Observations of climatologically invariant scale-invariance describing cloud horizontal sizes

DeWitt, Thomas D.; Garrett, Timothy J.; Rees, Karlie N.; Bois, Corey; Krueger, Steven K.

doi:https://doi.org/10.5194/egusphere-2023-943

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https://doi.org/10.5194/egusphere-2023-943

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14 Jun 2023

| 14 Jun 2023

Observations of climatologically invariant scale-invariance describing cloud horizontal sizes

Thomas D. DeWitt, Timothy J. Garrett, Karlie N. Rees, Corey Bois, and Steven K. Krueger

Abstract. The numbers of clouds of a given size is a defining feature of the earth's atmosphere. As well as cloud area, cloud perimeter p is interesting because it represents the length of the shared interface between clouds and clear-skies across which air and buoyant energy are dissipated. A recent study introduced a first-principles expression for the steady-state distribution of cloud perimeters, measured within a quasi-horizontal moist isentropic layer, that is a scale invariant power-law n (p) ∝ p^–^(1+β), where n (p) is the number density of cloud perimeters within [p, p + dp] and β = 1. This value of β was found to be in close agreement with output from a high-resolution, large eddy simulation of tropical convection. To further test this formulation, the current study evaluates n (p) within near-global imagery from nine full-disk and polar-orbiting satellites. A power-law is found to apply to measurements of n (p), and the value of β is observed to be remarkably robust to latitude, season, and land/ocean contrasts suggesting that, at least statistically speaking, cloud perimeter distributions are determined more by atmospheric stability than Coriolis forces, surface temperature, or contrasts in aerosol loading between continental and marine environments. However, the measured value of β is found to be 1.29 ± 0.05 rather than β = 1, indicating a relative scarcity of large clouds in satellite observations compared to theory and high-resolution cloud modeling. The reason for this discrepancy is unclear but may owe to the difference in perspective between evaluating n (p) along quasi-horizontal moist isentropes rather than looking down from space. As a test of this hypothesis, numerical simulation output shows that, while β ∼ 1 within isentropes, higher values of β are reproduced for a simulated satellite view. However, the simulated value is a function of the cloud detection sensitivity, but little such sensitivity is seen in satellite observations, suggesting a possible misrepresentation of the physics controlling cloud sizes in simulations. A power-law also applies to satellite observations of cloud areas covering a range between ∼ 3 km² and ∼ 3 × 10⁵km², a much wider range of scales than has been previously described in studies that we argue inappropriately treated the statistics of clouds truncated by the edge of a measurement domain.

Received: 09 May 2023 – Discussion started: 14 Jun 2023

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Thomas D. DeWitt et al.

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CC1:
'Comment on egusphere-2023-943', Simon R. Proud, 14 Jun 2023

Interesting manuscript, I have one minor comment. In table 1 there are a few corrections required:
The sensor name for GOES-16 and -17 should be 'ABI'
The sensor name for Meteosat-9 and -11 should be 'SEVIRI'
The sensor name for Himawari should be 'AHI'

Also, Meteosat-9 is incorrect, at that time it was Meteosat-8. Likewise, Himawari should be -8.

Citation: https://doi.org/10.5194/egusphere-2023-943-CC1
- AC2: 'Reply on CC1', Thomas DeWitt, 22 Sep 2023
  
  Thank you for the comment, and indeed several sensor names were listed incorrectly in the manuscript, as also noted by Reviewer 1. The sensor names have been corrected as suggested, and a new category called “Dataset Name” was introduced to differentiate between datasets (e.g. GOES -137° and GOES -75°). The corresponding mentions of the datasets in the text were also changed.
  
  Citation: https://doi.org/10.5194/egusphere-2023-943-AC2
RC1: 'Comment on egusphere-2023-943', Anonymous Referee #1, 07 Jul 2023

I enjoyed reading this work by DeWitt et al., ‘Observations of climatologically invariant scale-invariance describing cloud horizontal sizes ; however, I find that the study issue and the problematic of the article are not clear enough in the first three parts. I'd recommend revising the structure, especially parts 2 and 3, in order to better define the publication's issues.

