate is sometimes considered to be a constant. Perhaps this can be clarified.
Line 58: I didn’t notice that STBL has been defined. It’s hardly used at all in the paper, so maybe it’s easier to just spell it out.
Line 62: Typo with “discusses”.
Line 87: I would have assumed that “dynamics” and “chemistry” would be capitalized since their part of the title of a field project.
Figure 2: It looks like there are data points shown for \chi < 0, which does not make sense. Please explain… or correct if it is an error.
Line 145: I’m curious to know how the transit time for the chosen trajectory compares to the simulation time of 13320 s. Also, is there a reason that particular simulation time was chosen? Is the stratocumulus layer approximately in steady state, or continuously evolving? Presumably, at least, it is in approximate steady state on the time scale of the trajectories that were considered.
Equation 5, lines 179-180, and Appendix A: Apparently Equation 5 is an analytic result, but it is not really explained, either in the text or the appendix. Equation 6 appears to be purely empirical, which is fine, but then in the text it is stated that a “detailed derivation is provided in Appendix A. The appendix provides no derivation of either equation. Please provide the derivation(s) or revise the wording if not provided.
Figure 4: What is the gray color in panel a that is not shown in the color bar? Also, is this really a “contour plot” as stated in the caption? I would have called it a 2D histogram or frequency plot or similar. I think “contour plot is used elsewhere as well, such as in Figure 5.
Figure 5: There are no axis labels. Also, I puzzled over this figure for a long time before I finally noticed the tiny dots over r_m and d_r. Maybe it would be more reader-friendly to write them out as full time derivatives, or if not, to explicitly state “rates of change” in the caption and in the text.
Bottom of page 12: Again, it’s tricky that you move back and forth between correlations between r_m and d_r, and then between rates of change of r_m and d_r. Perhaps add some wording to alert the reader since the symbols are so similar.
Line 235: For the values in parentheses, specify \chi = so it is clear that they are \chi values.
Line 247: Here and in a few other places, the word “mixing” is used, and it’s not clear to me whether the authors are using this loosely as entrainment plus mixing, or if they are being precise and focusing on just the turbulent mixing process, which can progress throughout the descending region of cloud. Please clarify.
Line 249: It’s not clear to me why this indicates evaporation.
Line 257: When you say “directly affected by entrainment”, do you mean that there has been complete droplet evaporation, or do you just refer to the dilution effect?
Line 261: Perhaps reword “LEM represented SGS supersaturation” to be clearer.
Lines 267-268: It’s not clear to me what is meant by “not directly impacted by entrainment events.” Maybe I have missed something important, so perhaps you can refer back to the relevant place.
Line 344: Why do you need to assume a gamma distribution, given that the simulation produces a full droplet size distribution vs height? Is the observed DSD reasonably close to a gamma distribution, at least?
Line 361: How do you see the “high mixing fraction \chi” from Figure 13?
Line 374: What do you mean by “gravitational descent”?
Line 381: These “divergent pathways determined by their specific entrainment history” are consistent with the vertical circulation hypothesis, and with laboratory experiments suggesting that homogeneity of mixing is achieved when regions with different entrainment histories are averaged over (e.g., Wang et al. 2009 and Yeom et al. 2023). In other words, I agree with this finding, but I think it should be made clear that it is generally consistent with that conceptual picture. This is related to the main point raised at the beginning of the review.
Line 387: It’s not clear to me what is meant by “sorting droplets by their entrainment history.” I did not understand that droplets were sorted.
Lines 391-395: Obviously, given the discussion above, I disagree with these conclusions. I look forward to the authors’ response on whether these findings are significantly different than those attributed to the “vertical circulation” hypothesis that has received strong support in recent years.
Lines 403-404: I would suggest that Wang et al. (2009; reference above) could be added here, unless I’m misunderstanding the intended meaning.
Line 407: I don’t think the proposed formulation is “analytical-empirical”… it is empirical, right?
Citation: https://doi.org/10.5194/egusphere-2025-6099-RC2 - AC2: 'Reply on RC2', Jung-Sub Lim, 06 Mar 2026
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-6099', Anonymous Referee #1, 25 Jan 2026
Review of “Aging of Droplet Size Distribution in Stratocumulus Clouds: Regimes of Droplet Size Distribution Evolution” by Jung-Sub Lim and Fabian Hoffmann.
