Q. J. R. Mereorol. SOC. (2001), 127, pp. 2663-2682
Radiative influences on the structure and lifetime of cirrus clouds
By STEVEN DOBBJE* and PETER JONAS
UMiSC UK
(Received 22 January 2001; revised 26 June 2001)
SUMMARY
Our goal in this work is to determine the role of radiation in cirrus clouds. How it impacts the formation and
evolution of cloud structure, whether or not it initiates convective instability, and what effect it has on the lifetime
of these clouds. In this study, we simulate cirrus clouds using the Met Office large-eddy simulation model with a
broad-band solar and infrared ice-specificradiation scheme.
We find that radiation can have quite an effect on cirrus clouds. Results for runs with and without radiation
show many dramatic differences. In general, radiatively influenced clouds are observed to be much more dynamic
and inhomogeneous. The radiation is observed to strongly enhance cellular structure within the cloud layer,
and a Fourier analysis of the horizontal ice-water path (IWP) shows that this cellular enhancement gives rise
to inhomogeneity length-scales roughly related to the thickness of the layer. The Fourier amplitudes for the
radiative cases are usually two or three times larger in magnitude than the non-radiative cases. The inhomogeneity
length-scales do appear in the non-radiative cases but they are very weak. The radiatively driven clouds in these
simulations often had horizontally averaged IWPs larger in magnitude by more than double compared to the nonradiative cases once the radiation had taken effect, and the cloud lifetime was increased by between 30 minutes
and 2 hours.
To evaluate if radiation is causing convective instability, we derive and implement a radiation stability
number, Rsn. For radiative instability to occur, R,, must satisfy the condition 0 c R,, < 1. We also present
similar stability numbers for latent, and the combined radiation and latent processes. By evaluating these numbers
throughout the domain during the simulation, we can determine when these diabatic processes will overcome the
thermal stratificationof the layer and induce convective instability.These processes are found frequently to induce
instability for the radiative inclusive case. We find that radiative and latent instability usually occurs in updraught
regions, and that latent heating initially enhances the development of the plumes prior to the radiation. We also
find that the magnitude of the latent heating is also strongly coupled to the effects of radiation, since stronger cell
structure induced by radiation results in stronger latent heating at cloud top and less precipitation at cloud base.
KEYWORDS: Cirrus clouds Large-eddy simulation Radiative and latent instability
1. INTRODUCTION
Cirrus clouds are a major uncertainty in climate modelling (Liou 1986a; Intergovernmental Panel on Climate Change 1996). It is well known that, depending on their
optical thickness, height and microphysical properties, they can either exhibit a warming
(greenhouse effect) or a cooling (thermostatic effect) contribution to the global budget.
In addition to climate modelling, cirrus clouds are also not well treated in forecast
models despite their effect on the spatial distribution of water and influence on the
available potential energy (Stuhlmann 1988).
The reason that cirrus clouds are not well understood is that many atmospheric processes affect their development, structure and evolution. To name a few: cirrus clouds on
the local scale are affected by processes such as radiation, aerosol distributions, gravity
waves, shear instability, latent heating, microphysical changes, atmospheric chemistry,
and local meteorological effects such as orography, fronts, or various couplings between
cloud layers at different altitudes or the surface. On a larger scale, cirrus can be affected
by Coriolis effects, interaction with jet streams, interaction with planetary-scale waves,
volcanic eruptions which introduce high levels of aerosol loadings, and by meteorological processes such as passing pressure systems and large-scale lifting or descent.
Successful parametrization of cirrus clouds needs to be based on an understanding
of these interactions. This is clearly a formidable task. These processes will affect
* Corresponding author: Department of Physics, UMIST,PO Box 88, Manchester M60 lQD, UK.
e-mail: [email protected]
@ Royal Meteorological Society, 200 I.
2663
2664
J. S.DOBBIE and P. R. JONAS
cirrus clouds on different time and spatial scales, and some processes are also strongly
coupled together. To date, not enough is known about these processes or about which
mechanisms contribute to the structure of cirrus clouds (Chflek and Dobbie 1995;Smith
and Jonas 1996,1997;Boehm et al. 1999; Gu and Liou 2000). In this work, we seek to
understand the role that radiation takes in the local-scale development and evolution of
the structure and lifetime of cirrus clouds in the absence of other external cloud forcing
processes.
In this study, a high-resolution cloud-resolving model (CRM)is used-the Met
Office large-eddy simulation (LES) model. This version of the model includes an ice
microphysics package and a broad-band thermal infrared (IR) and solar radiation routine
(Fu and Liou 1992,1993).We use the LES model in two-dimensionalmode and generate
cirrus clouds in a similar way to the GEWEX* Cloud Systems Study (GCSS) cirrus
cloud intercomparison (Starr et al. 2000). The simulations are run with and without
radiation and a comparison of the cloud evolution is performed. Sensitivity of the results
to the spectral dependence of the radiation, cloud-layer thickness, and initial layer
stability are presented. After this, we investigate the role radiation and latent heating
takes in the generation of instability in the cirrus cloud layer, and we develop simple
stability numbers to determine when these processes lead to instability.
2. LARGE-EDDY
SIMULATION MODEL
The base version 2.1 of the Met Office LES model (Derbyshire et al. 1999) is used
in this work with the addition of an ice microphysics routine which is outlined below.
This model is based on an original code developed by !F Mason which was used to
study the convective boundary layer (Mason and Thomson 1987; Mason 1989; Mason
and Derbyshire 1990). Since the original version, the LES model has been developed to
handle a wider variety of atmosphericproblems (see MacVean 1993;Ghosh et al. 2000).