Citation: https://doi.org/10.5194/egusphere-2023-943-RC1
RC2:
'Comment on egusphere-2023-943', Anonymous Referee #2, 12 Aug 2023
Review of Observations of climatologically invariant scale-invariance describing cloud horizontal sizes by Thomas D. DeWitt, Timothy J. Garrett, Karlie N. Rees, Corey Bois, and Steven K. Krueger.
This is an excellent and important paper that examines cloud area and perimeter size distributions from a range of different satellite sensors and a cloud resolving model (CRM) to test hypotheses from the elegant theoretical model of Garrett et al. (2018), which uses a mixing engine idea based on Fick’s law to predict a universal perimeter scaling exponent of unity for cloud fields in steady state. Wide differences between different prior studies are convincingly shown to stem from truncation error issues associated with limited measurement domain sizes. The authors show that, when truncation issues are limited by avoiding resolution and domain size issues, area size distributions from all the sensors are indeed well-represented by power laws with scaling exponents close to unity. The satellite observed perimeter power laws, however, show scaling exponents that are somewhat larger (1.22-1.36) than the beta=1 hypothesized in Garrett et al. (2018), with only very small seasonal and regional variation. A large-domain CRM simulation, in contrast, does indeed show beta very close to 1 when perimeters are taken around horizontal slices through the domain rather than of the projected image as seen by satellite. The CRM data are used to demonstrate that when the layers are “compressed” to produce a single projected satellite-like image, the exponent becomes similar to that seen in the satellite data when a threshold optical thickness to define cloud is similar to that used to define satellite cloud masks.
Overall, this is a well thought out study and provides a satisfactory test of the theory of Garrett et al. (2018). It will be of interest both to those seeking a unifying cloud theory and those trying to reconcile disparate observational estimates of cloud size distributions. I found it to be one of the most enjoyable papers I have reviewed in r recent years, and the agreement with theory is likely to provide avenues for further theoretical work. Thus, I conclude that the manuscript should ultimately be accepted for publication. I have a number of relatively minor comments that may improve readability and clarity, and the authors are welcome to consider them in producing a revised version of the manuscript.
Primary comments:
While the CRM analysis does indeed point to a reconciliation between the larger exponents in the observations and the theory of Garrett et al. (2018), the dramatic sensitivity of the CRM exponent to the cloud-defining optical depth threshold is not seen in the observations, leaving something of a puzzle remaining for future work. It would be interesting to consider using much larger domain CRMs (e.g., the DYAMOND simulations) to understand if period boundary conditions may be having an influence, or if the single simulation has some features that are representative of only a subset of cloud structures and meteorological variability. That could be left for future work.
The Appendix, showing EPIC’s return to consistency when potentially spurious data at the small end of the size distribution are removed, is very interesting. It suggests a warning for future satellite missions where stringent compression methods are required (e.g., stereo camera methods using very high-resolution cloud imagery). Further work is needed in this area.
Minor/grammatical comments:
Line 43-44: The spurious effect of domain size on the size distribution was shown in Wood and Field (2011, e.g. Fig. 3), among others.

Line 47: "Suitable" for what specific aim? A better term might be "physically meaningful".

Line 53: Why does mixing of two air masses moisten the air? Where is the additional moisture coming from? Should this instead be "moistens the clear air outside of cloud" (which presumably is drier than the cloudy air)? Please clarify.

Line 67: "water vapor mixing ratio". Not total water mixing ratio.

Line 70: The full derivative (dq*/dT), rather than the partial derivative) is appropriate here, because T also depends upon p. Or is height and pressure assumed to be uniquely related (not T dependent)?

Line 71: The gz term is more variable than the T dependence? But T also varies with height systematically. Explain why this is true only in a convectively unstable atmosphere?

Line 74-76: Provide a reference where this is derived from Fick's law (perhaps the 2018 Garrett paper). Or derive it here.

Line 78: Do you mean that turbulence is fully isotropic in circulations near cloud edges? Isotropic means that circulations have no preferential direction. I can't visualize a circulation that is isotropic. Please help.

Line 79: Dissipation does not have directional components. Can this be clarified?

Line 87: Define pmin and pmax. Is pmin the Kolmogorov scale and pmax the circumference of the Earth?

Line 99: Does the "exponential cutoff" only apply to the large end of the distribution? Are there any such constraints at the small end?

Line 103: Wood and Field (2011) provide empirical evidence of such a cut off at approximately the Rossby radius. However, they also showed that in the Tropics, where the Rossby radius is very large the cut off is actually at smaller scales than in the extratropics.

Line 108: The perimeter or area power law exponent?

Line 179: Is the varying pixel size across the swath taken into account?

Line 191: Does the simulation self-aggregate as in the simulations shown in a number of different prior studies?

Simulations might show a steady state that is or is not aggregated, and I would imagine that these would have quite different scaling properties. Can the authors comment on this? Also, I do not believe that steady state can we reached in 12 hours in these simulations. How are the authors defining steady state here? Radiative-convective equilibrium often produces a steady state, but may also have bifurcating or oscillating organization, so I would be interested in the authors’ thoughts on how this may impact scaling.