This manuscript presents a well-designed and insightful study on the evolution of droplet size distributions in maritime stratocumulus clouds, combining large-eddy simulations with a Lagrangian cloud model. The identification of two distinct DSD evolution regimes—adiabatic growth and entrainment–descent—is physically well motivated, and the emphasis on droplet history provides a compelling framework for reconciling long-standing ambiguities in the interpretation of mixing signatures.
The manuscript is generally well written and scientifically sound, and the proposed combined analytical–empirical formulation for relative dispersion is a valuable contribution with potential implications for cloud parameterization. However, given that much of the analysis relies critically on the Lagrangian framework and particle tracking, the paper would benefit from clearer methodological descriptions and, in some sections, deeper physical discussion to strengthen the link between simulated droplet histories and observable quantities.
Specific Comments:
- The authors need to provide more detailed descriptions of the specific implementation of particle trajectory tracking, as a substantial portion of the analyses in this manuscript is based on this method.
- Lines 32-34: The authors use the mean radius ( rm ) for their analysis, whereas many previous studies (including those cited by the authors) have used the volume‐mean radius ( rv ). Although the results may be similar, the authors should explicitly clarify the differences between these two definitions to avoid inaccurate citation of the literature and potential misunderstanding by readers.
- Line 115: The mixing fraction used here is not newly defined; Equation (3) is a variant of the moisture conservation equation (see Yang et al. (2016) and Lu et al. (2018)). In addition, I am curious about how the mixing fraction would behave if it were calculated using the conservation equation of liquid water potential temperature.
- Section 3.4: While the authors attempt to analyze the potential effects of DSD aging on optical properties, the presentation of Figure 13 may lead to confusion. Despite the pronounced regional differences in DSD evolution shown earlier, these differences are not evident in Figure 13. The authors may wish to reconsider the necessity of this section. If Figure 13 is kept, additional discussion on the impacts of regional DSD evolution on optical properties is required.
Reference:
Yang, F., Shaw, R., & Xue, H. (2016). Conditions for super-adiabatic droplet growth after entrainment mixing. Atmospheric Chemistry and Physics, 16(14), 9421-9433. doi:10.5194/acp-16-9421-2016
Lu, C., Sun, C., Liu, Y., Zhang, G. J., Lin, Y., Gao, W., et al. (2018). Observational Relationship Between Entrainment Rate and Environmental Relative Humidity and Implications for Convection Parameterization. Geophysical Research Letters, 45(24), 13495-13504. doi:10.1029/2018gl080264
Citation: https://doi.org/10.5194/egusphere-2025-6099-RC1 - AC1: 'Reply on RC1', Jung-Sub Lim, 06 Mar 2026
-
RC2: 'Comment on egusphere-2025-6099', Anonymous Referee #2, 26 Jan 2026
Review of “Aging of Droplet Size Distribution in Stratocumulus Clouds: Regimes of Droplet Size Distribution Evolution”
Authors: Jung-Sub Lim and Fabian Hoffmann
MS No.: egusphere-2025-6099
This is a clearly-written paper presenting results and interpretation of a novel simulation of cloud microphysical behavior in stratocumulus clouds. The investigation rests on the Lagrangian representation of microphysics, and it is exciting to see the insights that come from this powerful tool. The L^3 model is especially compelling because it includes sub-grid representation of turbulent fluctuations that are likely important for droplet growth and evaporation, especially in regions where supersaturation variability is large due to entrainment and mixing. I find the simulation results to be rigorous, and most of the presentation of results is clear and convincing. At the culminating stage of the paper, however, I have a fundamental disagreement with the interpretation that is provided, and either I have misunderstood the authors’ argument, or the authors have reached a conclusion that I believe is a misinterpretation of the results. I say this with full respect, wishing to engage the authors as a curious and truth-seeking colleague. My recommendation is that the paper should eventually be published, but I sincerely hope the authors will meaningfully engage and, as needed, reconsider the interpretation of their results in Section 3.3.3, revising the paper as needed. My central concern is described in the next paragraph, followed by several other significant questions or requests. Finally, the review ends with a list of detailed comments that I hope will improve the paper.