The LES model is described by the basic equations for momentum, thermodynamics, and continuity. The model is non-hydrostatic; we make use of the deep
anelastic approximation (quasi-Boussinesq) which allows for small pressure and density deviations from a reference hydrostatic state (sound waves are filtered). The sideboundary conditions are essentially periodic, but allow for non-periodic temperature
and pressure gradients on scales large compared to the horizontal domain (on synoptic
scales). The moist thermodynamics is treated using two variables, the total-water mixing
and the liquid-water temperature
ratio, q-,
where T is the temperature, L , is the latent heat of vaporization, rr, is the liquid-water
mixing ratio, g is the acceleration due to gravity, z is the height, and c p is the specific
heat capacity of air at constant pressure. In addition, ice microphysics is handled by
the LES (see Swam 1998) in a two-moment scheme using the prognostic variables: ice
mass mixing ratio qi, and ice number concentration nj. In this work the main source of
ice particles is through homogeneous ice nucleation (see Brown and Heymsfield 2001).
The prognostic equations for both are of the form
* Global Energy and Water Cycle Experiment.
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
2665
where p is the density, and Vqi and Vni are the mass-weighted and number-weighted
mean fall velocities of the ice particles, respectively. There are similar equations for
snow particles (ice aggregates). Source terms represent the generation of ice through
nucleation processes and also conversions from other hydrometers (through aggregation
or break-up). In the LES model, ice begins to convert to snow once the mass-mean
diameter of the ice exceeds a size of 500 pm.In these simulations, snow is essentially
a category describing large ice particles, and we will refer to ice and snow as just ice.
Sink terms include sublimation, melting and losses associated with conversion to other
hydrometer types. In this work, the main source of ice particles is through homogeneous
ice nucleation, which occurs in the model at temperatures below -38 "C. It occurs
when there is excess water above the saturation mixing ratio with respect to water at the
ambient temperature and pressure. The excess saturation is formed into ice in one time
step so long as the ice number concentration is below a fixed parameter of 100 ~ m - ~ .
A typical time step for the microphysics is between 4 and 5 s. Khvorostyanov and
Sassen (1998) suggest that converting the excess water to ice in one time step results in
increased instability and heating rates, so we plan to account for this in a future version
of the Met Office LES. Primary ice nucleation is specified by the Meyers formulation
(Meyers et al. 1992).
The version of the LES used in this work is somewhat similar to the one used in the
GCSS Working Group 2 (WG2) intercomparison. Preliminary results from the GCSS
WG2 study show that there is still a large variance in the results obtained from various
bin and bulk cirrus CRMs (Starr et al. 2000). Results are sensitive to the prescripton of
the fall speeds in the models. The results using this model were found to be well within
the spread of results of the different models. There is much need for a comprehensive
observational test case against which the results of the models can be compared; cases
are now being considered as part of the GCSS WG2 intercomparison.
The LES simulations were performed in two dimensions for a domain extending
10 km in the horizontal and 20 km in the vertical. A horizontal grid resolution of 100 m
was used throughout, whereas the vertical grid resolution was varied. Between 6 and
11 km, which is where the cirrus clouds develop, the grid resolution is 125 m. Outside
this region the resolution is more coarse. The model simulations were run on a Linuxbased 500 MHz processor personal computer.
(a) Radiation model
The differences between this LES version and the one used in the GCSS intercomparison are that (i) a new radiation scheme has been installed and (ii) the generation
of the cirrus cloud layer has been altered slightly to produce different initial cloud
shapes. The latter difference will be discussed later. For the results presented in this
work, we used the well-tested radiation model by Fu and Liou (1992, 1993). Very
recently this was updated to the most current ice radiation package (Fu 1996; Fu et al.
1998), but selected comparison cases show little difference in the evolution of the cloud
ice-water content and structure in this work. The radiation moduIe solves the basic
radiative-transfer equation which is discussed at length in books by Liou (1986b) and
Goody and Yung (1989). The four-stream solution is used assuming all atmospheric
columns are independent. The radiation model is broad-band with six bands in the solar
region and twelve in the thermal infrared region.
The radiation routine uses single-scattering optical properties based on the ice
crystals being hexagonal columns and plates with an effective size of 50 pm. This
effectivesize is a typical value often found in in situ observations (Heymsfield and Platt
1984; Takano and Liou 1989; Francis 1995). The authors also note that there is a wide
2666
J. S. DOBBIE and P. R. JONAS
0 1 2 3 4 5 6 7 8 9 10
Horizontal Extent (km)
0 1 2 3 4 5 6 7 8 9 10
Horizontal Extent (km)
Figure 1. Ice-water path for (a) the inhomogeneousbase cloud and (b)the homogeneous base cloud, at 7200 s.
variability of observed values. Gaseous absorption by 0 3 , C02, C&, N20, and H20
are treated using the correlated kdistribution method. Rayleigh scattering of the gases
is also included. C02, C&, and N2O are taken to be uniformly mixed, with volume
mixing ratios of 330, 1.6 and 0.28 ppmv, respectively. The profile of ozone is taken to
be a typical midlatitude autumn vertical distribution and the surface albedo is chosen to
be 20%. The simulations begin at a simulation time of 1000 h and continue until 1600 h.
The radiative heating contributes every time step to the dynamics in the LES, but the
radiative heating and cooling distributions are only updated every five minutes, which
is short enough so that the cloud geometry is not appreciably changed between updates.
The radiative effect on the diffusional growth of ice crystals is not treated in this present
LES version. Recent works suggest it is an important effect (Gu and Liou 2000; Wu
et al. 2000), and so we plan to include it in the next version.
3 . CIRRUS CLOUD GENERATION: BASE RUNS
We generated our cirrus clouds in a very similar way to that of the GCSS WG2
case. We impose a cooling equivalent to ascent at 0.03 m s-l to the layer between 7
and 10 km. Between 8 and 9 km, the layer was initially saturated with respect to ice
but not with respect to water (70 to 80%).Below 8 km, the relative humidity is between
30 and 40%, and above 9 km it decreases to 25% at 10 km and to a couple of percent
above this region. The maximum relative humidity is between 8 and 9 km, where the
potential temperature is only very slightly increasing with height (about 1 K km-I),
the layer is initially stably stratified with respect to ice-saturated ascent. The potentialtemperature profile is set approximately equal to the reference potential temperature for
our atmosphere. The layers are initialized with zero wind shear. Then, artificial heat
perturbations of f O . O 1 K s-l are superimposed to give the layer turbulent structure.