Line 199: Is the simulation also used to construct a "satellite like" projected cloud mask?

Line 228: "In the satellite observations examined here,...."

Figure 8: What do the colors represent? They seem to be a distraction and are not discussed in the figure caption. Also, the caption refers to Appendix ??, so this needs correcting.

Line 319: “3x10^5 km^2, .a scale much larger than has previously been suggested”. Wood and Field (2011) showed no evidence of a scale break out to an area of 10^6 km^2, so this is not quite true. Also, there are two “beens” in the sentence, so please remove one of them.
Citation: https://doi.org/10.5194/egusphere-2023-943-RC2
AC1: 'Responses and changes to reviewer comments', Thomas DeWitt, 22 Sep 2023

We thank both reviewers for their helpful comments. Please see the attached file for our responses and changes made.

Citation: https://doi.org/10.5194/egusphere-2023-943-AC1

Status: closed

CC1:
'Comment on egusphere-2023-943', Simon R. Proud, 14 Jun 2023

Interesting manuscript, I have one minor comment. In table 1 there are a few corrections required:
The sensor name for GOES-16 and -17 should be 'ABI'
The sensor name for Meteosat-9 and -11 should be 'SEVIRI'
The sensor name for Himawari should be 'AHI'

Also, Meteosat-9 is incorrect, at that time it was Meteosat-8. Likewise, Himawari should be -8.

Citation: https://doi.org/10.5194/egusphere-2023-943-CC1
- AC2: 'Reply on CC1', Thomas DeWitt, 22 Sep 2023
  
  Thank you for the comment, and indeed several sensor names were listed incorrectly in the manuscript, as also noted by Reviewer 1. The sensor names have been corrected as suggested, and a new category called “Dataset Name” was introduced to differentiate between datasets (e.g. GOES -137° and GOES -75°). The corresponding mentions of the datasets in the text were also changed.
  
  Citation: https://doi.org/10.5194/egusphere-2023-943-AC2
RC1: 'Comment on egusphere-2023-943', Anonymous Referee #1, 07 Jul 2023

I enjoyed reading this work by DeWitt et al., ‘Observations of climatologically invariant scale-invariance describing cloud horizontal sizes ; however, I find that the study issue and the problematic of the article are not clear enough in the first three parts. I'd recommend revising the structure, especially parts 2 and 3, in order to better define the publication's issues.

Citation: https://doi.org/10.5194/egusphere-2023-943-RC1
RC2:
'Comment on egusphere-2023-943', Anonymous Referee #2, 12 Aug 2023
Review of Observations of climatologically invariant scale-invariance describing cloud horizontal sizes by Thomas D. DeWitt, Timothy J. Garrett, Karlie N. Rees, Corey Bois, and Steven K. Krueger.
This is an excellent and important paper that examines cloud area and perimeter size distributions from a range of different satellite sensors and a cloud resolving model (CRM) to test hypotheses from the elegant theoretical model of Garrett et al. (2018), which uses a mixing engine idea based on Fick’s law to predict a universal perimeter scaling exponent of unity for cloud fields in steady state. Wide differences between different prior studies are convincingly shown to stem from truncation error issues associated with limited measurement domain sizes. The authors show that, when truncation issues are limited by avoiding resolution and domain size issues, area size distributions from all the sensors are indeed well-represented by power laws with scaling exponents close to unity. The satellite observed perimeter power laws, however, show scaling exponents that are somewhat larger (1.22-1.36) than the beta=1 hypothesized in Garrett et al. (2018), with only very small seasonal and regional variation. A large-domain CRM simulation, in contrast, does indeed show beta very close to 1 when perimeters are taken around horizontal slices through the domain rather than of the projected image as seen by satellite. The CRM data are used to demonstrate that when the layers are “compressed” to produce a single projected satellite-like image, the exponent becomes similar to that seen in the satellite data when a threshold optical thickness to define cloud is similar to that used to define satellite cloud masks.
Overall, this is a well thought out study and provides a satisfactory test of the theory of Garrett et al. (2018). It will be of interest both to those seeking a unifying cloud theory and those trying to reconcile disparate observational estimates of cloud size distributions. I found it to be one of the most enjoyable papers I have reviewed in r recent years, and the agreement with theory is likely to provide avenues for further theoretical work. Thus, I conclude that the manuscript should ultimately be accepted for publication. I have a number of relatively minor comments that may improve readability and clarity, and the authors are welcome to consider them in producing a revised version of the manuscript.
Primary comments:
While the CRM analysis does indeed point to a reconciliation between the larger exponents in the observations and the theory of Garrett et al. (2018), the dramatic sensitivity of the CRM exponent to the cloud-defining optical depth threshold is not seen in the observations, leaving something of a puzzle remaining for future work. It would be interesting to consider using much larger domain CRMs (e.g., the DYAMOND simulations) to understand if period boundary conditions may be having an influence, or if the single simulation has some features that are representative of only a subset of cloud structures and meteorological variability. That could be left for future work.
The Appendix, showing EPIC’s return to consistency when potentially spurious data at the small end of the size distribution are removed, is very interesting. It suggests a warning for future satellite missions where stringent compression methods are required (e.g., stereo camera methods using very high-resolution cloud imagery). Further work is needed in this area.
Minor/grammatical comments:
Line 43-44: The spurious effect of domain size on the size distribution was shown in Wood and Field (2011, e.g. Fig. 3), among others.