The simulation results convincingly show that inhomogeneous mixing is predominant near cloud top (e.g., lines 247-248), and although there is a confusing statement on lines 391-392 that sounds contradictory to this, my understanding is that the earlier data presentation agrees with this: i.e., droplet diameter changes only slightly, and primarily it is droplet number concentration that is reduced due to entrainment and evaporation near cloud top. The authors then lead us through the compelling investigation of the diversity of pathways for droplet evaporation upon descent in the cloud. The confusion, or at least the argument that I do not follow, comes on lines 309-323, where the authors suggest signatures of homogeneous-like mixing. It is stated that the mixing is homogeneous-like because the phase relaxation time is small compared to the evaporation time, and that “droplets undergo gradual changes in r_m and N_c during descent…”. First, how does N_c change if there is no complete droplet evaporation? That seems inconsistent with the rest of the argument. Unless there is gradual mixing between more- and less-diluted parcels that are descending together, leading to some parcels having increasing N_c and others having decreasing N_c. After studying these results over quite some time, I find them largely consistent with (not contradicting and not providing an alternative interpretation to) the picture that has emerged over the last decade or so to explain the commonly-noted change from inhomogeneous signatures near cloud top to more homogeneous mixing signatures deeper in the cloud. That is, parcels that are mixed and diluted with entrained air at cloud top, to varying extents, i.e., resulting in different levels of \chi in this paper’s notation, then have reduced liquid water content, and therefore increased z at which all droplets evaporate upon descent. Assuming liquid water content decreases approximately linearly with height, droplets have to evaporate at larger z, and this is perfectly consistent with the observation in the paper that the deactivation zone height z increases steadily with increasing \chi (e.g., see Figure 9 e and h, specifically the blue region, and Figure 12 f and i, specifically the cyan region). The implication of this diversity in entrainment mixing near cloud top leading to diversity of parcel properties when descending through the cloud, is that droplet radius will change at different rates with decreasing height, in order to reach zero at different heights corresponding to the adjusted liquid water contents. Thus, what was unambiguously characterized as inhomogeneous mixing at cloud top, looks increasingly homogeneous with descent due to the different r vs z profiles. This concept was first introduced by Telford and Chai (“A new aspect of condensation theory” Pure Appl Geophys 1980), and the picture has been filled in with greater detail by many others, including Wang et al. (“Observations of marine stratocumulus microphysics and implications for processes controlling droplet spectra: Results from the Marine Stratus/Stratocumulus Experiment”, JGR 2009), Yum et al. (2015), and Yeom et al. (2023). [The latter two are already cited in the paper, the former two are not, so I have provided the journal and title for each.]
Lines 90-91: The resolution of 10 m x 10 m x 5 m is specified as essential for resolving the small-scale turbulence inherent in the entrainment problem. But of course we all know that the cascade extends to ~1 mm scales, so is there a justification for this being small enough, or somehow adequate for the entrainment problem? It’s fine if the answer is that this is a limitation due to computational resources, but if that’s the case, then perhaps it’s better not to imply that this resolution is adequate for a physically-based reason. If there is a reason, then that’s great… I look forward to learning what it is.
Line 96: Is it reasonable to neglect droplet sedimentation when the vertical resolution is 5 meters? Droplet setting is thought to be particularly important near stratocumulus cloud top. I guess the answer is yes, since this is a non-drizzling case, but perhaps some brief justification of the neglect could be provided.
Nitty-gritty:
Line 21: I wouldn’t call the DSD a “parameter”… usually I think of a parameter as being a coefficient or constant that describes the state of a system.
Line 39: I think I know what you mean by “transient process,” but in a mixed-layer model, entrainment rate is sometimes considered to be a constant. Perhaps this can be clarified.
Line 58: I didn’t notice that STBL has been defined. It’s hardly used at all in the paper, so maybe it’s easier to just spell it out.
Line 62: Typo with “discusses”.
Line 87: I would have assumed that “dynamics” and “chemistry” would be capitalized since their part of the title of a field project.
Figure 2: It looks like there are data points shown for \chi < 0, which does not make sense. Please explain… or correct if it is an error.
Line 145: I’m curious to know how the transit time for the chosen trajectory compares to the simulation time of 13320 s. Also, is there a reason that particular simulation time was chosen? Is the stratocumulus layer approximately in steady state, or continuously evolving? Presumably, at least, it is in approximate steady state on the time scale of the trajectories that were considered.
Equation 5, lines 179-180, and Appendix A: Apparently Equation 5 is an analytic result, but it is not really explained, either in the text or the appendix. Equation 6 appears to be purely empirical, which is fine, but then in the text it is stated that a “detailed derivation is provided in Appendix A. The appendix provides no derivation of either equation. Please provide the derivation(s) or revise the wording if not provided.