These perturbations are imposed across the layers between the heights 8 and 9 km and
during the first time step of the simulation. After a little over ninety minutes, a very
inhomogeneous cirrus cloud develops by homogeneous nucleation (cloud base is colder
than -38 "C). Figure l(a) shows the ice-water path (W)of the cloud after the base
two-hour run. The cloud exists between about 7.5 and 9.3 km in the vertical.
As a second base run, we wanted a cirrus cloud with a completely different horizontal scale of inhomogeneity to that shown in Fig. l(a). We chose the extreme case
of a nearly homogeneous layer. This was achieved by keeping everything the same as
for the inhomogeneous layer, except now only very small artificial heat perturbations
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
2667
were imposed within the layer between 4.6 and 5.4 km in the horizontal. Within the
horizontal regions 4.8-5.2 km and vertical heights of 8.5-9 km, the perturbations were
2.5 x
K s-', while, at the bordering regions, the perturbations were weaker at
2.5 x
K s-'. The resulting IWP at the end of the two-hour base run is shown in
Fig. l(b). The optical depths of the cloud layers at the end of the base run are approximately 1.25.
So, in summarizing the base runs, two very different cirrus cloud morphologies have
been generated. One is a very inhomogeneous layer and the other is a very homogeneous
layer. No radiation is imposed in any of the base runs. The base runs are only used to
generate the cirrus clouds ready for evolution and analysis.
4.
CIRRUS CLOUD EVOLUTION
The evolution of the cirrus clouds from the base state allowing for radiative effects
is now considered. During this second stage, the generated c h s clouds are allowed to
evolve for a further four hours. During this period, the large-scale ascent and artificially
imposed heat perturbations are stopped and so the cloud is allowed to freely evolve and
eventually decay in time. Since we are interested in looking at the radiative effects on
cloud evolution, we run two different cases, both starting from the same base-run cirrus
cloud. One run allows radiative-heating effects to be included and the other omits them.
(a) Inhomogeneous-layer results
From the base runs, we now use the inhomogeneous base cloud layer (Fig. l(a))
and let it evolve for an additional four hours with and without radiative effects included.
After a period of half an hour (after the base run), the differences between the radiative
case (RC) and the non-radiative case (NRC) are evident. Figure 2 shows the ice-water
content (IWC) for these cases at two different times in the simulation. We are most
interested in the distribution of ice rather than the magnitude in this section. From these
plots, we can see that the NRC layer tends to become more homogeneous, whereas,
the RC tends to maintain and further generate inhomogeneous structure. From this, it is
evident that latent-heat exchanges occurring in the NRC are not strong enough alone to
maintain the present degree of inhomogeneity, nor generate any further inhomogeneity.
Whereas, in the RC, radiative heating in conjunction with latent heating is able to drive
enough of a circulation to maintain an inhomogeneous structure as the cloud decays.
In order to quantify the degree of inhomogeneity within the layer at any time, a
Fourier series expansion of the horizontal distribution of the ice-water path, IWP(x), is
performed. Shown in Fig. 3 are the Fourier amplitudes as functions of the wavelength
for the same times as shown in Fig. 2 and also a later time. The range in wavelength
is dictated by the domain size and resolution. Peaks at 10 km and a couple of hundred
metres are not significant.
In Fig. 3, the NRC is shown to be losing its inhomogeneous structure as the
cloud dissipates. For the RC, not only can we see that the inhomogeneous structure
is being maintained, but it tells us something about the way new inhomogeneities are
being generated. The Fourier analysis shows that there is a disappearance of the highfrequency modes resulting from the random perturbations in the base run, and that
there is a progression of the scale of inhomogeneity to certain scales. For the RC, the
dominant length-scales of inhomogeneity are approximately 1-2 km and later in the
simulation length-scales of 2-5 km also develop. Inhomogeneity on the 1-2 km lengthscale were also noted in the two-dimensional night-time cirrus simulations of Boehm
et al. (1999). Horizontal inhomogeneity on the scales are also, in general, observed in
2668
J. S. DOBBIE and P. R. JONAS
"r--
Figure 2. Ice-water content for the inhomogeneous base cloud at 9300 and 10 200 s, respectively, for (a) and (b)
the radiative case (RC),and (c) and (d) the non-radiative case (NRC). The contours lines are 0.001,0.005,0.02,
and 0.05 g m-3. (Note:sometimes the higher-valuecontours rue not needed.)
RC, t=9300
RC, t=10200
RC, t=ll400
1
i r
.
j
12
9
6
3
0
lo-'
1
lo1
lo-'
1
lo1
NRC, t=10200
lo-'
1
lo1
NRC, t=ll400
.-
E 3
a
10-1
1
lo1
10-1
1
lo1
10-1
1
10'
Wavelength (km)
Figure 3. Fourier series amplitudes of ice-water path for the inhomogeneous cloud at times 9300, 10200 and
11 400 s. (a)-@) are radiative inclusive cases (RC). and (d)-(f) arc non-radiativecases (NRC).
the spectral analysis of data from observational campaigns (Heymsfield 1975; Sassen
et al. 1989; Smith and Jonas 1996, 1997). This comparison with observations is just to
give confidence in the model results, it is not meant to be a comprehensive comparison
with observations.We are now involved in a comprehensive comparison as part of the
GCSS WG2 intercomparison study.
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
2669
Figure 4. As in Fig. 2 except for the homogeneous base cloud layer. The same contours are also used.
It is of interest now to determine if the length-scales are dependent on the initial
morphology of the base cloud. In the next section we will begin with a homogeneous
layer and see if the same inhomogeneity length-scdes develop in the RC again.
(b) Homogeneous-layer results
In this section, we show the evolution of a cloud layer that is initially almost perfectly homogeneous (Fig. l(b)). In Fig. 4,we see the time evolution of the homogeneous
layer for both the RC and NRC. Even though we are beginning with a layer almost
devoid of inhomogeneity,we see differences in the inhomogeneity between the NRC and
RC appear within about forty minutes. The NRC tends to stay relatively homogeneous
as the layer dissipates. Some inhomogeneity is caused by the slight initial perturbation
and consequent latent-heat and dynamical exchanges, but for the most part the layer
remains homogeneous. For the RC, however, once again we see that intense plumes
develop within the layer and the layer progressively becomes more inhomogeneous as
it dissipates.
