Gravity waves are an ubiquitous feature of the atmosphere and influence clouds in multiple ways. Regarding cirrus clouds, many studies have emphasized the impact of wave-induced temperature fluctuations on the nucleation of ice crystals. This paper investigates the impact of the waves on the motion and distribution of ice particles, using the idealized 2-D framework of a monochromatic gravity wave. Contrary to previous studies, special attention is given to the impact of the wind field induced by the wave.
Assuming no feedback of the ice on the water vapor content, theoretical and
numerical analyses both show the existence of a
The wave-driven localization is consistent with temperature–cirrus relationships recently observed in the tropical tropopause layer (TTL) over the Pacific during the Airborne Tropical Tropopause EXperiment (ATTREX). It is argued that this effect may explain such observations. Finally, the impact of the described interaction on TTL cirrus dehydration efficiency is quantified using ATTREX observations of clouds and temperature lapse rate.
Atmospheric gravity waves have long been reckoned to interact with cirrus
clouds. They generate temperature fluctuations, with negative anomalies
favoring ice particle formation
The goal of this paper is hence to examine the influence of internal gravity
waves on ice crystal transport. Motivated by recent observations of
wave–temperature relations in the tropical tropopause layer (TTL) by
The article is organized as follows. In Sect.
To leading order (i.e., neglecting nonlinearities), propagating waves are not expected to affect transport, as
they reversibly slosh fluid parcels to and fro. Yet, the second-order Stokes
drift
In the following, we use a simple 2-D framework with the wind and temperature
structure of a monochromatic wave within an unsheared background
First, consider the case of a constant size particle, which is assumed to
sediment vertically with a downward speed
Then, there is an analytical formula for the vertical trajectory
As gravity waves in the upper troposphere mostly propagate from lower levels,
their vertical group velocity is positive, which implies that their vertical
phase speed
For illustration, we show the effect of a monochromatic wave on the vertical
motion of falling particles in a special configuration in
Fig.
Evolution of the positions of sedimenting particles (initial positions in red) being advected by the wind field induced by a monochromatic wave (blue dots) or not (green dots) during one wave period. See text for a full description of the wave characteristics. Also note that the vertical scale has been enhanced by a factor of about 200 compared to the horizontal scale.
Figure
Consistent with Eq. (
Now that we have explored the impact of wave advection on particle transport, we turn to the case of ice crystals which can grow and sublimate, exchanging water molecules with their environment. We will not, however, consider the effect of the ice crystals on the relative humidity, equivalent to assuming that few of them are present. Consistently, we will neglect ice crystal aggregation; diffusional growth and sedimentation are thus the only microphysical processes active in our setup.
For crystals with a spherical shape, the rate of growth of the radius
In the following, we introduce
To solve these equations, we need to know the temperature and relative
humidity at the position
Regarding the pressure
Regarding the water vapor mixing ratio, as mentioned above, it is estimated
assuming that the crystals do
For the reference-state
Finally, for the sedimentation speed
The previous set of equations will be the base for the simulations presented
in Sect.
Third, we use for
Under those additional approximations, the system of
Eq. (
This set of equations reveals the simple properties of the system studied. It
can be seen that the system has fixed points, characterized by
To gain further insights into the behavior of the trajectories in the
vicinity of the fixed points, it is common to examine the linearized system.
The Jacobian matrix at the fixed points is as follows:
Given those eigenvalues, the two fixed points of the system deduced from the
theoretical analysis are as follows:
The linear analysis above only provides qualitative insights into the system
behavior near the saddle point and cannot be applied rigorously near the
elliptic point. However, the behavior of the system can still be studied
further in a theoretical sense, since it turns out to be Hamiltonian (see
Appendix
The trajectories in the
Figure
Wave and background state characteristics assumed for the
sedimentation–growth simulations reported in this section.
Panels
Figure
The existence of the two fixed points can be easily understood physically.
The elliptic point is located at RH
In many aspects, the mechanism presented here is similar to the stabilization
mechanism proposed by
Returning to the location of the elliptic point where the crystals are
localized, it should furthermore be noted that, given the tendency of some of
the crystals to stay near the thermodynamic equilibrium phase of the wave
(i.e., RH
Representation in altitude–time space of an ice crystal trajectory
in the moist (RH
Figure
Another reason could be the different mean relative humidities between the
two regions, the convective western Pacific being moister on average than the
dry eastern Pacific. Two different explanations relying on the different
background humidities could then explain the observations. The first,
proposed by
Besides the strong sensitivity to the background relative humidity, it is
also interesting to investigate qualitatively the sensitivity of the
wave-driven localization to the wave parameters. One metric to quantify the
relevance of wave-driven localization is the fraction of phase space
From Appendix
Fraction
The dependency of
This exercise shows that low-frequency and large-vertical-wavelength waves
are in general more susceptible to exhibit the wave-driven localization
effect. However, it is quantitatively present (
In the previous section, a simplified framework was introduced to investigate the potential effects of the wave on ice crystal motions. The present section aims at confirming those effects with more realistic numerical simulations and to investigate them in observations.
Simulations of ice crystal growth and sedimentation in an idealized
wave field at RH
We now present numerical simulations of the full
Eq. (
Figure
Consistent with the analysis of the simplified system in Sect. Ice crystals initialized in (highly) subsaturated regions (RH Ice crystals initialized in supersaturated regions below the saddle point
grow and fall, and they cross the RH Ice crystals initialized near the elliptic fixed point (RH
The qualitative behavior between the full ice crystal trajectories and the
simplified system are thus similar. Now,
Simulations of ice crystal growth and sedimentation in an idealized
wave field at RH
In Fig.
When the background relative humidity RH
In Sect.