Line 47: "Suitable" for what specific aim? A better term might be "physically meaningful".

Line 53: Why does mixing of two air masses moisten the air? Where is the additional moisture coming from? Should this instead be "moistens the clear air outside of cloud" (which presumably is drier than the cloudy air)? Please clarify.

Line 67: "water vapor mixing ratio". Not total water mixing ratio.

Line 70: The full derivative (dq*/dT), rather than the partial derivative) is appropriate here, because T also depends upon p. Or is height and pressure assumed to be uniquely related (not T dependent)?

Line 71: The gz term is more variable than the T dependence? But T also varies with height systematically. Explain why this is true only in a convectively unstable atmosphere?

Line 74-76: Provide a reference where this is derived from Fick's law (perhaps the 2018 Garrett paper). Or derive it here.

Line 78: Do you mean that turbulence is fully isotropic in circulations near cloud edges? Isotropic means that circulations have no preferential direction. I can't visualize a circulation that is isotropic. Please help.

Line 79: Dissipation does not have directional components. Can this be clarified?

Line 87: Define pmin and pmax. Is pmin the Kolmogorov scale and pmax the circumference of the Earth?

Line 99: Does the "exponential cutoff" only apply to the large end of the distribution? Are there any such constraints at the small end?

Line 103: Wood and Field (2011) provide empirical evidence of such a cut off at approximately the Rossby radius. However, they also showed that in the Tropics, where the Rossby radius is very large the cut off is actually at smaller scales than in the extratropics.

Line 108: The perimeter or area power law exponent?

Line 179: Is the varying pixel size across the swath taken into account?

Line 191: Does the simulation self-aggregate as in the simulations shown in a number of different prior studies?

Simulations might show a steady state that is or is not aggregated, and I would imagine that these would have quite different scaling properties. Can the authors comment on this? Also, I do not believe that steady state can we reached in 12 hours in these simulations. How are the authors defining steady state here? Radiative-convective equilibrium often produces a steady state, but may also have bifurcating or oscillating organization, so I would be interested in the authors’ thoughts on how this may impact scaling.

Line 199: Is the simulation also used to construct a "satellite like" projected cloud mask?

Line 228: "In the satellite observations examined here,...."

Figure 8: What do the colors represent? They seem to be a distraction and are not discussed in the figure caption. Also, the caption refers to Appendix ??, so this needs correcting.

Line 319: “3x10^5 km^2, .a scale much larger than has previously been suggested”. Wood and Field (2011) showed no evidence of a scale break out to an area of 10^6 km^2, so this is not quite true. Also, there are two “beens” in the sentence, so please remove one of them.
Citation: https://doi.org/10.5194/egusphere-2023-943-RC2
AC1: 'Responses and changes to reviewer comments', Thomas DeWitt, 22 Sep 2023

We thank both reviewers for their helpful comments. Please see the attached file for our responses and changes made.

Citation: https://doi.org/10.5194/egusphere-2023-943-AC1

Thomas D. DeWitt et al.

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https://doi.org/10.5194/egusphere-2023-943-supplement

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Short summary

Viewed from space, a defining feature of Earth's atmosphere is the wide spectrum of cloud sizes. A recent study predicted the distribution of cloud sizes, and this paper compares the prediction to observations. Although there is nuance in viewing perspective, we find robust agreement with theory across different climatological conditions, including land/ocean contrasts, time of year, or latitude, suggesting a minor role for Coriolis forces, aerosol loading or surface temperature.


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