The Fourier analysis of the IWP for the same times and a later time, as in Fig. 3, are
shown in Fig. 5 . It shows that initially both the NRC and RC are largely homogeneous.
However, as time progresses, we see that two or more modes are discernable in the NRC
around the 1-2 and 2-3 km wavelength regions. These modes are not strong but they
are present. In the RC, the same modes appear but in this case the amplitude of the
inhomogeneity grows to substantially higher values because of the radiative influences.
Simulations for a larger domain of 50 km (same resolution) were also performed.
By comparing these runs with the previous results, we find that the Fourier amplitudes
of IWP,shown in Fig. 5 , at scales of 10 km and a couple hundred metres are affected by
the domain length and therefore are not significant.
(c) Development of cloud structure
For the homogeneous base cloud, how do the secondary plumes (secondary plumes
are those not manually initiated in the base run) develop in the horizontal when the
primary plumes (artificially initiated in the base run) are only located near 5 km?Also,
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J. S. DOBBIE and P.R.JONAS
;:a
RC, t=9300
6
3
0lo-'
1
10'
6
3
0
lo-'
1
10'
NRC, t=10200
a
1
10'
Wavelength (km)
lo-'
;:D
6
3
0lo-'
lo-'
RC, t=ll400
1
1
10'
NRC, t=ll400
10'
lo-'
1
10'
Figure 5 . As in Fig. 3 except for the homogeneous base cloud layer.
why are the secondary plumes distributed at roughly regular intervals along the horizontal,roughly corresponding to the depth of the cloud? Understanding the development of
the secondary plumes is certainly important because they largely characterize the cloud
structure in the horizontal and are responsible for important modes that appear in the
Fourier analysis.
We find that secondary plumes first develop in our runs nearby, and as a consequence
of, the cellular structure established by the primary plumes. In addition to columns of
rising air in the plume regions, there are also columns of descending air established to
the sides of the primary plume. These regions of descending motion have air converging
at the cloud top and air diverging at the cloud base. In time, the regions of convergence
and divergencebegin to dynamically affect the cloud region to the side of the decending
region away from the primary-plume region. The air in this neighbouring region (named
the secondary region) is being drawn away towards the region of descending air at cloud
top while air is pushing in from the descending region at cloud base. The result is that air
in the columns of the secondary region begins to ascend and a secondary-plume region
is established. As we will see in a later section, this secondary-plume region is greatly
intensified by latent and radiative processes.
Shown in Fig. 6 are the vector velocity distributions for the homogeneous base cloud
layer at 9000 and 9300 s. The maximum velocities are of the order of a metre per second
(in keeping with observations, see Smith and Jonas (1997)), but the magnitude of the
velocity is not important for this discussion). These times correspond to 25 and 30 min
after the base (no-radiation) run is completed. These plots are for an extended horizontal
domain (50 km) and we are viewing the velocity distributions just to the right of the
primary plume located at 5 km in the horizontal (you can see the downwelling region at
6 km resulting from the primary plume located at 5 km). In both parts of Fig. 6, we see
that there are regions of upwelling and downwelling generated within the cloud layer to
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
t=9000s
3;7,r,&,,..s
,,
8700
I
t=9300~
267 1
8700
-
...........................
(a)
6
7
8
9 10 11 12 13 14
Horizontal Dimension (km)
6
7
8
9 10 11 12 13 14
Horizontal Dimension (km)
Figure 6. Air velocity distributions for two time periods: (a) 9000 s and (b) 9300 s, showing the development of
secondary plumes. Arrow length is proportional to the velocity with a maximum of about 1 m s-' .
the right (and left, not shown) of the main plume and the beginning of secondary-plume
regions.
Comparison of the plots shows that the locations of strong upwelling and downwelling do not vary much in time. We also note that with time the upwelling and downwelling regions within the cloud intensify as the secondary plumes develop. The cellular
structure that is developing in these plots is what gives rise to the structure observed in
the IWP plots and the peaks observed in the Fourier analysis of the last section.
By comparing Figs. 6(a) and (b) we see the development in time of the secondary
plumes further and further away from the main plume region. For example, the beginning of a plume region near 12.5 km in the horizontal is noted at a time of 9300 s which
is not really evident at 9000 s. A rough order-of-magnitude speed for the propagation of
the cellular structure in the horizontal is about a metre per second.
Although we have only discussed the generation of the secondary plumes for the
homogeneous base cloud, the same occurs for the inhomogeneous base cloud; it is
just more difficult to observe because of all of the primary plumes present. In that
case, there is competition amongst neighbouring primary plumes once the base-run
perturbations are stopped. Since primary plumes are randomly located, primary plumes
can be initiated very closely together, as indicated by the high-frequency modes in the
Fourier analysis during the development of the cloud in the base run. The strength of the
primary-plume circulations determines which plumes remain and which ones diminish
in time.
( d ) Dependence on cloud thickness
Is the scale of inhomogeneity that develops in the previous cases dependent on the
thickness of the layer? Our calculations show that it is. We performed runs for the
homogeneous layer in which we generated base clouds with thicknesses of roughly 3
and 0.5 km. The optical depths are 2.5 and 0.25 for the thick and thin layers, respectively.
The cloud-top heights (9.2 km) for these two cases agree with the previous calculations
involving the intermediate thickness (optical depth 1.25). As before, both of these layers
evolved with and without radiation. The scale of inhomogeneity that develops is a
function of the thickness of the cloud layer. Figure 7 shows the Fourier amplitudes as a
function of wavelength 40 min after the base run for both the 3 and 0.5 km layers for
2612
J. S. DOBBIE and P. R. JONAS
0.8
l
i
-
0.6
Y
3 0.4
-w
.a
lo-’
1
10’
Fourier Wavelength (km)
0.2
0
10-’
1
10’
Fourier Wavelength (km)
Figure 7. Fourier amplitudesof WP corresponding to layers with (a) larger or (b) smaller initial thickness. RC
and NRC are shown in each of the plots. Both plots are for the homogeneous base layer at a time of 10 200 s.
the RC and NRC. It is observed that the dominant modes are now shifted towards the
wavelengths which are roughly in keeping with the thicknesses of the layers.