Figure 4: What is the gray color in panel a that is not shown in the color bar? Also, is this really a “contour plot” as stated in the caption? I would have called it a 2D histogram or frequency plot or similar. I think “contour plot is used elsewhere as well, such as in Figure 5.
Figure 5: There are no axis labels. Also, I puzzled over this figure for a long time before I finally noticed the tiny dots over r_m and d_r. Maybe it would be more reader-friendly to write them out as full time derivatives, or if not, to explicitly state “rates of change” in the caption and in the text.
Bottom of page 12: Again, it’s tricky that you move back and forth between correlations between r_m and d_r, and then between rates of change of r_m and d_r. Perhaps add some wording to alert the reader since the symbols are so similar.
Line 235: For the values in parentheses, specify \chi = so it is clear that they are \chi values.
Line 247: Here and in a few other places, the word “mixing” is used, and it’s not clear to me whether the authors are using this loosely as entrainment plus mixing, or if they are being precise and focusing on just the turbulent mixing process, which can progress throughout the descending region of cloud. Please clarify.
Line 249: It’s not clear to me why this indicates evaporation.
Line 257: When you say “directly affected by entrainment”, do you mean that there has been complete droplet evaporation, or do you just refer to the dilution effect?
Line 261: Perhaps reword “LEM represented SGS supersaturation” to be clearer.
Lines 267-268: It’s not clear to me what is meant by “not directly impacted by entrainment events.” Maybe I have missed something important, so perhaps you can refer back to the relevant place.
Line 344: Why do you need to assume a gamma distribution, given that the simulation produces a full droplet size distribution vs height? Is the observed DSD reasonably close to a gamma distribution, at least?
Line 361: How do you see the “high mixing fraction \chi” from Figure 13?
Line 374: What do you mean by “gravitational descent”?
Line 381: These “divergent pathways determined by their specific entrainment history” are consistent with the vertical circulation hypothesis, and with laboratory experiments suggesting that homogeneity of mixing is achieved when regions with different entrainment histories are averaged over (e.g., Wang et al. 2009 and Yeom et al. 2023). In other words, I agree with this finding, but I think it should be made clear that it is generally consistent with that conceptual picture. This is related to the main point raised at the beginning of the review.
Line 387: It’s not clear to me what is meant by “sorting droplets by their entrainment history.” I did not understand that droplets were sorted.
Lines 391-395: Obviously, given the discussion above, I disagree with these conclusions. I look forward to the authors’ response on whether these findings are significantly different than those attributed to the “vertical circulation” hypothesis that has received strong support in recent years.
Lines 403-404: I would suggest that Wang et al. (2009; reference above) could be added here, unless I’m misunderstanding the intended meaning.
Line 407: I don’t think the proposed formulation is “analytical-empirical”… it is empirical, right?
Citation: https://doi.org/10.5194/egusphere-2025-6099-RC2 - AC2: 'Reply on RC2', Jung-Sub Lim, 06 Mar 2026
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Jung-Sub Lim
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Review of “Aging of Droplet Size Distribution in Stratocumulus Clouds: Regimes of Droplet Size Distribution Evolution” by Jung-Sub Lim and Fabian Hoffmann.
This manuscript presents a well-designed and insightful study on the evolution of droplet size distributions in maritime stratocumulus clouds, combining large-eddy simulations with a Lagrangian cloud model. The identification of two distinct DSD evolution regimes—adiabatic growth and entrainment–descent—is physically well motivated, and the emphasis on droplet history provides a compelling framework for reconciling long-standing ambiguities in the interpretation of mixing signatures.
The manuscript is generally well written and scientifically sound, and the proposed combined analytical–empirical formulation for relative dispersion is a valuable contribution with potential implications for cloud parameterization. However, given that much of the analysis relies critically on the Lagrangian framework and particle tracking, the paper would benefit from clearer methodological descriptions and, in some sections, deeper physical discussion to strengthen the link between simulated droplet histories and observable quantities.
Specific Comments:
Reference:
Yang, F., Shaw, R., & Xue, H. (2016). Conditions for super-adiabatic droplet growth after entrainment mixing. Atmospheric Chemistry and Physics, 16(14), 9421-9433. doi:10.5194/acp-16-9421-2016
Lu, C., Sun, C., Liu, Y., Zhang, G. J., Lin, Y., Gao, W., et al. (2018). Observational Relationship Between Entrainment Rate and Environmental Relative Humidity and Implications for Convection Parameterization. Geophysical Research Letters, 45(24), 13495-13504. doi:10.1029/2018gl080264