To show that more precisely, we have also performed simulations without the
wave advection. The crystals just fall, seeing the relative humidity
perturbations created by the wave, but not the wave-induced wind
perturbations. The end position of the ice crystals for the different
simulations are represented in Figs.
The differences seen between these 2 simulations suggest that
Overall, the experiments described above show that advection by the
wave-induced wind has an impact on the sedimentation–growth of ice crystals
and can significantly diminish the sedimentation mass flux, which suggests a
mean impact of wave advection on the average dehydration efficiency of ice
crystals. The downward water mass flux needed to close the water budget of the
TTL may then be significantly affected by the waves. However, those
simulations remain idealized: for instance, the described wave-driven
localization is tied to the initialization of the crystals in all phases of
the wave, in particular in the phase where RH
To evaluate the impact of the wave vertical wind on the ice mass flux, it
would seem natural to use the standard altitude coordinate. In that case, the
average ice mass vertical flux
In practice, however, the method suggested by Eq. (
There is thus a systematic relation between clouds and anomalies of
Sedimentation water flux
The frequency distribution of RH
First, regarding (1), the explanation usually invoked is that the presence of
ice crystals damps relative humidity variations towards saturation, by
absorbing or releasing water molecules depending on the relative humidity.
Using a theoretical parcel model framework,
In the simulations presented above (Fig.
Regarding point (2), it is thought that the increased occurrence of high
supersaturations encountered in clear skies at low temperatures
Of course, our simplifications and the above considerations are not strictly
applicable to the Earth cirrus clouds, which behave in a more complicated
manner. For instance, in the TTL, clouds characterized by RH
The relevance of wave-driven localization to cirrus clouds' evolution and dehydration efficiency depends on their microphysical properties: size distribution and crystal shape. Those points are explained below.
First, regarding the size distribution, it is important to note that our
considerations are relevant for crystals whose sedimentation speed
Second, regarding crystal shape, we have been assuming so far that the ice
crystals all have spherical shapes. Although this is mostly the case in
observations of crystals dimensions below 65
Average ice crystal size distribution within cirrus clouds during
ATTREX 2014 flights, above
Our calculations emphasize the importance of an accurate representation of
the waves for cirrus modeling. In particular, the simulations presented in
Sect.
The role of equatorial and gravity waves has long been acknowledged in
Lagrangian cirrus cloud models, which generally include a parameterization of
wave fluctuations
We have analytically investigated the impact of a monochromatic gravity wave
on the motion of ice crystals. For an upward-propagating GW packet, assuming
no water vapor release or depletion by the crystals, an interesting
The existence of the
Two main conclusions can be drawn from our study. First, there is a
fundamental difference between air parcels and ice particles: due to
wave-driven localization, waves can have an average impact on the motion of
ice crystals even if they have none on air parcels'. Second, water vapor
quenching by the ice is
Although we focused on TTL cirrus, the theory introduced here is general and
might be relevant to other types of clouds or aerosols which are largely
influenced by waves and the associated wind field. An example is the case of
noctilucent clouds (NLCs) in the summer polar mesopause region.
Besides the atmosphere, many other media, such as oceans and lakes, are
perturbed by internal gravity waves. Those waves contribute to particle
transport through the classical Stokes drift, mixing due to wave breaking and
also through the resuspension of sediments due to the stress exerted by the
induced flow on the bottom
Specifically for the atmosphere, a number of previous works have stressed the impact of waves on UTLS clouds. Here, we have unraveled yet another effect, which possibly provides an explanation for recently observed relations between waves and cirrus. Our results hence call for more quantitative observations of waves and cirrus clouds, in order to more precisely nail down the wave impact on clouds and improve its representation in models. Quasi-Lagrangian cloud and wave observations coupled with particle-following model simulations would be especially convenient to investigate this effect.
The ATTREX aircraft data used in this paper can be
retrieved from NASA Earth Science Project Office (ESPO) at
To avoid strongly overestimating the effect of wave-driven vertical transport
on sedimentation, it is important to recall that the wave amplitude is
limited by a stability requirement. Shear and convective breaking of
monochromatic gravity waves have been treated in a number of studies
We take the criterion that the Richardson number
Figure
Minimum Richardson number over all wave phases, as a function of the
amplitude parameter
Writing
The existence of periodic orbits is equivalent to the existence of local
extrema of the Hamiltonian function. Noting that the existence of fixed
points (and extrema of
The expression of
The theoretical analysis presented in this paper accounts for both the
horizontal and the vertical wind components due to the wave.
Figure
It might seem surprising that, once the horizontal wind is neglected, the
downward speed of the crystals at the elliptic point
With only the wave vertical wind, the total vertical speed of the crystals
Same as Fig.
This appendix compares the stability (
Figure
This relationship between clouds and stability is further analyzed in
Fig.
Anomalies of stability
AP and RP designed the study. AP performed the study, with suggestions from RP, AH and EJ. AP wrote the paper with contributions from all co-authors.
The authors declare that they have no conflict of interest.
The authors thank the teams involved in the development and exploitation of the MMS, MTP, FCDP and 2DS instruments during the ATTREX campaign. Aurélien Podglajen thanks Martina Krämer, Bernard Legras and Claudia Stubenrauch for their comments on this work. We sincerely thank Peter Spichtinger and one anonymous referee for their helpful comments and suggestions on the paper. Aurélien Podglajen, Riwal Plougonven and Albert Hertzog acknowledge support from the French ANR project StraDyVariUS (Stratospheric Dynamic and Variability, ANR-13-BS06-0011-01) and from the French space agency (CNES) through the Strateole 2 project. Edited by: Peter Haynes Reviewed by: Peter Spichtinger and one anonymous referee