In Fig. 7(a) (3 km thick case) there are prominent amplitudes at 1, 2 and 5 km
wavelengths. These wavelength scales are very prominent in the radiative case, whereas
they are only one quarter of the magnitude in the non-radiative case. The velocity field
for this thick layer shows that there is substantial turbulence generated in the lower
and upper levels of the cirrus cloud. The turbulent cellular structure is on the scale of
about 1 km or a little less. There are a few modes in Fig. 7(a) at or just below the 1 km
scale. These are due to radiative (and latent) induced instability occurring locally near
the upper cloud levels due to the combination of solar heating and cloud-top thermal
IR cooling, and locally at cloud base by the combination of solar heating and thermal
IR heating upwelling from below. The 2 km mode is due to there being some degree of
cellular motions linking the full depth of the cloud. The 5 km mode arises because of
the way the plumes ascend to the upper layer and combine. We note that the magnitude
of the 5 km mode may be exaggeratedbecause of the domain size. For the NRC shown
in Fig. 7, the Fourier modes are much suppressed compared to the RC, and the velocity
distributions show very little activity by comparison to the RC.
For the thin layer of 0.5 km, the Fourier analysis (Fig. 7(b)) shows that indeed
the dominant scale of inhomogeneity is about 0.4 km, which is approximately the
characteristic thickness of the layer at this time when the Fourier analysis is performed.
In addition, there are three other scales with appreciable amplitudes, specifically, 0.25,
0.6 and 0.8 km. The Fourier amplitudes for the RC are larger than for the NRC (Fig. 7),
most prominently the 0.4 km length-scale which is a factor of two greater. This mode
is most important when analysing the IWP as a function of the horizontal dimension.
Inhomogeneity on the 0.4 km scale is clearly evident and is significantly deeper than for
the M C . The differences between the NRC and RC are much smaller for this thin layer
as compared to the thicker layers. The velocity-vectordistributions show little activity in
the NRC (max of 0.05 m s-l) and still only relatively small values for the RC (maximum
of 0.15 m s-l) as compared to other cases. The reason why there are small differences
between the NRC and the RC is that the layer is too thin for the radiative heating and
cooling to have a substantial effect, The typical combined solar and thermal IR heating
within the layer is only of the order of 1-2 K d-’ .
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
12
I
I
I
I
IIIII
I
I
I 1
IIIL-
1
10’
Fourier Wavelength (km)
lo-’
2673
lo-’
1
10’
Fourier Wavelength (km)
Figure 8. Fourier amplitudes of IWP corresponding to layers simulated with either solar or IR radiation but not
both. (a) Thick (3 km) and (b) intermediate (1.5 km) homogeneous base layer (t = 10 200 s).
(e) Dependence on radiative spectrum
It is of interest to determine whether solar and thermal infrared radiation are
together both responsible for the observed cloud inhomogeneity or if one spectral region
dominates. To investigate, we performed simulations allowing either thermal IR or solar
radiation alone to contribute. Shown in Fig. 8 are the Fourier amplitudes corresponding
to cases for clouds with intermediate (1.5 km) and thick (3 km) depths at a time of
10200 seconds.
For the intermediate thickness layer shown in Fig. 8, we see that solar heating is
most important in terms of initiating the inhomogeneity on the 1-2 and 2-3 km lengthscales. This is characteristic of the effects noted throughout the simulation for this cloud
thickness. The thermal IR case shows some structure at shorter wavelengths which is due
to the local instability associated with cloud-top cooling and cloud-base heating. The
thermal IR case shows more inhomogeneity than the no-radiation case (see Fig. 5), but
less than the solar-inclusive cases. The longer inhomogeneity length-scales, associated
with the solar-inclusivecases, result from the deeper convection which is on the scale of
the depth of the layer.
In the W C distributions corresponding to the intermediate thickness case in Fig. 8,
we note that the case with only solar heating has plumes ascending to higher levels as
compared to any of the other cases. The lack of cloud-top thermal IR cooling allows the
plumes to penetrate further into the stable cloud-top layer. The solar radiation causes the
plumes to attain higher vertical velocities which in turn result in the cloud layers tending
to spread more in the vertical for the cases in which solar heating is included. So solar
radiation is responsible for transport of water to higher altitudes in these cases.
When the same evaluation was performed for the thick layer, we found that the
results were largely reversed for the solar-only and thermal-IR-only cases (see the
thick case in Fig. 8). The combined solar and thermal IR case produced the most
inhomogeneity again and the no-radiation case produced the least, but now the second
most important case for generating inhomogeneity was the thermal IR radiation case.
The solar-only case had much suppressed inhomogeneity as compared to the thermalIR-inclusive cases. For the thick layer, even the non-radiative case had some structure
in the IWC distribution due to latent-heat exchanges from sublimation and deposition.
The structure for the non-radiative case is present because almost any heat perturbations
2614
J. S. DOBBIE and P.R. JONAS
in the thick layer can grow as the layer initially has a thick layer of moisture and ice at
near-neutral stability.
This is why the thermal IR case was more dominant for the thick layer. The IR
radiative heating at the cloud base is strong enough (because of the larger optical depth,
>2) to initiate plumes that rise through the depth of the layer. This is further enhanced
by cloud-top thermal IR radiative cooling which enhances the instability. For the solar
case the solar heating is distributed throughout the layer. The profile of radiative heating,
however, does not give rise to instability in the layer. This is because the heating profile
varies too smoothly with height in the cloud to generate instability.
(f) Dependence on initial cloud-layer stabilitj
If the initial stability of the layer in the base run is varied then how does this affect
the scales of inhomogeneity that form? We investigated this by varying the potentialtemperature profile with height for the base runs. We'll discuss two cases, one with a
profile which has an unstable region and another with a more thermally stratified profile
than in the base runs discussed earlier. The potential-temperature profiles are again set
roughly equal to the reference potential-temperature profiles. We will discuss the thicklayer runs because they show the largest effects due to instability. The unstable profile
has a decreasing potential temperature with height between 7 and 9 km, decreasing at
a rate of about 5 K km-l; elsewhere it increases with height. The more stable layer
has an increasing potential temperature with height throughout, increasing at a rate of
3 K km-' within the cloud region as opposed to the previous 1.5 K km-l.
For the unstable layer, results show that the layer quickly generates plumes of strong
magnitude. The ice-water contents reach values much larger than previously found
(0.2 g m-3). Plume ascent is enhanced by latent heating in the upper cloud levels. For
both the RC and the NRC,a thick layer is generated which spreads throughout the layer
from the heights 6.5 km to almost 10 km. The cloud top is formed in this case at much
higher levels than in previous runs because the strong instability is causing stronger
plumes to form. It is after this initial instability that we begin to see the differences
between the RC and NRC. This occurs about one hour after the base run. At this point,
plumes develop which are enhanced by radiative (and latent) heating and ascend towards
the cloud top. These plumes continue to develop throughout the rest of the simulation
for the RC and give rise to a more inhomogeneous structure in the IWC as compared to
the NRC.For the NRC, the pervasive region of high IWC that resulted from the initial
instability largely stays intact and decays with time. It is not until the NRC reaches
later stages of decay that the inhomogeneity in the layer begins to show as the cloud
dissipates.
For the more stable profile, the clouds for the RC and NRC are very similar at least
for the first two hours after base run. Various length-scales appear during this time, but
there is no consistent dominant length-scale of inhomogeneity. The initial perturbations
are damped by the thermal stratificationof the layer for both cases. For the RC, radiative
and latent processes acting on the initially inhomogeneous IWC distribution is not
energetic enough to overcome the stratification of the layer. The NRC and RC layers
decay steadily in time. After 1.2 hours (after the base run), the RC becomes distinct from
the NRC when some IWP inhomogeneity length-scales appear in the Fourier analysis.
This is when the cloud is dissipating and beginning to break up. The thermal IR heating
at the cloud base is the source of this break-up. The Fourier analysis shows that during
break-up the inhomogeneity length-scales are often 1 km and 2-3 km, but they do not
persist. The break-up for the NRC occurs at about 1.7 hours (after the base run). Shorter
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
cu-
::
100
80
Y
10
8
6
30
20
10
--,
8 12 16 20
Time (1000 s)
O
-
2675
!
Y
\ r
L-
8 12 16 20
Time (1000 s)
4
2
0
8 12 16 20
Time (1000 s)
Figure 9. Horizontally averaged IWP over the Lifetime of the cloud. (a) Thick, (b) normal, and (c) thin clouds
for the homogeneous base run.
wavelength modes are present in the Fourier analysis on average but no modes persist
for long time periods. We find that the rate of change of potential temperature with
height has to be about 1.5 K km-' or less in these simulations for radiation to initiate
inhomogeneity. A more general criterion will be presented later.
(g) Cloud lifetime
By plotting the horizontally averaged IWP in time for the RC and NRC, we can
determine whether radiatively driven clouds last for longer or shorter times than nonradiatively driven clouds. Shown in Figs. 9(a)-(c) are the plots of the time average of
the IWP for the homogeneous base cloud case for three cloud thicknesses (3, 1.5 and
0.5 km). In each plot, both the NRC and RC curves are shown beginning at 7500 s of
simulation time. Previous to this was just the base run used to generate the cloud. It is
observed that the radiative effects take about 40 min (at 10 000 s) to create differences
in the average IWP compared to the non-radiative case. After that time, the differences
between the cases (RC and NRC) are usually significant. From the graphs, we observe
an e-folding time of about 4 to 5 hours, which is in agreement with Boehm et al. (1999).
For the thick base layer (3 km thick initially) (Fig. 9(a)), the cloud has a deep layer
of moisture to begin with, which results in a large initial average IWP (90 g m-2) when
the cloud forms after about 1.5 hours (in the base run). Once into the second stage
(after 2 hours) the ascent (imposed cooling) of the layer and the artificial temperature
perturbations cease and so the cloud layer decays. During the second stage, radiation
begins acting on the layer. Radiation enhances the strength of plumes resulting in
increased updraughts and increased latent-heat release. In turn, the latent-heat release
also enhances the strength of the plumes.
The same trend with time is observed for the intermediate thickness layer (1.5 km)
as well. It is found that the RC cloud has substantially larger mean IWP for about two
hours longer than the non-radiative case. If we consider any time beyond 10000 s, then
the average IWP is a factor of two to three greater for the RC as compared to the NRC.
For the thin layer case (0.5 km thick), the layer is optically very thin (optical depth
is 0.25) and so there is weak radiative heating which, in turn, is unable to initiate
development of strong plumes. Without strong plumes, there is less latent-heating
release and so the IWC does not grow quickly in these regions. This, in turn, impacts
the radiative heating. The result is that radiation has only a mild enhancement of the
convective and turbulent activity which gives rise to the average IWP shown in Fig. 9(c).
J. S. DOBBIE and P. R.JONAS
2676
The same trends, but with reduced intensity are observed for the inhomogeneous
base-layer case. The thick and intermediate-thickness layers persist longer for the RC
than the NRC by about 30 min and have higher average IWPs by a factor of two
once the radiation has taken effect (again about 40 min after the base run is complete).
These effects are not as dramatic as for the homogeneous base cloud, but they are still
significant.The reason why they are not as dramatic is because the inhomogeneousbase
layer has a significant number of primary plumes already present in the layer for both
the RC and NRC, and so both cases obtain some cellular structure (which acts to retain
ice) by latent heating in regions of updraughts. Conversely,the homogeneous base layer
has few primary plumes, and it is only the cases with radiation that are able to generate
substantial numbers of secondary plumes and thus take advantage of the cell structure
that develops.
5 . GENERATION
OF INSTABILITY
In this section, we evaluate whether radiation is able to initiate instability in cirrus
cloud and we look at the role that latent heating takes in this process.
(a) Radiative-heating and latent-heatingstability numbers
To avoid limiting our discussion of radiative instability to the specific modelled cases
studied here, we derive stability numbers which can be used to identify the onset of
radiative and latent instability for a general cloud layer.
The change in virtual potential temperature, O,, from a time t to t 6t can be
obtained from a Taylor expansion of 6,
+
ev(z,t + s t ) = ev(z, t ) + (ae,/at)st,
(3)
where a&/at is the rate of increase of virtual potential temperature with time evaluated
at a time t. The derivative may be expanded as follows
where the terms on the right-hand side are the rate of change of virtual potential
temperature due to various diabatic processes.
For now, consider only the effect of radiation on the stability-latent process will be
added afterwards. The rate of change of temperature due to radiative heating and cooling
is given by
aT
at
(radiation)
pcp
where F is the net radiative flux and His the heating or cooling rate. Therefore, the rate
of change of virtual potential temperature due to radiative heating and cooling is given
by
a& = -0,R .
at
T,
So now the contribution to the virtual potential temperature at t
processes can be written as
ev(z,
+ 6t
by radiative
2677
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
+
Instability occurs when Ov(z, t St) decreases with increasing height. From Eq. (7),
this region is determined by requiring
aev(z, t + s t ) <
az
Using Eq. (7) in Eq. (8), we get
The third term on the left can be rewritten as
aTv-'
mvaTv
Rev-S t = ---St.
az
T? az
Using this in Eq. (9) and by rearranging we get
-
We find that 1 + (3tSt/Tv) 1 and that the second term in Eq. (1 1) is negligible
compared with the other terms. An order of magnitude calculation confirms these
statements: take 6r 500 s (discussed later), 6, and Tv 300 K, R 30 K d-' =
30186 400 K s-', Iax/azl- 0.1 K km-l, and (aev/az) I(aTv/az)l- 10 K km-l.
We are left with
-
--
-
The first term on the left-hand side is positive because we are interested in layers which
are initially stable at time t. The second term, however, can be either positive or negative
depending on the radiative heating or cooling profile with height. Equation (12) is
satisfied if
We can now define the 'radiationstability number' as
For radiative instability we require
0 < Rsn < 1.
(14)
This derivation is also satisfied if we replace the radiative heating with latent heating.
The resulting latent-heating stability number Lsn, has to satisfy the same criterion as in
Eq. (14) with Rsn replaced by Lsn.
By virtue of Eq. (4), we can define a radiative and latent stability number Csn as
(aeV(z, t)/az)
(15)
-(ev(t, t)iTv){(a%3elaz) (ad:c/az)W
where d: is the latent-heating rate. For instability to be initiated by combined radiative
and latent processes then Csn must satisfy the condition 0 < C,, < 1.
Csn
=
+
2678
J. S. DOBBIE and P.R. JONAS
(b) Instability: model results
We now evaluate the stability numbers, Rsn, LSn, and e,,, using the model runs
discussed earlier. In order to proceed, we need to assign the time interval St in Eqs. (13)
and (15). We define St as the time-scale over which radiation is able to heat or cool
the layer before the layer appreciably (dynamically) adjusts. One way to estimate this
is from the plots of IWC distributions; they do not vary much on the time scale of 5 or
10 min. As another estimate, we can consider a typical vertical velocity of 0.5 m s-l
of a parcel that is travelling from the base of one model layer to the top of the next,
a distance of 250 m. Then the time-scale for readjustment between layers would be
roughly 500 s. We will use this time interval in our evaluations that follow. We have
two main cases to consider. The first case includes radiation, so both latent and radiative
effects are considered in determining instability, and the second case excludes radiation
and so only latent heating will be considered for initiating instability.
(i) Radiative case. Our calculations show that the radiation stability number satisfies
its instability criterion, given by Eq.(14), at many times and locations for the simulated
cirrus clouds. So radiation appears to be trying to incite instability; however, instability
does not always occur. This is because latent heating (depending on its profile) can
counteract the radiative effects on the layer's stability. We find that early on in the
simulation (7200 to 8400 s) instability is typically caused by latent heating in the
primary-plume region as the air ascends and cools. It is not until after this time that
radiation causes instability. At 8700 s we see the first occurrence where both Rsn and
C,, satisfy their instability criteria. Interestingly enough Lsn does not. At this location,
radiation is generating instability in spite of the latent-heating profile acting against it.
As the simulation proceeds, instability is always noted to occur, as expected, in
plume regions where the IWC is large. Instability is typically generated by the combined
effects of radiative and latent heating, although, there are frequent locations in which
one or more satisfy their instability criterion. When the secondary-plume regions are
forming, instability at these locations is first noted to be caused by latent heating. Once
the updraughts begin then instability is caused by both or either of latent and radiative
heating.
In Fig. 10, we focus on one column in the model at a time of 10 200 s, and look
at various profiles. We have chosen the column at 4.6 km (in the horizontal) because it
is the location of a very strong plume. From Fig. 10, we see that the radiative heating
is a maximum of about 28 K d-' at a height of 8.5 km. This is due to the combined
effects of solar (from above) and infrared heating (upwelling from the surface and
below-cloud atmosphere). Thermal infrared cooling occurs above 9 km for this column.
Latent heating reaches a maximum of 48 K d-' at 8.75 km and decreases above and
below this height. Note, the horizontally averaged values of latent and radiative heating
would be significantly lower. The region that is most important in terms of initiating
instability is where the profiles of diabatic heating decrease with height, as explained in
the development of the stability numbers. This region occurs between 8.5 and 9.2 km
for radiation and between 8.75 and 9.3 km for latent heating. We see that instability
is initiated by both radiative and latent heating at the levels 8.8 and 8.9 km and that
radiation on its own initiates instability at 9.0 km, since it is such a strongly decreasing
profile at that level.
To complement the above work, we performed a simulation with an effective size
which varied linearly from 20 pm at cloud top to 100 p m at cloud base, based loosely
on observations contained in Francis et al. (1998). The following general points were
noted from the simulations. Although similar Fourier modes of the IWP were present,
2679
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
10000
10000
9500 0
9000 Y
.-
2
D
7000
r
I
I
I
I
O
8000 -
1
(b)
,
7000
I
0
~
8500 7500
I
:o
I
I
r
Figure 10. Values represent a slice taken at 4.6 km through the radiative inclusive simulation at 10200 s.
(a) Profiles of latent and radiative heating (bottom scale) and vertical air velocity (top scale). (b) Values of the
stability numbers R,, (circles), L,, (boxes), and esn(crosses) (see text).
10000
I
I
9500 -
--
2
9000
W
--_ _ _
Ea 8500 --.4 8000 -
\
\
\
7500 7000
\
1
-50
I
-25
I
,/
0
/
I
I
25
I
50
Radiative and latent (Wday)
Figure 11. Values represent a slice taken at 4.6km through the non-radiative simulation at 10 200 s. Profiles
of latent and radiative heating (bottom scale) and vertical air velocity (top scale). (The radiation is computed
off-line.)
they were reduced in magnitude because of a reduction in the instability within the
layer. This reduced instability was caused by reduced vertical gradients and magnitudes
of the radiative heating. A reduction in the latent-heating release was also noted due to
weaker updraught regions because of weaker radiative effects. These effects all resulted
in a reduced strength of the cellular structure. This is in keeping with the findings of
Khvorostyanov and Sassen (1998) and Boehm et al. (1999). A comprehensive study
based in observations of this is now planned.
2680
J. S. DOBBIE and P. R. JONAS
(ii) Non-radiative case. Shown in Fig. 11 are the same plots as in Fig. 10(a) except in
this case for cirrus cloud evolving without radiation. The radiation is still computed in
this simulation and plotted, but it is not allowed to contribute to the evolution of the cloud
(essentially an off-line calculation). In this case, the column is located at 4.9 km in the
horizontal since this is where the maximum updraught was found (less dramatic values
were found at 4.6km). By comparing Figs. 10 and 11, we find that the non-radiative case
has much reduced magnitudes for almost all of the parameters plotted. Only the latent
cooling at the cloud base is increased since more crystals are sublimating to the vapour
phase as they leave the cloud. The stability numbers are not plotted for this case since
none came close to satisfying their instability criterion. Kelvin-Helmholtz instability
was minimized in all runs by initializing the runs with zero shear. It was monitored
throughout runs for both radiative and non-radiative cases by evaluating the local flux
Richardson number. Kelvin-Helmholtz instability in the runs was rare and was observed
only to occur near updraught regions ufer they were established by radiative and latent
processes.
6 . CONCLUSIONS
Our work shows that radiation can have a dramatic effect on cirrus clouds, causing
substantial differences in the cloud inhomogeneity and lifetime compared to simulations
run without it. We find that radiation not only enhances the development of structure
and lifetime, it is instrumental in most cases. Radiation directly or indirectly has effect
on many aspects of cirrus clouds. The simulations including radiation showed stronger
cellular structure, more turbulent activity within the cloud, greater IWC inhomogeneity,
the cloud layers lasted between 30 min and 2 hours longer, there was less sublimation
to vapour at cloud base and more sublimation from vapour within the layer, and the
IWC was usually a factor of 2 greater than the non-radiative cases once the radiation
had taken effect. We found that, in general, solar radiation was more important in the
layers of 1-2 km thickness (1 -= optical depth < 2) whereas IR was more important
in the thicker layers (optical depth > 2). Thin layers (optical depth < 1) showed only
marginal effects from radiation on their structure.
We have derived stability numbers for radiative and latent-heating processes to
determine if these processes incite instability within the layer. Our results show that
radiation is causing convective instability within the layer at numerous locations and
times during the simulations. In some cases, radiation acts alone in causing instability
(as does latent heating), while at other times and locations it acts in conjunction with
latent heating. Sometimes neither can cause instabilility independently but together they
do. Latent heating is usually observed to be causing instability prior to radiation in
regions where plumes are developing. Radiatively induced convectiveinstability in these
regions is noted to follow once the IWC is large enough.
In the evolution of cirrus cloud structure, there is an interesting interplay between
dynamics, radiation, and latent heating as noted in the simulations. Initial turbulent activity in the layer causes slight updraughts. In these updraughts, cooling occurs and
latent heat is released, As the IWC increases, radiation becomes important. Radiation
enhances the plume region and drives a much stronger circulation than is present in
the non-radiative case. This strong cellular circulation dynamically initiates secondary
circulations which are driven first by latent then radiative processes. In time, this generation of neighbouring cellular activity leads to a largely turbulent and inhomogeneous
cirrus cloud throughout. The enhancement by radiation should not be overlooked; we
find it is a crucial step in the process (as are the other processes). Fourier analysis of
RADIATIVE INFLUENCE ON CIRRUS CLOUD STRUCTURE
2681
the IWP from the simulations shows us that the inhomogeneity develops in both the RC
and the NRC at certain length-scales, but in the RC the modes are much stronger. It is
the strong radiative enhancement of the cellular structure in the layer which gives rise
to these differences.Without radiation the cellular structure is weak and the layer tends
towards a more homogeneous state. If the radiative and latent processes are unable to
strongly enhance the plume regions, then the layer remains or tends towards an inactive,
more homogeneous state.
ACKNOWLEDGEMENTS
The authors would like to thank the two anonymous referees for helpful comments
and suggestions. Thanks to P. R. A. Brown (Met Office) for providing the LES model
and with help in becoming familiar with the model, Professor Q. Fu (Washington State
University, USA) for providing his radiation scheme, and to Dr S. Ghosh (Leeds, UK)
for reading the manuscript and making helpful suggestions. The authors would like to
acknowledge funding for this work from the Natural Environment Research Council
through grant GST/02/2867 and the Universities Weather Research Network through
grant DST 26/39.
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